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  • Abstract

SECTION 1

INTRODUCTION

Microwave photonic filter (MPF) has a lot of potential applications in dealing with radio frequency (RF) signals. By taking the advantages of photonic techniques, it is able to implement flexible filtering functions with low loss and high bandwidth, as well as immunity to electromagnetic interference (EMI), tunability, and reconfigurability [1], [2], [3]. The general concept of an MPF is a digital filter technology. The RF input signal is modulated onto one or multiple optical carriers via an electrical-optical modulator, and then, the modulated optical signals are fed to a photonic system that samples, weighs, and combines them by using optical delay lines or other photonic elements. When the signals are recovered at a photodetector (PD), the converted electrical signal is modified corresponding to the transfer function of the photonic system [3], [4].

In general, the incoherent light sources are employed to implement a stable MPF since the phase fluctuation will have no much influence on the performance of an MPF and consequently against environmental changes. There are two main approaches to obtain the incoherent optical taps. One is to use multiwavelength lasers, an array of independent lasers, or an optical frequency comb [5], [6], [7]; the other is to use a wide-band optical source (WBOS) sliced by a periodic or programmable multichannel optical filter [8], [9], [10]. In all cases, each source implements a filter sample, and the sampling period is determined by dispersive media.

For the MPFs based on multiwavelength lasers, laser arrays, or optical frequency comb, the main drawbacks are related to the high cost of their configuration and the electrical filtering response with an undesired periodic spectral characteristic, which impose limitations in some specific applications. A cost-effective way to realize single-bandpass MPFs is using a sliced WBOS. In this case, the taps are not a discrete distribution as the former case, then the free spectral range (FSR) goes to infinity, which is able to contribute a single-band response [9], [10].

Although a single-passband MPF is very important for some photonic microwave applications, e.g., an optoelectronic oscillator [10], one fact is that, in modern wireless and satellite systems, a bandpass filter with multiple passbands is considered as a key component, which is neither periodic nor single RF response and can simultaneously transmit multiple desired noncontiguous channels [11]. As far as we know, MPFs with such response have not been reported.

In this paper, we propose a novel multiband bandpass MPF, which has selectable one or more passband responses. The schematic of the proposed MPF is illustrated in Fig. 1. A WBOS is sliced by an optical filter to generate sampling taps, where a high-birefringence fiber loop mirror (HB-FLM) with two segments of high-birefringence fiber (HBF) is employed. Corresponding to the polarization rotation of the light in the loop, the HB-FLM shows various periodical spectral characteristics, which lead to uniform or multiple periods on the transmission spectrum. After the multiwavelength source modulated by a phase modulator (PM) and delayed by dispersive medium, the RF response exhibits one or multiple passbands in accordance with the sampling periods. In addition, the response on baseband is suppressed.

Figure 1
Fig. 1. Schematic of the proposed MPF. VNA: vector network analyzer.
SECTION 2

THEORETICAL ANALYSIS

In order to simplify the formula derivation and make comparisons, let us briefly review a single-passband MPF based on a WBOS sliced by a Mach–Zehnder interferometer (MZI) first, which has been analyzed and demonstrated in [9] and [12]. For a typical MZI, it consists of two ideal 3-dB fiber couplers with the arm lengths of Formula${\rm L}_{\rm up}$ and Formula${\rm L}_{\rm down}$, as shown in Fig. 2. When the light field is launched into port 1 and output from port 3, the transmittivity is given by Formula TeX Source $$T_{MZI} (\omega) = {1 \over 2}\left[1 - \cos \phi (\omega)\right].\eqno{\hbox{(1)}}$$

Figure 2
Fig. 2. Configuration of MZI.

