-
Light propagation in a highly birefringent photonic crystal
fiber infiltrated with a nematic liquid crystal
K.A. Rutkowska, T.R. Wolinski, P. Lesiak, A. Czapla, S. Ertman,
K. Nowecka Faculty of Physics, Warsaw Univ. of Technology,
Koszykowa 75, 00-662, Warsaw, Poland, [email protected]
Abstract: Theoretical analyses as well as experi-mental results
of light propagation in a new micro-structured photonic liquid
crystal fiber (PLCF) are presented. The analyzed PLCF was composed
of a commercially available highly birefringent (HB) photonic
crystal fiber (PCF) infiltrated with a low-birefringence nematic
liquid crystal (LC) introduced into the selected micro-holes by the
capillary effect. Introduction
For more than last twenty years the anisotropic optical fibers
exhibiting particular polarization prop-erties have been
extensively investigated [1] includ-ing also the fibers with the
liquid crystal cores [2]. Recently, a really great interest in the
photonic crys-tals fibers and particularly in the photonic liquid
crystal fibers [3-6] is observed. The latter, consisting of a PCF
structure infiltrated with a LC, possess the unique and uncommon
propagation and polarization properties as a result of the
combination of a passive PCF host structure and an active LC guest
material.
In the last ten years the photonic crystal fibers have become
the subject of the intensive investiga-tions and the great number
of scientific publications [7,8]. This new class of optical fibers
is typically composed of the large number of air micro-holes placed
in the silica cladding. The change of the both location and the
size of the holes allows for the de-signing and creating of the
optical fibers with re-quired properties for the particular
practical applica-tions. Recently, the particular attention has
been de-voted to the possibility of infiltration of the air holes
with the different materials. This fact leads to the possibility of
the bandgap tuning, as well as of the switching between two
different waveguiding mechanisms – Total Internal Reflection (TIR)
and Photonic Band Gap (PBG) [4,5]. Moreover, depend-ing on the
infiltrating material, some of the infused PCFs enable new
applications in the area of the tem-perature and electrical
controlled sensing, as well as in the all-optical information
processing. Modal analysis of HB PLCF In this paper the custom
software (i.e. the vectorial mode solver) was used. It is based on
the full-vector wave equation, where two transverse components of
the electric field intensity Ex and Ey are given in the following
form [9]:
(1) where:
and k is wavevector, Neff is effective refractive index of the
resultant mode, n is refractive index distribu-tion in the fiber
cross section.
As one can see, the equation (1) is a full-vector eigenvalue
equation, which describes the modes that propagates in the analyzed
structure. For its discreti-zation a finite-difference technique
was used. In this way the partial-differential equation was
translated into an equivalent matrix eigenvalue equation, which was
solved by implementing of the Matlab library.
(a)
(b)
(c)
Fig. 1: The photos of the cross sections of the analyzed
PM-1550-01 Blazephotonics PCF (a-b) and the calculating window
(axis labels in micrometers) used for the numeri-cal simulations
(c).
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡
y
xeff
y
x
yyyx
xyxx
EE
NkEE
PPPP 22
( ),1 222
22
2 xxx
xxx EknyE
xEn
nxEP +
∂∂
+⎥⎦
⎤⎢⎣
⎡∂
∂∂∂
=
( ),1 222
22
2 yyy
yyy EknxE
yEn
nyEP +
∂
∂+
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂
∂
∂∂
=
,122
2 yxE
yEn
nxEP yxyxy ∂∂
∂−⎥
⎦
⎤⎢⎣
⎡∂
∂∂∂
=
xyE
xEn
nyEP xyxyx ∂∂
∂−
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂
∂
∂∂
=22
2
1
ThG34
-
The investigated structure was based on the commer-cially
available highly birefringent PCF fabricated by Blazephotonics (UK)
(Fig. 1a-b) with only two large holes infiltrated with LC. The
geometrical parameters of such a fiber are as follows: pitch
(spacing between adjusted holes) Λ=4.4μm, large hole diameter
dH=4.5μm, small hole diameter d=2.2μm, diameter of the holey region
D=40μm. In the numerical simula-tions the grid period was taken as
0.1μm in both x and y direction within the calculating window of
the size of 48.4μm x 48.4μm (all holey region) (Fig. 1c). The value
of the refractive index of the glass clad-ding was taken as 1.444
at the wavelength of 1550nm.
Any change in the value of the refractive index of the LC (which
can be easily realized by the tem-perature tuning) within the large
holes allows for magnificent changes in the modal field and
therefore also in the optical properties of the fiber. As it is
shown in Fig. 2 by the increasing the value of the LC refractive
index the transition from the single to the double core (when the
refractive index of LC is above the refractive index of silica
glass) propagation is possible. In the case of double core
propagation the modal birefringence B of the fundamental mode
reaches the zero value.
