Understanding the dynamics of Fourier domain mode-locked (FDML) lasers is crucial for determining physical coherence limits, and for finding new superior methods for experimental realization. In addition, the rich interplay of linear and nonlinear effects in a laser ring system is of great theoretical interest. Here we investigate the dynamics of a highly dispersion-compensated setup, where over a bandwidth of more than 100 nm, a highly coherent output with nearly shot-noise-limited intensity fluctuations was experimentally demonstrated. This output is called the sweet-spot. We show by numerical simulation that a finite amount of residual dispersion in the fiber delay cavity of FDML lasers can be compensated by the group delay dispersion in the swept bandpass filter, such that the intensity trace exhibits no dips or high-frequency distortions, which are the main source of noise in the laser. In the same way, a small detuning from the ideal sweep filter frequency can be tolerated. Furthermore, we find that the filter's group delay dispersion improves the coherence properties of the laser, and acts as a self-stabilizing element in the cavity. Our theoretical model is validated against experimental data, showing that all relevant physical effects for the sweet-spot operating regime are included.
We present a theoretical model and its efficient numerical implementation for the simulation of wavelength-swept waveform propagation in fiber systems such as Fourier domain mode-locked (FDML) lasers, fully accounting for the polarization dynamics in fiber spools and further polarization dependent optical components in the setup. This approach enables us to perform long-time simulations of the FDML laser dynamics over more than 100000 cavity roundtrips, as required for some FDML configurations to ensure convergence to the steady state operating regime. The model is validated against experiment…
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…
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…
High frequency fluctuation in the optical signal generated in Fourier-Domain Mode Locked fiber laser (FDML-FL), which is the major problem and degrades the laser performance, is not yet fully analyzed or studied. The basic theory which is causing this high frequency fluctuation is required to clearly understand its dynamics and to control it for various applications. In this letter, by analyzing the signal and system dynamics of FDML-FL, we theoretically demonstrate that the high frequency fluctuation is induced by the intrinsic instability of frequency offset of the signal in cavity with nonl…
FDML lasers provide sweep rates in the MHz range at wide optical bandwidths, making them ideal sources for high speed OCT. Recently, at lower speed, ultralong-range swept-source OCT has been demonstrated1, 2 using a tunable vertical cavity surface emitting laser (VCSEL) and also using a Vernier-tunable laser. These sources provide relatively high sweep rates and meter range coherence lengths. In order to achieve similar coherence, we developed an extremely well dispersion compensated Fourier Domain Mode Locked (FDML) laser, running at 3.2 MHz sweep rate and 120 nm spectral bandwidth. We demons…
Optical coherence tomography (OCT) applications like ultra-widefield and full eye-length imaging are of high interest for various diagnostic purposes. In swept-source OCT these techniques require a swept light source, which is coherent over the whole imaging depth. We present a zero roll-off 1060 nm Fourier Domain Mode Locked-Laser (FDML-Laser) for retinal OCT imaging at 1.7 MHz A-scan rate and first long-range imaging results with it. Several steps such as improved dispersion compensation and frequency regulation were performed and will be discussed. Besides virtually no loss in OCT signal ov…
We present a new design of a Fourier Domain Mode Locked laser (FDML laser), which provides a new record in sweep range at ~1um center wavelength: At the fundamental sweep rate of 2x417 kHz we reach 143nm bandwidth and 120nm with 4x buffering at 1.67MHz sweep rate. The latter configuration of our system is characterized: The FWHM of the point spread function (PSF) of a mirror is 5.6um (in tissue). Human in vivo retinal imaging is performed with the MHz laser showing more details in vascular structures. Here we could measure an axial resolution of 6.0um by determining the FWHM of specular reflex…
High-precision passive stabilization of repetition rate for a mode-locked fiber laser based on optical pulse injection
East China Normal University（华东师范大学）；University of Shanghai for Science and Technology（上海理工大学）；Chongqing Institute of East China Normal University（华东师范大学重庆研究院）；Jinan Institute of Quantum Technology（济南量子技术研究院）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