Here, Formula$\omega$ is optical frequency, and Formula$\phi (\omega)$ is the phase difference between the two arms, which can be calculated as Formula TeX Source $$\phi (\omega) = \beta_{0} (L_{up} - L_{down}) = \beta_{0}\Delta L\eqno{\hbox{(2)}}$$ where Formula$\beta_{0}$ is the propagation constant, and the wavelength spacing (FSR of the optical spectrum) is Formula TeX Source $$FSR_{MZI} = 2\pi c/n\Delta L$$ where Formula$c$ and Formula$n$ are the light velocity and effective index of fiber. When a WBOS is sliced by this MZI, an approximately cosinoidal transmission spectrum can be obtained. There is only one FSR is presented for a certain Formula$\Delta L$. If the multiwavelength light from the slicing filter is modulated by a PM with modulation indexes of Formula$m_{1}$ and Formula$m_{2}$ for the two first-order modulation sidebands and pass through a dispersive medium with the transfer function of Formula$H_{disp}(\omega) = \vert H_{disp}(\omega)\vert \exp [-j\Phi (\omega)]$, the overall system response is Formula TeX Source $$H_{RF} (f) = \int T_{MZI}(\omega) \left[m_{1}H_{disp}^{\ast}(\omega) H_{disp}(\omega - 2\pi f) - m_{2}H_{disp}(\omega)H_{disp}^{\ast}(\omega + 2\pi f) \right]d\omega\eqno{\hbox{(3)}}$$ where Formula$f$ is RF signal frequency. Due to the dispersive medium acting as a phase filter, we can assume Formula$\vert H_{disp}(\omega)\vert = 1$, and the phase dependence can be given by means of a Taylor expansion centered at Formula$\omega_{0}$, as shown in Formula TeX Source $$\Phi (\omega) = \Phi (\omega_{0}) + \tau_{d}(\omega_{0}) (\omega - \omega_{0}) + {1 \over 2}\beta L(\omega - \omega_{0})^{2} + {1 \over 3}\chi L(\omega - \omega_{0})^{3}\eqno{\hbox{(4)}}$$ where Formula$\tau_{d}$ is the group delay, Formula$\beta$ is the dispersion, Formula$\chi$ is the dispersion slope, and Formula$L$ is the length of the dispersive medium. Then, the frequency response of the MPF can be derived as [9], [12] Formula TeX Source $$\eqalign{H_{RF} (f) = &\, \exp \left\{- j \left[2\pi f\tau_{d} (\omega_{0}) + (\chi L/3) (2\pi f)^{3}\right]\right\}\cr\noalign{\vskip-1pt} & \times \bigg\{m_{1}\exp \left[- j (\beta L/2) (2\pi f)^{2}\right] \times \int T_{MZI} (\omega) \cr\noalign{\vskip-1pt} & \qquad\times \exp \left \{- j \left[(2\pi \beta f + 4\pi^{2}\chi f^{2}) (\omega - \omega_{0}) + 2\pi \chi (\omega - \omega_{0})^{2}f\right] L\right\} d\omega\cr\noalign{\vskip-1pt} & \qquad - m_{2}\exp \left[+ j (\beta L/2) (2\pi f)^{2}\right] \times \int T_{MZI} (\omega) \cr\noalign{\vskip-1pt} & \qquad \times \exp \left\{- j \left[(2\pi \beta f - 4\pi^{2}\chi f^{2}) (\omega - \omega_{0}) + 2\pi \chi (\omega - \omega_{0})^{2}f\right] L\right\} d\omega\bigg\}.}$$

The equation above gives a response of single RF passband, and the baseband response is suppressed. The center frequency Formula$f_{c}$ of the MPF is determined by the delay time of the dispersive media as [9], [13] Formula TeX Source $$f_{c} = {1/\left[ \beta L(FSR_{MZI})\right]}.\eqno{\hbox{(5)}}$$

In addition, if the effect of the dispersion slope within the optical spectral bandwidth can be neglected, the 3-dB bandwidth of the RF passband is independent of Formula$f_{c}$ and can be expressed as [9] Formula TeX Source $$\Delta f_{c} = {\sqrt{8\ln 2}/\left(\beta L \cdot \Delta \omega \right)}\eqno{\hbox{(6)}}$$ where Formula$\Delta \omega$ is the optical source bandwidth.

