## Abstract

A wavelength switchable all-fiber comb filter with flat-top spectral response based on a double-loop Mach-Zehnder (M-Z) interferometer is proposed and demonstrated. The proposed flat-top filter consists of a rotatable polarizer and a double-loop M-Z interferometer composed of two fiber couplers with a polarization controller (PC) in the first loop. In the theoretical analysis, when the second coupler of the M-Z interferometer is a non-3dB one, with proper settings of the polarization state of the input light and the PC, the wavelength switchable comb filter with flat-top passband can be obtained. Theoretical prediction was verified by experimental demonstration. The measured 1 dB bandwidth was 0.51 nm with a channel spacing of 0.98 nm, indicating that the flat-top passband of 1 dB bandwidth extends to about 50% of the comb spacing.

©2010 Optical Society of America

## 1. Introduction

Optical comb filters have attracted much attention as wavelength selective elements in dense wavelength-division-multiplexed (DWDM) optical fiber communication systems. As the increasing capacity of the communication system, wavelength switchable comb filters are regarded as important optical components for dynamic channel adding/dropping in optical communications. Several methods were used to realize the wavelength switchable comb filters, such as using polarization-diversity loop configuration [1], exploiting a semiconductor optical amplifier in Sagnac loop interferometer [2], incorporating a PZT in Hi-Bi Sagnac loop [3], employing a Mach-Zehnder (M-Z) filter [4]. One limitation of the wavelength switchable comb filters reported above is that their transmission bands are not flat which have a sinusoid shape. A filter with flat-top passband bandwidth is preferred for signal fidelity and tolerance of signal wavelength drift which can relax the requirements on wavelength control in a DWDM system. Therefore, it is desirable to design a filter with flat-top spectral response. Up to date, many techniques have been proposed to implement flat-top filter operation. For example, by using silicon nitride-based double-ring resonator [5], Gires-Tournois etalons [6,7], Sagnac loop with birefringent crystals [8], planar lightwave circuit (PLC) [9], cascaded high birefringence fiber [10], and the fiber Bragg grating [11], the filters with flat-top spectral passband were successfully demonstrated. Generally, the all-fiber comb filters have the advantages of low insertion loss, low cost, and good compatibility with the fiber communication systems. Furthermore, in some applications, the flat-top comb filter with dynamic wavelength switching operation should also be investigated. However, there are few reports on the all-fiber wavelength switchable flat-top comb filters. Lee et al reported an all-fiber wavelength switchable comb filter with flat-top passband based on a birefringence combination Sagnac loop [12]. By changing the polarization state of the light in the loop, channel wavelength switching operation with flat-top passband was realized. Recently, we have demonstrated a tunable and switchable multiwavelength fiber laser based on a modified M-Z interferometer [4]. However, the comb spectra of the filter in Ref [4]. have a sinusoid shape and no flat-top spectral response was observed. In this paper, we propose and demonstrate a wavelength switchable flat-top all-fiber comb filter based on a double-loop M-Z interferometer. Instead of using the combination of a polarization-dependent isolator and a polarization controller to change the polarization states of the input light in Ref [4], we employed a rotatable polarizer to accurately and simply measure the rotation angle of the input light which also leads to lower insertion loss. The proposed filter consists of a rotatable polarizer and a double-loop M-Z interferometer composed of two fiber couplers with a PC in the first loop. Different coupling ratio combinations have been investigated. When the second coupler is a non-3dB one, by properly adjusting the orientation of the PC and the polarization state of the input light, the wavelength switchable comb filter with flat-top spectral response was successfully obtained. Theoretical prediction was verified by experimental results.

## 2. Experimental setup and theoretical analysis

Figure 1 shows the schematic of the proposed wavelength switchable flat-top comb filter, which consists of a rotatable polarizer and a double-loop M-Z interferometer composed of two fiber couplers with a PC in the first loop. The PC is used to generate the flat-top comb spectral response as well as control the flatness of the comb spectrum. The rotatable polarizer is employed to make the input light linearly polarized and adjust the polarization state. An amplified spontaneous emission (ASE) light source is used to measure the transmission characteristics of the proposed filter.

