## Abstract

In this paper a polarization-independent wavelength-switchable flat-top fiber comb filter is newly proposed, which is based on a Solc type birefringence combination and polarization-diversity loop configuration. The proposed filter consists of a polarization beam splitter, two concatenated polarization-maintaining fibers, and two half-wave plates. Our theoretical analysis shows that the proposed apparatus has a much flatter passband and sharper notch than the conventional Sagnac birefringence filter. Particularly, by interchanging the Solc type birefringence combination within the filter between the folded and fan designs, channel wavelength switching operation, more specifically channel interleaving operation, can be achieved through the proper adjustment of the half-wave plates contained within the apparatus. Theoretical prediction was verified by experimental demonstration.

©2005 Optical Society of America

## 1. Introduction

Optical fiber filters have been taken special interest in as the important components for the next-generation wavelength division multiplexed optical networks because their dynamic wavelength-selective property can provide high system performance. So a great many techniques for implementing optical fiber filters have been proposed until the present. Among lots of filters, fiber comb filters based on a Sagnac birefringence loop (Sagnac birefringence filter: SBF) [1] have obtained much attention for their simple design and ease of use and have been demonstrated to be useful in the development of multiwavelength fiber lasers [2–4], optical pulse train generation [5,6], high-speed wavelength routing [7], all-optical label swapping [8], and so forth. In classical bulk-optic birefringent filters chiefly composed of Lyot and Solc filters [9,10], a wide range of intensity transfer functions could be obtained by orienting linear birefringence elements in an appropriate way [11,12]. Similarly, in order to achieve various intensity transfer functions in the SBF, Lyot and Solc type birefringence combination (BC) using polarization-maintaining fibers (PMF’s) can be incorporated into the Sagnac birefringence loop of the filter [13–16]. By inserting and adjusting polarization controllers (PC’s) composed of half-wave plates (HWP’s) or quarter-wave plates (QWP’s) between the combined PMF sections with a set of rotation angles, flattened passband and sharpened stopband spectra can be generated [13–16], which can make the SBF be more flexible and effective in specific applications [16]. In the previously reported passband flattened SBF’s [15,16], however, the inherent insertion loss was observed in the calculated transmission [15] and experimentally measured insertion loss seemed to be of a bit high value [16]. Especially, although there were many preceding works associated with wavelength switching in the optical comb spectrum [17–19], there was no previous investigation into the wavelength switching technique in the passband flattened version. In this paper a polarization-independent wavelength-switchable flat-top fiber comb filter is newly proposed, which is based on a Solc type BC and polarization-diversity loop configuration (PDLC). The proposed filter consists of a polarization beam splitter (PBS), two concatenated PMF’s which have a 45° angle offset between their fast axes, and two HWP’s. Our theoretical analysis shows that the proposed apparatus has a much flatter passband and sharper notch than the conventional SBF besides the features of input polarization-independence, low insertion loss, and high channel isolation. Particularly, by interchanging the Solc type BC within the filter between the folded and fan designs, channel wavelength switching operation, more specifically channel interleaving operation, can be achieved through the proper adjustment of the HWP’s contained within the apparatus. Theoretical prediction was verified by experimental demonstration.

## 2. Principle of operation

Before we begin to explain the principle of operation of the proposed comb filter, let us start from the basic theory of the classical Solc filter. A conventional Solc filter [10], which has been incorporated in the optical spectroscopy for many years due to its narrow bandwidth, is classified into two types such as the folded and fan ones, whose geometrical arrangements are shown in Fig. 1(a) and (b), respectively. As shown in the figure, the filter consists of only two polarizing elements between which N birefringent plates (BP’s) with the same retardation Γ are sandwiched. In the folded design, BP’s between crossed polarizers are located with their fast axes oriented at *θ* or -*θ* with respect to the input polarization (*x*-axis), where *θ*=*π*/4*N*. In this case, the light passes through the analyzer without any loss of intensity only at the wavelength where the BP’s have an odd number of half-waves of retardation (or half-wave retardation) and the light at the other wavelength, where the BP’s do not have half-wave retardation any more, suffers loss at the analyzer. In the fan design, unlike the folded one, each BP between parallel polarizers is placed with its fast axis oriented in an increasing sequence *θ*, 3*θ*, 5*θ*, …, and (2*N*-1)*θ* with respect to the input polarization (*x*-axis). In this case, the unity transmission happens only at the wavelength where the BP’s have an even number of half-waves of retardation (or full-wave retardation) and the light at the other wavelength, where the BP’s do not have full-wave retardation any more, undergoes loss at the analyzer.

