Vernier spectrometer using counter-propagating soliton microcombs
Acquisition of laser frequency with high resolution under continuous and abrupt tuning conditions is important for sensing, spectroscopy and communications. Here, a single microresonator provides rapid and broad-band measurement of frequencies across the optical C-band with a relative frequency precision comparable to conventional dual frequency comb systems. Dual-locked counter-propagating solitons having slightly different repetition rates are used to implement a Vernier spectrometer. Laser tuning rates as high as 10 THz/s, broadly step-tuned lasers, multi-line laser spectra and also molecular absorption lines are characterized using the device. Besides providing a considerable technical simplification through the dual-locked solitons and enhanced capability for measurement of arbitrarily tuned sources, this work reveals possibilities for chip-scale spectrometers that greatly exceed the performance of table-top grating and interferometer-based devices.
Frequency-agile lasers are ubiquitous in sensing, spectroscopy and optical communications wilner2008communications (); allen1998diode (); choma2003sensitivity () and measurement of their optical frequency for tuning and control is traditionally performed by grating and interferometer-based spectrometers, but more recently these measurements can make use of optical frequency combsjones2000carrier (); holzwarth2000optical (); diddams2010evolving (). Frequency combs provide a remarkably stable measurement grid against which optical signal frequencies can be determined subject to the ambiguity introduced by their equally spaced comb lines. The ambiguity can be resolved for continuously frequency swept signals by counting comb teeth del2009frequency () relative to a known comb tooth; and this method has enabled measurement of remarkably high chirp rates coddington2012characterizing (). However, signal sources can operate with abrupt frequency jumps so as to quickly access a new spectral region or for switching purposes, and this requires a different approach. In this case, a second frequency comb with a different comb line spacing can provide a Vernier scale giorgetta2010fast () for comparison with the first comb to resolve the ambiguity under quite general tuning conditions ma2003new (); peng2008optical (); giorgetta2010fast (). This Vernier concept is also used in dual comb spectroscopycoddington2016dual (); suh2016microresonator (), but in measuring active signals the method can be significantly enhanced to quickly identify signal frequencies through a signal correlation technique giorgetta2010fast (). The power of the Vernier-based method relies upon mapping of optical comb frequencies into a radio-frequency grid of frequencies, the precision of which is set by the relative line-by-line frequency stability of the two frequency combs. This stability can be guaranteed by self-referencing each comb using a common high-stability radio-frequency source or through optical locking of each comb to reference lasers whose relative stability is ensured by mutual locking to a common optical cavity.
Here, a broad-band, high-resolution Vernier soliton microcomb spectrometer is demonstrated using a single miniature comb device that generates two mutually-phase-locked combs. The principle of operation relies upon an optical phase locking effect observed in the generation of counter-propagating solitons within high-Q whispering gallery resonators yang2017counter (). Soliton generation in microcavities is being studied for miniaturization to the chip-scale of complete comb systems Kippenberg2018 () and these so-called soliton microcombs have now been demonstrated in a wide range of microcavity systems herr2014temporal (); yi2015soliton (); brasch2016photonic (); wang2016intracavity (); joshi2016thermally (); gong2018high (). In the counter-propagating soliton system, it is found that the clockwise (cw) and counter-clockwise (ccw) comb frequencies can be readily phase locked with distinct repetition rates that are also locked. This mutual double-locking creates line-by-line relative frequency stability for the underlying microcomb spectra that is more characteristic of fully self-referenced dual comb systems. The resulting Vernier of comb frequencies in the optical domain maps to an exceptionally stable radio frequency grid. Application of the signal correlation method giorgetta2010fast () to this system, then enables a microresonator soliton spectrometer (MSS) for rapid and high accuracy measurement of frequency.
To establish its performance and for comparison with dual fiber-mode-locked-laser spectrometers giorgetta2010fast () the MSS is applied to measure a 10 THz/s laser frequency chirping rate, step tuning of a laser, as well as acquisition of high-resolution molecular vibronic spectra over the optical C-band. Moreover, a method for signal frequency extraction is developed that uses the high relative stability of the cw and ccw combs to unambiguously determine frequencies in complex spectra containing 100s of frequencies.
The measurement concept in the frequency domain is depicted in Fig. 1A where comb spectra from doubled-locked cw and ccw solitons are shown. The solitons are pumped from a single laser source that is modulated as shown in figure 1B to produce the two mutually-coherent pump lines at order with frequency separation . The difference in pumping frequencies (MHz range) causes the soliton repetition rates to differ by which sets up a vernier effect in the respective soliton comb frequencies. As detailed elsewhere, the cw and ccw combs will experience frequency locking at order for certain pumping frequencies yang2017counter (). This locking requires that . Also, because the two pump frequencies are derived from a single laser source and have a high relative frequency stability ( is very stable), the two combs are also effectively locked at order . The order can readily increased or decreased by adjusting . The line-by-line relative frequency stability caused by this double locking is comparable to an excellent radio-frequency source. Moreover, the frequency spacings between comb tooth pairs occur at precise integer multiples of (the stability of which is ensured through the relation ), and thereby creates an extremely stable optical frequency vernier for mapping of the comb spectra into a radio frequency grid spectrum.
