Frequency-tuning dual-comb spectroscopy using silicon Mach-Zehnder modulators.

Dual-comb spectroscopy using a silicon Mach-Zehnder modulator is reported for the first time. First, the properties of frequency combs generated by silicon modulators are assessed in terms of tunability, coherence, and number of lines. Then, taking advantage of the frequency agility of electro-optical frequency combs, a new technique for fine resolution absorption spectroscopy is proposed, named frequency-tuning dual-comb spectroscopy, which combines dual-comb spectroscopy and frequency spacing tunability to measure optical spectra with detection at a unique RF frequency. As a proof of concept, a 24 GHz optical bandwidth is scanned with a 1 GHz resolution.

While OFCs could be exploited by spatially demultiplexing the generated comb teeth, the most attractive use of these devices is the multi-heterodyne or dual-comb configuration, which enables high frequency resolution and accuracy, within a fast detection technique, with many applications in spectroscopy and metrology [16][17][18][19][20][21][22][23][25][26][27][28][29][30][31][36][37][45][46][47][54][55]. By combining two combs with slightly different repetition rates on a photodetector, an image of the optical spectrum can be obtained by measuring the RF spectrum. The analysis of the optical spectrum thus relies on the measurement of the RF spectrum at the photodetector output. In this context, EOFCs present two key features: they provide frequency spacing tunability, and using the same laser source to generate both combs enables a high mutual coherence time, avoiding the need for mutual comb locking.
In terms of photonics integration, Si photonics is a mature technology which benefits from high-volume fabrication. Low cost, small size, low weight systems are thus expected. High speed depletion-based silicon electro-optical modulators have shown robust performance in telecommunications for many years [56]. However the use of silicon modulator to generate EOFC is still sparse [10][11][12][41][42][43][44][45].
In this paper, the benefits of EOFC in terms of tunability are used to propose a new method for fine resolution absorption spectroscopy. Indeed dual-comb spectroscopy is combined with the agility to tune the frequency spacing of EOFCs to scan the optical spectrum while generating beat notes at fixed RF frequencies. The detection is then performed at fixed RF frequencies, allowing simple instrumentation. This is possible by tuning simultaneously the frequency spacing of both EOFCs, while keeping constant the difference between the two EOFCs frequency spacings. In the experimental demonstration, both EOFCs are generated on chip using a fixed wavelength laser source and two silicon-based Mach-Zehnder modulators (Si MZM). In the reported experiment, the mutual coherence between both combs is first investigated, showing a mutual coherence time better than 50 µs. The tunability of the EOFCs repetition rates is then studied between 1 and 12 GHz. Finally the proposed method is demonstrated by recovering the transfer function of an optical band-pass filter. Interestingly, using a fixed wavelength source and detecting two beat-notes, a 24 GHz optical bandwidth is scanned with a 1 GHz resolution.

Si modulator design, fabrication and performances
The Si modulator is a single-drive Mach-Zehnder modulator. The phase modulation is obtained by carrier depletion in PN diodes embedded in each arm of the Mach-Zehnder interferometer (MZI). Both PN junctions share the same electrical potential for the N side. The applied RF signal is thus distributed in opposite phases on the two arms, intrinsically setting the modulator in push-pull operation as illustrated in Fig. 1(b). The modulator was fabricated by STMicroelectronics, in their 300-mm SOI technological platform [57]. The waveguide width is 400 nm and its height is 300 nm, a slab thickness as low as 50 nm ensures a strong confinement of the guided mode, as shown in Fig. 1(a). Ion implantation is used to form the PN diode. Each phase shifter length is 4 mm. The modulator is working at a wavelength of 1.55 µm, with a 3 dB optical bandwidth of 35 nm, essentially limited by the grating couplers. Metallic resistive strip lines are placed above each arm as heaters to tune the static phase difference between the two arms by thermo-optic effect, under the application of a small DC voltage.
The measured V π is 8 V and an 18 GHz small-signal electro-optic bandwidth was measured using a Lightwave component analyzer. Optical losses due to free carrier absorption have been estimated by numerical simulation. A value of 1.24 dB×mm −1 is obtained at 0 V, decreasing to 0.63 dB×mm −1 at -14 V.

