Final Report Summary - ULTRA-COMELI (Ultrafast dual-comb multidimensional lidar) Since their inception in 2000, optical frequency combs have caused a deep impact in optical metrology due to their unique characteristics. This fact was explicitly recognized with one half of the Nobel Prize in Physics, which was shared by John L. Hall and Theodor W. Hänsch in 2005. A frequency comb is a spectrum composed of a set of repeating, evenly spaced spectral lines (or ‘teeth’). This ‘frequency ruler’ can be generated through several mechanisms. One of the most employed techniques, for instance, is the stabilization of a train of pulses produced by a modelocked laser. This kind of frequency combs made it possible the development of optical clocks and constitutes a powerful tool for high-precision spectroscopy. However, there are other applications, such as light detection and ranging (LIDAR) and optical telecommunications, which are less demanding in terms of stabilization and number of spectral components. They require a platform with higher robustness and simplicity. These challenging features can be easily met by an electro-optic comb generator, a decades-old method to produce frequency combs that is highly compatible with optical communications instrumentation. Basically it consists of injecting a continuous-wave (CW) laser into a set of electro-optic modulators, used to modulate the phase and/or the amplitude of light. These modulators are driven by an external radio-frequency (RF) source, which controls the line spacing of the comb.Taking advantage of the spectral resolution and frequency accuracy provided by a comb requires to resolve (or ‘read’) every one of its lines. This can be performed in a very elegant manner by means of a measurement technique called dual-comb interferometry. The basic idea is simple in concept. The spectral information of a sample is codified on the spectral lines of a comb that acts as a probe. The line-by-line operation is achieved by mixing that comb with another one, called local oscillator, which has a slightly different line spacing. As a result, a set of RF beat notes is generated, each one coming from the interference of a different pair of lines. In this way, the spectral response of the sample can be retrieved in a line-by-line manner by analyzing an RF electrical signal. This multi-heterodyne process was firstly applied to spectroscopy. Compared to state-of-the-art spectrometers, dual-comb systems provide a superior frequency resolution without significant loss in sensitivity, as has been demonstrated in many reported works in the last decade. Beyond spectroscopy, dual-comb interferometry has been exploited for other metrology applications. For instance, a dual-comb interferometer was used to implement a LIDAR system with a nanometer resolution for a non-ambiguity range of more than one meter. These features were possible by the fact that a dual-comb LIDAR combines the usual distance measurement, based on the time of flight of light pulses, with a more precise interferometric measurement based on the spectral phase. The most precise dual-comb interferometric measurements so far have been conducted with mode-locked lasers. To this end, both combs must be carefully phase locked to each other. This process is challenging and requires a sophisticated hardware. For this reason, electro-optic frequency combs have been recently employed for dual-comb interferometry. In this configuration, a single CW laser feeds simultaneously the two comb generators, so the dual-comb setup is phase-locked by default. Apart from this advantage, an electro-optic comb differs fundamentally from a mode-locked laser in that the formation of a train of coherent pulses does not require an optical cavity. This fact allows the line spacing of the comb to be substantially higher (>10 GHz) than what is possible with standard mode-locked laser oscillators (typically, around 100 MHz). As a consequence, the frequency offset between the two combs, which fixes the maximum refresh rate of the dual-comb interferometer, can be increased in several orders of magnitude, reaching values on the sub-microsecond time scale. The main research objective of this project was to implement an ultrafast LIDAR system by means of an electro-optic dual-comb interferometer. This laser ranging system had to be multidimensional, that is, it had to be capable of retrieving information from a target not only from the light power but also from other relevant magnitudes, such as phase and polarization. In addition, the system had to operate at unprecedented speeds (~1MHz refresh rates).The project has achieved a great part of their objectives and technical goals. A dual-comb interferometer based on the electro-optic technology was implemented in the Photonics Laboratory at Chalmers University of Technology. This interferometer was a fiber-based system that