Jan 2, 1987 - An internal rotation of the birefringence axes has been measured in a variety of polarization-holding fibers. The rotation of the axes causes ...
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OPTICS LETTERS / Vol. 12, No. 1 / January 1987
Internal rotation of the birefringence axes in polarization-holding fibers M. J. Marrone,
C. A. Villarruel, N. J. Frigo, and A. Dandridge
Code 6570, Naval Research Laboratory, Washington, D.C. 20375-5000
Received July 14, 1986; accepted October 9, 1986
An internal rotation of the birefringence axes has been measured in a variety of polarization-holding fibers. The rotation of the axes causes coupling of the major-field components of the fundamental modes, which limits the ratio in short lengths of birefringent fibers to -45 dB in some cases. A practical consepolarization-extinction quence of the rotation of the axes is a reduction of the polarization-holding ability of devices such as fiber couplers
that are made with these fibers.
High-birefringence single-mode fibers have been developed to preserve polarization in interferometric sensors and coherent communication systems. Typical fibers with high stress-induced birefringence exhibit a polarization-extinction ratio, defined as the ratio of output power in the unexcited mode to that in the excited mode, of the order of -30 dB over a length of 1 km. To find performance limitations in the applications of these fibers it is of interest to determine both the internal and the external factors that limit their polarization-holding ability. Internally, it has been estimated that anisotropic Rayleigh scattering results in coupling to the unexcited cross-polarized mode of -40 to -50 dB over 1 km of fiber length.' However, this limit is not realized in actual fibers because of random perturbations or fiber imperfections that couple the two polarization modes.2 An example of external effects that cause mode coupling is twisting3 or winding the fibers into small-diameter 4 coils. Another effect, not strictly a perturbation, is associated with the property that in a birefringent fiber the fundamental mode is not completely plane polarized but exhibits a field curvature with a minorfield component approximately -40 dB below the intensity of the major-field component.5 In principle, however, it can be alleviated by spatial mode filtering techniques.5 In the present work an apparently unintentional rotation of the birefringence axes (RBA) in a number of polarization-holding fibers is investigated. Small twists of the symmetry axes are known to occur during the drawing process such that even conventional single-mode fibers exhibit a variation in the optical polarization along the fiber.6 The RBA in this investigation, however, is apparently continuous as a function of length in high-birefringence fibers. It is distinct from twist-induced rotation and is present to some degree in all currently available high-birefringence fibers. An analysis of the mode coupling resulting from the rotation of the axes is used to estimate the limitation on the ability of short birefringent fibers to hold polarization and suggests that this limitation, unlike that which is due to the minor field, cannot be alleviated. The fibers used here are a variety of commercial 0146-9592/87/010060-03$2.00/0
high-birefringence polarization-holding fibers. The common feature of all of them is a cross section with
dopant regions of noncircular symmetry that produce a stress asymmetry in the fiber core& The- stressproducing region in the York Technology fiber has the shape of a bow tie, while the Corning fiber contains a pair of stress rods isolated from the core. Both the Hitachi and the 3M fibers employ elliptical regions surrounding the core to produce the asymmetric stress. The polarization properties of six fiber samples are listed in the second and third columns of Table 1. The birefringence beat lengths Lp were measured with a traveling magneto-optic modulator3 and a laser diode operating at 0.83 pm. The polarizationextinction ratios in column 3 were measured with a superluminescent diode on fiber lengths of 200 m or longer and were normalized to a length of 1 km. These data are indicative of the ability of the fiber to hold polarization over long lengths and could also be expressed by the h parameter,2 e.g., h = 2.0 X 10-6 mfor the Corning fiber. However, extrapolation of the long-length h parameter to meter lengths does not yield a proper extinction ratio, because effects such as the minor field or the RBA described in this Letter limit the extinction ratio to -40 to -45 dB. The polarization cross coupling that is due to these effects is essentially independent of length. To measure the RBA as a function of length, the plastic jacket was removed from a 1-m sample to release any external twist introduced by the coating process. A superluminescent diode (peak wavelength 0.830Amwith bandwidth 0.015 pm) was used to locate the axes in the usual manner by rotating linear polarizers at the input and output until a minimum was obtained in the output intensity. This technique gives the most accurate location of the axes when a broadband low-coherence rather than a monochromatic source is used.7 With the fiber resting freely on a flat block and the input end fixed, approximately 1 cm of fiber was removed from the output end, and the output polarizer was rotated to give minimum intensity again. This procedure was repeated along the length of the fiber, and typical data are shown in Fig. 1. The measured rotation rate ranges from 11.00 /cm for © 1987, Optical Society of America
January 1987 / Vol. 12, No. 1 / OPTICS LETTERS
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Table 1. Polarization Properties of High-Birefringence Fibers Birefringence Beat Length
Long-Length Polarization Holding
Manufacturer
(mm)
(dB/km)
(deg/cm)
2(r/fl) 2 (dB)
Corning Hitachi A Hitachi B 3M Corp. York Tech. A York Tech. B
1.28 3.21 3.79 3.38 2.06 1.65
-27.0 -24.9 -26.4 -25.8 -11.2 -23.0
7.85 0.44 1.61 6.22 1.15 11.0
-48.1 -66.1 -52.4 -41.6 -60.6 -43.0
700
z 0
No
0
o
1
w
CD
Z
5100 0
10
20
30
40
50
so
70
9 go
100
FIBER LENGTH (cm)
Fig. 1. Rotation of birefringence axes versus length along a fiber. 0, York Technology; A, 3M Corporation; 0, Hitachi A; v, Hitachi B.
