## Abstract

we propose and demonstrate a bandpass microwave photonic filter (MPF) with ultrahigh stopband attenuation and skirt selectivity based on a simple signal cancellation technique. By injecting two phase modulated signals located on opposite sides of two resonant gain peaks of a Fabry-Pérot semiconductor optical amplifier (FP-SOA), two microwave frequency responses can be generated by the two input signals, respectively. The two frequency responses will add together within the passband but cancel each other out within the stopband, thus generating a MPF with simultaneous ultrahigh stopband attenuation and skirt selectivity. In the experiment the obtained MPF exhibits single passband in the range from 0 to 18 GHz and is tunable from 4 to 16 GHz by adjusting the laser wavelengths. During the tuning process the maximum stopband attenuation is 76.3 dB and the minimum 30-dB to 3-dB bandwidth shape factor is 3.5.

© 2016 Optical Society of America

## 1. Introduction

Microwave photonic filter (MPF) is a promising substitute for the traditional pure electrical filter in modern signal processing systems benefiting from its intrinsic advantages of low loss, large bandwidth, wideband tunability, good reconfigurability and immunity to electromagnetic interference (EMI) [1–3]. To be applied in a system where multiple microwave signals are processed, MPFs with single passband have been attracting great research interest. Some single-bandpass MPFs have been proposed by using the mapping technique, in which the microwave frequency response is simply the mapping of an optical filter [4–10], such as the Fabry-Pérot cavity [4], the ring resonator [5], the fiber Bragg grating (FBG) [6–8], and the stimulated Brillouin scattering (SBS) filter [9, 10]. A filter of bandpass type is basically demanded with high stopband attenuation and high skirt selectivity in practical applications. However, for the MPFs based on the mapping technique, their passband characteristics are subject to the employed optical filters, and most of the reported MPFs have a rejection ratio of no more than 40 dB and the skirt selectivity is generally low.

In order to overcome the limitation on the MPF set by the optical filter, extra signal cancellation effects have been introduced to minimize the microwave frequencies in the targeted region [11–13]. Photonic microwave notch filter with peak rejection ratio higher than 60 dB has been demonstrated by manipulating the amplitude and phase of the modulation sidebands [11, 12]. Dual cavity cancellation topology has been proposed in the operation of a photonic bandpass filter with high skirt selectivity and stopband attenuation, where two similar frequency responses are electrically subtracted in a balanced photodetection configuration [13]. Another approach to increasing the stopband attenuation and skirt selectivity of the MPF is realized by directly employing performance-elevated higher order filters with coupled cavities [14–16]. Nevertheless the performance improvement of high-order filters inevitably results in increased structural complexity.

In this paper we demonstrate a simple bandpass MPF with ultrahigh stopband attenuation and skirt selectivity based on an electro-optic phase modulator (EOPM) and a Fabry-Pérot semiconductor optical amplifier (FP-SOA). In the proposed scheme, two continuous-wave (CW) lights are modulated by the EOPM and injected into the FP-SOA. The two phase modulated lights are placed on opposite sides of two resonant peaks of the FP-SOA to be converted into intensity signals and thus two respective microwave frequency responses are generated. According to the phase-modulation to intensity-modulation (PM-IM) conversion, we can demonstrate in this paper that the two frequency responses will add together in their passbands but cancel each other out in their stopbands, producing a resultant MPF with ultrahigh rejection ratio and skirt selectivity. In the experiment the obtained MPF shows a center frequency tunable from 4 to 16 GHz, with the maximum stopband attenuation of 76.3 dB and the minimum 30-dB to 3-dB bandwidth shape factor of 3.5. To our best knowledge, this is the first report of a single bandpass MPF centered in GHz range with so high stopband attenuation and skirt selectivity.

## 2. Principle

The schematic diagram of the proposed MPF based on dual-wavelength injection is shown in Fig. 1. Two continuous-wave (CW) lights emitted from two tunable laser sources (TLS_{1} and TLS_{2}) are power adjusted by the variable optical attenuators (VOA_{1} and VOA_{2}) and polarization adjusted by the polarization controllers (PC_{1} and PC_{2}) before combined by a 50:50 optical coupler (OC). The combined CW lights are injected into an electro-optic phase modulator (EOPM) and phase modulated by the radio frequency (RF) signal emitted by the vector network analyser (VNA). Then the two phase modulated signals are polarization adjusted by the third PC (PC_{3}) before launched into a FP-SOA via an optical circulator (CIR). The processed optical signal output from the FP-SOA experiences optical-to-electrical conversion through a high speed photodiode (PD). The filter response is measured by the VNA.

