1. Introduction

Optical frequency combs are a powerful tool that have been used for applications including spectroscopy, ranging, optical communications, and metrology [1]. These diverse applications require combs with varying bandwidth, repetition rate, and operating wavelength. In addition, many applications require the ability to customize the shape of the comb or manipulate the comb on a line-by-line basis [2,3]. Complex control of each comb tooth—sometimes called optical arbitrary waveform generation—opens up additional applications in the areas of microwave photonics [4–6], optical communication [7], microscopy and non-linear spectroscopy [8].

Fourier pulse shaping is the most widely used approach to manipulate a frequency comb [2,9]. In this scheme, the comb is spectrally dispersed so that each comb tooth can be manipulated separately (e.g., using a spatial light modulator) before being recombined. Fourier pulse shapers based on free space optics are commercially available and have already broadened the application space for optical frequency combs. However, these systems provide limited spectral resolution (typically >10 GHz) and a slow update rate (typically <100 Hz) which is a significant limitation for many RF photonic applications [10]. Faster update rates have been achieved using integrated photonics based Fourier pulse shapers that combine arrayed waveguide gratings (AWGs) with on-chip modulators [10–12]. However, the resolution of AWGs is typically >10 GHz while cross-talk and fabrication tolerances limit the number of comb teeth which can be manipulated using this approach [12]. Higher spectral resolution is required to manipulate individual lines in combs generated by fiber lasers, which typically exhibit a repetition rate on the order of 100 MHz. In addition, higher spectral resolution enables longer waveforms, which are of interest for microwave photonics applications [13].

One promising approach to high-resolution comb manipulation relies on the inherently narrow-band stimulated Brillouin scattering (SBS) process [14–17]. SBS has been used to manipulate comb lines separated by only ∼100 MHz. However, these demonstrations used a dedicated pump laser to manipulate each comb tooth and were limited to selecting one or two comb teeth at a time while rejecting the rest of the comb. In this work, we introduce a technique that uses SBS to manipulate the entire frequency comb with high spectral resolution. Starting from a single seed laser, we use a pair of frequency shifting loops (FSLs) to (1) generate an optical frequency comb and (2) generate a train of control pulses that are used to manipulate the original comb via SBS. To our knowledge, this is the first approach that uses SBS to manipulate an entire frequency comb.

The frequency shifting loops consist of a fiber optic ring containing a frequency-shifting modulator, an amplifier to compensate for loss, and a bandpass filter. Since the modulator introduces a frequency shift after each round-trip, this simple approach can convert a continuous wave (CW) seed laser into a broadband frequency comb using a low frequency modulator and drive electronics [18]. If a pulsed laser is coupled into the FSL, the output will be a train of pulses that are progressively spaced in both time and frequency [19]. Since their first introduction in 1990 [18,19], this simple platform has been used for a wide range of applications including dual comb spectroscopy [20], optical Fourier analysis [21], frequency-multiplexed fiber optic sensing [22], and programmable spectral shaping [23] including the generation of chirped waveforms [24].

Here, we show that linking two FSLs via SBS provides line-by-line control of a frequency comb. As an initial demonstration, we create and manipulate a comb consisting of 50 lines with 200 MHz spacing, covering a total bandwidth of 10 GHz. We show that this technique is able to address individual comb lines with ∼30 dB of modulation depth. The entire system is constructed using standard off-the-shelf fiber-coupled components and the modulation pattern can be updated at 10 kHz.

2. Operating principle

Our approach relies on two FSLs with matched frequency shifting modulators. The first FSL is seeded with CW light to create a standard optical frequency comb while the second FSL is injected with pulsed light to generate a train of “control” pulses. These control pulses will be used to selectively amplify individual comb teeth using the SBS process. Since these control pulses are temporally separated, we can use a modulator to adjust the amplitude of each control pulse and thereby control the amplification experienced by each comb tooth. This effectively converts the challenging problem of addressing comb teeth that are closely spaced in the frequency domain to the much easier task of modulating a train of pulses that are separated in the time domain.

This approach is outlined in the schematic shown in Fig. 1. A single, narrowband laser (kHz linewidth) was used to seed both FSLs, ensuring that their outputs are frequency locked. Along the upper path, CW light is coupled into the first FSL through a 50:50 splitter. The loop contains an erbium-doped fiber amplifier (EDFA), a tunable bandpass filter (Santec OTF-980), and an acousto-optic modulator (AOM). The AOM imparts a frequency shift of 200 MHz while the EDFA gain was adjusted to compensate for loss. The bandpass filter, which was set to 10 GHz, dictates the bandwidth of the comb and suppresses amplified spontaneous emission (ASE). The output of this first FSL is a 10 GHz wide comb with teeth spaced by $\mathrm{\Delta }f = 200\; MHz$.

