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OPTO−ELECTRONICS REVIEW 24(4), 196–208
DOI: 10.1515/oere−2016−0027
Influence of a thin metal layer on a beam propagation in a biconical
optical fibre taper
K.A. STASIEWICZ* and J.E. MOŚ
Institute of Applied Physics, Military University of Technology,
ul. Gen. Kaliskiego 2, 00–908 Warsaw, Poland
The paper presents results of a simulation of the plasmon effect achieved between a thin precious metal layer and a biconical
optical fibre taper, manufactured on a standard single mode fibre. Gold, silver and titanium were used as a metal which ful−
filled a cladding function for a small diameter structure. For simulation Mode Solution software was used on which modal
and frequency analyses of a wavelength were provided in the range of 800–1700 nm. A displacement of a plasmon pick in de−
pendence of thickness of a deposited precious layer for the highest plasmon effects was observed.
Key words: optical fibre technology, tapered technology, plasmon effect, precious metal layer.
1. Introduction
The development of optical fibre technology over the last
century was significant. Fibre technology can be divided
into two parts: telecommunication and non−telecommuni−
cation. The telecommunication part is a good compound
and now many of guided researches are oriented on capac−
ity increase, optimization or existing systems’ improve−
ment. Development of a non−telecommunication area gives
a lot of possibilities for manufacturing new advanced ele−
ments and arrangements, as well as discovering or develop−
ing new applications for the existing solution. One of the
promising technologies is optical fibre taper technology
[1–4]. This technique provides a small insertion loss to
a propagating beam and is comparable with standard opti−
cal fibres’ dimension. The basic element, which is a bi−
conical optical fibre taper, allows controlling light beam
propagation in the structure. This element is a base for man−
ufacturing advanced hybrid elements like polarization con−
trollers [5], optical switchers [6], white lasers [7] or optical
sensors [8,9]. Finally, the tapering technology is relatively
easy and cheap. The most important fact about this technol−
ogy is that it enables continuous monitoring of the light
propagation through the tapering process [10]. Tapering
process enables obtaining demanded diameters of a fibre
structure without the necessity of a new fibre’s drawing.
Process of tapering makes decrease the fibre diameter to the
*e−mail:
196
state in which a beam propagates in the whole taper struc−
ture and the surrounding air becomes a cladding. This ef−
fect gives possibility to change a boundary condition by re−
placing air with materials with different optical parameters
like refractive index, chemical composition, extinction in−
dex, transparency. A very interesting phenomenon as sur−
face plasmon resonance can be obtained by using a metal
layer. For the last few years a research on manufacturing
different optical sensors by using a metal layer as an active
material has been carried out [11–16]. Gupta worked on
SPR effect in tapered optical fibres and described it mathe−
matically. [11,13,16].
The research presented in this paper describes an influ−
ence of a boundary condition modification on propagation
of the light parameters in a taper region. In this paper we
present the simulation results of a thin, precious metal layer
influence on spectral characteristics of attenuation and dis−
persion. These results give information about SPR effect
which will be useful for design and manufacturing of ad−
vanced and hybrid optical fibre sensors. In Sect. II the main
parameter of an optical fibre taper and beam propagation
parameters like penetration depth and dispersion are des−
cribed. In Sect. III optical characteristics of applied materi−
als are presented. Section IV contains results of a simula−
tion of a thin metal layer influence on dispersion and atten−
uation characteristics. Section V contains conclusions and
additional information about development of the presented
work.
[email protected]
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2. Taper as an element allowing to control light
beam penetration depth in a cladding and
dispersion properties in a structure
In a standard or microstructured fibre light propagates along
the structure of a core surrounded by a cladding – using
material or geometrical properties. Such structure has on
purpose to achieve as small propagation losses as possible.
These properties require an adequate dimension of a core or
cladding keeping an optical beam from propagating outside
the fibre structure. There is no possibility to direct external
influence on the beam. One of the ways allowing the light
beam to propagate inside such structure is to reduce the fibre
diameter to few microns.
