We calculate the quantum-limited shape of the comb lines from a mode-locked Ti:sapphire laser using experimentally-derived parameters for the linear response of the laser to perturbations. The free-running width of the comb lines is found across the laser spectrum. By modeling the effect of a simple feedback loop, we calculate the spectrum of the residual phase noise in terms of the quantum noise and the feedback parameters. Finally, we calculate the frequency uncertainty in an optical frequency measurement if the limiting factor is quantum noise in the detection of the optical heterodyne beat.
We report on the formation of various intensity pattern types in detuned Fourier domain mode-locked (FDML) lasers and identify the corresponding operating conditions. Such patterns are a result of the complex laser dynamics and serve as an ideal tool for the study of the underlying physical processes as well as for model verification. By numerical simulation we deduce that the formation of patterns is related to the spectral position of the instantaneous laser lineshape with respect to the transmission window of the swept bandpass filter. The spectral properties of the lineshape are determined…
Impact of Angle Misalignment on the Performance of a combined Optical and millimeter-wave Transceiver enabled by a pair of Optical Harmonically Locked Lasers
We report on the observation of a novel mode locked optical comb generated at the Raman offset (Raman comb) in an optically pumped crystalline whispering gallery mode resonator. Mode locking is confirmed via measurement of the radio-frequency beat note produced by the optical comb on a fast photodiode. Neither the conventional Kerr comb nor hyper-parametric oscillation is observed when the Raman comb is present.
Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental results that show a variety of independent comb generation mechanisms. Here, we present frequency-domain experiments that illuminate the transition of microcombs into phase-locked states, which show characteristics of injection locking between ensembles of comb modes. In addition, we demonstrate the existence of equidistant optical frequency combs that are …
We report on an optical frequency comb with 14nm (~1.8 THz) spectral bandwidth at -3 dB level that is generated using a passively mode-locked quantum-well (QW) laser in photonic integrated circuits (PICs) fabricated through an InP generic photonic integration technology platform. This 21.5-GHz colliding-pulse mode-locked laser cavity is defined by on-chip reflectors incorporating intracavity phase modulators followed by an extra-cavity SOA as booster amplifier. A 1.8-THz-wide optical comb spectrum is presented with ultrafast pulse that is 0.35-ps-wide. The radio frequency beat note has a 3-dB …
We introduce a time-dependent generalized Floquet (TDGF) approach to calculate attosecond transient absorption spectra of helium atoms subjected to the combination of an attosecond extreme ultraviolet (XUV) pulse and a delayed few-cycle infrared (IR) laser pulse. This TDGF approach provides a Floquet understanding of the laser-induced change of resonant absorption lineshape. It is analytically demonstrated that, the phase shift of the time-dependent dipole moment that results in the lineshape changes consists of the \emph{adiabatic} laser-induced phase (LIP) due to the IR-induced stark shifts …
Microresonator frequency combs harness the nonlinear Kerr effect in an integrated optical cavity to generate a multitude of phase-locked frequency lines. The line spacing can reach values in the order of 100 GHz, making it an attractive multi-wavelength light source for applications in fiber-optic communications. Depending on the dispersion of the microresonator, different physical dynamics have been observed. A recently discovered comb state corresponds to the formation of mode-locked dark pulses in a normal-dispersion microcavity. Such dark-pulse combs are particularly compelling for advance…
Amplified spontaneous emission (ASE) causes fluctuations of pulse energy, of the optical phase and of the timing of the pulse intensity envelope in a mode-locked laser or frequency comb. Starting from the assumption of one ASE photon per longitudinal laser mode and roundtrip, we rederive analytic equations for the three fundamental types of quantum noise in a laser. To this end, we analyze the interference of the coherent intracavity field and a spectrally localized ASE photon as a function of wavelength and phase of the latter. Performing an integration over all wavelengths and phases and tak…
We propose a simple approach to implement a tunable, high power and narrow linewidth laser source based on a series of highly coherent tones from an electro-optic frequency comb and a set of 3 DFB slave lasers. We experimentally demonstrate approximately 1.25 THz (10 nm) of tuning within the C-Band centered at 192.9 THz (1555 nm). The output power is approximately 100 mW (20 dBm), with a side band suppression ratio greater than 55 dB, and a linewidth below 400 Hz across the full range of tunability. This approach is scalable and may be extended to cover a significantly broader optical spectral…
A bidirectional mode-locked fiber laser producing two correlated frequency combs of the same repetition rate is demonstrated. The intensity dependence of pulse and phase velocities are measured simultaneously. As expected, the phase delay is determined by the linear and nonlinear indices of refraction. The nonlinear Kerr effect contribution to the pulse velocity is dwarfed by a contribution from saturable gain dynamics.
