arXiv subjects

Curtis R. Menyuk

Publications and source records attributed to Curtis R. Menyuk.

At least 19 recordsLinked to original sources

arXiv2026

Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

nlin.PS↗

arXiv2026

Self-aligned optical microcomb emerging between octave separated lasers

Optical frequency combs (OFCs) are frequency rulers essential for precision metrology, next generation navigation, and testing of fundamental physics. Despite intense efforts, chip-integrated OFCs remain laboratory-bound, unable to fulfill their promise of compact and cost-effective deployment. While improvement in fabrication and integration are important, a conceptual limitation has fundamentally stymied progress: on-chip OFC architectures have aimed to miniaturize their table-top counterparts and relied on cascading outward from (i.e., spectrally broadening) a single pump. In integrated platforms, this approach does not readily allow for the generation of strong and low-noise octave-spaced signals that are crucially needed for robust zero-frequency offset detection. Here, we overcome this limitation via an architectural inversion where an optical microcomb forms by filling the spectrum between two octave-separated pump lasers. The two pumps generate a parametrically driven cavity soliton (PDCS) in an integrated $χ^{(3)}$ resonator, which robustly self-aligns to (i.e., synchronizes with) the pump lasers across multiple foundry-fabricated devices and operating configurations. This produces a single octave-spanning comb extending from telecom to visible wavelengths, whose zero-frequency offset is completely defined by the two harmonically-related pump lasers, and can therefore be reliably detected and stabilized. We showcase our platform's capabilities by executing all of the three core tasks of OFC metrology: optical frequency synthesis, low-noise millimeter-wave generation, and integrated optical clock readout, using the same self-aligned microcomb with only its input locks changed.

physics.optics↗

arXiv2026

Universal Bright-Bright Integrated Soliton Molecule via Parametric Binding

Dissipative Kerr solitons (DKSs) have emerged as the preferred solution for on-chip integrated optical frequency comb (OFC) generation in metrology. A multi-pumped DKS enables either all-optical trapping in the Kerr-induced synchronization regime, or a multi-component OFC with \greg{a locked repetition rate yet with constant frequency offsets between the components} in the multi-color DKS regime. The multi-color DKS regime is of particular interest since nonlinear mixing between the DKS and the secondary pumped component generates idler waves at different frequencies that are useful for spectral extension of the DKS comb. Here, we explore multi-color idler generation at frequencies in which the resonator free spectral range matches that at the DKS. We demonstrate theoretically and experimentally that without phase matching, the idler forms a bright pulse fundamentally bound to the bright DKS through parametric interaction, despite occurring in normal dispersion. Our work can enable new applications in metrology and spectroscopy of quantum systems toward visible wavelengths, as the parametric nature of our bright-bright state eliminates dependence on dispersion regime or visible wavelength pumping.

physics.optics↗

arXiv2026

Dissipative Kerr Soliton Self-Balancing from Kerr-Induced Synchronization

Integrated frequency comb sources are a key enabling technology for frequency metrology applications. Their on-chip integration promises to bring metrology capacity outside of the lab, particularly since they can operate at low continuous-wave pump laser power in the dissipative Kerr soliton (DKS) regime. Yet, such small foot-print and low power comes at a cost: higher noise and overall lower comb power. In particular, this translates to highly challenging detection and locking of the carrier-envelope offset, necessary for complete stabilization of the comb. Recently, Kerr-induced synchronization (KIS) of a DKS to a reference laser has been demonstrated as a tool for passive all-optical stabilization of DKS microcombs, with fundamental modification to the DKS and microcomb properties. Here, we demonstrate that the combination of additional power from the reference laser (now part of the DKS) and the KIS phase locking that pins the repetition rate together fundamentally alter the DKS, forcing an energy redistribution to maintain its center of mass. We demonstrate this self-balancing effect theoretically, which in a pure quadratic dispersion resonator leads to reference-dependent recoil. With higher-order dispersion through which the DKS yields phase-matched dispersive waves (DWs), we demonstrate that self-balancing increases the DW radiation, experimentally showing a 22 dB increase of comb teeth at 780 nm in an octave-spanning microcomb for efficient deployable carrier-envelope offset detection.

