1. Introduction

Bandpass filters are one of the most crucial elements present in modern communication and signal processing systems. These filters enable the selection of signals of interest in densely-packed frequency spectra, multiplexed with multiple signals. However, designing widely tunable and reconfigurable bandpass filters operating in the GHz regimes remains quite challenging for conventional Radio frequency (RF) systems [1]. Conventional tunable filters require the use of several switches between different electronic components limiting the continuous tuning or cavity tunable filters which offer a limited fractional bandwidth. Microwave photonics (MWP) has evolved as a next-generation technology for numerous crucial coarse and high-resolution signal processing applications of conventional RF systems [2–5]. It also offers several distinct advantages such as tunability, immunity to electromagnetic interference (EMI), large operational bandwidth, and higher extinction ratios in filters [6–9]. The photonic integration of various optical components can potentially result in the reduction in the form factor of the photonic filters. Most importantly, it is easier to design tunable subsystems in the GHz frequency regime which are crucial for modern communication applications. The basic principle of designing an MWP subsystem involves upconverting the RF signal to the optical domain, employing a suitable modulation scheme, processing the signal in the optical domain using optical functionalities, and down-converting the processed signal back to the RF domain upon photodetection [10–12].

One commonly used optical phenomenon for high-resolution MWP signal processing is stimulated Brillouin scattering (SBS). SBS is a nonlinear optical effect in which energy is transferred from an intense optical signal (pump) to a counter-propagating optical signal (probe) having a specific frequency separation (known as the Brillouin shift) through the interaction with a moving acoustic grating. The gain and the phase profile of SBS has been of particular interest, as it has been utilized for several MWP signal processing applications, including bandpass filtering [13–16]. Most Brillouin-based filters utilize SBS gain responses to achieve bandpass filtering and several narrowband high-resolution bandpass filters using a single SBS pump have been realized [17–19]. However, these are limited due to the fundamental linewidth of SBS ∼30 MHz, and are tunable only up to a few MHz by adjusting the pump powers. In order to realize broadband filters, either multiple gain pumps such as frequency combs [20–22] or specialized RF input waveforms are required [23], making the systems less power-efficient and more complex.

In this work, we present a solution to the problem of power-inefficiency of SBS-based broadband filters by utilizing the phase response of SBS in combination with RF interference to achieve wide bandpass filtering operation with only two low-power SBS pumps. Using this novel technique employing the SBS Stokes and anti-Stokes resonances and advanced phase manipulation for RF interferometry, we exhibit a power-efficient bandpass filter with a flat phase response in the passband. We also demonstrate wide tunability in terms of bandwidth (up to >700 MHz) and frequency of operation (up to 22 GHz). While Brillouin pump modulation to achieve widely bandwidth-reconfigurable filters [20,22,23] has been widely explored, the manipulation of the Brillouin phase response to synthesize wideband bandpass filters with very low power is demonstrated for the first time, to the best of our knowledge. Such a filter also doesn’t suffer from Brillouin-induced noise in the passband, which is a major improvement compared to typical SBS-based systems. Furthermore, the flat phase response in the passband of the filter enables zero delay compared to when the SBS is not switched ON, opening up new possibilities of delay and chirp engineering through precise gain and phase control of the SBS response.

2. Principle of operation

The proposed microwave photonic bandpass filter is realized by employing a phase modulator combined with a programmable optical filter (POF) and imparting the Stokes and the anti-Stokes resonances of SBS on the analog photonic link. The same effect can also be achieved using a dual parallel Mach Zehnder interferometer [17] through precise control of the DC biases to accurately control the relative amplitude and phase of the sidebands. When an RF signal of frequency ${\omega _{RF}}$ is phase-modulated over an optical carrier of frequency ${\omega _c}$, it results in two out-of-phase sidebands (π-offset) with equal amplitude at frequencies ${\omega _c} \pm {\omega _{RF}}$. Direct photodetection of this signal leads to only DC power, and no signal component at the frequency ${\omega _{RF}}$ since both the sidebands cancel each other (for clarity, consider two vectors of equal amplitude and π phase-difference). Instead, if a phase and/or amplitude offset is applied to one or both the sidebands, the cancellation condition is violated (for clarity, consider two unequal vectors at an angle). This can be used to realize meaningful passband responses upon photodetection for filtering. The SBS magnitude and the associated phase responses [24] have been utilized in this work, to tailor the upper sideband of a phase-modulated signal to create a bandpass response.

