Tunable multiple-passband microwave photonic filter based on external optical injected Fabry-Pérot laser

This paper proposes a tunable multiple-passband microwave photonic filter (MPF) that is incorporated with an injection-locked Fabry-Pérot (FP) laser. In the proposed MPF, multiple passbands can be easily generated based on the frequency-selection effects of the laser structure in the case of multiple light waves injection. The novelty here is that the obtained multiple-passband MPF can achieve either a dual-passband or a single-passband by using merely one experimental scheme. Moreover, since the laser injection ratio of the proposed scheme is high, the central frequency of each passband has a large tunable range. More tunable passbands can be generated by employing more external wavelengths. By finedetuning the injection parameters, the frequency tuning range of 17 GHz and the out-of-band rejection ratio of 24.1 dB are achieved for the dual-passband MPF, and the out-of-band rejection ratio of 22 dB and the 3-dB bandwidth of 360 MHz are achieved for the singlepassband MPF. In addition, the attained peak power and bandwidth of the proposed MPF are investigated with respect to the injection parameters, including detuning frequency, injection ratio and bias current of FP laser. The stability and dynamic range of the MPF are also evaluated through experiments. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Microwave photonic filter (MPF) has attracted much research attention due to the utilization of microwave photonics technologies, which offers significant advantages of electromagnetic interference immunity, broad bandwidth and low dispersion [1,2]. The MPF with high quality factor or narrow bandwidth can provide high frequency selectivity, spectral purity, resolution and bandwidth to overcome the limitations of electronic approaches [3]. Due to these advantages, the MPF is a significant component for optoelectronic oscillators (OEO) [4], microwave signal measurements [5,6] and target identification radar systems [7], etc. Recently, to meet the increasing demand for multiband or multifunction filters, many approaches have been proposed to realize multiple-passband MPFs [4,[8][9][10][11][12]. The use of MPFs can prevent multiple cascaded filters and provide promising OEO applications in the microwave photonic sensor system [4]. However, most of the multiple-passband MPFs have the fixed passbands or the limited tunable range [10][11][12].
One of the commonly used multiband MPFs is implemented using a tapped-delay-line structure with the finite impulse response (FIR) [8,13]. However, since the periodic spectral response of the FIR may lead to the spectral overlapping, the processing frequency has to be a fraction of free spectral range (FSR). If FIR is replaced by infinite impulse response (IIR), the numbers of taps will also determine the width of the passbands, the tunability is limited by the time delay and the stability is poor. Another approach to implement the MPF is based on a sliced broadband source combined with a dispersive element or a spectrum slicer, such as the standard single mode fiber or a Mach-Zehnder Interferometer (MZI) [9,14,15]. Nevertheless, since the spectrum slicer that consists of various optical components is complicated and the MZI is extremely sensitive to environment disturbances [7,9], the broadband source is not commonly used for communications [14]. In most of the approaches, the MPFs are realized by phase-shifted fiber Bragg grating (PS-FBG) or equivalent phase-shifted fiber Bragg grating (EPS-FBG) [10,16,17]. In [10], the authors convert phase-modulation (PM) into intensity-modulation (IM) through two notches at the ± 1st channels of the EPS-FBG. However, the beating note will fall out of the desired frequency because of the small spacing between the two passbands. This will cause a more limited tunable range of the multiband MPF compared with other schemes. In addition, the scheme in [3] uses a stimulated Brillouin scattering (SBS) assisted filter incorporated in the system for carrier suppression, which significantly increases the system cost and complexity. In [12,17], a dual-passband or multiple-passband MPF is proposed based on a PS-FBG or multi-channel PS-FBG, which uses two orthogonal polarized optical waves or multiple PS-FBGs to realize multiband. The corresponding performance of the frequency tuning range and the stability are restricted due to the reflection responses of the FBG. Many approaches have been proposed to map an optical filter by using the Fabry-Pérot cavity, such as the FP laser [18] and the Fabry-Perot semiconductor optical amplifier (FP-SOA) [19,20]. Both of FP laser and FP-SOA have the active cavity that can amplify multiple input optical signals, since FP cavity possesses multiple modes. However, the single optoelectronic oscillator (OEO) proposed in [18] is based on an intensity modulator and an FP laser, which has the limited frequency tunability of 4.44 GHz. In [19], the authors proposed to use two tunable lasers and an FP-SOA, by adding the microwave frequency responses with dual-wavelength injection together in their passbands, a single-passband MPF can be generated. A tunable MPF is proposed in [20], whose tunability and the number of passbands are determined by the spectrum deviation of optical carrier and two longitudinal-mode peaks. The tunability of the MPFs in [19,20] can merely be realized by adjusting the bias current of FP-SOA. Here, we aim to propose a new approach to implement the multifunctional MPF with both a single-passband and a multiplepassband. Furthermore, the proposed MPF has a wide tunable frequency range and simple structure which reduces the complexity and cost of the system.
