The insertion of a rotating halfwave plate (RHWP) into a polarimetric fiber optic scheme is analyzed. The RHWP allows phase control of the autointerference signal and can be used to pseudoheterodyne the polarimetric setup. The scheme is applied to a polarimetric sensor of a dynamic strain and permits full recovery of the elongation signal.
Among the coherent optical fiber sensors, the polarimetric family has been an extensive subject of interest because of its peculiar characteristics. The sensing and reference beams are led by the same fiber, thus guaranteeing intrinsic constructive simplicity, infield stoutness, and noise immunity. These features are purchased at the cost of reduced sensitivity compared with the common interferometric sensor.1 On the other hand, a reduced sensitivity means an extended unambiguous range that may be an important advantage in certain applications.2
From the phase-processing point of view, the polarimetric sensor presents all the characteristics of the coherent sensor with the pecularity that the two arms of the interferometer are not independently accessible. Hence unwanted phase drift is introduced during the recovery process in the same way as any other fiber optic interferometer. The control of the phase noise with the usual methods requires splitting two guided modes and consequently elimination of one of the most important polarimetric sensor features.
The aim of this Letter is to point out a novel scheme of polarimetric fiber sensors that permits phase processing the signal with no limitation of the intrinsic polatimetric features. An experimental confirmation is given for a polarimetric strain sensor operating in the FM mode.
The novel scheme differs from the classical one (Fig. 1) by the insertion of a rotating halfwave plate (RHWP) just before the quarterwave plate.
A RHWP has been proposed to induce a phase shift or a frequency shift in an optical3 and fiber optic4 interferometric setups. How the presence of the polarization maintaining fiber (PMF) in the fiber-optic polarimetric schemes is equivalent to the presence of the polarization beam splitter in the setup previously mentioned is shown.
Let us analyze the classical polarimetric scheme in terms of the Jones matrix formalism. With reference to Fig. 1 (scheme without RHWP), the light intensity on the photode-tector is (by using a complex wave notation)
Fig. 1. Polarimetric configuration with an added rotating half wave plate for phase control. Fig. 2. Power spectrum of the polarimetric interference signal in
the quadrature working point.
where V H , T Q W P , T L A are the Jones matrices for the incoming polarized light, the 45° degree-oriented quarterwave plate, the linear analyzer, respectively, and
is the equivalent matrix for a PMF 5 of length L and characterized by a beat length B. By introducing Eqs. (3) and (2) into Eq. (1) the detected intensity is
Any external perturbation affecting the fiber birefringence causes an equivalent change of B and consequently, according to Eq. (4), a detected fringe shift. Fading problems arise because the phase term ψ in Eq. (4), which represents a constant phase delay between the two orthogonal modes, is subject to unwanted change in time, thereby moving the working point of the interferometer. The use of the scheme of Fig. 1 with the RHWP allows control of the fading problems with no substantial change of the polarimetric scheme. In fact, with reference to Fig. 1,
where
is the transformation matrix for a rotating halfwave plate when the angle is χ. By substitution of Eqs. (6) and (5) in Eq. (1), the detected intensity becomes
It is evident how a rotation of the RHWP permits the control of the phase noise term ψ.
As a particular application of the scheme, let us consider its use as a frequency shifter to pseudoheterodyne a polarimetric strain sensor. The PMF is used to detect the dynamic strain state of a vibrating cantilever. The fiber transduces the time-dependent sinusoidal elongation Δl = Δl0 sinωt of the cantilever in terms of a differential phase change:
where φ0 depends on the birefringence characteristics of the PMF. Then the detected signal expressed by Eq. (7) becomes
If the RHWP is in a fixed position, the interference signal expressed by Eq. (9) is subjected to fading. In Fig. 2 the
Fig. 3. Frequency shifted power spectrum of the polarimetric interference signal obtained with the novel method.
power spectrum of Eq. (9) is shown with φ0 ≈ 5 rad, and ψ equals π/2 (maximum sensitivity point). Due to slow temperature drift, a different Bessel composition of this spectrum takes place overtime.
Let us now assume the RHWP rotates with constant angular frequency ωc. Equation (9) becomes
and the whole spectrum in Fig. 2 is frequency shifted as shown in Fig. 3. Hence the RHWP acts as an effective frequency shifter and permits detection of the wanted phase signal Φ0 with a standard FM demodulator. In this way, the polarimetric scheme results in pseudoheterodyne, and a full reconstruction (with the phase sign) of the sinusoidal elongation is recovered.
This work has veen partially supported by the National Research Council, MADESS Project, that kindly authorized the publication.
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3. G. E. Sommargren, "Up/Down Frequency Shifter for Optical Heterodyne Interferometry," J. Opt. Soc. Am. 65, 960-961 (1975).
4. M. Martinelli, "Unlimited Phase Compensator for Fiber-Optic Interferometric Detection of Slow Temperature Change," Opt. Lett. 9, 429-431 (1984).
5. R. M. Taylor, D. J. Webb, J. D. C. Jones, and D. A. Jackson, "Extended-Range Fiber Polarimetric Strain Sensor," Opt. Lett. 12, 744-746 (1987).