Laser frequency combs are coherent light sources that simultaneously provide pristine frequency spacings for precision metrology and the fundamental basis for ultrafast and attosecond sciences. Recently, nonlinear parametric conversion in high-Q microresonators has been suggested as an alternative platform for optical frequency combs, though almost all in 100 GHz frequencies or more. Here we report a low-phase-noise on-chip Kerr frequency comb with mode spacing compatible with high-speed silicon optoelectronics. The waveguide cross-section of the silicon nitride spiral resonator is designed to…
Femtosecond frequency combs have boosted progress in various fields of precision metrology. Nevertheless, demanding applications such as front-end frequency and time standards, ultrastable microwave generation or high-resolution spectroscopy still necessitate improved stability. The spectral bandwidth and absolute position of individual comb lines are crucial in this context. Typically, both parameters are controlled on short and long time scales by tight locking to external optical and microwave references which represent costly and cumbersome additions to the entire setup. Here, we demonstra…
In this paper, we present an experimental study of the metrological stabilization of a solid-state frequency comb for embedded metrology applications. The comb is a passively mode-locked laser diode based on InGaAs/InP Quantum-dash structure emitting optical lines into a 9 nm bandwidth centered at 1.55 $μ$m with a repetition rate of 10.09 GHz. The frequency stabilization is achieved by optical injection locking of the comb with an external cavity laser diode referenced onto a metrological frequency standard. One observes the transfer of the spectral purity from the injection laser to the neigh…
We propose and theoretically investigate a dispersion-engineered Si3N4 microring resonator, based on a cross-section containing a partially-etched trench, that supports phase-locked, two-color soliton microcomb states. These soliton states consist of a single circulating intracavity pulse with a modulated envelope that sits on a continuous wave background. Such temporal waveforms produce a frequency comb whose spectrum is spread over two widely-spaced spectral windows, each exhibiting a squared hyperbolic secant envelope, with the two windows phase-locked to each other via Cherenkov radiation.…
We report on the observation of strong transmission line shape alterations in a cold-atom hollow-core fiber interface. We show that this can lead to a significant overestimation of the assigned resonant optical depth for high atom densities. By modeling light beam propagation in an inhomogeneous dispersive medium, we attribute the observations to micro lensing in the atomic ensemble in combination with the mode selection of the atom-fiber interface. The approach is confirmed by studies of Rydberg EIT line shapes.
