Mitigation of Dispersion Induced Impairments in Brillouin-Based Microwave Photonic Bandpass Filter

—Interference based microwave photonic bandpass ﬁl-ters (MPBF) form an important component of modern RF signal processing. Presence of multiple optical components in an RF photonic system e.g. ﬁber ampliﬁers, waveguides, cause a degradation intheMPBFproﬁleandtheout-of-bandrejectionduetothedisper-sioninducedphaseshift.Here,wecomparetheperformance,using simulationsandexperiments,oftwointerferencebasedMPBFconﬁgurations:(i)double-sidebandphasemodulation(DSB-PM) and(ii)double-sidebandintensitymodulation(DSB-IM),whichexploitstimulatedBrillouinscattering(SBS)forsidebandpro-cessing,underdifferentdispersionconditions.Whiletheproﬁleandout-of-bandrejectionfortheDSB-PMbasedMPBFdegrade drasticallyundertheeffectofdispersion,DSB-IMbasedMPBFachievesanout-of-bandrejectionof > 40 dB and maintain the 3 dB and 20 dB bandwidths of 16.7 ± 0.4 MHz and 104.5 ± 5.4 MHz, respectively, under different dispersion conditions. The DSB-IM based MPBF exploits the bias dependent phase of the modulation sidebands of a z-cut intensity modulator to mitigate the dispersion induced impairment. The use of an intensity modulator for dispersion compensation makes our approach dynamic and compatible with integrated microwave photonic systems.


I. INTRODUCTION
I NTERFERENCE based photonic processing of radiofrequency (RF) signals has emerged as a potential technique for developing applications such as phase manipulation, RF filtering, true-time delay, and sensing [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. However, dispersion induced phase shift severely impacts the overall performance of interference-based microwave photonic systems [16], [17]. In long-distance fibre optic links and other microwave photonic systems, which are designed to operate over a wide RF frequency spectrum, the severity of dispersion induced effects increases with frequency [18], [19], [20], [21]. Various techniques have been proposed and demonstrated to compensate dispersion in- duced impairments in microwave photonic systems [16], [18], [22], [23], [24], [25], [26], [27], [28], [29], [30]. Among different signal processing tasks, interference-based microwave photonic bandpass filter (MPBF) is one of the well-developed branch that can deliver better performance compared to an electronic bandpass filter [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. High frequency selectivity, large out-of-band rejection, wide operational bandwidth, bandwidth reconfigurabilty, and immunity from electromagnetic interference makes them a suitable candidate for various real-world applications such as RADAR, RF communication, electronic warfare and sensing. The destructive interference between the π phase shifted RF signals at out-of-band frequency regions is the key factor determining filter selectivity in such MPBFs. Because interference-based MPBFs rely heavily on the π phase shift, any deviation in this condition reduces the effective out-of-band rejection dramatically. When modulated signals travel through a dispersive medium, they experience dispersion induced phase shift before reaching a photodetector. The contribution of dispersion-induced phase shift, therefore, disturbs the condition for destructive interference, which causes a distortion in the filter shape and a reduction in the magnitude of the out-of-band rejection. For many applications, such as ground radar systems for detecting moving objects, it is essential to eliminate clutter, noise, and unwanted interferers while selectively retaining the signal from the moving target [2]. Dispersion induced degradation of out-of-band rejection of a MPBF will therefore reduce the suppression of the undesirable signals compared to the intended signal. In addition to the value of the dispersion parameter, the operating frequency of the filter plays a significant role in the resulting phase shift. As a result, the dispersion-induced phase contribution of photonic components cannot be ignored in MPBF systems. While it is difficult to completely eliminate the dispersion induced by transmission fiber, fiber amplifiers, and other photonic components used in a photonic link, the use of a photonic chip, instead of fiber, as the SBS medium may help in reducing the dispersion induced by the Brillouin medium. However, the extremely small effective mode area of a photonic chip may result in large group-velocity dispersion (GVD) parameter D [16], [41]. Since the effect of dispersion depends on the product of D and the device length L, it is important to minimize the L × D product. Recently, dispersion engineered chalcogenide waveguide-based photonic circuits with L × D ∼1.74x10 −3 ps/nm [42] have been demonstrated. Use of these photonic chips as the SBS medium, therefore, helps in reducing the degradation of the out-of-band rejection of the MPBF.