A diameter of several micrometres can be acquired in an
easy way in a process of fibre tapering. We can describe few
methods of tapering including: elongation in a low pressure
gas burning [10], CO2 laser [17,18], heating gravitation
elongation [1], elongation in a filament fusion technology
[19] or chemical etching [20]. All of these methods of fibre
tapering are different from technological point of view (sys−
tem of heating and elongation), but not for the output shape –
the taper. The shape of manufactured tapers, as well as modi−
fication of beam propagation parameters in structure were
widely described [10,11,21], so now we concentrate only on
a possibility to control a penetration depth and dispersion
properties.
Process of tapering in a low pressure gas burner makes
decrease the diameter of a core and cladding simulta−
neously. A change of the core−cladding boundary causes an
increase of the mode field diameter (w0). In the beginning,
a part of the beam spot which propagates outside the core
can be described as an evanescent field which does not
propagate along the structure of a fibre. In a particular case,
a beam spot covers the whole structure of a taper. From the
Maxwell equation appears that a part of the beam propa−
gates outside the guiding material (depth of penetration)
(Fig. 1) [22–24].
dp =
l
2
2
2p n core
sin 2 q - n cladding
The depth of beam penetration in the region of cladding
for a chosen wavelength is given by the following equation
[23]
Opto−Electron. Rev., 24, no. 4, 2016
(1)
where l is the determined wavelength of light, q is the angle
of incident light on the core/cladding surface, ncore, ncladding
are the refractive indices of core and cladding.
As a result of the tapering process, the penetration depth
of a light beam increases more and more the cladding section
to the point where the light beam is guided in a whole taper
structure which remains a core and surrounding air becomes
a cladding The boundary conditions and the refractive index
are modified according to geometrical changes of the core
and cladding diameters. The normalized frequency is written
as [25]
V =a
2p
2
2
,
n cladding
- n air
l
(2)
where a is the radius of a taper, l is the wavelength, ncladding
is the taper refractive index, nair is the surrounding refractive
index.
This effect of a light beam leaking an optical fibre over
the structure determines the use of an additional material as
a cladding. In this paper the results of simulation using gold,
silver and titanium forming an additional thin layer as a clad−
ding part are presented.
For description of an influence of a thin layer on propa−
gation parameters, two kinds of coefficients were simulated:
attenuation and dispersion. Attenuation characteristics were
obtained as a ratio between input power and output power in
a wide wavelength range [22,26]. Dispersion can be des−
cribed as a dependence of a refractive index on a wavelength
and is linked with a change of propagating impulse shape
depending on its velocity in a fibre.
In the paper all research is focused on a chromatic disper−
sion. Such dispersion is set for two components: material
dispersion and waveguide dispersion. First of them is associ−
ated with a dispersion property of the material from which
the fibre is made. The waveguide dispersion is connected
with the wavelength dependency on fibre geometry as well
as on propagation constant [27,28]. The waveguide dis−
persion can be written as
D=
Fig. 1. Course of a propagating optical beam in the standard optical
fibre with the marked beam penetration depth [23].
,
2pc
u 2g l 2
´
du g
dw
,
(3)
where u g = dw db is the group velocity: w is the optical fre−
quency, b is the propagation constant of light in the structure
[28].
It should be noticed that in an optical fibre taper most of
the guided power is concentrated in a very small region of
a waist. Strong nonlinear effects including soliton genera−
tion, four−wave mixing, self−phase cross−phase modulation,
197
K.A. Stasiewicz
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Influence of a thin metal layer on a beam propagation in a biconical optical fibre taper
Raman scattering and change of dispersion made by change
of propagation condition [29,30] arise from this concentra−
tion of power in a small region. Effects can appear simulta−
neously. The result of the mentioned effects is a shift of dis−
persion characteristics towards shorter wavelengths which is
shown in the further part of this paper.
3. Description of material layers
A refractive index of the absorption medium can be des−
cribed by a formula which contains the real (n) and imagi−
nary (k extinction index) parts. The real part is connected
with the phase velocity and the imaginary part influences the
light attenuation.
(4)
n~ = n + ik.
The extinction index is a material constant and is impor−
tant for description of an electromagnetic field attenuation
which goes into the material. In our case the absorption
material is one of the used precious metals. Light absorption
in a metal material is linked with attendance of free elec−
trons. Metals can be characterized as materials containing
high density of free electrons (1028 m–3) which is coupled
with an electric permeability in dependence on light fre−
quency.
