Download Optical Studies of Periodic Microstructures in Polar Materials

Digital Comprehensive Summaries of Uppsala Dissertations
from the Faculty of Science and Technology 189
Optical Studies of Periodic
Microstructures in Polar Materials
HERMAN HÖGSTRÖM
ACTA
UNIVERSITATIS
UPSALIENSIS
UPPSALA
2006
ISSN 1651-6214
ISBN 91-554-6578-1
urn:nbn:se:uu:diva-6896
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Omistettu mummolleni Elsa Laurinheimolle,
todelliselle sankarittarelle…
Dedicated to my Grandmother Elsa Laurinheimo,
a true hero…
List of papers
I
H. Högström and C. G. Ribbing, “Polaritonic and photonic gaps
in Si/SiO2 and SiO2/air periodic structures”, Photonics and nanostructures – fundamentals and application 2, p.23-32, 2004
II
H. Högström, G. Forssell, and Carl G Ribbing, “Realization of
selective low emttance in both thermal atmospheric windows”,
Optical Engineering 44(2), 026001, 2005
III
H. Högström and C. G. Ribbing, “On the angular dependence of
gaps in 1-D Si/SiO2 periodic structures”, Submitted 2006 to Optics Communications
IV
H. Högström, S. Valizadeh, C. G. Ribbing, “Optical excitation of
surface phonon polaritons in silicon carbide by a hole array fabricated by a focused ion beam”, Submitted 2006 to Optics express
V
H. Högström and C. G. Ribbing, “Experimental observation of
photonic and polaritonic gaps in a silica opal”, Submitted 2006
to Applied optics.
Work not included in the thesis
1. Carl G. Ribbing, Herman Högström, and Andreas Rung, “Studies of
polaritonic gaps in photonic crystals”, Applied Optics, 45(7), 15751582, 2006
2. Carl G. Ribbing, H. Högström, A. Rung, “Interaction between photonic
gaps and lattice excitations in 1-3 dimensions”, Deutsche Forschungsgemeinschaft, Annual meeting, Berlin, Mars 7-8 (2005), invited presentation HL-42.5
3. Herman Högström, Andreas Rung, Carl G. Ribbing, “Si/SiO2 multilayer
– a 1-dimensional photonic crystal with a polaritonic gap”, in proceedings of SPIE 5184 (Ed. P. Lalanne, San Diego, August 2003) p. 22-29
4. Andreas Rung, Herman Högström, Carl G. Ribbing, “Interaction between photonic and polaritonic gaps studied with photonic band structure calculations”, in proceedings of SPIE 5184 (Ed. P. Lalanne, San
Diego, August 2003) p. 126-133
5. M. Karlsson, H. Högström, and F. Nikolajeff, ”Diamond micro-optics”,
Proceeding of the Seventh applied diamond conference/Third frontier
carbon technology joint conference 2003, M. Murakwa, Y. Koga, M.
Miyoshi (Editors)
Contents
List of papers ..................................................................................................v
Work not included in the thesis .....................................................................vi
Contents ....................................................................................................... vii
1. Introduction.................................................................................................9
2. Optical materials .......................................................................................11
2.1 Electromagnetic waves in matter .......................................................11
2.2 Dielectric materials ............................................................................14
2.3 Polar materials....................................................................................15
2.3.1 The Lorentz model......................................................................15
2.3.2 The polaritonic gap .....................................................................17
2.4 Metals .................................................................................................19
3. Effect of periodicity ..................................................................................21
3.1 The light line and the Brillouin zone..................................................21
3.2 The photonic band gap .......................................................................22
3.2 Polaritonic photonic crystals ..............................................................27
4. Surface polaritons .....................................................................................31
4.1 General theory ....................................................................................31
4.1.1 Coupling by periodic structure ...................................................34
4.1.2 Coupling by ATR and nano structures .......................................35
4.2 Enhanced optical transmission ...........................................................36
5. Experimental .............................................................................................38
5.1 Fabrication of periodic structures.......................................................38
5.1.1 One-dimensional structures ........................................................38
5.1.2 Two-dimensional structures........................................................41
5.1.3 Three-dimensional structures......................................................45
5.2 Optical analysis ..................................................................................47
5.2.1 One-dimensional structures ........................................................47
5.2.2 Two-dimensional structures........................................................47
5.2.3 Three-dimensional structures......................................................48
6. Signature management in the thermal infrared .........................................49
6.1 Black-body radiation ..........................................................................49
6.2 Atmospheric windows........................................................................50
6.3 Infrared camouflage ...........................................................................51
6.4 Emittance determination.....................................................................53
7. Conclusions and discussion ......................................................................56
8. Summary in Swedish ................................................................................58
Acknowledgements.......................................................................................61
References.....................................................................................................63
1. Introduction
Historically it has often been the discovery of new materials or new ways of
using already existing materials that has radically developed our society. The
materials humans use play such an important part that epochs have been
named after the material, e.g., the Stone Age and the Bronze Age.
During the last 40 years the society has seen enormous developments because of the efforts in semiconductor physics that has given the possibility to
tailor the conducting properties of these materials. In the field of semiconductors the engineers are striving for smaller and better components such
that the products, e.g. computers and mobile phones, will be faster and
smaller.
The developments of semiconductor components lead to the rise of another field, MEMS (micro electro-mechanical systems), which in the beginning was using the same materials and the same fabrication techniques. The
main advantage with MEMS was to make high quality small mechanical
structures that would be much cheaper, thanks to the miniaturization, than
the larger counterpart. In future history our days on the planet may be labeled the Semiconductor era…?
Thus, semiconductor physics made it possible to control the conducting
behavior of the material and MEMS made it possible to fabricate microsized mechanical structures. What was/is the next challenge in the materials
“evolution”? With a growing field of optical communication it became more
and more interesting to control the propagation of light in matter, just as it
had been important to control the conducting behavior of semiconductors. It
was well known that the optical reflectance and transmittance in one dimension could be engineered by a multilayer composed of a high and a low refractive index material, where the thickness of each layer was a quarterwavelength thick. The result of this kind of structures was a material with
almost 100% reflectance for a certain wavelength interval. So, if it was possible to control light in one dimension, how would it be possible in two and
three dimensions?
In 1987 Eli Yablonovitch[1] and Sajeev John[2] published reports that
suggested that this kind of light-control was possible. It was the birth of a
new field in solid state physics: photonic crystals. Their idea was to extend
the periodic structure into two and three dimensions and thereby create
photonic band gaps in which there are no allowed states for photons. In the
beginning the field was widely applauded for creating the possibility of lo9
calization of photons, wave guiding and construction of optical components
of very small size. However, skeptical comments were also aired[3].
Within the photonic gap in a photonic crystal the propagation constant,
the wave vector k, is imaginary. This is also the case for metals, for frequencies below the plasma frequency, and in polar materials, for the frequency
interval between the transverse and longitudinal optical phonon resonance
frequencies. So, we therefore have three different origins of an imaginary
wave vector, one associated with a periodic structure and two originating
from the optical properties of the bulk material. When a material posses an
imaginary wave vector in an interval several phenomena can be noticed. It
becomes highly reflective, it quenches emittance and it can support surface
waves.
The field of photonics has mostly focused on materials with “simple” optical behavior. But during the last years the field has matured and more interest has been focused on using materials with more complex optical properties, and the new optical phenomena discovered and applications associated with them.
In this thesis we have worked with the combination of the bulk optical
properties of polar materials and the effects added by a periodic structure.
The bulk properties appear, for the material at specific wavelengths, whilst
the structural behavior can be shifted in position by changing the lattice constant of the periodic structure. When working with this project during the last
four years we have tried to combine both possible applications and basic
research.
In the first part of the thesis a general introduction is given to the fields discussed in the papers (second part) together with some results cited from
them.
10
2. Optical materials
2.1 Electromagnetic waves in matter
Already in the 19’th century James Clerk Maxwell summarized the knowledge concerning electromagnetism in four equations. Even though it was
not Maxwell who had developed all the theory included in the equations,
they were named after him.
’˜D
U
’u E
wB
wt
’˜B 0
’u H
j
(1 a-d)
wD
wt
These equations are valid and describe the behavior of electromagnetic fields
in different kinds of environment. They need to be supplemented by two
constitutive equations that include the response of the material to the applied
electromagnetic field.
D H0 E P
B
P0 H M
(2 a, b)
Assuming that the electromagnetic radiation is traveling through vacuum,
the following apply: P = 0; M = 0; U = 0 and j = 0. The wave equation
’2 E
P 0 H 0 E
(3)
can then easily be derived by eliminating the magnetic fields H and B. One
of the most important features of Maxwell’s equations was that an electromagnetic field could propagate as a plane complex wave
E=E0ei(k·r-Zt),
(4)
11
where E0 is the amplitude, Z the angular frequency and k the wave vector.
The fact that electromagnetic radiation propagates as a transverse wave was
of great importance since it supported the theories suggested by Thomas
Young. When Maxwell determined the velocity of an electromagnetic wave
in vacuum he ended up with the expression that the phase and group velocities were c=1/(µ0H0)1/2. By using empirically determined values for these
quantities, he obtained a numerical value for the speed, which was equal to
the experimentally determined value for the speed of light. Since then there
has not been any doubts that the field of optics was a special case of electromagnetism. From this point it was possible to derive e.g. Snell’s law[4] of
refraction and Fresnel’s law[4] by using the theories of electromagnetism,
and thereby get a deeper understanding of optical phenomena.
Maxwell’s equations give a complete description of the electromagnetic
field. So, by inserting (4) into (1b) one can deduce that the magnetic field
appears similar, but perpendicular, to the electric field and that electromagnetic waves are transverse. It is also possible to describe the propagation of
light in different media.
If it is assumed that no free space charges are present, i.e. U=0, the wave
equation in a medium will have the general form
’ 2 E P 0 H 0 E
P 0 P P 0 j ’ u M .
(5)
(5) is the inhomogeneous analogue to (3), and states that an electromagnetic
wave can be generated by a polarization with a non-vanishing second derivative, a time varying current density or the curl of a time-varying magnetization. The magnetic field appears similar also for this case.
The different optical behavior for various materials can all be described
by using (5). The materials studied in this thesis are assumed to have no free
space charges and that they are nonmagnetic. Actually, all materials have a
diamagnetic contribution but it is of the order of 10-6, and therefore neglected. Materials that are para- or ferromagnetic can have a countable magnetic contribution for lower frequencies, Z<1012, but the contribution vanishes rapidly with increased frequency because of magnetic inertia. This
inertia is so high that even ferromagnetic materials can be treated as nonmagnetic, µ ~ 1, for Z> 1012. M will therefore be neglected henceforth.
The current density term, j, will be determined by the electric field and
the conductivity, V, of the material:
j VE.
(6)
In anisotropic cases j does not need to be parallel to E and the conductivity
will then be a tensor. If non-conducting materials are considered, j is ne-
12
glected. In this thesis conducting materials will only be considered in section
2.3 where the optical properties of metals are discussed.