Mitigation of dispersion induced impairments due to transmission fiber and other photonic components is still necessary to realize efficient, large out-of-band rejection MPBFs. However, there have been very few reports of dispersion compensation in MPBFs [35], [43], [44].
Here, we demonstrate mitigation of dispersion induced impairments in Brillouin-based MPBF by exploiting the bias dependent phase shift in a z-cut intensity modulator. We compare the performance of an interference-based MPBF exploiting double sideband phase modulation (DSB-PM) with a double sideband intensity modulation based MPBF (DSB-IM), where a z-cut intensity modulator is used. To study the effect of dispersion induced impairments, we tune the dispersion induced phase by introducing single-mode fibers (SMFs) of different lengths as well as operating the MPBF at different radio frequencies. For both, the DSB-PM and DSB-IM configuration, we process one modulation sideband with stimualted Brillouin scattering (SBS) gain. For a DSB-PM MPBF, presence of dispersion induced phase disturbs the condition for destructive interference far away from the MPBF center frequency, which results in a degradation of the filter profile and out-of-band rejection. For the DSB-IM MPBF, we exploit the bias-dependent phase of the modulation sidebands of a z-cut intensity modulator to achieve a symmetric MPBF profile with an out-of-band rejection of > 40 dB under different dispersion conditions, demonstrating mitigation of dispersion induced impairments. The 3 dB and 20 dB bandwidth of filter are 16.7± 0.4 MHz and 104.5 ± 5.4 MHz respectively. Fig. 1(a) shows a typical microwave photonic (MWP) link that consists of a laser, RF modulation, transmission, photonic processing, and detection of the radio frequency signal. Transmission of a modulated optical signal through an optical fiber and other stages affect the overall link performance due to dispersion induced impairments and degradation of link parameters such as signal-to-noise ratio (SNR), noise figure, and link gain. Effects of RF link on the SNR, RF gain, and noise figure of microwave photonic filters have been studied and ways to improve these using optimal placing of RF and optical amplifiers and different modulation parameters have been suggested [14], [32], [34], [40]. The use of extra optical amplifiers for improving SNR, link gain and other parameters induce additional dispersion due to fiber amplifiers and other components [16]. In this work, we study dispersion induced degradation of a MWP bandpass filter response using two different modulation schemes (i) Phase modulation, (ii) Intensity modulation using a z-cut modulator and demonstrate mitigation of it.

B. MPBF Based on Phase Modulation
Phase modulation (PM) of a laser carrier of frequency ω c with a radio frequency signal Ω RF generates two out-of-phase sidebands at ω c − Ω RF and ω c + Ω RF , as shown in Fig. 1(b) (i). The optical field at the output of a phase modulator is given by [39], Here, J n (.) represent the first kind Bessel function of order n with n = 0, ±1. Parameter m represents the modulation index.
Since the sidebands generated through phase modulation have equal amplitudes and π phase shift between them, the radio frequency (RF) signals obtained from beating of the sidebands with the carrier undergo destructive interference to cancel out each other on photodetection. Creating an amplitude imbalance at a desired frequency region can generate a pass band response at frequencies for which the condition for destructive interference is not met. For stimulated Brillouin scattering (SBS) based interference MPBFs, application of narrow band Brillouin gain to one of the sidebands, using a pump (ω p ), creates an amplitude imbalance between the sidebands (see Fig. 1(b) (ii)). Resulting optical field is then expressed as: where the spectral profile for the Brillouin gain is given as [37], [45], Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. and the corresponding phase response is given by [37], [45] φ sbs (ω c + Ω RF ) = g Here, Ω B and Γ B are the Brillouin resonance frequency and full-width at half-maximum (FWHM) bandwidth of the gain profile, respectively. For a given pump power P p , the Brillouin gain exponent (g) at the resonance frequency is g = , where g B is the Brillouin gain coefficient, and L ef f and A ef f are the effective length of the Brillouin active medium and mode area, respectively. The dispersion induced phase shift where D, λ c , and c are dispersion coefficient, carrier wavelength, and speed of light, respectively, arises as the phase modulated signal propagate through different components of an RF photonic system [16]. For example, for a standard single mode fiber (SMF) D = 17 ps/nm-km at 1550 nm. Besides the dispersion parameter D, the value of φ D depends on the square of the modulation frequency Ω RF , which causes large dispersion induced impairment at higher radio frequencies.