A schematic representation of the concept is illustrated in Fig. 1 with the individual SBS gain and loss responses being shown in Fig. 1(a). The magnitude and phase response of both the sidebands upon application of SBS is shown in Fig. 1(b). The SBS gain and loss responses applied to the upper sideband with frequency separation, $\beta $ imparts a negative phase region to the frequencies between the two responses, leading to almost equal amplitudes but phase difference between the two sidebands not being equal to $\pi $. Suppose an additional positive phase offset is applied to the lower sideband, then this further prohibits cancellation in this central frequency region since now the phase between the two sidebands is significantly less than $\pi $, as it can be observed in Fig. 1. Regions to the right of the SBS gain response and left of the SBS loss response have a good cancellation (though not perfect) due to the phase difference between the two sidebands being close to $\pi $. At exact frequencies where the SBS Stokes and anti-Stokes resonances are applied, we see slightly higher amplitudes than the passband in a ∼30 MHz bandwidth due to amplitude offsets created by the Lorentzian SBS profiles of both responses.

 

Fig. 1. Schematic explanation of the principle of operation. (a) Individual SBS gain and loss profiles, (b) both sidebands of the phase-modulated spectra, with SBS Stokes and anti-Stokes resonances applied to the upper sideband (USB) and a phase offset to the lower sideband (LSB), (c) bandpass filter gain and phase response after RF interference, and (d) the schematic description of RF interference to realize bandpass response, using the concept of vector addition.

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The filter magnitude and the phase responses obtained after photodetection are shown in Fig. 1(c). This concept of RF interference employed to obtain the bandpass filter response can also be understood in terms of vectors, as illustrated in Fig. 1(d). The two sidebands of any modulated signal can be treated as two vectors, whose resultant determines the overall response at the output upon photodetection. We can observe that within the frequency range between the two SBS responses, vector addition results in higher amplitudes primarily because the angle between the vectors is significantly less than 180 degrees. In contrast, on either side of SBS responses, the upper sideband (USB) and lower sideband (LSB) vectors have identical amplitudes, and the angle between them is close to 180 degrees leading to good cancellation and formation of a stopband.

To describe the filter operation quantitatively, we have utilized a mathematical model based on [8–9,25], demonstrating the effect of phase shift and SBS responses on a phase-modulated analog photonic link. The SBS induced complex gain, ${G_B}(\mathrm{\omega } )$ is mathematically given by [14]:

Let $\beta $ be the angular frequency separation between the peak SBS gain and loss response applied to the upper sideband of the phase-modulated probe, with center frequency ${\omega _0} = {\omega _c} + {\omega _{RF}}$. The combined complex gain and loss imparted can be quantified as:

For small-signal modulation considering only first-order sidebands, the electric field at the output of a phase modulator, modulated by a single tone RF signal of amplitude ${V_{RF}}$ and angular frequency ${\omega _{RF}}$ is given by [7–8]:

A constant phase shift ${\phi _l}\; $ applied to the lower sideband, and SBS Stokes and anti-Stokes resonances imparted on the upper sideband of a phase-modulated signal can be expressed in the form of transfer function ${H_l}(\omega )$ and ${H_u}(\omega )$, respectively. These can be quantified as:

Upon application of the two transfer functions, using Eqs. (4) and (5), the processed electric field equation can be written as:

Photodetection of this processed signal with a detector of responsivity ${R_0}$ results in a current proportional to the intensity of the input field, given by:

The final expression is obtained after solving Eq. (7) and filtering the DC term and higher-order terms. The output current for the frequency ${\omega _{RF}}$ is given by:

The phase ${\phi _u}$ and gain ${G_u}$ imparted by SBS responses on the upper sideband can be mathematically written as:

Hence, the photodetector current at frequency ${\omega _{RF}}$ is given by:

As the input RF frequency ${\omega _{RF}}$ is swept using a vector network analyzer (VNA), we get output current at different frequencies.

