1. Introduction

There has been significant interest in developing direct optical frequency comb spectroscopy for applications that take advantage of the comb’s broadband and parallel nature, including optical breath analysis [1], atmospheric sensing [2] and industrial processing [3]. Extracting spectral information from such a measurement can be challenging, requiring either relatively complex optics [4,5] or a second comb [6–8]. However, there are applications that only require optical bandwidths of a few 10s of GHz; for example high resolution spectroscopy aimed at Doppler broadening thermometry [9, 10] and measurements of the drift of fundamental constants [11,12]. These applications also benefit from parallel interrogation with the narrow probing linewidths and inherent stability of an optical frequency comb source. With these restricted bandwidths, it becomes practical to use a single CW laser as a local oscillator to access the spectral information sampled by the comb. The CW laser is combined with the comb and allowed to interfere on a fast photodetector, where the optical beat-notes between the two encode the amplitude and phase of each comb mode with respect to the local oscillator. Previous work [13–15] has successfully used fast acquisition techniques to extract the spectral information from this signal, but must use sampling rates of order GHz to ensure that a sufficiently broad spectral region is captured.

Fortunately, if the phase coherence between the comb-modes and CW laser is sufficiently good then it is possible to compress the available spectral information and reduce the required data acquisition bandwidth by several orders of magnitude, allowing the use of acquisition electronics commonly found in the lab. This work describes the use of an injection locking technique for achieving a very narrow and stable local oscillator relative to the interrogating comb and explores two methods for extracting spectral information at significantly reduced sampling rates when compared to the direct detection approach.

2. Methods

There are three key steps involved in this work: frequency stabilisation of a CW local oscillator with respect to the interrogating comb modes; down-mixing spectral information from the optical to microwave domain; and the final down-mixing from the microwave to the RF domain. The first two steps are achieved using primarily optical techniques, the third is purely electronic.

2.1. Stabilisation of the CW local oscillator

The optical system shown in Fig. 1 was used to stabilise a CW extended cavity laser diode (ECDL) local oscillator and perform optical to microwave down-mixing. The interrogating light was provided by a commercial optical frequency comb (Menlo Systems FC1500-250-WG), with repetition rate ∼250 MHz and carrier offset frequency of 20 MHz, both referenced to a cesium reference (Datum CsIII). The comb was optically bandpass filtered by spatially dispersing the comb with a diffraction grating and coupling a small section into a single-mode optical fibre, resulting in a spectrally narrow comb consisting of ∼400 modes centred around 894 nm. A fibre splitter routed 10% of the filtered comb light through the rejection port of a Faraday isolator which then seeded a home-built Littrow-configuration ECDL, allowing injection locking to a single comb mode. The (∼17 nW) power-per-mode of the injected comb limited the injection locking range to ∼1 MHz. This narrow range ensured that the ECDL was locked to a single comb mode as well as ensuring good phase coherence between the ECDL and the interrogating comb. However, the free-running ECDL was not sufficiently frequency stable to remain injection locked for more than a few seconds, so an active injection locking scheme was implemented. Following the approach described in [16], a signal generated by a photodetector, PD_R, monitoring the comb repetition rate f_R, was used to demodulate the beat note signal between the slaved ECDL and the two adjacent comb modes directly amplified by the laser diode, measured by photodiode, PD_I. These modes acted as a phase reference for the slaved ECDL output, giving rise to a dispersive error signal that was used to lock (via a proportional-integral (PI) controller) both the laser diode current and the position of the ECDL grating (via a piezo-electric actuator) to the centre of the injection locking range.

 

Fig. 1 Optical down-mixing scheme. A small amount of comb light is used to actively injection lock an extended cavity diode laser (ECDL) to a single comb mode. This light is then passed through a Fabry-Perot filter, frequency shifted and power stabilised before being combined with the main part of the interrogating comb light. This signal is then passed through a sample and reference arm of a spectrometer with the resulting optical signals recorded by a pair of fast photodetectors.

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The CW laser was then passed through a Fabry Pérot filter cavity (FP) that acted to reject directly amplified comb-modes as well as the spontaneous emission and relaxation-oscillation features of the laser diode, ensuring a high-purity CW signal. The cavity had a finesse of ∼250 and a free spectral range of ∼17.5 GHz and tracked the ECDL output via a dither lock (DL). The cavity length was dithered via a piezo-electric ring actuator behind one of the cavity mirrors at 8.4 kHz, and the reflected signal was demodulated by a lock-in amplifier (SRS SR530). The resulting error signal was passed to a proportional-integral controller and back to the piezoelectric actuator to stabilise the length of the cavity.