 

Fig. 1. (a) Diagram of the experimental setup used to generate and manipulate a frequency comb. The upper FSL outlined in blue was used to generate a CW frequency comb. The components in the green box including the lower FSL were used to generate a train of frequency shifted control pulses. These control pulses were used to selectively modulate individual comb teeth via polarization pulling assisted SBS. The modulated comb was combined with a LO and recorded on a high-speed detector. (b) Frequency diagram showing the relative optical frequencies of the LO, the comb, and the control pulses. Each control pulse was shifted by ${f_{SBS}}$ relative to its corresponding comb tooth. Note that the solid blue lines indicate polarization maintaining fiber (PMF) while the solid yellow lines indicate single mode fiber (SMF).

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The lower path shown in Fig. 1 was used to generate a train of frequency shifted “control” pulses. The system was designed so that each control pulse was shifted by the Brillouin frequency (of optical fiber) relative to its corresponding comb tooth. We first used an EOM (EOSpace, ${V_\pi }\sim 3.4V$) driven at the Brillouin frequency (∼10.8 GHz) with a peak-to-peak voltage of ∼${V_\pi }$ in the suppressed carrier mode to produce a pair of sidebands. A tunable Fabry-Perot filter was used to select the upper sideband. We then used AOM₂ to carve an initial pulse with a duration ${\tau _{control}}$ at a repetition period ${T_{control}}$. This pulse was coupled into the FSL via a 50:50 coupler. As in the upper loop, AOM₃ was driven at 200 MHz. The same RF signal generator was used to drive both AOM₁ and AOM₃, ensuring that the control pulses were frequency locked with the comb teeth. However, in the lower FSL, an RF switch was used to modulate the electronic RF drive applied to AOM₃ into a series of N pulses with a duration ${\tau _{control}}$ at a repetition period of ${T_{loop}}$, corresponding to the round-trip time in the FSL. This allowed us to control the number of pulses generated in the loop. A 100 GHz wavelength division multiplexing (WDM) filter was used to suppress ASE. In this work, we generated $N = 50$ pulses with a pulse duration of ${\tau _{control}} = 2\; \mu s$ (${T_{loop}}\sim 2.07\; \mu s$). Thus, the total pulse train had a duration of ${T_{control}} = N \cdot {T_{loop}} = 103.5\; \mu s$. Figure 1(b) shows the relative frequencies of the comb generated in the upper loop, the control pulses, and a local oscillator (LO) at the original laser frequency which was used to characterize the comb. Since the control pulses were temporally separated, AOM₄ was able to selectively modulate the amplitude of each control pulse. This allowed the system to adjust the Brillouin amplification applied to each comb tooth. Note that AOM₂ and AOM₄ were used as intensity modulators and introduced counter-acting frequency shifts of $\mathrm{\Delta }\nu ={\pm} 55\; MHz$ to avoid changing the frequency offset between the control pulses and the comb.

In order to modulate the comb, we adopted a polarization pulling assisted SBS technique [16,25]. If the pump and probe beams have different (but not completely orthogonal) polarization states, the polarization state of the amplified probe signal will be “pulled” toward the polarization state of the pump. This technique enables large modulation depth with modest Brillouin gain (generally limited by the polarization extinction ratio) by using this SBS-induced change in polarization to separate the amplified comb teeth from the remaining comb teeth. As shown in Fig. 1, the comb generated in the upper FSL was first coupled through a polarization controller and then directed through a 10 km spool of single mode fiber (SMF) using a pair of circulators before reaching a polarizing beamsplitter (PBS). The polarization controller was used to minimize transmission through the PBS in the absence of Brillouin amplification. The control pulses were coupled into the 10 km SMF spool travelling in the opposite direction from the comb. The Brillouin amplification process served to rotate the polarization of the comb teeth, leading to transmission of the amplified comb teeth at the PBS.

3. Experimental demonstration

In order to characterize the modulated frequency comb, we diverted part of the original laser to serve as a local oscillator (LO). AOM₅ imparted a frequency shift of -100 MHz to the comb in order to offset the intermediate frequencies between the comb teeth and the LO from the intermediate frequencies produced by the comb teeth interfering with each other. The interference signal was detected on a 10 GHz photodetector and recorded on a 25 GHz oscilloscope.