physics.optics↗

arXiv2025

Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings

We present an easy-to-implement numerical method for analyzing electromagnetic wave propagation in dielectric rings. Our approach employs a finite-difference-based solver in cylindrical coordinates, solving a mixed electric-magnetic field formulation to accurately enforce boundary conditions and compute resonant modes. The method avoids geometric transformations; instead, it directly discretizes the Helmholtz wave equation in cylindrical coordinates and solves the resulting generalized eigenvalue problem. We validate our model against commercial solvers for various structures, including a Si3N4 ring embedded in SiO2, a ring on a thin-film-coated substrate, and a torus, achieving agreement in effective refractive indices within 0.3%. The formulation accurately captures field confinement, curvature effects, and dispersion, enabling precise determination of propagation constants and mode profiles. As an application, we model optical frequency comb generation in a high-Q microresonator, predicting a free spectral range of 99.6 GHz and a loaded quality factor of 1.6 million, corroborated by experimental measurements.

physics.optics↗

arXiv2025

Dynamics of interacting cavity solitons

We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton molecules and crystals. Here we analyze the effective interaction that arises from the coupling of soliton-tail overlap nonlinearity with global soliton variables associated with the breaking of translation symmetry. The interaction is either purely repulsive, or alternates between attraction and repulsion, according to whether the decay of soliton tails is monotone or oscillatory. In the latter case, stable fixed points of the effective dynamical system signify stable soliton molecule configuration, but the exponential weakening of the interaction with increasing inter-soliton separation may prevent the molecule from forming in experimentally accessible time scales. Our theory becomes asymptotically exact in the large-separation limit, and we verify the theoretical calculations using soliton trajectories extracted from direct numerical solutions of the wave equation.

nlin.PS↗

arXiv2025

On-Chip Parametric Synchronization of a Dissipative Kerr Soliton Microcomb

Synchronization of oscillators is ubiquitous in nature. Often, the synchronized oscillators couple directly, yet in some cases synchronization can arise from their parametric interactions. Here, we theoretically predict and experimentally demonstrate the parametric synchronization of a dissipative Kerr soliton frequency comb. We specifically show that the parametric interaction between the soliton and two auxiliary lasers permits the entrainment of the frequency comb repetition rate. Besides representing the first prediction and demonstration of parametric synchronization of soliton frequency combs, our scheme offers significant flexibility for all-optical metrological-scale stabilization of the comb.

physics.optics↗

arXiv2024

Multi-color solitons and frequency combs in microresonators

Multi-color solitons that are parametrically created in dual-pumped microresonators generate interleaved frequency combs that can be used to obtain combs at new frequencies and when synchronized can be used for low-noise microwave generation and potentially as an element in a chip-scale clockwork. Here, we first derive three-wave equations that describe multi-color solitons that appear in microresonators with a nearly quartic dispersion profile. These solitons are characterized by a single angular group velocity and multiple angular phase velocities. We then use these equations to explain the interleaved frequency combs that are observed at the output of the microresonator. Finally, we used these equations to describe the experimentally-observed soliton-OPO effect. In this effect, the pump frequency comb interacts nonlinearly with a signal frequency comb to create an idler frequency comb in a new frequency range, analogous to an optical parametric oscillation (OPO) process. We determine the conditions under which we expect this effect to occur. We anticipate that the three-wave equations and their extensions will be of use in designing new frequency comb systems and determining their stability and noise performance.

physics.optics↗

arXiv2023

Optimal dimensions of cone and pyramid moth-eye structures for $\mathrm{SiO}_{2}$ windows

