Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering

We report the first demonstration of a photonic chip based dynamically reconfigurable, widely tunable, narrow pass-band, high Q microwave photonic filter (MPF). We exploit stimulated Brillouin scattering (SBS) in a 6.5 cm long chalcogenide (As2S3) photonic chip to demonstrate a MPF that exhibited a high quality factor of ~520 and narrow bandwidth and was dynamically reconfigurable and widely tunable. It maintained a stable 3 dB bandwidth of 23 ± 2MHz and amplitude of 20 ± 2 dB over a large frequency tuning range of 2-12 GHz. By tailoring the pump spectrum, we reconfigured the 3 dB bandwidth of the MPF from ~20 MHz to ~40 MHz and tuned the shape factor from 3.5 to 2 resulting in a nearly flat-topped filter profile. This demonstration represents a significant advance in integrated microwave photonics with potential applications in on-chip microwave signal processing for RADAR and analogue communications.


Introduction
Microwave filters form a critical part of microwave signal processing with applications in RADAR, radio over fiber (RoF), and mobile communications [1]. However, microwave filters implemented in the electrical domain suffer from electromagnetic interference (EMI), are difficult to tune and difficult to reconfigure in terms of the filter shape and its bandwidth [1]. Microwave photonic filters (MPFs), on the other hand, can provide a wide tuning range, are naturally immune to EMI, and some schemes exhibit the ability to be reconfigured [1]. In recent years, a number of MPF designs exhibiting either a periodic transfer function or a single pass-band have been demonstrated in optical fiber. These MPFs have been based on tapped delay lines and single pass-band architectures, realized using technologies such as Fiber Bragg Gratings (FBGs) [2][3][4][5]; Mach-Zehnder interferometers (MZIs) [6][7][8]; dispersion based tap delay [9,10]; semiconductor optical amplifiers (SOAs) [11]; Sagnac loops [12]; or stimulated Brillouin scattering (SBS) [13][14][15][16][17].
When the MPF has a periodic transfer function, the tuning range is obviously limited by the free spectral range (FSR) and this also restricts the amount by which the bandwidth can be reconfigured. MPFs with a single pass-band are, therefore, better suited for applications where large tuning and large dynamic bandwidth are required [1]. Recently widely tunable single pass-band MPFs with high Q have been demonstrated by exploiting the narrow gain spectrum of SBS [13,14,16]. However, these impressive results were achieved in an optical fiber ~10-20 km long [13,14,16,17] which makes them incompatible with all-optical integration [18,19]. Quite impressive results have also been reported using chip-based photonic microwave signal processors, however, current MPF bandwidths have been limited to > 1 GHz and a Q factor of ~10 [20][21][22]. In this paper we report the first demonstration of an on-chip tunable, narrowband microwave photonic filter with a high Q. We also demonstrate that the shape and bandwidth of such a filter can be easily reconfigured. In this work we exploited the large SBS gain coefficient (g B ~0.74 x 10 −9 m/W) [23,24] and small effective mode area (~2.3 µm 2 ) of an As 2 S 3 rib waveguide to achieve large SBS gain in a 6.5 cm long rib waveguide at moderate pump power (~300mW). Our device provided a narrow 3dB bandwidth f 3dB ~23 ± 2MHz with stable amplitude ~20 ± 2 dB over a wide frequency range (2-12 GHz) resulting in a Q ~520: 52 times the Q values previously reported for on-chip MPFs [21]. The shape factor (S) of the MPF, which is defined as the ratio of −20 dB to −3 dB bandwidth, was also tuned from 3.5 to 2 by tailoring the pump profile [13,25]. This demonstration represents a significant advance in the field of integrated microwave photonics.

Principle of operation
In this section we present the principle of operation of our microwave photonic filter. This principle was first demonstrated in [14] for the case of a long optical fiber. Here we review the basic operating principle, which is illustrated in Fig. 1, and also discuss some specific aspects that are unique to our device based on an As 2 S 3 photonic chip.