We first characterized the comb generated by the upper FSL before introducing the control pulses. In this case, we adjusted the polarization controller to allow the comb to be transmitted through the PBS and recorded the interference pattern produced by the comb and LO. The normalized power spectral density (PSD) of the interference pattern is shown in Fig. 2(a), revealing a uniform frequency comb with 50 lines spaced by 200 MHz. The slight roll off in comb amplitude near 10 GHz is due to the edge of the tunable bandpass filter used in the upper FSL.

 

Fig. 2. (a) The frequency comb generated by the upper FSL was measured by calculating the PSD of the interference signal produced on the detector between the comb and the LO. The comb contains 50 teeth spaced by 200 MHz across 10 GHz. (b) The frequency shifted pulse train generated after the lower FSL recorded in the time-domain. (c) The modulated pulse train after AOM_4. In this case, the 2^nd and 5^th control pulses were selected. (d) The modulated frequency comb after selecting the 2^nd and 5^th comb teeth showing a modulation depth of ∼30 dB. The measurement time was 200 $\mu s$ and the resolution bandwidth was set to ∼27 kHz.

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We then confirmed that we can use the approach shown in Fig. 1 to select arbitrary combinations of comb teeth. The frequency shifted pulse train generated after the lower FSL is shown in Fig. 2(b). The pulse train consists of 50 pulses. Each pulse is 2 $ \mu s$ in duration and the total pulse train is $103.5\; \mu s$. The length of the pulse train was matched to the round-trip time in the ∼10 km SMF fiber spool. The slight variation in pulse power could be controlled by fine tuning the EDFA gain. However, AOM₄ can also be used to compensate for this variation by adjusting the transmission of each control pulse. In practice, EDFA₃ also introduces some distortion in the control pulse amplitudes due to gain saturation. To compensate for both effects, we could adjust the transmission through AOM₄ to achieve a desired pulse train after EDFA₃. In Fig. 2(c), we show the modulated pulse train after selecting the 2^nd and 5^th control pulses. After adjusting the polarization controller to minimize transmission of the frequency comb through the PBS, we used these control pulses to select the 2^nd and 5^th comb teeth. The control pulses were amplified to a peak power of ∼100 mW before being coupled into the SMF spool. As shown in Fig. 2(d), this allowed us to select the 2^nd and 5^th comb teeth with a modulation depth ∼30 dB. We repeated this experiment by selecting various combinations of comb teeth across the 10 GHz comb bandwidth and consistently achieved a modulation depth of ∼30 dB.

In addition to selecting arbitrary combinations of comb lines, this approach is amenable to tailoring the intensity profile of the entire comb. Shaping the intensity profile of a comb could be valuable for a host of applications including tunable RF filters [4,10] or generating Nyquist pulses [7]. In Fig. 3, we show a series of frequency combs with varying modulation patterns. In these experiments, we sinusoidally modulated the pulse train with varying periods to highlight the flexibility of this approach. The drive voltage applied to the $ {n^{th}}$ control pulse (which will modulate the ${n^{th}}$ comb tooth) was set as ${V_{mod}}(n )= {V_{AOM}} \cdot [{1 + \cos ({2\pi n/{T_{mod}}} )} ]/2$, where ${V_{AOM}}$ is the voltage required for maximum transmission through the AOM and ${T_{mod}}$ is the modulation period. In these experiments, ${T_{mod}}$ was set to ${N_{pulse}}\textrm{ / }3$, ${N_{pulse}}\textrm{ / }4$, ${N_{pulse}}\textrm{ / }5$, or ${N_{pulse}}\textrm{ / }8$, where ${N_{pulse}} = 50$ is the number of control pulses. The frequency combs generated with these four modulation patterns are shown in Fig. 3. The slight non-uniformities in the modulated combs are due to gain saturation in EDFA₃ which distorted the control pulse train. In the future, active feedback or calibration could be used to pre-distort the control pulse train using AOM₄ in order to compensate for this effect. Nonetheless, this illustrates the ability of this technique to generate frequency combs with arbitrary intensity profiles.

 

Fig. 3. Arbitrary comb profiles generated using sinusoidally modulated pulse train patterns with varying period. The modulation period applied to the control pulse train is labelled in each sub-panel.

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This approach is also capable of generating reconfigurable frequency combs. Each time a new pulse train is generated by the lower FSL in Fig. 1, we can adjust the modulation pattern introduced by AOM₄. In our current system, this corresponds to updating the comb modulation at ∼10 kHz (set by the ∼$100\; \mu s$ pulse train period). To illustrate this functionality, we setup the system to select three different sets of comb teeth every $100\; \mu s$. A spectrogram of the modulated frequency comb over time is shown in Fig. 4(a). A series of individual comb lines were selected for $100\; \mu s$ intervals. Three cross-sections showing the PSD at varying times are presented in Fig. 4(b), confirming that individual sets of comb teeth can be selected for short time intervals. This ability to quickly reshape the frequency comb is crucial for a number of applications in RF photonics including dynamic RF generation and reconfigurable RF filtering [5]. Lastly, note that the variations in the selected comb teeth amplitude are due to gain saturation at EDFA₃ and could be compensated for in the future by adjusting the power of the control pulses injected into the EDFA.

