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• Abstract

SECTION I

## INTRODUCTION

Microwave photonic filters (MPFs) have attracted considerable attentions during the past few years since they can process radiofrequency (RF) signals directly in the optical domain and bring many advantages, e.g., high bandwidth, light weight, low loss, and immunity to electromagnetic interference [1], [2], [3]. Most of the reported MPFs are limited by the periodic frequency response due to the nature of discrete time signal processing [4], [5], [6]. This is undesirable in a lot of applications that require a wide frequency rejection range. In this context, many single-passband filters have been proposed based on, e.g., a broadband spectrum sliced multi-wavelength source [7], an optical intensity modulation combing with optical filtering via ring resonators or a virtually imaged phase array [8], [9], and a phase modulation in conjunction with optical filters, e.g., a pair of fiber Bragg gratings (FBGs) [10], an optical bandpass filter [11], and a phase-shifted FBGs [12]. Apart from these approaches, the use of stimulated Brillouin scattering (SBS) in optical fiber is an attractive technique for implementing a single-passband filter [13], [14], [15], [16], [17], [18], [19]. In [13] and [14], the sideband of an intensity modulated signal is amplified through SBS to obtain an RF gain in a narrow bandwidth. However, the undesirable RF components can also be recovered in photodetector (PD) due to the intensity modulation. To fully reject the undesirable RF components out of the passband, phase modulation has been used in [15]. The undesirable RF components cannot be detected because of the phase modulation. Meanwhile, the desirable RF signal in the passband is recovered through SBS-based phase-to-intensity modulation conversion. Recently, the pump wave involved in the SBS process was replaced by a wavelength tunable laser to overcome the bias drifting problem of the modulator [16]. On the other hand, Zhang et al. have demonstrated that although the intensity-modulation-based approach suffers from some limitations to implement a single-passband filter, it is a good choice to implement a notch filter using an equivalent intensity-to-phase modulation conversion [17], [18]. To further extend the tuning range of the single passband filter, a multi-pump scheme has been proposed by combining the SBS gain and loss spectra [19].

It is noted that the signal wave with different modulation formats have been used in these schemes, e.g., single-sideband (SSB) modulation [13], [14], phase modulation [15], [16], and out-of-phase ($\pi/4$ and $3\pi/4$) double sideband (DSB) modulation [18]. For each scheme, the pump wave has to be designed according to the modulation formats of the signal wave using, e.g., carrier-suppressed (CS)-DSB modulation [13], [15], CS-SSB modulation [14], or a wavelength tunable laser [16]. Therefore, the transmitter and the configuration of the fiber-optic link must be modified for each structure. In practical applications, however, it is highly desirable to have a MPF structure that can be inserted anywhere in existing fiber-optic links without modifying the link configuration and the transmitter [20]. Moreover, the filter structure should be independent of the modulation formats of the incoming signal wave.

This paper presents a novel microwave photonic single-passband filter based on polarization control through SBS. To the best of our knowledge, this is the first time that the SBS-assisted polarization control is used to implement a microwave photonic single-passband filter. It should be noted that the previously reported works [13], [14], [15], [16], [17], [18], [19] are all based on scalar Brillouin selective amplification of the RF modulated sideband where co-polarized signal and pump waves are required to maximize the optical gain. In our scheme, the operational principle of the filter is based on a vector SBS process, which is different from that reported in [13], [14], [15], [16], [17], [18], [19]. The state of polarizations (SOPs) of the signal and pump waves are detuned to realize a single-passband filter. The filter structure can be inserted anywhere in conventional fiber-optic links without the need for modifying the link configuration and the transmitter. Moreover, it is independent of the modulation formats of the incoming signal wave. In addition, for any modulation format, it is converted to the SSB modulation by the proposed filter. Therefore, the system is expected to be immune to the fiber dispersion-induced power fading.

