Crystalline germanium high-Q microresonators for mid-IR.

High-quality-factor optical microresonators have become an appealing object for numerous applications. However, the mid-infrared band experiences a lack of applicable materials for nonlinear photonics. Crystalline germanium demonstrates attractive material properties such as high nonlinear refractive index, large transparency window including the mid-IR band, particularly long wave multiphonon absorption limit. Nevertheless, the reported optical losses in germanium microresonators might not allow the potential of the Ge-based devices to be revealed. In this study, we report the fabrication of germanium microresonators with radii of 1.35 and 1.5 mm, exhibiting exceptional quality factors (Q-factors) exceeding 20 million, approaching the absorption-limited values at a wavelength of 2.68 µm. These Q-factors are a hundred times higher than previously reported, to the best of our knowledge. We measured the two-photon absorption coefficient combined with free-carrier absorption leveraging the high-Q of the resonators (obtained ßTPA = (0.71 ± 0.12) · 10-8 m/W at 2.68 µm). This research underscores the potential of whispering gallery mode microresonators as valuable tools for measuring absorption coefficients at different wavelengths, providing a comprehensive analysis of various loss mechanisms. Furthermore, the exceptional Q-factors observed in germanium microresonators open intriguing opportunities for the advancement of germanium-based photonics within the mid-infrared spectral band.

Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator: experimental study.

Self-injection locking of a diode laser to a high-quality-factor microresonator is widely used for frequency stabilization and linewidth narrowing. We constructed several microresonator-based laser sources with measured instantaneous linewidths of 1 Hz and used them for investigation and implementation of the self-injection locking effect. We studied analytically and experimentally the dependence of the stabilization coefficient on tunable parameters such as locking phase and coupling rate. It was shown that precise control of the locking phase allows fine-tuning of the generated frequency from the stabilized laser diode. We also showed that it is possible for such laser sources to realize fast continuous and linear frequency modulation by injection current tuning inside the self-injection locking regime. We conceptually demonstrate coherent frequency-modulated continuous wave LIDAR over a distance of 10 km using such a microresonator-stabilized laser diode in the frequency-chirping regime and measure velocities as low as sub-micrometer per second in the unmodulated case. These results could be of interest to cutting-edge technology applications such as space debris monitoring and long-range object classification, high-resolution spectroscopy, and others.

Platicon stability in hot cavities.

Stability of platicons in hot cavities with normal group velocity dispersion at the interplay of Kerr and thermal nonlinearities was addressed numerically. The stability analysis was performed for different ranges of pump amplitude, thermal nonlinearity coefficient, and thermal relaxation time. It was revealed that for the positive thermal effect (i.e., the directions of the nonlinear and thermal resonance shifts are the same), the high-energy wide platicons are stable, while the negative thermal coefficient provides the stability of narrow platicons.

Multi-frequency self-injection locking of a FSR-tunable multimode laser diode.

This study presents the controllable multi-frequency self-injection locking regimes realization with an original experimental setup composed of a reflective semiconductor optical amplifier, an external feedback mirror, and a high-Q chip-scale Si3N4 ring microresonator. Our findings demonstrate the conditions of multiple modes' simultaneous locking being analogous to Vernier effect. We varied the free spectral range of the external-cavity laser by its length tuning, enabling the robust generations from 1 to 4 self-injection locked narrow lines on demand, that is important for optical telecommunications, and photonic-based microwave and THz sources.

Ultrahigh-Q WGM microspheres from ZBLAN for the mid-IR band.