The polarization term, P, is the dipole moment per unit volume. It describes the material response both to the applied and the local electric
field[5]. A linear relationship is often assumed for E and P:
1
H0
P
FE
(7)
When (7) is inserted into (2a) the displacement field will appear as:
D = HH0E.
(8)
The quantities H and Fare called the dielectric function (or permittivity) and
the dielectric susceptibility respectively, and they are the linear response
functions describing the polarization of the material. Both depend on the
frequency, and in general they both have a real and an imaginary part,
H(Z)=H1(Z)+iH2(Z).
The optical properties of matter thus are determined by the coupling between incoming electromagnetic (EM) radiation and charged particles/charges in the material. The charged particles/charges are accelerated by
the electromagnetic field and cause a polarization. The macroscopic polarization created by the dipoles adds to the vacuum contribution and sums up to
the displacement field D, (2a). For different frequencies, different types of
oscillators will dominate the response. The strength of this response depends
also on the oscillator density and on the inertia of the excitation mechanism.
Figure 1 presents a schematic picture of different polarization mechanisms
that occur in solid materials.
Figure 1. A schematic
picture of the frequency
dependence of the real
part of the dielectric
function and the different polarization mechanisms that can occur in
a material. The parts of
the spectrum where the
resonances are located
are indicated above
each peak. Cited from
[5]
13
The figure shows that for different frequencies, different oscillators are excited. In these frequency intervals, close to the oscillator resonances, the
polarization/dielectric function of the material varies strongly with frequency, i.e., dispersion. For frequencies between the resonances the dielectric function is almost constant. It is characteristic for an oscillator that there
is a resonance region with strong absorption and dispersion. A resonance
located at a high frequency will give a frequency independent contribution at
all lower frequencies, whilst a low frequency resonance will not contribute at
sufficiently high frequencies due to inertia. It should be noted that the low
frequency excitations of permanent dipoles is characteristic only for a small
group of materials containing molecules with dipole character, such as H2O.
In the next sections the optical properties for materials will be discussed
with (5) as the starting point.
2.2 Dielectric materials
Materials that are purely dielectric for all frequencies do actually not exist.
For some frequency range in the electromagnetic spectrum the material will
have a resonance and the polarization of the material will vary with frequency, as indicated in figure 1. But if we assume that there is no strong
coupling between the electromagnetic radiation and oscillators within the
frequency region considered, then the dielectric function is constant and real.
For dielectric materials j is neglected in (5) and the wave equation will then
look like
’2 E
P 0 H (Z )H 0 E .
(9)
When inserting the plane wave (4) into (9) a relation between the wave vector and the frequency is obtained, i.e., a dispersion relation
Z
2
c2 2
k .
H (Z )
(10)
c is the speed of light in vacuum and HZ is the complex dielectric function.
For the dielectric case, when HZ is constant and real, the dispersion relation
will look like a straight line called the lightline. Glass is a typical dielectric
material for visible frequencies and is therefore used in windows and optical
components such as lenses and optical fibers. Glass is made of silicon dioxide, and it will be discussed in the next section that it is not purely dielectric
throughout the entire spectrum.
The square root of (10) will have a factor which is H(Z)1/2. For simplicity
a new symbol, N(Z), which is the complex refractive index factor, was introduced. N(Z)=n(Z)+ik(Z)=H(Z)1/2, where n is associated with the propagation characteristics of the light (phase velocity, wavelength, refraction at an
14
interface) and k is a damping parameter indicating the propagation length
within a material. For dielectric materials k<10-4. It is important to distinguish the k belonging to the refractive index from the wave vector k.
2.3 Polar materials
The second type of materials that will be discussed are polar materials. They
typically have a lattice resonance in the infrared part of the spectrum caused
by the bonds in the material that are ionic, or partly ionic. It is neighboring
ion pairs that constitute dipoles that interact, i.e., move and create phonons,
i.e. quantified lattice vibrations with the EM radiation, and form quasiparticles named polaritons. The oscillations caused by the electromagnetic
radiation are additional movements, besides the ordinary lattice vibrations,
phonons. Since both polaritons and phonons include lattice vibrations, the
optical response from the material within the resonance region will be
somewhat affected by changes in the temperature[6].
2.3.1 The Lorentz model
Close to the resonance, the dielectric function varies strongly with frequency. The optical behavior in this wavelength region can be described by a
Lorentz one-oscillator model[7]. Although the oscillator is classical, the
model shows good agreement with optical measurements using only a few
parameters. The equation of motion for one oscillator is
d2r
dr
P 2 P* N r
dt
dt
q E (Z )
(11)
where µ is the reduced mass of the dipole, N a “spring constant” and q the
charge. * is a phenomenological damping constant representing the “friction” the particles experience in the material. The driving force is an oscillating electric field E, with frequency Z, as given in (4). Since the materials
studied here are dense, corrections for the local electric field exciting the
oscillator are included in E. Equation (11) has a homogenous and a particular
solution, and the former is damped after a small number of periods 2S/Z, so
we only need to consider the particular solution.
r
(q / P ) E
,
Z Z 2 i *Z
2
0
(12)
where Z0 = ( N/µ )1/2 is the resonance frequency of the oscillator. If there are
N oscillators per unit volume, the total macroscopic polarization of the material will be
15
P
Np
Nq r
Nq 2 / µ
E.
Z 02 Z 2 i*Z
(13)
The polarization is used in the constitutive relation for the displacement field
D equation (2a), which is then inserted in (1a)
’˜D
’ ˜ H 0 H (Z ) E
’ ˜ (H 0 E P)
0.
(14)
The complex dielectric function is obtained by using the middle expressions
in (14), as
H (Z ) 1 Nq 2 /(H 0 µ)
.
Z 02 Z 2 i*Z
(15)
Because of the damping, *, there will be both a real (H1) and an imaginary
(H2) part of the dielectric function. In figure 2 they are both plotted for silicon
dioxide. The data used for this calculation where published optical constant
values from the literature[8, 9].
Figure 2. The real, H1, and the imaginary, H2, part of the complex dielectric function
for silicon dioxide. The corresponding reflectance is also plotted and indicated on
the right y-axis. Data from[8, 9].
So far, the contributions from other sources of polarization within the material have been neglected when deriving this particular response for the infrared region. When taking them into account in the simplest way, the dielectric
function will appear as
16
H (Z ) H f Nq 2 /(H 0 µ)
,
Z 02 Z 2 i*Z
(16)
where H’is a constant contribution, named screening constant. It originates
from oscillators within the material. It is necessary for this simple representation that these oscillators have resonance frequencies that are much higher
than Z0.
If Z=0 is inserted in equation 10, the static dielectric constant, H(0), is obtained as
H (0) H f Nq 2 /(H 0 µ)
Z 02
.
(17)
The Maxwell equation 1a implies that the electromagnetic field has to be
transverse in vacuum. However, in a polarizable material with a varying
dielectric function, HZ can be equal to zero, allowing excitations that are
not purely transverse. If HZ is inserted in (14), E can be parallel to the
wave vector, and D will still fulfill Maxwell’s equation. In this case P= -HoE.
This shows that longitudinal waves are possible inside a material at a frequency where HZ . The frequency where HZ is therefore named ZL
(longitudinal mode), and Z0 is renamed as ZT (transverse mode). As seen in
figure 2 the real part of the dielectric function is negative between ZT and
ZL. If the damping, *, is neglected and Z ZL in (16), ZT and ZL are related
to the static and screening dielectric constants by
Z L2
ZT2
H (0)
.
Hf
(18)
This famous equation is named the Lyddane-Sachs-Teller (LST) relation [5].
It has been found that this relation is valid for a surprisingly wide range of
materials and it can be generalized to cases with more than one resonance
frequency[10].
2.3.2 The polaritonic gap
In the interval between ZL and ZT, HZ<0, as seen in figure 2. When this is
the case the dispersion relation, (10) implies that the wave vector is imaginary. An imaginary wave vector causes a strong attenuation of the wave.
This results in an interval of high reflectance: the Reststrahlen band.
In the vicinity of the resonance frequency the Lorentz model provides a
surprisingly good description of the optical behaviour. A material can exhibit
more than one resonance frequency caused by ions. This is actually the case
for silicon dioxide. The second oscillator is much weaker, but it can be noticed as the shoulder on the short wavelength side of the high reflectance
17
interval. These additional oscillators typically have their resonance frequencies close to the major resonance, and then a screening constant cannot be
used. For a complete analysis all the oscillators in the vicinity have to be
summarized in a multi-oscillator expression for the dielectric function[7].
The case of multiple oscillators will not be discussed in more detail.
To excite the oscillator in the material a photon must couple to a phonon.
This means that their energies and momenta have to be equal. To illustrate
where this is possible, the dispersion relations for phonons and light are
sketched together in figure 3.
Figure 3. Schematic picture of the free photon (dashed line) and phonon dispersion
relations in a crystal. The gray square shows where coupling between photons and
phonons occurs, and the zone boundary represents the atomic Brillouin zone. The
slope of the light line is underestimated in this representation.
The grey rectangle at the intersection of the light line and the transverse optical phonon represents the only interval where the two can couple to first
order. In this region the polariton is formed. To show how this coupling will
affect the dispersion relation, the area around the intersection is enlarged in
figure 4.
Figure 4. A schematic picture of the polariton dispersion relation. Between ZT
andZL a polaritonic gap is formed.
In figure 4 we see that the coupling between the photon and the phonon creates a gap in the dispersion relation, the polaritonic gap (PG). The energies
18
associated with the polaritonic gap are in the meV range, whilst visible light
has energies around and above 1 eV. It should be underlined that this gap
originates from the interaction between oscillators in the material and electromagnetic waves, and not from any kind of periodicity.
In this thesis we have chosen to work with crystalline silicon carbide and
amorphous silicon dioxide as polaritonic material, but there are many other
materials that exhibit polaritonic behavior[5, 11].
2.4 Metals
A semi-classical model dielectric function for metals is obtained much in the
same way as for polar materials. The difference is that here moving electrons, which are treated as free, are causing the polarization of the material.
Because of the free electrons some adjustments needs to be done in (11). Z0
is set to zero since we are dealing with free oscillators – the conduction electrons, and * which represents the damping is replaced by its inverse W, a
parameter describing the time between scattering events. With these changes
the equation for the conduction electron motion will be:
P
d 2r P dr
dt 2 W dt
q E (Z ) .
(19)
The metallic dielectric function is then derived in the same way as in the
previous section. The final expression will be
H (Z ) 1 Z p2W
Z 2W iZ
(20)
where Zp = (Nq2/H0µ)1/2, the plasma frequency[5], which is a collective longitudinal oscillation of the free electrons. The dielectric function for metals
also has a real and an imaginary part. Figure 5 is a schematic picture of H1
and H2 for metals on a normalized Z-axis.
19
Figure 5. A Schematic picture showing the real and imaginary parts of the metal
dielectric function plotted as a function of Z/Zp. When Z=Zp the real part goes from
negative to positive values.
From figure 5 it can be seen that the dielectric function will be negative for
frequencies below Zp. With the dispersion relation (10) in mind one realizes
that the wave vector will be complex for these values, create evanescent
waves and cause high bulk reflectance.