SECTION II

## SBS-BASED ALL-OPTICAL POLARIZATION CONTROL

The proposed microwave photonic single-passband filter is based on polarization control through SBS. SBS is a parametric process that involves two counterpropagating waves (pump and signal) and an idler acoustic wave [21], [22]. A specific Brillouin frequency shift, $f_{\rm B} \sim 10 - 11\ \hbox{GHz}$, between the pump and signal waves is required, which is determined by the acoustic velocity in silica. The SBS operates in an extremely narrowband ($\sim$20 MHz), which results in a power transfer from the higher frequency optical wave to the lower one, leading to the amplification of the latter wave and the attenuation of the former [23]. Moreover, the SBS interaction is found to be polarization-dependent [24], [25], [26]. In the SBS interaction, the SOP of the signal wave is pulled toward that of the conjugate of the pump signal in the Brillouin amplification process. For a Brillouin attenuation process, the roles of the signal and pump waves are reversed [25]. The degree of dragging depends on the pump power and the SOP relationship between the signal wave and the pump wave.

We take the SBS amplification as an example to show the principle of the polarization pulling. Zadok et al. [25] have reported that the SBS amplification in a birefringent fiber is characterized by maximum and minimum values of the signal amplitude gain, $G_{\max}(\omega_{\rm s})$ and $G_{\min}(\omega_{\rm s})$, respectively. $\omega_{\rm s}$ denotes the signal angular frequency. Moreover, the maximum and minimum SBS gain is related to a pair of orthogonal SOPs of the signal wave [25], [27], [28]. The SOP of the maximum gain is the same as the conjugate of the pump wave $(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over E}_{p}^{\ast})$, which can be characterized by the SOP of SBS amplified spontaneous emission (ASE) [26], [27]. As shown in Fig. 1, the projections of the signal wave $(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over E}_{s})$ into the SOPs of the maximum and minimum SBS gain, denoted as $\mathord{\buildrel{\lower3pt\hbox{$ \scriptscriptstyle\rightharpoonup$}}\over E}_{s\_\max}$ and $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over E}_{s\_\min}$, are amplified. Generally, we have $G_{\max}(\omega_{\rm s}) \gg G_{\min}(\omega_{\rm s})$. Hence, the SOP of the signal wave is pulling toward that of the conjugate of the pump wave. Therefore, it provides an opportunity to all-optically control the SOP of an optical signal.

Fig. 1. Principle of polarization pulling in the SBS amplification process. $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over E}_{s}$ and $\mathord{\buildrel{\lower3pt\hbox{$ \scriptscriptstyle\rightharpoonup$}}\over E}_{s}^{\prime}$ are the electrical field of signal wave before and after SBS interaction, respectively.

It is noticed that a 90° polarization pulling is hardly realized due to the fact that the pulling is very small when the original optical signal wave and the conjugate of the pump wave are perfectly orthogonal at the output of the fiber [26]. In order to overcome this limitation, we have recently proposed a two-step SBS approach using both SBS gain and loss to change the SOP of the signal wave by 90° [29]. Two pump waves are used to generate SBS gain and loss at the optical signal separately. In the first SBS process, the signal wave enjoys the Brillouin gain and the SOP of the signal wave is changed by a degree of $\alpha\ (0\ <\ \alpha\ <\ 90)$. In the second SBS process, the signal wave suffers the Brillouin loss, and the SOP of the signal wave is further detuned by $\beta^{\circ}\ (0\ <\ \beta\ <\ 90)$. Therefore, a 90° polarization rotating can be achieved at $\alpha + \beta = 90$. Moreover, the amplitude of the signal wave can be adjusted by separately tuning the gain and loss for the signal wave.

