## Abstract

In this paper a polarization-independent all-fiber multiwavelength-switchable filter based on a polarization-diversity loop configuration is newly proposed. The proposed apparatus consists of a polarization beam splitter, high birefringence fibers, and polarization controllers. Our theoretical analysis shows that the apparatus exhibits unique feature which allows it to operate as a polarization-independent multiwavelength periodic filter with a good channel isolation and to make its channel wavelength switchable by varying effective birefringence of the polarization-diversity loop through the proper adjustment of the polarization controllers contained within the loop. Theoretical prediction was experimentally verified.

©2003 Optical Society of America

## 1. Introduction

Rapid increase in the capacity of fiber telecommunication systems by orders of magnitude creates strong demands of novel devices such as multiwavelength light sources or all-fiber wavelength-selective filters. Especially, all-fiber filters are attractive components in all-optical network because they have the advantages of low loss, small size, and better performance compared with conventional optical filters based on bulk dispersive components. So far, a great many techniques for implementing all-fiber filters have been proposed, such as the fused fiber filters [1,2], the Fabry-Perot filter [3], the Mach-Zehnder filter [4], the fiber grating filter [5], the acoustooptic filter [6], and the birefringent filters based on a Sagnac interferometer [7,8]. Generally, the polarization state in conventional fibers is random in communication systems; hence polarization-independent fiber filters are preferred. In this paper a new polarization-independent all-fiber multiwavelength-switchable filter is proposed which is based on a polarization-diversity loop configuration (PDLC). To our best knowledge it is the first time the PDLC is applied for achieving polarization independence in optical filtering, though the polarization-diversity loop by itself is not a new concept [9,10]. Compared to the Mach-Zehnder interferometer-based filters, the PDLC-based all-fiber filter is more robust to environmental changes because the two lights rotating the high birefringence fiber (HBF) loop travel along a common light path. The proposed apparatus consists of a polarization beam splitter (PBS), HBF’s, and polarization controllers (PC’s). Our theoretical analysis shows that the apparatus exhibits unique feature which allows it to operate as a polarization-independent multiwavelength periodic filter with a good channel isolation and to make its channel location switchable by varying effective birefringence of the polarization-diversity loop including the HBF through the proper adjustment of the PC’s contained within the loop. Theoretical prediction was successfully demonstrated by experiments.

## 2. Principle of operation

Figure 1(a) shows the basic structure of the PDLC-based all-fiber filter. The basic components comprising the filter shown in Fig. 1(a) are a PBS and HBF whose fast axis is rotated 45 ° relative to horizontal axis of the PBS. To facilitate discussion, let us assume that the horizontal and vertical axes of the PBS are designated as the *x*- and *y*-axes, respectively. First, let us also assume that the light introduced into the port 1 of the filter is *x*-polarized light (*x* polarization). Then, as shown in clockwise (CW) path of Fig. 1(b), the input light propagates through the polarizer (*x*-polarized), the HBF with its fast axis 45 ° oriented with respect to *x*-axis, and the analyzer (*x*-polarized) sequentially, rotating in a CW direction. During the passage through the HBF, the *x*-polarized light is decomposed into two polarization components corresponding to those aligned to the fast and slow axis of the HBF, respectively, and the phase difference Γ (=2*πBL*/*λ*) between them is generated due to birefringence of the HBF. Here *B* is the birefringence, *L* is the HBF length and *λ* is the wavelength in vacuum. When these two components come out of the port 2, therefore, they can interfere because we select the same polarization (*x* polarization) components in the two lights. Similarly, when the input light is *y*-polarized, the light travels the filter in a counterclockwise (CCW) direction as shown in CCW path of Fig. 1(b) but the same interference spectrum is obtained as the above one. Especially, as an arbitrarily polarized light can always be decomposed into *x*- and *y*-polarized components, the transmitted intensity becomes the superposition of intensity spectra of two interference patterns due to *x* and *y* input polarizations and thus the transmitted output of the filter becomes independent of the input polarization.

This physical discussion can be supported with the help of the following mathematical formulation. According to Jones matrix formulation [11] the Jones matrices of the proposed apparatus along the CW and CCW directions are

$${T}_{\mathit{CCW}}=\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]R\left(\frac{\pi}{4}\right)\left[\begin{array}{cc}{e}^{\frac{i\Gamma}{2}}& 0\\ 0& {e}^{-\frac{i\Gamma}{2}}\end{array}\right]R(-\frac{\pi}{4})\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& \mathrm{cos}\left(\frac{\Gamma}{2}\right)\end{array}\right]$$

where *R*(*θ*) is coordinate transformation matrix. If we assume an arbitrary input field *E _{in}* as Eq. (2), output field

*E*and output intensity

_{out}*I*of the filter are expressed as follows.