From Eq. (11), we can analyze the filter operation in the passband and the stopband. When ${G_u}$ is close to unity inside the passband (${\omega _c} + {\omega _{RF}} - \frac{\beta }{2} < \omega < {\omega _c} + {\omega _{RF}} + \frac{\beta }{2}$), the phase imparted by SBS responses ${\phi _u}$ is negative, but the phase on the negative cosine term ${\phi _l}$ is positive, creating a mismatch in cosine amplitudes violating the cancellation condition. In the stop bands on either side of the SBS gain and loss response $\left( {\omega > {\omega_c} + {\omega_{RF}} + \frac{\beta }{2}\; \& \; \; \omega < {\omega_c} + {\omega_{RF}} - \frac{\beta }{2}} \right)$, again, ${G_u}$ is close to unity. However, the phase on the upper sideband cosine term is close to 0 and slightly positive. The phase of the negative cosine term is also slightly positive, leading to good cancellation (however, not perfect), i.e., enabling a bandstop region for all those frequencies. We also observe that ${G_u}$ has a large magnitude at frequencies near the passband edge due to individual SBS responses, leading to higher magnitudes as compared to the center of the passband.

Since the phase response imparted by the SBS response ${\phi _u}$ on the upper sideband is very flat in the passband, and the phase imparted on the LSB is also constant, the overall phase response of the filter in the passband is very flat, and linear thereby ensuring that there is zero delay in the passband. From our mathematical model, we also infer that the phase parameter dominantly affects the overall filter response and hence can be used to tailor the filter gain profiles. This is novel and power-efficient since the MWP Brillouin bandpass filters have predominantly relied on altering gain responses to tailor the overall filter response, which is power-intensive. Furthermore, another major advantage of this technique is that the SBS noise is only added at the edges of the filter as the SBS noise would only be added within the SBS gain/loss profile as seen in Fig. 1(c). Since most of the SBS noise is added around the gain/loss peak, minimal noise is added in the passband as the peak SBS responses are spectrally well-separated from the center of the passband. A previous demonstration of a noiseless filter, required high-bandwidth anti-Stokes responses to carve out a passband [26].

3. Experimental setup

A schematic diagram of the experimental setup used to implement the proposed bandpass filter is shown in Fig. 2. Two separate lasers were used to generate two SBS pumps and a probe. A swept RF signal with an instantaneous frequency of ${f_{sw}}$ is generated by a VNA and is used to phase-modulate the carrier generated by LASER 1 at frequency ${f_c}$. The modulated signal is passed through a programmable optical filter to create a phase offset at the lower sideband. The optical signal from LASER 2 at a frequency of ${f_c} + {f_{RF}}$ is intensity-modulated by a single tone RF signal of frequency ${f_P}$ and amplified using Erbium-Doped Fiber Amplifier (EDFA) to generate two amplified sidebands, acting as SBS pumps. The pump and probe signals were made to counter-propagate in a 3.2-km-long optical fiber using a circulator. The interaction of the pump and probe enables the SBS interaction on the upper sideband of the phase-modulated probe, and the modified signal is then incident on a photodetector. After photodetection, the RF signal goes to the VNA. Comparing this signal with a swept input RF signal to the PM, the VNA computes the filter's magnitude, phase, and delay response.

 

Fig. 2. Experimental setup for realizing the low-power bandwidth reconfigurable bandpass filter. PC: Polarization Controller, PM: Phase Modulator, POF: Programmable Optical Filter, SMF: Single-Mode Fiber, OC: Optical coupler, VOA: Variable Optical Attenuator, PD: Photodetector, VNA: Vector Network Analyzer, OSA: Optical Spectrum Analyzer, MZM: Mach Zehnder Modulator, EDFA: Erbium-doped fiber Amplifier, USB: Upper sideband, LSB: Lower sideband.

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An input signal to the PM is swept around a center frequency ${f_{RF}}.$ The SBS pumps generated from a low-biased intensity modulator are at frequencies ${f_C} + {f_{RF}} \pm {f_P}$. In the standard single-mode fiber, frequency separation between the peak SBS gain, and the counter-propagating probe ${f_{SBS}}$ is a constant at ∼10.9 GHz, hence the frequency separation between the peak SBS gain and peak SBS loss response $({\Delta f} )$ is dependent on ${f_P}$ and is given by:

This separation between the SBS gain and loss response dictates the filter bandwidth, i.e., the filter bandwidth can be altered by just changing one parameter, i.e. the input frequency of the RF signal to the intensity modulator (${f_P}$), making this technique extremely versatile and precise.