The transmission of each Solc filter can be calculated by using Jones matrix formulation and is given as follows.

According to the above spectral functions, the transmission spectra of the folded and fan Solc filters have identical narrow passband except that they are shifted by half the free spectral range, that is, of an interleaved relationship with each other. In order to obtain the passband flattened transmission spectra in these narrow band Solc filters, like those in a sharp notch filter, one need to complement their spectral functions and this can be accomplished by rotating the analyzer by 90° in each design, i.e., orienting the analyzer along the x and y-axes in the folded and fan designs, respectively. Then, transmission functions of the complemented Solc filter (with the flattened passband) can be expressed as follows.

As can be seen from Eqs. (3) and (4), the complemented spectral functions also have identical flattened passband except that they have an interleaved relationship with each other. In other words, the passband flattening can be achieved by rotating the analyzer by 90° in each design of the Solc filter and interleaving operation of the flat-top passband can also be performed by alternating the folded and fan designs.

Now, let us consider the case of the fiber comb filter based on a Sagnac interferometer. Considering the above discussion about the Solc filter, it is also possible to make the filter passband narrower or flatter by introducing the Solc type BC with the PMF’s into the birefringence loop of the conventional SBF, like the case incorporating Lyot type BC [13–16]. In the conventional SBF, however, any adjustment of the waveplates (which is located on either side of the PMFs’ chain) cannot play the same role as that of rotating the analyzer by 90° in the bulk Solc filter, because there is no polarizing element within the filter. This means that the transmission functions of this filter, which has the narrow passband in the transmission spectrum, cannot be complemented and the complemented output can be obtained only in the reflection spectrum. That is, for obtaining the passband flattened transmission spectra, an additional directional coupler or optical circulator is needed. Thus, the passband flattened transmission spectra without inherent insertion loss cannot be obtained by simply controlling the waveplates within the filter. This issue can be settled by adopting a PDLC, in which the PBS is utilized as the polarizer or analyzer [18]. If we introduce a PDLC as the filter structure, the waveplates can effectively rotate the principal axes of the PMF’s with respect to the horizontal axis of the PBS, which makes possible an effective 90° rotation of the analyzer from the standpoint of the stationary PMF’s. In the PDLC-based comb filter introducing the Solc type BC, therefore, the narrow band transmission functions can be complemented or the comb filter can produce the passband flattened transmission spectrum without inherent insertion loss. Particularly, the Solc type BC can readily be changed into the folded or fan design by effectively rotating the PMF’s, polarizer, and analyzer, that is, interleaving operation of the flat-top comb filter can be realized by simply adjusting the orientation of the waveplates in the filter.

Figure 2(a) shows the schematic diagram of the proposed PDLC-based fiber comb filter incorporating the Solc type BC. The optical components comprising the filter shown in Fig. 2(a) are a PBS, two HWP’s, and two identical PMF’s concatenated with a 45° angle offset between their principal axes (which play a role of two BP’s constructing the Solc type BC). In order to facilitate discussion, let us assume that the horizontal and vertical axes of the PBS are designated as *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. 2(b), the input light propagates through the polarizer (*x*-polarized), HWP 1 (with its fast axis *θ*
* _{h1}* oriented with respect to

*x*-axis), PMF 1 (

*θ*

_{p}_{1}oriented), PMF 2 (

*θ*

_{p2}=

*θ*

_{p1}+45° oriented), HWP 2 (

*θ*

_{h2}oriented), and analyzer (

*x*-polarized) sequentially, rotating in a CW direction. The angle offset (45°) between principal axes of two PMF’s (the PMF 1 and 2) was determined from the equation

*θ*=π/4

*N*(2

*θ*=2×π/8=π/4 rad). When the light passes through the HWP 1, input polarization (

