Soliton Crystal Research Articles

Soliton crystals in optical Kerr microresonators in the presence of thermo-optic effects

The influence of thermo-optic effects on shape profiles of soliton crystals in optical Kerr microresonators is investigated. The study rests on a model that consists of the Lugiato–Lefever equation, coupled to the one-dimensional heat diffusion equation with a source term proportional to the average power of the optical field. Using appropriate variable changes the model equations are transformed into a set of coupled first-order nonlinear ordinary differential equations. These equations are solved numerically with emphasis on the influence of thermo-optic effects on the amplitude and instantaneous frequency of the optical field, as well as on the temperature profile in the microresonator cavity. It is found that thermo-optic effects do not prevent soliton crystals from forming in optical Kerr microresonators, however, a strong thermal detuning will decrease the soliton-crystal amplitude. The model predicts a temperature profile in the microresonator cavity which is insensitive to the specific spatio-temporal profile of the soliton crystal propagating in the microresonator, a feature peculiar to the model.

Dual-mode microresonators as straightforward access to octave-spanning dissipative Kerr solitons

The Kerr soliton frequency comb is a revolutionary compact ruler of coherent light that allows applications from precision metrology to quantum information technology. The universal, reliable, and low-cost soliton microcomb source is key to these applications. As a development and extension of the direct creation of a soliton microcomb with the dual-mode scheme in an aluminum nitride microresonator, this paper thoroughly presents the design strategy to reliably attain such dual-modes in the silicon nitride (Si3N4) platform, separated by ∼10 GHz, which stabilizes soliton formation without using additional auxiliary laser or RF components. We demonstrate the deterministic generation of the refined single-solitons that span 1.5-octaves, i.e., near 200 THz, via adiabatic pump wavelength tuning. The ultra-wide soliton existence range up to 17 GHz not only suggests the robustness of the system but will also extend the applications of soliton combs. Moreover, the proposed scheme is found to easily give rise to multi-solitons as well as the soliton crystals featuring enhanced repetition rate (2 and 3 THz) and conversion efficiency greater than 10%. We also show the effective thermal tuning of mode separation to increase the possibility to access the single-soliton state. Our results are crucial for the chip-scale self-referenced frequency combs with a simplified configuration.

Thermal tuning of mode crossing and the perfect soliton crystal in a Si3N4 microresonator.

Dissipative Kerr solitons in high quality microresonators have attracted much attention in the past few years. They provide ideal platforms for a number of applications. Here, we fabricate the Si3N4 microring resonator with anomalous dispersion for the generation of single soliton and soliton crystal. Based on the strong thermal effect in the high-Q microresonator, the location and strength of the avoided mode crossing in the device can be changed by the intracavity power. Because the existence of the avoided mode crossing can induce the perfect soliton crystal with specific soliton number, we could choose the appropriate pumped resonance mode and appropriate pump power to obtain the perfect soliton crystals on demand.

Deterministic generation of a perfect soliton crystal microcomb with a saturable absorber.

We numerically investigate the deterministic generation of a perfect soliton crystal (PSC) in an optical microresonator functionalized with a saturable absorber (SA). The SA allows the direct formation of a PSC from an initial, periodic Turing roll. It prevents passage through a chaotic state, which induces a stochastic nature with regard to the number of generated dissipative Kerr solitons. We show that PSCs form deterministically, and the number is controlled by adjusting the input power and SA parameter. Our work provides a simple approach for obtaining a stable PSC that offers an ultrahigh repetition rate and a high comb output power.

Mode crossing induced soliton frequency comb generation in high-Q yttria-stabilized zirconia crystalline optical microresonators

We demonstrate for the first time, to the best of our knowledge, the fabrication of high- Q crystalline optical microresonators from cubic yttria-stabilized zirconia (YSZ). Intrinsic Q factors up to 80 million are obtained, indicating an upper bound absorption coefficient of 0.001 cm − 1 for YSZ crystals at the telecom wavelength. Through laser-scanned spectroscopy on a few-mode YSZ microresonator with a radius of 300 μm, we find that the mode crossing effect in the case of weak coupling can induce a repelling disruption of free spectral range values between transverse mode families. Generation of soliton and soliton crystals in such a YSZ microcomb platform operated in the normal dispersion regime is observed. A breathing comb behavior is also reported. Our finding has enriched comb generation platforms with potential multidisciplinary capabilities linked to properties of YSZ crystals in superconducting films and sensors.