_{out}where *a, b*, and *ϕ* correspond to magnitudes of two field components and phase difference, (which are arbitrary real values), respectively, and *ε*
_{0}and *µ*
_{0} are permittivity and magnetic permeability, respectively. From Eq. (3), it is clear that the output intensity of the light is a wavelength-dependent sinusoidal function and is independent of the input polarization whenever the input intensity is constant.

In this basic structure, wavelength location of the transmission spectrum can be shifted by varying the phase difference due to the birefringence of the entire polarization-diversity loop, which is composed of the HBF and ordinary fibers spliced to the HBF (except a lead-in and lead-out fiber), in the filter. For example, a change of π rad in the phase difference due to birefringence will move the transmission spectrum from maximum to minimum at a specific wavelength. If we insert a PC within the polarization-diversity loop, therefore, it is expected to be possible to move maxima/minima wavelengths (channel wavelengths) of the transmission spectrum because the effective birefringence of the entire loop can be controlled by adjusting the PC. In order to achieve channel wavelength-switching in the PDLC-based filter, we now consider the case in which PC’s are added to the basic structure of the filter as shown in Fig. 2. Two quarter-wave plates (QWP’s; QWP 1 & QWP 2) and one half-wave plate (HWP) in Fig. 2 are placed for controlling the effective loop birefringence and the orientation of the HBF with respect to the *x*-axis, respectively. Based on the above Jones matrix formulation, the Jones matrix *T* (1^{st} term: CW direction, 2^{nd} term: CCW direction) and transmittance *TR* of the proposed filter are calculated as the following expressions;

$$\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}+\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]{T}_{\mathit{HWP}}\left({\theta}_{h}\right)R\left({\theta}_{p}\right)\left[\begin{array}{cc}{e}^{\frac{i\Gamma}{2}}& 0\\ 0& {e}^{-\frac{i\Gamma}{2}}\end{array}\right]R(-{\theta}_{p}){T}_{\mathit{QWP}1}\left({\theta}_{1}\right){T}_{\mathit{QWP}2}\left({\theta}_{2}\right)\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]$$

$$\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}-\frac{1}{2}\left\{\mathrm{sin}\left[2\left({\theta}_{1}-{\theta}_{2}\right)\right]\mathrm{cos}\left(2{\theta}_{2}\right)\right\}\mathrm{sin}\left(\Gamma \right)$$

where *T _{QWP 1}*,

*T*, and

_{QWP 2}*T*are Jones matrices of the QWP 1, QWP 2, and HWP, respectively. And

_{HWP}*θ*

_{1}and

*θ*

_{2}are fast-axis orientation (azimuthal) angles of the QWP 1 and 2 with respect to

*x*-axis, respectively, and

*θ*is that of the HBF. The fast axis orientation of the HWP (

_{p}*θ*) is set to (

_{h}*θ*- 45 °)/2 for arbitrary

_{p}*θ*to be effectively 45 ° with respect to the

_{p}*x*-axis by rotating the polarization plane of the propagating light. In the calculation, ideal PBS and PC’s were assumed and any insertion loss due to optical components that construct the filter was not considered.