Different from the MZI-based MPFs, a two-section HB-FLM, which can also be referred to as a two-order Solc-type filter, is employed as a slicing filter in our proposed MPF. As shown in Fig. 3, the incident light at the input port (port 1) is split by the coupler into two beams with clockwise (CW) and counter-CW (CCW) propagation directions, respectively. The two beams propagate along the loop and then recombine and interfere at the coupler with different phases due to the birefringence of the HBFs. In the loop, the two segments of HBF have lengths of Formula$L_{1}$ and Formula$L_{2}$, and the refractive indexes of the fast and slow axes are Formula$n_{f}$ and Formula$n_{s}$. Formula$\theta_{i}\ (i = 1, 2, 3, 4)$ denotes the angle between the fast axis of the HBFs and the Formula$x$-axis of the local coordinate at the incident plane. For a coupler with the power-splitting ratio of Formula$k$, the E-fields at ports 3 and 4 can be given by Formula TeX Source $$\left[\matrix{E_{3}\cr E_{4}}\right] = \left[\matrix{\sqrt{1 - k} & j\sqrt{k}\cr j\sqrt{k} & \sqrt{1 - k}} \right]\left[\matrix{E_{1in}\cr 0}\right]\eqno{\hbox{(7)}}$$ where Formula$E_{1in}$ is the input light field at port 1.

Figure 3
Fig. 3. Schematic illustration of a two-section HB-FLM. The right figure shows the connection details in the loop.

Now, let us consider the Jones transfer matrices of this HB-FLM. Assuming that the two segments of the HBF have the same beat length, the matrices along the two directions are given by [14] Formula TeX Source $$\eqalignno{M_{cw} = &\, R (\theta_{3}) J_{2}R (\theta_{2}) J_{1}R (- \theta_{1})&\hbox{(8a)}\cr M_{ccw} = &\, R (\theta_{1}) J_{1}R (- \theta_{2}) J_{2}R (-\theta_{3})&\hbox{(8b)}}$$ where Formula$R(\theta_{i}) (i = 1, 2)$ denotes the rotation matrix of the polarization state induced by the HBF with the incident angle Formula$\theta_{i}$, and Formula$J_{i}$ is the phase delay matrix caused by the HBFs. The expressions of Formula$R (\theta_{i})$ and Formula$J_{i}$ are Formula TeX Source $$\eqalignno{R (\theta_{i}) = &\, \left[\matrix{\cos \theta_{i} & - \sin \theta_{i}\cr\noalign{\vskip-1pt} \sin \theta_{i} & \cos \theta_{i}}\right]&\hbox{(9a)}\cr\noalign{\vskip-1pt} J_{i} = &\, \left[\matrix{\exp (- j2\pi n_{f}L_{i}/ \lambda) & 0\cr\noalign{\vskip-1pt} 0 & \exp (- j2\pi n_{s}L_{i}/\lambda)}\right]&\hbox{(9b)}}$$ where Formula$L_{i}\ (i = 1, 2)$ are the lengths of the HBFs used in the Sagnac loop. Then, the transmittivity can be expressed as Formula TeX Source $$\displaylines{T_{FLM}(\omega) = (1 - 2k)^{2} + 4k (1 - k) \left[\sin \left(\theta_{1} - \theta_{3}\right)\cos \theta_{2}\cos \left({\pi \Delta n (L_{1} + L_{2}) \over \lambda}\right)\right.\hfill\cr\noalign{\vskip8pt}\hfill \left. +\ \cos \left(\theta_{1} - \theta_{3}\right)\sin \theta_{2}\cos \left({\pi \Delta n (L_{1} - L_{2}) \over \lambda}\right) \right]^{2}.\quad\hbox{(10)}}$$