In Fig. 1, a microwave signal A(Ω) is first encoded into an optical carrier (ω o ) using phase modulation. The phase encoding results in equal amplitude upper and lower sidebands that are out of phase by π. The beat signals between these out-of-phase sidebands and the carrier interfere destructively and, hence, no filtered signal appears in the microwave spectrum. However, when one of the side bands is amplified using SBS, the beat signals have different amplitudes and no longer cancel, resulting in the generation of a filtered signal in the microwave domain that has the spectrum and bandwidth of the SBS gain profile (see Fig. 1). The key to our photonic chip based microwave photonic filter (PCMPF) is the strong SBS cross-section (g B ) and small effective optical mode area (A eff ) of our chalcogenide (As 2 S 3 ) waveguide [23,24]. For SBS, the gain exponent G = g B P p L eff /A eff depends on both g B , and the pump intensity I p = P P /A eff , where P p is the pump power, and effective length L eff . To achieve large SBS gain in a short device at moderate pump powers, therefore, requires a material with large g B and a device with small A eff . The gain coefficient g B is enhanced using high refractive index materials, because g B scales with n 8 . Further enhancement can be achieved by ensuring that the photons and phonons are both guided within the same structure. An As 2 S 3 chalcogenide glass waveguide satisfies these conditions [18] having a large refractive index n = 2.43 at 1550nm, which results in large g B and also allows tight confinement of both the optical and acoustic modes in a rib waveguide structure. For our chalcogenide chip g B ~0.74 x 10 −9 m/W (~70 x silica) and A eff = 2.3 µm 2 , which results in large G at small pump powers.

Theory
Next we present a generalized theory of a MPF exploiting SBS and phase modulation of an optical carrier. The theory considers filtering of an arbitrary microwave signal A(Ω) instead of a sinusoidal signal and analyses the effect of any unwanted signals that may arise due to beating of the phase modulated signal with a co-propagating parasitic pump, introduced by the reflection at the lensed fiber-chip interface. First we consider the ideal case of Fig. 1 where a microwave signal A(Ω) is phase encoded onto an optical carrier (ω ο ) and filtered using SBS. After encoding, the resulting optical signal is given as: Using the fact that for a phase modulated signal the intensity I(t) = |E(t)| 2 = constant, the contribution from non-DC terms must be zero. Assuming small-signal modulation and considering only the first order non-DC terms in I(t), we obtain: which implies that for a phase modulated signal A* -(Ω) = -A + (Ω). This condition arises because no signal should appear on the radio frequency spectrum analyzer (RFSA) for a pure phase modulated signal. When the SBS gain is applied to one of the phase modulated side bands (e.g. the upper sideband), the signal on the RFSA (assuming small-signal modulation) arises from the following non-DC terms: Using the fact that A* -(Ω) = -A + (Ω) in Eq. (3), the detected signal is given by: From Eq. (4), it is evident that the output in the microwave domain has a spectrum [G(Ω)-1]A + (Ω) and thus, with respect to the input microwave signal A(Ω), the output microwave signal is filtered by the SBS gain response G(Ω)-1.The result in Eq. (4) shows that in the ideal case of Fig. 1, under the small-signal modulation approximation i.e. higher-order non-DC terms are neglected, the SBS process can be used to filter a microwave signal. In our specific implementation that will be discussed in more detail below, due to the reflections at the ends of the chip, the injected counter-propagating pump generates a parasitic pump co-propagating with the phase modulated signal. Below we analyze the degradation of the filter response due to such a parasitic effect.
