Dynamic spectral tailoring of a 10 GHz laser frequency comb for enhanced calibration of astronomical spectrographs

Laser frequency combs (LFCs) are an important component of Doppler radial velocity (RV) spectroscopy that pushes fractional precision to the 10-10 level, as required to identify and characterize Earth-like exoplanets. However, large intensity variations across the LFC spectrum that arise in the nonlinear broadening limit the range of comb modes that can be used for optimal wavelength calibration with sufficient signal-to-noise ratio. Furthermore, temporal spectral-intensity fluctuations of the LFC, that are coupled to flux-dependent detector defects, alter the instrumental point spread function (PSF) and result in spurious RV shifts. To address these issues and improve calibration precision, spectral flattening is crucial for LFCs to maintain a constant photon flux per comb mode. In this work, we demonstrate a dynamic spectral shaping setup using a spatial light modulator (SLM) over the wavelength range of 800-1300 nm. The custom shaping compensates for amplitude fluctuations in real time and can also correct for wavelength-dependent spectrograph transmission, achieving a spectral profile that delivers the constant readout necessary for maximizing precision. Importantly, we characterize the out-of-loop properties of the spectral flattener to verify a twofold improvement in spectral stability. This technique, combined with our approach of pumping the waveguide spectral broadener out-of-band at 1550 nm, reduces the required dynamic range. While this spectral region is tailored for the LFC employed at the Habitable-zone Planet Finder (HPF) spectrograph, the method is broadly applicable to any LFC used for astronomical spectrograph calibration.

Linear optical wave energy redistribution methods for photonic signal processing

Manipulating the phase of an optical wave over time and frequency gives full control to the user to implement a wide variety of energy preserving transformations directly in the analogue optical domain. These can be achieved using widely available linear mechanisms, such as temporal phase modulation and spectral phase filtering. The techniques based on these linear optical wave energy redistribution (OWER) methods are inherently energy efficient and have significant speed and bandwidth advantages over digital signal processing. We describe several recent OWER methods for optical signal processing, including denoising passive amplification, real-time spectrogram analysis, passive logic computing, and more. These functionalities are relevant whenever the signal is found on a classical or quantum optical wave, or could be upconverted from radio frequencies or microwaves, and they are of interest for a wide range of applications in telecommunications, sensing, metrology, biomedical imaging, and astronomy. The energy preservation of these methods makes them particularly interesting for quantum optics applications. Furthermore, many of the individual components have been demonstrated on-chip, enabling miniaturization for applications where size and weight are a main constraint.

Advancements in ultrafast photonics: confluence of nonlinear optics and intelligent strategies

Automatic mode-locking techniques, the integration of intelligent technologies with nonlinear optics offers the promise of on-demand intelligent control, potentially overcoming the inherent limitations of traditional ultrafast pulse generation that have predominantly suffered from the instability and suboptimality of open-loop manual tuning. The advancements in intelligent algorithm-driven automatic mode-locking techniques primarily are explored in this review, which also revisits the fundamental principles of nonlinear optical absorption, and examines the evolution and categorization of conventional mode-locking techniques. The convergence of ultrafast pulse nonlinear interactions with intelligent technologies has intricately expanded the scope of ultrafast photonics, unveiling considerable potential for innovation and catalyzing new waves of research breakthroughs in ultrafast photonics and nonlinear optics characters.

Acoustic frequency comb generation on a composite diamond/silicon microcantilever in ambient air

Acoustic frequency combs (AFCs) contain equidistant coherent signals with unconventional possibilities on metrology. Previously, implementation of AFCs on mechanical microresonators with large air damping loss is difficult, which restricted their atmospheric applications. In this work, we explore the potentials of a composite diamond/silicon microcantilever for parametric generation of AFCs in ambient air. We discover that the diamond layer provides a viable route to reduce the linewidth of the primary flexural mode, yielding a 7.1-times increase of the quality factor. We develop a parametric driving scheme that enables generation of AFCs through injection locking and sequential nonlinear dynamic transitions involving subharmonic synchronization (Arnold tongue), and chaotic dynamics. Ultimately, we realize AFCs with a frequency range extending 800 kHz in the air. This work advances the understanding of AFCs and provides a viable route towards their applications in ambient air for high precision metrology.

Understanding low-threshold mode-locking at multi-GHz repetition rate

Continuous-wave mode-locking at multi-GHz repetition rates is achieved in an ultrashort laser cavity at critical pulse energies 100 times lower than predicted by conventional theory. The authors reveal that dynamic gain depletion and recovery between consecutive round-trips is the key factor behind a low-pulse-energy transition from Q-switched mode-locking (QSML) to continuous-wave mode-locking (CWML). As well as providing new insight into gain dynamics, the results suggest a practical route to low-threshold lasing at very high-repetition rates.

Theory and application of cavity solitons in photonic devices

Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity dispersion are balanced by the nonlinear interaction with the medium while cavity losses balance the input energy. The history, properties, physical interpretation and wide application of cavity solitons are reviewed. Cavity solitons in the plane perpendicular to light propagation find application in optical information processing, while cavity solitons in the longitudinal direction produce high-quality frequency combs with applications in optical communications, frequency standards, optical clocks, future GPS, astronomy and quantum technologies.This article is part of the theme issue 'The quantum theory of light'.