The advantages of high-quality-factor (high-Q) whispering gallery mode (WGM) microresonators can be applied to develop novel photonic devices for the mid-infrared (mid-IR) range. ZBLAN (glass based on heavy metal fluorides) is one of the most promising materials to be used for this purpose due to low optical losses in the mid-IR. We developed an original, to the best of our knowledge, fabrication method based on melting of commercially available ZBLAN-based optical fiber to produce high-Q ZBLAN microspheres with the diameters of 250 to 350 µm. We effectively excited whispering gallery modes in these microspheres and demonstrated high quality factor both at 1.55 µm and 2.64 µm. Intrinsic quality factor at telecom wavelength was shown to be (5.4 ± 0.4) × 108 which is defined by the material losses in ZBLAN. In the mid-IR at 2.64 µm we demonstrated record quality factor in ZBLAN exceeding 108 which is comparable to the highest values of the Q-factor among all materials in the mid-IR.

Thermally induced generation of platicons in optical microresonators.

We demonstrate a numerically novel mechanism providing generation of the flat-top solitonic pulses, platicons, in optical microresonators at normal group velocity dispersion (GVD) via negative thermal effects. We found that platicon excitation is possible if the ratio of the photon lifetime to the thermal relaxation time is large enough. We show that there are two regimes of the platicon generation depending on the pump amplitude: the smooth one and the oscillatory one. Parameter ranges providing platicon excitation are found and analyzed for different values of the thermal relaxation time, frequency scan rate, and GVD coefficient. Possibility of the turn-key generation regime is also shown.

Numerical study of solitonic pulse generation in the self-injection locking regime at normal and anomalous group velocity dispersion.

We developed an original model describing the process of the frequency comb generation in the self-injection locking regime and performed numerical simulation of this process. Generation of the dissipative Kerr solitons in the self-injection locking regime at anomalous group velocity dispersion was studied numerically. Different regimes of the soliton excitation depending on the locking phase, backscattering parameter and pump power were identified. It was also proposed and confirmed numerically that self-injection locking may provide an easy way for the generation of the frequency combs at normal group velocity dispersion. Generation of platicons was demonstrated and studied in detail. The parameter range providing platicon excitation was found.

Spectral Purification of Microwave Signals with Disciplined Dissipative Kerr Solitons.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb's repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling.

We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core guiding structure with inter-core coupling dispersion (CD). We show that CD profoundly affects properties of the solitons, causing the complete stabilization of the otherwise highly unstable spatiotemporal solitons in Kerr media with focusing nonlinearity. We also find that the presence of CD stimulates the formation of bound states, which, however, are unstable.

Fundamental, multipole, and half-vortex gap solitons in spin-orbit coupled Bose-Einstein condensates.

Using the parity and time reversal symmetries of a two-dimensional spin-orbit coupled Bose-Einstein condensate in a lattice created by the Zeeman field, we identify and find numerically various families of localized solutions, including multipole and half-vortex solitons. The obtained solutions may exist at any direction of the gauge field with respect to the lattice and can be found either in finite gaps (for repulsive interatomic interactions) or in a semi-infinite gap (for attractive interactions). The existence of half-vortices requires higher symmetry (the reflection with respect to the field direction). Stability of these modes makes them feasible for experimental observation.

Red narrow-linewidth lasing and frequency comb from gain-switched self-injection-locked Fabry-Pérot laser diode.

Narrow-linewidth lasers are in extensive demand for numerous cutting-edge applications. Such lasers operating at the visible range are of particular interest. Self-injection locking of a laser diode frequency to a high-Q whispering gallery mode is an effective and universal way to achieve superior laser performance. We demonstrate ultranarrow lasing with less than 10 Hz instantaneous linewidth for 20 [Formula: see text]s averaging time at 638 nm using a Fabry-Pérot laser diode locked to a crystalline MgF[Formula: see text] microresonator. The linewidth measured with a [Formula: see text]-separation line technique that characterizes 10 ms stability is as low as 1.4 kHz. Output power exceeds 80 mW. Demonstrated results are among the best for visible-range lasers in terms of linewidth combined with solid output power. We additionally report the first demonstration of a gain-switched regime for such stabilized Fabry-Pérot laser diode showing a high-contrast visible frequency comb generation. Tunable linespacing from 10 MHz to 3.8 GHz is observed. We demonstrated that the beatnote between the lines has sub-Hz linewidth and experiences spectral purification in the self-injection locking regime. This result might be of special importance for spectroscopy in the visible range.

