1. Introduction

Optical Frequency Combs (OFC) consist of equalized and periodically spaced coherent lines in wavelength space. Frequency combs have found extensive applications across sensing [1], spectroscopy [2] and precision measurements [3]. In the development of integrated transceivers for high speed optical communications applications, frequency combs have also been considered as natural replacements for multi-laser based Wavelength Division Multiplexing (WDM) sources for use in photonic transmitters. On-chip WDM in silicon photonic transceivers, has typically been implemented by hybrid integration of multiple III-V platform lasers onto a silicon photonic chip [4].

Several approaches have been considered for generating optical frequency combs on-chip in CMOS compatible platforms: harnessing third-order susceptibility in micro-resonator structures in materials like silicon nitride [5], oxide [6], Hydex [7] etc. Frequency combs generated by cascaded four-wave mixing processes in such microresonators have large, octave spanning bandwidths, but on the other hand, have discretely tuneable centre frequencies [8] and fixed repetition rates that is determined by the microresonator dimensions thus making them unsuitable for applications that require a flexible grid.

In our previous work [9,10], we demonstrated stable, on-chip, optical frequency comb generation through strong phase modulation of an optical carrier in linear silicon-based charge injection modulators. Frequency combs generated this way, have continuously tuneable centre wavelength, that is only limited by input-output grating coupler bandwidth and possess flexible and tuneable repetition rate spanning several GHz [Fig. 1(a)]. An attractive feature of this method is the ease of integration with other pre-existing devices in silicon photonics and CMOS compatible fabrication. Comb generation using this principle has also been recently investigated in silicon microring modulators [11–13], and in various Mach-Zehnder modulator configurations [14–16] as flexible-grid based WDM transmitters, for pulse generation, microwave synthesis etc.

 

Fig. 1. a) Standard single carrier approach to on-chip frequency comb generation. b) Multi-carrier approach to bandwidth scaling on-chip frequency combs using a single comb generator. Resultant comb lines have uncorrelated frequency drifts. c) Frequency offset locking the two lasers using lines in an overlapped region removes the uncorrelated drifts.

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In this comb generation technique, maximizing the number of lines generated, typically requires optimizing on-chip modulator properties, for example, increasing modulator length or doping concentration at the cost of increased free carrier absorption loss. Another method involves cascading of multiple modulators [17], however this requires additional RF-components like phase-shifters for temporal phase alignment, amplifiers etc. that increase system cost and complexity and also loss due to the modulator cascade.

Alternatively, a modulator can be driven with multiple offset optical carriers to result in scaling of the number of lines. However, the uncorrelated drifts between the offset optical carriers create uncorrelated drifts between the two groups of generated lines [Fig. 1(b)]. Thus, this approach is more akin to a multiwavelength source than a frequency comb. However, if the frequency offset of the multiple carriers can be locked, then this approach provides a convenient technique for scaling the bandwidth of the comb [Fig. 1(c)].

In this work, we demonstrate a proof of concept experiment of this approach [18] by using dual carrier inputs to a single silicon modulator based comb generator and link the resulting two optical frequency combs generated with active stabilization. Linking of frequency combs from individual sources has previously been investigated in the context of fiber based combs for spectroscopy applications [19], using bulk electro-optic modulators in a Fabry-Perot cavity [20] and for generating tuneable THz sources [21].

Using this technique, we demonstrate an increase from 6 comb lines of a 10 GHz comb source from a single input carrier, to 11 lines using dual-offset input carriers in a 20 dB band. The two combs are locked to each other to within a 3 dB bandwidth of 4.305 MHz at a 75 MHz frequency offset from a local oscillator. Further, we note that as III-V on silicon integration technologies that integrate multiple semiconductor optical sources on a silicon chip mature, this technique allows for a convenient means to accomplish on-chip comb bandwidth scaling in these systems.

We also note that owing to the general nature of this technique, it can easily be extended to other recently demonstrated electro-optic on-chip comb generation platforms like Indium Phosphide [22,23], Silicon-Organic-Hybrid (SOH) modulators [24] and lithium niobate on insulator based systems [25].

2. Bandwidth scaling

An optical phase/frequency-locked loop (OPLL) is an optical frequency stabilization technique that uses a secondary laser (as a current controlled oscillator) to track the relative phase, frequency drifts of a reference laser and has been extensively used in optical receivers [26], optical frequency synthesis [27], locking widely spaced optical carriers [28] etc. Here we implement an optical frequency locked loop using commercial off-the-shelf components to lock two optical frequency combs generated from a common on-chip silicon modulator, to each other, resulting in a bandwidth scaled comb. We note that for combs phase locked to each other, the OPLL maintains coherence of comb lines [29] due to coherence cloning across the bandwidth scaled comb lines, for all frequencies below the loop-bandwidth.