20
3. Effect of periodicity
3.1 The light line and the Brillouin zone
When studying the dispersion relation, Z(k), (mentioned in section 2) for a
material with a constant H (vacuum or a purely dielectric material), it is obvious that it appears as a straight line named the light line, with the slope
c/H1/2.
Z2
c2 2
k .
H (Z )
(10)
In section 2.3 figure 3, the typical light line is plotted together with the phonon (quantified lattice vibrations) dispersion relations for a diatomic lattice[5]. The optical phonon frequencies in figure 3 belong to the microwave
and infrared parts of the spectrum. The right part of the plot represents the
Brillouin zone (BZ) boundary[12] for a normal atomic unit cell and the grey
square indicates where coupling between EM waves and optical phonons can
occur, as discussed in section 2.3. The size of the “atomic” Brillouin zone is
determined by the inverse of the typical inter-atomic distance, i.e., a~0.5 nm,
whilst the k-vector of light is 2SO For O ~1.55 µm, 1/a >> 1/O. It is well
known that when the dispersion relation for propagating waves in a periodic
medium interacts with the BZ, energy gaps may appear. One can see that the
ordinary Brillouin zone boundary is too distant to affect the light line for
visible/infrared light. The slope of the light line is much too steep. Eventually the light line intersects the atomic Brillouin zone boundaries. This will
occur far above the part of the dispersion plot shown in the diagram, i.e., in
the X-ray region. At these frequencies the order of magnitude of the wavelength and the inter-atomic distance in the material are equal. The result is
well known, X-rays are diffracted in crystals and the diffraction pattern is
characteristic for the symmetry of the atomic crystal.
So, to get an effect of a Brillouin zone for optical or infrared frequencies
the zone boundary needs to be moved to the left, i.e. to lower k-values. The
BZ is characterized by the crystalline structure of the material, and the size is
determined by the lattice constant[13]. This means that a periodic structure
on the same length scale as the wavelength of light needs to be accomplished
in order to have effects of the interaction for visible/IR wavelengths (O =
21
0.3-13µm). We have thus arrived at a generalized grating concept as a tool
for diffraction of electromagnetic waves with any wavelength.
3.2 The photonic band gap
Electromagnetic wave propagation through periodic media was studied by
Lord Rayleigh already in 1887[14]. He noticed that some frequency ranges
of the waves could be totally reflected by the periodic structure.
His results later opened up the field of multi layers[15], where it became
possible to design the optical properties since the range of frequencies that
are totally reflected are determined by the materials and the lattice constant.
The structures designed have e.g. been used in lasers. The common feature of
X-ray diffraction in crystals and multilayer reflectance is that the wavelength of the electromagnetic radiation that is diffracted is of the same order of magnitude as the period of the diffracting structure. An essential difference is that X-rays are diffracted in specific directions by atomic planes
and that light is reflected by the boundaries between the different materials
in the multilayer, and not in several directions within the structure. The reflectance for visible wavelengths in a multilayer is possible to accomplish by
creating a man-made periodic structure. We can describe that as a construction that shifts the Brillouin zone to smaller k-values. As mentioned above, it
is when the Brillouin zone interacts with the lightline that effects of the periodicity appear.
Much work has been performed on one-dimensional periodic structures[16] and the applications range from frequency selective lasers to window coatings. In 1970 Bloembergen et al. discussed “stop bands” and “forbidden gaps” for certain frequencies in a study on laminar structures[17]. He
presented a photonic band calculation showing both a gap caused by the
periodic structure as well as a gap originating from one of the materials. The
concept of photonic stop bands was also adapted by Yariv and Yeh[16]
In 1987 two reports[1, 2] were published in the same volume of Physical
Review Letters about controlling electromagnetic wave propagation/spontaneous emission from electronic levels, in man-made periodic
structures of dielectric matter. This new type of structure was eventually
named a photonic crystal (PhC)[18-22] and the idea was to extend the
photonic gap from one to two and three dimensions. As for the onedimensional case and x-rays in crystals, discussed above, the periodicity of
the structures should be of the same order of magnitude as the wavelength
corresponding to photon energy where the gap is wanted. The major differences between these structures and the multilayers were the way of describing propagating modes, which adopted its nomenclature from solid state
physics[13], where band diagrams are used for describing electron states in
solids, and the possibility of localization of photons in three dimensions.
22
This had not been possible for one dimensional structures since propagating
modes are allowed in the plane perpendicular to the periodicity. Another
difference was that air typically is one of the dielectric “materials” used in
the multi-dimensional periodic structures. The “solid-state way” of describing mode propagation was extended to one-dimensional structures [23, 24].
Different methods have been used to analyze optical properties of
photonic crystals. Mostly it is done by transmission and reflectance measurements (for gap determination) but the obvious similarity between threedimensional photonic structures and atomic crystals has lead to similar
methods of analysis where the diffraction of light is investigated[25-27]. A
more complete picture of the optical behavior of the photonic crystal is
thereby achieved.
As mentioned above, the authors of the first two first reports argued that a
band gap (BG), should be possible to accomplish in two and three dimensions by the use of a multi-dimensional periodic structures. The possibility to
have a complete, or omnidirectional, gap, no allowed photonic states in any
direction for a certain frequency range was also introduced. The existence of
such a gap was verified by Ho et al[28] who showed that dielectric spheres
put in a diamond lattice would create an omnidirectional gap if the refractive
index ratio was ~2. It is somewhat intuitive that an as spherical BZ as possible is wanted in order to have a complete gap. If so, the gap does not have to
be as wide, for overlap in all directions.
From the knowledge of X-ray diffraction and multilayers, it should not be
a surprise that if a periodic structure of two, or more, materials with different
dielectric functions is prepared, one might end up with a photonic band gap.
As already discussed, the periodicity of the material can be 1-, 2- and 3dimensional. The number of principal axis along which the dielectric function is periodic, determines the dimension of the photonic crystal. Figure 6
contains schematic pictures of all three cases where the different colors represent materials with different dielectric functions[18].
Figure 6. Schematic picture of a 1-, 2- and 3-dimensional photonic crystal. The
number of principal axis that exhibits a periodicity determines the dimension of the
crystal. From [18].
23
The way a photonic band gap is created by a periodically varying dielectric
function has a clear relationship with electronic gaps in ordinary crystals.
The ion cores in a crystal create a periodic potential, giving rise to an energy
gap for electrons. For photonic crystals the difference is that the periodic
potential is replaced by a periodicity in the dielectric function, H= H(r +R), if
R is a lattice vector, and on a length scale that is about 103 times as large.
Even calculations for photonic crystals appear very similar to calculations
made for electrons with Schrödinger’s equation. Joannopoulos et al. present
a good review how to handle EM waves in mixed dielectric media. They
also list the equations for photonic band gap calculations together with their
corresponding quantum mechanical expressions[18].
Within a gap, there are no allowed states for photons in the photonic crystal. This means that the wave vector, k, is purely imaginary for the frequencies in the gap and the waves are strongly attenuated. In the same way as for
metals and polaritonic materials, corresponding frequencies will exhibit high
reflectance.
To give a more illustrative description of the origin of the photonic gap,
three band diagrams, Z=Z(k), for three configurations of a 1-D photonic
crystal are shown in figure 7.
Figure 7. Schematic pictures of band diagrams for a one-dimensional photonic crystal. Left: All layers have the same dielectric function, centre: a small difference in
the dielectric function between the layers, right: Large difference between the dielectric functions. After[18].
The leftmost plot is for a periodic structure where all layers have the same
dielectric constant. This is a virtual periodic structure. Here one can see that
the light line is folded back into the first Brillouin zone with no resulting gap
at the boundary. We could by analogy with the electronic structure name it
“The free photon band structure”. The center plot shows the band diagram
for a case with a small difference between the two constant dielectric functions. One can see that a small gap has opened up at the Brillouin zone
boundary. This is a photonic gap. We have chosen to specify it with the
name structural gap, since it originates from the structure, i.e. the periodic
length, of the material and we wish to separate it form bulk photonic gaps,
such as the polaritonic gap. In the rightmost plot the difference between the
24
two constant values of the dielectric functions has been increased. As seen in
the figure the width of the gap has increased considerably. This is again
analogous with gaps in electronic band structures that grow with the strength
of the crystalline potential [5]. Yet, one may wonder why the width of the
gaps can increase so much, in the optical case, with the difference between
the dielectric functions. By studying the shortest interesting wave, with
wavelength 2a, one can see that the electric field can be placed in two ways
in the crystal without disturbing the symmetry of the unit cell about its center. One way is to place the nodes in the high index material and another
with the nodes in the low index material, as shown in figure 8 a, b. The
darker material represents the high index material.
Figure 8. Illustration showing that two waves with the same wavelength can be
placed in a one-dimensional periodic structure (a & b) and the corresponding localization of the energy associated with the mode (c & d). From [18].
If the effective dielectric function (the average of the dielectric function of
where the energy, in figure 8 c & d, is located) for each wave is considered
and inserted in equation 10, it becomes obvious that two waves with the
same wavelength (same wave vector) will have different frequencies, and the
difference will be bigger for larger refractive index ratio. This means that for
the frequencies between the two just mentioned, there will be no allowed
states, i.e. a photonic gap. The variational theorem can then be used to show
that high-frequency modes concentrate their power to low-H regions and that
low-frequency modes concentrate their power to high-H regions[18].
This description of the principles according to which a photonic crystal
should be manufactured may make it sound very simple. However, in a practical case it is not straightforward to obtain a photonic gap, in particular not a
25
complete gap. To succeed, the periodicity has to be close to perfect and the
parameters have to be right. If the lattice constant, a, the symmetry and the
packing fraction U is right, and most importantly, the refractive index ratio
nh/nl is large enough, it is possible to end up with a photonic gap. Different
symmetries have different requirements for the refractive index ratio[18, 28].
One way of finding possible new optical structures is by studying nature,
which has had millions of years of time to develop functional structures.
Micro-optical structures, including photonic crystal structures, have been
found in stones, flowers, birds and insects[29-33]. The function of the structures varies from thermal control to enhanced/minimized reflectance and
focusing of light.
The prospects of a new kind of components for control of light raised
high expectations within the opto-electronics industry, and therefore immense worldwide development efforts to produce/analyze photonic crystals
have begun since the 1990’s. The possibility of strong localization of photons in two or three dimension has been the driving force because the opportunity for wave guiding and lasing applications. These features are possible
to have by introducing defects in the crystal where the mode can propagate/have a resonance. The analogue to defects in a photonic crystal is doping levels in a semiconductor.
Because of the difficulties with large scale fabrication of three dimensional periodic structures, most optical components have been twodimensional photonic crystals. By sticking to 2-D structures the well developed fabrication tools within the micro-electronics industry can be used and
no new machines need to be made. But even though the prospects look good
for 2-D optical components, where the signal is propagating in the plane[3436], the most successful application yet has been for photonic crystal fibers[37, 38]. In these fibers the signal is guided parallel to the twodimensional periodic structure and it has been shown that the signal can be
guided both in air[39] and silica.