Solitons supported by spatially inhomogeneous nonlinear losses.

We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate η (in one dimension) faster than |η|. The spatially-inhomogeneous absorption also supports new types of solitons, that do not exist in uniform dissipative media. In particular, single-well absorption profiles give rise to spontaneous symmetry breaking of fundamental solitons in the presence of uniform focusing nonlinearity, while stable dipoles are supported by double-well absorption landscapes. Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity.

Asymmetric solitons and domain walls supported by inhomogeneous defocusing nonlinearity.

We show that an inhomogeneous defocusing nonlinearity that grows toward the periphery in the positive and negative transverse directions at different rates can support strongly asymmetric fundamental and multipole bright solitons, which are stable in wide parameter regions. In the limiting case, when nonlinearity is uniform in one direction, solitons transform into stable domain walls (fronts), with constant or oscillating intensity in the homogeneous region, attached to a tail rapidly decaying in the direction of growing nonlinearity.

Soliton generation by counteracting gain-guiding and self-bending.

We introduce a concept for stable spatial soliton formation, mediated by the competition between self-bending induced by a strongly asymmetric nonlocal nonlinearity and spatially localized gain superimposed on a wide pedestal with linear losses. When acting separately both effects seriously prevent stable localization of light, but under suitable conditions they counteract each other, forming robust soliton states that are attractors for a wide range of material and input light conditions.

Anderson localization in Bragg-guiding arrays with negative defects.

We show that Anderson localization is possible in waveguide arrays with periodically spaced defect waveguides having a lower refractive index. Such localization is mediated by Bragg reflection, and it takes place even if diagonal or off-diagonal disorder affects only defect waveguides. For off-diagonal disorder the localization degree of the intensity distributions monotonically grows with increasing disorder. In contrast, under appropriate conditions, increasing diagonal disorder may result in weaker localization.

Stable bright and vortex solitons in photonic crystal fibers with inhomogeneous defocusing nonlinearity.

We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright solitons and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber. The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear.

Rotating vortex solitons supported by localized gain.

We show that ringlike localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.

Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain.

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.

General quasi-nonspreading linear three-dimensional wave packets.

We introduce a general approach for generation of sets of three-dimensional quasi-nonspreading wave packets propagating in linear media, also referred to as linear light bullets. The spectrum of rigorously nonspreading wave packets in media with anomalous group velocity dispersion is localized on the surface of a sphere, thus drastically restricting the possible wave packet shapes. However, broadening slightly the spectrum affords the generation of a large variety of quasi-nonspreading distributions featuring complex topologies and shapes in space and time that are of interest in different areas, such as biophysics or nanosurgery. Here we discuss the method and show several illustrative examples of its potential.

Dynamics of soliton self-injection locking in optical microresonators.

Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The demonstration of soliton formation via self-injection locking of the pump laser to the microresonator has significantly relaxed the requirement on the external driving lasers. Yet to date, the nonlinear dynamics of this process has not been fully understood. Here, we develop an original theoretical model of the laser self-injection locking to a nonlinear microresonator, i.e., nonlinear self-injection locking, and construct state-of-the-art hybrid integrated soliton microcombs with electronically detectable repetition rate of 30 GHz and 35 GHz, consisting of a DFB laser butt-coupled to a silicon nitride microresonator chip. We reveal that the microresonator's Kerr nonlinearity significantly modifies the laser diode behavior and the locking dynamics, forcing laser emission frequency to be red-detuned. A novel technique to study the soliton formation dynamics as well as the repetition rate evolution in real-time uncover non-trivial features of the soliton self-injection locking, including soliton generation at both directions of the diode current sweep. Our findings provide the guidelines to build electrically driven integrated microcomb devices that employ full control of the rich dynamics of laser self-injection locking, key for future deployment of microcombs for system applications.