Here, we have Formula$\Delta n = \vert n_{f} - n_{s} \vert$. For a 3-dB coupler Formula$(k = 0.5)$, the transmittivity is simplified as Formula TeX Source $$\eqalignno{T_{FLM}(\omega) = &\, \left\{A\cos \left[{\phi_{1}(\omega) + \phi_{2}(\omega) \over 2}\right] + B\cos \left[{\phi_{1}(\omega) - \phi_{2}(\omega) \over 2}\right] \right \}^{2}\cr\noalign{\vskip8pt} = &\, \left({A^{2} \over 2} + {B^{2} \over 2}\right) + {A^{2} \over 2}\cos \left[ \phi_{1}(\omega) + \phi_{2}(\omega)\right] + AB\cos \phi_{1}(\omega) + AB\cos \phi_{2}(\omega) \cr\noalign{\vskip8pt} & + {B^{2} \over 2}\cos \left[\phi_{1}(\omega) - \phi_{2}(\omega)\right]&\hbox{(11)}}$$ where Formula$A = \sin (\theta_{1} - \theta_{3}) \cos \theta_{2}$, Formula$B = \cos (\theta_{1} - \theta_{3}) \sin \theta_{2}$, Formula$\phi_{1}(\omega) = 2\pi \Delta nL_{1}/\lambda$, and Formula$\phi_{2}(\omega) = 2\pi \Delta nL_{2}/\lambda$ are defined. Angles Formula$\theta = \theta_{1} - \theta_{3}$ and Formula$\theta_{2}$ can be controlled and varied by the two polarization controllers (PCs) in the loop. According to (11), Formula$T_{FLM}(\omega)$ includes four types of wavelength spacing, which are determined by Formula$\lambda^{2}/\Delta nL_{1}$, Formula$\lambda^{2}/\Delta nL_{2}$, Formula$\lambda^{2}/\Delta n (L_{1} + L_{2})$, and Formula$\lambda^{2}/\Delta n (L_{1} - L_{2})$, respectively.

Assuming the two HBFs have Formula$L_{1} = 2L_{2}$, hence, Formula$\phi_{1}(\omega) = 2\phi_{2}(\omega)$. Formula$T_{FLM}(\omega)$ can be deduced as Formula TeX Source $$\eqalignno{T_{FLM}(\omega) = &\, \left({A^{2} \over 2} + {B^{2} \over 2}\right) + {A^{2} \over 2}\cos 3\phi_{2}(\omega) + AB\cos 2\phi_{2}(\omega) + \left(AB + {B^{2} \over 2}\right)\cos \phi_{2}(\omega)\cr\noalign{\vskip8pt} = &\, - 2AB + {A^{2} \over 2}\left[1 + \cos 3\phi_{2}(\omega)\right] + AB\left[1 + \cos 2\phi_{2}(\omega)\right] + \left(AB + {B^{2} \over 2}\right)\left[1 + \cos \phi_{2}(\omega)\right]\cr\noalign{\vskip8pt} = &\, - 2AB + T_{MZI, 1}(\omega) + T_{MZI, 2}(\omega) + T_{MZI, 3}(\omega).&\hbox{(12)}}$$