Programmable spectral peak generation by a mode-locked Er-fiber laser with an intracavity LCOS-SLM filter

Applying intracavity spectral phase and/or intensity modulation to a mode-locked laser can control the state of circulating pulses in the cavity and produce unique and useful pulse outputs. In this study, a mode-locked Er-doped fiber laser with an intracavity high-resolution liquid crystal-on-silicon spatial light modulator (LCOS-SLM) spectral filter was developed, and programmable narrow linewidth spectral peak generation directly from the oscillator was demonstrated. Furthermore, by simultaneously controlling the intracavity group delay dispersion (GDD), the generation of 20 spectral peaks with a linewidth of 100 pm over a bandwidth of 17 nm was demonstrated. Spectral modulation also affects the temporal waveform, and burst-like pulse trains with intra-burst repetition rates up to 252 GHz were observed.

Tunable 30 GHz laser frequency comb for astronomical spectrograph characterization and calibration

The search for Earth-like exoplanets with the Doppler radial velocity (RV) technique is an extremely challenging and multifaceted precision spectroscopy problem. Currently, one of the limiting instrumental factors in reaching the required long-term 10-10 level of radial velocity precision is the defect-driven subpixel quantum efficiency (QE) variations in the large-format detector arrays used by precision echelle spectrographs. Tunable frequency comb calibration sources that can fully map the point spread function (PSF) across a spectrograph's entire bandwidth are necessary for quantifying and correcting these detector artifacts. In this work, we demonstrate a combination of laser frequency and mode spacing control that allows full and deterministic tunability of a 30 GHz electro-optic comb together with its filter cavity. After supercontinuum generation, this gives access to any optical frequency across 700-1300 nm. Our specific implementation is intended for the comb deployed at the Habitable-Zone Planet Finder (HPF) spectrograph and its near-infrared Hawaii-2RG array, but the techniques apply to all laser frequency combs (LFCs) used for precision astronomical spectrograph calibration and other applications that require broadband tuning.

Ultraviolet astronomical spectrograph calibration with laser frequency combs from nanophotonic lithium niobate waveguides

Astronomical precision spectroscopy underpins searches for life beyond Earth, direct observation of the expanding Universe and constraining the potential variability of physical constants on cosmological scales. Laser frequency combs can provide the required accurate and precise calibration to the astronomical spectrographs. For cosmological studies, extending the calibration with such astrocombs to the ultraviolet spectral range is desirable, however, strong material dispersion and large spectral separation from the established infrared laser oscillators have made this challenging. Here, we demonstrate astronomical spectrograph calibration with an astrocomb in the ultraviolet spectral range below 400 nm. This is accomplished via chip-integrated highly nonlinear photonics in periodically-poled, nano-fabricated lithium niobate waveguides in conjunction with a robust infrared electro-optic comb generator, as well as a chip-integrated microresonator comb. These results demonstrate a viable route towards astronomical precision spectroscopy in the ultraviolet and could contribute to unlock the full potential of next-generation ground-based and future space-based instruments.

A synthetic moving-envelope metasurface antenna for independent control of arbitrary harmonic orders

Flexible frequency controls are crucial in many photonic and electronic applications, ranging from communications systems, spectroscopy, and metrology to quantum information processing. However, the state-of-the-art solutions based on nonlinear bulk media, electro-optic effect, and nonlinear metasurfaces incur very limited spectral controllability, and merely a couple of harmonic orders can be independently manipulated. Here, we theoretically propose and experimentally demonstrate synthetic moving-envelope metasurface antennas capable of simultaneously generating arbitrary harmonic orders and independently manipulating their wave properties in a software-defined manner. As proof-of-principle examples, we demonstrate unidirectional frequency transition, frequency comb generation, arbitrary harmonic orders independent control, and their applications in frequency-division multiplexing communications. All these complicated functionalities are achieved by the 1-bit spatiotemporally ON-OFF switching of meta-atoms of the waveguide-integrated metasurface antenna. Our proposed synthetic metasurface antenna solution greatly expands the frontiers of wave engineering and information manipulation, showing promising potential in wireless communications, spectroscopy, metrology, and quantum science.

Cross-dispersion spectrograph calibration using only a laser frequency comb

High-resolution cross-dispersion spectrographs are widely used in spectroscopy, but the two-dimensional format of the spectrum requires sophisticated calibration, conventionally performed by illuminating the instrument with a broadband hollow-cathode lamp and cross-referencing the result to an emission-line atlas. Here, we introduce a new technique to completely calibrate a high-resolution echelle spectrograph using only a laser frequency comb. Selected individual comb lines are removed from a broadband 20 GHz laser frequency comb-revealing their exact location in the spectrograph echellogram-and wavelength-tagged with sub-fm accuracy. In a complementary procedure, the comb is reduced to contain one line per echellogram order, enabling the spectrograph's free spectral range to be visualized and the exact concatenation between orders to be determined. In this way, the complete calibration of the high-resolution spectrograph is achieved using only a laser frequency comb, directly providing GPS-referenced accuracy without the need to bootstrap the calibration by indexing the comb modes using a broadband atomic-line source.