Heterodyne detection of frequency combs from Si EOFC generator
The principle of electro-optic comb generation lies in the nonlinearity of the electro-optical modulation [ Fig. 2(a)]. By undergoing a sinusoidal phase modulation (frequency f REP ), the optical carrier alternatively experiences positive and negative chirps. The instantaneous frequency of the electric field is thus periodically oscillating at the repetition rate f REP . The corresponding spectrum therefore contains a set of discrete frequency lines, separated by the modulation frequency [43]. Indeed, if we consider an electric field E IN at the input of a phase modulator, oscillating at the angular frequency ω 0 , it can be expressed as: After undergoing phase modulation, the field at the output becomes: where A is the phase modulation amplitude, and ω REP = 2π×f REP is the angular frequency of the modulation. According to the Jacobi-Anger expansion, Eq. (2) can be written as: where J n () is the n th order Bessel function of the first kind. As it can be seen from this expression, new lines are generated at angular frequencies (ω 0 + n×ω REP ), and the nth order line is weighed by a coefficient J n (A). When the electric field E OUT,1 at the output of the first MZM arm is combined with the electric field E OUT,2 at the output the second MZM arm, with a heater phase offset ϕ H , the total electric field exiting the modulator is: In plasma dispersion effect-based silicon phase modulators, an amplitude modulation of the electric field occurs along with phase modulation, which makes the Jacobi-Anger expansion formalism unsuitable in this situation. A numerical model of the MZM is therefore implemented to simulate the Si EOFC generator. Both the effective index and the optical loss due to free carrier concentration variation with applied voltage are considered in the modeling of phase shifters. After using Eq. (4) to combine the modulated output of each MZM arm, a fast Fourier transform algorithm converts the temporal evolution of the field into the optical spectrum. Figure 2(b) shows the simulated spectrum, for a 22 dBm-RF signal at 2 GHz frequency. A set of frequency lines separated by f REP is obtained. The amplitude of the different lines, i.e. the achieved spectrum shape depends on the static optical phase difference between both arms of the MZM. Each comb line is labeled by its frequency f n , n being a line number, the carrier is f 0 . As standard grating-based optical spectrum analyzers do not provide enough resolution to resolve the individual lines of an EOFC with a line spacing of a few GHz, a heterodyne technique can be used to map the optical comb in the RF domain. This method is schematically illustrated in Fig. 2(c). The laser output is separated in two beams, one that is sent to the Si MZM to generate the optical comb, while the frequency of the second beam is shifted using an acousto-optic modulator. The shifted line acts as a local oscillator when mixed with the comb in a photodiode. The resulting electrical spectrum thus contains an image of the optical comb, folded on itself by its beating with the shifted laser-line. Such heterodyne detection technique has been modeled, and the electrical spectrum obtained from the simulation can be seen in Fig. 2(d). It can be observed that the resulting spectrum is a set of groups of 3 lines, repeated around the multiples of the comb repetition frequency (2 GHz for the considered frequency). In each set of 3 lines, the right and left lines (f n∆ ) are images of the EOFC lines f n [ Fig. 2(b)], beating with the local oscillator whose optical frequency is f 0 +f AOM . Finally, the middle line in each set corresponds to multiple beatings between EOFC lines themselves.
The set-up in Fig. 2(c) was used to measure EOFCs generated by a Si modulator. For all the experiments, the PN junctions are reverse biased by a -6 V DC voltage. A 22 dBm (peak to peak voltage of 8 Volts) sinusoidal RF signal at 2 GHz is applied to the modulator, and a 40 MHz sinusoidal signal is applied to the acousto-optic modulator to shift the laser line. The laser wavelength is set to 1.55 µm and the total optical power received on the photodiode is 0 dBm. The photodiode is connected to an electrical spectrum analyzer (ESA), with a resolution bandwidth of 100kHz. The measured spectrum is shown in Fig. 3. A total of 11 EOFC lines were recovered (the beating between the carrier and the local oscillator at 40 MHz is not shown in Fig. 3), in good agreement with those obtained by simulation [ Fig. 2(d)]. Similar experiments were performed, with Si modulator driving frequencies of 1, 3, and 5 GHz, showing equivalent performance.