Another area in which photonic crystals may be of interest is for negative
refraction. This optical phenomenon has been showed for two-dimensional
photonic crystals [40]. Berrier et al. presented in 2004 an experimental verification of negative refraction for infrared wavelengths[41].
The field of photonic crystals is growing and since 1987, when the field
was initiated, the number of yearly publications has increased exponentially.
According to accessible bibliographic information[42], the total number of
publications at the end of this year (2006) is predicted to be around 2800. A
majority of the publications concern dielectric photonic crystals, but work
has also been made for metallic[43, 44] and polar materials, which will be
discussed in more detail in the next section.
26
3.2 Polaritonic photonic crystals
So far we have discussed three different origins of stop bands for photons: a
strongly varying dielectric functions with a negative real part, metals and
photonic crystals made of purely dielectric materials. Two bulk material
properties and one originating from the structure. The possibility to combine
two stop bands and make them interact has caught the interest of some research groups with the hope of finding new applications and new optical
behavior. In this section the combination of polaritonic and structural gaps
will be discussed as mentioned above. Bloembergen et al. [17] presented in
1970 experimental and calculated results for the one-dimensional case,
where he showed the co-existence of structural and polaritonic gaps. The
first results for more than one dimension were due to Sigalas et al. [45, 46],
who presented transmission calculations for a two-dimensional photonic
crystal made of a polar material, GaAs. Their calculations were made by
transfer matrix technique and showed that the position of the structural gap
changes when it is located close to the polaritonic gap, compared to a purely
dielectric photonic crystal. We will call this type of photonic crystals, where
one of the materials has a polaritonic gap, a polaritonic photonic crystal,
PPC. The first calculated band diagrams for PPC’s where made by Zhang et
al [47, 48]. They showed by plane-wave calculations that the photonic band
gap can be enhanced in a PPC and that nearly dispersionless bands occur in
the vicinity of ZT. Both phenomena have later been confirmed by different
reports[49-51]. Optical behavior related to the dispersionless bands for
PPC’s is the change of the symmetry of the EM field patterns and the relocation of the light into and out of the polaritonic material, studied by Huang et
al [50]. Calculations showing gap maps for a two-dimensional PPC has been
published by Rung et al.[52]. Their gap maps concern four different configurations: the polaritonic material is placed in the cylinders or the matrix, and
it is the high or low index material. A destruction of the polaritonic gap has
also been demonstrated[53]. Recently Huang et al also proposed that PPC
could be used to create metamaterials with both negative permeability and
permittivity (mentioned above) in the infrared part of the electromagnetic
spectrum [54]. Even though most studies have been made for twodimensional polaritonic photonic crystals, some recent calculations have
been made for the three-dimensional case [51, 55, 56].
Published experimental results for PPC’s have, to our knowledge, only
been shown for the one-dimensional case [17, 57, 58]. It has been shown that
the structural and polaritonic gap can co-exist, the polaritonic gap can be
both strengthened and enhanced, but also eliminated. In figure 9 calculated
results for a finite one-dimensional photonic crystal (7 Si layers with 6 intervening SiO2 layers, all layers have the same thickness) show all three cases.
27
Figure 9. A color graph, consisting of 40 separate spectra, showing the reflectance
by different colors for a finite one-dimensional PPC with seven Si layers and six
intervening SiO2 layers. All layers have the same thickness which is marked on the
x-axis and vary from 0.1 to 4.0 µm. The wavelength for the spectra is on the y-axis.
The color scale indicates the reflectance. The horizontal line shows the position of
the polaritonic reflectance and the three vertical lines indicates where the polaritonic
reflectance is strengthened and widened (a), un-affected (b) and erased (c). From
paper I.
Figure 9 is a color graph put together of 40 separate reflectance spectra
where each one is for a different lattice constant. The reflectance spectrum
for each “lattice constant” (layer thickness) is represented on the x-axis and
indicated by the color. The wavelength is represented on the y-axis. Since
SiO2 is the polaritonic material in figure 9 the polaritonic reflectance is located at wavelengths around 9 µm (see figure 22). The polaritonic reflectance causes a horizontal stripe in red/yellow when it is not affected by the
structural reflectance. For such a case please consult paper 1. The position is
indicated by the horizontal line. In the graph three vertical lines have been
inserted to highlight the positions where the polaritonic reflectance is
strengthened (a), stands by itself (b) and extinguished (c).
Since the origins of the photonic gaps in a one-dimensional polaritonic
photonic crystal are different there is also a difference in the angular dependence. The peaks originating from the structure will shift to shorter
wavelengths with increasing angle. This behavior is not a surprise. The polaritonic reflectance is widened with angle in both directions for s-polarized
light and is decreased for p-polarized. If the polaritonic material is thin
enough the longitudinal mode can be excited[59]. In figure 10 a calculated
color graph is shown which summarizes the angular behavior for both struc28
tural and polaritonic reflectance. The structure was designed that the polaritonic and structural reflectances do not interact, line b in figure 9. Paper III
contains a more detailed discussion and the corresponding experimental
color graph.
Figure 10. A color graph summarizing the angular dependence for structural and
polaritonic reflectance. The polaritonic reflectance band is located at ~0.15 eV.
In figure 11 normal incidence IR reflectance spectra for four threedimensional PPC’s, with different lattice constants are shown.
Figure 11. Normal incidence reflectance spectra for four PPS’s with different lattice
constants. The crystals are made by sedimented silica spheres of different sizes,
indicated in the inset. The four peaks to the left are gaps originating from the periodic structure and the peak to the right is the polaritonic reflectance. From paper V.
The crystals were made of sedimented silica spheres of different size: d =
0.49, 0.73, 0.99 and 1.57 µm. In the spectra two types of reflectances can be
seen, structural and polaritonic. To the left the structural reflectance shifts to
longer wavelengths with increasing sphere size, while the polaritonic reflectance stays at the same spectral position. The polaritonic reflectance is surprisingly robust for structures as small as O/20. For details see paper V. Op29
tical measurements on crystals made of larger spheres, where the structural
gap overlaps the polaritonic gap, would be of great interest, but have not
been possible to acquire.
Park et al have presented related results for a three-dimensional photonic
crystal with a frequency dependent component [60]. They sedimented doped
215 nm polystyrene spheres into an opal structure. The gap originating from
the periodicity was overlapping the absorption peaks for the dopant, Oil Blue
N, which resulted in an enhanced photonic gap. Their results verified experimentally the gap enhancement for multidimensional structures. The difference between figure 11 and the results presented by Park et al is that his
frequency dependence does not originate from the bulk optical behavior.
A potential application for PPC’s is as a selective low emittance coating
in the thermal infrared. This will be discussed in more detail in section 6 and
paper II.
30
4. Surface polaritons
In sections 2.2, 2.3 and 3.1 in this thesis, different origins of a complex wave
vector for an electromagnetic wave have been discussed. Metals, dielectrics
and polar materials can all cause a complex wave vector. The difference is
that metals and polar materials create it as a bulk property, while dielectrics
need to be periodically structured such that a photonic band gap is achieved.
The intervals, regardless the material, where the wave vector is complex do
not just have high reflectance in common, they can also support bound surface waves, i.e., surface polaritons. These surface excitations can be used
within many different fields and different applications: biosensing[61, 62],
biophotonics[63], thermal emission control[64], data storage[65], microscopy[66], optical filters[67] and waveguiding [68, 69]. Because of the nature
of surface polaritons they are suitable in interconnects in electro-optic devices, and for nano-imaging and spectroscopy.
Most of the work within the field has been made for metals[70, 71], but
work has also been published for non-conducting materials [64, 72-74] and
photonic crystals[18, 75, 76].
4.1 General theory
It has been known for a long time, that a propagating quasi particle composed of a photon and a polarization wave is possible along the interface of
two materials if the optical conditions are right[71]:
Re(H II ) 0
Re(H II ) ! Re(H I ) ! 0
(21 a, b)
where I and II indicate the two media, forming the interface along which the
surface polariton travels. H is the complex frequency dependent dielectric
function (H H(Z)). Equations 21 a and b state that one of the materials must
have a negative real part of the dielectric function at some frequency and the
absolute value for that frequency must be larger than the corresponding
value for the other medium. As mentioned earlier, a negative dielectric function causes a complex wave vector, which is the fundamental physical condition. For metals H1 is <0 when Z<Zp[71], i.e. the plasma frequency[5]. For
31
polar materials HZ<0 in the Reststrahlen region Z7<Z<ZL[7], and for
photonic crystals it is for frequencies within the photonic gap(s)[18]. Within
these intervals the amplitude of the electric field for the surface polariton
will decay exponentially away from the interface. Figure 12 is a schematic
picture of the surface excitation in a x-z plane. It displays the propagation of
the electromagnetic field in the x-direction, the exponentially decaying fields
in the z-direction and the orientation of the magnetic field in the y-direction.
The wavelength of the surface polariton OSP is also indicated.
Figure 12. A schematic picture showing the propagation in the x-direction of the
electromagnetic field along an interface. In the left part the exponential zdependence of the electric fields are shown in the two media. The magnetic field is
oriented in the y-direction.
As mentioned above, the surface oscillation can have different sources. If the
polarization wave in the material is composed of electrons they are named
surface plasmon polaritons, in case of phonons they are named surface phonon polaritons (SPP). If the surface excitation is located on a photonic crystal it is called a surface state[18].
The wave vector for surface polaritons can be derived from Maxwell’s
equations by using the correct boundary conditions [71], one obtains
k SP
H I H II
c H I H II
Z
(22)
where kSP is the surface polariton wave vector, c the speed of light, Z the
angular frequency. kSP is, as most EM waves in a medium, composed of a
real and imaginary part (kSP=k’SP+ik’’SP). The real part describes the propagation of the polarization wave and the imaginary part gives the damping.
The propagation length, LSP, of surface polaritons is given by:
LSP
32
''
(2k SP
) 1
(23)
In figure 13 the real and imaginary part of the dispersion curve for a SiC/air
interface is presented together with the light line for vacuum. In the figure
the negative side of the x-axis displays the imaginary part of kSP. If calculations are made with these values the absolute value of k’’SP should be used.
Figure 13. The real part and imaginary parts of the dispersion relation for surface
phonon polaritons on an air / SiC interface calculated according to (22) together with
the vacuum light line. The negative values display the imaginary part and the absolute value should be used for calculations. The imaginary part is here presented on
the negative side of the x-axis for convenience. The oscillator parameters for SiC
used for the calculation are[8]: ZL=969cm-1, ZT=793cm-1, *=4.76cm-1, e’=6.7.
For surface polaritons to be tied to the interface, i.e. called non-radiative, the
frequency interval where they can exist is where the dispersion relation is
located to the right of the light line for the dielectric medium. In figure 13
this is where Z7<Z<ZL, i.e. between 793 and 969 cm-1. It can be seen in the
figure that for Z<ZT the dispersion relation is located to the left of the vacuum light line and therefore are the states here not bound to the interface.
For metals the dispersion relation is located to the right of the light line for
Z<ZP.