Phenomenon of a light propagation on a dielectric−metal
boundary uses a surface plasmon polaritions’ effect (SPP).
This effect can be described as a propagation of the electro−
magnetic field along a dielectric−metal boundary. Electric
permittivity of a dielectric is higher than zero, however for
the metal it is complex. For the dielectric−metal boundary
there is a real part of dielectric constant with an opposite sign
which enables SSP propagation. It is made by a density
oscillation of electric charge on the medium boundary.
Quantum of the oscillation is called a surface plasmon which
is a transverse wave (TM) which sinks exponentially in
a metal layer [31].
By solving the Maxwell equation it is possible to find
a relation between a surface plasmon wave number and fre−
quency [13,16,32]:
k sp
w e me d
,
= kx =
c em +ed
(5)
here c is the light speed in vacuum, em and ed are the per−
mittivity of a metal and dielectric, respectively.
The real part of a wave plasmon vector describes a sur−
face plasmon phase velocity and the imaginary part des−
cribes the attenuation which is united with the width of the
resonance peak [32].
Characteristics of the refractive index (n) and the extinc−
tion index (k) vs. wavelengths for gold, silver and titanium
metals are presented below in Fig. 2. As it can be seen, char−
198
acteristics for gold and silver are similar [33,34]. Refractive
indices for both of them are lower than 2, the extinction
index increases in a linear way to above 16. So it can be seen
that the extinction index is much higher than refractive in−
dex. Characteristics of refractive and extinction indices for
titanium present a totally different shape. Both, refractive
and extinction indices present similar value for the chosen
wavelength and their changes are similar. The reason for
which we have chosen precious metals was connected with
their optical parameters like refractive and extinction indi−
ces, permittivity etc., as well as with a well−known technol−
ogy for their deposition on an optical fibre which are nece−
ssary for further research.
4. Simulation of a mode field diameter for
a taper waist with an external layer
This section describes results of the simulation of the mode
field diameter modification (MFD) for light propagation in
a biconical optical fibre taper with deposited three different
metal layers (Fig. 3). All simulations were provided by the
Mode Solution® software form Lumerical Solution Inc.
Material parameters of a fibre and taper like refractive
indices of core and cladding used for simulation, as well as
their diameters were chosen from the catalogue of material
properties of a standard single−mode fibre SMF28 Corning
[36]. For a taper only diameters of core and cladding chan−
ged, refractive indices remained unchanged.
A non−tapered fibre, a fibre tapered to 50% of SMF, 20%
of SMF and 10% of original size of SMF were submitted to
simulation. A simulated region was limited to the taper waist
region in which the beam flows out from the dielectric. In the
process of simulation it was assumed that for the fused taper,
the diameters of core and cladding decrease in a linear way
(Table 1).
Table 1. Diameter of core and cladding for simulated elements.
SMF
Core (μm)
Cladding (μm)
8.2
125
50%
of SMF
4.1
62.5
20%
of SMF
1.64
25
10%
of SMF
0.82
12.5
In Fig. 4 the simulation of a fundamental mode propaga−
tion in a structure described in Sect. II (mode analysis) is
presented. In the picture a cladding, core and distribution of
fundamental mode are shown.
In an untapered fibre, a light beam is bound in a core. In
the process of tapering the structure diameter is reduced and
the beam propagates not only in the core – some part of
a light leaks to the cladding area. For a taper size of 10% of
the original dimension of an SMF a diameter of the core is so
small that it can be neglected in the propagation. A guided
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Fig. 2. Refractive index n and extinction index k for gold Au (a) [33], silver Ag (b) [34] and titanium Ti (c) [35].
simulation was provided for the wavelength of 1550 nm
from which the most valuable information according to the
dimension of a Mode Field Diameter (MFD) and the effec−
tive refractive indies (neff) is presented in Table 2 and
Table 3, respectively.
Table 2. MFD dependence on an optical fibre taper structure for
a 1550 nm wavelength.
Fig. 3. Scheme of the optical fibre taper with a mark of main ele−
ments.