All-Optical Manipulation of Elastic Soliton Crystals in a Mode-Locked Fiber Laser

All-Optical Manipulation of Elastic Soliton Crystals in a Mode-Locked Fiber Laser

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator.

Temporal solitons have attracted great interest in the past decades for their behavior in a steady state, where the dispersion is balanced by the nonlinearity in a propagation Kerr medium. The development of dissipative Kerr solitons (DKSs) in high-Q microcavities drives a novel, compact, chip-scale soliton source. When DKSs serve as femtosecond pulses, the repetition rate fluctuation can be applied to ultrahigh precision metrology, high-speed optical sampling, and optical clocks, etc. In this paper, the rapid repetition rate fluctuation of soliton crystals (SCs), a special state of DKSs where particle-like solitons are tightly packed and fully occupy a resonator, is measured based on the well-known delayed self-heterodyne method. The SCs are generated using a thermal-controlled method. The pump is a frequency fixed laser with a linewidth of 100 Hz. The integral time in frequency fluctuation measurements is controlled by the length of the delay fiber. For a SC with a single vacancy, the repetition rate fluctuations are ~53.24 Hz within 10 µs and ~509.32 Hz within 125 µs, respectively.

Switching dynamics of dissipative cnoidal waves in dual-coupled microresonators

Dual-coupled structure is typically used to actively change the local dispersion of microresonator through controllable avoided mode crossings (AMXs). In this paper, we investigate the switchability of dissipative cnoidal waves (DCWs) based on dual-coupled microresonators. The switching dynamics of DCWs are numerically simulated using two sets of nonlinear coupled-mode equations. It is found that the pulse number of DCWs can only be decreased (i.e. switched unidirectionally) when working as perfect soliton crystals and can either be decreased or increased (i.e. switched bidirectionally) when working as Turing rolls. Moreover, the stable regions of DCWs can be greatly expanded due to the existence of AMXs. The switchability of DCWs would further liberate the application potential of microcombs in a wide range of fields, including frequency metrology, optical communications, and signal-processing systems.

Defect-engineered ring laser harmonic frequency combs

A monochromatic wave that circulates in a nonlinear and dispersive optical cavity can become unstable and form a structured waveform. This phenomenon, known as modulation instability, was encountered in fiber lasers, optically pumped Kerr microresonators and, most recently, in monolithic ring quantum cascade lasers (QCLs). In ring QCLs, the instability led to generation of fundamental frequency combs—optical fields that repeat themselves once per cavity round trip. Here we show that the same instability may also result in self-starting harmonic frequency combs—waveforms that repeat themselves multiple times per round trip, akin to perfect soliton crystals in ring Kerr microresonators. We can tailor the intermode spacing of harmonic frequency combs by placing two minute defects with a well-defined separation between them along the ring waveguide. On-demand excitation of frequency comb states with few powerful modes spaced by hundreds of gigahertz may find their use in future sub-terahertz generators.

Control of single and multiple phase solitons in a ring cavity.

Phase solitons are localized structures characterized by phase jumps of 2π or multiples arising in forced ring lasers. Here, we show numerically that they can be created by superimposing to the constant driving field a suitable control beam matched in frequency with a different cavity mode for a time of the order of ten cavity round trip times. If the two beams are separated in frequency by n free spectral ranges of the cavity, a train of solitons like a perfect soliton crystal consisting of n equispaced phase solitons is generated. This may represent a simple way to produce frequency combs with flexible frequency spacing and high power per line.

Low-noise Kerr frequency comb generation with low temperature deuterated silicon nitride waveguides.

We report very low-loss deuterated silicon nitride (SiNx:D) micro-ring resonators fabricated by back-end CMOS compatible low-temperature plasma-enhanced chemical vapor deposition (PECVD) without annealing. Strong confinement micro-ring resonators with a quality factor of > 2 million are achieved, corresponding to a propagation loss in the 1460-1610 nm wavelength range of ∼ 0.17 dB/cm. We further report the generation of low-noise coherent Kerr microcomb states including different perfect soliton crystals (PSC) in PECVD SiNx:D micro-ring resonators. These results manifest the promising potential of the back-end CMOS compatible SiNx:D platform for linear and nonlinear photonic circuits that can be co-integrated with electronics.