We experimentally investigate the RF linewidth and timing jitter over a wide range of delay tuning in a self-mode-locked two-section quantum dash lasers emitting at ~ 1.55 micron and operating at ~ 21 GHz repetition rate subject to single and dual optical feedback into gain section. Various feedback conditions are investigated and optimum levels determined for narrowest linewidth and reduced timing jitter for both single and dual loop configurations. We demonstrate that dual loop feedback, with the shorter feedback cavity tuned to be fully resonant, followed by fine tuning of the phase of the …
We review the conventional phase-locking technique in the long-term stabilization of the mode-locked fiber laser and investigate the phase noise limitation of the conventional technique. To break the limitation, we propose an improved phase-locking technique with an optic-microwave phase detector in achieving the ultra-low phase noise and phase drift. The mechanism and the theoretical model of the novel phase-locking technique are also discussed. The long-term stabilization experiments demonstrate that the improved technique can achieve the long-term stabilization for the MLFL with ultra-low p…
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…
It is demonstrated that RF current modulation of a frequency stabilized injection-locked diode laser allows the stabilization of an optical cavity to adjustable lengths, by variation of the RF frequency. This transfer cavity may be used to stabilize another laser at an arbitrary wavelength, in the absence of atomic or molecular transitions suitable for stabilization. Implementation involves equipment and techniques commonly used in laser cooling and trapping laboratories, and does not require electro- or acousto-optic modulators. With this technique we stabilize a transfer cavity using a RF cu…
We present an experimental realization of the Optical Frequency Locked Loop (OFLL) applied to long-term frequency difference stabilization of broad-line DFB lasers. The presented design, based on an integrated phase-frequency detector chip, is digitally tunable in real-time, robust against environmental perturbations and compatible with commercially available laser current control modules. We present a simple model and a quick method to optimize the loop for given hardware using only simple measurements in time domain and approximate laser linewidth. We demonstrate frequency stabilization for …
Injection locking of diode lasers is commonly used to amplify low power laser light, but is extremely sensitive to perturbations in the laser current and temperature. To counter such perturbations, active stabilization is often applied to the current of the injection locked diode. We observe that the diode laser's polarization extinction ratio (PER) greatly increases when injection locked, and therefore the PER provides a measure of injection lock quality. We report robust active stabilization of a diode laser injection lock based on the PER, demonstrating the technique at 399 nm wavelength wh…
Controlling the carrier envelope phase (CEP) in mode-locked lasers over practically long timescales is crucial for real-world applications in ultrafast optics and precision metrology. We present a hybrid solution that combines a feed-forward technique to stabilize the phase offset in fast timescales and a feedback technique that addresses slowly varying sources of interference and locking bandwidth limitations associated with gain media with long upper-state lifetimes. We experimentally realize the hybrid stabilization system in an Er:Yb:glass mode-locked laser and demonstrate 75 hours of stab…
A phase modulated RF current source is applied to an injection locked diode laser operating at $780\unit{nm}$. This produces tunable phase modulated sidebands of the laser suitable for stabilizing the length of an optical transfer cavity using the Pound-Drever-Hall technique. The Pound-Drever-Hall signal is anti-symmetric about the lock point, despite the presence of significant diode laser amplitude modulation. The stabilized optical transfer cavity is used to frequency stabilize a 776 nm external cavity diode laser. The stability and tunability of this transfer cavity locked laser is establi…
We stabilize a chosen radiofrequency beat note between two optical fields derived from the same mode-locked laser pulse train, in order to coherently manipulate quantum information. This scheme does not require access or active stabilization of the laser repetition rate. We implement and characterize this external lock, in the context of two-photon stimulated Raman transitions between the hyperfine ground states of trapped 171-Yb+ quantum bits.
We demonstrate theoretically that robust mode-locking can be achieved on a semiconductor chip with a waveguide array architecture. The waveguide arrays are used as an ideal saturable absorption mechanism for initial noise start-up as well as pulse shaping and stabilization. The cavity gain is provided by an injection current and forward biasing of the semiconductor material. The technology can be integrated directly with semiconductor architectures and technologies, thus allowing for the potential of an on-chip, broadband device.