Figure 2 shows the experimental system. We drive the silicon modulator with a reference laser (Laser-1) centered at $\lambda_1$ and another laser (Laser-2) with an offset at $\lambda_1$. The resultant frequency combs have a small overlap region. A Bandpass Filter (BPF) is used to select lines from the overlapped region that is captured on a Photodiode (PD). The beat signal is further downmixed using a signal generator at 75 MHz before being processed by the loop-filter. A current control signal from the loop filter regulates the wavelength of Laser-2 and hence the frequency comb from Laser-2 so as to track changes from the frequency comb generated by Laser-1.

 

Fig. 2. Setup to frequency lock and bandwidth scale combs from individual carriers. OSA: Optical Spectrum Analyzer, BPF: Bandpass filter ESA: Electronic spectrum analyzer, PD: Photodetector, D.C: RF-Directional coupler.

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As described in our previous work [9], we fabricate a 4.5 mm long travelling wave, PN-doped, silicon phase modulator in a rib-waveguide configuration on a 220 nm Silicon-on-Insulator (SOI) platform using a Europractice multi-process wafer (MPW) run [30]. We estimate the Vpi of the modulator at 5 GHz to be ∼4.56 V peak voltage using the carrier nulling method [31]. Both lasers (Keysight N7714A and Thorlabs SFL1550S) at a source power of +14 dBm are used to drive the silicon modulator. Light is vertically coupled to the modulators, using input-output silicon grating couplers with ∼4 dB loss per coupler. The optical carrier is modulated sinusoidally with a microwave power source (HMC-T2220) through on-chip Ground-Signal-Ground (GSG) microwave wafer probes, at 7.8Vpp and 10GHz drive frequency. The modulator is externally terminated at the other end of the GSG-configuration travelling-wave electrodes using a 50-ohm load. No DC bias is necessary for the comb generation. Figures 3(a)–3(b) shows Optical Spectrum Analyzer (OSA) spectra of individually generated combs with Laser-1 centered at 1549.972 nm and Laser-2 at 1550.376 nm each having 6 lines in a 20 dB band captured at a 0.02 nm resolution. We note that the proposed technique is independent of the choice of the flatness margin which can be chosen appropriately based on application of interest. When the modulator is simultaneously driven by both lasers, [Fig. 3(c)] the common overlapping lines between the two unlocked combs are located at ∼1550.216 nm and are filtered out using an optical band-pass filter.

 

Fig. 3. a) OSA spectra of individual 10 GHz repetition rate frequency comb of Laser-1 at a center wavelength of 1549.972 nm with 6 lines in a 20 dB band and b) from Laser-2 with center wavelength: 1550.376 nm also with 6 lines in 20 dB. c) Combs generated from both lasers generated using the same modulator with 11 lines in 20 dB band. The overlapped comb line located at 1550.216 nm.

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The greater the wavelength offset between the input lasers is, the weaker is the amplitude of the lines in the overlapped region. This results in a weaker photodiode signal and thus, the photodetector sensitivity decides the wavelength offset between the two lasers.

For the comb generator and photodiode utilized in this experiment, a 0.4 nm offset between the two lasers is utilized. The two overlapping combs are unlocked at this stage. A free-running electrical beat signal from the overlapping comb lines is captured by the high-speed (10 GHz) photodetector and the instantaneous drift of the signal was measured through a directional coupler on an Electronic Spectrum Analyzer (ESA) as approximately 142 MHz [Fig. 4(a)] at a resolution bandwidth (RBW) of 1 MHz. The beat signal eventually drifts beyond the bandwidth of the photodetector within 1-2 minutes of free running operation if no active system stabilization is used.

 

Fig. 4. a) ESA signal of instantaneous free running beat signal between overlapped comb lines at 1550.216 nm with a frequency drift of ∼142 MHz, at a RBW of 1 MHz. b) ESA signal of frequency locked beat signal with a FWHM of 4.305 MHz, at a RBW of 10 MHz.

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The beat signal is amplified and further downmixed with a local oscillator at 75 MHz to form an error signal that is passed into a commercial tuneable loop filter (Toptica Mfalc 110) which modulates the current and hence the wavelength of Laser-2. Thus, relative frequency drift between the individual combs is captured by the beat signal and is compensated for by current modulation signals applied by this active loop filter to the laser current controller to minimize the error signal. The minimum tuning wavelength resolution attainable using our laser current controller (Thorlabs LDC205C) is ∼929 kHz corresponding to a step resolution of 10 uA. The implemented system was found to have sufficient tuning resolution and is much smaller than the loop propagation delay of the electro-optic control loop.