included some basic components employed in fiber-optic communication, such as erbium doped fiber amplifiers (EDFAs) and a balanced photoreceiver. To check the capability of the above dual-comb interferometer to measure the complex amplitude of a sample, some experiments were performed with a commercial pulse shaper. This component made it possible to change arbitrarily the amplitude and phase of every spectral line of the probe comb. One of the tradeoffs considered in our contingency plan, namely, that existing between the measurement speed (refresh rate) and the sensitivity of the dual-comb scheme, was carefully analyzed. The results achieved during this first stage were disseminated in a prestigious conference (CLEO-Europe 2015) and led to the publication of a paper [V. Durán et al.,“Ultrafast electrooptic dual-comb interferometry”, Optics Express 23, 30557 (2015)]. In this work we demonstrated a dual-comb system that worked at a refresh rate of 25 MHz (that is, on the sub-microsecond time scale). Due to the novelties existing in this work, a pre-print of it has been published in a non-profit academic repository (Arxiv). A common drawback in all reported electro-optic dual-comb interferometers is that the operational bandwidth is only a few-nanometer-wide at best. For this reason, our next step was implementing a dual-comb spectrometer that operated over the entire telecommunications C-band (1530-1570 nm) at refresh rates of 100 kHz. The central concept lied in realizing external broadening of the parent combs in a highly nonlinear fiber. The bandwidth and number of lines was increased by a factor of four. To the best of our knowledge, our broadband interferometer had the largest spectrum ever demonstrated with an electro-optic dual-comb system. This work was presented in a top-notch conference (CLEO 2016) and led to the writing of a paper, published in ArXiv [V. Duran et al., “Electro-optic dual comb interferometry over 40-nm bandwidth,” ArXiv: 1607.04575 (2016)]. This work was submitted to a peer-reviewed journal too. After the above exhaustive analysis of our electro-optic dual-comb system, we concluded that it was well matched for laser ranging of rapid vibrating targets, whose movement lied within the unambiguity range offered by our combs (~1 cm at a repetition rate of 25 GHz). To demonstrate it, we resolved the movement of an ultrasound speaker driven at 50 kHz. The vibrations of this target were measured with a sub-nanometer resolution at a refresh rate of 250 kHz. This achievement was possible thanks to the ability of our system to measure not only the light intensity but also the spectral phase. A paper based on this result was accepted at an international conference [E. L. Teleanu et al. “Electro-optic dual-comb vibrometry” in Frontier in Optics 2016]. The above experiment demonstrated the potentiality of our ultrafast dual-comb interferometry for dealing with dynamic samples on the sub-millisecond time scale. This result opens the door to perform multipoint vibrometry in the near future. Concerning the training objectives, V. Durán attended an advance photonics course about Fiber Optical Communication at Chalmers University. He collaborated with one postdoc researcher (Santiago Tainta, co-author of the first paper published in Optics Express) and a master student (Elena Teleanu, co-author of the last paper on vibrometry). He also acquired skills in the use of electronic and microwave components in the daily work. In fact, one of the employed electro-optic frequency combs was completely assembled by him during the first year. In addition, V. Durán attended a basic Swedish course in Folkuniversitetet. In conclusion, the ultrafast interferometric technique implemented during the project showed a great potentiality for metrology applications. First, the reported results made evident that electro-optic dual-comb interferometry allows us to measure amplitude, phase (and, eventually, polarization) on the sub-microsecond time scale. Second, the modest bandwidth usually offered by electro-optic frequency combs was overcome through a standard technique involving a non-linear fiber. That offers new prospects for electro-optic dual-comb interferometry as a suitable technology for high-speed broadband measurement systems, for example in optical coherence tomography or coherent Raman microscopy. Finally, the implemented system was evaluated to find the best application for distance measurement. As a result, we used it for vibrometry, achieving sub-wavelength precision at hundreds of kHz. In all the above experiments, the ability of our system to characterize arbitrary optical waveforms was essential. The results attained during the project showed the potentiality of electro-optic dual-comb interferometry for future metrology developments, such as multipoint vibrometry and, strikingly, ultrafast multidimensional imaging.