one of the York Technology samples to 0.4 0/cm for one
of the Hitachi samples. Although the rotation varies among fibers from the same manufacturer, the rate is approximately the same along a given fiber. The fact that the physical axes themselves were rotating along the fiber was demonstrated by taking photomicrographs of a 3M fiber cross section before and after removing a length of 3 cm. The difference in orientation of the elliptical stress region at the end face was approximately 150. This corresponds to about 50 /cm, which is close to the average value of 6.2°/cm in Table
1. An additional feature observed in the Corning fiber is plotted in Fig. 2. A small "dip," or reversal in sign,
of the rotation of 5° to 100 over a segment of about 5 cm appeared at intervals of 32 cm. A supposition is
that this is due to an additional periodic mechanical perturbation in the drawing process. The RBA that has been measured here has both practical and fundamental implications. An application that illustrates the practical effect of the RBA is found in couplers designed to hold polarization by using birefringent fibers. One technique used to fabricate these couplers requires chemical etching and thermal tapering of the fibers. However, both the etching and the tapering processes have been determined to reduce the birefringence substantially in the
Estimated Rotation of Axes Extinction Ratio
treated section of fiber.8 For present purposes, the fiber can be modeled as two high-birefringence fibers connected by the treated section of low birefringence. Light polarized along one of the axes at the input approximately followsthe rotation of that axis until it enters the section of low birefringence. In the absence of any other perturbations, the plane of polarization is maintained as it passes through this region. As the light enters the final section of high birefringence the plane of polarization is not aligned with either of the axes because of the internal rotation of the axes along the fiber. This effect was demonstrated by etching a 3-cm section of a 1-m sample of Hitachi fiber to remove the birefringence. After the etch the polarization-extinction ratio was aproximately -20 dB, compared with -40 dB in an unetched fiber. Since the RBA in this fiber is 1.60 /cm, the rotation angle a for a length of 3 cm is 4.80 and the expected extinction ratio is tan 2 a, or -21.5 dB, which agrees well with the -20 dB observed in the etched fiber. Accordingly, this represents a significant limitation to the performance of polarization-preserving couplers fabricated with this technique. In addition to influencing the performance of devices such as fiber couplers, the RBA has the more fundamental effect of causing coupling between the two principal modes in a single fiber. This might be expected since the RBA imitates circular birefringence in that it rotates linear states of polarization, and systems with mixed linear and circular birefrin180
160 140 0
120 20
100 In
80 X
60
U 0i:
40 20
0
20
40
60
80
100
FIBERLENGTH(cm)
Fig. 2. Rotation of birefringence axes (module 180°) versus length along a Corning fiber.
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OPTICS LETTERS / Vol. 12, No. 1 / January 1987
gence are known to exhibit coupling.3 In order to analyze the mode coupling and estimate the limitation on the ability of short fibers to hold polarization, we use the geometrical representation of polarization in fibers developed by Ulrich and Simon3 to analyze the evolution of polarization along a twisted fiber with linear birefringence. This analysis technique has been extended to nonadiabatic coupling by Frigo9 in a generalized geometrical representation of coupledmode theory. As in the Poincare representation of polarization, each state of polarization (SOP) is associated with a vector r on the unit sphere. A birefrin-
frame results in the cycloidal trajectory shown for an initial state IX). This describes purely linear states only when the trajectory makes contact with the equatorial plane. Otherwise the SOP is in the lower hemisphere with a degree of ellipticity determined by the relative magnitudes of 13and '. Now consider the experiment of analyzing the SOP at the fiber output with a linear polarizer represented by P in Fig. 3. As in the Poincar6 representation, the projection of an arbitrary state onto a basis state is given by the factor
gence is represented by a vector fi whose direction is
sion the appropriate
determined by its two orthogonal polarization eigenstates and whose amplitude is the spatial beat frequency. Under the influence of a birefringence fi the evolution of any SOP r is given by
latitude, and the power through the polarizer is
dr/dz = , X r,
(1)
where z is the distance along the fiber. Equation (1) describes a rotation of r around fi. In Fig. 3, IX) and IY) are taken to be the linear polarization eigenstates of the fiber, and IX) is initially excited. Consider the case of a linear birefringence
fi, rotating at a rate
X
in
the laboratory frame. The rotation is represented by 2r in Fig. 3 since a rotation of 0 in the fiber appears as
in this geometrical representation. 3' 9 The equation of motion for fi is dfl/dz = 2r X i. (2) 20
Although Eqs. (1) and (2) can be solved analytically, 3 they can also be solved conveniently by a transforma-
tion to a coordinate system rotating with the birefringence if. In the rotating frame, the equation of motion for a SOP r is
dr/dz = (t- 2r) X r,
(3)
mechanics.9
in analogy to the result for classical According to Eq. (3), the evolution of r is a rotation about an effective birefringence (ft - 2') shown in the inset of Fig. 3. Transformation back to the laboratory
8-
X
I
cos 0/2, where 4 is the angle between the two states.
In the case where P is adjusted for minimum transmisfactor is sin 0/2, where 0 is the
sin2 0/2. The angle varies between zero and tan- 1(4,r/f), and for «1