For an interference based MPBF exploiting Brillouin gain and phase modulation, the RF power at the photodetector is given as: where K depends on the photodetector responsivity, load resistance, and modulation index [39]. Since one of the modulation sidebands is processed with the Brillouin gain (5), the condition for destructive interference is disturbed in the vicinity of the gain resonance due to an amplitude imbalance between the sidebands and the deviation of the phase difference from π, which enables creation of a passband. Far from the Brillouin gain resonance, where the sidebands have equal amplitudes i.e. |G(ω c + Ω RF )| ∼ 1 and φ sbs ∼ 0, a large out-of-band rejection occurs in the absence of dispersion (φ D = 0) (see (5)). However, the presence of frequency dependent dispersion induced phase φ D in real systems causes the phase difference between the interfering signals to differ from π, which results in an asymmetric filter response with reduced out-of-band rejection.

C. MPBF Based on DSB-IM
In the previous section, we have seen that a double sideband phase modulation (DSB-PM) based MPBF is highly prone to dispersion effects. Mitigation of dispersion induced impairments is, therefore, important to maintain the consistency of filter performance under different dispersion conditions. Here, we exploit the bias dependence of the phase shift experienced by the modulation sidebands of a z-cut intensity modulator (IM) to compensate φ D and achieve π phase difference between the interfering signals as in Fig. 1(b) (iii). A z-cut intensity modulator employs an asymmetrical design that provides higher modulation efficiency (Low half voltage) and better voltage control over the sideband phase compared to an x-cut intensity modulator. We call the bandpass filter with double sideband intensity modulation as DSB-IM based MPBF. The working principle remains the same as that of the DSB-PM based MPBF except the introduction of a bias dependent phase shift tan −1 α. The optical filed at the output of a z-cut IM is given as [46], where m = m 2 − m 1 , m 1 and m 2 are modulation parameters in the two arms of IM.
where φ 01,02 are the bias induced phase in the two arms of the modulator. The bias voltage dependent parameter α is defined as α = − m 1 +m 2 m 1 −m 2 cotΔφ 0 . The bias induced phase tan −1 α can therefore take values between [0, 2π] [47]. Further, one sideband of the modulated signal is processed with the SBS gain using a Brillouin pump as shown in Fig. 1(b) (iv). Electric field after Brillouin processing is given as, The RF power after photodetection is given according to: Where the phase response of the MPBF is, Here, I 0 = |E 0 | 2 , R and are the load resistance and responsivity of the photodetedtor. The out-of-band rejection of the MPBF is determined by the overall phase shift φ DSB−IM MP BF , which is the phase difference between the two sidebands shown in Fig. 1(b) (iv). By varying the bias voltage, the α parameter can be tuned to a value such that φ DSB−IM MP BF ∼ π over a wide frequency range around the filter frequency, even in the presence of dispersion, which leads to a large out of band rejection and consistent filter profile at different radio frequencies.