The CW light was also passed through an acousto-optic modulator (AOM) to provide power stabilisation (via a proportional-integral power control (PC) servo) as well as introducing a frequency shift of ∼ f_R/4 to simplify subsequent signal processing. The power control servo was used to counter CW power fluctuations primarily introduced by the cavity and by alignment fluctuations at the input to the fibre combiner. A modest locking bandwidth of order 1 kHz was more than adequate to eliminate the effects of CW power fluctuations on the retrieved spectra.

With these systems in place the CW laser became a power-stabilised, frequency-shifted copy of the seed comb mode, exhibiting sub 100 Hz linewidth relative to the other comb modes, with stability at a similar level over many hours. The available CW after coupling into single-mode fibre was 3.8 mW (out of an initial 25 mW).

2.2. First stage down-mixing: Optical to microwave

The remaining 90% of the filtered comb light (with 60.2 μW total power, ∼ 150 nW power-per-mode) was combined with the stabilised and frequency shifted CW laser and then equally split, with half of the combined signal passing through a Brewster-windowed cesium reference cell (sample path), while the other half traversed an equivalent length of optical fibre (reference path). The CW and comb signals are combined prior to the split into sample and reference paths to ensure an identical phase relationship between the CW light and the comb modes for both paths. Both sample and reference path outputs were captured by high-speed photodetectors (Discovery Semiconductors R401HG), giving rise to signals V_sig and V_ref, respectively. Each path transmitted (and each photodetector was exposed to) ∼ 700 μW of CW power, and ∼ 10 μW comb power (∼ 25 nW power-per-mode).

Optical interference at the photodetectors results in the production of a microwave comb with strong, narrow features resulting from harmonics of the comb repetition rate at intervals of f_R and a series of beat-notes between the local oscillator and the interrogating comb that preserve the sampled spectral information as a microwave comb folded about DC. An illustration of the down-mixing process is shown in Fig. 2. Here, the grey features represent the repetition rate harmonics, and the positions of the beat-notes formed between the local oscillator and the comb-modes on either side are colour coded to show their final positions. Amplitude and phase information sampled by the interrogating comb modes (with respect to the local oscillator) are preserved by the down-mixing process.

 

Fig. 2 Optical to microwave down-mixing. The frequency-shifted CW local oscillator interferes with each comb mode producing a series of optical beat-notes. The solid line indicates how the absorption spectrum is folded about the local oscillator at the output of the photo-detector. Also present are large signals at the harmonics of the interrogating comb’s repetition rate (grey).

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At this point, the photodetector signals can be extracted directly, by use of a spectrum analyser, for example, to capture transmittance [14] or, more elegantly, by sampling at high bandwidth to capture the full complex spectra [13,15]. However, if the features of the photodetector signal are sufficiently narrow it is possible to further down-mix this signal to the RF domain where the amplitude and phase information can be extracted using cheap and readily available RF electronics.

2.3. Second stage down-mixing: microwave to RF

The second down-mixing stage shifts spectral information from the GHz range down to the RF. We present two different ways to achieve this: First, we tune a CW microwave source to each beat-note in turn and extract the spectral information in a serial fashion. Second, we use a parallel interrogation technique, similar to that used in dual-comb spectroscopy, whereby the microwave comb at the output of the photodetector is mixed with an electronically generated microwave comb with a slightly detuned repetition rate, creating a new RF comb containing the desired spectral information. It is important to note that this second down-mixing step comes at a cost in the form of a fundamental reduction in the amount of retrieved spectral information over that available to high-speed acquisition techniques. The general scheme for both methods is shown in Fig. 3.

 

Fig. 3 Microwave to RF down-mixing scheme. Microwave interrogation signals provided by either a stepped CW source (pink region) or microwave comb generated by a step recovery diode (SRD) (blue region) are mixed with the optically down-mixed signals V_sig and V_ref (see Fig. 1). The mixing products are recorded by the two input channels of a fast Fourier transform (FFT) vector signal analyser.

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2.3.1. Serial readout

The serial approach uses a CW microwave signal generated by an RF synthesiser (Agilent E8257D) to interrogate each beat-note in turn. In this case, the fundamental spectral information reduction comes about because at each interrogation frequency we can only interrogate the equivalent of a single comb mode, rather than the entire spectrum. Hence it takes N times longer to take the equivalent spectrum, where N is the number of distinct interrogation frequencies.