In order to analyze this non-ideal case, shown in Fig. 2, we rewrite Eq. (1) in the presence of a co-propagating backscattered pump with gain on the upper phase modulated sideband as:  Once again assuming small-signal modulation and considering only the first-order non-DC terms in I(t), we obtain: The first term in Eq. (6) represents the filter operation as derived in Eq. (4). The remaining terms in Eq. (6) contribute to the degradation of the filter response by generating undesired signals. The second term arises from the beating between the carrier and residual pump and gives rise to a signal at ω p -ω 0 ; the third term arises from the beating between the residual pump and unamplified sideband; and the final term results from beating between amplified sideband and the residual pump, which results in a microwave signal at the Brillouin shift Ω B . In order to reduce these unwanted signals, we removed the parasitic pump signal at the output using a Bragg grating, however, there is still some residual pump which generates a small amount of unwanted beat signals. Furthermore, a small signal is generated from beating between the amplified and unamplified PM sideband. These unwanted terms, however, arise from practical constraints such as stray or scattered light from the pump, which can be eliminated by improving coupling into the rib waveguide using, for example, on-chip tapers. Figure 3 shows the experimental set up used to realize a PCMPF. Continuous wave (CW) light from a distributed feedback (DFB) laser was passed through an isolator and then split into two parts using a 99/1 coupler. The 1% port became the "pump arm" and was amplified using a 2W C-band EDFA (EDFA1) and passed through a polarization controller (PC1) before being launched into the chip via a circulator (C1) and a lensed fiber. The 99% port was used to generate a carrier suppressed intensity modulated signal using an intensity modulator (IM), which split the light into upper and lower sidebands. One of the IM sidebands was removed using a fiber Bragg grating (FBG1) before it entered a 90/10% coupler. The 90% port acted as the optical carrier on which the RF signal was encoded using a phase modulator (PM). The PM signal was then coupled into the chip via C2 and a lensed fiber. The polarization of light going into the phase modulator and the chip was controlled using polarization controllers PC3 and PC5 respectively. The 10% arm was amplified using a lownoise EDFA (EDFA2), and passed through a polarization controller (PC4). The output of the chip was collected through circulator C1 and passed through FBG2, where the back-reflected pump due to reflections at the end faces of the chip was removed. The signal after pump removal was then coupled with the amplified carrier wave using a 50/50 coupler, one arm of which lead to an OSA and the other to a high-speed photo detector connected to a RFSA. The power of the re-injected amplified optical carrier was kept fixed throughout the experiment. The rib waveguide used in the experiments was 6.5 cm long with a cross-section of 4 µm x 850 nm with anti-reflection coatings applied to the end facets. The Brillouin shift of the chalcogenide (As 2 S 3 ) chip is ~7.7 GHz.

General operation
In the experiment to demonstrate the PCMPF, the Brillouin pump frequency was kept fixed at the laser frequency (ω L ) while the frequency of the carrier, on which the RF signal (ω RF ) was phase encoded, was tuned using an intensity modulator (IM). The intensity modulator was biased to suppress the laser frequency as shown in Figs. 4(a) and 4(c). In the case when the RF frequency ω RF was smaller than the frequency (ω M ) of the IM, the lower IM side band was used as the carrier while the upper IM sideband was removed using a tunable fiber Bragg grating (FBG1) as shown in Fig. 4(a). In this case, the upper phase modulated sideband experienced gain (see Fig. 4(b)). The parasitic pump, which originated from reflections at the interface of lens fiber and chip was removed using FBG2 (see Fig. 4(b)). The MPF center frequency (ω RF ) could be tuned in the range from 0 to ω max M -Ω B , where ω max M is the maximum frequency determined by the IM and its driver. In our experiment the maximum frequency of the IM driver was ω max M = 15 GHz and therefore the MPF tuning range for this case i.e. when ω M > ω RF was restricted from 0 to ω max M -Ω B ~7.2 GHz. In order to increase the tuning range beyond ω max M -Ω B , we operated in a region where ω M < ω RF . Note that a single-sideband (SSB) IM and a signal generator with larger ω max M would provide much larger tuning range without going into the ω M < ω RF operating regime. This would also simplify the device operation by avoiding the need for FBG1. Fig. 4. Principle of general MPF operation when IM frequency greater than RF frequency ωM > ωRF (a, b) and for IM frequency smaller than RF frequency ωRF > ωM (c, d). For ωM > ωRF, lower IM sideband is used as a carrier for phase modulation and the upper phase modulated sideband experiences SBS gain. For ωRF> ωM, upper IM sideband acts as the carrier for phase modulation and lower phase modulated sideband experiences SBS gain. For ωM > ωRF, the IM carrier is blocked by FBG2, which was used to remove the parasitic pump.