Opto−Electron. Rev., 24, no. 4, 2016
Structure
SMF
Core (μm)
Cladding (μm)
MFD (μm)
8.2
125
10.98
50%
of SMF
4.1
62,5
38.45
20%
of SMF
1.64
25
15.51
10%
of SMF
0.82
12.5
7.86
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Influence of a thin metal layer on a beam propagation in a biconical optical fibre taper
Fig. 4. Simulation of a propagating light in an optical fibre taper structure for 100%, 50%, 20% and 10% of original dimension of a standard
optical fibre.
Table 3. Effective refractive index dependence on an optical fibre
taper structure for a 1550 nm wavelength.
Structure
Core ncore
Cladding ncladding
Surroundings nextrenal
neff
SMF
1.4509
50%
20%
of SMF of SMF
1.4548
1.4443
1
1.4439
1.4433
10%
of SMF
1.4411
As it can be seen, for a standard SMF, the fundamental
mode is guided in a core. A small difference in an MFD
value from the catalogue can be explained as the used differ−
ence in a boundary condition. For the other structures it can
be observed that the fundamental mode propagates more and
200
more in a cladding – increasing MFD to the size higher than
the core diameter, as well as changing the effective refractive
index which is going to be close to the cladding one. For
a taper size of 10% of the original dimension of an SMF, the
whole structure is going to be the core, and the cladding is
made of surrounding air with a refractive index equalling 1.
The value of effective refractive index of a taper structure is
below the refractive index value of a cladding in a single
mode fibre. In order to recognize theoretical assumption, the
next simulation of a thin precious metal layer was applied.
Three thicknesses of layers: 25 nm, 50 nm and 100 nm were
chosen for the simulation. Selection of such thicknesses was
suggested by literature [11,12,16] as the best optimized
layer, as well as multiplying thickness to get the best solu−
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Table 4. The MFD for the simulated structure with different metal thickness results for 1550 nm wavelength.
MFD (μm)
50% of SMF
20% of SMF
10% of SMF
Au
Ag
Ti
Au
Ag
Ti
Au
Ag
Ti
25 nm
37.82
37.68
38.28
14.88
14.69
15.38
7.26
7.24
7.77
50 nm
37.80
37.69
38.14
14.82
14.72
15.27
7.30
7.21
7.72
100 nm
37.81
37.72
38.01
14.78
14.70
15.10
7.32
7.21
7.52
tion enabled farther use in future research in our laboratory.
In Table 4 there are presented results of the MFD of different
precious metal layers with a combination of different thick−
nesses of the layers.
As it can be noticed in Table 4 in most cases MFD
decreases when thickness of a layer and a diameter of the
structure increase. In all cases the MFD is insignificantly
smaller than the MFD value of a non−deposited structure
what is corrected with the theoretical meaning [15,19], an
additional layer does not allow to leak the beam out of its
space. As it can also be noticed the difference in dispersion
characteristics for different metal layers is an influence of
optical parameters of metals like refractive or extinction
indices which are associated with the metal permittivity.
A spectral analysis was provided for the wavelength
range from 600 nm to 1700 nm which covers the first, sec−
ond and third optical transmission window. Evaluated para−
meters for these simulations are dispersion and attenuation
characteristics. These properties are the most important and
interesting ones for design of a sensor.
In order to compare the simulation of a coated taper with
a standard one, there was calculated a dispersion dependence
on the wavelength for the SMF28 fibre from Corning with
using the following formula [36,37]
s
D( l) = o
4
é
l 4o ù ps
,
l
ê
ú
l s úû nm × km
êë
(6)
where lo is the zero dispersion wavelength from the range of
1304–1324 nm, So = 0.092 ps/nm2 × km describes a slope of
the dispersion curve.
First there was provided a simulation for a standard
SMF28 and a tapered structure 50%, 20% and 10% of the
original SMF size (Fig. 5). Comparison of the obtained
results with the catalogue ones from Corning proved that
boundary condition in our simulation are correct. As it can
be observed with the decreasing size of the tapered structure,
the received curves are shifted into the shorter wavelength.
This effect is a consequence of MFD, as well as an effective
refractive index change.