*x*polarization) is azimuthally rotated by 2

*θ*

_{h1}with respect to

*x*-axis. From a different angle, this situation can be regarded as rotating the polarizer by 2

*θ*

_{h1}with respect to

*x*-axis. Similarly, the

*x*-polarized analyzer following the HWP 2 with an orientation angle of

*θ*

_{h2}can be considered as the polarizer rotated by 2

*θ*

_{h2}with respect to

*x*-axis (orientation angle of 2

*θ*

_{h2}). Hence, on the one hand, if we adjust two orientation angles of the HWP 1 and 2 to effectively rotate both the polarizer and analyzer by (

*θ*

_{p1}+22.5°) with respect to

*x*-axis, it is possible to make the geometrical arrangement of the polarizer, two PMF’s, and analyzer form that of the folded Solc filter with two BP’s and the 90° rotated analyzer. This arrangement is same as that of the filter design in Fig. 1(a) with the analyzer rotated by 90°, which gives the flat-top transmission spectrum. On the other hand, if the polarizer and analyzer is effectively rotated, respectively, by (

*θ*

_{p1}-22.5°) and (

*θ*

_{p1}+67.5°) with respect to

*x*-axis through the proper adjustment of the HWP’s, it is also possible to make the geometrical arrangement of the optical components build that of the fan Solc filter with two BP’s and the 90° rotated analyzer. This arrangement is same as that of the filter design in Fig. 1(b) with the analyzer rotated by 90°, which also gives the flat-top transmission spectrum except that half the free spectral range is shifted. Similarly, when the input light is ypolarized, the light travels the filter in a counterclockwise (CCW) direction as shown in CCW path of Fig. 2(b) and the left and right sides of each optical component are interchanged because

*y*-axis (vertical axis) is assumed to be an axis of symmetry. Thus, the same geometrical arrangement can be obtained as the case of the

*x*-polarized input light due to the reversed sequence and

*y*-axis symmetry of the optical components in the CCW direction. Consequently, the Solc type combination of the PMF’s in the proposed filter can readily be changed into the folded or fan design by effectively rotating the polarizers, that is, interleaving operation of the flat-top transmission spectrum can be achieved by simply adjusting the HWP’s in the loop of the filter. It is notable that, although the birefringent elements as well as polarizers should be effectively rotated for the interleaving operation of the proposed filter with

*N*≥3, the interleaving operation is possible by effectively rotating only the polarizers when

*N*=2. Especially, as an arbitrarily polarized light can always be decomposed into x and

*y*-polarized components, the transmitted intensity becomes the superposition of intensity outputs of two interference spectra 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. Based on the Jones calculus, the Jones matrix *T* (1^{st} term: CW direction, 2^{nd} term: CCW direction) and transmittance *t _{filter}* of the proposed filter are calculated as the following expressions;

$$+\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]{T}_{\mathit{HWP}\phantom{\rule{.2em}{0ex}}1}\left(-{\theta}_{h1}\right){T}_{\mathit{PMF}\phantom{\rule{.2em}{0ex}}1}\left(-{\theta}_{p1}\right){T}_{\mathit{PMF}\phantom{\rule{.2em}{0ex}}2}\left(-{\theta}_{p2}\right){T}_{\mathit{HWP}\phantom{\rule{.2em}{0ex}}2}\left(-{\theta}_{h2}\right)\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]\phantom{\rule{.9em}{0ex}}\left(\mathrm{CCW}\right)$$

$$-\mathrm{sin}2\left(2{\theta}_{h1}-{\theta}_{p1}\right)\mathrm{cos}2\left(2{\theta}_{h2}-{\theta}_{p1}\right){\mathrm{cos}}^{2}\Gamma ]$$

where *T _{HWP 1}*,

*T*,

_{HWP 2}*T*, and

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

_{PMF 2}*θ*

_{h1},

*θ*

_{h2},

*θ*

_{p1}, and

*θ*

_{p2}are fast-axis orientation (azimuthal) angles of the HWP 1, HWP 2, PMF 1, and PMF 2 with respect to

*x*-axis, respectively (

*θ*

_{p2}=

*θ*

_{p1}+45°). And Γ (=2

*πBL/λ*) is the phase difference generated due to birefringence

*B*and length

*L*of one PMF (

*λ*is the wavelength in vacuum). In the formulation, entire optical components that construct the filter were assumed to be ideal. So any insertion loss due to optical components was not considered and the retardation of the HWP’s was assumed wavelength-independent.

