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Highly birefringent index-guiding photonic crystal fibers
Hansen, Theis Peter; Broeng, Jes; Libori, Stig E. Barkou; Knudsen, Erik; Bjarklev, Anders Overgaard;
Jensen, Jacob Riis; Simonsen, Harald R.
Published in:
I E E E Photonics Technology Letters
Link to article, DOI:
10.1109/68.924030
Publication date:
2001
Document Version
Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Hansen, T. P., Broeng, J., Libori, S. E. B., Knudsen, E., Bjarklev, A. O., Jensen, J. R., & Simonsen, H. R. (2001).
Highly birefringent index-guiding photonic crystal fibers. I E E E Photonics Technology Letters, 13(6), 588-590.
https://doi.org/10.1109/68.924030
588 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 6, JUNE 2001
Highly Birefringent Index-Guiding Photonic Crystal
Fibers
Theis P. Hansen, Jes Broeng, Stig E. B. Libori, Erik Knudsen, Anders Bjarklev, Jacob Riis Jensen, and
Harald Simonsen
Abstract—Photonic crystal fibers (PCFs) offer new possibilities
ofrealizinghighly birefringentfibersduetoahigher intrinsic index
contrast compared to conventional fibers. In this letter, we ana-
lyze theoretically the levels of birefringence that can be expected
using relatively simple PCF designs. While extremely high degrees
of birefringence may be obtained for the fibers, we demonstrate
that careful design with respect to multimode behavior must be
performed.We further discuss the cutoff properties of birefringent
PCFs and present experimental results in agreement with theoret-
ical predictions on both single- and multimode behavior and on
levels of birefringence.
Index Terms—Birefringence, optical fiber polarization, optical
fibers, photonic crystal fiber.
I. INTRODUCTION
I
N RECENT years, there has been a significant interest
in photonic crystal fibers (PCFs) [1]–[4]. Generally, two
different kinds of PCFs exist, classified by their light-guiding
mechanism. The first experimentally realized-type guides by a
modified form of total internal reflection (M-TIR) and fibers of
this type are also known as index-guiding PCFs [3]. The second
type of fiber provides guidance by the photonic bandgap (PBG)
effect, allowing for novel features such as light confinement to
a low-index core [2]–[4]. The polarization properties of these
fibers, known as PBG PCFs, have been investigated in [5]. In
this letter, we will focus on index-guiding PCFs, as these fibers
are presently most common and have less stringent require-
ments on structural uniformity, and as the spectral behavior of
the polarization properties have yet to be covered in literature.
PCFs are commonly characterized by a series of holes that
run throughout the length of the fiber arranged in a microscale
structure around the core. Prior to drawing, the structure is cre-
ated by stacking a number of silica tubes, whereby a preform is
created that may be drawn into fiber using conventional drawing
techniques [1]. The stacking procedure allows fabrication of
close-packed, air-hole cladding structures, and the fiber core
may readily be realized by replacing a number of tubes by solid
rods of silica. This way of making fiber preforms allows for a
large tailorability of the core geometry, where the core may be
made almost circularly symmetric or highly asymmetric by re-
Manuscript received January 24, 2001; revised March 7, 2001. This work was
supported by the Danish Technical Research Council under the Technology by
Highly Oriented Research (THOR) program.
T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, and A. Bjarklev are with
the Research Center COM, Technical University of Denmark (DTU), DK-2800
Kgs. Lyngby, Denmark.
J. R. Jensen and H. Simonsen are with the Crystal Fiber A/S, DK-3460 Birk-
erød, Denmark.
Publisher Item Identifier S 1041-1135(01)04547-5.
placing one or more tubes. The replacement of silica tubes with
solid rods results in fibers having a high-index core region—al-
lowing for light confinement through M-TIR. One possible use
of asymmetric core fibers is as PMFs. In standard fiber trans-
mission systems, imperfections in the core-cladding interface
introduce random birefringence that leads to light being ran-
domly polarized. These problems with random birefringence
are in PMFs overcome by deliberately introducing a larger uni-
form birefringence throughout the fiber. Current PMFs, such
as PANDA or Bow-tie fibers [6], achieve this goal by applying
stress to the core region of a standard fiber, thereby creating a
modal birefringence up to
[7], [8]. In this letter,
we demonstrate that by utilizing the intrinsically large index
contrast in PCFs in combination with asymmetric core designs,
it becomes feasible to create modal birefringence of at least one
order of magnitude larger than for conventional PMFs. While
previousexperimentalresults for polarization maintaining PCFs
have yielded a birefringence as high as
[9], our
results provide important insight into realization of single-mode
PCFs with even higher birefringence.