Firstly, when only TLS_{1} is turned on and the CW light emitted by TLS_{1} is modulated by the EOPM under small signal modulation, the corresponding phase modulated signal can be written as

_{1}and the modulating RF signal from the VNA, respectively.

Subsequently the phase modulated optical signal is injected into the FP-SOA. The FP-SOA can be considered as a traditional SOA with two reflective facets. The reflectivity of the input and output facets, the gain factor, the effective refractive index, and the cavity length of the FP-SOA are denoted as$R$,$G$,${n}_{eff}$and$L$, respectively. Then, we will derive the gain and phase spectra of the FP-SOA. When the input optical field with angular frequency of${\omega}_{o}$is defined as${E}_{in}({\omega}_{o})$, the optical beam output from the FP-SOA after reflected by the FP cavity for k times can be expressed as

With Eq. (3) the amplitude transmission spectrum$G({\omega}_{o})$and the phase transmission spectrum$\phi ({\omega}_{o})$of the FP-SOA are expressed as

Therefore by combing Eqs. (1), (4) and (5), the output optical signal${E}_{out,1}(t)$from the FP-SOA can be derived as

When${E}_{out,1}(t)$is applied to the PD, the corresponding RF current${I}_{1}(t)$after the PD satisfies

Secondly, when only TLS_{2} is turned on and the emitted power is adjusted at the same level as TLS_{1}, similar to Eq. (7), we can obtain the corresponding recovered RF current${I}_{2}(t)$after the PD as

_{2}.

Finally, when TLS_{1} and TLS_{2} are simultaneously turned on, the RF current after the PD will be the summation of the two photocurrents${I}_{1}(t)$and${I}_{2}(t)$under incoherent operation of the light waves from TLS_{1} and TLS_{2}

To provide a more intuitive illustration of the wavelength relationship between the input phase-modulated signals and the resonant gain peaks of the FP-SOA, the amplitude and phase transmission properties of the FP-SOA are plotted in Fig. 2 based on Eqs. (4) and (5) respectively. The two phase modulated optical input signals are also displayed in Fig. 2 with the two optical carrier wavelengths denoted as λ_{1} and λ_{2}. According to the employed FP-SOA in the experiment, the$R$,$G$,${n}_{eff}$and$L$of the FP-SOA are set at 0.3, 11, 3.5 and 1171 μm, respectively in the simulation. Note that within each resonant peak of the FP-SOA there is a phase jump of π, which is critical in the proposed MPF for the stopband attenuation and skirt selectivity improvement. In order to introduce effective signal cancellation between the two frequency responses, one carrier wavelength must be located on the left side of a FP-SOA resonant peak while the other wavelength must be located on the right side of a FP-SOA resonant peak. To generate a MPF centered at 6 GHz, the wavelength of the CW light emitted from TLS_{1} is set at 1544.51 nm and located on the left side of the FP-SOA resonant peak centered at 1544.56 nm. The wavelength of the CW light emitted from TLS_{2} is set at 1545.78 nm and placed on the right side of another FP-SOA resonant peak centered at 1545.73 nm. It should be indicated that in order to avoid severe competition in the carrier consumption between λ_{1} and λ_{2}, the wavelength separation must be set large enough [17]. In the simulation, a wavelength separation of about 1 nm is selected.

When the two phase modulated signals are located on the opposite slopes of their nearest resonant peaks symmetrically as shown in Fig. 2, we can have the approximations that$\sqrt{G({\omega}_{1})}\approx \sqrt{G({\omega}_{2})}$, $\sqrt{G({\omega}_{1}-{\omega}_{m})}\approx \sqrt{G({\omega}_{2}+{\omega}_{m})}$and$\sqrt{G({\omega}_{1}+{\omega}_{m})}\approx \sqrt{G({\omega}_{2}-{\omega}_{m})}$. The modulation sidebands will experience selective amplification, which means