III. SIMULATION RESULTS
We perform a simulation study to demonstrate the effect of dispersion induced impairments on different MPBF configurations and its mitigation using DSB-IM. Fig. 2 shows the effect of dispersion induced phase shift on DSB-PM-based MPBFs. Fig. 2(a) shows the MPBF response (dotted blue) in the absence of dispersion D = DL = 0. Here, D' is the total amount of dispersion, which is defined as D × L, where D is the groupvelocity dispersion parameter and L is the length of the extra fiber introduced to tune dispersion. Fig. 2(a) also shows the  amplitude response for individual modulation sidebands. The solid black line shows the amplitude response of the upper sideband (S usb RF ), which is processed with 20 dB of Brillouin gain, whereas the green dotted line shows the amplitude response of the unprocessed lower sideband (S lsb RF ). Outside the Brillouin gain resonance, the out-of-phase RF signals (see inset Fig. 2(a)) of equal amplitudes undergo destructive interference, which results in an MPBF response with large out-of-band rejection (S F ilter RF : Dotted blue). To study the effect of dispersion on the MPBF response at the radio frequency of 10 GHz, we increase the dispersion value to D = 42.5 ps/nm (see Fig. 2(b)) by introducing an extra length of SMF before the SBS medium, which consists of a 500 m long SMF in our experiments, in the probe path. Due to the dispersion-induced phase, the overall phase shift outside the Brillouin gain profile deviates from π, which leads to an asymmetric filter response and causes the appearance of a dip in the filter profile as the phase shift approaches π. The out-of-band rejection is reduced by 17 dB as shown in Fig. 2(b). The phase response plotted in the inset of Fig. 2(b) clearly shows that the phase difference is far from π for frequencies higher than the filter frequency ω MP BF , whereas, for frequencies smaller than ω MP BF , the phase value approaches π at the frequency where a dip appears in the MPBF response ( Fig. 2(b)). To show the effect of operating frequency, we simulate the filter response at a higher radio frequency (35 GHz) while keeping the dispersion value at D = 25.5 ps/nm. The filter shows an asymmetric filter response with a 29.7 dB reduction in the out-of-band rejection, as shown in (see Fig 2(c)). The simulation results in Fig. 2(a)-(c) show that the performance of a DSB-PM based MPBF is prone to dispersion induced impairments. The MPBF response shows a drastic reduction in the out-of-band rejection and degradation of filter profile with an increase in the operating frequency and/or amount of dispersion. Compensating the dispersion induced phase shift is, therefore, necessary for real-world applications. Fig. 3 shows the simulation results for a DSB-IM based MPBF. We use (8) and (9) to obtain the amplitude and phase response, respectively. The simulations are performed under the same dispersion conditions that are used for DSB-PM based MPBF. Fig. 3(a) show the simulation results for a DSB-IM Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
based MPBF in the absence of dispersion. The upper sideband is processed with 20 dB of Brillouin gain (S usb RF , solid black line in Fig. 3(a)), same as used in DSB-PM configuration, and the lower sideband is kept unprocessed (S lsb RF , dotted green line in Fig. 3(a)). The value of the α parameter is choosen in such a way that outside the Brillouin resonance the overall phase shift is ∼ π, as shown in the inset of the Fig. 3(a). The radio frequency signals obtained from beating of the carrier with the modulation sidebands, therefore, destructively interfere to create a large out-of-band rejection outside the Brillouin resonance (S F ilter RF , dotted blue line in Fig. 3(a)). The corresponding phase response, plotted in the inset of Fig. 3(a), clearly shows that a ∼ π phase difference is achieved on both sides of the filter frequency.
To demonstrate the mitigation of dispersion induced impairment at a fixed radio frequency of 10 GHz, we increase the total dispersion value D to 42.5 ps/nm. In the presence of dispersion, the filter response becomes asymmetric with drastic reduction in the out-of-band rejection (see dotted red line Fig. 3(b)) compared to the filter response (dotted blue Fig. 3(a)) for D = 0 ps/nm. To compensate the dispersion induced phase shift φ D , we tune the α parameter to vary the bias dependent phase shift tan −1 α and regain the same phase profile (see blue solid inset Fig. 3(b)), as shown in the inset of Fig. 3(a) for the dispersionless case. Using tan −1 α = 83.818 • , we regained the symmetric MPBF response with an out-of-band rejection of > 40 dB (see solid blue in Fig. 3(b)). The phase response before (dotted red line) and after (solid blue line) the compensation of φ D are shown in the inset of Fig. 3(b). To study the mitigation of dispersion induced impairments at higher radio frequencies, the filter operating frequency was tuned to 35 GHz while keeping D = 25.5 ps/nm. The filter experiences a significant reduction in the out-of-band rejection compared to the dispersionless case shown in Fig. 3(a). Fig. 3(c) shows the amplitude and phase (inset) response of the filter before (dotted red line) and after (solid blue line) compensating the dispersion effects. Tuning the value of the α parameter helps in realizing an MPBF with symmetric filter profile and large out-of-band rejection.