In this paper, we propose and experimentally demonstrate a simple multiple-passband MPF with wide tunable frequency range, based on an injection-locked Fabry-Perot laser. It is designed based on the wavelength selective amplification effect of an FP laser with multiple longitudinal modes under external optical injection. The FP laser used as the slave laser, is mode-locked by the multiple modulated optical signals which couple the lightwaves from multiple tunable lasers (TL), and the lower sidebands of the modulated signals can be resonantly amplified by the multiple cavity modes. We carry out the experiments by incorporating two tunable lasers. By using the same experimental scheme, we can achieve the multiple-passband filter with either a single-passband or a dual-passband. The frequency response of the proposed MPF can be controlled by the injection parameters, including detuning frequency, injection ratio and bias current of the FP laser. In the experiment, the central frequency tuning range of each passband of 17 GHz, the out-of-band suppression of 24.1 dB, and the shape factor of the 1st passband of 2.9 can be achieved for the dual-passband MPF. The shape factor of 3.7 and the insertion loss of 22 dB are achieved for the singlepassband MPF. For the dual-passband MPF, the stability is investigated. The fluctuations of the central frequency and the magnitude of the 1st passband are within ± 29 MHz and ± 0.14 dB, and those of the 2nd passband are within ± 43 MHz and ± 0.27 dB, respectively. As far as we know, stronger injection ratio expands the locking range [18]. In the proposed scheme, the injection ratio is beyond 15 dB which is higher than other existing solutions and no device is required to amplify the optical or electronic signal. In addition, the structure is simple and compact, which is suitable for integrating on a chip.

Principle
The principle of the proposed MPF based on an optical injection-locked (OIL) Fabry-Perot laser is shown in Fig. 1(a). The solid line indicates the optical path and the dotted line indicates the electrical path. There are multiple tunable lasers named as master lasers (ML), which emit continuous wave lights into the electro-optic modulator (EOM) driven by the radio frequency (RF) signal. The polarization controllers (PC) are incorporated to adjust the polarization states between the MLs and the EOM. Taking the mth ML (ML m ) for example, the frequencies of ML m and FP laser are denoted by f ML (m) and f SL (n) (m = 1,2, …, M; n = 1, 2, 3…), respectively. The signal at point A before injection consists of a strong carrier and two sidebands ( ± 1st order) [21] as shown in Fig.  1(b). The frequency difference between the carrier (f ML (m) ) and the ± 1st order sideband (f ± 1 (m) ) is equal to the RF frequency (f RF (m) ). The EOM is connected to an FP laser via a PC and a circulator. The multi-longitudinal cavity modes of FP laser are equally spaced as shown in Fig. 1(c), with the mode spacing denoted as D m . The injection signals around the cavity modes are be amplified because of the cavity enhancement of FP resonator. This phenomenon can be usually regarded as the periodic resonant peaks centered at the red-shifted cavity modes under external injection [7,20,22]. The power spectrum of the signal at point B is shown in Fig. 1 is within the range of a gain, the FP laser will be locked by the resonantly amplified −1st order sideband when enough amplification is obtained depending on the injection parameters. When f -1 (m) equals the frequency of the red-shifted cavity mode ), the sideband will obtain the highest power close to the carrier. Only the −1st order sideband will obtain high conversion efficiency while the other sidebands cannot be affected strongly. Furthermore, the combined optical signal after FP laser which origins from the multiple ML sources can be written as , β is the phase modulation index of the EOM, J n is the nth order Bessel function of the first kind, and G(ω) represents the effective gain of the FP laser with periodic resonant peaks, as shown in Fig.  1(c). At the output of the photonic detector (PD), one gain spectrum of the FP laser is mapped to one passband. At the point C ( Fig. 1 where R is a parameter related to the responsivity and the load impedance of the PD, and the path losses and V π is the half-wave voltage of the EOM.