Phase structure of harmonically mode-locked optical frequency combs

Carrier phase of a harmonically mode-locked optical frequency comb (OFC) is investigated in detail. While harmonically mode-locked OFCs show promise for high-repetition-rate applications, their mode spacing is not the same as the pulse repetition rate, unlike fundamentally mode-locked OFCs. Consequently, harmonically mode-locked OFCs are unsuitable for applications requiring OFCs with wide mode spacing. This study examines the pulse-to-pulse carrier phase evolution of 4th- and 5th-order harmonically mode-locked OFCs, revealing uneven carrier phase evolution responsible for the narrow mode spacing. The possibility of achieving harmonically mode-locked OFCs with wide mode spacing is suggested by implementing pulse-to-pulse phase modulation to ensure even phase evolution.

Continuous ultraviolet to blue-green astrocomb

Cosmological and exoplanetary science using transformative telescopes like the ELT will demand precise calibration of astrophysical spectrographs in the blue-green, where stellar absorption lines are most abundant. Astrocombs-lasers providing a broadband sequence of regularly-spaced optical frequencies on a multi-GHz grid-promise an atomically-traceable calibration scale, but their realization in the blue-green is challenging for current infrared-laser-based technology. Here, we introduce a concept achieving a broad, continuous spectrum by combining second-harmonic generation and sum-frequency-mixing in an MgO:PPLN waveguide to generate 390-520 nm light from a 1 GHz Ti:sapphire frequency comb. Using a Fabry-Pérot filter, we extract a 30 GHz sub-comb spanning 392-472 nm, visualizing its thousands of modes on a high-resolution spectrograph. Experimental data and simulations demonstrate how the approach can bridge the spectral gap present in second-harmonic-only conversion. Requiring only [Formula: see text]100 pJ pulses, our concept establishes a new route to broadband UV-visible generation at GHz repetition rates.

Erbium-doped-fiber-based broad visible range frequency comb with a 30 GHz mode spacing for astronomical applications

We have realized a comb system with a 30 GHz mode spacing, 62 % available wavelength coverage in the visible region, and nearly 40 dB spectral contrast by combining a robust erbium-doped-fiber-based femtosecond laser, mode filtering with newly designed optical cavities, and broadband-visible-range comb generation using a chirped periodically-poled LiNbO₃ ridge waveguide. Furthermore, it is suggested that this system produces a spectrum with little change over 29 months. These features of our comb will contribute to fields requiring broad-mode-spacing combs, including astronomical observations, such as exoplanet exploration and the verification of the cosmic accelerating expansion.

Distortion-free amplification of 100 GHz mode-locked optical frequency comb using quantum dot technology

Semiconductor mode-locked optical frequency comb (ML-OFC) sources with extremely high repetition rates are central to many high-frequency applications, such as dense wavelength-division multiplexing. Dealing with distortion-free amplification of ultra-fast pulse trains from such ML-OFC sources in high-speed data transmission networks requires the deployment of semiconductor optical amplifiers (SOAs) with ultrafast gain recovery dynamics. Quantum dot (QD) technology now lies at the heart of many photonic devices/systems owing to their unique properties at the O-band, including low alpha factor, broad gain spectrum, ultrafast gain dynamics, and pattern-effect free amplification. In this swork, we report on ultrafast and pattern-free amplification of ∼100 GHz pulsed trains from a passively ML-OFC and up to 80 Gbaud/s non-return-to-zero (NRZ) data transmission using an SOA. Most significantly, both key photonic devices presented in this work are fabricated from identical InAs/GaAs QD materials operating at O-band, which paves the way for future advanced photonic chips, where ML-OFCs could be monolithically integrated with SOAs and other photonic components, all originated from the same QD-based epi-wafer.

Nonlinear spectral broadening of a dual-carrier electro-optic frequency comb in a graphene oxide cladded silicon-rich nitride hybrid waveguide

We demonstrate a detailed theoretical analysis describing the generation of an electro-optic comb (EOC) in the near-IR range through discrete phase and amplitude modulation driven by radio frequency (RF) signal generators. Furthermore, the generated EOC spectra suffer nonlinear spectral broadening while propagating through a hybrid Si-rich nitride (SRN) waveguide structure integrated with two-dimensional (2D) layered graphene oxide (GO) films. We perform a detailed analysis to investigate the influence of GO layers, pump wavelength detuning, and other waveguide parameters on the evolution of comb spectra propagating through the hybrid waveguide structure. Owing to the strong modal overlapping between the SRN waveguides and the highly nonlinear GO films, the nonlinearity of the system is enhanced effectively, and broadband comb spectra have been achieved in the near-IR range. Furthermore, we investigate the spectral coherence of the generated comb spectra under different input conditions. The results exhibit strong potential to generate a tunable frequency comb with high spectral coherence in the near-IR range by employing the hybrid waveguide structure.

Recent advances in ultrafast plasmonics: from strong field physics to ultraprecision spectroscopy

Surface plasmons, the collective oscillation of electrons, enable the manipulation of optical fields with unprecedented spatial and time resolutions. They are the workhorse of a large set of applications, such as chemical/biological sensors or Raman scattering spectroscopy, to name only a few. In particular, the ultrafast optical response configures one of the most fundamental characteristics of surface plasmons. Thus, the rich physics about photon-electron interactions could be retrieved and studied in detail. The associated plasmon-enhanced electric fields, generated by focusing the surface plasmons far beyond the diffraction limit, allow reaching the strong field regime with relatively low input laser intensities. This is in clear contrast to conventional optical methods, where their intrinsic limitations demand the use of large and costly laser amplifiers, to attain high electric fields, able to manipulate the electron dynamics in the non-linear regime. Moreover, the coherent plasmonic field excited by the optical field inherits an ultrahigh precision that could be properly exploited in, for instance, ultraprecision spectroscopy. In this review, we summarize the research achievements and developments in ultrafast plasmonics over the last decade. We particularly emphasize the strong-field physics aspects and the ultraprecision spectroscopy using optical frequency combs.