SECTION III

## PRINCIPLE OF THE MICROWAVE PHOTONIC SINGLE-PASSBAND FILTER

The schematic configuration of the proposed microwave photonic single-passband filter is shown in Fig. 2(a). The RF modulated incoming optical signal that carriers the RF signal to be filtered launches the front port of the processor. Fig. 2(b) shows the principle of the proposed filter and the optical and electrical signals before and after SBS interactions. An optical isolator (ISO) is added to ensure unidirectional transmission. An optical circulator (OC) is used to counterpropagate the RF modulated signal wave and the two pump waves in a length of dispersion-shifted fiber (DSF). In the fiber, the SOP of the optical carrier is rotated by 90° through pump1, as shown in Fig. 2(b). It should be noted that we used the two-step SBS method [29] to ensure a 90 ° polarization rotating in the following experiment. As a result, the RF signals cannot be recovered in the PD because the SOPs of the optical carrier and the RF modulated sidebands are orthogonal [see Fig. 2(b)]. To recover the desirable RF signal, the SOP of the RF modulated sideband is rotated by a degree of $\gamma$ through pump2. Since the orthogonal polarization condition between the optical carrier and the sideband is destroyed, the desirable RF signal can be detected in the PD. In this way, a microwave photonic single-passband filter can be realized as shown in Fig. 2(b).

Fig. 2. (a) The schematic configuration of the microwave photonic single-passband filter and (b) the principle of the filter. For an RF modulated incoming optical signal, all the frequency components could be recovered in the PD. If the SOP of the optical carrier is rotated by 90° through SBS interaction with pump1, there is no RF component could be recovered in the PD. Finally, one of the RF modulated sidebands is also rotated by a degree of $\gamma$ through pump2. The desirable RF signal can be detected in the PD since the orthogonal polarization condition between the optical carrier and the sideband is destroyed. In this way, a microwave photonic single-passband filter can be realized. The optical signals and corresponding electrical signals are schematically illustrated. DSF: dispersion shifted fiber.

It is noted that only the optical carrier and the desirable RF modulated sideband could beat in the PD. Therefore, the proposed technique is independent of the RF modulation formats as long as the processed signal includes an optical carrier and an RF modulated sideband. Next, we take DSB intensity-modulated signal as an example to show the principle of the proposed filter. Under small-signal condition, the DSB intensity-modulated incoming signal [see Fig. 3(a)] can be expressed as TeX Source $$\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle \rightharpoonup}}\over E}_{in}(t) = \left[\matrix{E_{x} \cr E_{y}}\right] = \left[\matrix{A_{0}\exp(j\omega_{0}t) + A_{1}\left\{\exp\left[j(\omega_{0} + \omega_{RF})t\right] + \exp\left[j(\omega_{0} - \omega_{RF})t\right]\right\} \cr 0}\right]\eqno{\hbox{(1)}}$$ where $A_{0}$ and $A_{1}$ are the amplitudes of the optical carrier and sidebands, respectively. $\omega_{0}$ and $\omega_{\rm RF}$ are the angular frequencies of the optical carrier and the RF signal, respectively. The reference frame of polarization state $E_{\rm x}$ is aligned with the SOP of the incoming signal at the output of the fiber, and the polarization state of $E_{\rm y}$ is orthogonal to that of $E_{\rm x}$. If the SOP of the optical carrier is rotated by 90 ° through pump1, as shown in Fig. 3(b), the optical field becomes TeX Source $$\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}}\over E}_{out1}(t) = \left[\matrix{E_{x}\cr E_{y}} \right] = \left[\matrix{A_{1}\left\{\exp\left[j(\omega_{0} + \omega_{RF})t\right] + \exp\left[j(\omega_{0} - \omega_{RF})t\right]\right\} \cr \eta A_{0}\exp(j\omega_{0}t)}\right].\eqno{\hbox{(2)}}$$ where $\eta$ is the amplitude gain which is controlled by the SBS gain and loss in the two-step SBS process [29]. In Eq. (2), we assume that the frequency of the RF signal is larger than the bandwidth of SBS interaction ($\sim$20 MHz). Therefore, the SOP of the optical sideband is unchanged.

