Download NicholasBarbutoPoster - Physics

Photoluminescence in One Dimensional
Photonic Crystals
Nicholas Barbuto1, Tomasz Kazmierczak2, Joseph Lott2, Hyunmin Song2, Yeheng Wu1,
Eric Baer2, Anne Hiltner2, Christoph Weder2,
1Department
of Physics, Case Western Reserve University, Cleveland, OH
2Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, OH
ABSTRACT
METHODS
DISCUSSION
PHOTONIC CRYSTALS
Photonic crystals are any dielectric material with periodic
dielectric properties. The figure below gives a visualization to the
notion of the periodicity. Macroscopically this corresponds to a
periodic index of refraction. This periodicity can happen in one,
two, or three dimensions. This study focuses on 1-D crystals
made from stacked polymer films.
1. A tunable wavelength laser is used to
pump the sample at the dopant’s peak
absorption wavelength .
Melt Pump A
AB Feedblock
Extruder A
Extruder B
1
2. A linear polarizer is mounted on a
rotational stage. This is used to vary the
power of the pump beam.
Melt Pump B
Layer
Multipliers
Surface Layer
Extruder
Surface Layer
Feedblock
The intensity of the emission from a Fabry-Perot cavity
(as an approximation to a photonic crystal) is the product of three
different parameters.
1
I
 D( )  E ( )
 
1  F sin 2  
2
4 nd

c
2
Transfer Tube
Melt Pump
Interference effects inside photonic crystals provide mechanisms
for the precise control of light both within and outside of the
photonic crystal. In particular the emission direction, spectrum,
and intensity can be affected by the band structure. We will study
photoluminescence properties in one-dimensional polymeric
photonic crystals containing photoluminescent organic dopants,
which are fabricated by a co-extrusion/multiplication process.
We will also be investigating applications of such structures in
surface emitting distributed feedback lasers and as color and
emission control elements for efficient solid state lighting.
3. In order to project a round beam shape
onto the sample, the pump beam is directed
through a spatial filter.
Exit Die
Where F is the finesse of the cavity, D(ω) is the density of states,
E(ω) is the emission of the fluorescent dye outside of the cavity,
ω is the angular frequency, n is the relative index of refraction,
and d is the length of the cavity.
The first term corresponds to the photon modes which can
exist in any cavity. To find the expected modes, the effective
length of the cavity, nd, needs to be known. We can calculate the
separation of mode peaks seen in the emission spectrum of the
sample using the following relationship fit to the oscillations of
the emission spectrum.
Skin layer
Core
layers
Skin layer
To make the samples, we use a extrusion process melts two
polymers and combines them, one on top of the other. The layer
multipliers cut the sample in half vertically, again place one on
top of the other, and spreads them out to the previous width. After
a number of multiplications, a surface layer is applied for
evenness and protection and the sample is forced out an exit die
which spreads the sample further.
DFB
A Distributed Feedback sample
is created by stacking ~100 nm
thick films of polymers with
alternating indices of refraction.
The fluorescent dye is doped
into individual, alternating
layers.
A photonic crystal is the optical analog to semiconductors
in electronics. Semiconductors control the flow of electrons by
creating energy bands where electrons are not able to flow,
usually referred to as the band gap. This stems from the periodic
nature of the atoms or molecules in a crystal lattice. In photonic
crystals, the same type of periodic structure exists, only in place
of electron conduction properties, the dielectric properties, or
photon conduction properties are periodic. The photonic crystal
forms a band gap where photons of a specific energy, or
wavelength, cannot flow. The photon states normally contained in
the gap are pushed out of the band, drastically increasing the
density of states at the edge of the band gap.
4. Another linear polarizer polarizes the light
vertically with respect to the sample to
guarantee the polarization is consistent.
5. The sample contains one of two
fluorescent dyes, R6G or C1RG.
Spontaneous emission occurs when the
pump beam excites electrons in the dye
and then fall back to the ground state,
releasing a photon.
3
4
5
6. A spectrometer is mounted on a rotational
stage that measures the spectrum of the
emitted light from 0° to ±90°.
6
RESULTS
The BLUE curve is the emission of the fluorescent dye if
it were in a cavity in the absence of a photonic band gap.
The effective length of the sample was found to be 6 ± 1
μm which is approximately half the known thickness of the
sample. This tells us that the spontaneous emission of the sample
is concentrated in the middle 6 μm of the sample.
Using this information we calculated the expected modes
of emission and divided that by the measured emission to
calculate the density of states found in the lower section of the
middle portion of this poster. The density of states corresponds to
what we would expect from a photonic crystal. The density of
states has a well defined band gap and spikes on the edges of that
gap.
The BLACK curve shows the photonic band gap location
in relation to the emission.
ACKNOWLEDGEMENTS
This graph shows the parameters used to calculate the
density of states.
The RED curve shows the emission of the photonic
crystal while it is pumped with the laser light.
Spontaneous Emission
  E2  E1
Where ω is the angular frequency of the photon, E2 is the energy
of the higher state and E1 is the energy of the lower state.
To find the likelihood of a transition, we use Fermi’s
Golden Rule to calculate transition rates of the atoms.
W12 
2
M 12 g   
2
Where M12 is the matrix element for the transition rate and g( ħω)
is the density of states. Note that the density of states is an
important concept to spontaneous emission in a photonic crystal
since the photonic crystal modifies the states significantly.
Where ωavg is the average wavelength of the emission and Δω is
the distance between mode peaks.
To approximate the density of states, we can simply solve
the above equation for D(ω) by multiplying the fluorescent gain
curve, E(ω), by the mode equation and dividing the emission
spectrum by that value.
CONCLUSION
The GREEN curve is the emission we would expect if
there was no cavity or photonic band gap. It is simply the
gain of the fluorescent dye, R6G.
Spontaneous emission refers to the quantum mechanical
phenomenon when an atom in a higher state jumps down into a
lower state and emits a photon of a specific energy. The energy
released by this state transfer is governed by conservation of
energy which manifests in the following equation.
c
nd 

Acknowledgements are due to the Center for Layered Polymeric
Systems for the funding they provided for the study, Brent Valle
of the Case Western Reserve University Department of Physics
for the consistent support with optics and discussion, and
Professor Gary Chottiner for his support in the poster creation
process.
REFERENCES
The density of states is the number of final photon states with that
specific energy. In free space the density of states is proportional to
the angular frequency squared, or:
D( ) 
2
In a photonic crystal, the photon states cannot exist in the photoinc
band gap. Those states get pushed to the edges of the band gap
causing a large spike there.
To the right is the measured density of states for a Distributed
Feedback laser. The band gap is apparent, as well as the spikes on
the edges.
Joannopoulous J. et al. Photonic Crystals: Molding the Flow of
Light. Princeton Univerity Press. (1995)
Ouellette J. Seeing the Future in Photonic Crystals. The Industrial
Physicist. December/January: 14-17. (2002)
M. H. Bartl. http://www.chem.utah.edu/faculty/bartl/