By comparison with characteristics of losses, it can be
seen that for a standard fibre and a taper structure in the
range close to 1550 nm the attenuation is similar. For other
Opto−Electron. Rev., 24, no. 4, 2016
Fig. 5. Dispersion characteristics for a real and tapered SMF to the
size of 50%, 20%, 10% of the original SMF28, as well as their attenu−
ation characteristics.
wavelengths in a taper it can be observed a higher attenua−
tion increasing to 2 dB/cm what is confirmed by the theoreti−
cal description point of view.
4.1. Wavelength analysis of the proposed structure
with gold layers
In the simulation we observe that deposition of gold layers
increases the attenuation. Reducing the taper structure di−
mension and simultaneously increasing the layer thickness,
a shift of the highest peak of attenuation towards the shorter
wavelength is observed, as is shown in Fig. 6. Attenuation
for the structure of 50% size of an original dimension of
SMF possesses similar characteristics of attenuation as an
uncoated structure. This is coupled with the MFD which is
smaller than the diameter of a taper waist. For a wavelength
close to 1.4 um it can be observed an increasing attenuation
in comparison to the uncoated one. Considering the compar−
ison of attenuation characteristics with dispersion ones it can
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Influence of a thin metal layer on a beam propagation in a biconical optical fibre taper
Fig. 6. Characteristics of attenuation for 50%, 20% and 10% of an
original dimension SMF of the structure with gold layers.
be noticed that for a wavelength in which appears an amplifi−
cation of attenuation with reference to the uncoated charac−
teristics, a resonance peak in dispersion characteristics is
also obtained. This peak is assembled from two parts, first
when a dispersion increase described as a normal dispersion
and after decreasing below zero described as an abnormal
dispersion (Fig. 7).
From data presented in Table 5 one can see that the high−
est dispersion change is provided by tapers with a 50 nm
Table 5. Resonance peak wavelengths and dispersion values for dif−
ferent taper structure with gold layers.
Thickness
of layer (nm)
25
50
100
202
Structure
of taper
50% of SMF
20% of SMF
10% of SMF
50% of SMF
20% of SMF
10% of SMF
50% of SMF
20% of SMF
10% of SMF
Resonance peak
Dispersion
wavelength (μm) [ps/(nm × km)]
1.66
58.35
1.43
66.54
1.60
786.56
1.53
49.26
1.33
74.35
1.46
3135.11
1.51
84.26
1.30
290.90
1.43
2968.70
Fig. 7. Dispersion characteristics for 50%, 20% and 10% of an origi−
nal dimension SMF of the fibre structure with gold layers.
gold layer (3135.11 [ps/(nm × km)]). It should be mentioned
that for a taper equal to the size of 50% of original dimension
of SMF the change of dispersion for a gold layer possesses
the smallest differences in results depending on thickness of
these layers
Looking at changes of a wavelength for a characteristic
dispersion peak it can be observed that with increasing of
a gold layer thickness the peak is shifted towards the shorter
wavelengths for taper structures (Fig. 8).
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Fig. 9. Attenuation characteristics for 50%, 20% and 10% of the orig−
inal dimension SMF of the structure with silver layers.
a result of flatter characteristics of silver refractive index
compared to gold. For the taper structure with 50% of a fibre
original size not high increase of attenuation or dispersion
characteristics can be also observed. This effect can be ex−
plained in this same way as for gold – light leaking for such
structure is not high and still most of power propagates in
a centre region.
In Table 6 the values of resonance peak wavelengths and
dispersion are presented. It can be noticed that for the taper
Fig. 8. Normalized dispersion for the resonance peak for the simu−
lated structure with different thickness of gold layers.
Table 6. Resonance peak wavelengths and dispersion values for dif−
ferent taper structures with silver layers.