Resultantly Eq. (9) can be further simplified as

Figure 3 shows the calculated microwave frequency response with dual-wavelength injection (λ_{1} and λ_{2}) based on Eq. (9). The calculated microwave frequency responses when λ_{1} and λ_{2} are injected into the FP-SOA separately are also plotted for comparison based on Eq. (7) and Eq. (8) respectively. For the sake of clarity the generated MPF when λ_{1}, λ_{2} and both λ_{1} and λ_{2} are injected into the FP-SOA are denoted as MPF_{1}, MPF_{2} and MPF_{1+2}, respectively. In the case of single-wavelength injection, the filter passband center is determined by the frequency separation between the optical carrier and the adjacent resonant gain peak of the FP-SOA. The filter passband shape is determined by the shape of the corresponding resonant peak. From Fig. 3(a) it can be observed that for the microwave frequencies outside of the filter passband, there exists a phase difference of π between MPF_{1} and MPF_{2}. This is because MPF_{1} is generated by the beating between the 1st-order lower modulation sideband and the optical carrier while MPF_{2} is generated by the beating between the 1st-order upper modulation sideband and the optical carrier. However for the frequencies within the filter passband, as shown in the inset, the phase difference is reduced from π to smaller values due to the phase jump within the FP-SOA resonant peak and the slight center frequency separation between MPF_{1} and MPF_{2}. Thus, the subtraction between MPF_{1} and MPF_{2} in the microwave stopband is changed to partial summation. When the phase difference is reduced to 0, the fully summation between MPF_{1} and MPF_{2} is realized. The inset of Fig. 3(a) demonstrates the phase variation detail in a span of 1 GHz around the filter center, from which we can see that the phase difference between MPF_{1} and MPF_{2} reduces from π to smaller values in the microwave passband. Consequently, as shown in Fig. 3(b), in the case of dual-wavelength injection, the amplitude response of MPF_{1+2} is the subtraction of MPF_{1} and MPF_{2} outside the passband but is fully or partially the summation of MPF_{1} and MPF_{2} within the passband. The inset of Fig. 3(b) shows the amplitude response detail in a span of 1 GHz around the filter center, and it shows that the amplitude response of MPF_{1+2} is the combination of MPF_{1} and MPF_{2} in this area. Compared with MPF_{1} and MPF_{2}, the stopband attenuation of MPF_{1+2} is increased from 36 dB to 86 dB and the shape factor is reduced from 33.5 to 6.0. The passband shape factor represents the filter skirt selectivity and is defined as the ratio of 30-dB to 3-dB bandwidth in this paper. The effectiveness of the dual-wavelength scheme to elevate the stopband attenuation and skirt selectivity of the bandpass microwave frequency response is thus theoretically verified.

## 3. Experimental results and discussion

Based on the experimental setup shown in Fig. 1, the effectiveness of the proposed scheme is experimentally investigated. The bias current of the FP-SOA is adjusted at 87.75 mA and the operating temperature is controlled at 25°C during the experiment. The optical power of the two phase modulated signals at the input of the FP-SOA are controlled at the same level of −10 dBm by adjusting VOA_{1} and VOA_{2}. In order to achieve a bandpass MPF centered at 6 GHz, the two optical carriers are set at 1544.376 and 1545.640 nm, respectively, so that both wavelengths are about 0.05 nm away from their neighbouring resonant peaks of the FP-SOA. The output optical spectrum from the FP-SOA is measured by an optical spectrum analyser (OSA, Yokogawa AQ6370C) with the resolution bandwidth (RBW) set at 0.02 nm. The corresponding filter response is measured by the VNA (Anritsu MS4647B).

Figures 4(a)-(c) plot the measured optical spectra before the PD when λ_{1}, λ_{2} and both λ_{1} and λ_{2} are injected into the FP-SOA, respectively. It should be noted that the ASE resonant peaks of the FP-SOA are not equal to each other due to the unequal gain spectrum of the SOA and the unequal reflective spectrum of the cavity facets. The ASE resonant peak of the FP-SOA near λ_{1} is naturally higher than that near λ_{2}. The resultant MPF responses are shown in Figs. 4(d)-4(f) accordingly. It can be observed that the microwave frequency response with single-wavelength injection in Fig. 4(d) is similar to that in Fig. 4(e) because the two microwave frequency responses are mapped from the resonant peaks of the same FP-SOA. The difference between the stopband attenuation of MPF_{1} and MPF_{2} is due to the different optical rejection ratios of the corresponding FP-SOA resonant peaks nearest to the input optical carriers. Due to the cancellation process between MPF_{1} and MPF_{2}, the stopband of MPF_{1+2} rapidly drops off. In the experiment, the stopband attenuations of MPF_{1} and MPF_{2} are 48.5 dB and 40.0 dB, respectively. However, for MPF_{1+2}, the stopband attenuation is dramatically increased to 76.3 dB. The peak of MPF_{1+2} is only about −20 dB as the optical powers of the two phase modulated signals injected into the FP-SOA are intentionally attenuated to a relatively low level to ensure they will be linearly amplified by the FP-SOA. The limited conversion efficiency of modulator and the photodetector also contribute to the insertion loss. The insertion loss of the proposed MPF could be lowered by cascading a proper optical amplifier after the FP-SOA. It should be noted that the transfer function of the FP-SOA is periodic and the FP-SOA employed in our experiment exhibits a free spectral range (FSR) of about 36.6 GHz. The obtained MPF is of single passband within the range from 0 to 18.3 GHz, which is equal to FSR/2 of the FP-SOA. If a single-bandpass MPF with larger operation bandwidth is needed, a FP-SOA with shorter cavity can be employed. The noise spikes at the bottom is the beat noise when the remained amplified spontaneous emission (ASE) noise output from the FP-SOA is injected into the PD. Employing a FP-SOA with much larger FSR should be able to mitigate such noise. Further depression of the beat noise induced by the ASE of the FP-SOA need deeper investigation of the optimization of the FP-SOA.