Fig. 3. Evolution of the RF modulated signal in the SBS interaction: (a) The original double-sideband modulated incoming signal; (b) the optical carrier is rotated by 90° by the two-step SBS process; (c) the SOP of the upper frequency sideband is also rotated by a degree of $\gamma$ through pump2; (d) the same condition as (c) but with more information added to understand Eq. (3). $A_{0}$ and $A_{1}$ are the amplitudes of the optical carrier and sidebands, respectively; $A_{1}^{\prime}$ is the amplitude of the sideband after SBS interaction with pump2; $\omega_{0}$ and $\omega_{\rm RF}$ are the angular frequencies of the optical carrier and the RF signal, respectively; $\eta$ is the amplitude gain which is controlled by the SBS gain and loss in the two-step SBS process; $\theta$: the SOP detuning of the conjugate of pump2 from the original position of the RF modulated signal; $G_{\max}(\omega_{\rm s})$ and $G_{\min}(\omega_{\rm s})$ are the maximum and minimum amplitude gain in a birefringent fiber, respectively. $E_{\rm x}$ and $E_{\rm y}$ are the reference frame of the polarization state, $E_{\rm x}$ is aligned with the SOP of the incoming signal at the output of the fiber and the polarization state of $E_{\rm y}$ is orthogonal to that of $E_{\rm x}$.

To implement a microwave photonic single-passband filter, the SOP of the RF modulated sideband (e.g., the upper frequency sideband) is rotated by a degree of $\gamma$ through pump2. To this end, the SOP of the conjugate of pump2 is detuned by a degree of $\theta$ from the original position of the RF modulated signal. As shown in Fig. 3(c), the projections of the sideband into the SOPs of the maximum and minimum SBS gain of pump2 are amplified, leading to the polarization dragging of the sideband toward that of the conjugate of pump2. After SBS interaction, the optical field is given by TeX Source \eqalignno{&\mathord{\buildrel{\lower3pt\hbox{ \scriptscriptstyle\rightharpoonup}}\over E}_{out2}(t)\cr&\quad = \left[\matrix{E_{x}\cr E_{y}}\right]\cr& \quad = \left[\matrix{A_{1}\left\{\left[G_{\max}(\omega_{RF})\cos^{2}\theta + G_{\min}(\omega_{RF})\sin^{2}\theta \right] \cdot \exp\left[j(\omega_{0} + \omega_{RF})t\right] + \exp\left[j(\omega_{0} - \omega_{RF})t\right]\right\} \cr \eta A_{0}\exp(j\omega_{0}t) + {A_{1}\left[G_{\max}(\omega_{RF}) - G_{\min}(\omega_{RF})\right] \cdot \sin 2 \theta \cdot \exp\left[j(\omega_{0} + \omega_{RF})t\right] \over 2}}\right].\cr&&{\hbox{(3)}}}

Fig. 3(d) is helpful to understand Eq. (3). If the fiber linear loss is ignored, $G_{\max}(\omega_{\rm RF})$ and $G_{\min}(\omega_{\rm RF})$ can be expressed as [28] TeX Source \eqalignno{G_{\max}(\omega_{RF}) = &\, \exp\left[g(\omega_{RF})L/3\right]&{\hbox{(4)}}\cr G_{\min}(\omega_{RF}) = &\, \exp\left[g(\omega_{RF})L/6\right]&{\hbox{(5)}}} where $g(f_{\rm RF})$ is given by [27] TeX Source $$g(\omega_{RF}) = \int{{1 \over 2}g_{0}P(\omega_{p}) \over 1 - j2\left[\omega_{p} - \omega_{B} - (\omega_{0} - \omega_{RF})\right]/\Gamma_{B}}d\omega_{p} \eqno{\hbox{(6)}}$$ where $g_{0}$ is the SBS gain coefficient [25], [27], $P(f_{\rm p})$ is the power spectral density of the pump wave, $\omega_{\rm p}$ is the angular frequency of the pump wave, $\omega_{\rm B} = 2\pi \cdot f_{\rm B}$, and $\Gamma_{\rm B} \sim 2\pi \cdot 20\cdot 10^{6}\ \hbox{rad/sec}$ is the Brillouin bandwidth.