As shown in (12), Formula$T_{FLM}(\omega)$ is a superimposition of three cosine functions with different periods. It can also be found that the transmission spectrum of the two-order HB-FLM is equivalent to three parallel (not cascaded) MZI slicers with coupled and modified weight coefficients as compared to (1). The corresponding periods are Formula$\lambda^{2}/3\Delta nL_{2}$, Formula$\lambda^{2}/2\Delta nL_{2}$, and Formula$\lambda^{2}/\Delta nL_{2}$, respectively. The minimum period is Formula$\lambda^{2}/3\Delta nL_{2}$, which is referred to the fundamental FSR and determined by Formula$L_{1} + L_{2}$. When Formula$\theta$ and Formula$\theta_{2}$ are adjusted, the contribution of each term is changed and the dominant FSR is varied consequently. For example, if the conditions of Formula$\theta = 0.5\pi$ and Formula$\theta_{2} = 0$ are fulfilled, we will have Formula$A = 1$ and Formula$B = 0$. Formula$T_{FLM}(\omega)$ can be rewritten as Formula TeX Source $$T_{FLM}(\omega) = {1 \over 2} \left[1 + \cos 3\phi_{2}(\omega)\right]$$ which is equivalent to the case of one MZI with spectral period of Formula$\lambda^{2}/3\Delta nL_{2}$. For another example, if Formula$\theta = -0.25\pi$ and Formula$\theta_{2} = 0.375\pi$ are selected, we have Formula$\vert AB \vert : \vert A^{2}/2 \vert : \vert AB + B^{2}/2 \vert = 4.83: 1: 1$, which means that Formula$\lambda^{2}/2\Delta nL_{2}$ is the dominant spectral period in Formula$T_{FLM}(\omega)$. Fig. 4 shows the numerically calculated transmittivity. Here, Formula$L_{1}$, Formula$L_{2}$, and Formula$\Delta n$ are set to be 6 m, 3 m, and 0.000385, which has a corresponding beat length of 4 mm. From Fig. 4, the dominant wavelength spacing shows fundamental, doubled, and tripled FSR, when Formula$(\theta, \theta_{2})$ is equal to Formula$(0.5\pi, 0)$, Formula$(-0.25\pi, 0.375\pi)$, and Formula$(0, 0.5\pi)$, respectively. It should be noticed, just like the description above, that the case of 2 × FSR (dot curve) is always mixed with the spectral period of FSR and 3 × FSR; therefore, it has no clear periodical boundary like the case of solid curve and dash curve. However, it can also be distinguished from the comparison with solid curve. Obviously, once other angles are chosen, the sliced spectrum will present various mixing period properties. When this HB-FLM is used as a slicer in an MPF, the corresponding RF frequency response will be Formula TeX Source $$H_{RF} (f) = \int T_{FLM}(\omega) \left[m_{1}H_{disp}^{\ast}(\omega)H_{disp}(\omega - 2\pi f) - m_{2}H_{disp}(\omega)H_{disp}^{\ast}(\omega + 2\pi f)\right]d\omega.\eqno{\hbox{(13)}}$$

Figure 4
Fig. 4. Calculated transmittivity of a two-order HB-FLM with HBF lengths of 6 m and 3 m. The solid curve, dot curve and dash curve are plotted by setting Formula$(\theta, \theta_{2})$ to be Formula$(0.5\pi, 0)$, Formula$(-0.25\pi, 0.375\pi)$, and Formula$(0, 0.5\pi)$.

Compared with (3), the transfer function includes three possible passband responses, and each one has the same features as the case of MZI. So, by varying Formula$\theta_{i}$, single- or multiple-passband MPF can be realized for adapting different applications.

It should be noticed that even a small length deviation of the HBF can cause great optical spectral change because HBF has a very small beat length, e.g., even 2-mm deviation lead to Formula$\pi$ phase shift on Formula$\phi_{2}(\omega)$. However, the influence on FSR can be ignored. Let us take HBF lengths of 6 m and 2.9991 m for example. Fig. 5 gives the normalized transfer function (13) as a function of the RF frequency Formula$f$, and the insets present the corresponding optical spectrum. Here, we consider that the optical source has Gaussian distribution, the dispersion slope of fiber is null, and Formula$\Delta n$, Formula$\beta$, and Formula$\Delta \omega$ are 0.000385, Formula$-23\ \hbox{ps}^{2}/\hbox{km}$, and 5 THz, respectively. Fig. 5(a)(c) gives three different situations with uniform optical spectral periods (corresponding to single-band filters), and Fig. 5(d)(f) show three mixed situations with various periodic combinations (corresponding to multiple passbands filters). From Fig. 5, one can see that the number of the passband is dependent on the dominant optical spectral periods included in the taps. The center frequencies and RF bandwidth are governed by (5) and (6).