The spectrometer operates as follows. A test laser frequency is measured using either of the following expressions: where is the comb order nearest to the laser frequency, are the comb repetition rates, are the heterodyne beat frequencies of the test laser with the two frequency comb teeth at order , and is the frequency at . Comb repetition rates and the beats are measured by co-detection of the combs and the test laser to produce the electrical signals in Fig. 1B. The correlation method giorgetta2010fast () is used to determine . This method can be understood as a calculation of the frequency difference by formation of followed by fast Fourier transform (FFT). A typical FFT spectrum of is shown in Fig. 1C and gives a spectral line at . To determine requires which is measured by heterodyne of the solitons to produce electrical signal . Figure 1D is a narrow frequency span of the FFT of and shows how the optical frequency vernier is mapped into a stable radio-frequency grid with line spacing . The order corresponding to the FFT of the signal (Fig. 1C spectrum) is also indicated. These steps are performed automatically to provide a real time measurement of relative to . To determine the order of a comb tooth nearest a reference laser (with known and stable frequency) is determined. This can be done, for example, by application of the correlation procedure to the reference laser. Then, as illustrated in Fig. 1B, the beat of the reference laser with this comb order is monitored for real time measurement of during operation of the MSS. In the current system the reference laser is stabilized using an internal molecular reference.
The counter-propagating solitons are generated in a high- silica microresonator with 3 mm diameter and corresponding 22 GHz soliton repetition rate lee2012chemically (). Details of the soliton generation process can be found elsewhere yi2015soliton (); yi2016active (); yang2017counter (). Typical optical spectra of cw and ccw solitons are plotted in Fig. 1E and span the telecommunication C-band. The distinct pumping frequencies enable repetition rate tuning to control through the Raman self-frequency shift milian2015solitons (); karpov2016raman (); yi2016theory (); yang2016spatial (); yang2017counter (). For example, a repetition rate difference of kHz as seen in Fig. 1D results from a pumping frequency difference of MHz ().
As a preliminary test, the frequency of an external-cavity-diode-laser is measured and compared against a wavemeter. Fig. 1C and 1D () are from this measurement. The real-time measured wavelength of the laser is presented in Fig. 1F and fluctuates within pm over a 5 ms time interval. The measurement is repeated from 1545 to 1560 nm and the acquired wavelengths are plotted in Fig. 1G. The data show residual deviations less than 0.1 pm versus a wavemeter measurement, which is believed to be limited primarily by the wavemeter resolution ( pm). The systematic uncertainty of the absolute wavelength measurement in the current setup is around MHz ( pm) and is dominated by stability of the reference laser.
The large, microwave-rate, free-spectral range of the MSS enables tracking of fast-chirping lasers in real time and discontinuous broadband tuning. Although correlation is performed with a time interval , the instantaneous frequency of the laser relative to the combs can be acquired at a much faster rate set by the desired time-bandwidth-limited resolution. To avoid aliasing of correlation measurement (i.e., to determine uniquely), the amount of frequency-chirping should not exceed the repetition rate within the measurement window , which imposes a maximum resolvable chirping-rate of . This theoretical limit is 1 PHz/s for the MSS and represents a boost of compared with previous Vernier spectrometers giorgetta2010fast ().
To test the MSS dynamically, it is first used to measure rapid continuous-tuning of an external cavity diode laser. As shown in the upper panel of Fig. 2A, the correlation measurement evolves as the laser is tuned over multiple FSRs of the comb and thereby determines the index as a function of time. The frequency of the scanning laser is displayed at low resolution in the middle panel of Fig. 2A and shows a linear chirping-rate of THz/s. Finally, the lower panel in Fig. 2A shows the measured frequency versus time at higher resolution by removing the average linear frequency ramp. As discussed in the Methods Section, the discontinuities in the measurement are caused by electrical frequency dividers used to reduce the detected signal frequency for processing by a low-bandwidth oscilloscope. These dividers can be eliminated by using a faster oscilloscope. In Fig. 2B the MSS is used to resolve broadband step tuning (mode hopping) of an integrated ring resonator based tunable III-V/Silicon laser diode Tran2018 (). Fast step tuning between 1551.427 nm and 1557.613 nm every 1 ms with the corresponding index stepping between and is observed. The lower panel in Fig. 2B gives a higher resolution zoom-in of one of the step regions. The data points in these measurements are each acquired over 1s so the resolution is approximately 1 MHz.