Then, if the output optical signal were detected in the PD, the RF signal would be proportional to TeX Source $$i(t) \propto E_{out2} \cdot E_{out2}^{\ast} \propto \eta A_{0}A_{1} \left[G_{\max}(\omega_{RF}) - G_{\min}(\omega_{RF})\right] \cdot \sin 2\theta \cdot \cos(\omega_{RF}t).\eqno{\hbox{(7)}}$$

As can be seen from Eq. (7), the optimum SOP of the conjugate of pump2 is $\theta = 45^{\circ}$. The amplitude gain $G_{\max}(\omega_{\rm RF})$ in the scalar SBS scenario is replaced by $G_{\max}(\omega_{\rm RF}) - G_{\min}(\omega_{\rm RF})$ in the vector SBS case [27], [28]. $G_{\min}(\omega_{\rm RF})$ cannot be ignored under modest pump power level. For RF modulation sidebands around the SBS resonance, the corresponding RF components could be recovered by the PD since $G_{\max}(\omega_{\rm RF}) \gg G_{\min}(\omega_{\rm RF}) \gg 1$. For other undesirable RF components, they cannot be recovered upon detection because the SBS has no effect on the modulation sidebands. Hence, we have $G_{\max}(\omega_{\rm RF}) = G_{\min}(\omega_{\rm RF}) = 1$ and $i(t) = 0$. This means that the polarization-based discrimination can achieve very high out-of-band rejection (theoretically infinite). At this point, the principle of the proposed technique is similar to the polarization-enhanced Brillouin optical filters [27], [28] where a polarizer was added to enhance the rejection of the out-of-band optical components. It should be noticed that the power transfer for these out-of-band RF components in the scalar SBS process [13], [14] (i. e. the SOP of the signal wave is aligned with that of the conjugate of the pump wave) is unity. As can be seen from Eq. (6), the SBS will also induce a frequency-dependent phase shift of the optical signal within the bandwidth of interaction, which is known as “slow light” and has been used to generate broadband true time delay for microwave signal processing applications [23].

The proposed processor can be inserted anywhere in conventional fiber-optic links without the need for modifying the link configuration and the transmitter because it is an all-optical processing technique. It is well-known that the DSB modulation (intensity or phase modulation) suffers from fiber dispersion-induced power fading. In the proposed processor, the DSB modulation is converted to an equivalent SSB modulation. Therefore, the system is expected to be immune to the fiber dispersion-induced power fading. In addition, the frequency response of the filter is tunable by adjusting the wavelength of the pump2.

SECTION IV

## EXPERIMENT AND RESULT

An experiment was designed based on the configuration shown in Fig. 4 to demonstrate the proposed microwave photonic single-passband filter. As mentioned in Section 2, a two-step SBS process has to be implemented to drag the SOP of optical carrier by 90 °. Two pump waves, i.e., pump1(a) and pump1(b), are required to generate SBS gain and loss at the optical carrier separately. In addition, pump2 has to be used to rotate the SOP of the RF modulated sideband. Therefore, three pump waves are required in our scheme. Unfortunately, there are not enough tunable laser sources (TLSs) available in our lab. To implement a proof-of-concept experiment, pump1(a) and pump1(b) were provided by the same laser diode (LD) as the RF modulated signal (see Fig. 4).

Fig. 4. Experimental setup. LD: laser diode; EDFA: erbium-doped fiber amplifier; MZM: Mach–Zehnder modulator; ISO: optical isolator; DSF: dispersion-shifted fiber; OC: optical circulator; PC: polarization controller; TOF: tunable optical filter; PD: photodetector; PA: polarization analyzer; TLS: tunable laser source; VNA: vector network analyzer.