Figure 5
Fig. 5. Theoretically calculated system responses of the proposed multiband bandpass MPF. The responses are plotted by setting Formula$(\theta, \theta 2)$ to be, (a) Formula$(0.5\pi, 0)$, (b) Formula$(-0.25\pi, 0.375\pi)$, (c) Formula$(0, 0.5\pi)$, (d) Formula$(0.243\pi, 0.26\pi)$, (e) Formula$(0.111\pi, 0.68\pi)$, (f) Formula$(0.225\pi, 0.14\pi)$. The solid curve shows the case of using 10-km fiber and the dot curve is that of using 25-km fiber. The insets are the corresponding optical spectrum.

Although these results show good passband characteristic, there are still some unwanted peaks especially in Fig. 5(b), (d), and (e). These can be explained by (12). For the case of Fig. 5(b), the dominant term is Formula$AB\cos [2\phi_{2}(\omega)]$, which means that coefficients Formula$A$ and Formula$B$ cannot be zero. What we can do is to balance and optimize the values to make Formula$\vert AB \vert \gg \vert A^{2}/2 \vert$ and Formula$\vert AB \vert \gg \vert AB + B^{2}/2 \vert$. Since Formula$A^{2}/2$ and Formula$AB + B^{2}/2$ are not zero, the relative small contributions of Formula$\cos 3 \phi_{2}(\omega)$ and Formula$\cos \phi_{2}(\omega)$ appeared. Similarly, an unwanted weak responses from Formula$\cos 3\phi_{2}(\omega)$ and Formula$\cos \phi_{2}(\omega)$ also appeared in Fig. 5(d) and (e). As a comparison, in order to eliminate the coupled weight coefficients on each term, the WBOS needs to be split into several paths and sliced by individual MZIs to generate desired spectral period on each path, and then amplified (or attenuated) independently. After recombining these optical fields as sampling taps, a multiband MPF without interaction can be obtained. But this configuration is more complicated and less cost efficient.

SECTION 3

EXPERIMENTAL RESULTS AND DISCUSSION

In order to verify the proposed MPF, the experimental demonstration was carried out. The experimental setup is shown in Fig. 6. The used WBOS, whose bandwidth covers the C +L band, is centered at 1570 nm, as shown in inset I. It is first sliced by the two-order HB-FLM to generate taps as shown in the inset II, where two commercial available HBF patchcords with nominal lengths of 6 m and 3 m are used. In order to obtain a quasi-Gaussian-like profile, the sliced source is shaped by an extra HB-FLM with an 8-cm-length HBF inside. When the WBOS directly passes through it, a main lobe centered at 1560 nm with a 3-dB bandwidth about 6 nm is obtained as shown in inset III. The following semiconductor optical amplifier (SOA) also has a quasi-Gaussian-like gain spectrum, which is able to reshape the envelope of the light source approaching Gaussian distribution and compensate the insertion loss caused by the former optical components. Inset IV shows the spontaneous emission spectrum of the SOA. Two isolators (ISOs) are employed to prevent optical reflection. The output of the SOA is modulated by a PM and then delayed by a coil of single mode fiber (SMF), where the fiber lengths of 10 km or 25 km are used for tuning the RF response. After the photodetection by a 12-GHz PD, the corresponding frequency response is characterized by a VNA. By properly aligning the PCs inside the HB-FLM, several typical cases are obtained, whose frequency responses are shown in Fig. 7. The insets are the corresponding sliced optical spectrum with span of 70 nm for the overall spectrum and 5 nm for details, respectively.

Figure 6
Fig. 6. Experimental setup of the proposed multiband bandpass filter.
Figure 7
Fig. 7. Experimental measurement of the RF filters responses. (a)–(c) single-band response, (d)–(f) multiband response. Dash line is the case of using 25-km SMF and solid line is the case of using 10-km SMF. The insets are the corresponding sliced optical source with span of 70 nm and 5 nm.