We sequentially program the tuneable loop filter to implement a four-stage filter that mimics the operation of a proportional-integral- derivative (PID) controller. The first stage comprises of a lag-lead filter that acts as an integrator that eliminates tracking errors corresponding to the low frequency components of the drift in the down-converted beat signal. This output is then passed to a second stage comprising of a slow lead-lag filter that acts as a derivative controller that ensures fast locking in the low frequency range. In the third stage, the error signal is further shaped by a fast lead-lag filter that acts as a derivative control to enhance the tracking response speed for the high frequency components of the beat signal drift. Finally, the error signal is passed through a proportional gain filter that is tuned such that the closed-loop system is stable with respect to disturbances arising from signal propagation delays, measurement and system noise etc. The filter parameters are carefully optimized by tuning the time constants of the lead-lag and lag-lead filters, and the proportional gain to eliminate the steady-state tracking error corresponding to the beat signal drift.

In our setup, the tuning bandwidth of the laser (Laser-2: Thorlabs SFL1550S) between successive mode-hops is 5GHz. While a slower time-scale temperature modulation as well as a faster time-scale current modulation can be employed as actuating components to control the wavelength of the laser, we choose to employ a current-only control architecture due to the aforementioned bandwidth limitation. Further, this system was successful in providing stable tracking performance over a long period, eliminating the need for the slower temperature controller to compensate for long-term drifts.

Using this configuration, the beat signal was locked at a 75 MHz heterodyne offset and was confined to a 3 dB linewidth of 4.305MHz [Fig. 4(b)]. The resultant locked 11 frequency lines [Fig. 3(c)] now form a single composite optical frequency comb.

The performance of our OPLL is limited by significant electro-optic loop delay, >100 ns in our setup and use of discretely tuneable loop filter gain values. This is due to the use of off-the-shelf bulk components with fiber extensions of considerable length and also the response time (∼6.6 µs) of the external laser current controller. This however, is not a fundamental limitation, since custom optical frequency locked loops can be implemented in compact, low power, integrated systems [32,33] where the loop propagation delay is minimal and optimized.

A means to further bandwidth scale frequency combs with this system (Fig. 5). requires the use of three input carriers. Here, Laser-2 and Laser-3 are offset from the master, Laser-1 by multiples of the frequency comb repetition rate on either side of comb-1.

 

Fig. 5. System to bandwidth scale on-chip silicon modulator based frequency combs using three input carriers. A composite frequency locked comb made of three individual combs can be generated on-chip from appropriately offset carriers and use of two optical frequency locking systems.

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Beat signals generated from overlapping lines on both sides of comb-1 monitor drift. In this manner use of two independent integrated loop filters, would allow for linking multiple frequency combs to form a larger composite frequency locked comb. However, in order to scale this system to a larger number of carriers (N >3), the OPLL would ideally have to be designed with consideration of the following issues: a) delay induced instabilities that would arise from adding more lasers and hence nesting the OPLL systems; and b) the design of the Nth OPLL would require a detailed knowledge of the closed loop dynamics of the system interconnected with all the previously designed (N-1) nested OPLL’s; and c) the power consumption of the electro-optic control loops would scale as (N-1) P. Where ‘P’ is the total power consumed by the individual components of a single electro-optic control loop i.e. of the added control laser, photo-detector and active loop-filter. However, the use of compact and integrated implementations can minimize power consumed and, finally, d) the system design would have to ensure that the relative phase errors between the overlapping combs in a cascaded system be small for stability of the composite system and will be the subject of future investigation.

3. Summary

In this work, we have demonstrated a comb-to-comb locking based bandwidth scaling technique suitable for frequency combs generated in on-chip linear charge injection based silicon modulators using an optical frequency locked loop. In this work, we demonstrated a proof of concept experiment which approximately doubled the bandwidth of a 6 line, 10 GHz integrated frequency comb to 11 lines at 10 GHz. We can also extend this technique to multiple input offset carriers to further scale the frequency comb bandwidth. We note that the method proposed here is applicable to combs generated from modulators without wavelength selectivity of operation and cannot be employed directly for e.g. with microring modulator based frequency combs due to their wavelength selective behavior in the form of discretely spaced, thermally sensitive, resonances.