Firstly, the transmission characteristics of the proposed flat-top comb filter are theoretically analyzed. The polarization state of the input light is forced into aligning with the rotatable polarizer. Suppose that the linearly polarized light at an angle *α* with respect to one of the principal axes of the fiber is launched into the double-loop M-Z interferometer, where *α* can be tuned by the rotatable polarizer. Therefore, the filter transmission characteristics can be analyzed by the following Jones matrix representation:

*A*is the amplitude of the light. $\left[I\right]$ is the identity matrix. $[{C}_{m}](m=1,2)$, $[P]$ and $[{F}_{n}](n=1,2)$ represent the matrices of the fiber couplers, the PC and the two arms of the first loop, respectively. Then we can obtain:

*θ*is the rotation angle of the propagating light through the PC,

*L*is the length of the shorter arm in the first loop, ${\phi}_{x}=k{n}_{x}\Delta L$ and ${\phi}_{y}=k{n}_{y}\Delta L$ are the phase differences of two axes between the two arms of the first loop due to the path difference $\Delta L$ which determines the spectral spacing ($\Delta \lambda ={\lambda}^{2}/\Delta L$). Since the birefringence of the single-mode fiber is sufficient low comparing to the refractive indices of the two fiber axes, to simplify the calculation, we assume that ${\phi}_{x}={\phi}_{y}=\phi =kn\Delta L$, where

*n*is the effective refractive index of the fiber and

*k*is the wave number. Then, we can obtain the transmission function in port 2:

*φ*, and the channel spacing in the second term is exactly half that of the third term. It’s due to this character that the proposed filter can realize flat-top spectrum output. In order to give a detailed explanation, we extract individually the last two terms of Eq. (2):

*α*or

*θ*. Two cases (${c}_{1}=0.5,{c}_{2}\ne 0.5$ and ${c}_{1}\ne 0.5,{c}_{2}\ne 0.5$) are considered in the following analysis:

1) ${c}_{1}=0.5,{c}_{2}\ne 0.5$. In this case, Eqs. (3) and (4) are simplified to:

As discussed above, it acts as a flat-top filter by counteracting the maximum intensity of ${T}_{2}$ and has the switching (interleaving) function by properly setting *α* or *θ*. Figure 2(a)
presents the transmission curves of ${T}_{1}$ (red curve) and ${T}_{2}$ (blue curve) with the parameters of $L=60\text{cm}$, $\Delta L=1.63mm$, ${n}_{x}-{n}_{y}=3\times {10}^{-7}$, $n=1.46$, $\theta =0.7\pi ,\text{}\alpha \text{=0 .15}\pi $, and ${c}_{2}=0.2$ when the flat-top spectral response was obtained. As shown in Fig. 2(a), the stopband of ${T}_{1}$ exactly locates at the passband of ${T}_{2}$. The transmission intensities commendably balance between ${T}_{1}$ and ${T}_{2}$ which makes the filter have the flat-top response. Correspondingly, the combined flat-top output of ${T}_{1}$ and ${T}_{2}$ is plotted as black curve in Fig. 2(a). The output spectrum in Fig. 2(a) excludes the DC component of Eq. (2). However, the flat-top shape of the output spectrum is unaffected with the DC component since it only contributes to the intensity of the transmission. Then *θ* was fixed at $0.7\pi $, by setting the orientation of the polarizer with an angle of $\alpha +\pi /2$, the wavelength switching operation with flat-top spectral response of the proposed filter was achieved, as shown in Fig. 2(b). It is worthy to note that the wavelength switching operation can also be achieved by rotating the PC with an angle of $\theta +\pi $ when *α* is fixed at $0.15\pi $. It is evident from Eqs. (5) and (6) since Eq. (5) keeps invariable while Eq. (6) only changes to the opposite sign with *π* shift of *θ*. From Eq. (2), we found that the maximum flatness of the comb filter is related to the PC setting (*θ*) with a fixed *α*. Figure 3
presents the dependence of the flatness of the comb filter on the PC settings when $\alpha =0.15\pi $. We can obtain the maximum flat-top situation when $\theta =0.7\pi $. In this case, the insertion loss is about 1.8 dB. However, we can optimize the insertion loss by properly setting *δ* and coupling ratios. If *θ* is less than $0.7\pi $, the comb spectrum shows convex, and when *θ* is greater than $0.7\pi $, the spectrum is concave. It is also to note that the shape of the wavelength response varies with the coupling ratios when other parameters are fixed. However, for the specific coupling ratios when the second coupler is a non-3 dB one, we can always obtain the wavelength switchable flat-top comb filter by properly setting the PC and polarizer.