Depending on the set of *θ*
_{1} and *θ*
_{2}, both modulation depth (channel isolation) and maxima/minima wavelengths (channel wavelengths) of interference pattern in transmission spectrum of the proposed filter change. If we select the combination [*θ*
_{1}, *θ*
_{2}] of two orientation angles of the QWP 1 and 2 to make the linear input polarization rotate by (*θ*
_{p}+45 °) or (*θ*
_{p}-45 °) (e.g. [*θ*
_{p}/2+22.5 °, *θ*
_{p}/2+22.5 °] or [*θ*
_{p}/2-22.5 °, *θ*
_{p}/2-22.5 °]), mathematical expressions of the filter transmittance are given by [1-cos(Γ)]/2 or [1+cos(Γ)]/2, respectively, vanishing the effect of the 3^{rd} term of the transmittance of Eq. (5). It is clear that two interleaved interference spectra like *π* phase-shifted spectrum pair can be obtained at the above two selected sets of the QWP’s. This is because the above two QWP combinations make effective loop birefringence in each setting be different by π rad with each other. Meanwhile, if the QWP combination [*θ*
_{1}, *θ*
_{2}] is chosen to make the linear input polarization be right circular polarization or left circular polarization (e.g. [45 °, 0 °] or [-45 °, 0 °]), mathematical expressions of the filter transmittance are given by [1-sin(Γ)]/2 or [1+sin(Γ)]/2, respectively, vanishing the effect of the 2^{nd} term of the transmittance. We can find that two output interference spectra are also in an interleaved relation and these spectra are quarter-period shifted versions of the previous two spectra represented by a cosine function. As a result, channel wavelength-switching operation, whose switching displacement can be determined as one of three displacements (a quarter-, a half-, and three quarters-period in the aspect of a sinusoidal function) through the proper selection of QWP sets shown in Table 1, can be obtained in the proposed filter. As an example, when we assume QWP combination in set I as reference one, switching displacements of a quarter-, a half- and three quarters-period can be achieved at those in set IV, II, and III, respectively. It is notable that four QWP combinations in Table 1 are optimal ones, at which two polarization components decomposed at the HBF have same magnitude at port 2, giving the maximum visibility in the interference pattern. At other combinations, each magnitude of two decomposed polarization components will become different and partial interference is supposed to occur, resulting in the decrease of the visibility. On the basis of the above theoretical analysis, the transmission spectrum of the proposed filter is plotted at four optimal combinations of [*θ*
_{1}, *θ*
_{2}] for channel wavelength-switching operation in Fig. 3: Solid line (set I), dotted line (set II), dashed line (set III), and dash-dotted line (set IV).

## 3. Experimental results and discussions

To verify the theoretical results, we constructed a PDLC-based all-fiber filter as shown in Fig. 2 and measured the transmission spectrum at four optimal QWP combinations by adjusting each QWP. The proposed filter is composed of a PBS (OZ optics), HBF, one HWP (OZ optics), and two QWP’s (OZ optics). The birefringence and length of the HBF is ~4.8×10^{-4} and 6.25 m, respectively. The length of the HBF was determined so that wavelength spacing (channel spacing) between transmission maxima becomes 0.8 nm. Figure 4 shows the measured transmission spectrum of the proposed filter at four optimal sets for channel wavelength-switching. As predicted in the theoretical results, the switching displacement between channels, whose spacing at any QWP combination was measured to be ~0.8 nm, could be chosen as one of three displacements (0.2, 0.4, and 0.6 nm) by selecting proper sets of QWP’s. The channel isolation of the implemented filter at all optimal settings was measured to be larger than 20 dB. Insertion loss of the filter was measured to be ~4.2 dB which mainly comes from that of two QWP’s (~1.3 dB) and the PBS (~0.93 dB for one way, totally ~1.86 dB) including fiber fusion splicing loss between the HBF and ordinary fiber. The insertion loss can be diminished by using low-loss PC’s and PBS and by improving the fusion splicing of fiber splices between the HBF and ordinary fiber. Spectral flatness of the transmission in each optimal set was measured to be less than 0.16 dB and spectral flatness variation among four optimal settings was measured to be less than 0.37 dB. Especially, in order to examine the input polarization independence of the proposed filter, the polarization sensitivity of the transmission spectrum was measured by placing an additional PC (Agilent 8169 A) in front of the lead-in fiber (port 1 of the filter). During the measurement, we rotated both one QWP and one HWP, which are contained (with one input polarizer) within the additional PC, in a random way each time, ensuring that the signal polarization had been varied over the entire Poincare sphere. The maximum polarization sensitivity we observed was less than ~0.5 dB, which could be affected by polarization sensitivity of the photodetector and also imperfection of the PBS used in the experiments. This result deviates by less than ~0.5 dB from the theoretical expectation obtained from Eq. (5). In addition, the absolute channel wavelength control of the periodic transmission band can be done by controlling the voltage of the PZT drum wound by the HBF [12], or by controlling the tension/pressure applied to the HBF [13].

## 4. Conclusion

In this paper a new polarization-independent all-fiber multiwavelength-switchable filter based on a PDLC was proposed. The proposed filter is composed of a PBS, HBF, one HWP, and two QWP’s. The spectral characteristics of the proposed filter were theoretically and experimentally studied. Typical values of measured channel isolation and insertion loss of the implemented filter were ~20 dB and ~4.2 dB, respectively. The maximum input polarization sensitivity we observed was less than ~0.5 dB, which could be affected by polarization sensitivity of the photodetector and also imperfection of the PBS used. Particularly, the switching displacement between channels could be chosen as one of three displacements (0.2, 0.4, and 0.6 nm) in the wavelength-switching operation by selecting proper sets of QWP’s. The developed PDLC-based filter can be utilized in many applications in WDM optical network systems as well as in various multiwavelength optical sources.

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