The two-frequency problem of synchronization of the pulse train of a passively mode locked soliton laser to an externally injected pulse train is solved in the weak injection regime. The source and target frequency combs are distinguished by the spacing and offset frequency mismatches. Locking diagrams map the domain in the mismatch parameter space where stable locking of the combs is possible. We analyze the dependence of the locking behavior on the relative frequency and chirp of the source and target pulses, and the conditions where the relative offset frequency has to be actively stabilize…
Photonic technologies have received considerable attention for enhancement of radio-frequency (RF) electrical systems, including high-frequency analog signal transmission, control of phased arrays, analog-to-digital conversion, and signal processing. Although the potential of radio-frequency photonics for implementation of tunable electrical filters over broad RF bandwidths has been much discussed, realization of programmable filters with highly selective filter lineshapes and rapid reconfigurability has faced significant challenges. A new approach for RF photonic filters based on frequency co…
Microresonator-based Kerr frequency comb (microcomb) generation can potentially revolutionize a variety of applications ranging from telecommunications to optical frequency synthesis. However, phase-locked microcombs have generally had low conversion efficiency limited to a few percent. Here we report experimental results that achieve ~30% conversion efficiency (~200 mW on-chip comb power excluding the pump) in the fiber telecommunication band with broadband mode-locked dark-pulse combs. We present a general analysis on the efficiency which is applicable to any phase-locked microcomb state. Th…
Broadband dual-comb spectroscopy (DCS) based on portable mode-locked fiber frequency combs is a powerful tool for in situ, calibration free, multi-species spectroscopy. While the acquisition of a single spectrum with mode-locked DCS typically takes microseconds to milliseconds, the applications of these spectrometers have generally been limited to systems and processes with time changes on the order of seconds or minutes due to the need to average many spectra to reach a high signal-to-noise ratio (SNR). Here, we demonstrate high-speed, continuous, fiber mode-locked laser DCS with down to 11 $…
We report on a new design for a femtosecond Ti:sapphire oscillator in which dispersion compensation is realized exclusively using mirrors, including special mirrors with third order dispersion. This makes the oscillator dynamically tunable over a spectral range of 45 nm using an intracavity wedge-pair; and it delivers 40 fs pulses at 80 MHz repetition rate. Due to the all-mirror design, the oscillator represents an attractive base for a tunable frequency comb for high precision spectroscopy applications.
By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schrödinger equation, we unveil the existence condition of the quadratic soliton mode-locked degenerate optical parametric oscillator in the previously unexplored parameter space of near-zero group velocity mismatch. We study the nature of the quadratic solitons and divide their dynamics into two distinctive branches depending on the system parameters. We find the nonlinear interaction between the resonant pump and signal results in phenomena that resemble the dispersive two-photon absorp…
We achieve a quantum-noise-limited absorption sensitivity of 1.7/times10$^{-12}$ cm$^{-1}$ per spectral element at 400 s of acquisition time with cavity-enhanced frequency comb spectroscopy, the highest demonstrated for a comb-based technique. The system comprises a frequency comb locked to a high-finesse cavity and a fast-scanning Fourier transform spectrometer with an ultra-low-noise autobalancing detector. Spectra with a signal-to-noise ratio above 1000 and a resolution of 380 MHz are acquired within a few seconds. The measured absorption lineshapes are in excellent agreement with theoretic…
We have specifically investigated the free-space mode locking dynamics of erbium-doped fiber (EDF) mode-locked ultrafast lasers via nonlinear polarization rotation (NPR) in the normal dispersion regime. To do so, we built a passively mode-locked fiber laser based on NPR with a repetition rate of 89 MHz producing an octave-spanning spectrum due to supercontinuum (SC) generation in highly nonlinear fiber (HNLF). Most significantly, we have achieved highly stable self-starting NPR mode-locked femtosecond fiber laser based frequency comb which has been running mode locked for the past one year wit…
Quantum cascade laser (QCL) frequency combs are a promising candidate for chemical sensing and biomedical diagnostics, requiring only milliseconds of acquisition time to record absorption spectra without any moving parts. They are electrically pumped and have a small footprint, making them an ideal platform for on-chip integration. Until now, optical feedback is fatal for frequency comb generation in QCLs and destroys intermodal coherence. This property imposes strict limits on the possible degree of integration. Here, we demonstrate coherent injection locking of the repetition frequency to a …