Figure 5 shows the enlarged filter passbands of MPF_{1}, MPF_{2} and MPF_{1+2} presented in Fig. 4 (d), (e) and (f), respectively. It can be observed that the shape factors of MPF_{1} and MPF_{2} are 21.0 and 29.1, respectively. However the shape factor of MPF_{1+2} is dramatically decreased to 7.1 due to the cancellation effect. The shape factor of MPF_{1+2} could be further improved by optimizing the optical power and the polarization states of λ_{1} and λ_{2}. Obviously the passband of MPF_{1+2} is the summation of the passbands of MPF_{1} and MPF_{2} and the center frequency of MPF_{1+2} equals to the mean value of the center frequencies of MPF_{1} and MPF_{2}. Therefore, the specific passband shape of MPF_{1+2} could be fine tuned by slightly altering the center frequencies of MPF_{1} and MPF_{2} without altering the passband center. According to the wavelength relationship between the input phase-modulated signals and the resonant gain peaks of the FP-SOA, the center frequencies of MPF_{1} and MPF_{2} can be conveniently tuned by shifting the gain spectrum of the FP-SOA via altering the bias current of the FP-SOA. In consideration of the flatness of the passband top, the frequency separation between the centers of MPF_{1} and MPF_{2} should not be too large.

The center frequency of MPF_{1+2} is tunable by simultaneously adjusting the wavelengths of TLS_{1} and TLS_{2}. Figure 6 shows the superimposed frequency responses of MPF_{1+2} when the center frequency is tuned at 4,6,8,10,12,14 and 16 GHz, respectively. During the tuning process, the 3-dB bandwidth of MPF_{1+2} is around 139.3 MHz. The major limitation of the proposed MPF brought by the using of two independent TLSs as the light source is the inconsistency of the MPF’s 3-dB bandwidth when the filter center is tuned as shown in Fig. 6. Each time when the center frequency of the MPF is supposed to be changed, the wavelengths of the two independent TLSs are required to be altered by the same value towards opposite directions. However, limited by the wavelength tuning resolution of the TLSs, it is hard to make the wavelength alteration value of the two independent TLSs to be exactly the same, which will result in the variation of the 3-dB bandwidth of the proposed MPF. This problem can be solved by applying laser sources with continuous wavelength tunability.

When the center frequency is tuned from 4 to 16 GHz, the stopband attenuation of MPF_{1+2} varies between 61.0 dB to 76.3 dB and the 30-dB to 3-dB bandwidth shape factor varies between 3.5 and 9.7, respectively. The specific values of the corresponding stopband attenuation and the shape factor are shown in Fig. 7. Variations in the stopband attenuation and the shape factor of MPF_{1+2} are mainly attributed to the polarization state fluctuations of the two phase modulated signals. This problem can be solved by employing polarization maintaining fibers or applying polarization-independent devices.

## 4. Conclusion

We have presented a simple dual-wavelength injection technique to increase the stopband attenuation and skirt selectivity of a bandpass MPF. The key point is that when two input phase modulated signals are placed on opposite sides of two resonant peaks of a same FP-SOA respectively, the two corresponding microwave frequency responses will cancel each other out within their stopband and add together within their passband. Therefore a MPF with simultaneous ultrahigh stopband attenuation and skirt selectivity is achieved. In the experiment the obtained MPF exhibits single passband in the range from 0 to 18 GHz. While the center frequency of the MPF is tuned from 4 to 16 GHz, the stopband attenuation and the 30-dB to 3-dB bandwidth shape factor are averaged to be 66.1 dB and 6.0, respectively. Additionally the proposed topology has the potential to be monolithically integrated based on the InP/InGaAsP platform.

## Funding

The work is partially supported by the National Science Fund for Distinguished Young Scholars (61125501); Foundation for Innovative Research Groups of the Natural Science Foundation of Hubei Province (G2014CFA004); National Natural Science Foundation of China (NSFC) (61501194); Natural Science Foundation of Hubei Province (2015CFB231); Fundamental Research Funds for the Central Universities (HUST: 2016YXMS025); Director Fund of WNLO.

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