Spectrum collapse, narrow linewidth, and Bogatov effect in diode lasers locked to high-Q optical microresonators.

We present a novel method allowing high-power single-frequency emission with sub-kHz linewidth from a compact multi-frequency diode laser locked to high-Q optical microresonator. Using high-Q MgF2microresonator and multi-frequency diode laser operating at 1535 nm with the output power of 100 mW and an emission spectrum consisting of approximately 50 lines with MHz linewidth, we observed a spectrum collapse to a single line or several lines with a sub-kHz linewidth and output power power of 50 mW. The Bogatov effect predicted more than 30 years ago was observed and studied in the spectrum of the locked laser. For analysis of the considered effect, original theoretical model taking into account self-injection locking effect, mode competition and Bogatov asymmetric mode interaction was developed and numerical modeling was performed. All numerical results are in a good agreement with our experimental data. Accurate analytical estimations for the parameters critical for the considered effect were obtained. The proposed method may be applied for different types of diode lasers operating in different spectral ranges.

From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs.

The model, that is usually called the Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs-first observed in 2007, i.e. 20 years after the original formulation of the LLE-and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Two-dimensional nonlinear modes and frequency combs in bottle microresonators.

We theoretically investigate frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that appear as tilted resonances bifurcating from the spectrum of linear axial modes. We then study azimuthal modulational instability of these modes and show that families of two-dimensional (2D) soliton states localized both azimuthally and axially bifurcate from them at critical pump frequencies. Depending on detuning, 2D solitons can be stable, form persistent breathers or chaotic spatio-temporal patterns, or exhibit collapse-like evolution.

Highly efficient coupling of crystalline microresonators to integrated photonic waveguides.

Crystalline optical whispering gallery mode resonators made from alkaline earth fluorides can achieve exceptionally large optical finesse, and are used in a variety of applications, from frequency stabilization and narrow linewidth lasers, to low-noise microwave generation or soliton Kerr frequency combs. Here we demonstrate an efficient coupling method to resonators of these materials, which employs photonic integrated waveguides on a chip based on silicon nitride. By converting a mode from silicon nitride to a free-hanging silica waveguide on a silicon chip, coupling to a crystalline resonator is achieved with a high extinction, while preserving a quality factor exceeding 200 million. This compact, heterogeneous integration of ultra-high Q-factor crystalline resonators with photonic waveguides provides a proof of concept for wafer scale integration and robust, compact packaging for a wide range of applications.

Raman-Kerr frequency combs in microresonators with normal dispersion.

We generalize the coupled mode formalism to study the generation of frequency combs in microresonators with simultaneous Raman and Kerr nonlinearities and investigate an impact of the former on the formation of frequency combs and dynamics of platicons in the regime of the normal group velocity dispersion. We demonstrate that the Raman effect initiates generation of sidebands, which cascade further in four-wave mixing and reshape into the Raman-Kerr frequency combs. We reveal that the Raman scattering induces a strong instability of the platicon pulses associated with the Kerr effect and normal dispersion. This instability results in branching of platicons and complex spatiotemporal dynamics.

Breathing dissipative solitons in optical microresonators.

Dissipative solitons are self-localised structures resulting from the double balance of dispersion by nonlinearity and dissipation by a driving force arising in numerous systems. In Kerr-nonlinear optical resonators, temporal solitons permit the formation of light pulses in the cavity and the generation of coherent optical frequency combs. Apart from shape-invariant stationary solitons, these systems can support breathing dissipative solitons exhibiting a periodic oscillatory behaviour. Here, we generate and study single and multiple breathing solitons in coherently driven microresonators. We present a deterministic route to induce soliton breathing, allowing a detailed exploration of the breathing dynamics in two microresonator platforms. We measure the relation between the breathing frequency and two control parameters-pump laser power and effective-detuning-and observe transitions to higher periodicity, irregular oscillations and switching, in agreement with numerical predictions. Using a fast detection, we directly observe the spatiotemporal dynamics of individual solitons, which provides evidence of breather synchronisation.Dissipative Kerr solitons enable optical frequency comb generation in microresonators, but these solitons can undergo a breathing transition which impacts the stability of such microcombs. Here, Lucas et al. deterministically induce soliton breathing and directly observe the spatiotemporal dynamics.

Soliton dual frequency combs in crystalline microresonators.

We present a novel compact dual-comb source based on a monolithic optical crystalline MgF2 multi-resonator stack. The coherent soliton combs generated in the two microresonators of the stack with the repetition rate of 12.1 GHz and difference of 1.62 MHz provided after heterodyning a 300 MHz wide radio frequency comb. An analogous system can be used for dual-comb spectroscopy, coherent LIDAR applications, and massively parallel optical communications.

Harmonization of chaos into a soliton in Kerr frequency combs.

Dissipative Kerr solitons have paved the way to broadband and fully coherent optical frequency combs in microresonators. Here, we demonstrate numerically that slow frequency tuning of the pump laser in conjunction with phase or amplitude modulation corresponding to the free spectral range of the microresonator, provides reliable convergence of an initially excited chaotic comb state to a single dissipative Kerr soliton (DKS) state. The efficiency of this approach depends on both frequency tuning speed and modulation depth. The relevance of the proposed method is confirmed experimentally in a MgF2 microresonator.

Mid-infrared ultra-high-Q resonators based on fluoride crystalline materials.