Equation (22) and figure 13 explains why surface polaritons can become
sub-wavelength and be used for nano-imaging at optical frequencies: the
wavelength of SP’s kSP goes to infinity when HI+HII ĺ 0, which implies that
the wavelength goes to zero (the surface polariton resonance frequency).
Since the light line is located to the left of the dispersion relation the surface states can not be excited by just shining light onto the surface. The difference between the two curves indicates a momentum mismatch. This implies that the momentum mismatch between SP’s and the incoming light
must be added. Coupling of incoming light to the surface states can be done
in three ways: grating coupler[71], attenuated total reflection (ATR)[71] and
coupling by nanostructures[77]. Surface plasmons can also be excited by
electrons that are accelerated into a metal foil and when hitting the material
33
the momentum is transferred to the electrons in the metal[71]. This excitation method will not further be discussed.
4.1.1 Coupling by periodic structure
If light hits a surface with an angle T, the parallel component of the wave
vector, kx, will be:
k1
Z
c
sin T
(24)
If the material is structured periodically with a lattice constant a, the added
parallel component, g, will be: g=2S/a. So, when light hits a periodically
structured surface the total parallel component will be:
kx
Z
c
sin T ng
(25)
where n is an integer and ng is 'k in figure 14. If the geometrical setup is
correct the momentum mismatch will be overcome, i.e. kx=kSP, and a surface
polariton can be exited. The process is schematically illustrated in figure 14,
with labels according to (24) and (25). Light hits the structured surface under
an angle T, and will then have a parallel wave vector component k1. The
structure adds 'k to the incoming light and thereby the momentum mismatch
is satisfied, i.e. surface polaritons can be excited. If the light hits the surface
at normal incidence there will not be any parallel component, i.e. k1=0, and
the entire momentum has to be added by the periodic corrugation.
Figure 14. A schematic picture showing the dispersion relation for a surface polariton (SP), the vacuum light line (LL), the vacuum light line for an angle (T with its
parallel wave vector component (k1), and the added momentum from the periodic
structure ('k). (after [71])
34
In figure 15 three reflectance spectra are shown: a calculated reflectance for
an infinite hole array, an experimental reflectance for a finite hole array and
the bulk SiC reflectance.
Figure 15. Three reflectance spectra showing the calculated reflectance for an infinite hole array, the experimental reflectance for a finite hole array and the bulk reflectance for SiC.
In the calculated and experimental reflectance spectra, in figure 15, two distinct dips can be noticed. These dips are associated with the excitation of
surface phonon polaritons which can be launched in the high reflectance
interval, where H1<0. The long wavelength dip is associated with the geometrical parameters of the periodic structure, lattice constant 11µm and hole
radius 6 µm. The short wavelength dip is the result of surface polariton excitation at the polariton resonance frequency, i.e. at the frequency for the asymptote in figure 13. At that frequency almost any wave vector can excite a
surface state. For a more detailed discussion and pictures of the periodic
structure, please consult paper IV or the cover of this thesis.
Periodic structures can also have another effect on surface polaritons.
Bozhevolnyi et al. have shown that in the same way as light can be totally
reflected for a range of frequencies by a photonic crystal (section 3), surface
plasmons exhibit the same effect by a periodic array of scatterers made by
gold nanoparticles[78]. By removing some rows of scatterers in the periodic
structure, surface plasmons are localized to the unstructured surface and
wave guiding is possible through the array.
4.1.2 Coupling by ATR and nano structures
When light travels through a dielectric medium (H>1) the light line will be
shifted to the right compared to the vacuum light line. If the dielectric constant is large enough the dielectric light line will be placed to the right of the
dispersion relation for surface polaritons (for a H<0/air interface) for a range
35
of frequencies. This means that if light comes from the dielectric material
and hits the H<0-material it can excite surface polaritons on the air interface
side of the H<0 material. This is done by tunneling of the electric field
through the H<0 material. This way of launching surface polaritons is called
the Kretschmann configuration and used for bio-sensing[61]. The excitation
of surface polaritons will be noticed as a strong dip in the reflectance just as
in figure 15. The frequency at which the dip appears varies with both film
thickness and angle of incidence.
Figure 16. A schematic figure showing the coupling of light to surface polaritons by
ATR (after [71]). LL/H is the light line for a dielectric medium, and TH is for an
incidence angle T. SP indicates the air/(H<0) interface surface polariton dispersion
relation and LL the vacuum light line.
The third way of launching surface plasmon by light is by using nano particles. Ditlbacher et.al [77] presented results for cylindrical spots and a wire,
fabricated by e-beam lithography on a silver film. Different shapes excite
surface plasmons with different lateral intensity distributions, which were
imaged by fluorescence.
4.2 Enhanced optical transmission
In 1998 Ebbesen et al. published a paper in which extraordinary optical
transmission through sub-wavelength hole arrays in optically thick metal
films was reported[67]. They showed that even though transmission through
apertures, which are smaller than the wavelength, is extremely low[79] they
had zero-order transmission peaks for wavelengths as large as ten times the
hole-diameter. The position and the spectral appearance of the transmission
peak can be shifted by changing the lattice constant[70] and shape of the
hole[80]. They suggested that enhanced optical transmission (EOT) was
associated with the excitation of surface plasmons. The same phenomena
was not seen for germanium.
36
Many contributions have since then developed the theory for the enhanced transmission for hole arrays and one dimensional gratings [73, 8189] . The authors show that the enhanced transmission is associated with
modes on the two surfaces which are coupled by resonant tunneling through
the holes, transmission maxima occur at the same wavelength as reflectance
minima and absorbance maxima and that transmission minima occurs at the
same wavelength as reflectance maxima and absorbance minima. Their conclusions are that enhanced transmission occurs when excitation of surface
polariton plasmons is allowed on one or both surfaces. It has also been theoretically demonstrated that if the entire system (holes and metal) is considered as one material it will support “spoofed” surface plasmons[82].
However, there has also been reports arguing that surface polariton plasmons should have no, or even negative effect on the transmission [86-88].
They show by calculations that transmission is nearly zero for frequencies
corresponding to the excitation of surface plasmons[88]. According to these
reports the EOT is due to a waveguide mode resonance and diffraction. It
should be noted that all the contributions claiming the negative role of surface plasmons have presented their results for gratings of slits and not for an
array of holes. It seems like the field is converging to a physical explanation
where light couples to surface polaritons which generate surface waves that
couples through modes in the holes/slits to states on the other surface which
then re-radiates the light. Several key aspects have been realized concerning
EOT, but a more detailed explanation still needs to be presented.
Almost all contributions within the field are dealing with EOT through
metallic substrates, but some reports have been published for nonconductors. Laroche et al. showed calculated results for resonant transmission through a photonic crystal in the forbidden gap[76] by launching surface states that couples through the 3.5µm thick crystal. Marquier et al. published a paper showing calculated results for EOT through a grating of slits
in SiC[73]. Based on the lack of experimental contributions we shall describe an attempt to accomplish EOT in a non-conducting material in sections 5.1.2 and 5.2.2 in this thesis.
37
5. Experimental
5.1 Fabrication of periodic structures
5.1.1 One-dimensional structures
The materials we have used in the one-dimensional structures are silicon, as
the dielectric material, and silicon dioxide as the polaritonic material. This
material combination was primarily chosen for of their optical properties in
the wavelength interval of interest. Another important factor was the possibility of simple sample preparation. The samples were grown by chemical
vapor deposition (CVD) on a 550 µm thick (100) Si-wafer. Both processes
are standard techniques used in the micro-electronics industry. The materials
obtained by the CVD processes are polycrystalline silicon (poly-Si) and
amorphous silicon-dioxide. In figure 17 the electron diffraction patterns for
the poly-Si (a) and SiO2 (b) films are presented. The sharp dots, e.g. 220, as
marked in the SAED (Selected Area Electron Diffraction) pattern of the
poly-Si indicate that the grains are textured. If the film had been truly polycrystalline, the pattern would only consist of circles. The diffraction pattern
for the SiO2 film verifies that the film is amorphous, as assumed in the
choice of optical constants.
a
b
Figure 17. Selected area electron diffraction image of (a) poly-Si, and (b) amorphous SiO2. The sharp dot marked in (a) is the [220] direction, which indicates that
there is some structure in the film. In (b) there is no structure in the image which
verifies that the film is amorphous.
38
Polycrystalline Si (poly-Si) is obtained from decomposition of silane
(SiH4)[90] gas at a working temperature of 650o C resulting with a deposition rate of 10.4 nm/min. The amorphous SiO2 originates from hydrolyzation
of tetra-ethyl-ortho-silicate (TEOS, Si(OC2H5)4)[90] at a working temperature of 710o C and with a deposition rate 5.6 nm/min. The oxide formed is a
stoichiometric oxide, i.e., the molecular unit is a tetrahedral structure where
one central silicon atom is bound to four oxygen atoms. The bond angle for
different tetrahedrae varies between 120o and 180o, centered about 145o[91].
Both processes were carefully calibrated to achieve good thickness control.
Two types of samples were prepared. A finite one-dimensional photonic
crystal consisting of three poly-Si layers interspaced with three SiO2 layers,
and a double layer of poly-Si and SiO2. The justification for using so few
layers for analysis of periodic structures is that the dominant optical features
are already present, and will not be changed with an increased number of
layers. The difference will be that most interference fringes between the
dominant reflectance peaks will disappear.
As mentioned above, both samples were grown on a 550µm thick (100)
silicon wafer. In Figure 18 a transmission electron microscope (TEM) picture shows a cross section of one of the finite one-dimensional photonic
crystals
.
Figure 18. A TEM picture of a cross section of a one-dimensional photonic crystal.
The silicon wafer is at the bottom of this image. The bright layers are SiO2 and the
striped layers are poly-Si.
It is evident that the SiO2 layers are not perfectly equal in thickness (despite
the careful calibration). In figure 19 a) and b) high resolution TEM pictures
show the material boundaries between the layers for the structure in figure
18. Figure 19 a) shows the interface between the mono-crystalline Si-wafer
and the first SiO2-layer and b) the interface between SiO2 and the polycrystalline Si.
39
a
b
Figure 19. High resolution TEM images of the interfaces between the different layers of the structure shown in figure 18. a) shows the interface between the monocrystalline wafer and SiO2, and b) the interface between SiO2 and poly-Si. It is possible to see some kind of texture in the poly-Si
In both pictures one can see that Si is more ordered than SiO2, and also that
the Si-wafer is more ordered than the poly-Si.
Since the Reststrahlen peak of SiO2 is of particular interest in this thesis,
we plot an experimental spectrum together with a calculated spectrum in
figure 20. The sample is a 2.9 µm thick silicon dioxide layer, deposited with
the same technique as used for the samples, on a silicon wafer. The calculations were made without fitting, for the same system.
Figure 20. Experimental and calculated reflectance spectra for a 2.9 µm thick SiO2
layer deposited on a Si wafer.
It can be seen in the figure that the experimental reflectance peak has a small
red shift with respect to the calculated. This red-shift of the peak is also present in the papers included in this thesis. Some claim[92] that this red shift is
40
caused by a difference in density. They show that a deposited TEOS-film has
lower density, than a thermally grown oxide, because of impurities. Analyzing transmittance measurements, they show that there are both OH-ions and
free water in the films.