Versatile optical frequency combs based on multi-seeded femtosecond optical parametric generation

This study proposes and demonstrates a versatile method for near- and mid-infrared optical frequency comb generation using multi-seeded femtosecond optical parametric generation. The method allows one to divide the repetition rate by an arbitrarily large integer factor, freely tune the offset frequency, and adjust the common phase offset of the comb modes. Since all possible degrees of freedom are adjustable, the proposed method manifests itself as versatile optical frequency synthesis.

Mode spacing multiplication of optical frequency combs without power loss

We demonstrate the mode spacing multiplication of optical frequency combs (OFCs) using interleaving technique. The pulse train of an OFC after interleaving is phase modulated, and phase demodulation is necessary for mode spacing multiplication. This scheme enables mode spacing multiplication without power loss in principle, which is in contrast to the conventional mode filtering technique. During demonstration, the mode spacing of the OFC of a mode-locked Er-doped fiber laser (repetition rate of 97 MHz) is quadrupled by the interleaving process and successive phase demodulation.

Real-time distance and velocity measurement based on the dual-comb system

With the development of laser metrology, the dual-comb system has natural superiority in the measuring fields. Specifically, distance and velocity represent a basic state for the target in space. We propose an application mode of the dual-comb interferometry integrated into the field programmable gate array. A high-speed parallel processor truly gives full play to the benefit of the data processing rate. The algorithm of the peak extraction and the address matching also bring an efficient working mode into the whole scheme. To verify the performance of this system, we devise a series of experiments for distance and velocity, respectively. The data processing rate of the distance is 425 Hz and that of the corresponding average velocity is 0.425 Hz, which is flexible for different measuring conditions. The experimental results show that the difference can be well within 252.8 µm at 5 m range and 284.9 µm/s over 0.5 m/s.

Avoiding Bias in Measurements of Fundamental Constants from High Resolution Quasar Spectra

Recent advances in spectroscopic instrumentation and calibration methods dramatically improve the quality of quasar spectra. Supercomputer calculations show that, at high spectral resolution, procedures used in some previous analyses of spacetime variations of fundamental constants are likely to generate spurious measurements, biased systematically towards a null result. Developments in analysis methods are also summarised and a prescription given for the analysis of new and forthcoming data.

Space-time coupling of the carrier-envelope phase in ultrafast optical pulses

The carrier-envelope phase (CEP) plays an increasingly important role in precise frequency comb spectroscopy, all-optical atomic clocks, quantum science and technology, astronomy, space-borne-metrology, and strong-field science. Here we introduce an approach for space-time calculation of the CEP in the spatially defined region of interest. We find a significant variation of CEP in the focal volume of refracting focusing elements and accurately calculate its value. We discuss the implications and importance of this finding. Our method is particularly suitable for application to complex, real-world, optical systems thereby making it especially useful to applications in research labs as well as in the engineering of innovative designs that rely on the CEP.

Real-time observation of chaotic and periodic explosions in a mode-locked Tm-doped fiber laser

We experimentally characterize the dynamics of soliton explosions in a transient chaotic state between a single and double pulsing state, as well as periodic explosions induced by soliton collisions in a dual wavelength soliton state. These explosions occurring in a thulium-doped linear fiber laser with net anomalous dispersion are characterized with real-time measurements based on a modified time-stretched dispersive Fourier transform method relying on second-harmonic generation.

All-fiber mode-locked gigahertz femtosecond laser at 1610 nm using a self-developed long-wavelength gain fiber

We report a compact all-fiber passively mode-locked ultrafast laser with a fundamental repetition rate of 1.6 GHz that uses a self-developed long-wavelength active fiber, i.e., a fluoro-sulfo-phosphate-based Er³⁺/Yb³⁺ co-doped fiber (only 6.2 cm in length). This active fiber can provide a net gain coefficient of 0.6 dB/cm at 1610 nm. The high-repetition-rate all-fiber mode-locked laser operates at a low pump power of only approximately 90 mW. The mode-locked pulse train has a period of 625 ps and a 3 dB bandwidth of 7.0 nm, which can support a transform-limited pulse width of 390 fs.

Direct f-3f self-referencing using an integrated silicon-nitride waveguide

We have achieved the simultaneous generation of a 2.6-octave-wide supercontinuum (SC) spectrum over 400-2500 nm and third-harmonic light solely by a dispersion-controlled silicon-nitride waveguide (SiNW). To increase the visible intensity of the SC light component, we fabricated low-loss 5-mm-long deuterated SiNWs with spot-size converters by low-temperature deposition. We succeeded in measuring the carrier-envelope-offset (CEO) signal with a 34-dB signal-to-noise ratio because this short deuterated SiNW provides a large temporal overlap between the f and 3f components. In addition, we have demonstrated this method of CEO locking at telecommunications wavelengths with f-3f self-referencing generated solely by the SiNW without the use of highly nonlinear fiber and an additional nonlinear crystal. Compared with the method of CEO locking with a highly nonlinear fiber and a standard f-2f self-referencing interferometer, this method is not only simple and compact but also stable.