Perfect Soliton Crystals in the High-Q Microrod Resonator

The coherent temporal soliton in optical microresonators has attracted great attention recently. Here, we have fabricated the microrod resonator with Q factor as high as 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> and demonstrated the dissipative Kerr soliton generation in such a microresonator, by utilizing an auxiliary-laser-assisted thermal response control. In addition, we have changed the pump laser and observed the perfect soliton crystals. With the simulation, we found that the perfect soliton crystals are generated based on the avoided mode crossing, which is affected by the pump resonance and pump power.

Widely stretchable soliton crystals in a passively mode-locked fiber laser.

We present the first direct demonstration of a new type of stable and extremely elastic soliton crystals, the bond length and bond strength of which can be individually controlled in a wide range. The stretching and compressing can be repeated many times, conserving the overall structure by incorporating a highly asymmetric tunable Mach-Zehnder interferometer into a specially designed passively mode-locked fiber laser. The temporal structure and dynamics of the generated soliton crystals were measured using an asynchronous optical sampling system with picosecond resolution. We demonstrated that a stable and robust soliton crystal can be formed by two types of primitive structures: single dissipative solitons and (or) pairs each consisting of a dissipative soliton and a pulse with a lower amplitude. Continuous stretching and compression of the soliton crystal by an extraordinarily high factor of more than 30 has been demonstrated, the smallest recorded separation between the pulses being as low as 5 ps, corresponding to an effective repetition frequency of 200 GHz. Collective pulse dynamics, including soliton crystal cracking and transformation of crystals comprising high/low-amplitude pulse pairs to the crystals of similar pulses, has been observed experimentally.

Near-octave-spanning breathing soliton crystal in an AlN microresonator.

The soliton crystal (SC) was recently discovered as an extraordinary Kerr soliton state with regularly distributed soliton pulses and enhanced comb line power spaced by multiples of the cavity free spectral ranges (FSRs), which will significantly extend the application potential of microcombs in optical clock, signal processing, and terahertz wave systems. However, the reported SC spectra are generally narrow. In this Letter, we demonstrate the generation of a breathing SC in an aluminum nitride (AlN) microresonator (FSR ∼374GHz), featuring a near-octave-spanning (1150-2200 nm) spectral range and a terahertz repetition rate of ∼1.87THz. The measured 60 fs short pulses and low intensity-noise characteristics confirm the high coherence of the breathing SC. Broadband microcombs with various repetition rates of ∼0.75, ∼1.12, and ∼1.5THz were also realized in different microresonators of the same size. The proposed scheme shows a reliable design strategy for broadband soliton generation with versatile dynamic control over the comb line spacing.

Dissipative Kerr solitons in a photonic dimer on both sides of exceptional point

Exceptional points are a ubiquitous concept widely present in driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. To date, exceptional points have been extensively examined in the systems supporting only a few optical modes, thereby leaving the observation of collective (multimode) effects outside of the scope of the study. In the present paper, we analyze the role of exceptional points in nonlinear multimode photonics. Specifically, we provide insights into the complex nonlinear dynamics arising in a continuous wave-driven pair of strongly coupled microresonators. Investigating this system, we demonstrate mechanisms of dissipative Kerr soliton formation in two fundamentally different regimes separated by a line of exceptional points. Highlighting the diversity of emergent nonlinear effects, we describe the on-demand generation of single-solitons, perfect soliton crystals and bright-dark soliton pairs on either side of exceptional points.

Soliton‐mode proliferation induced by cross‐phase modulation of harmonic waves by a dark‐soliton crystal in optical media

AbstractThe generation of high‐intensity optical fields from harmonic‐wave photons, interacting with dark solitons via a cross‐phase modulation coupling, both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time‐entangled dark‐soliton patterns, forming a periodic waveguide along the path of the harmonic‐wave probe. It is shown that an increase of the strength of cross‐phase modulation coupling respective to the self‐phase modulation coupling, favors soliton‐mode proliferation in the bound‐state spectrum of the trapped harmonic‐wave probe. The induced soliton modes, which display structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.