We have also made investigations with electron energy loss spectroscopy
(EELS). The results show that besides a measurable amount of O-H bonds,
there are also small clusters of phase-separated amorphous silicon in the
film. The EELS mapping of Si in a SiO2 matrix was acquired by selecting
the Si plasma peak at 17 eV, with a narrow energy window. The analysis
shows that the amount of silicon is large compared with the amount of O-H
bonds. Figure 21 is an image where the clusters of phase-separated amorphous silicon are mapped by high intensity.
Figure 21. Small clusters of
phase-separated silicon shown by
EELS mapping. High intensity
represents areas with additional
silicon.
As seen there are substantial amounts of silicon in the film, and the Si clusters with average diameter of 2-3 nm, are clearly shown. The effect of this
on the Reststrahlen reflectance is not further discussed in this thesis.
5.1.2 Two-dimensional structures
To overcome the momentum mismatch between the vacuum light line and
the surface phonon polariton dispersion relation and obtain coupling between
incoming radiation and surface states, a square array of circular holes were
milled in SiC (the substrates were provided by [93]). The milling was performed with a FEI dual beam 235 focused ion beam (FIB) system[94, 95]. A
FIB was chosen as tool because of the need for high resolution preparation
patterning and the fact that the ions have enough energy and momentum to
remove material even in such a hard material as SiC. Most materials can be
processed by a FIB, but the milling parameters must be optimized to obtain
the best final result.
41
The parameters of importance in FIB patterning are: the type of ions used,
ion beam current, ion beam density (ions/cm2), beam dwell time (the time the
ion beam stays within a specific spot), overlap (percentage indicating the
beam overlap between two adjacent spots) and scan speed. To optimize the
milling parameters holes were made with different ion currents, and cross
section images were taken to analyze the hole shape. Figure 22 is a graph
showing the influence of the ion beam current on the actual hole diameter.
The current was varied between 1 and 12 nA and the preset diameter and
depth were 6 µm.
Figure 22. Experimental values showing the influence of the ion beam current on
the final hole diameter. The preset diameter and depth of the hole was 11 µm.
In figure 22 it can be seen that 3 and 5 nA gives the diameter closest to the
preset (6 µm) and that for higher ion currents the diameter is strongly affected.
In figure 23 SEM images showing holes made by ion currents 3, 5 and 7
nA, and corresponding cross sections, are presented.
42
Figure 23. Six SEM images showing holes produced by FIB with different ion currents. The corresponding cross section is displayed in images d-f. Images a and d, b
and e, c and f are made with the ion beam current 3, 5 and 7 nA respectively.
It can be seen from the SEM images, a-c, that the resolution is affected by
increased ion-current. For 5 and 7 nA the hole edges are affected and the
diameter is also changed as discussed above. Images d-f show cross sections
of the holes made with the same currents as the image above. One can see
that the holes have a Gaussian hole shape. Holes made with ion currents
lower than 3 nA produce holes of good quality, but the time needed makes it
almost impossible to produce larger structures than individual holes. At the
other end, holes made with currents higher than 7 nA are not of high enough
quality for optical structures. Non-uniform holes would cause too much
damping and scattering. Our conclusion is therefore that an ion current of 5
nA is optimum for micro hole fabrication in SiC. The optimized parameters
are dwell 2µs, the ion beam dose 1018 ions/cm2, 50 % overlap, scan speed 50
µm/s for a serpentine scan. More details concerning the fabrication can be
found in paper IV.
The structure fabricated with the parameters mentioned above was a
square array of circular holes (21*21) with diameter 6 µm and lattice constant 11 µm. The choice of having 21*21 holes was motivated by the calculations. The structured area needs to be large enough so that measurements
are possible, and the excitation of surface states is made possible through an
interaction between the radiation and the periodic structure which requires
that the structure has a minimum area. Details concerning the calculations
can be found in [81].
Two types of hole arrays were fabricated: one with surface pits only and
one with holes going through the membrane. In figure 24 two SEM images
43
are presented showing a hole array where the holes do not penetrate the
membrane.
Figure 24. Two SEM images showing a square array of circular holes with diameter
6 µm and a lattice constant of 11 µm. The holes do not go through the sample. The
right image is taken at a tilt angle of 52o.
In figure 24 it can be seen that the fabrication process, which takes between
40 and 50 hours, is very stable, i.e., the sample stage has stayed in the right
position during the process. One can also see that there are no traces at the
top surface of redeposition or other surface structures originating from the
fabrication process.
In figure 25 two optical images are presented showing a sample with
holes going through the membrane. Both images are taken at the exit side of
the sample for the beam.
Figure 25. Two optical images of a hole array with holes penetrating the sample.
The left image is taken in transmission mode and the right in reflectance mode.
The left optical image is taken in transmission mode and the right in reflectance mode. From the left image it can be seen that the holes penetrate the
sample. One can also notice that the beam has not penetrated the sample for
all spots. One of these spots is shown in the right image. In the right picture
44
it is also obvious that there is dirt on the sample surface. It is small islands of
metal that has been evaporated onto the sample surface. The metal originates
from the sample holder on which the membrane was attached with carbon
tape. To ensure that no glue from the tape would be on the area of the structure the array was fabricated on a piece of the SiC that had no tape beneath.
Instead metal was evaporated to the surface when the beam penetrated and
heated the sample holder.
Because of the Gaussian hole shape shown in figure 23 the diameter of
the holes was measured on the exit side. The exit side diameter was approximately 5.4 µm, which is 0.6 µm less than desired.
5.1.3 Three-dimensional structures
Fabrication techniques for high quality three-dimensional photonic crystals
have been developed for several years. The possibility to have a complete
photonic bandgap which can guide light in three dimensions[96] and have
strong localization of photons is driving the research. During the years several different techniques have been developed for the preparation of the three
dimensional structures [97-99]. In this thesis we choose to work with gravitation sedimentation of monodispersed spherical microspheres.
When monodispersed colloids (usually silica or polystyrene) are allowed
to sediment slowly, they place themselves in the energetically most favorable structure, a fcc (face centered cubic) lattice[100]. This structure is called
a synthetic opal and has got its name from natural opals, which are formed
by close packed silica nanospheres. The structure has one sphere in each of
the lattice points of an fcc crystal. The colloids form a crystal with the (111)
surface at the top. Figure 26 shows a (111) face of a colloidal crystal made
of silica micro spheres with the diameter 1.6µm
Figure 26. A colloidal crystal (the (111) face) made of silica micro spheres.
45
If the connected void volume within the crystal is filled with another material it forms a structure named an inverse opal is formed. The inverse opal
exhibits a complete photonic bandgap if the refractive index ratio is large
enough[101]. The opal structure does not have a complete gap.
A range of approaches have been suggested to infiltrate the inverse structure including sol-gel[102], chemical vapor deposition[103], electrochemical
growth[104], hot imbibing[105] and atomic layer deposition[106].
Problems involved with sedimentation of microspheres into crystals are
defect and small mono-crystalline domain sizes. Different sedimentation
techniques have therefore proposed [107-109] to overcome the problems.
The synthetic opals discussed in this thesis have been prepared with a
technique developed by Lu et. al[109]. The main advantages with this technique are that it is very easy to use, it is inexpensive and does not require
clean room environment. The sedimentation of the monodispersed colloids
takes place in a rectangular Mylar film gasket between two glass slides (all
cleaned with acetone and ethanol). A square hole is cut into the film so that
it forms a frame. The glass slides and the Mylar frame create a cavity in
which the colloids can sediment. The advantage of using a Mylar film is that
it is available in different well-defined thicknesses and by choosing a certain
film thickness one can adjust the crystal thickness. The suspension with the
colloids is injected in the cavity through a hole in the top glass slide. On top
of the hole a glass tube is glued as a tank for the suspension before it has
enters the cavity. To create channels in the Mylar frame for the extraction of
liquid it is dipped in a dilute suspension of colloids before sandwiched.
When the pressure is applied by the paperclips over the sandwich the colloids attached to the surface of the frame will get pressed into the Mylar
creating spacing smaller than the colloidal diameter. Through this spacing
the liquid can flow, whilst the colloids are kept in the cavity. When the suspension is in the glass tube, a rubber bulb is place on the top. It prevents the
solvent to evaporate and applies a small external pressure that helps the suspension to enter the cavity. Figure 27 shows photo of the packing cell.
Figure 27. A packing-cell used for sedimentation of
colloidal microspheres. The technique was developed
by Lu et al.[109]. In the photograph the suspension is
just placed in the glass tube. One can see that the
microspheres are starting to sediment in the cavity.
46
The packing cell is then placed on a vibrating ultra sonic cleaner where it is
kept until the colloids have sedimented. The rubber bulb is removed and the
crystal is left to dry. After drying the top glass slide, with the glass tube, is
removed, and the crystal is out in the open. To prevent sticking to the top
surface and cracking of the crystal, the top surface it is made hydrophobic by
dipping it into a solution 5 ml dichlorodimethylsilane (Aldrich) and 45 ml
trichloroethylene.
Monodispersed silica spheres were used because of their optical properties in the infrared, and the availability of high quality colloids[110]. Crystals made of microspheres with four different diameters have been prepared:
d= 0.49, 0.73, 0.99 and 1.57 µm.
5.2 Optical analysis
A general comment concerning the optical measurements: Because of the
wavelength interval of interest discussed in this thesis, around 10 µm, there
has been a difficulties finding analyzing equipment. The reason is ironically
the scope of this thesis, the strong dispersion. Most often when optical microstructures are analyzed optical fibers are used. This has not been possible
since there are no optical fibers working in the thermal infrared. We have
therefore been forced to prepare samples which can either be analyzed by
normal incidence reflectance measurements with an IR microscope, or large
enough samples, 10*10 mm, that they can be analyzed with a spectrophotometer.
5.2.1 One-dimensional structures
The one dimensional periodic structures were analyzed with a Perkin Elmer
983 IR spectrophotometer. For the angular measurements a “Variable angle
specular accessory 186-0445” was used permitting measurements between
15o and 75o. Measurements were made for both s- and p-polarized light with
a gold mirror as reference. For each angle of incidence, the signal was maximized by adjustments of the mirrors in the accessory.
5.2.2 Two-dimensional structures
The optical properties of the hole array was examined by transmittance and
reflectance spectra recorded with a IR microscope, Bruker Hyperion 1000
with a MCT-detector. A gold mirror was used as reference for the reflectance spectra and spectra were collected both for the hole array and the unstructured surface. The optical images were taken with an Olympus AX 70
microscope.
47
5.2.3 Three-dimensional structures
The three-dimensional photonic crystals were analyzed by normal incidence
reflectance measurements. The spectra were recorded with two IR microscopes: a Bruker Hyperion 3000 using an InSb detector and a Bruker Hyperion 1000 with an MCT detector. The Hyperion 3000 provided reflectance
data in the wavelength interval between 0.83 and 2.8µm, and the Hyperion
1000 in the interval 2.8 to 12 µm. A gold mirror was also here used as reference.