The intrinsic bandwidth of the individual SBS gain and loss response is ∼30 MHz in a standard single-mode fiber which puts a fundamental lower limit (due to the material dependant linewidth of SBS) on the filter tunability. However, by simply changing the frequency separation between the two SBS responses, we have demonstrated bandwidth tunability of >700 MHz, thus going significantly (by more than 20 times) beyond the fundamental limit. To change the center frequency of the filter response, we need to tune the optical source in the lower branch (LASER 2) at a frequency ${f_C} + {f_{RF}}$. The filter is thus easily tunable to a range of different frequencies depending upon the tunability of the laser.

4. Results and discussion

Bandpass filters are implemented using the setup described in Fig. 2, and corresponding simulations are performed in order to validate the experimental results. We have considered the 3-dB bandwidth of the filter with respect to the center frequency of the passband as the filter bandwidth. The simulated and experimental magnitude and phase response for a bandpass filter having 390 MHz bandwidth, corresponding to $\mathrm{\Delta }f$ being equal to 309 MHz, and a single-sideband modulated link with SBS gain and loss acting on USB are shown in Fig. 3(a) and Fig. 3(b), respectively. In order to measure the frequency separation between the peak SBS gain and loss responses, a programmable optical filter (POF) is used to suppress the lower sideband and the response is observed for a single sideband modulated link. In order to obtain the filter response, RF interference is enabled. Demonstrated results showing filter passband being >10 dB higher in a bandwidth of ∼400 MHz than the stopband are obtained. The peak SBS gain and loss response magnitudes used are only ∼8 dB each, with an intrinsic bandwidth of 30 MHz, consuming overall just ∼14 dBm of pump power, signifying the power-efficiency of the proposed setup.

 

Fig. 3. (a) Simulated magnitude and phase response of a single-sideband analog photonic link with SBS Stokes and anti-Stokes resonances applied, and simulated magnitude and phase response of bandpass filter after RF interferometry, and (b) experimental results for simulated single-sideband link with SBS response and the resultant filter with RF interferometry.

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Experimental filter responses at different bandwidths are shown in Fig. 4. The bandpass response of the filter is widely tunable up to a bandwidth of >700 MHz, far beyond the individual SBS response (∼30 MHz). A mirror filter response can also be obtained when the position of the SBS gain and loss responses are swapped. If the frequency separation of two sidebands from intensity-modulated signal acting as SBS pumps (${f_P}$) is less than ${f_{SBS}}$, in that case, we observe SBS gain response occurs at a lower frequency, and the SBS loss response occurs at a higher frequency with respect to the center frequency ${f_{RF}}$. Experimental filter responses for this configuration at various bandwidths are shown in Fig. 4(a) and for the flipped condition (gain on the right and loss on the left) are shown in Fig. 4(b). We have experimentally determined the variation of filter bandwidth as a function of $\mathrm{\Delta }f$, as shown in Fig. 5(a).

 

Fig. 4. Experimental single sideband and filter magnitude responses for different separations between SBS gain and loss responses. (a) SBS gain on the left of the center frequency and loss on the right, and (b) SBS loss on the left of the center frequency and gain on the right.

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Fig. 5. (a) Plot of filter bandwidth with respect to the separation between the SBS gain and loss response ($\mathrm{\Delta }f$), and (b) the experimentally-measured amplitude response of the bandpass filters for different phase offsets on the LSB.

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The passband magnitude response of the filter depends on the phase offset imparted on the lower sideband of the phase-modulated probe using the POF, as demonstrated mathematically in Eq. (11). To validate this dependence, experiments were carried out imparting different phase offsets on the lower sideband and the different filter magnitude responses thus obtained are shown in Fig. 5(b). We observe that as the phase offset is increased, the filter roll-off becomes sharper, albeit at the expense of the passband level. For lower offsets, we have a higher passband level but with a reduced roll-off. An optimum phase shift can be chosen, depending upon the application, in order to tune the filter response. This adds an extra dimension to the tunability of the filter, making the filter extremely flexible.