The optical carrier at 1549.466 nm with power of 11 dBm was provided by a LD. The signal was split into two branches by an optical coupler. In the lower branch, the optical carrier was modulated by an RF signal through a Mach–Zehnder modulator (MZM2). MZM2 was biased at null point to generate CS-DSB modulation, as shown in the inset of Fig. 4. The frequency of the RF signal equals to the Brillouin frequency shift $f_{\rm B}$, which was measured to be 10.501 GHz at 1549.466 nm for the fibers used in our experiment. Following MZM2, the two sidebands of the CS-DSB signal were separated by two tunable optical filters (TOF1 and TOF2, respectively). The higher and lower frequency sidebands were boosted by the erbium-doped fiber amplifiers (EDFA1 and EDFA2) and acted as pump1(a) and pump1(b), respectively. The SOPs of pump1(a) and pump1(b) were controlled by two polarization controllers (PC1 and PC2, respectively). Pump2 was provided by a TLS, boosted by EDFA3, and polarization-controlled by PC3 before coupling with pump1(b).

In the upper branch, the optical carrier was modulated by the RF signal to be filtered through MZM1. The SOP of the RF modulated signal was measured by a polarization analyzer (PA) and is shown in Fig. 5 (marked as point $A$). The corresponding polarization ellipse and the Stokes vector parameters are also shown in the inset of Fig. 5. OC1 was used to counterpropagate the RF modulated signal and pump1(a) (with optical power of 9.5 dBm) in a 4.1-km length of DSF1. In the fiber, SBS gain interaction was stimulated between the optical carrier and pump1(a). The SOP of the optical carrier was pulling toward that of the conjugate of pump1(a). By adjusting PC1, the maximum detuned SOP of the optical carrier is marked as Point $B$ in Fig. 5. This is the first step SBS process. In order to rotate the SOP of the optical carrier by 90°, the second step SBS process has to be implemented. The other OC2 was used to counterpropagate the signal wave and pump1(b) (with optical power of 9 dBm) in the other 4.1-km length of DSF2, where the SBS loss process took place. By adjusting PC2, the SOP of the optical carrier was rotated by 90° from its original position, as shown in Fig. 5 (marked as point $C$).

Fig. 5. Poincaré sphere showing the measured SOP of the optical signal involved in the SBS processing. Open symbol denotes SOP in the back of the sphere. The insets indicate the corresponding polarization ellipse and the Stokes vector parameters.

As discussed in Section 3, the SOP of the conjugate of pump2 should be detuned by 45° from the original position of the RF modulated signal. For pump2 at 1549.306 nm with power of 9.8 dBm, the SOP of its conjugate was adjusted to 45 ° (90° in Poincaré sphere) by PC3 and is marked as Point $D$ in Fig. 5. It was measured by switching off the LD so that spontaneous Brillouin scattering was excited, acting as a polarization mirror of pump2 [24], [26]. Fig. 6 shows the frequency response $(S_{21})$ of the single-passband filter operating at a center frequency of 9.5 GHz for pump2 at 1549.306 nm. The out-of-band rejection is $\sim$30 dB. The inset shows the zoom-in view of the passband. It can be seen that the filter exhibits an excellent shape factor with −3 dB bandwidth of 20 MHz, −10 dB bandwidth of 38 MHz, and −20 dB bandwidth of 80 MHz. By adjusting the wavelength of pump2 from 1549.222 to 1549.367 nm, the frequency response of the single-passband filter is tunable in a frequency range from $\sim$2 to 20 GHz with the out-of-band rejection of $\sim$30 dB, as shown in Fig. 7. It is noted that the undesirable RF signals out of the passband cannot be recovered in the PD and fall into the noise of the system. This is different from that reported in [13] and [14] where the undesirable RF signals can also be recovered in the PD due to the intensity modulation.

