We present an analysis of the effects of input polarization on the output fringe ... the existence of interferometer input-polarization eigenmodes for which opti-.
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OPTICS LETTERS / Vol. 13, No. 4 / April 1988
Dependence of visibility on input polarization in interferometric fiber-optic sensors A. D. Kersey, A. Dandridge, and A. B. Tveten Optical Sciences Division, Code 6574, Naval Research Laboratory, Washington, D.C.20375 Received November 12, 1987; accepted January 25, 1988 We present an analysis of the effects of input polarization on the output fringe visibility of two-beam interferometric fiber-optic sensors, which predicts the existence of interferometer input-polarization eigenmodes for which opti-
mum visibility is obtained. Experimental results that verify this are also presented.
Interferometric fiber-optic sensors have been configured to detect a wide range of physical fields in recent years, and many prototype sensors have been field tested. Usually, conventional low-birefringence single-mode optical fiber and fiber components are used to construct interferometric sensors. As a result, random fluctuations in the state of polarization (SOP) of the interfering beams guided in the nominally circular fiber core can lead to fading of the interference signal. This phenomenon is termed polarization-induced fad1 2 (PIF), and several schemes have been proposed ingl to overcome the effect, ranging from the use of simple mechanical, electro-optic, or magneto-optic polarization controllers3 - 5 in the interferometric arms to polarization diversity-detection techniques based on output SOP selection.6' 7 An obvious alternative approach is to construct the interferometer using high-
birefringence (polarization-preserving)
length of fiber can be described by means of a general elliptic retarder,9 - 1 l denoted here by an operator Rj of rotational magnitude (phase delay) Qj [expressed as
Jj(Qj)]on the Poincar6 sphere. Figure 1(b) shows the birefringent network used to model the interferometric system; this comprises four elliptic retarders, which describe the net birefringence in the input and output fibers and the signal and reference arm fibers. The couplers are modeled as ideal 1:1 power splitters (i.e.,
polarization-independent power splitters), with any associated birefringence effects lumped into the four primary operators. The net evolution of an input state, Ci, along the signal and reference arms is thus described by Poincar6 sphere operators Y?8(Q,) and ir(2r), respectively, coupler
fiber.
Because of the lack of high-quality polarization-preserving fiber components, notably directional couplers, however, this solution is not at present a viable alternative. In this Letter we present an analysis of PIF in interferometric sensors, showing that inputpolarization eigenstates of the interferometer exist for
. Signalarm
a) outputfiber
Fiber
inputfiber
Mach-Zehnder L
r_
Consider the schematic of a Mach-Zehnder interferometer and the Poincar6 sphere8'9 representation of the SOP's of the light at the input to the first coupler and in the signal (C8) and reference (Cr) arms of the interferometer at the point of recombination in the output coupler shown in Fig. 1. Assuming polar-
,
Referencearm
,--,r.___1
which the optimum visibility can always be achieved.
ization-insensitive
(note that Cj is a Stokes vector
and Rj is a 4 X 4 Mueller matrix operator). In general,
-L
H; HXI'
0 for all input SOP's, i.e., the visibility varies between the limits Vmax= 1 and Vmin = cos(Qir./2), which occur when 0 Circle (c)
Fig. 2. Poincar6 sphere representation of input and output SOP's for an arbitrarily chosen input SOP and elliptic retarders Rr and R, in (a) a fixed frame of reference, (b) a
rotated output frame of reference. (c) Angular shift imparted in the input SOP (Ci - Ci') by the operator Rr-s.
=
0 and 0 = -xI2
respectively. In order to test the above theory, a fiber MachZehnder interferometer (MZ), constructed using lowbirefringence fibers, was arranged such that the birefringence in the arms (both of -1-m length) and input lead could be adjusted by twisting and bending sections of fiber into small loops. The couplers used (Amphenol 945 Series) showed minimal dependence (