We further provide a detailed investigation on the tunability of these passbands. The slave laser injected by external light can be described by rate equations [23][24][25] which modify the free-running laser equation within the framework of the classic semiconductor laser theory proposed by Lamb [26] in 1965. By applying the small-signal linear approximation and stability analysis to the rate equations, it is concerned about the steady locking range which is shown as the detuning angular frequency and expressed as 2 1 , where A in and A S are the normalized and the steady-state value of electric field amplitude of the master laser, α is the linewidth enhancement factor, k inj named as the injection coupling coefficient has relation to the ratio of external optical injection to intra-cavity laser and the time that the light travels back and forth inside the cavity once time. In the literature, taking account to the injection ratio R, which defined as the injected power and the emitting power of the external cavity of the FP laser, Furthermore, derivation from [27], the central angular frequency of the mth passband (ω c (m) ) is equal to the resonance frequency between the master laser and the red-shifted cavity mode of the slave laser, namely: where g is the linear gain coefficient, N S and N th are the carrier density in steady-state and the threshold carrier just as the loss is equal to the gain, and ∆ω (m) also refers to the resonance frequency enhancement. Here we define that In Eq. (5), ω c (m) is related to ∆f (m) , R (m) and I b . The detuning frequency ∆f (m) is defined as the frequency difference between the mth master laser and the longitudinal mode of the freerunning FP laser, and the bias current makes an effect on the output power of the FP laser directly. If the aforementioned parameters can be tuned on the large scale, the multiple passbands of the proposed MPF have a wide tunability. However, due to the limitation of experimental conditions, we carried out the experiment incorporating two MLs with at most two passbands.

Experimental setup
According to the analysis given in section II, a proof-of-concept experiment shown in Fig. 2 is performed. Two lightwaves are emitted from TL1(Santac, TSL-210) and TL2(Agilent, 81989A) with output powers of 7 dBm and 8 dBm, respectively, which are limited by the instrument performances. They are coupled with PC and OC and then sent to the PM (EOspace, PM-DV5-40-PFU-PUF-LV, 40GHz, V π = 5V). By tuning PC1 and PC2, the polarization states of two input optical sources are aligned with the PM. A vector network analyzer (VNA) is used to acquire the frequency response of MPF, which can import the microwave signal into PM as well as a sweep from 0 to 50 GHz with a stable magnitude. The modulated signal is injected into the slave FP laser through an optical circulator (OC). The polarization direction of the injected light is matched with that of the FP laser using the PC3. PC3 is adjusted to align the polarization of the injection light to the FP laser. The FP laser diode is controlled by a laser diode controller (Thorlabs, LDC 205C) and a temperature controller (Thorlabs, TED 200C). The threshold current of the FP laser diode is 12mA. The output lightwave of the FP laser diode is routed by the OC and divided into two parts. 1% portion is connected to an OSA (Yokogawa, AQ6370), and 99% portion is directed to a PD (u2t XPDV2120R) for optical-to-electrical conversion. The bandwidth and the responsivity of the PD are 50 GHz and 0.65 A/W, and the frequency resolution of OSA is 0.02 nm. In our experiment, the FP laser operates in the C band, and the mode spacing D m is about 1.34 nm. The two other tunable lasers also play important roles in this experiment, that TL1 works in short wavelength range and generates a low-frequency response which composes the first passband, and similarly TL2 works in long wavelength range and generates a high-frequency response which forms the second passband. Considering the injection ratio and the detuning frequency of TL1 and TL2 according to Eq. (6) and (7), we have (1) (1) (2) (2) 1 2 , , ∆f 1 is the detuning frequency as the frequency difference between the first master laser and the first longitudinal mode of FP laser, and R 1 is the injection ratio as the power ratio between them. There is the same definition for the second master laser and the second longitudinal mode of FP laser.