From Fig. 7, three available passbands with good out-of-band rejection ratio are clearly seen [e.g., Fig. 7(a)(c)], and the center frequencies are 3.2 GHz, 2.1 GHz, and 1.05 GHz when using 25-km SMF and 7.78 GHz, 5.21 GHz, and 2.6 GHz when using 10-km SMF, which show a good agreement with the theoretical prediction. As indicated by the theoretical analysis, any of these passbands can be selected to appear alone or as a form of combination provided the desired adjustment of the slicer. For example, two dual-band filters are shown by Fig. 7(d), (e), and (f) gives a triple-band filter.

Comparing the cases of using 25-km and 10-km SMF, the former has a lower power level than the later. The reason is that the taps suffer more transmission loss in longer fiber; meanwhile, the frequency response gets larger suppression when closer to dc due to phase modulation [13]. The width of a RF passband is determined by optical-source bandwidth and the amount of dispersion as described in (4); therefore, for the same optical spectral distribution, the narrower RF bandwidth is observed in the case of using longer SMF. However, under a certain fiber length, one may notice from Fig. 7 that the filter response gives different RF bandwidth on each passband. This is caused by nonnegligible dispersion slop in the SMF [9].

According to the theoretical analysis and experimental demonstration, we can summarize the method for designing a multiband bandpass filter. First, the number of the required passband is determined by the involved periods of the sliced optical spectrum, which is depended on the number of segments of the HBF used and the length relationship among them. Second, the RF response has strict relationship to the wavelength spacing and the accumulated dispersion. A reasonable wavelength spacing combinations with suitable time delay decides a desired passband interval. Finally, under a certain amount of dispersion, the width of RF passbands is determined by the bandwidth of the light source. By using dispersion flattened medium, the bandwidth difference among RF passbands can be eliminated. Based on these factors above, a desired multiband bandpass filter can be obtained by carefully choosing the relevant parameters.

SECTION 4

CONCLUSION

A novel scheme of a selectable multiband bandpass MPF has been proposed. Theoretical analysis has been carried out to describe the implementation of a two-order HB-FLM, which acted as a spectrum slicer for the optical spectrum. Different from the conventional configuration by using MZI, there are three periods included into the transmission function of the two-order HB-FLM when the length of one HBF is twice of the other. Thanks to its various periodic spectral characteristics, the sliced WBOS provides the taps with single or mixing of different wavelength spacings, which can be considered as the combinations of three MZI slicers with tunable weight. After the time delay and dispersion by SMF, RF response may finally show up to be either three single-band filters, two dual-band filters, or a triple-band filter. Both analytical investigation and experimental demonstration show that the center frequency and width of the RF passbands have the same characteristics as that of MZI-based MPFs but simpler configuration and lower cost.

The proposed multiband MPF shows good flexibility and high spectrum efficiency. If one of the HBFs in the slicer is substituted by a tunable differential group delay line, the periodicity of the optical spectrum can be adjusted. It will induce a tunable multiband bandpass filter consequently. It is worth noticing that, if the original WBOS has a bell-shaped spectrum (i.e., a superluminescent LED) [15], the second HB-FLM and the SOA can be omitted. The MPF configuration has been then further simplified.

Footnotes

This work was supported in part by the National Nature Science Foundation of China under Grant 61061004, by the Foundation for Excellent Young Talents of Guizhou Province of China under Grant NCET-10-0099, by the Foundation for Excellent Young Talents of Guizhou Province of Chinaunder Grant 2009-09, and by the advanced optoelectronic materials and technology innovation talent team of Guizhou province under Grant Qiankehe Talent Team (2011) 4002. Corresponding author: Y. Jiang (e-mail: jiangyang415@hotmail.com).

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Yang Jiang

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Perry Ping Shum

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Peng Zu

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Junqiang Zhou

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Guangfu Bai

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Jing Xu

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Zhuya Zhou

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Hengwen Li

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