Dual-comb spectroscopy using Si EOFC generators
Dual-comb spectroscopy is a well-known technique that enables high frequency resolution measurements. It relies on the beating of two OFCs with slightly different frequency spacings (f REP,1 and f REP,2 = f REP,1 + ∆f REP ). Each pair of comb lines creates a beat note at a frequency given by the separation between the comb lines. Thus it is possible to map the optical spectrum to an RF spectrum, with a resolution of about f REP,1 while the spectral width is stretched by a factor ∆f REP /f REP . If one or both OFC pass through a substance to be detected it is possible to recover its transmission spectra, by the measurement of the beat notes in the RF domain. Interestingly, by ensuring a high mutual coherence between the two OFCs, the dual-comb interferogram can be recorded over a long period of time, and the resulting high amount of collected optical power provides an improved signal-to-noise ratio [16][17][18][19][20]22,[26][27]53]. On the other side, real-time measurement can also be performed, enabling direct observations of transient responses of complex optical spectra [16][17][18][26][27]37,47]. In both cases, EOFC is a well suited solution for dual-comb spectroscopy: since a single laser can be used to generate the two EOFCs, a high mutual coherence is naturally ensured between them, avoiding the need to lock one comb to the other, and the flexibility of EOFCs allows to tune straightforwardly the combs frequency spacings [3][4]16,[28][29][30][31]47].
In the experimental demonstration, the two EOFCs are generated on a chip using single drive Si MZMs. Coherence properties and repetition rate tuning of Si-based EOFCs in dual-comb configuration are evaluated using the experimental set-up represented in Fig. 4(a). To avoid aliasing in the measured beat notes, an acousto-optic modulator (AOM) is used to shift one OFC in frequency by 40 MHz. The two combs are then combined and sent to a 32 GHz-photodiode, followed by an electrical spectrum analyzer.
The two RF synthesizers deliver a 24 dBm signal and are synchronized with a 10 MHz reference. Figure 4  To assess the coherence properties of the Si-based EOFCs, a zoomed superposition of the different beat notes is reported in Fig. 5(a), the resolution bandwidth of the ESA is set to 10 kHz for this measurement. Interestingly their 3 dB linewidth is below 20 kHz, which corresponds to a mutual coherence time better than 50 µs [26]. To confirm the simple tuning of Si-based EOFCs, their frequency spacings have been tuned by adjusting f REP,1 and f REP,2 , while ∆f REP is kept constant and equal to 4 MHz. In Fig. 5(b), the RF power levels of the 5 main beat notes are shown, when f REP,1 is swept from 1 to 12 GHz. The RF power applied on each modulator is 24 dBm. It can be seen that the power of all beat notes remains steady over this frequency range, and the effect of the modulator bandwidth is barely noticeable.

Frequency tuning dual-comb spectroscopy (FT-DCS): proof of concept
Frequency-tuning dual-comb spectroscopy (FT-DCS) is proposed for fine resolution spectroscopy using detection at fixed RF frequencies. Thus it would be possible to use electronic band-pass filters and amplifiers to extract the power of individual lines without affecting the system flexibility. This method relies on the extremely easy tuning of the frequency spacing of EOFCs to measure optical spectra with a high precision.
In the FT-DCS, both EOFCs frequency spacing (f REP,1 and f REP,2 = f REP,1 +∆f REP ) are tuned simultaneously to cover the optical spectrum around the laser frequency, while ∆f REP is kept constant. Thus, by measuring the power of the fundamental beat notes at frequencies f AOM + ∆f REP and/or f AOM -∆f REP for the different values of f REP,1 , it is possible to image the entire optical spectrum.
As a proof of concept, an optical band-pass filter (YENISTA XTM-50) was placed just before the photodiode [i.e. the output of the combiner is switched to the grey dashed path in Fig. 4(a)]. To recover the transfer function of this filter, the powers of the fundamental beat notes [i.e. B2 and B4 in Fig. 4(b)] were measured for different repetition rates (f REP,1 was swept manually from 0.5 GHz to 12.5 GHz), while the repetition rate difference between the two EOFCs was kept constant (∆f REP = 4 MHz). A reference dual-comb spectrum was also taken at each step by bypassing the filter. It is then possible to reconstruct the optical spectrum by subtraction and normalization of the two measurements. Figure 6(a) shows the optical transfer function of the filter, recovered by the Si-based FT-DCS method (red points). The grey dashed line indicates the measurement noise floor, given by the difference between the fundamental beat note power of the reference dual-comb spectrum and the ESA noise floor, while the resolution bandwidth is 100 kHz. The resulting optical signal-to-noise ratio (OSNR) is about 15 dB. An alternative measurement of the filter transfer function was later performed using a YENISTA CT400 component tester. By direct sweeping the tunable laser over the 25 GHz span, with a 125 MHz step, the optical transmission was recorded at each step, resulting in the blue curve in Fig. 6(a). Due to a ±5 GHz uncertainty on the tunable external cavity laser output absolute frequency, the two measurements initially showed a static 4.75 GHz mismatch. To reduce this static mismatch, a referenced laser with higher frequency accuracy has to be used [29,52]. However to compare the shape of the recover filter spectra, both measurements have thus been normalized in frequency, relatively to the filter transfer function center. When comparing both measurements, a very good agreement is seen. A 10 dB bandwidth of 24 GHz (0.19 nm) is obtained in both cases. The difference between both measurements is displayed in a linear scale as residuals in Fig. 6(b), and the standard deviation is estimated to be 2.7%, confirming the very good precision of the FT-DCS method for spectral measurements.