Controlling Microresonator Solitons with the Counter-Propagating Pump

Considering a bidirectionally pumped ring microresonator, we provide a concise derivation of the model equations allowing us to eliminate the repetition rate terms and reduce the nonlinear interaction between the counter-propagating waves to the power-dependent shifts of the resonance frequencies. We present the simulation results of the soliton control by swiping the frequency of the counter-propagating wave in the forward and backward directions and with the soliton-blockade effect either present or not. We highlight the non-reciprocity of the forward and backward scans. Furthermore, we report the soliton crystals and breathers existing in the vicinity of the blockade interval.

Pulse Train Triggered Single Dissipative Kerr Soliton in Microresonator and Application in Terahertz Rate Optical Clock Recovery

Single dissipative Kerr soliton (DKS) formed in microresonator shows few-cycle femtosecond pulses along with smooth and phase-coherent comb spectra that easily reaching an octave spanning. Such unique characteristics lead to revolutionary breakthrough in advanced communications, spectroscopy, metrology, etc. However, as hidden deepest inside the multistable states of driven-damped microresonator, the single DKS state remains challenging to generate deterministically and straightforwardly. Here, we theoretically show that a train of energetic pulse trigger imposed on an external continuous-wave driving pump can quickly kick start the cavity to deterministically evolve into a single DKS state. Neither the pump frequency nor the cavity resonance frequency requires to be scanned, thus possessing the potential for turnkey soliton microcombs generation. The additional degrees of freedom given by the combined pump enables the manipulation of multi-DKS and even perfect soliton crystals generation in the same microresonator. The proposed pulse train triggering method can also be harnessed for ultrahigh speed all-optical clock recovery with a potential rate up to terahertz. Our results open up a new path for manipulating single and multi-DKS in microesonators and a robust optical clock recovery module simultaneously possessing ultrahigh speed, on-chip integration, and cost-efficiency.

Synthesized soliton crystals

Dissipative Kerr soliton (DKS) featuring broadband coherent frequency comb with compact size and low power consumption, provides an unparalleled tool for nonlinear physics investigation and precise measurement applications. However, the complex nonlinear dynamics generally leads to stochastic soliton formation process and makes it highly challenging to manipulate soliton number and temporal distribution in the microcavity. Here, synthesized and reconfigurable soliton crystals (SCs) are demonstrated by constructing a periodic intra-cavity potential field, which allows deterministic SCs synthesis with soliton numbers from 1 to 32 in a monolithic integrated microcavity. The ordered temporal distribution coherently enhanced the soliton crystal comb lines power up to 3 orders of magnitude in comparison to the single-soliton state. The interaction between the traveling potential field and the soliton crystals creates periodic forces on soliton and results in forced soliton oscillation. Our work paves the way to effectively manipulate cavity solitons. The demonstrated synthesized SCs offer reconfigurable temporal and spectral profiles, which provide compelling advantages for practical applications such as photonic radar, satellite communication and radio-frequency filter.

Nonlinear-mode-coupling-induced soliton crystal dynamics in optical microresonators

Dissipative Kerr solitons based on microresonators have wide applications from optical communications to optical ranging for the high-repetition rate and broad bandwidth. Restricted by the bending losses and dispersion control of the optical waveguide, it could be hard to further realize ultrahigh-repetetion rate reaching several terahertz by simply reducing the size of microresonators. Soliton crystals, which completely fill the microresonator with a series of equidistant temporal pulses, can be an effective approach to realize ultrahigh-repetition rate in the common cavity length. In this paper, we investigate the generation of soliton crystals in the presence of nonlinear mode coupling, which can induce a modulation on the background wave and modify the cavity dynamics. Under the condition of suitable wave vector mismatch and nonlinear-coupling-coefficient, high-deterministic perfect soliton crystals can be realized. Besides, the drifting behavior of the soliton crystals is demonstrated to be determined by the match between the wave vector mismatch and nonlinear coupling coefficient. Finally, we successfully observe the recrystallization of the perfect soliton crystals.