We report the first experimental demonstration of frequency-locking of an extended-cavity quantum-cascade-laser (EC-QCL) to a near-infrared frequency comb. The locking scheme is applied to carry out absolute spectroscopy of N2O lines near 7.87 μm with an accuracy of ~60 kHz. Thanks to a single mode operation over more than 100 cm^{-1}, the comb-locked EC-QCL shows great potential for the accurate retrieval of line center frequencies in a spectral region that is currently outside the reach of broadly tunable cw sources, either based on difference frequency generation or optical parametric oscil…
The frequency of the Calcium ^3P_1--^1S_0 intercombination line at 657 nm is phase-coherently measured in terms of the output of a primary cesium frequency standard using an optical frequency comb generator comprising a sub-10 fs Kerr-lens mode-locked Ti:Sapphire laser and an external microstructure fiber for self-phase-modulation. The measured frequency of ν_Ca = 455 986 240 494 276 Hz agrees within its relative uncertainty of 4 10^-13 with the values previously measured with a conceptually different harmonic frequency chain and with the value recommended for the realization of the SI unit of…
A general mechanism for the generation of frequency combs referenced to atomic resonances is put forward. The mechanism is based on the periodic phase control of a quantum system's dipole response. We develop an analytic description of the comb spectral structure, depending on both the atomic and the phase-control properties. We further suggest an experimental implementation of our scheme: Generating a frequency comb in the soft-x-ray spectral region, which can be realized with currently available techniques and radiation sources. The universality of this mechanism allows the generalization of…
A fully integrated dispersion-managed femtosecond mode-locked laser
Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Institute of Electrical and Micro Engineering, Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院电气与微工程学院）；EDWATEC SA（EDWATEC公司）；Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗森多夫亥姆霍兹中心）
We report on the characterization of the timing stability of passively mode-locked discrete mode diode laser sources. These are edge-emitting devices with a spatially varying refractive index profile for spectral filtering. Two devices with a mode-locking frequency of 100 GHz are characterized. The first device is designed to support a comb of six modes and generates near Fourier limited 1.9 ps pulses. The second supports four primary modes resulting in a sinusoidal modulation of the optical intensity. Using a cross-correlation technique, we measured a 20 fs pulse to pulse timing jitter for th…
We have measured the frequency of the $6s^2S_{1/2} - 5d^2D_{3/2}$ electric-quadrupole transition of $^{171}$Yb$^+$ with a relative uncertainty of $1\times 10^{-14}$, $ν_{Yb}$ = 688 358 979 309 312 Hz $\pm$ 6 Hz. A femtosecond frequency comb generator was used to phase-coherently link the optical frequency derived from a single trapped ion to a cesium fountain controlled hydrogen maser. This measurement is one of the most accurate measurements of optical frequencies ever reported, and it represents a contribution to the development of optical clocks based on an $^{171}$Yb$^+$ ion standard.
The influence of Raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. The Raman effect introduces a threshold value in the resonator quality factor above which the frequency locked solitons can not exist and, instead, a rich dynamics characterized by generation of self-frequency shift- ing solitons and dispersive waves is observed. A mechanism of broadening of the Cherenkov radiation through Hopf instability of the frequency locked solitons is also reported.
Dual-comb lasers from which asynchronous ultrashort pulses can be simultaneously generated have recently become an interesting research subject. They could be an intriguing alternative to the current dual-laser optical-frequency-comb source with highly sophisticated electronic control systems. If generated through a common light path traveled by all pulses, the common-mode noises between the spectral lines of different pulse trains could be significantly reduced. Therefore, coherent dual-comb generation from a completely common-path, unidirectional lasing cavity would be an interesting territo…
Fourier domain mode-locking (FDML) has been a popular laser design for high speed optical frequency domain imaging (OFDI) but achieving long coherence lengths, and therefore imaging range, has been challenging. The narrow instantaneous linewidth of a frequency comb (FC) FDML laser could provide an attractive platform for high speed as well as long range OFDI. Unfortunately, aliasing artifacts arising from signals beyond the principle measurement depth of the free spectral range have prohibited the use of a FC FDML for imaging so far. To make the enhanced coherence length of FC FDML laser avail…
Fano resonance in molecular spectroscopy is reported with a dual-comb instrument. The effect is observed as asymmetric absorption lines of H12CN. Pulse chirping conditions in the gas cell are varied to show that Fano resonance is dependent on the pulse peak power. A model adding the Fano profile to Voigt lines is used to estimate Fano phase as a function of pulse peak power. A pulse peak power condition is derived from this analysis to avoid lineshape distortion in pulsed laser experiments.