Dual-passband
In the experiment, the wavelengths of two light waves from TL1 and TL2 are set at 1549.192 and 1562.730 nm, respectively. When I b = 25.14 mA, R 1 = 24.38 dB, R 2 = 18.09 dB, ∆f 1 = 16.00 GHz, and ∆f 2 = 18.90 GHz in Fig. 3 that the dual-passbands are centered at 13.3 and 20.7 GHz and the out-of-band rejection ratio is 24.1 dB better than [9,13,18]. It is proved that a stable dual-mode operation with a large suppression ratio has been achieved by OIL. By defining as the ratio of the 20-and 3-dB bandwidths, the shape factor of 2.  It shows the different frequency responses of dual-passband MPFs under the same I b of 26.40 mA in Fig. 4(a). The black solid line and the red dashed line represent the different stable-locking states by setting different ∆f and R. For both passbands, the central frequency, out-of-band suppression, and peak amplitude are significantly decreased when increasing ∆f and decreasing R at the same time. Conversely, the 3-dB bandwidth gets larger.
In addition, the corresponding optical spectrum of the first passband is shown in Fig. 4(b). The magnitude of the cavity mode labeled with the red dashed line is decreased worse because the gain spectrum reduces with ∆f and R. Here, ∆λ is defined as the wavelength difference between the master laser (λ) and the longitudinal mode of FP laser (λ FP ). Denoting ∆λ = λ-λ FP , the central frequency of the MPF response can be calculated as f c = c∆λ/λ 2 [22]. Take the 1st passband of the black solid line for an example, as λ 1 = 1549.346 nm and λ FP1 = 1549.443 nm observed in Fig. 4(b), f c1 = 12.123 GHz can be calculated by the above formula. It is close to the central peak at the frequency of 12.072 GHz measured in Fig. 4(a). Therefore, if we set ∆f and R properly, a dual-passband MPF with high gain, large out-ofband suppression ratio and wide tunability centered at the desired frequency can be achieved. The experimental results shown in Fig. 5, Fig. 6 and Fig. 7 illustrate the change regulation between the frequency response of MPF and the tunable parameters. Firstly, Fig. 5(a) shows the amplitude responses of the MPFs achieved by tuning ∆f 1 from 17.87 to 23.12 GHz, while I b = 25.14 mA, R 1 = 24.38 dB, R 2 = 18.09 dB, ∆f 2 = 19.87 GHz and the 2nd passband with a central frequency of about 19.5 GHz kept unchanged. Then, Fig. 5(b) shows the amplitude responses of the MPFs achieved by tuning ∆f 2 from 11.79 to 19.16 GHz, while I b = 25.14 mA, R 1 = 24.38 dB, R 2 = 18.09 dB, and ∆f 1 = 16.00 GHz. Moreover, the 1st passband with a central frequency of about 13.3 GHz is kept unchanged and the 2nd passband is tuned by changing the wavelength of TL2 with a tuning step of 0.006 nm. The central frequency and magnitude as a function of detuning frequency are demonstrated in Figs. 5(c) and 5(d), respectively. As shown in these figures, the central frequency increases with the increase of the detuning frequency. And according to Eq. (5), the central frequency of each passband can be increased by increasing ∆f. The measurement results agree well with the theoretical analysis and mathematical representation in section II. Meanwhile, the magnitude decreases along with the growing detuning frequency because of the out-of-band rejection ratio increment while the shape of the other passband is almost unchanged. To illustrate the independent tunability with the injection ratio of the dual-passband, when I b = 25.85 mA, R 2 = 16.46 dB, ∆f 1 = 13.10 GHz, and ∆f 2 = 15.23 GHz, we firstly fix the central frequency of the 2nd passband at 16.3 GHz and the central frequency of the 1st passband is shifted from 9.7 to 10.5 GHz by tuning R 1 from 23.44 to 18.89 dB, and the result is shown in Fig. 6(a). Then when I b = 25.72 mA, R 1 = 20.43 dB, ∆f 1 = 12.00 GHz, and ∆f 2 = 14.74 GHz, we fix the central frequency