The CW signal is split and each copy is sent to the LO port of a microwave mixer. The optically down-mixed comb appearing on each of the sample and reference photodetectors is amplified and sent to the RF port of the corresponding mixer. The CW interrogation signal is stepped to each beat-note (offset by f_C=1 MHz) and the resulting IF mixer outputs for the reference and sample paths are sent to the channel 1 (CH1) and 2 (CH2) inputs, respectively, of a fast-Fourier-transform (FFT) vector signal analyser (Hewlett-Packard HP89410A). Both the synthesiser and FFT signal analyser were phase-locked to the same cesium reference as the comb. The transmittance and phase information from each beat-note were acquired by sampling the CH2/CH1 response function at an offset frequency of 1 MHz with a resolution bandwidth of 100 Hz, span of 1 kHz and 10 averages.

2.3.2. Dual-comb readout

The dual-comb readout borrows the central idea from dual-comb spectroscopy [6], employing a second, electronically generated microwave comb with a repetition rate slightly detuned from the spacing of the optically generated microwave comb found at the output of each fast photodetector. Mixing these combs gives a new comb with features spaced by the difference in repetition rate. This process can also be thought of as a resampling of the optically down-mixed comb by the second, detuned comb [17], which creates a slowed copy of the impulse response signal appearing at the photodetector output with a new repetition rate characterised by the frequency detuning. This process necessarily rejects most of the available spectral information, increasing measurement time for an equivalent spectrum by a factor of f_R/Δf, where Δf is the frequency detuning of the second comb.

Here, the detuned comb is generated by a step-recovery diode (SRD) (Herotek GC110RC) driven at 27 dBm at a frequency of f_R/4 + 8 kHz, generated by an amplified frequency synthesiser (Agilent N5181A) phase-locked to the same cesium reference as the comb. This creates a microwave comb with a repetition rate equal to the drive frequency. Power-per-mode is reduced at higher frequencies, but only by ∼20 dB at 12 GHz, leaving sufficient power at high frequencies to cover the useful bandwidth of the mixers. A high-pass filter was employed to attenuate the strong feature at the drive frequency and more evenly distribute signal power among the comb modes. The resulting RF comb is qualitatively similar to the microwave comb but with characteristic spacing reduced from f_R/4 (62.5 MHz) to 8 kHz, a reduction factor of ∼8000.

As in the serial case, the output from each high-speed photodetector was amplified and passed to the RF input of a microwave frequency mixer and down-mixed by a copy of the detuned microwave comb at the LO port. Again, the IF mixer outputs for both reference and signal paths were recorded by channel 1 and 2, respectively, of the FFT signal analyser. The magnitude and phase of the CH2/CH1 response function encode the optical transmittance and phase, respectively.

In our case, the vector signal analyser was set with a bandwidth of 1.6 MHz, a resolution bandwidth of 1.9 kHz and resolved 3201 frequency points, giving point spacing of 500 Hz. Adjacent, doubly-down-mixed comb features were thus separated by 16 frequency bins and, to be confined to one frequency bin, we required that the linewidth of each comb mode relative to the frequency shifted CW laser to to be less than 500 Hz. The injection lock ensured effective linewidths of less than 100 Hz, with long term stability at the same level. This allowed transmittance and phase spectra to be determined by simply extracting the magnitude and phase of the corresponding frequency bins in the response function.

3. Complex optical spectra measurements

3.1. Calibration

For a linear system, with well matched signal and reference paths, the optical transfer function of the signal path can be recovered directly from the CH2/CH1 response function. In this ideal system, the transmittance and phase information sampled by the interrogating comb modes propagate identically through both down-mixing steps and simply measuring the magnitude ratio and phase difference for each beat-note is sufficient to reconstruct the optical transfer function. In practice, building such a system is very difficult. Poor matching of the RF transfer functions of the electronics in the two paths gave rise to dramatic cumulative effects on the relative magnitudes and phases of the doubly down-mixed beat-notes. For both the serial and parallel technique, amplitude and phase variations were of order 10s of dB and 10s of degrees, respectively, over the ∼12 GHz bandwidth of the system.

Fortunately, if the system is sufficiently linear, these variations remain constant over time and can be effectively removed by introducing a calibration path. Replacing the cesium cell with an approximately path matched length of single-mode fibre and ensuring a sufficiently good power match (within ∼1%) results in a new system that experiences the same differing transfer functions as the cesium case, but does not contain the cesium spectral information. This magnitude and phase information is then used to normalise the magnitude and zero the phase of the system transfer function containing the cesium spectral information. After this correction, we also observe a phase ramp induced by the small residual path length imbalance between the cesium and calibration paths, resulting in a fixed phase shift between adjacent comb mode frequencies. This can be corrected if we assume that the optical phase far from the absorption features is zero and correct the phase shifts accordingly. This entire process is robust as long as the system is relatively linear with respect to optical power and stable as a function of time.