II. D
ESIGN AND CUTOFF PROPERTIES
In one of the simplest design cases of an asymmetric core
PCF, the core consists of two neighboring rods. This design is
different from the PCF design studied in [9] and is shown in
Fig. 1. The purpose of creating highly birefringent fiber is to
reduce the coupling between the orthogonal states of the funda-
mental mode. This is mostly relevant, if no higher order modes
are supported. Triangular-lattice PCFs with a symmetric core
consisting of one rod are endlessly single mode for normalized
hole sizes up to a value as large as
0.4 (where is the
hole diameter and
is the hole spacing) [1]. This is not expected
to be the case for the present fiber, due to the different (larger
area) core design. Using a full-vectorial method [10], we have
accurately simulated the guided modes as a function of propaga-
tion constant for fibers according to the above-presented design;
see Fig. 2. For a hole size of
0.40, the design is indeed
found to support a second-order mode with a cutoff for a nor-
malized frequency of
1.67. Further investigation shows
that fibers with a hole size as small as
0.35 support a
second-order mode.
In order to obtain a better visualization of the birefringence
that occurs in the fibers, we introduce an effective normalized
propagation constant
, based on standard fiber techniques
[8].
is defined by replacing the constant cladding index
of a standard fiber with the highly frequency-dependent effec-
tive cladding index,
, of a PCF. is given as (
1041–1135/01$10.00 © 2001 IEEE
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HANSEN et al.: HIGHLY BIREFRINGENT INDEX-GUIDING PHOTONIC CRYSTAL FIBERS 589
Fig. 1. Scanning electron micrograph of innerpart of an asymmetric core PCF.
The claddingof the fiber consistsof a highly regulartriangular lattice of air holes
with a pitch,
3
, of 4.5
m. The core is formed by the omission of two adjacent
air holes.
Fig. 2. Modal index illustration of the operation of asymmetric core PCF.
The fiber has air holes of diameter 0.4
3
and is seen to become multimode at
normalized frequencies,
3
=
, larger than 1.67. Ideal, nonsymmetric core PCF,
as studied in [1], are found to be endlessly single mode for an air hole diameter
of 0.4
3
.
, where , the refractive index of the
core, is a constant equal to the index of fused silica, and
is equal to the index of the fundamental space-filling mode of
the cladding. Finally,
denotes the effectiveindex of a guided
mode. Fig. 3 shows the
-parameter as a function of the nor-
malized frequency for the same fiber as in Fig. 2. Here, the
lifted degeneracy of the two polarization states is apparent. In
the low-frequency limit, the normalized propagation constant
tends to zero causing the field to extend far beyond the core re-
gion. In this limit, the asymmetric core shape has a vanishing
influence on the polarization splitting and the birefringence be-
comes negligible. It should, however, be noticed that in the case
of noncircularly shaped cladding holes, which is not studied
here, it does become possible to achieve significant polarization
effects due to also a splitting of the degeneracy of the funda-
mental cladding mode [11]. As for the low-frequency limit, we
find that the birefringence becomes vanishing in the high-fre-
quency limit, providing an optimum frequency window for the
design of high-birefringent fibers. The fiber in Fig. 3 was found
to exhibit a highest birefringence of 6.9
10 at a normalized
Fig. 3. Effective normalized propagation constant
B
for a fiber with hole
size
d=
3=
0.40. The nondegeneracy of polarization state 1 and 2 of the
fundamental mode is evident. Second-order cutoff is seen to occur at the same
frequency as in Fig. 2.