 

Fig. 4. Demonstration of a reconfigurable frequency comb. (a) Spectrogram showing the selection of varying comb teeth at different times. (b) Cross-sections of the spectrogram are shown at the three times marked in (a). The resolution bandwidth was 8.5 MHz.

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4. Conclusion

In this work, we introduced a technique to manipulate closely-spaced frequency combs on a line-by-line basis using SBS. Depending on the application, the setup could be adjusted to manipulate frequency combs with more teeth or to update the modulation pattern more frequently. For example, the FSL platform has been used to generate frequency combs with 1000 lines covering more than 100 GHz [24], although ASE eventually limits the bandwidth and number of comb teeth which can be generated using this technique [26]. This approach could also be used to modulate frequency combs generated using other techniques, such as an electro-optic frequency comb or a mode-locked laser.

While the approach presented in this work is quite flexible, there are trade-offs between modulation depth, update speed, and the number of comb teeth which are controlled. One of the main drivers for these trade-offs is the Brillouin amplification process, since the modulation depth is dictated by the Brillouin gain and the PBS extinction. The Brillouin gain is proportional to the product of the pump power and the duration of the pump pulse. Since the peak pump power should be kept below ∼200 mW to avoid the onset of modulation instability [27], increasing the gain requires longer pulses. On the other hand, the update rate is set by the length of the pulse train, so achieving a faster update rate would require shorter pulses which would reduce the Brillouin gain or limit the system to manipulating fewer comb teeth. In addition, if the pulse duration approaches the phonon lifetime (∼10 ns), the gain spectrum will be broadened and the gain will be significantly reduced [28]. To some degree, this trade-off could be mitigated by using highly non-linear fiber which enables higher Brillouin gain at the same pump power (e.g., by reducing the mode field diameter). We also note that the length of the interaction fiber is set by the length of the pulse train as ${L_{fiber}} = {T_{control}} \cdot ({c/2n} )$ where c is the speed of light and n is the refractive index of the fiber. This ensures that each comb tooth always interacts with its corresponding control pulse once while passing through the interaction fiber. This is essential to avoid introducing amplitude modulation at the pulse train period. If the pulse train requires very long fiber, optical attenuation could be a concern.

In this work, the total comb bandwidth of 10 GHz was slightly less than the Brillouin frequency of ∼10.8 GHz. If the comb bandwidth exceeds the Brillouin frequency, care should be taken to ensure that none of the comb teeth overlap with the anti-Stokes resonances produced by the control pulses. This could be accomplished by adjusting the comb spacing, or adjusting the Brillouin frequency by selecting a different fiber type.

One potential challenge with this technique is that the Brillouin amplification process will introduce noise [29]. In previous works using SBS to select individual comb teeth, phase locking techniques were shown to compensate for modulation introduced by the SBS amplification process [14,17]. In the implementation presented in this work, which leverages the polarization pulling effect to increase the modulation depth, position dependent polarization fading can also introduce a temporal modulation to the selected comb teeth. This could be avoided by using polarization maintaining (PM) fiber. While PM fiber would preclude the use of polarization pulling, the anti-Stokes interaction could be combined with the Stokes interaction to maintain a high modulation depth by attenuating some lines while amplifying others. This would require two trains of control pulses—one in which the control pulses are shifted by $- {f_{SBS}}$ relative to the comb and one in which the control pulses are shifted by $+ {f_{SBS}}$. The lower frequency control pulses could then be selected to attenuate some comb lines while the higher frequency control pulses could be used to amplify others.

In summary, we introduced a technique to generate and manipulate a frequency comb in a line-by-line manner with high spectral resolution. This approach uses a single seed laser to generate the comb and the control pulses, providing a scalable approach to manipulate large numbers of comb teeth. We showed that polarization pulling assisted SBS can enable the selection of individual comb lines with modulation depth ∼30 dB. Using this technique, we demonstrated the simultaneous modulation of 50 comb teeth. In this work, we focused on the ability of this technique to modulate the amplitude of individual comb lines. The SBS effect could also be used to modulate the phase of individual lines by slightly detuning the control pulses from the Brillouin frequency. In the future, we plan to investigate this functionality which could enable full control over the amplitude and phase of an optical frequency comb.