This combination of speed and precision is also useful for spectroscopic measurements of gas-phase chemicals using tunable, single-frequency lasers. Figure 2C is an absorption line of HCN at 5 Torr obtained by a scanning laser calibrated by the MSS. The linewidth is around 2.6 GHz and the absorbance is as weak as 0.12 dB. Separate measurements on vibronic transitions between the ground state and 2 states were performed. Fig. 2D summarizes the corresponding pseudo-Voigt fitting for the transition wavenumbers, which are in excellent agreement with the HITRAN database gordon2017hitran2016 ().
To illustrate a measurement of more complex multi-line spectra, a fiber mode-locked laser (FMLL) is characterized as shown in Fig. 3A. For this measurement, the FMLL was first sent through a bandpass filter to prevent detector saturation. Also, the frequency extraction procedure differs and is modified to enable unique identification of many frequencies (see Supplement). The FMLL line spacing of 249.7 MHz (measured by photodetection) is not resolved in the Fig. 3B spectrum measured using a grating spectrometer. On the other hand, the reconstructed FMLL spectrum measured using the MSS is plotted in Fig. 3C; here, the comb lines are resolved and their frequency separations closely match the value measured by photo detection. Further details on this measurement are provided in the Supplemental section. In a second study of the FMLL, the MSS is used to measure 6 closely-spaced-in-frequency groups of lines located at various spectral locations spanning 2500 free-spectral-range’s of the mode locked laser. The measured frequencies are plotted in Fig. 3D. A linear fitting defined as is plotted for comparison by using the measured FMLL repetition rate MHz where and represents the relative comb index and fitted offset frequency at , respectively. The residual deviation between the measurement and linear fitting is shown in Fig. 3E and gives excellent agreement. The slight tilt observed in Fig. 3E is believed to be related to drifting of soliton repetition rates which were not monitored real-time. Also, variance of residuals within each group comes from the 300 kHz linewidth of each FMLL line. Drifting of the reference laser and FMLL carrier-envelope offset also contributes to the observed residuals across different measurements.
In conclusion, a soliton spectrometer has been demonstrated using dual-locked counter-propagating soliton microcombs. The device provides high resolution measurement of rapid continuously and step tuned lasers as well as complex multi-line spectra. In combination with a tunable laser, precise measurement of absorption spectra including random spectral access (as opposed to only continuous spectral scanning) can be performed. Further optimization of this system could include generation of solitons from distinct mode families thereby allowing tens-of-MegaHertz repetition rate offset to be possible lucas2018spatial (). If such solitons can be dual-locked, the increased acquisition speed would enable measurement of chirping-rates close to 1 EHz/s. Operation beyond the telecommunications band would also clearly be useful and could employ soliton broadening either internally brasch2016photonic () or using on-chip broadeners lamb2018optical (). Besides the performance enhancement realized with the soliton microcombs, the use of dual-locked counter-propagating solitons provides a considerable technical simplification by eliminating the need for a second mutually phase locked comb. Also, it is interesting to note that the counter-propagating dual-locked solitons are potentially useful in a different application wherein dual-comb down conversion is used to perform TeraHertz spectroscopy kliebisch2018unambiguous (). Finally, chip integrable versions of the current device employing silicon nitride waveguides are possible yang2018bridging (). These and other recently demonstrated compact and low-power soliton systems stern2018battery (); liu2018ultralow () point towards the possibility of compact microresonator soliton spectrometers.
Experimental details. The bandwidth limit of the oscilloscope used in this experiment is 2.5 GHz and in order to measure frequencies up to 11 GHz, microwave frequency dividers were used that function between 0.5 GHz to 10 GHz and provide an 8 division ratio. The use of these dividers created 3 GHz frequency unresolvable bands within one FSR of the optical combs, which caused the discontinuities in the lower panel in Fig. 2A. Meanwhile, the repetition rate difference corresponding to the divided signals will also decrease proportionally by a factor of 8, which in turn reduces the maximum resolvable chirping rate to 125 THz/s. The dividers can be omitted by using a higher-bandwidth oscilloscope, which eliminates the above unresolvable bands and allows chirp-rate measurements approaching the theoretical limit.
The pump is a fiber laser with free-running linewidth less than 2 kHz over 100 ms Lee2014spiral (). The long term stability of the soliton is maintained by introducing a feed back loop control yi2015soliton (); yi2016active ().
The authors gratefully acknowledge the Defense Advanced Research Projects Agency (DARPA) under the SCOUT (W911NF-16-1-0548) and DODOS (HR0011-15-C-055) programs; the Air Force Office of Scientific Research (FA9550-18-1-0353) and the Kavli Nanoscience Institute.
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