Fig. 6. Measured frequency response of the microwave single-passband filter for pump2 at 1549.306 nm with power of 9.8 dBm.
Fig. 7. Measured tunable frequency response of the microwave photonic single-passband filter.
SECTION V

## CONCLUSION AND DISCUSSION

We have demonstrated a new microwave photonic single-passband filter based on polarization control through SBS. The filter structure can be inserted anywhere in conventional fiber-optic links without the need for modifying the link configuration and the transmitter. Moreover, it is independent of the modulation formats of the signal wave. For an RF modulated signal launched to the processor, the SOP of the optical carrier is rotated by 90 ° through a two-step SBS. To implement a single-passband filter, the SOP of the optical sideband is changed through pump2. By adjusting the wavelength of the pump2, the frequency response of the filter is tunable in a frequency range from $\sim$2 to 20 GHz with out-of-band rejection of $\sim$30 dB and −3 dB bandwidth of $\sim$20 MHz. In addition, for any modulation format, it is converted to the SSB modulation by the proposed filter. Therefore, the system is expected to be immune to the fiber dispersion-induced power fading.

In our scheme, we have used two wavelength-fixed pump waves, i.e., pump1(a) and pump1(b), to rotate the SOP of the optical carrier by 90°. However, they would also generate Brillouin gain and loss at the position of $\sim$21 GHz far from the optical carrier. This will limit the frequency tuning range of the proposed filter. To overcome this restriction, multi-pump-based approach [19] can be used to separately compensate the Brillouin gain and loss spectra.

SBS as an optical amplifier, in general, induces ASE noise to the signal wave [30], [31], [32]. As a result, the recovered RF components would be contaminated by the ASE noise. It was reported [32] that the ASE noise can be significantly reduced for relatively high signal power when the SBS operated in the saturation regime. Furthermore, the ASE noise power increases with signal wave detuning [32] (defined as the frequency interval between the signal wave and the center of the SBS resonance). Hence, the ASE noise power can be notably reduced if the signal wave locates in the center of the SBS resonance. In our scheme, the optical carrier has been optimized at the center of the SBS resonance to minimize the ASE noise. On the other hand, the RF modulated sideband swept over the whole SBS gain profile of pump2. Ferreira et al. [32] reported that the signal to noise ratio (SNR) of the optical signal decreases with signal wave detuning due to the combined effect of the SBS gain reduction and of the SBS-ASE noise enhancement. Therefore, the SNR or the out-of-band rejection of the proposed microwave filter would also degrade with RF detuning.

Apart from the SBS-ASE noise, the proposed microwave photonic filter was also affected by many other noise sources, e.g., the noise from EDFA, PD, and the VNA. It is noticed that other scalar SBS-based techniques are also affected by these noise sources. In this context, the selectivity of the vector SBS-based technique [27], [28] is expected to be higher than its scalar counterpart [13], [14], [15], [16], [33], [34], [35]. However, significantly better rejection has not been achieved in the experiment. This can be attributed to the deviation of the optical carrier from the orthogonal polarization state. It affected the selectivity of the proposed microwave filter greatly, which determined the noise floor shown in Figs. 6 and 7. To overcome the non-perfect orthogonal polarization rotating of the optical carrier, sophisticated polarization and power controls of the pump waves have to be done.

The stability of the system is highly dependent on the frequency stability of the laser sources, as well as the polarization control of the light wave. In our experiment, pump1(a) and pump1(b) were provided by the same laser source with the signal wave, so that the relative frequency stability was ensured. In a practical system, however, pump1(a) and pump1(b) should be provided by individual laser sources. The frequency drift and the polarization variation of the laser sources would lead to a non-perfect 90° polarization rotating of the optical carrier, resulting in a reduced out-of-band rejection of the microwave single-passband filter. Moreover, the frequency drift of pump2 would cause the variation of the center frequency of the single-passband resonance. In this paper, we have demonstrated a proof-of-concept experiment to verify the principle of the proposed microwave photonic single-passband filter. In practical systems, however, frequency-stabilized laser sources with highly precise current and temperature control have to be used.

## Footnotes

This work was supported by the National Natural Science Foundation of Chinaunder Grants 61108002, 61127018, 61021003, 61177060, 61090390, 61275031, 61177080, and 60820106004. Corresponding author: N. H. Zhu (e-mail: nhzhu@semi.ac.cn).

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