2) ${c}_{1}\ne 0.5,{c}_{2}\ne 0.5$. In this case, the proposed filter also serves as a flat-top comb filter. However, when the flat-top operation was obtained initially by rotating the PC in a proper position, the wavelength interleaving operation with flat-top spectral response could not be achieved by only adjusting the orientation of the rotatable polarizer. Figure 4 illustrates the output wavelength tunable comb flat-top spectra with the parameters of ${c}_{1}=0.7,{c}_{2}=0.2$, $\theta =0.663\pi $, $\alpha =0.61\pi $ (black curve), $\alpha =1.11\pi $ (red dotted curve). As can be seen in Fig. 4, the transmission passband of the proposed filter can be tuned but it does not locate exactly at the interleaving position. Nevertheless, once the flat-top operation was obtained ($\theta =0.663\pi $ and $\alpha =0.61\pi $), the wavelength switching (interleaving) operation was still able to be realized by adjusting the PC with an angle of $\theta +\pi $ while other parameters were fixed, as shown in Fig. 4 with blue curve. It is worthy to note that once the interleaving operation with blue curve was achieved, one can rotate the polarizer with an angle of $\alpha +\pi /2$ to further tune the wavelength flat top spectrum, as shown in Fig. 4 with dotted green curve. Therefore, it indicates that the proposed filter can be discretely tuned to the wavelength positions in which cover one period of the channel spacing.

## 3. Experimental results and discussion

To verify the theoretical prediction, we constructed the proposed flat-top comb filter as shown in Fig. 1 and measured the transmission spectra at different orientations of the polarizer and the PC. First, we concentrated on the case of ${c}_{1}=0.5,{c}_{2}\ne 0.5$. The coupling ratios of two fiber couplers used in the experiment are 50:50 and 20:80. *L* is about 60 cm, and the path difference between two arms $\Delta L=1.63mm$ indicates that the comb spacing of 0.98 nm can be obtained. When the PC and the polarizer were appropriately adjusted, the wavelength switching operation with flat-top spectral response was obtained, as shown in Fig. 5
. The insertion loss was measured to be about 3.5 dB in the experiment. As predicted in the theoretical calculation, once the flat-top comb spectrum was obtained, the switching operation of the proposed flat-top filter could be implemented by rotating the polarizer or the PC (*θ*) with an additional angle of $\pi /2$ or *π*, respectively. The experimentally measured 1 dB bandwidth of 0.51 nm and 3 dB bandwidth of 0.66 nm with a free spectral range of 0.98 nm were obtained.

Then we replaced the first 3 dB coupler by a non-3 dB one, for this experiment, a 30:70 fiber coupler was used. Here, $\Delta L=1.52mm$. The results were shown in Fig. 6 . With a proper adjustment of the PC, we could easily obtain the flat-top comb spectrum (black curve). Note that the peak-to-notch contrast ratio in the experimental observation was ~15 dB, which was not as high as the theoretical calculation. It was mainly due to the limited precision of manually controlled PC and the insertion loss between the fiber components. When we further rotated the polarizer with an additional angle of $\pi /2$, the wavelength tunable operation (dotted red curve) but not interleaving operation with a ~0.23 nm wavelength shift of about 22% comb spacing was obtained. Nevertheless, as discussed in the theoretical analysis, the wavelength switching (interleaving) operation (black and blue curve) still could be achieved by rotating the PC when the other parameters were fixed in the experiment. As the interleaving operation (blue curve) was achieved, with the further adjustment of the polarizer, we can tune the flat-top spectrum with a wavelength of 22% comb spacing again, as shown in Fig. 6 with dotted green curve. The experimental results are well consistent with the theoretical predictions.

## 4. Conclusion

In conclusion, we have theoretically and experimentally demonstrated a wavelength switchable flat-top comb filter based on a double-loop M-Z interferometer which consists of two fiber couplers with a PC in the first loop. With proper settings of the polarization state of the input light and the PC, the wavelength switching comb filter with flat-top spectral response can be obtained by using a non-3dB coupler as the second coupler of the M-Z interferometer. In the experiment, the measured 1 dB bandwidth of 0.51 nm with a free spectral range of 0.98 nm was obtained, indicating that the flat-top passband of 1 dB bandwidth extends to about 50% of the channel spacing. Moreover, the proposed filter provides the advantages of simple implement and all fiber design.

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