From Eq. (6), one can find out that both modulation depth (channel isolation) and wavelength location of interference pattern in transmission spectrum of the proposed filter can be changed by adjusting the values of *θ*
_{h1} and *θ*
_{h2}. If we choose the combination [*θ*
_{h1}, *θ*
_{h2}] of two orientation angles of the HWP 1 and 2 so as to orient both the polarizer and analyzer at the effective angle of (*θ*
_{p1}+22.5°) with respect to *x*-axis (e.g. [*θ*
_{p1}/2+π/16, *θ*
_{p1}/2+π/16]), the geometrical arrangement of the optical components of the proposed filter becomes that of the folded Solc filter with two BP’s and the analyzer rotated by 90° and the filter transmittance is given by {1-[1-cos(Γ)]^{2}/4} (which is the same expression as Eq. (3) when *N*=2). Similarly, if the HWP combination [*θ*
_{h1}, *θ*
_{h2}] is selected to orient the polarizer and analyzer, respectively, at the effective angle of (*θ*
* _{p}1*-22.5°) and (

*θ*

_{p1}+67.5°) with respect to

*x*-axis (e.g. [

*θ*

_{p1}/2-

*π*/16,

*θ*

_{p1}/2+3π/16]), the geometrical arrangement becomes that of the fan Solc filter with two BP’s and the analyzer rotated by 90° and the filter transmittance is given by {1-[1+cos(Γ)]

^{2}/4} (which is the same expression as Eq. (4) when

*N*=2). From these calculated filter transmittances, it is clear that two interleaved flat-top transmission spectra like

*π*phaseshifted spectrum pair can be obtained at the above two selected sets of the HWP’s ([

*θ*

_{p1}/2+π/16,

*θ*

_{p1}/2+π/16] and [

*θ*

_{p1}/2-

*π*/16,

*θ*

_{p1}/2+3

*π*/16]). As a result, passband switching operation, of which switching displacement is a half-period in the aspect of a sinusoidal function (that is, interleaving operation), can be obtained in the proposed flat-top comb filter through the proper selection of HWP sets shown in Table 1. On the basis of the theoretical analysis, the transmission spectra of the proposed filter are plotted at two HWP combinations of [

*θ*

_{h1},

*θ*

_{h2}] for interleaving operation in Fig. 3: Solid (set I) and dotted (set II) lines have an interleaved relationship with each other. In Fig. 3, the retardation, i.e., birefringence

*B*and length

*L*, of the PMF was determined so that the wavelength spacing between passband (channel) centers in the transmission spectrum became 0.8 nm.

At other general HWP combinations except above ones for interleaving operation of flat-top transmission spectra, spectral characteristics of the proposed filter, as a rule, can be classified as four categories, depending on the combination of the HWP angles. The four categories are as follows: 1) conventional SBF with the channel spacing of 0.8 nm; 2) narrow band-pass filter with the channel spacing of 0.8 nm; 3) conventional SBF with the channel spacing of 0.4 nm except an inherent insertion loss of 3 dB; and 4) 3 dB loss filter. The specific HWP combinations for four categories and corresponding filter transmittances are shown in Table 2. These four cases were also confirmed from the experiments.

## 3. Experimental results and discussions

To verify the theoretical results, we constructed a PDLC-based flat-top fiber comb filter as shown in Fig. 2(a) and measured the transmission spectrum of the implemented filter by adjusting each HWP. The proposed filter is composed of a PBS, two concatenated Bow-tie type PMF’s (Fibercore) whose principal axes have a 45° angle offset, and two HWP’s. The birefringence and length of two PMF’s are same as ~4.8×10^{-4} and 6.25 m, respectively. The length of the PMF was determined so that the channel spacing in the transmission spectrum became 0.8 nm. The splicing points between the PMF and ordinary single-mode fiber (SMF) or two PMF’s were marked with crosses (X’s) in the figure. The amplified spontaneous emission of an erbium-doped fiber amplifier was used as the nearly unpolarized broadband light source, whose degree of polarization was measured to be 2~3 %.