Temporal Localized States (TLSs) are individually addressable structures traveling in optical resonators. They can be used as bits of information and to generate frequency combs with tunable spectral density. We show that a pair of specially designed nonlinear mirrors, a 1/2 Vertical-Cavity Surface-Emitting Laser and a Semiconductor Saturable Absorber, coupled in self-imaging conditions, can lead to the generation of such TLSs. Our results indicate how a conventional passive mode- locking scheme can be adapted to provide a robust and simple system emitting TLSs and it paves the way towards the…
Nonlinear systems with two competing frequencies show locking or resonances. In lasers, the two interacting frequencies can be the cavity repetition rate and a frequency externally applied to the system. Conversely, the excitation of breather oscillations in lasers naturally triggers a second characteristic frequency in the system, therefore showing competition between the cavity repetition rate and the breathing frequency. Yet, the link between breathing solitons and frequency locking is missing. Here we demonstrate frequency locking at Farey fractions of a breather laser. The winding numbers…
Chip-scale frequency comb generators have the potential to become key building blocks of compact wavelength-division multiplexing (WDM) transceivers in future metropolitan or campus-area networks. Among the various comb generator concepts, quantum-dash (QD) mode-locked laser diodes (MLLD) stand out as a particularly promising option, combining small footprint with simple operation by a DC current and offering flat broadband comb spectra. However, the data transmission performance achieved with QD-MLLD was so far limited by strong phase noise of the individual comb tones, restricting experiment…
We combine a graphene mode-locked oscillator with an external compressor and achieve~29fs pulses with~52mW average power. This is a simple, low-cost, and robust setup, entirely fiber based, with no free-space optics, for applications requiring high temporal resolution.
We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability affects timing jitter.
We demonstrate a self-referenced fiber frequency comb that can operate outside the well-controlled optical laboratory. The frequency comb has residual optical linewidths of < 1 Hz, sub-radian residual optical phase noise, and residual pulse-to-pulse timing jitter of 2.4 - 5 fs, when locked to an optical reference. This fully phase-locked frequency comb has been successfully operated in a moving vehicle with 0.5 g peak accelerations and on a shaker table with a sustained 0.5 g rms integrated acceleration, while retaining its optical coherence and 5-fs-level timing jitter. This frequency comb sh…
Narrow linewidth lasers and optical frequency combs generated with mode-locked lasers revolutionized optical frequency metrology. The advent of soliton Kerr frequency combs in compact crystalline or integrated ring optical microresonators opens new horizons for applications. These combs, as was naturally assumed, however, require narrow-linewidth single-frequency pump lasers. We demonstrate that a regular multi-frequency Fabry-Perot laser diode self-injection locked to an optical whispering gallery mode (WGM) microresonator can be first efficiently transformed to a single-frequency ultra-narro…
We present a method of phase-locking any number of continuous-wave lasers to an optical frequency comb (OFC) that enables independent frequency positioning and control of each laser while still maintaining lock to the OFC. The scheme employs an acousto-optic modulator (AOM) in a double pass configuration added to each laser before its light is compared by optical heterodyne with the comb. The only requirement is that the tuning bandwidth of the double pass AOM setup be larger than half the OFC repetition rate. We demonstrate this scheme and achieve an arbitrary frequency tuning precision, a tu…
We present full phase stabilization of an amplified Yb:fiber femtosecond frequency comb using an intra-cavity electro-optic modulator and an acousto-optic modulator. These transducers provide high servo bandwidths of 580 kHz and 250 kHz for frep and fceo, producing a robust and low phase noise fiber frequency comb. The comb was self-referenced with an f - 2f interferometer and phase locked to an ultra-stable optical reference used for the JILA Sr optical clock at 698 nm, exhibiting 0.21 rad and 0.47 rad of integrated phase errors (over 1 mHz - 1 MHz) respectively. Alternatively, the comb was l…
We present the detailed characterization of the phase dynamics of a telecom hybrid III-V-on-silicon passively mode-locked laser with a ring cavity. We explore the various regimes of operation as a function of gain current and saturable absorber bias voltage. We use a stepped-heterodyne measurement to quantify the spectral chirp and reconstruct the pulse envelop. With this technique we are able to identify regimes of near-transform-limited operation and we assess the degradation of mode-locking in the comb phase relationship when saturable absorber bias voltage is changed. Finally, we present a…