Thickness
of layer (nm)
4.2. Wavelength analysis of the proposed structure
with silver layers
Dispersion and attenuation characteristics of silver layers
deposition are similar to the structure with gold layers what
results from similar characteristics of refractive and extinc−
tion indices (see Fig. 2). For higher attenuation in all ana−
lyzed wavelengths (Fig. 9) the formed peaks are related to
dispersion peaks as is shown in Fig. 10. This effect can be
Opto−Electron. Rev., 24, no. 4, 2016
25
50
100
Structure
of taper
50% of SMF
20% of SMF
10% of SMF
50% of SMF
20% of SMF
10% of SMF
50% of SMF
20% of SMF
10% of SMF
Resonance peak
Dispersion
wavelength (μm) [ps/(nm × km)]
1.40
20.20
1.29
255.61
1.46
3349.66
1.45
23.65
1.26
568.25
1.36
4133.28
1.46
25.09
1.20
621.30
1.34
4713.72
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Influence of a thin metal layer on a beam propagation in a biconical optical fibre taper
Fig. 11. Normalized dispersion for resonance peak for simulated
taper structures with different thickness of silver layers.
4.3. Wavelength analysis of the proposed structure
with titanium layers
Fig. 10. Dispersion characteristics for 50%, 20% and 10% of the
original dimension SMF of the structure with silver layers.
structure equal to 50% of the original size, dispersion is on
the same level of 20–25 [ps/ (nm × km)]. For the other taper
structure the value of dispersion reaches even 4713.72
[ps/(nm × km)].
Observing the position of the resonant peak, it can be
noticed that it is shifted towards shorter wavelengths with
the increase of a silver layer (Fig. 11). For the structure of
50% of the standard size of a fibre the peak’s size can be
skipped.
204
Considering the analysis of attenuation characteristics for
a tapered fibre with a titanium layer, it can be observed that
the losses characteristics increase with the wavelength and
decrease with a structure diameter (Fig. 12). Losses for the
taper structure equal to 50% size of the original SMF are
similar to the losses of non−deposited tapers (Fig. 5) Small
changes in characteristics for each case are placed in the
same position between 1.47–1.49 μm (Fig. 13). The peak
that occurs in a dispersion characteristics is placed for the
same wavelength as in the attenuation characteristics. In
Figs. 12 and 13 characteristics for attenuation and dispersion
are smoother than for gold and silver. Peaks for titanium start
as a normal dispersion (increasing value) and, next, go to the
anomaly dispersion (decreasing dispersion below zero)
(Fig. 13). For previously analysed metals sequence of nor−
mal and abnormal dispersion was reversed. Dispersion char−
acteristics for tapers deposited with titanium layers are
smooth and possess only one peak in distinction of other
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Fig. 12. Attenuation characteristics for 50%, 20% and 10% of the
original dimension SMF of the structure with titanium layers.
simulated structures. This difference can be a result of opti−
cal properties (refractive and extinction indices) of each
metal and of change of permittivity which are strictly linked
with the refractive index.
As it can be observed in Fig. 13, the resonance peaks for
different thickness of a titanium layer, as well as for the
tapered structure dimension, oscillate between 1.47 and
1.49 μm, only the value of dispersion changes. For the taper
structure equal to 50% of the standard fibre, the difference
between dispersion characteristics for a different thickness
layer of deposited material is negligible. For the structure of
50 % size of an original SMF, when light propagates inside
the structure of a taper waist, only the small part of power
leaks out and the thickness of layers in fact influences only
Opto−Electron. Rev., 24, no. 4, 2016
Fig. 13. Dispersion characteristics for 50%, 20% and 10% of the
original dimension SMF of the structure with titanium layers.
a no large way, the differences are of the order of 0.2−0.3
dB.For structures of 20% and 10% size of an original dimen−
sion of an SMF the thinnest layer in the lower way influ−
ences on light propagating in a taper waist. For the structures
of 20% and 10% of the original dimension of an SMF thin−
ner layers, to a lesser extent, affect the propagation of light in
the taper area, what may be associated with the lack of
impact of the titanium layers with light due to their optical
properties as described in the first chapter (Fig. 2). Structures
of 10% and 20% with a titanium layer do not have as high
dispersion value as in other materials (Table 7).
Provided simulations unequivocally show that titanium
layers change only value of a dispersion but not shift it. The
fact that titanium influences only a value of dispersion is
associated with the characteristic of refractive and extinction
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Influence of a thin metal layer on a beam propagation in a biconical optical fibre taper
Fig. 14. Normalized dispersion for resonance peak for simulated taper structures with different thickness of titanium layers.
Table 7. Resonance peak wavelength and dispersion value for dif−
ferent taper structures with titanium layers.