When ω M < ω RF , the upper IM sideband acted as the optical carrier on which the RF signal was phase modulated while the lower IM sideband was removed using a FBG (see Fig. 4(c)). In this case, the lower PM sideband experienced gain (see Fig. 4(d)) and the MPF center frequency could be tuned from ω min M + Ω B to ω max M + Ω B , where ω min M is the minimum frequency of the signal generator driving the IM. In our experiment, the maximum MPF tuning frequency was restricted to 12 GHz because both the phase modulator and its driver have a maximum range of 12 GHz. The lowest MPF center frequency in this operating regime (ω M < ω RF ) was limited by the lowest frequency (ω min M ) of the IM driver. The ω min M of 2 GHz restricted the lowest MPF frequency for this operating regime to ~10 GHz. Thus, the PCMPF could not be operated at 8 and 9 GHz in these experiments, however, this constraint is not a fundamental limitation of the system. For both the operation regimes i.e. ω M < ω RF and ω M > ω RF , the optical carrier wave was reintroduced after removing the residual back-reflected pump using FBG2. The reintroduced carrier makes up for the reduced carrier power after propagation through the chip where ~12 dB insertion loss was experienced by the phase modulated signal. The coupling to the chip was performed using lens-tip fibers with a spot size of 2.5 µm, which resulted in ~4dB coupling loss at each facet. For ω M < ω RF , the IM carrier was suppressed by the FBG2 (see Fig. 4(d)). A fixed carrier power was reintroduced for both the operating regimes before detection. Figure 5 shows the RFSA trace when a phase modulated (PM) signal centered at ω RF = 7 GHz counter-propagated with a pump such that the upper PM sideband was downshifted from the pump by Ω B . In this condition the gain experienced by the upper PM sideband resulted in large amplitude mismatch between the two out-of-phase sidebands creating a large signal (~20 dB) on the RFSA at ω RF = 7 GHz. As predicted in the theory section, a small unwanted signal (~1.3dB) appeared at Ω B (see inset Fig. 5), due to beating of the residual backscattered pump with the amplified PM sideband. Another small signal (~2.2 dB) appeared at 2ω RF = 14 GHz, due to beating between the amplified and unamplified sidebands. The extinction measured in comparison to the noise level is ~20 ± 2 dB. However, the unwanted beat signals, predicted by Eq. (6) and shown in the inset of Fig. 5 reduced the sideband suppression by ~3dB. With the pump off, a small signal (~4dB) appeared at ω RF = 7GHz on the RFSA. We attributed this to imbalance between the power in the upper and lower PM sidebands due to asymmetry in the modulator and the presence of the grating (FBG2), which affected the sidebands differently. This resulted in incomplete cancellation of the out-of phase beat signals. To tune the MPF center frequency, we tuned both the IM frequency and the PM driver frequency so that one PM sideband was always at the Brillouin shift from the pump. Figure 6 shows that the PCMPF could be tuned over a wide range (2-12GHz). A constant SBS gain of ~20dB was used to obtain Fig. 6. The amplitude and bandwidth fluctuations in the MPF response over the tuning range are shown in Fig. 7 demonstrating good amplitude (~20 ± 2 dB) and bandwidth (f 3dB ~23 ± 2 MHz) stability. The inset in Fig. 7 shows the MPF profiles centered at RF frequencies of 4 GHz and 11 GHz, obtained by scanning the PM driver frequency over 1 GHz. The maximum Q-factor, defined as the MPF center frequency divided by the f 3dB , was calculated to be ~520 for a RF center frequency of 12 GHz.  To reconfigure the MPF 3dB bandwidth and shape factor, S, we tailored the pump profile [13,25]. Figures 8(a) and 8(c) show that when we changed the pump spectrum from a single to dual-pump configuration the overall MPF profile (solid Fig. 8(c)), which results from the overlap of two individual gain profiles (dashed Fig. 8(c)), has a flat top and larger f 3B . Figures 8(b) and 8(d) show the measured PCMPF profiles for single and dual pumps (separated by 18 MHz), respectively. Using two pumps, a nearly flat-topped MPF profile was achieved with f 3dB increased from ~20 MHz to ~40 MHz, which in turn improved S from ~3.5 for a single pump to ~2 for the dual pump.

Conclusion
In conclusion, we have presented the first demonstration of a photonic chip based tunable, high Q, narrowband MPF with shape and f 3dB reconfiguration. A PCMPF with a stable 3dB bandwidth (~23 ± 2 MHz) and amplitude response (~20 ± 2 dB) over the tuning range of 2-12 GHz was demonstrated. The filter response was reconfigured by tailoring the pump profile, resulting in shape factor enhancement from 3.5 to 2 and f 3dB improvement from ~20 MHz to ~40 MHz. The sideband suppression was reduced due to unwanted signals arising from pump reflections. Improved coupling to the chip using, for example, inverse tapers would have reduced facet reflections and increased the extinction ratio and sideband suppression substantially allowing a simpler experimental set-up by eliminating the need for FBG2. Further, use of a single-sideband intensity modulator with larger modulation frequency would increase the MPF tuning range and further simplify the experiment. This demonstration represents a significant advance in the field of integrated microwave photonics and enables the realization of potential applications in microwave signal processing for radar and analog communications.