48
6. Signature management in the thermal
infrared
6.1 Black-body radiation
All objects emit electromagnetic radiation in the infrared part (IR) of the
spectrum. For a blackbody[111] the spectral radiance L, at a certain temperature is given by Planck’s law
L (O , T )
c1
O5 ˜ ( e
c2
O ˜TK
, [W / m2 sr µm]
(26)
1)
where c1=1.91044*105 [W µm4/m2 sr], c2=14387.69 [µm K] and TK the absolute temperature. In Figure 28 the spectral radiances for two blackbodies
with different temperature, 60o C and 14o C, are plotted. These temperatures
were chosen to represent different objects. 60o is typical for the surface of a
car with a running motor and 14o represents the temperature of clothes covering a human body.
Figure 28. The spectral radiance for two blackbodies with the temperature 14 and
60 oC
49
As seen, at different temperatures the blackbody curves have their maxima at
different wavelengths. This is described by Wien’s displacement law[111].
For all wavelengths, the spectral radiance will be higher for higher temperatures, i.e., if T1>T2 then L(O,T1) > L(O,T2). The radiance drops fast on the
short wavelength side and has a long tail on the long wavelength side. This
explains why iron when is heated it appears red, and when the temperature is
increased it looks white (and not blue). The black smiths used this technique
for determining the temperature of iron by its’ color.
A unit often used when dealing with radiating objects is the emissivity, e,
of a surface/object. It is defined as the ratio of the radiance of a given body
to that of a blackbody[112]. The emissivity is a function of temperature,
wavelength and polarization. If the emissivity of a certain body is wavelength independent it is called a gray body.
6.2 Atmospheric windows
To detect an object one can use different kinds of sensors that work in different wavelength intervals. For example there are sensors available in the
visual, UV, IR (heat cameras/IR seekers) and radar. Because of the limitations of the human vision, that only monitors wavelengths between 380 and
780 nm, we are forced to use sensors if we wish to work in other wavelength
intervals. The visual spectrum is an exception, the atmosphere has high
transmittance for the wavelengths therein. This is not the case for most of the
electromagnetic spectrum. Wavelength intervals with high transmittance are
called atmospheric windows. Most parts of the atmosphere are in fact
opaque for electromagnetic waves, due to absorbtion in gas molecules and
scattering by particles. Both parameters vary with altitude and geographical
location. A transmittance spectrum for 1 km of mid-winter atmosphere in the
thermal infrared is shown in figure 29. We notice that infrared atmospheric
windows exist, one between 3-5 µm (MW) and one between 8-13 (LW). The
MW is split into two parts by a strong narrow absorbtion band originating
from carbon dioxide
50
Figure 29. A transmittance spectrum for 1 km of mid-winter atmosphere according
to ModTrans (see paper II)
Consequently, to detect heat radiation through the atmosphere from distant
objects at moderate temperature, one is limited to look in these two windows
(wavelength intervals). When an object has higher or lower temperature than
its’ surroundings it may be detected by a heat camera, working in one or
both of the two windows. This is used e.g. in the combat field to detect the
enemy or enemy platforms, but also when rescue personnel in helicopters are
searching for people e.g. in water.
6.3 Infrared camouflage
To avoid detection by a heat camera when an object has higher, or lower,
temperature than the surroundings, signature management has to be used.
This is achieved by minimizing the contrast between the object and the
background, just as a soldier dresses in beige when located in the desert or
green in the jungle. Objects used by humans often have considerably higher
temperature than the surrounding, e.g. a car engine or the nose cone of an
airplane. This means that signature management in the infrared part of the
spectrum boils down to reducing the thermal emittance to the same level as
the background in the two atmospheric windows. It is important that the
emittance does not reach zero. This will cause negative contrast, i.e., the
object is easy to detect because it appears cooler than the surrounding. This
is also the case when an object is cooler than the surroundings. Then the
thermal emittance has to be increased in the two windows.
In this thesis we only consider the most common case, i.e., when an object has to have a reduced thermal emittance. Kirchhoff’s law states that the
emittance, e of a blackbody is equal to the absorbance $. In optics it is well
51
known that the reflectance, the transmittance and the absorption for an object
summarized is equal to one,
1 = R + T + A
(27)
If the object has zero transmittance (15) changes to
e = 1 – R.
(28)
This means that high reflectance will give low emittance. Intervals with high
reflectance located in the two thermal atmospheric windows will then have
low emittance in the same intervals. To improve radiative cooling of the
object, high emittance is an advantage in the opaque parts of the spectrum.
Earlier in this thesis, two optical phenomena causing high reflectance
have been discussed, structural and polaritonic gaps. Structural gaps originate from the periodicity of the material. The position of the gap can be
shifted to different wavelengths by changing the lattice constant. Material
properties determine the position of the polaritonic reflectance, i.e., the spectral position cannot be changed. If the polaritonic material is chosen such
that the polaritonic gap is located in one of the two thermal infrared atmospheric windows it will reduce the emittance in that interval[113]. The same
holds for the structure gap[114]. To achieve simultaneously low emittance in
both infrared atmospheric windows the combination of these two optical
phenomena is an option. Since there is no material known to have a polaritonic gap for the MW wavelengths the structural reflectance has to be used
there and the polaritonic reflectance in the LW window. By design (materials and layer thickness) of a multilayer selective low emittance can be realized simultaneously in both windows.
We have worked with the materials combination of silicon and silicon dioxide. The main reason for this choice is that silicon dioxide has a polaritonic gap located for wavelengths around 9 µm (which is in the LW) and that
silicon is a material with high refractive index that can create a structural gap
together with silicon dioxide. It is of course also a major advantage that both
materials can be easily deposited with standard clean-room techniques.
The design was made with a multilayer program[9] and the final result
was a double layer, placed on a silicon wafer, with silicon as the top layer.
An increased number of layers affected the integrated window reflectance
behavior negatively. When the structure was made of more than two layers
the reflectance peak in the MW was narrowed and did not cover the entire
window. In figure 30 both the calculated and the experimental reflectance
are plotted together. Also included in the figure is the transmittance of the
filters on the heat cameras indicating the wavelength interval where high
reflectance is desired.
52
Figure 30. Calculated and measured normal incidence reflectance for the designed
double layer. No fitting has been performed. The thickness of the layers is 0.9µm
(Si) and 2.45µm (SiO2). Also included is the filter transmittance for the heat cameras
indicating the two atmospheric windows where high reflectance is wanted.
6.4 Emittance determination
The evaluation of the emittance properties of the structure was made with
heat cameras (Agema Thermovision“ 900). The cameras provide a realistic
(similar to the combat field) picture of how the improved emittance properties are perceived. The sample was placed, together with other reference
samples, as “windows” in a water tank. Figure 31 shows a photograph of the
sample holder.
Figure 31. A photo of the water
tank used in the emittance analysis.
The black hole in the middle is an
exit from a spherical hole-roam
which represents a black-body
radiator.
53
In the sample holder the samples were in direct contact with the water,
which was heated to 60o C. To ensure a constant water temperature throughout the water tank the water was set in motion by a water pump. Figure 32
shows a schematic picture of the experimental set up. The sample holder is
surrounded by a black curtain so that measurements can be made without
noise from the surrounding (other objects that are heated).
Figure 32. Schematic figure of the experimental setup. Two heat cameras (Agema
Thermovision“ 900) are placed in a small opening in a cylindrical black curtain.
Heat camera pictures were recorded and analyzed for different angles of
incidence, 10o – 60o. Because of the “Narcissus”-effect normal incidence
measurements are not possible. In figure 33 a) and b) heat camera pictures
are presented for both atmospheric windows.
a
b
Figure 33. Heat camera pictures for MW a) and LW b). Bright color indicates high
emittance. The circular bright area to the left, in both pictures, is the exit of a black
body radiator heated by the hot water. To the right the black area is a curtain surrounding the sample holder. In both pictures the samples are the four rectangles. In
the upper row: SiO2/Si to the left and Si/SiO2/Si to the right; in the lower row: bulk
BeO to the left and a aluminum plate with rough surface to the right.
54
The circular area to the left in the pictures indicates a black body radiator
and the rough aluminum surface the ideal case. It should be noticed that the
sample of interest, the upper right, has almost as good emittance properties
(same intensity) as the aluminum plate. An important difference is that aluminum has high emittance throughout the infrared spectrum whilst, our
structure has selective low emittance in the two wavelength intervals where
heat detectors are working. This property enables radiative cooling for other
wavelengths preventing overheating of the object. It can also be noted that
both the BeO and SiO2/Si samples, which both have a reststrahlen band located in th LW, have low emittance in b) and high emittance in a). By numerically analyzing the heat camera pictures one can obtain a value of how
much the emittance is reduced. We made angle dependent measurements for
both s- and p-polarized emittance. In figure 34 the emittance (mean value of
s- and p-polarized light) is plotted as a function of emittance angle. One can
see that the emittance at low angles is reduced to 0.37 in the LW and to 0.24
in the MW. Paper II presents a more complete analysis of the emittance
properties for both polarizations.
Figure 33 and 34 together evidence proofs that the proposed design can
be an alternative for selective emittance control in the thermal infrared. More
details are given in paper II[58].
Figure 34. The mean value of the s- and p-polarized emittance for both MW and
LW, for angles between 10 and 60 deg.
55
7. Summary of papers and conclusions
Paper I
H. Högström and C G. Ribbing, “Polaritonic and photonic gaps in Si/SiO2
and SiO2/air periodic structures”, Photonics and nanostructures – fundamentals and application 2, p.23-32, 2004
This paper discusses how the polaritonic gap is affected when it interacts
with a structural gap. This is done by multilayer calculations and experiments for a one-dimensional photonic crystals made by Si and SiO2, where
SiO2 is the polaritonic material. It is shown that a polaritonic and a structural
reflectance can: co-exist, have constructive interaction, i.e. the polaritonic
peak is strengthened and widened by the structural reflectance, and that the
polaritonic reflectance can be destroyed by the periodic structure.
Paper II
H. Högström, G. Forssell, and Carl G Ribbing, “Realization of selective low
emittance in both thermal atmospheric windows”, Optical Engineering
44(2), 026001, 2005
Here we investigate the possibility of using the combination of a structural
and polaritonic reflectance in order to selectively reduce the emittance in the
thermal infrared. A double-layer (made of S and SiO2) was designed in such
way that the structural reflectance was placed in the short wavelength IR
atmospheric window (O = 3-5µm) and an enhanced polaritonic reflectance is
automatically positioned in the long wavelength window (O = 8-13µm), because of the optical properties of SiO2. The sample was analyzed by heat
cameras in both windows, and for both polarizations, showing a reduction of
the emittance to 0.24 in the short, and 0.38 in the long wavelength window.
Paper III
H. Högström and C. G. Ribbing, “On the angular dependence of gaps in 1-d
Si/SiO2 periodic structures”, Submitted 2006 to Optics Communications
In this manuscript the angular behavior of the polaritonic and structural reflectance in a periodic structure is investigated by calculations and experiments. It is shown that the structural reflectance shifts to shorter wavelengths
with increasing angle of incidence. The polaritonic reflectance is sensitive
56
for polarization. For s-polarized light the peak is widened in both directions
and for p-polarized it is going through a minimum at the pseudo Brewster
angle.