Thickness
of layer (nm)
25
50
100
Structure
of taper
Resonance peak
Dispersion
wavelength (μm) [ps/(nm × km)]
50% of SMF
1.48
25.99
20% of SMF
1.48
77.79
10% of SMF
1.47
349.99
50% of SMF
1.48
25.27
20% of SMF
1.48
111.88
10% of SMF
1.47
664.52
10% of SMF
1.48
278.86
20% of SMF
1.49
64.44
50% of SMF
1.48
25.08
indices. Both of them possess similar course. Additionally, it
can be observed that attenuation characteristic possesses
smooth shape and one peak for a resonance wavelength.
A layer of thickness of 50 nm gives the highest change of
dispersion which can be caused by optical properties like
refractive and extinction indices (imaginary and real part),
reflectance and transmittance as well as absorption for cho−
sen wavelength, and it is the best thickness to obtain the
plasmon effect. The 100 nm thickness gives the least change
of dispersion, so it can be explained that for these thic−
knesses the absorption process is meaningful.
5. Conclusions
Chosen well−known metals can be divided in two groups
according to their optical parameters which are directly con−
nected with the refractive and extinction indices. Gold and
silver form the first group – in the dispersion characteristics
an abnormal dispersion appears at first, then it changes into
a normal dispersion for increased wavelengths. Gold and sil−
206
ver layers are most often used in biochemical and chemical
sensors. As for sensors it is united with the fact that the metal
layers shift the resonance peak in dependence on change of
the refractive index. For gold it is linked with a higher real
part of dielectric constant than in silver. For silver the imagi−
nary part of dielectric constant is higher than for gold. Dif−
ference in the mentioned parameter is due to the fact that in
silver there is a lower signal to noise ratio SNR. However,
silver in comparison to gold possesses lower chemical stabil−
ity. Gold is resistant to oxidation in a liquid or gas environ−
ment. In order to protect the silver layer in sensors, the com−
plex structure consists of two metal layers – the silver layer
and the gold layer should be used for protection.
The second group should include titanium in which dis−
persion is normal at first,, then it becomes abnormal. For tita−
nium layers the SPR effect can be also observed, but there is
no wavelengths shift in dependence on the layer thickness.
Titanium possesses different optical properties like refrac−
tive and extinction indices, absorption etc. and can be used
as a sensitivity enhancer or enhancing mechanical proper−
ties. Considering the simulation it is evident to see the differ−
ence in attenuation and dispersion characteristics for a taper
with an external layer for the above groups of metals.
The investigation on individual materials presented in
the article is an essential step in the development of appro−
priate technological processes – selecting thickness of layer
and diameter of the taper waist for new sensors design and
fabrication. As it can be noticed for the taper structure equal
to 50% of the fibre original size , an increase of dispersion
occurs for all kinds of simulated layers thicknesses and is
within 20–80 [ps/(nm × km)]. Much higher difference in dis−
persion characteristics can be observed for tapers of a 20%
size of an original dimension of SMF. Analyzing results of
the influence of metal layers on light propagation in a fi−
bre taper, silver gives the highest fluctuation even to 621
[ps/(nm × km)]. For titanium fluctuation of a dispersion is
Opto−Electron. Rev., 24, no. 4, 2016
© 2016 SEP, Warsaw
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three times smaller (66–290 [ps/(nm × km)]). The most sig−
nificant difference of dispersion characteristics can be ob−
served in a taper structure with a 10% dimension of the origi−
nal fibre size. The fluctuation of dispersion for different
thickness of metal reaches even to 4713 [ps/(nm × km)] how−
ever for such a thin taper the structure losses are high. Con−
sidering the results of the simulation, it is noted that the opti−
mal diameter is about the size of a 20% of an original dimen−
sion of an SMF fibre. Such a choice was coupled with the
balance between the minimum losses and possible opportu−
nities to control propagation of light inside the structure and
to influence its parameters (polarization, phase modulation,
etc.) The best results can be obtained for the thickness of
a metal layer in the range of 25–50 nm in which the SPR
effect is the most significant.
Acknowledgement
This work was supported by the Polish Ministry of Science
and Higher Education the Statutory Activity PBS−654 of
Military University of Technology in 2016.
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