Our simulation results clearly show that by choosing appropriate values for the bias voltage dependent α parameter, effect of dispersion can be mitigated for a DSB-IM MPBF. For a phase modulation based MPBF, the phase difference between the modulation sidebands is fixed at π and, therefore, dispersion compensation is not possible without using an extra dispersion compensation module. Fig. 4 shows the experimental setup for studying dispersion induced degradation in DSB-PM and DSB-IM based MPBFs. In both cases the setup is similar except the modulator, which is used to generate the sidebands. In the lower arm of the setup, a narrow linewidth laser (NLL) is modulated using the RF signal from a vector network analyser (VNA) to generate the upper and lower modulation sidebands. In the DSB-PM approach, a phase modulator (PM) is used to create two out-of-phase modulation sidebands, whereas, in the DSB-IM configuration, the PM is replaced by a DC voltage biased z-cut intensity modulator. For a z-cut IM, the relative phase difference between the sidebands, with respect to the carrier, can be controlled using the bias voltage from a DC voltage source. The output signal from the modulator acts as an optical probe, which is further amplified using a low-noise erbuim doped fiber amplifier (EDFA). The Brillouin pump is generated in the upper arm using light from a tunable narrow linewidth laser (TNL). The frequency of the TNL is upshifted from the upper modulation probe sideband by the Brillouin resonance frequency Ω B . The optical pump is further amplified using a high power EDFA. Both the pump and the probe signals are allowed to counter propagate through a 500 m long SMF, which acts as the SBS gain medium, using circulators C2 and C1. As a result the upper sideband experiences a Brillouin gain, and the processed probe signal is collected at port 3 of circulator C2. Using the polarization controllers PC1 and PC3 the Brillouin gain is maximized. The signal is down converted using a high bandwidth photodetector and the filter responses is observed on the VNA. To introduce different amounts of dispersion, SMF with different lengths (L) are added before the circulator C1. We used a Brillouin gain of ∼20 dB in all experimental studies. Fig. 5(a)-(c) show the filter response for the DSB-PM based MPBF under different dispersion conditions. The filter response in Fig. 5(a) is obtained when no extra fiber was added except the 500 m long SMF, which is used as the SBS gain medium. The DSB-PM based MPBF in Fig. 5(a) achieves an out-of-band rejection of ∼33.8 dB. We attribute the asymmetry in the filter response in Fig. 5(a) to dispersion associated with components in the MPBF setup, which modify the π phase shift between the two sidebands. To increase the amount of dispersion, 2 km and 5 km long SMFs are introduced before the circulator C1. As the fiber length increases, the filter response shows a drastic reduction in the out-of-band rejection and degradation of the filter profile. For the SMF lengths of 2 km and 5 km, the out-ofband rejection reduced to ∼20.6 dB (Fig. 5(b)) and ∼15.8 dB (Fig. 5(c)), respectively, from the case where no extra fiber was used (Fig. 5(a)). For L = 5 km, increasing the operating frequency to 35 GHz increases the dispersion induced phase shift further, which causes a shift of the dip position to the lower frequency side (see Fig. 5(d)).   When no extra fiber was added before circulator C1, we achieve a symmetric MPBF profile with an out-of-band rejection of ∼43.8 dB by tuning the bias voltage to V b = 1.350 V (see Fig. 6(a)). For V b = 1.350 V, when SMFs of lengths 2 km and 5 km are added, the out-of-rejection reduced to 25.1 dB and 19.73 dB respectively. Further, the filter profile at 11 GHz becomes asymmetric (see solid red Fig. 6(b), (c)), as observed for the DSB-PM configuration, and shows a dip at the higher frequency side of the MPBF profile. To demonstrate the mitigation of dispersion induced degradation of the DSB-IM MPBF response, we tune the bias voltage to 1.520 V and 1.841 V for L = 2 km and L = 5 km cases, respectively, to vary the bias dependent phase and regain the symmetric filter profile and achieve large out-of-band rejection (solid