Multi-order cascade lag control for high precision tracking systems

Error attenuation capacity of a target tracking system is the key indicator for the system's tracking precision. Without changing the system's feedback control structure, the traditional first order integral control, which is widely used in traditional tracking systems, cannot meet a higher precision for those fast targets with high mobility. The work described in this paper concerns about this problem, and proposes a cascade lag control scheme with one or more order to level up the system's active error suppression capacity in low-frequency range. By substituting the cascade lag controllers for additional integral operator, a higher amplitude ratio system, which implies higher tracking precision, is obtained without loss of stability. As a difficult task for massive parameters' designing, a concept of relative order and a configuration proportion law is proposed to simplify the analysis as well as parameters tuning. Relationship between the relative order and system performance is given. The multi-order cascade lag control scheme's efficiency is proved in both theoretical analysis and experiments in an electro-optical tracking system.

Non-singleton interval type-2 fuzzy PID control for high precision electro-optical tracking system

In this paper, two non-singleton interval type-2 fuzzy PID (NIT2F-PID) controllers for the high precision electro-optical tracking system (ETS) are presented to improve anti-interference ability. Specifically, two types of non-singleton fuzzifiers, including type-1 (T1) and type-2 (T2), are considered to construct the proposed NIT2F-PID (N1IT2F-PID and N2IT2F-PID) controllers. Faced with the optimization problem of parameters, particle swarm optimization (PSO), quantum-behaved PSO (QPSO), weighted QPSO (WQPSO) and improved QPSO with adaptive coefficients (LTQPSO) are employed for comparison of convergence performance to optimize the parameters of controllers. In addition, to demonstrate the superiority of the proposed NIT2F-PID controllers, PID, singleton T1 fuzzy PID (ST1F-PID), singleton interval T2 fuzzy PID (SIT2F-PID), T1 non-singleton interval T2 fuzzy (N1IT2F) and T2 non-singleton interval T2 fuzzy (N2IT2F) controllers are also designed. All of these controllers are tested under the circumstances of step disturbance and sinusoidal disturbance. At last, a series of simulation analyses and experimental results explicitly show performance of proposed NIT2F-PID controllers are superior to their counterparts.

Laser frequency measurement in the short-wavelength region using an intermediate laser and a frequency noise cancellation method

Optical frequency combs play a crucial role supporting optical frequency standards and cover a wide range of wavelengths (octaves). However, broadening the comb spectrum to the short-wavelength visible region (λ < 500 nm), where GaN-based blue diode lasers are available, is not an easy task. In this study, we propose a method for measuring the laser frequency in the short-wavelength region using an intermediate laser and a noise-canceling scheme. We demonstrate this method by measuring the frequency of a GaN-based laser at 399 nm and confirming that the frequency measurement is not affected by the frequency noise of the intermediate laser.

Design of Broadband Flat Optical Frequency Comb Based on Cascaded Sign-Alternated Dispersion Tellurite Microstructure Fiber

We designed a tellurite microstructure fiber (TMF) and proposed a broadband optical frequency comb generation scheme that was based on electro-optical modulation and cascaded sign-alternated dispersion TMF (CSAD-TMF). In addition, the influence of different nonlinear effects, the ultrashort pulse evolution in the CSAD-TMF with the anomalous dispersion (AD) zones and the normal dispersion (ND) zones were analyzed based on the generalized nonlinear Schrodinger equations (GNLSE) modelling. According to the simulations, when the input seed comb had a repetition rate of 20 GHz and had an input pulse peak power of 30 W, the generation scheme could generate optical frequency combs with a 6 dB spectral bandwidth spanning over 170 nm centered at 1550 nm. Furthermore, the generated combs showed good coherence in performance over the whole 6 dB spectral bandwidth. The highly coherent optical frequency combs can be used as high-repetition-rate, multi-wavelength light sources for various integrated microwave photonics and ultrafast optical signal processing applications.

Interferogram-based determination of the absolute mode numbers of optical frequency combs in dual-comb spectroscopy

Dual-comb spectroscopy (DCS), which uses two optical frequency combs (OFCs), requires an accurate knowledge of the mode number of each comb line to determine spectral features. We demonstrate a fast evaluation method of the absolute mode numbers of both OFCs used in DCS system. By measuring the interval between the peaks in the time-domain interferogram, it is possible to accurately determine the ratio of one OFC repetition frequency (f_rep) to the difference between the f_rep values of the two OFCs (Δf_rep). The absolute mode numbers can then be straightforwardly calculated using this ratio. This method is applicable to a broad range of Δf_rep values down to several Hz without any additional instruments. For instance, the minimum required measurement time is estimated to be about 1 s for Δf_rep ≈ 5.6 Hz and f_rep ≈ 60 MHz. The optical frequencies of the absorption lines of acetylene gas obtained by DCS with our method of mode number determination shows good agreement with the data from the HITRAN database.

High-power femtosecond all-fiber laser system at 1.5 µm with a fundamental repetition rate of 4.9 GHz

In this Letter, we demonstrate a high-power femtosecond all-fiber laser system at 1.5 µm that operates at a fundamental repetition rate of up to 4.9 GHz. This high repetition rate laser system delivers an average power of 10 W and a pulsewidth of 63 fs in an all-fiber configuration-the best overall performance at 1.5 µm, so far, in terms of the all-fiber design, high average power, short pulsewidth, and high fundamental repetition rate. Integrated from 10 Hz to 10 MHz, this high-power femtosecond all-fiber laser system exhibits a relative intensity noise of only 0.4%. It is anticipated that this femtosecond laser system is promising for various applications, such as high-speed micromachining, wide-field multiphoton bioimaging, and nonlinear optics.