Figure 4(a) and (b) show the measured passband flattened transmission spectra in a wavelength range of 20 nm and passband switching (interleaving) operation of the proposed filter, respectively. As predicted in the theoretical results, the channel spacing and the switching displacement between channels were measured to be ~0.8 nm and ~0.4 nm at two interleaving sets of HWP’s, respectively. The typical channel isolation and spectral flatness of the implemented filter were measured to be >20 and <0.15 dB, respectively. The discrepancy between the measured and calculated channel isolations comes from the limited resolution bandwidth (0.02 nm) of the optical spectrum analyzer used for spectral measurement. Insertion loss of the filter was measured to be ~3.41 dB which mainly comes from that of two HWP’s (~0.89 dB) and the PBS (~1.17 dB for one way, totally ~2.34 dB) including fiber fusion splicing loss between the PMF and SMF. The insertion loss can be reduced by using low-loss waveplates and PBS and by improving the fusion splicing of fiber splices between the PMF and SMF. In order to investigate the input polarization independence of the proposed filter, the polarization sensitivity of the transmission spectrum, that is, polarization-dependent loss (PDL), was measured by placing and adjusting an additional PC (Agilent 8169A) in front of the input port (port 1) of the filter. The PC used in the investigation was composed of a rotatable linear polarizer, a QWP, and a HWP, sequentially. During the PDL measurement, we rotated both the QWP and the HWP contained within the PC in a random way each time, ensuring that the trace of the evolved signal polarization had covered the entire Poincare sphere. And the maximum polarization sensitivity was measured to be < 0.5 dB, which could be affected by polarization sensitivity of the photodetector and also imperfection of the PBS used in the experiments.

To make a comparison between the passband bandwidths of the proposed filter and conventional SBF [1], we measured both 1 and 3 dB passband bandwidths with respect to both the proposed filter and conventional SBF (constructed for comparison) as shown in Fig. 5(a) and (b), respectively. Solid and dotted lines indicate the transmission spectra of the proposed filter and the conventional SBF without the Solc-type combination of the PMF’s, respectively. For convenience, the figures of merit (FOM’s) with respect to 1 and 3 dB bandwidths were defined as (1 dB FOM=1 dB bandwidth [nm]/20 dB bandwidth [nm]) and (3 dB FOM=3 dB bandwidth [nm]/20 dB bandwidth [nm]), respectively. With these definitions, experimental FOM’s (1 and 3 dB FOM’s) of both filters were calculated based on the measured bandwidths. Measured 1 and 3 dB bandwidths and experimental FOM’s calculated based on them are shown in Table 3, also including theoretical FOM’s in order to examine the deviation of the experimental results from theoretical ones. As a result, experimental 1 and 3 dB FOM’s of the proposed filter were larger by ~53.5 and ~24.5 % than those of the conventional SBF, respectively, and the deviations of experimental FOM’s in both filters were within 1.4 % compared with the theoretical FOM’s.

## 4. Conclusion

In this paper a polarization-independent wavelength-switchable flat-top fiber comb filter is newly proposed, which is based on the Solc type BC and PDLC. The proposed apparatus consists of a PBS, two concatenated PMF’s which have a 45° angle offset between their fast axes, and two HWP’s. On the basis of the theoretical prediction of the spectral characteristics of the filter, we have demonstrated that the proposed filter had a much flatter passband and sharper notch than the conventional SBF and, particularly, channel interleaving operation could be achieved by interchanging the Solc type combination of the PMF’s between the folded and fan designs through the proper adjustment of the HWP’s contained within the apparatus. Typical values of measured channel isolation and insertion loss of the implemented filter were >20 dB and <3.41 dB, respectively. And experimental FOM’s with respect to 1 and 3 dB bandwidths of the proposed filter were larger by ~53.5 and ~24.5 % than those of the conventional SBF, respectively.

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