of the 1st passband at 10.1 GHz and the central frequency of the 2nd passband is tuned from 15.3 to 16.8 GHz by tuning R 2 from 18.26 to 12.82 dB, and the result is shown in Fig. 6(b). In Figs. 6(a) and 6(b), the resonance frequency and peak value both increase with the increasing injection ratio. The same principle as Fig. 5 that ω c is proportional to the external power injection ratio. Moreover, according to Eq. (4), the range of the detuning frequency or resonance frequency enhancement is increased with the increasement of injection ratio, and the maximum value expressed as ∆ω max = k inj R . So, it illustrates the trend that strong optical injection locking (R >10 dB) can broaden the stable locking range. Most of the measurement results are obtained under a large optical injection ratio, however, the external power of optical injection is in the range of −3 dB to −5 dB.     [19]. source, the pro two independ PF by two pas = 15.79 dB, ∆f 3.8 GHz, the pe n other implem e-of-merit indic , Fig. 9  By adjusting the parameters of Eq. (4) and (5), the single-passband MPF also has the tunability. In Fig. 10(a), The bias current (I b = 25.56 mA) and detuning frequency (∆f 1 = 3.57 GHz, ∆f 2 = 3.70 GHz) are unchangeable, while the larger injection ratio, the higher peak power, and the lower 3-dB bandwidth are changeable. It has been shown the regularity again that the central frequency and the magnitude of the passband are increased with the injection ratio, in accordance with Eq. (5) and similarly to the dual-passband. It is worth noting that there are two peaks in the response curves of red and blue lines, and the second peak stands for the amplification of + 1st order sideband [29]. According to the experimental results, the range edges are R 1 >13 dB and R 2 >14 dB. The generated response is tunable by controlling the bias current from 23.0 to 25.5 mA with a step of 0.5 mA as shown in Fig. 10(b). In contrast to the variation of magnitude, the resonance frequency increases with the increment of I b like Fig. 7(a). Because the bandwidth of MPF is determined by the bandwidth of the gain at one longitudinal mode of the FP laser, the 3-dB bandwidth can be reduced as increasing the bias current [20]. However, when the + 1st order sideband nears to the slave laser mode, the interaction between the two modes leads to the second peak and the central frequency decrease.

Conclusions
We have demonstrated a novel multiple-passband microwave photonic filter with wide tunable frequency based on an injection-locked Fabry-Perot laser. In our proposed MPF, due to the frequency-selection effects caused by the structure of laser under multiple optical sources, the multiple passbands can be easily generated. The experiment incorporating two TLs has demonstrated the MPF function including both dual-passband and single-passband. We discuss the variation regularity between the frequency response and the injection parameters. By adjusting these parameters, the dual-passband MPF achieves the central frequency tuning range of 17 GHz and the out-of-band suppression of 24.1 dB. The singlepassband MPF achieves the 3-dB bandwidth of 360 MHz, the shape factor of 3.7 and the insertion loss of 22 dB. In the experiment, we investigate the stability as well as the dynamic range of the dual-passband MPF, and its central and detuning frequency as a function of the injection ratio. The MPF based on injection locking has the potential for multiple microwave photonic applications such as high performance OEO, low and stable transmitters for WDM-PON and optical single-sideband modulation. We foresee continuous improvements in both bandwidth and resonance frequency when wide tunable sources are implemented, or by engineering and optimizing the slave laser for superior injection-locking performance.