Paper IV
H. Högström, S. Valizadeh, C. G. Ribbing, “Optical excitation of surface
phonon polaritons by a hole array fabricated by a focused ion beam”, Submitted 2006 to Optics express
Here we show that a FIB can be used for structuring a crystalline SiC surface
with deep holes. Optimized FIB parameters for fabrication and the influence
of ion current on the final hole diameter are presented. It is also shown that
the sensitive optical parameters of SiC, needed e.g. for surface excitations in
the wavelength interval between ZT and ZL, are not destroyed by the milling.
Excitations of surface states by a periodic structure are shown both by reflectance calculations and experiments.
Paper V
H. Högström and C. G. Ribbing, “Experimental observation of photonic and
polaritonic gaps in silica opal”, Submitted 2006 to Applied Optics.
In this contribution we present reflectance measurements on silica opals
showing the coexistence of photonic and polaritonic gaps in a threedimensional photonic crystal. Four different opals were prepared with different diameters between 0.5 and 1.6µm. It is shown that particles with a diameter close to O/20 still possess a robust polaritonic gap.
57
8. Summary in Swedish, svensk sammanfattning
Den svenska titeln på denna avhandling är ”Optiska studier av periodiska
mikrostrukturer i polära material”.
Olika material har olika optiska egenskaper. Ett fönster och ett nypolerat
silverfat är ett bra exempel på vardagliga saker som har olika optiska egenskaper. Fönster har vi på hus för att vi vill släppa in ljus och för att kunna se
ut. Man benämner detta som att glaset i fönstret har hög transmittans. Glas
reflekterar också en liten del av ljuset, och detta kan bäst ses på kvällarna då
det är mörkt utomhus. Om man tittar rakt ned i ett silverfat kan man alltid se
en spegelbild av sig själv. Man säger att metallen har mycket högre reflektans än glas.
Det som bestämmer ett materials optiska egenskaper är hur elektromagnetisk strålning (ljuset) växelverkar med olika oscillatorer i materialet. Dessa
oscillatorer kan bestå av elektroner (som i det reflekterande silverfatet), joner
och molekyler. De två sistnämnda oscillatorerna har sina resonansfrekvenser
vid mycket lägre frekvenser än det synliga ljuset, vilket gör att effekten av
dem ej kan observeras av ögat.
I denna avhandling har vi jobbat med material som har en oscillator skapad av en gitterresonans, en så kallad fononexcitation. Denna excitation
finns hos material vars bindning har jonkaraktär och. När ljus, med rätt frekvens (våglängd) träffar denna typ av material kommer jonkärnorna att börja
oscillera på grund av att de accelereras av det inkommande elektromagnetiska ljuset. Resultatet blir ett litet våglängdsintervall där materialet kommer att
vara högreflekterande, precis som en metall. I fortsättningen kommer detta
intervall benämnas som polaritonreflektans eller polaritongap, efter en quasipartikel som är en kombination av en foton och fonon. Metalliknande innebär i detta sammanhang att de är högreflekterande, lågemitterande samt att
de kan hysa ytvågor. De är dock inte goda elektriska ledare, som metaller är.
Skillnaden mellan metaller, och material som optiskt beter sig som en metall,
är att de sistnämnda endast har dessa egenskaper i ett smalt våglängdsintervall, medan metallers egenskaper (som diskuterats ovan) gäller upp till
plasmafrekvensen. De polära material som vi arbetat med i denna avhandling
är kiselkarbid och kiseldioxid (samma material som vi har i fönster). Kisel-
58
dioxid beter sig alltså optiskt som en metall, fast vid våglängder som vi inte
kan se med ögat.
Kan man då påverka ett materials optiska egenskaper så att de blir som vi
vill, eller måste man nöja sig med de egenskaper som ges av den atomära
strukturen? Svaret är man kan styra ett materials optiska egenskaper, och att
det låter sig göras på flera sätt dessutom. Ett exempel är att ändra ett material
på atomär nivå, som man t ex gör i smarta fönster. Där ändrar man absorbtionsenergin för materialet, genom att tillföra eller ta bort joner, så att det
kan skifta mellan att vara ljust och mörkt. Detta kan vara till stor nytta i t ex
skidglasögon, fönster och displayer. Ett annat sätt att ändra ett materials
optiska egenskaper är att skapa en periodisk struktur av olika material. Man
kan med beräkningar bestämma hur en periodisk struktur ska se ut för att
man ska få hög reflektans för en viss våglängd. Hög reflektans för en viss
våglängd uppfattar ögat som en färg. Exempel på var en periodisk struktur
skapar en färg är den skimrande färgen hos skalbaggar, opal, bensinfilmer på
vatten samt färgen hos vissa fjärilar.
Vad finns det då för möjligheter om man kan skräddarsy ett materials optiska egenskaper? Man kan t ex skapa lasrar, häftiga solglasögon och även
bestämma hur ljuset ska ledas genom ett material, precis som vägarna styr
var vi kör våra bilar.
Arbetet som har lett fram till denna avhandling har innefattat två av de
ovan beskrivna optiska egenskaperna, en materialoptisk egenskap samt en
egenskap kopplad till en periodisk struktur. Materialegenskapen hör till icke
ledande material som har en gitterresonans i de termiskt infraröda området
(våglängder runt 10 µm). Arbetet har gått ut på är att se hur de materialoptiska egenskaperna i det våglängdsintervallet kan användas och förändras
genom att tillföra en periodisk struktur.
Papper I-III samt V undersöker hur dessa två skilda optiska fenomenen
påverkas om de placeras i varandras närhet på våglängdsaxeln. Resultaten
visar att materialreflektansen kan förstärkas, tas bort samt vara oförändrad i
en periodisk struktur. Vi visar även, i papper II, att kombinationen av en
materialreflektans och en struktur-reflektans kan kombineras så att den termiska utstrålningen från ett material kan undertryckas selektivt. Detta är av
intresse för t ex militära plattformar där man vill undvika att stråla ut värme
eftersom den kan detekteras av IR-sensorer. Papper III visar att reflektansens
vinkelberoende skiljer sig hos de två fenomenen. Strukturreflektansen flyttas
mot kortare våglängder med ökande infallsvinkel på ljuset, medan polaritonreflektansen vidgas åt båda håll för s-polariserat ljus, och passerar ett minimum för p-polariserat.
I papper IV används en periodisk struktur för att excitera ytvågor i ett
polärt material. Ytvågor är en polarisationsvåg som är bunden till ett gränsskikt mellan ett material som beter sig optiskt som en metall, och ett dielektriskt material. För att kunna excitera denna typen av vågor måste viss manipulation ske för att ”lura” ljuset att binda sig till ytan. Detta kan t ex göras
59
med hjälp av en skapad periodisk struktur. De geometriska parametrarna för
den periodiska strukturen bestämmer vilken våglängd som kommer att excitera ytvågen. Denna typ av ytvågor är av stort intresse för de kan användas
till kemiska och biologiska sensorer samt till att leda ljus och skapa möjligheten att utföra mikroskopi på nanostrukturer. Det som presenteras i papper
IV är resultat som visar att det går att tillverka periodiska strukturer som
exciterar ytvågor i kiselkarbid med hjälp av en fokuserad jonstråle. Problemet med en jonstråle är att den kan förstöra materialet, och då även förmågan att excitera ytvågor.
Sammanfattningsvis kan sägas att i denna avhandling har undersökts hur de
optiska egenskaperna hos polära material ändras/kan användas, då de får
samverka med optiska egenskaper tillhörande en periodisk struktur. För att
denna undersökning skall vara möjlig måste periodiciteten vara av samma
storleksordning som det våglängdsintervall där de materialoptiska egenskaperna finns, dvs. mikrometerområdet (10-6 m). Periodiciteten är skapad genom kemisk deponering av tunna skikt, sedimentering av mikrosfärer och
genom direkt strukturering med en fokuserad jonstråle. Analysen har främst
gjorts genom olika typer av reflektansmätningar.
60
Acknowledgements
This work was carried out at the Division of Solid State Physics, Department
of Engineering Sciences, the Ångström Laboratory, Uppsala University. The
project was financially supported by: The Swedish Foundation for Strategic
Research (SSF), the Swedish Research Council (VR) and the Swedish
Nanotechnology in Defense Applications Program.
Of course there are a lot of people who deserves to be mentioned in this part
of the thesis.
I would like to thank...
- Prof. Carl G. Ribbing, who has been my supervisor during my time as a
PhC-PhD-student. You have made my time as a student much easier, thanx.
Our trips around the world have been great and I’ve really enjoyed: a cold
lager when looking at the sunset in California, eating huge steaks and testing
what Sam Adams has to offer in Boston, visiting the fish-market in Tokyo
and drinking the worst wine ever in Greece.
- Prof. Claes-Göran Granqvist for giving me the opportunity to work at the
Division of Solid State Physics, and for showing me what it feels like to wait
for a flight in an airline lounge.
- Andreas, my closest co-worker, for being a cool office-mate who shares
my passion for music, and sports ;-). Our discussions about different aspects
of life will always be remembered.
- Dr. Göran Forssell, my co-author, for interesting discussions
- Dr. Sima Valizadeh, my co-author, for sample preparation and helping me
with the FIB.
- Prof. Paul V. Braun and Stephanie Pruzinsky, University of Illinois Urbana-Champaign, for having me as a guest and sharing their knowledge.
- Prof. John B. Pendry, Imperial College London, and Prof Francisco GarciaVidal, Universidad Autonoma de Madrid, for fruitful discussions
61
- Dr. Stefan Björkert (FOI Linköping) for helping me with sedimentation of
microspheres.
- All my present and former colleagues at the Division of Solid State Physics
and the Department of Engineering Sciences, for a friendly atmosphere.
- The people at the Dept. of Functional Materials, FOI Linköping, for showing interest in my work and providing me with a framework of applications.
- Bengt Nelander, at beamline 73 MAX-lab for helping me with reflectance
measurements.
- Anders Heljestrand for all the help with the sample preparation.
- Jun Lu for the TEM analysis.
- My lunch-pals for all the meaningless discussions. No subject has been too
stupid or trivial, I have loved it. If everything else fails, we’ll always have
our great business plans which will make us filthy rich.
- All my friends around the world, you know who you are and I will never
forget what you have done for me!
Slutligen vill jag självklart även tacka
- Anna-Maija & Håkan, dvs mor o far, för allt det stöd ni ger mig. Jag är er
evigt tacksam.
- Hanna o Maija, mina systrar… Vad kan jag skriva som på ett rättvist sätt
beskriver hur jag känner för er? Ni är mina änglar…
- dig, för att du är den du är!
I think it was John Lennon who said “Life is what happens when you’re
making other plans.” Although he also said: “I am the walrus, I am the
eggman” so I don’t know what to believe…
Tim in “The office”
62
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69
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Digital Comprehensive Summaries of Uppsala Dissertations
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