Results and discussion Preliminary experimental results
confirmed that if the refractive index of the LC infiltrating the
PCF holes increases over the refractive index of the fused silica
two-core propagation is possible. In the unfilled PCF, the mode
profile is located in the silica core of the fiber (Fig. 3a.), but
after the infiltration of the large holes with the
low-birefringence nematic LC mix-ture, cat. number 1550
(manufactured at the Military Univ. of Technology, Poland and
described else-where [6]) the shape of the propagating field
con-fined in the core was changed. Assuming that the predominant
planar LC molecular alignment within the holes is obtained, only
the changes of the ordi-nary refractive index of LC mixture affect
the modal structure of the propagating electromagnetic field. If
the refractive index in the holes is equal or higher than the
refractive index of the fused silica (for 1550 LC mixture it is
truth for the temperatures below 40oC) the propagating field
distributed between the fused silica solid core and two liquid
crystal cores (Fig. 3b) was obtained. For temperatures above 40oC
the light propagation in the infiltrated holes disap-pears
(refractive index in the holes is lower than the refractive index
of the fused silica) and in conse-quence, the mode is again located
mainly in the solid core. Hence the switching between single-core
and two-core propagation was obtained.
Fig. 2: Modal birefringence B for the fundamental mode (LP01) as
a function of the refractive index of NLC (nLC) infiltrat-ing the
region of the large holes. The examples of the modal light
intensity distributions for the different values of nLC are also
presented.
ThG34
-
Fig. 3: Experimental observation of the end face of the
unfiltrated PCF (a) and PLCF (b) for λ= 633 nm.
Fig. 4: Intermodal Δλ for PLCF filled with 1550 LC (a) and DGD
changes in PLCF filled with 1550 LC (open
circles) in comparison to the numerical calculations of modal
birefringence (line) (b).
The group birefringence is the difference in the
group indices for both orthogonal polarization modes. It
contributes to the polarization mode disper-sion (PMD) of the
anisotropic fiber. In the wave-length sweeping method, the group
birefringence can be calculated by counting maxima of the light
inten-sity after analyzer as a function of the wavelength and by
averaging their period of repetition over the total scanned
wavelength spectrum [10]:
where: λ1 and λ2 are the wavelengths (maxima) that contribute
with the same states of polarization and Δλ= λ2- λ1 is a period of
the polarization state repeat-ability and L is the length of tested
PLCF. Hence, the differential group delay (DGD) in the measured
fiber, defined as a difference in the velocities between two
orthogonal modes of the fundamental mode can be described by the
following formula:
The maxima shown in Fig. 4a are responsible for differential
group delays (DGDs) between first three modes (i.e. LP01, LP02 and
LP11) that can propagate in the HB Blazephotonics PCF infiltrated
with 1550 LC mixture [11]. Precise measurements of DGD between
polarization modes LP01x and LP01y clearly demon-strate that the
birefringence of the fundamental LP01 mode decreases to the
negative value of the birefrin-gence (Fig. 4b). Results obtained
fully confirm nu-merical simulations shown in Fig. 2. Conclusions
In this paper light propagation in a highly birefrin-gent photonic
crystal fiber infiltrated with a nematic liquid crystal was
analyzed. It has been demonstrated that such a photonic structure
exhibits an unusual propagation properties. The experimental
results con-firm the numerical simulations predictions and in
particular the switching between single-core and two-core
propagation was observed. Moreover by using the 1550 LC mixture the
temperature-induced changes in DGD, switching between fundamental
and higher order mode propagation in the PLCF was possible.
Obtained results hold the great potential for both fiber-optic
sensing and in-fiber polarization mode dispersion control and
compensation. Acknowledgments The work was supported by the Polish
Ministry of Science and Education under the grant 3T10C 016 28 and
also partially by European Network of Excel-lence on Micro Optics
(NEMO).
,21λλλΔ
=L
Bg
.21λλλΔ
=c
DGD
(a)
(b)
ThG34
-
The authors are very grateful to Prof. Roman Dab-rowski and Dr.
Edward Nowinowski-Kruszelnicki from Military University of
Technology, Poland for fruitful collaboration. References 1.
T.R.Wolinski, in Encyclopedia of Optical Engi-
neering, R. G. Diggers, ed., (M. Dekker, New York), 2150-2175,
2003.
2. T.R.Wolinski P. Lesiak, R. Dabrowski, J. Kedzierski, E.
Nowinowski, Mol. Cryst. Liq. Cryst. 421, 175-186, 2004.
3. T.T. Larsen, A. Bjarklev, D.S. Hermann, J. Bro-eng, Opt. Exp.
11, 2589-2596, 2003,
4. T.R. Wolinski, K. Szaniawska, K. Bondarczuk, P. Lesiak, A.W.
Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, J. Wojcik,
Opto-Electr. Review 13(2), 59-64, 2005.
5. T.R Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A.W.
Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, J. Wojcik,
Meas. Sci. Technol., 17, 985-991, 2006.
6. T.R. Wolinski, P. Lesiak, A.W. Domanski, K. Szaniawska, S.
Ertman, R. Dabrowski, J. Wojcik, Mol. Cryst. Liq. Cryst. 454,
333-350 (2006).
7. J.C. Knight, Nature 424, 847-851 (2003). 8. J.C. Knight, T.
Birks, B. Mangan, P. Russell,
Opt. & Photon. News 30, 26-30 (2002). 9. C.L. Xu, W.P.
Huang, M.S. Stern, S.K.
Chaudhuri. IEEE Proc. Opt. 141(5), 281–286 (1994).
10. K. Kikuchi, T. Okoshi, Opt. Lett. 8, 122-124 (1983).
11. P. Lesiak, T.R. Wolinski, K. Brzdakiewicz, K. Nowecka, S.
Ertman, M. Karpierz, A.W. Domanski and R. Dabrowski,
Opto-Electronics Rev. 15 (1), 27-31 (2007).
ThG34