Vector soliton dynamics in a high-repetition-rate fiber laser

The existence of vector solitons that arise from the birefringence nature of optical fibers has been increasingly of interest for the stability of mode-locked fiber lasers, particularly for those operating in the high-fundamental-repetition-rate regime, where a large amount of fiber birefringence is required to restore the phase relation between the orthogonally polarized vector solitons, resulting in stable mode-locking free of polarization rotation. These vector solitons can exhibit diverse time-varying polarization dynamics, which prevent industrial and scientific applications requiring stable and uniform pulse trains at high fundamental repetition rates. This pressing issue, however, has so far been rarely studied. To this end, here we theoretically and experimentally dissect the formation of vector solitons in a GHz-repetition-rate fiber laser and investigate effective methods for suppressing roundtrip-to-roundtrip polarization dynamics. Our numerical model can predict both dynamic and stable regimes of high-repetition-rate mode-locking by varying the amount of fiber birefringence, resulting in the polarization rotation vector soliton (PRVS) and linearly polarized soliton (LPS), respectively. These dynamic behaviors are further studied by using an analytical approach. Interestingly, our theoretical results indicate a cavity-induced locking effect, which can be a complementary soliton trapping mechanism for the co-propagating solitons. Finally, these theoretical predications are experimentally verified, and we obtain both PRVS and LPS by adjusting the intracavity fiber birefringence.

Sub-100 fs all-fiber broadband electro-optic optical frequency comb at 1.5 µm

A sub-100 fs all-fiber broadband optical frequency comb seeded from a 12.5 GHz electro-optic modulated pulse is presented. Combining pulse reshaping, nonlinear mixing with dispersion compensation processes, a frequency comb with the main pulse width of 86 fs was achieved. The frequency comb has a 6 dB spectral bandwidth spanning over 150 nm which corresponding to more than 1500 comb tones. The measured average power of the broadband comb is over 550 mW, and the calculated average power of each comb line is roughly -4 dBm. To illustrate the whole spectral broadening process, a numerical investigation was also brought out, showing a very good match with the experiments. With a delayed self-heterodyne interferometer, the evolutions of the seed comb linewidths and the broadened comb linewidths were measured revealing the same parabolic trend. Specifically, the linewidths of the 20 seed comb lines are less than 10 kHz, while the linewidths of the 400 broadened comb lines are less than 1 MHz. The results also indicate that the nonlinear mixing led to an accumulation of the phase noise with respect to the comb line number, indicating that a low phase noise RF source or phase locking technique is essential to produce ultra-low phase noise broadband electro-optic combs.

Interrogating the Temporal Coherence of EUV Frequency Combs with Highly Charged Ions

A scheme to infer the temporal coherence of EUV frequency combs generated from intracavity high-order harmonic generation is put forward. The excitation dynamics of highly charged Mg-like ions, which interact with EUV pulse trains featuring different carrier-envelope-phase fluctuations, are simulated. While demonstrating the microscopic origin of the macroscopic equivalence between excitations induced by pulse trains and continuous-wave lasers, we show that the coherence time of the pulse train can be determined from the spectrum of the excitations. The scheme will provide a verification of the comb temporal coherence at timescales several orders of magnitude longer than current state of the art, and at the same time will enable high-precision spectroscopy of EUV transitions with a relative accuracy up to δω/ω∼10^{-17}.

Optical frequency combs: Coherently uniting the electromagnetic spectrum

Optical frequency combs were introduced around 20 years ago as a laser technology that could synthesize and count the ultrafast rate of the oscillating cycles of light. Functioning in a manner analogous to a clockwork of gears, the frequency comb phase-coherently upconverts a radio frequency signal by a factor of [Formula: see text] to provide a vast array of evenly spaced optical frequencies, which is the comb for which the device is named. It also divides an optical frequency down to a radio frequency, or translates its phase to any other optical frequency across hundreds of terahertz of bandwidth. We review the historical backdrop against which this powerful tool for coherently uniting the electromagnetic spectrum developed. Advances in frequency comb functionality, physical implementation, and application are also described.

Stretched-Pulse Soliton Kerr Resonators

Kerr resonators support novel nonlinear wave phenomena including technologically important optical solitons. Fiber Kerr resonator solitons enable wavelength and repetition-rate versatile femtosecond-pulse and frequency-comb generation. However, key performance parameters, such as pulse duration, lag behind those from traditional mode-locked laser-based sources. Here we present new pulse generation in dispersion-managed Kerr resonators based on stretched-pulse solitons, which support the shortest pulses to date from a fiber Kerr resonator. In contrast to established Kerr resonator solitons, stretched-pulse solitons feature Gaussian temporal profiles that stretch and compress each round trip. Experimental results are in excellent agreement with numerical simulations. The dependence on dispersion and drive power are detailed theoretically and experimentally and design guidelines are presented for optimizing performance. Kerr resonator stretched-pulse solitons represent a new stable nonlinear waveform and a promising technique for femtosecond pulse generation.