We computationally investigate the transmission efficiency through moth-eye nanostructures that are fabricated on $\mathrm{SiO}_{2}$ windows in the wavelength range from 0.4 to 2 $\mathrm{μm}$. We investigated both truncated cones and truncated pyramids, and we varied the height, bottom width, and top width of these shapes in order to maximize the transmission efficiency. We found that there is no substantial difference in transmission between truncated cone and pyramid structures. Using the constraints from the current achievable experimental limits, a relatively uniform transmission coefficient of larger than 98.8% can be obtained from 0.4 $\mathrm{μm}$ to 2 $\mathrm{μm}$. These transmission results are only 0.4% in absolute value lower than the transmission of a structure that is not constrained by current experimental limits.

physics.optics↗

arXiv2021

Accurate and Efficient Modeling of the Transverse Mode Instability in High Energy Laser Amplifiers

We study the transverse mode instability (TMI) in the limit where a single higher-order mode (HOM) is present. We demonstrate that when the beat length between the fundamental mode and the HOM is small compared to the length scales on which the pump amplitude and the optical mode amplitudes vary, TMI is a three-wave mixing process in which the two optical modes beat with the phase-matched component of the index of refraction that is induced by the thermal grating. This limit is the usual limit in applications, and in this limit TMI is identified as a stimulated thermal Rayleigh scattering (STRS) process. We demonstrate that a phase-matched model that is based on the three-wave mixing equations can have a large computational advantage over current coupled mode methods that must use longitudinal step sizes that are small compared to the beat length.

physics.optics↗

arXiv2020

Thermal instabilities, frequency comb formation, and temporal oscillations in Kerr microresonators

We analyze the consequences of dissipative heating in driven Kerr microresonators theoretically and numerically, using a thermal Lugiato-Lefever model. We show that thermal sensitivity modifies the stability range of continuous wave in a way that blocks direct access to broadband frequency-comb forming waveforms, and we propose a deterministic access path that bypasses the thermal instability barrier. We describe a novel thermal instability that leads to thermooptical oscillations via a Hopf bifurcation.

physics.optics↗

arXiv2020

Existence Conditions for Phononic Frequency Combs

The mechanical analog of optical frequency combs, phononic frequency combs, has recently been demonstrated in mechanical resonators and has been attributed to coupling between multiple phonon modes. This paper investigates the influence of mode structure on comb generation using a model of two nonlinearly coupled phonon modes. The model predicts that there is only one region within the amplitude-frequency space where combs exist, and this region is a subset of the Arnold tongue that describes a 2:1 autoparametric resonance between the two modes. In addition, the location and shape of the comb region are analytically defined by the resonance frequencies, quality factors, mode coupling strength, and detuning of the driving force frequency from the mechanical resonances, providing clear conditions for comb generation. These results enable comb structure engineering for applications in areas as broad as sensing, communications, and quantum information science.

cond-mat.mes-hall↗

arXiv2019

Mechanisms of Spatiotemporal Mode-Locking

Mode-locking is a process in which different modes of an optical resonator establish, through nonlinear interactions, stable synchronization. This self-organization underlies light sources that enable many modern scientific applications, such as ultrafast and high-field optics and frequency combs. Despite this, mode-locking has almost exclusively referred to self-organization of light in a single dimension - time. Here we present a theoretical approach, attractor dissection, for understanding three-dimensional (3D) spatiotemporal mode-locking (STML). The key idea is to find, for each distinct type of 3D pulse, a specific, minimal reduced model, and thus to identify the important intracavity effects responsible for its formation and stability. An intuition for the results follows from the 'minimum loss principle,' the idea that a laser strives to find the configuration of intracavity light that minimizes loss (maximizes gain extraction). Through this approach, we identify and explain several distinct forms of STML. These novel phases of coherent laser light have no analogues in 1D and are supported by experimental measurements of the three-dimensional field, revealing STML states comprising more than $10^7$ cavity modes. Our results should facilitate the discovery and understanding of new higher-dimensional forms of coherent light which, in turn, may enable new applications.