Fig. 4. Dependence of modal birefringence on hole size. The hole sizes
shown are ranging from
d=
3=
0.30 to 0.70 in steps of 0.10. In each case the
second-order cutoff is shown, except for a hole size of 0.30, as this fiber is
endlessly single mode (dashed curves indicate multimode operation).
frequency of 1.05. The knowledge of an optimum normalized
frequency is, naturally, important from a design point of view,
as it provides information on the exact fiber dimensions of opti-
mized high-birefringent fibers.If the fiber in Fig. 3, for example,
were to be designed to provide highest birefringence at a wave-
length of 1.55
m, the optimum normalized frequency dictates
a pitch of 1.7
m. Furthermore, it is important to notice that the
optimum normalized frequency for the fiber in Fig. 3 is found
under single-mode operation. As shall be demonstrated, this is
a valuable property valid for all studied fibers with a design as
in Fig. 1.
III. B
IREFRINGENCE RESULTS—THEORY AND EXPERIMENTS
The theoretically predicted birefringence for a series of fibers
with different hole sizes is illustrated in Fig. 4. As expected, the
birefringence is seen to strongly increase with increasing hole
size. Also marked on the figure is the second-order cutoff of the
fibers. It is important to notice that only fibers with a hole size
of
0.30 or smaller may be classified as endlessly single
mode, making cutoff analysis of high-birefringence fibers vital.
For all studied hole sizes, however, the birefringence is seen to
reach its maximum value while the fiber is single mode. For
a fiber with air holes of size
0.70, a maximum value
of
is reached at a normalized frequency of
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590 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 6, JUNE 2001
Fig. 5. Group delay between different polarization states of fundamental and
higher order mode for the fiber in Fig. 1. The corresponding birefringence
is 9.3
1
10 and 3.6
1
10 for the fundamental and higher order mode,
respectively. The central peak is due to autocorrelation.
0.66. As this fiber reaches cutoff at a normalized fre-
quency of
0.72, strict requirements on fabrication are
imposed when the fibers are to be operated at a desired wave-
length (e.g., an operation around 1.55
m results in a -tol-
erance of less than 100 nm). We have fabricated a number of
asymmetric core PCFs, and Fig. 5 shows the measured fringe
envelope as a function of delay for the interference between the
two polarization states of the fundamental mode and a higher
order mode of a fiber with
3.38 m/4.50 m 0.75.
The measurement was performed over 5 m of the fiber, using an
incoherent light source centered at 1.55
m, yielding a birefrin-
gence of 9.3
10 and 3.6 10 for the fundamental and higher
order mode, respectively. In order to compare the experimental
result to theory, we first determine the normalized frequency to
be
2.9. In agreement with Fig. 4, we find that the fiber
is multimode and that the measured birefringence of 9.3
10
is in good agreement with the predicted value of approximately
1.0
10 . In general agreement with Fig. 3, we find the bire-
fringence for the higher order mode to be lower than that for the
fundamental mode. Further, it is worth noticing that no interfer-
ence between polarization states in different modes is observed
experimentally. This observation may be understood from the
significantly larger splitting between polarization states of dif-
ferent modes compared to intramode splitting (see Fig. 3). The
interference between polarization states in the fundamental and
the higher order mode in Fig. 3 would result in a delay of more
than 200 ps, significantly beyond the measured range in our ex-
periments.
IV. C
ONCLUSION
By utilizing the intrinsically large index contrast in PCFs
in combination with asymmetric core designs, we have found
that it is possible to create modal birefringence of at least one
order of magnitude larger than for conventional high birefrin-
gent fibers.We havefurther addressed the important design con-
sideration that must be performed with respect to cutoff prop-
erties. Our results provide valuable insight into realization of
single-mode PCFs with even higher birefringence than previ-
ously demonstrated in literature.
A
CKNOWLEDGMENT
The authors wish to thank K. G. Hougaard, J. Riishede, and
T. Sørensen for fruitful discussions while doing this work.
R
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![Fig. 2. Modal index illustration of the operation of asymmetric core PCF. The fiber has air holes of diameter 0.4 and is seen to become multimode at normalized frequencies, = , larger than 1.67. Ideal, nonsymmetric core PCF, as studied in [1], are found to be endlessly single mode for an air hole diameter of 0.4 .](/figures/fig-2-modal-index-illustration-of-the-operation-of-3fx9arvm.webp)