Filter responses were also synthesized at different center frequencies by tuning the pump laser and are shown in Fig. 6(a). The tuning speed is determined by the tuning speed of the pump laser and can be on the order of milliseconds. We have demonstrated that filter response can be generated from 8.14 GHz to 22.13 GHz. A full trace of the VNA showing filter centered at 15.5 GHz is shown in the inset of Fig. 6(b). Due to the limited resolution of the VNA resulting in less number of points in a large frequency range, fine details and magnitude variations could not be captured.

 

Fig. 6. (a) Filter response measured at different central frequencies. (b) Full trace of the filter magnitude response centered at 15.5 GHz.

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One can observe in Fig. 3 that both simulation and experimental results reveal that the proposed filter has a flat phase response in the center of the passband in a bandwidth of ∼200 MHz. Since the filter delay response is the derivative of the phase response with respect to the angular frequency, a flat phase response implies a zero-group delay. This means that if a pulse is an input to this filter such that all the frequency components of the pulse lie in this flat phase region, it would not experience pulse delay. While the Brillouin effect has been used for pulse delays [27], we have engineered the phase response to enable zero delays. Figure 7(a) shows the simulated and experimental group delay response for the filter illustrated in Fig. 3.

 

Fig. 7. (a) Simulated and experimental group delay response of the filter, and (b) comparison between the output pulse through SSB- analog photonic link with respect to output pulse sent through the filter. It can be observed that the pulse experiences zero delay.

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We have carried out an experiment to demonstrate the zero-delay concept. A rectangular pulse is passed through the filter of bandwidth 310 MHz and it is compared with a similar pulse sent through a single-sideband modulated analog photonic link. For the experiment, the baseband rectangular pulse of duration 20 ns is generated by an arbitrary waveform generator (AWG) and is upconverted to 10.25 GHz using an RF mixer since the center frequency of the filter is 10.25 GHz. 3 dB bandwidth of the filter with respect to the passband is itself 310 MHz, but as is evident from Fig. 7(a), the region of zero group delay distortion is much lower (∼ 200 MHz). Consequently to demonstrate zero group delay distortion, a pulse of a lower bandwidth is chosen.

First, the pulse is passed through the APL with the SBS pumps off, and the lower sideband is suppressed using the POF. Later the pulse is sent through the filter. After photodetection, both the pulses are down-converted to the baseband using another RF mixer and measured on a low-frequency oscilloscope. A comparison of both the pulses is shown in Fig. 7(b). We can observe that, although the pulse shape is distorted in amplitude due to the filter's magnitude response, it has not experienced any group delay. This demonstration shows that the proposed filter can be used for applications in which group delay distortion needs to be avoided.

It should be noted that the use of a programmable filter limits the minimum frequency of operation to 8 GHz while the upper frequency of operation is limited by the modulator and photodetector bandwidth. The programmable optical filter is used to demonstrate the proof of concept and the same effect can be achieved by using a dual parallel Mach Zehnder modulator, to control the relative amplitude and phase of the sidebands [17].

5. Conclusion and future outlook

We have demonstrated a novel microwave photonic bandpass filter concept based on stimulated Brillouin scattering (SBS) and RF interference, exhibiting high tunability in terms of bandwidth (30 MHz to >700 MHz), roll-off, selectivity, and frequency of operation (8-22 GHz). The filters have been realized, consuming significantly lesser pump powers compared to any other Brillouin-based filters. Furthermore, this filter doesn’t suffer from added Brillouin noise in the majority of the passband, thereby solving a major bottleneck faced by Brillouin-based microwave photonic sub-systems. The proposed filter also exhibits a flat phase response in the passband resulting in zero delay in the passband. The zero delay concept is experimentally verified through the propagation of a rectangular pulse. The methodology and concept of the filter design is primarily based upon utilizing SBS phase responses rather than the amplitude response as has been done traditionally, thus exhibiting a pathway for demonstrating low-power novel filter architectures based on phase manipulation and RF interference.

The unique magnitude and phase response of the filter implies that the proposed microwave photonic bandpass filter can be used for several versatile applications including gain flattering along with bandpass filtering. The filter is based on SBS, allowing it to be later implemented using chip-based platforms, acting as a potential integrated photonic subsystem for next-generation communication and signal processing systems.