physics.optics↗

arXiv2019

Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators

Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode circumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instability mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both continuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. This result explains in part why it is difficult to access single solitons deterministically.

nlin.PS↗

arXiv2018

Efficiently Modeling the Noise Performance of Short-Pulse Lasers with a Computational Implementation of Dynamical Methods

Lowering the noise level of short pulse lasers has been a long-standing effort for decades. Modeling the noise performance plays a crucial role in isolating the noise sources and reducing them. Modeling to date has either used analytical or semi-analytical implementation of dynamical methods or Monte Carlo simulations. The former approach is too simplified to accurately assess the noise performance in real laser systems, while the latter approach is too computationally slow to optimize the performance as parameters vary over a wide range. Here, we describe a computational implementation of dynamical methods that allows us to determine the noise performance of a passively modelocked laser within minutes on a desktop computer and is faster than Monte Carlo methods by a factor on the order of 1000. We apply this method to characterize a laser that is locked using a fast saturable absorber---for example, a fiber-based nonlinear polarization rotation---and a laser that is locked using a slow saturable absorber---for example, a semiconductor saturable absorbing mirror.

physics.app-ph↗

arXiv2017

Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator

Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have dispersions of opposite sign in spectral regions that would otherwise be characterized by either positive (normal) or negative (anomalous) dispersion. In this paper, we study, both analytically and computationally, the general properties of nonlinear frequency comb generation at an avoided crossing using the coupled Lugiato-Lefever equation. In particular, we find that bright solitons and broadband frequency combs can be excited when both branches are pumped for a suitable choice of the pump powers and the detuning parameters. A deterministic path for soliton generation is found.

physics.optics↗

arXiv2017

Computational Study of Amplitude-to-Phase Conversion in a Modified Uni-Traveling Carrier (MUTC) Photodetector

We calculate the amplitude-to-phase (AM-to-PM) noise conversion in a modified unitraveling carrier (MUTC) photodetector. We obtained two nulls as measured in the experiments, and we explain their origin. The nulls appear due to the transit time variation when the average photocurrent varies, and the transit time variation is due to the change of electron velocity when the average photocurrent varies. We also show that the AM-to-PM conversion coefficient depends only on the pulse energy and is independent of the pulse duration when the duration is less than 500 fs. When the pulse duration is larger than 500 fs, the nulls of the AM-to-PM conversion coefficient shift to larger average photocurrents. This shift occurs because the increase in that pulse duration leads to a decrease in the peak photocurrent. The AM-to-PM noise conversion coefficient changes as the repetition rate varies. However, the repetition rate does not change the AM-to-PM conversion coefficient as a function of input optical pulse energy. The repetition rate changes the average photocurrent. We propose a design that would in theory improve the performance of the device.

physics.ins-det↗

arXiv2016

Comparison of Models of Fast Saturable Absorption in Passively Modelocked Lasers

Fast saturable absorbers (FSAs) play a critical role in stabilizing many passively modelocked lasers. The most commonly used averaged model to study these lasers is the Haus modelocking equation (HME) that includes a third-order nonlinear FSA. However, it predicts a narrow region of stability that is inconsistent with experiments. To better replicate the laser physics, averaged laser models that include FSAs with higher-than-third-order nonlinearities have been introduced. Here, we compare three common FSA models to each other and to the HME using the recently-developed boundary tracking algorithms. The three FSA models are the cubic-quintic model, the sinusoidal model, and the algebraic model. We find that all three models predict the existence of a stable high-energy solution that is not present in the HME and have a much larger stable operating region. We also find that all three models predict qualitatively similar stability diagrams. We conclude that averaged laser models that include FSAs with higher-than-third-order nonlinearity should be used when studying the stability of passively modelocked lasers.

physics.optics↗