Discussion
In this work the FT-DCS has been proposed as a fine resolution spectroscopy technique, and only two beat notes (b 2 and b 4 ) were measured while scanning the spectrum. However, Si-based EOFC generators can also be used in more classical dual-comb spectroscopy experiments where a large number of flat lines are usually required. In this case the performances in terms of spectral spanning are given by the modulator electro-optic bandwidth, which gives the maximum line spacing, and by the modulation efficiency which gives the maximum number of lines above a given power threshold. Optimizing simultaneously those parameters to map a wide spectral range using a single modulator usually leads to a tradeoff as, when increasing the phase shifter length to optimize the phase modulation efficiency, the electro-optic bandwidth is then limited by RF signal propagation loss, and by the mismatch between the optical and electrical propagating velocities. This tradeoff has been studied already in LiNbO 3 modulators, and the results can be translated to Si modulators. Among the possible solutions to optimize the EOFC performances it is possible: (i) to cascade several modulators and/or to cascade amplitude and phase modulation, to flatten the frequency comb as shown in [4,58]; (ii) to use electrical signals containing two or more frequencies to drive each modulator [41]; (iii) to use a resonant cavity, so that when the modulation frequency meets the cavity free spectral range, the light is being constructively modulated at each round trip, which is also equivalent to an increase of the effective modulator length [40]. All of these solutions could be implemented in Si photonics, for the generation of flat, frequency tunable and wide bandwidth frequency combs. Furthermore it can be added that the external AOM used in the experiment can also be replaced by an on-chip frequency shifter, such as a dual-parallel IQ modulator also achievable within Si photonics platform.

Conclusion
Dual-comb spectroscopy using silicon single-drive push-pull MZMs is reported for the first time. The general properties of Si-based EOFCs (tunability, coherence, number of lines) have been assessed. Then, taking benefit of the frequency agility of EOFCs, we proposed a new technique for fine resolution spectroscopy within a simple experimental set-up. This method, named frequency-tuning dual-comb spectroscopy (FT-DCS), relies on the extremely easy tuning of the frequency spacing of EOFCs to measure optical spectra with a high precision, using a single-wavelength laser and a simple detection at a unique RF frequency. By sweeping the repetition rate of the two EOFCs within the modulator bandwidth, and keeping their frequency spacing difference constant, the measurement of the fundamental beat notes allows to scan the optical spectrum and to measure sample absorption. As a proof of concept, the amplitude transfer function of an optical filter has been measured. The 10 dB-bandwidth of 24 GHz (0.19 nm) was retrieved, and the transfer function was successfully compared with classical tunable laser experiment. These results pave the way for further absorption spectroscopy applications as the achievable frequency range are compatible with typical molecules absorption linewidth. Furthermore, the use of silicon photonics, as a mature technology platform which benefits from CMOS fabrication facilities opens the path towards large scale fabrication of compact spectroscopic systems.