The unavailability of highly transparent materials in the mid-infrared has been the main limitation in the development of ultra-sensitive molecular sensors or cavity-based spectroscopy applications. Whispering gallery mode microresonators have attained ultra-high-quality (Q) factor resonances in the near-infrared and visible. Here we report ultra-high Q factors in the mid-infrared using polished alkaline earth metal fluoride crystals. Using an uncoated chalcogenide tapered fibre as a high-ideality coupler in the mid-infrared, we study via cavity ringdown technique the losses of BaF2, CaF2, MgF2 and SrF2 microresonators. We show that MgF2 is limited by multiphonon absorption by studying the temperature dependence of the Q factor. In contrast, in SrF2 and BaF2 the lower multiphonon absorption leads to ultra-high Q factors at 4.5 µm. These values correspond to an optical finesse of , the highest value achieved for any type of mid-infrared resonator to date.

Photonic chip-based optical frequency comb using soliton Cherenkov radiation.

Optical solitons are propagating pulses of light that retain their shape because nonlinearity and dispersion balance each other. In the presence of higher-order dispersion, optical solitons can emit dispersive waves via the process of soliton Cherenkov radiation. This process underlies supercontinuum generation and is of critical importance in frequency metrology. Using a continuous wave-pumped, dispersion-engineered, integrated silicon nitride microresonator, we generated continuously circulating temporal dissipative Kerr solitons. The presence of higher-order dispersion led to the emission of red-shifted soliton Cherenkov radiation. The output corresponds to a fully coherent optical frequency comb that spans two-thirds of an octave and whose phase we were able to stabilize to the sub-Hertz level. By preserving coherence over a broad spectral bandwidth, our device offers the opportunity to develop compact on-chip frequency combs for frequency metrology or spectroscopy.

Frequency combs and platicons in optical microresonators with normal GVD.

We predict the existence of a novel type of the flat-top dissipative solitonic pulses, "platicons", in microresonators with normal group velocity dispersion (GVD). We propose methods to generate these platicons from cw pump. Their duration may be altered significantly by tuning the pump frequency. The transformation of a discrete energy spectrum of dark solitons of the Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is demonstrated. Generation of similar structures is also possible with bi-harmonic, phase/amplitude modulated pump or via laser injection locking.

Modeling the whispering gallery microresonator-based optical modulator.

We present a theoretical analysis and numerical simulations of an electro-optic double resonant modulator based on interaction of fundamental whispering gallery modes with a radio frequency field in a dielectric microdisk made from electro-optical material. Models of the modulator in two dimensions and three dimensions are developed and compared. Both optical and RF fields are simulated using the finite element method. The magnitude of the effect in such a system may be maximized with an optimum configuration of a microstrip resonator used for radio-frequency coupling.

Mode spectrum and temporal soliton formation in optical microresonators.

The formation of temporal dissipative solitons in optical microresonators enables compact, high-repetition rate sources of ultrashort pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the microresonator mode spectrum on temporal soliton formation in a crystalline MgF2 microresonator. While an overall anomalous group velocity dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Avoided mode crossings induced by linear mode coupling in the resonator mode spectrum are found to prevent soliton formation when affecting resonator modes close to the pump laser frequency. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations. The presented results provide for the first time design criteria for the generation of temporal solitons in optical microresonators.

Octave spanning tunable frequency comb from a microresonator.

We report the generation of an octave-spanning optical frequency comb in a continuous wave laser pumped microresonator. The generated comb spectrum covers the wavelength range from 990 to 2170 nm without relying on additional external broadening. Continuous tunability of the generated frequency comb over more than an entire free spectral range is demonstrated. Moreover, the linewidth of individual optical comb components and its relation to the pump laser phase noise is studied. The ability to derive octave-spanning spectra from microresonator comb generators represents a key step towards f-2f self-referencing of microresonator-based optical frequency combs.

Determination of the vacuum optomechanical coupling rate using frequency noise calibration.

The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate g0 analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe field and knowledge of the mechanical oscillator's occupation. The method is experimentally verified for a micromechanical mode in a toroidal whispering-gallery-resonator and a nanomechanical oscillator coupled to a toroidal cavity via its near field.

Microtorus: a high-finesse microcavity with whispering-gallery modes.

We demonstrate a 165-mu;m oblate spheroidal microcavity with a free spectral range of 383.7 GHz (3.06 nm), a resonance bandwidth of 23 MHz (quality factor Q approximately 10(7)) at 1550 nm, and finesse F>/=10(4) . The highly oblate spheroidal dielectric microcavity combines a very high Q factor, typical of microspheres, with a vastly reduced number of excited whispering-gallery modes (by 2 orders of magnitude). The very large free spectral range in this novel microcavity-a few hundred gigahertz instead of a few gigahertz as in typical microspheres-is desirable for applications in spectral analysis, narrow-linewidth optical and rf oscillators, and cavity QED.

Ultimate Q of optical microsphere resonators.

We demonstrate the quality factor Q - (0.8 +/- 0.1) x 10(10) of whispering-gallery modes in fused-silica microspheres at 633 nm, close to the ultimate level determined by fundamental material attenuation as measured in optical fibers. The lifetime of ultimate Q is limited by adsorption of atmospheric water. Monitoring of adsorption kinetics with submonolayer sensitivity by Q factors and frequencies of whispering-gallery modes is demonstrated. The possibility of supermaterial Q's owing to intrinsic suppression of scattering losses in micropheres is discussed.