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 taking stochastic noise into account, we compute ASE-induced jitters for all quantities considered. Continuing this approach, we then derive an expression for the resulting carrier-envelope phase noise of the comb, for which so far only numerical estimates exist. We further compute analytical estimates for ASE induced pulse chirp and duration variations and address the issue of resulting pulse contrast in a mode-locked laser and the resulting coherence properties. Considering three example cases, we finally compute estimates for all quantities analyzed. Taken together, our analysis provides a comprehensive view of ASE effects in a mode-locked laser, which unites numerous scattered reports across the literature.
Beat note measurements between a mode-locked and a continuous-wave laser as well as between two mode-locked sources were used to demonstrate that the sub-threshold, cavity filtered, amplified spontaneous emission is not stationary even when a fast mode-locking mechanism, such as nonlinear polarization rotation, is used to generate short pulses. A relatively small gain modulation of a few percents created by high intensity pulses can produce a significant modulation of the amplified noise once synchronously accumulated over several cavity round-trips, even if the repetition rate is faster than …
Temporally stabilized optical pules, confined in microresonators driven by a continuous-wave laser, have attracted tremendous attention due to their fascinating features with many applications. Here we report the observations of mode-locked platicon frequency microcomb formation in normal dispersion dispersion-managed microresonators operating at microwave K-band repetition rate for the first time. Facilitated by the thermally controllable modulated background induced by avoided mode-crossings, various platicon bound state patterns with regular and irregular temporal separation are stably gene…
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 demonstrate a complete Silicon Photonics WDM link relying on a single section semiconductor mode-locked laser and a single SOA to support up to 12 multiplexed channels with a bit error rate of 1e-12 at serial data rates of 14 Gbps without channel pre-emphasis, equalization or forward error correction. Individual channels reach error free operation at 25 Gbps and multi-channel operation at 25 Gbps is shown to be compatible with standard 7% overhead hard decision forward error correction. Silicon Photonics transmitter and receiver chips are hybridly integrated with driver and receiver electro…
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 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…
Stochastically driven nonlinear processes limit the number of amplified modes in a natural system due to competitive mode interaction, which is accompanied by loss of coherence when increasing the complexity of system. Specifically, we find that modulation instability, which exhibits great fluctuations when it is spontaneously grown from noise in conservative systems, may possess a high degree of coherence in dissipative laser system with gain. Nonlinear mode interactions can be competitive or cooperative: adjusting the intracavity polarization state controls the process of loss of coherence. …
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…
We experimentally demonstrate the spontaneous synchronization and the exceptional point (EP) induced pulse generation mechanism in the breather complex. The breathing frequency and phase are found to be synchronized during the formation of a 9-breather assembled complex in a mode-locked fiber laser. The breathers are formed at exactly the time point of the complex's breathing frequency leaving or entering the subharmonic entrainment. Such new pulse generation mechanism should be related to the non-Hermitian EPs or the time translation symmetry breaking. The investigations of destroying and reb…
We predict and observe the appearance of an excess noise factor due to the non-Hermiticity of the modes of two actively harmonically mode-locked lasers. The non uniform distribution of gain and losses in the ring cavities of these lasers causes a non-orthogonality of the longitudinal modes, which is responsible for an increase of the rate of spontaneous emission falling in the lasing pulsed mode. This leads to an increase of the phase noise of the pulse train generated by these lasers by more than 20 dB at some offset frequencies. This degradation can be prohibitive for the use of these lasers…
Spontaneous transverse mode locking to generate optical vortex arrays is already widely studied for the frequency degenerated transverse modes. While, the mode locking between transverse modes in different orders (non-frequency degenerated families) to achieve spatial stationary beam patterns is rarely reported. The theory of transverse mode locking is discussed. Concepts of general transverse mode locking (G-TML) and restricted transverse mode locking (R-TML) are mentioned. It's experimentally shown that R-TML is possible in microchip cavities with high nonlinearity. More interestingly, some …
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…
We demonstrate 14.3-attosecond timing jitter [integrated from 10 kHz to 94 MHz offset frequency] optical pulse trains from 188-MHz repetition-rate mode-locked Yb-fiber lasers. In order to minimize the timing jitter, we shorten the non-gain fiber length to shorten the pulsewidth and reduce excessive higher-order nonlinearity and nonlinear chirp in the fiber laser. The measured jitter spectrum is limited by the amplified spontaneous emission limited quantum noise in the 100 kHz - 1 MHz offset frequency range, while it was limited by the relative intensity noise-converted jitter in the lower offs…
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…
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…
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.…
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 $…
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…
As self-sustained oscillators, lasers possess the unusual ability to spontaneously synchronize. These nonlinear dynamics are the basis for a simple yet powerful stabilization technique known as injection locking, in which a laser's frequency and phase can be controlled by an injected signal. Due to its inherent simplicity and favorable noise characteristics, injection locking has become a workhorse for coherent amplification and high-fidelity signal synthesis in applications ranging from precision atomic spectroscopy to distributed sensing. Within integrated photonics, however, these injection…
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.
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…
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…
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…
Dissipative solitons are self-localised structures that can persist indefinitely in "open" systems characterised by continual exchange of energy and/or matter with the environment. They play a key role in photonics, underpinning technologies from mode-locked lasers to microresonator optical frequency combs. Here we report on the first experimental observations of spontaneous symmetry breaking of dissipative optical solitons. Our experiments are performed in a passive, coherently driven nonlinear optical ring resonator, where dissipative solitons arise in the form of persisting pulses of light …
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…
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 …
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…
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…
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…
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 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.
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.
Two-photon excitation spectroscopy with broad spectral span is demonstrated at Doppler-limited resolution. We describe first Fourier transform two-photon spectroscopy of an atomic sample with two mode-locked laser oscillators in a dual-comb technique. Each transition is uniquely identified by the modulation imparted by the interfering comb excitations. The temporal modulation of the spontaneous two-photon fluorescence is monitored with a single photodetector, and the spectrum is revealed by a Fourier transform.
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…
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…