3.2. Serial readout

Figure 4 shows the reconstructed optical transfer function retrieved via the serial interrogation method, including the calibration steps outlined above. The darker points indicate the retrieved spectrum for an interrogating comb repetition rate of 250 MHz. This represents relatively sparse spectral sampling for the cesium features, with Doppler-broadened width of order 1 GHz. Changing the comb repetition rate slightly shifts the ensemble of interrogating comb modes and allows sampling at a new set of optical frequencies offset from the first. Here, we have taken spectral and calibration information and then shifted the repetition rate in increments of 46.52 Hz (shifting optical frequencies by ∼62.5 MHz) and repeating the measurement four times to fill in the rest of the spectrum.

 

Fig. 4 Reconstructed complex spectrum measured via the serial interrogation method, including calibration. Darker points represent the spectrum retrieved with the comb held at a repetition rate of 250 MHz, with the other points derived by shifting the comb mode frequencies by a quarter of the repetition rate. Solid curves represent a complex Voigt profile fit to the spectrum.

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We only show measurements between 3 and 12 GHz offset from the CW frequency, with performance outside this band severely limited by the microwave components comprising the final down-mixing stage. Also shown is a complex Voigt profile fit to the retrieved spectrum. Deviation from the expected line-shape is of order 1% for the transmittance component and 1° for the phase component. Off-resonance scatter is of similar order and is consistent with single-point fluctuations between repeated measurements. It is limited by the effective signal-to-noise ratio of the doubly down-mixed comb lines, varying somewhat across the spectrum and primarily due to variations in microwave component performance as a function of frequency. It can also be seen from the residuals that there was a small relative drift in both transmittance and phase for each successive set of comb modes. This was attributed to small drifts in attenuation and optical path length of the calibration path over time.

Frequency spacing of the line centres was measured to be 1162(7) MHz, which is consistent with the accepted value (1168 MHz) [18]. It is also possible to measure absolute frequency with this approach, though this has not been attempted for this work.

3.3. Dual-comb readout

Figure 5 shows the complex spectrum derived from the dual-comb interrogation method, including the calibration steps outlined above. Again, the darker points indicate the retrieved spectrum at a single comb repetition rate tuning, with the rest of the spectrum filled in by stepping the comb repetition rate, as before. The spectrum is of lower quality than that derived from the serial method, impacting both the useful bandwidth of the doubly-demodulated signal as well as the effective signal-to-noise ratio of the instrument. We also note large systematic errors in the spectra. A complex Voigt profile with the width, relative depths and spacing of the features taken from the serial data returns a satisfactory fit to the measured spectrum.

 

Fig. 5 Reconstructed complex spectrum measured via the dual-comb interrogation method, including calibration. Again, darker points represent the spectrum retrieved with the comb held at a repetition rate of 250 MHz, with the other points derived by shifting the comb mode frequencies, as before. Solid curves represent a complex Voigt profile fit to the spectrum.

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The generation of a microwave comb via a SRD is the cause of this degraded signal-to-noise ratio and stability. First, the total power in the SRD output is spread between the microwave comb modes, leading to reduced signal-to-noise ratios when compared to the CW case. Second, the SRD output is a pulse train and thus, to avoid over-driving the mixer at the voltage peaks, requires that the total SRD output power be kept relatively low, further reducing the available power-per-mode. Third, narrow pulses place great demands on the linearity requirement for the microwave mixers. We believe that mixer non-linearity is the most likely cause of much of the systematic error shown in Fig. 5. Other comb generation schemes, for example the pseudo random bit sequence scheme reported in [15], would give far better distribution of microwave power as a function of time, allowing for higher microwave powers and thus improved power-per-mode, while still operating in the linear regime of the microwave mixers.

4. Conclusion

We have demonstrated two approaches for retrieving complex spectra by interrogation with a single optical frequency comb. Demodulation by a CW laser injection locked to the interrogating comb resulted in new microwave combs with very narrow features containing the spectral information. Further demodulation using either a serial or dual-comb interrogation of these features allowed the use of common RF electronics to extract both optical transmittance and phase spectra for a room temperature cesium vapour cell. For the serial approach, measured complex spectra were consistent with the expected response with deviations from expected lineshape of 1% and 1° for the transmittance and phase respectively. Frequency spacing of the line centres was also consistent with the expected value. The parallel approach did not perform as well as hoped, but clearly shows the expected spectral response.