We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with equidistantly increasing peak separation. This family was identified by two alternative numerical schemes and the bound state instability was disclosed by a linear stability analysis. Moreover, similar families of unstable bound state solutions have been found in a more realistic lumped laser model with an idealized saturable absorber (instantaneous response). We sh…
We report experimental studies of the influence of symmetric dual-loop optical feedback on the RF linewidth and timing jitter of self-mode-locked two-section quantum dash lasers emitting at 1550 nm. Various feedback schemes were investigated and optimum levels determined for narrowest RF linewidth and low timing jitter, for single-loop and symmetric dual-loop feedback. Two symmetric dual-loop configurations, with balanced and unbalanced feedback ratios, were studied. We demonstrate that unbalanced symmetric dual loop feedback, with the inner cavity resonant and fine delay tuning of the outer l…
We study optical cavity locking for laser stabilization through spatial modulation of the phase front of a light beam. A theoretical description of the underlying principle is developed for this method and special attention is paid to residual amplitude modulation (RAM) caused by experimental imperfections, especially the manufacture errors of the spatial phase modulator. The studied locking method owns the common advantages of the Pound-Drever-Hall method and the tilt-locking one, and it can provide a more artful way to eliminate RAM noise in phase modulation for the ultimate stability of las…
We stabilized the frequency of a compact planar-waveguide external cavity laser (ECL) on a Fabry-Pérot cavity (FPC) through a Pound-Drever-Hall scheme. The residual frequency stability of the ECL is 1E-14, comparable to the stability achievable with a fiber laser (FL) locked to a FPC through the same scheme. We set up an optical link of 100 km, based on fiber spools, that reaches 1E-19 relative stability, and we show that its performances using the ECL or FL are comparable. Thus ECLs could serve as an excellent replacement for FLs in optical links where cost-effectiveness and robustness are im…
Semiconductor mode-locked lasers can be used in a variety of applications ranging from multi-carrier sources for WDM communication systems to time base references for metrology. Their packaging in compact chip- or module-level systems remains however burdened by their strong sensitivity to back-reflections, quickly destroying the coherence of the mode-locking. Here, we investigate the stabilization of mode-locked lasers directly edge coupled to a silicon photonic integrated circuit, with the objective of moving isolators downstream to the output of the photonic circuit. A 2.77 kHz 3 dB RF line…
Lasers stabilized to vacuum-gap Fabry-Pérot optical reference cavities display extraordinarily low noise and high stability, with linewidths much less than 1 Hz. These lasers can expand into new applications and ubiquitous use with the development of compact, portable cavities that are manufacturable at scale. Here we demonstrate an 8 mL volume Fabry-Pérot cavity constructed with mirrors that are fabricated lithographically with finesse near 1 million. A laser locked to the cavity exhibits phase noise limited by the cavity thermal noise for offset frequencies ranging from 1 Hz to $\approx$ 1 k…
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…
Self-injection locking is a dynamic phenomenon representing stabilization of the emission frequency of an oscillator with a passive cavity enabling frequency filtered coherent feedback to the oscillator cavity. For instance, self-injection locking of a semiconductor laser to a high-quality-factor (high-Q) whispering gallery mode (WGM) microresonator can result in multiple orders of magnitude reduction of the laser linewidth. The phenomenon was broadly studied in experiments, but its detailed theoretical model allowing improving the stabilization performance does not exist. In this paper we dev…
Dual-comb sources with equally spaced and low phase noise frequency lines are of great importance for high resolution spectroscopy and metrology. In the terahertz frequency range, electrically pumped semiconductor quantum cascade lasers (QCLs) are suitable candidates for frequency comb and dual-comb operation. For a single laser frequency comb, the repetition rate can be locked using a microwave injection locking and the carrier frequency can be locked to a highly stable source. However, for the locking of two laser combs, four frequencies (two repetition rates and two carrier offset frequenci…
We have developed experimental methods for the generation of chirped laser pulses of controlled frequency evolution in the nanosecond pulse length range for coherent atomic interaction studies. The pulses are sliced from the radiation of a cw external cavity diode laser while its drive current, and consequently its frequency, are sinusoidally modulated. By the proper choice of the modulation parameters, as well as of the timing of pulse slicing, we can produce a wide variety of frequency sweep ranges during the pulse. In order to obtain the required frequency chirp, we need to stabilize the ce…
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…
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 investigate the effect of tunable optical feedback on a commercial DFB laser edge coupled to a Silicon Photonics planar integrated circuit in which a tunable reflector has been implemented by means of a ring resonator based add-drop multiplexer. Controlled optical feedback allows for fine-tuning of the laser oscillation frequency. Under certain conditions it also allows suppression of bifurcation modes triggered by reflections occurring elsewhere on the chip. A semi-analytical model describing laser dynamics under combined optical feedback from the input facet of the edge coupler and from t…