blue lines Fig. 6(b), (c)). To demonstrate the compensation of dispersion induced impairment at higher radio frequencies, the filter response is obtained at a radio frequency of 35 GHz while keeping the bias voltage at 1.350 V, the same as in Fig. 6(a), and using additional SMF length of L = 5 km. Fig. 6(d) plots the uncompensated (solid red) and dispersion-compensated (solid blue) MPBF response at 35 GHz. The uncompensated MPBF response shows a dip on the lower frequency side of the filter response showing that the dispersion induced phase shifts the condition for destructive interference to the lower frequency side of the MPBF response. Further, the dispersion induced phase reduces the out-of-band rejection to < 20 dB. To demonstrate the dispersion compensation of the filter response at 35 GHz, we tune the bias voltage to achieve a symmetric MPBF profile with large out-of-band rejection (∼47.4 dB) at V b = 4.247 V. From Figs. 3 and 6, we note that the measured dispersion compensated MPBF profiles are consistent with the simulated profiles and achieve an out-of-band rejection similar to predicted from simulations. The simulations are performed by only considering the dispersion induced by different SMF lengths. However, during the experiment, there are contributions from other components to net link dispersion. As a result, the dip positions for the uncompensated MPBF profiles vary in simulations and experiments. The experimental results show that a DSB-IM based MPBF allows mitigation of dispersion induced degradation of the filter response simply by tuning the bias voltage of the intensity modulator.

IV. EXPERIMENTAL SETUP AND RESULTS
To compare the performance of DSB-PM and DSB-IM based MPBF techniques under different dispersion conditions, we measure the out-of-band rejection of the MPBF profiles at a radio frequency of 11 GHz when different SMF lengths (L = 0 km, 0.5 km, 2 km, 3 km, and 5 km) are introduced before the circulator C1 and plotted it in Fig. 7. PM-based MPBF shows ∼17.7 dB reduction in the out-of-band rejection when L is varied from 0 km to 5 km. In the case of DSB-IM, the filter maintained an out-of-band rejection of 48.85 ± 4 dB for all the SMF lengths through bias voltage control. Overall, the DSB-IM based MPBF shows out-of-band rejection of >40 dB and maintains 3 dB and 20 dB bandwidths of 16.7 ± 0.4 MHz and 104.5 ± 5.4 MHz, respectively, under different dispersion conditions. This study explicitly shows that an IM-based MPBF enables mitigation of dispersion induced impairments through control of the bias induced phase shift and helps in realizing a consistent filter profile and out-of-band rejection under different dispersion conditions.

V. DISCUSSION AND CONCLUSIONS
Wide operational bandwidth and large out-of-band rejection are considered as the important advantages of MPBFs. However, maintaining a large out-of-band rejection and a consistent filter profile under different operating conditions is restricted by dispersion induced impairments. It is, therefore, important to mitigate the dispersion induced impairments for real life applications. In this paper we demonstrated mitigation of dispersion induced impairments in MPBF based on double sideband intensity modulation and stimulated Brillouin scattering exploiting the bias induced phase shift in a z-cut intensity modulator. The results are compared with the DSB-PM based MPBF scheme. The comparison explicitly shows that, as operating frequency or amount of dispersion increases, the out-of-band rejection in PM-based MPBF drastically reduces while an IM-based MPBF maintains a symmetric profile with large out-of-band rejection through control of the bias voltage. For a DSB-IM MPBF, we achieve a large out-of-band rejection (> 40 dB) and symmetric filter profile under different dispersion conditions by controlling the bias-dependent phase using the bias voltage to a z-cut intensity modulator. The use of an intensity modulator for mitigation of dispersion induced impairments has the potential to enable real-world integrated microwave photonic bandpass filter with large out-of-band rejection and a consistent filter profile over wide radio frequency range under different dispersion conditions.