High performance quantum cascade laser frequency combs at λ ∼ 6 μm based on plasmon-enhanced dispersion compensation

We demonstrate quantum cascade laser (QCL) optical frequency combs emitting at λ ∼ 6 μm. A 5.5 μm-wide, 4.5 mm-long laser exhibits comb operation from -20 °C up to 50 °C. A maximum output power of 300 mW is achieved at 50 °C showing a robustness of the system. The laser output spectrum is ∼80 cm^-1 wide at the maximum current, with a mode spacing of 0.334 cm^-1, resulting in a total of 240 modes with an average power of 0.8 mW per mode. To achieve frequency comb operation, a plasmonic-waveguide approach is utilized. A thin, highly-doped indium phosphide (InP) layer is inserted in the top cladding design to compensate the positive dispersion of the system (material and waveguide). This approach can be further exploited to design QCL combs at even shorter wavelengths, down to 4 μm. Different ridge widths between 2.8 and 5.5 μm have been fabricated and characterized. All of the devices exhibit frequency comb operation. These observations demonstrate that the plasmonic-waveguide is a robust and reliable method for dispersion compensation of a semiconductor laser systems to achieve frequency comb operation.

Development of a photoelectric phase-locked loop model to better synchronize frequency combs and microwaves

The high phase coherence between ultralow-noise microwaves and ultrahigh-stable optical frequency combs (OFCs) is of both scientific and technological relevance for telecommunication, timekeeping, astronomy, and metrology. Here, a photoelectric phase-locked loop (PLL) model with ultralow phase noise based on the optical-microwave phase detector technique has been proposed and experimentally demonstrated. A detailed mathematical model for tight, real-time phase synchronization of OFCs and microwaves is developed to investigate the feasibility and analyze the characteristics of the phase-coherent system. We fabricate a compact PLL circuit with a proportional-integral-derivative regulator for the synchronization of an OFC to a microwave reference. Once synchronized, the long-term stability of the OFC agrees to 2.4×10^-14 at a 1000 s averaging time, which is enhanced by more than 4 orders of magnitude. Besides, the OFC almost acquires the same frequency stability as the microwave source. The ability to better phase synchronize OFCs and microwaves enables a wide range of applications beyond the laboratory.

Optical Frequency Combs in Quadratically Nonlinear Resonators

Optical frequency combs are one of the most remarkable inventions in recent decades. Originally conceived as the spectral counterpart of the train of short pulses emitted by mode-locked lasers, frequency combs have also been subsequently generated in continuously pumped microresonators, through third-order parametric processes. Quite recently, direct generation of optical frequency combs has been demonstrated in continuous-wave laser-pumped optical resonators with a second-order nonlinear medium inside. Here, we present a concise introduction to such quadratic combs and the physical mechanism that underlies their formation. We mainly review our recent experimental and theoretical work on formation and dynamics of quadratic frequency combs. We experimentally demonstrated comb generation in two configurations: a cavity for second harmonic generation, where combs are generated both around the pump frequency and its second harmonic and a degenerate optical parametric oscillator, where combs are generated around the pump frequency and its subharmonic. The experiments have been supported by a thorough theoretical analysis, aimed at modelling the dynamics of quadratic combs, both in frequency and time domains, providing useful insights into the physics of this new class of optical frequency comb synthesizers. Quadratic combs establish a new class of efficient frequency comb synthesizers, with unique features, which could enable straightforward access to new spectral regions and stimulate novel applications.

Intelligent control of mode-locked femtosecond pulses by time-stretch-assisted real-time spectral analysis

Mode-locked fiber lasers based on nonlinear polarization evolution can generate femtosecond pulses with different pulse widths and rich spectral distributions for versatile applications through polarization tuning. However, a precise and repeatable location of a specific pulsation regime is extremely challenging. Here, by using fast spectral analysis based on a time-stretched dispersion Fourier transform as the spectral discrimination criterion, along with an intelligent polarization search algorithm, for the first time, we achieved real-time control of the spectral width and shape of mode-locked femtosecond pulses; the spectral width can be tuned from 10 to 40 nm with a resolution of ~1.47 nm, and the spectral shape can be programmed to be hyperbolic secant or triangular. Furthermore, we reveal the complex, repeatable transition dynamics of the spectrum broadening of femtosecond pulses, including five middle phases, which provides deep insight into ultrashort pulse formation that cannot be observed with traditional mode-locked lasers.

Iodine-stabilized laser at telecom wavelength using dual-pitch periodically poled lithium niobate waveguide

We demonstrate the third harmonic generation of a 1542-nm laser using a dual-pitch periodically poled lithium niobate waveguide with a conversion efficiency of 66%/W². The generated 514-nm light is used for saturation spectroscopy of molecular iodine and laser frequency stabilization. The achieved laser frequency stability is 1.1×10^-12 at an average time of 1 s, which is approximately one order of magnitude better than the acetylene-stabilized laser at 1542 nm. Uncertainty evaluation and absolute frequency measurement are also performed. The developed frequency-stabilized laser can be used as a reliable frequency reference at the telecom wavelength for various applications including optical frequency combs and precision interferometric measurement.

Gigahertz-repetition-rate, narrowband-deep-ultraviolet light source for minimization of acquisition time in high-resolution angle-resolved photoemission spectroscopy

Ultrahigh-repetition-rate (1.1 GHz), deep-ultraviolet coherent light at 208.8 nm is generated by applying an external Fabry-Pérot cavity for repetition-rate multiplication to the fourth harmonics of a 10-ps, mode-locked Ti:sapphire laser. Its small pulse energy minimizes the unwanted space charge effect, while its high repetition rate drastically reduces the acquisition time in high-energy resolution angle-resolved photoemission spectroscopy using hemispherical electron analyzers. The absence of the space charge effect in the photoemission spectrum near the Fermi edge of polycrystalline Au at 8 K demonstrates this idea.