We demonstrate an asymmetric dual-loop feedback scheme to suppress external cavity side-modes induced in self-mode-locked quantum-dash lasers with conventional single and dual-loop feedback. In this letter, we achieved optimal suppression of spurious tones by optimizing the length of second delay time. We observed that asymmetric dual-loop feedback, with large (~8x) disparity in cavity lengths, eliminates all external-cavity side-modes and produces flat RF spectra close to the main peak with low timing jitter compared to single-loop feedback. Significant reduction in RF linewidth and reduced t…
Few-cycle pulsed laser technology highlights the need for control and stabilization of the carrier-envelope phase (CEP) for applications requiring shot-to-shot timing and phase consistency. This general requirement has been achieved successfully in a number of free space and fiber lasers via feedback and feed-forward methods. Expanding upon existing results, we demonstrate CEP stabilization through the feed-forward method applied to a SESAM mode-locked Er:Yb:glass laser at 1.55 um with a measured ultralow timing jitter of 2.9 as (1 Hz - 3 MHz) and long-term stabilization over a duration of eig…
We present a current-modulation technique for diode-laser systems that is specifically designed for high-bandwidth laser-frequency stabilization and wideband frequency modulation with a flat transfer function. It consists of a dedicated current source and an impedance-matching circuit both placed close to the laser diode. The transfer behaviour of the system is analysed under realistic conditions employing an external-cavity diode laser (ECDL) system. We achieve a phase lag less than 90$°$ up to 25 MHz and a gain flatness of $\pm$ 3 dB in the frequency range of DC to 100 MHz while the passive …
We demonstrate two fully and tightly phase locked 750 MHz ytterbium (Yb) fiber frequency combs that are independently stabilized to a continuous wave (CW) laser with <1 rad RMS phase error. A bulk EOM and a single stack PZT are separately utilized as the fast actuators for cavity length stabilization. The carrier envelop frequencies are phase locked by single loop feedback to laser diode current, showing 1.6 MHz servo bumps. The in-loop fractional frequency instabilities are ~1.5e-18 at 1s for both combs. To the best of our knowledge, this is the highest repetition rate in fiber based low phas…
We consider the phase stability of a local oscillator (or laser) locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. The atoms are cooled to millikelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state-of-the-art. Furthermore, the inhomogen…
We numerically investigate the complex nonlinear dynamics for two independently coupled laser systems consisting of (i) mutually delay-coupled edge emitting diode lasers and (ii) injection-locked quantum nano-structures lasers. A comparative study in dependence on the dynamical role of alpha parameter, which determine the phase-amplitude coupling of the optical field, in both the cases is probed. The variation of alpha lead to conspicuous changes in the dynamics of both the systems, which are characterized and investigated as a function of optical injection strength for the fixed coupled-cavit…
We demonstrate the use of a flexible digital servo system for the optical stabilization of both the repetition rate and carrier-envelope offset frequency of a laser frequency comb. The servo system is based entirely on a low-cost field programmable gate array, simple electronic components, and existing open-source software. Utilizing both slow and fast feedback actuators of a commercial mode-locked laser frequency comb, we maintain cycle-slip free locking of optically-derived beatnotes over a 30 hour period, and measure residual phase noise at or below ~0.1 rad, corresponding to <100 attosecon…
Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery mode microresonators ("microcombs") has been developed recently, which represents a promising route towards chip-level integration and out-of-the-lab use of these devices. Presently, two families of microcombs have been demonstrated: combs with electronically detectable mode spacing that can be directly stabilized, and broadband combs with up to octave-spannin…
Frequency stabilization of laser light is crucial in both scientific and industrial applications. Technological developments now allow analog laser stabilization systems to be replaced with digital electronics such as field-programmable gate arrays, which have recently been utilized to develop such locking systems. We have developed a frequency stabilization system based on a field-programmable gate array, with emphasis on hardware simplicity, which offers a user-friendly alternative to commercial and previous home-built solutions. Frequency modulation, lock-in detection and a proportional-int…
Progress made in optical references, including ultra-stable Fabry-Perot cavities, optical frequency combs and optical atomic clocks, have driven the need for ultra-stable optical fiber networks. Telecom-wavelength ultra-pure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this manuscript, we present a Doppler-cancellation setup based on a digital phase-locked loop for ultra-stable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup,…
Frequency microcombs, successors to mode-locked laser and fiber combs, enable miniature rulers of light for applications including precision metrology, molecular fingerprinting, and exoplanet discoveries. To enable the frequency ruling function, microcombs must be stabilized by locking their carrier-envelop offset frequency. So far, the microcomb stabilization remains compounded by the elaborate optics external to the chip, thus evading its scaling benefit. To address this challenge, here we demonstrate a nanophotonic chip solution based on aluminum nitride thin films, which simultaneously off…
We present a flexible all-polarization-maintaining (PM) mode-locked ytterbium (Yb):fiber laser based on a nonlinear amplifying loop mirror (NALM). In addition to providing detailed design considerations, we discuss the different operation regimes accessible by this versatile laser architecture and experimentally analyze five representative mode-locking states. These five states were obtained in a 78-MHz configuration at different intracavity group delay dispersion (GDD) values ranging from anomalous (-0.035 ps$^2$) to normal (+0.015 ps$^2$). We put a particular focus on the characterization of…