Visible blue-to-red 10 GHz frequency comb via on-chip triple-sum-frequency generation

A broadband visible (VIS) blue-to-red, 10 GHz repetition rate frequency comb is generated by combined spectral broadening and triple-sum-frequency generation in an on-chip silicon nitride waveguide. Ultra-short pulses of 150 pJ pulse energy, generated via electro-optic modulation of a 1560 nm continuous-wave laser (CW), are coupled to a silicon nitride waveguide giving rise to a broadband near-infrared (NIR) supercontinuum. Modal phase matching inside the waveguide allows direct triple-sum-frequency transfer of the NIR supercontinuum into the VIS wavelength range covering more than 250 THz from below 400 to above 600 nm wavelength. This scheme directly links the mature optical telecommunication band technology to the VIS wavelength band and can find application in astronomical spectrograph calibration, as well as referencing of CW lasers.

Gain-through-filtering enables tuneable frequency comb generation in passive optical resonators

Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint. We propose here a technique for the generation of OFCs with a tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to asymmetric spectral filtering on one side of the pump wave. We demonstrate a proof-of-concept experimental result in a fibre resonator, pioneering a new technique that does not require specific engineering of the resonator dispersion to generate frequency-agile OFCs.

Probing Dark Matter Using Precision Measurements of Stellar Accelerations

Dark matter comprises the bulk of the matter in the Universe, but its particle nature and cosmological origin remain mysterious. Knowledge of the dark matter density distribution in the Milky Way Galaxy is crucial both to our understanding of the standard cosmological model and for grounding direct and indirect searches for the particles comprising dark matter. Current measurements of Galactic dark matter content rely on model assumptions to infer the forces acting upon stars from the distribution of observed velocities. Here, we propose to apply the precision radial velocity method, optimized in recent years for exoplanet astronomy, to measure the change in the velocity of stars over time, thereby providing a direct probe of the local gravitational potential in the Galaxy. Using numerical simulations, we develop a realistic strategy to observe the differential accelerations of stars in our Galactic neighborhood with next-generation telescopes, at the level of 10^{-8}  cm/s^{2}. Our simulations show that detecting accelerations at this level with an ensemble of 10^{3} stars requires the effect of stellar noise on radial velocity measurements to be reduced to <10  cm/s. The measured stellar accelerations may then be used to extract the local dark matter density and morphological parameters of the density profile.

Numerical investigation of GHz repetition rate fundamentally mode-locked all-fiber lasers

GHz repetition rate fundamentally mode-locked lasers have attracted great interest for a variety of scientific and practical applications. A passively mode-locked laser in all-fiber format has the advantages of high stability, maintenance-free operation, super compactness, and reliability. In this paper, we present numerical investigation on passive mode-locking of all-fiber lasers operating at repetition rates of 1-20 GHz. Our calculations show that the reflectivity of the output coupler, the small signal gain of the doped fiber, the total net cavity dispersion, and the modulation depth of the saturable absorber are the key parameters for producing stable fundamentally mode-locked pulses at GHz repetition rates in very short all-fiber linear cavities. The instabilities of GHz repetition rate fundamentally mode-locked all-fiber lasers with different parameters were calculated and analyzed. Compared to a regular MHz repetition rate mode-locked all-fiber laser, the pump power range for the mode-locking of a GHz repetition rate all-fiber laser is much larger due to the several orders of magnitude lower accumulated nonlinearity in the fiber cavity. The presented numerical study provides valuable guidance for the design and development of highly stable mode-locked all-fiber lasers operating at GHz repetition rates.

Design of a hybrid chalcogenide-glass on lithium-niobate waveguide structure for high-performance cascaded third- and second-order optical nonlinearities

Dispersion engineering for efficient supercontinuum generation (SCG) is investigated in a hybrid nonlinear photonic platform that allows cascaded third- and second-order optical nonlinearities in transverse-electric (TE) guided modes. The highly nonlinear chalcogenide waveguides enable SCG spanning over 1.25 octaves (from about 1160 nm to more than 2800 nm at 20  dB below maximum power), while the TE polarization attained is compatible with efficient second-harmonic generation in a subsequent thin-film lithium niobate waveguide integrated monolithically on the same chip. A low-energy pump pulsed laser source of only 25 pJ with 250 fs duration, centered at a wavelength of 1550 nm, can achieve such wideband SCG. The design presented is suitable for the f-to-2f carrier-envelope offset detection technique of stabilized optical frequency comb sources.

Comb segmentation spectroscopy for rapid detection of molecular absorption lines

We perform fast comb spectroscopy by dividing the probe comb into several sub-comb segments so as to produce multi-heterodyne beats focused around targeted molecular absorption lines. This concentrated scheme of comb spectroscopy is able to achieve a 30 dB signal-to-noise ratio with just a single shot measurement of 10 μs acquisition time. Such high signal sensitivity is verified by measuring separate absorption lines of H¹³C¹⁴N and ¹²CO₂ gases simultaneously. In addition, atmospheric ¹²CO₂ concentration over a 1.3 km open-air path is traced with a signal repeatability of 15 ppm at a 5 kHz update rate.