arXiv subjects

Pradyoth Shandilya

Publications and source records attributed to Pradyoth Shandilya.

14 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

Quantum Dispersive Waves and Multimode Squeezing in Pure-Kerr Parametrically Driven Cavity Solitons

Parametrically driven cavity solitons (PDCS), unlike single-pumped cavity solitons, are localized optical pulses arising from parametric processes. These cavity solitons, recently discovered in pure-Kerr media, offer great promise for nonlinear dynamics studies and metrology. Here, we present the first multimode quantum description of pure-Kerr PDCS. In the below threshold regime, we verify single- and two-mode squeezing, while above threshold we uncover novel "quantum" dispersive waves - the quantum analog of soliton Cherenkov radiation. Besides revealing these unexplored quantum properties, we show that PDCS generates up to 20 dB of squeezing, only limited by overcoupling and intrinsic losses for experimentally routine parameters. We therefore provide a pathway to observe strong multimode quantum noise reduction in these systems.

quant-ph↗

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↗

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 $\chi^{(3)}$ 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↗

arXiv2025

Toward Chaotic Group Velocity Hopping of an On-Chip Dissipative Kerr Soliton

Chaos enables randomness-based applications, particularly in photonic systems. Integrated optical frequency combs (microcombs) have previously been observed in either chaotic modulation instability or stable, low-noise dissipative Kerr soliton (DKS) regimes. In this work, we demonstrate a new microcomb state where a single DKS exhibits chaotic behavior. By phase modulating the Kerr-induced synchronization (KIS) between a DKS and an externally injected reference laser, we observe chaotic group velocity hopping of the soliton, causing random transitions of the repetition rate. Using a chip-integrated octave-spanning microcomb, we experimentally validate the second-order Adler equation describing KIS, allowing us to predict and demonstrate this chaotic DKS hopping. This work connects nonlinear dynamics with optical soliton physics, providing a deterministic framework for triggering microcomb chaos in the solitonic state.

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↗

arXiv2024

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↗

arXiv2024

All-Optical Azimuthal Trapping of Dissipative Kerr Multi-Solitons for Relative Noise Suppression

Temporal cavity solitons, or dissipative Kerr solitons (DKS) in integrated microresonators, are essential for deployable metrology technologies. Such applications favor the lowest noise state, typically the single-DKS state where one soliton is in the resonator. Other multi-DKS states can also be reached, offering better conversion efficiency and thermal stability, potentially simplifying DKS-based technologies. Yet they exhibit more noise due to relative soliton jitter, and are usually not compatible with targeted applications. We demonstrate that Kerr-induced synchronization, an all-optical trapping technique, can azimuthally pin the multi-DKS state to a common reference field. This method ensures repetition rate noise independent of the number of solitons, making a multi-DKS state indistinguishable from a single-DKS state in that regard, akin to trapped-soliton molecule behavior. Supported by theoretical analysis and experimental demonstration in an integrated microresonator, this approach provides metrological capacity regardless of the number of cavity solitons, benefiting numerous DKS-based metrology applications.

physics.optics↗

arXiv2024

All-Optical Noise Quenching of An Integrated Frequency Comb

Integrated frequency combs promise transformation of lab-based metrology into disruptive real-world applications. These microcombs are, however, sensitive to stochastic thermal fluctuations of the integrated cavity refractive index, with its impact becoming more significant as the cavity size becomes smaller. This tradeoff between microcomb noise performance and footprint stands as a prominent obstacle to realizing applications beyond a controlled lab environment. Here, we demonstrate that small footprint and low noise become compatible through the all-optical Kerr-induced synchronization (KIS) method. Our study unveils that the phase-locking nature of the synchronization between the cavity soliton and the injected reference pump laser enables the microcomb to no longer be limited by internal noise sources. Instead, the microcomb noise is mostly limited by external sources, namely, the frequency noise of the two pumps that doubly pin the microcomb. First, we theoretically and experimentally show that the individual comb tooth linewidths of an octave-spanning microcomb remain within the same order-of-magnitude as the pump lasers, contrary to the single-pumped case that exhibits a more than two order-of-magnitude increase from the pump to the comb edge. Second, we theoretically show that intrinsic noise sources such as thermorefractive noise in KIS are quenched at the cavity decay rate, greatly decreasing its impact. Experimentally, we show that even with free-running lasers, the KIS microcomb can exhibit better repetition rate noise performance than the predicted thermorefractive noise limitation in absence of KIS.

physics.optics↗

arXiv2024

Versatile Optical Frequency Division with Kerr-induced Synchronization at Tunable Microcomb Synthetic Dispersive Waves

Kerr-induced synchronization (KIS) provides a new key tool for the control and stabilization of the repetition rate of a cavity soliton frequency comb. It enables direct external control of a given comb tooth of a dissipative Kerr soliton (DKS) thanks to its capture by an injected reference laser. Efficient KIS requires its coupling energy to be sufficiently large, and hence both the comb tooth and intracavity reference power must be optimized, which can be achieved through higher-order dispersion that enables phase-matched dispersive waves (DWs), where comb teeth are on resonance. However, such a design is highly restrictive, preventing arbitrary use of reference wavelengths away from the DW(s). In particular, for large spectral separations from the main pump the cavity dispersion yields large detuning between comb teeth and their respective cavity resonances, thereby decreasing the coupling energy and rendering KIS to be highly inefficient or practically impossible. Here, we demonstrate an alternative KIS method where efficient synchronization can be tailored at arbitrary modes as needed. Using a multi-color DKS created from multi-pumping a microresonator, a synthetic DW at the second-color wavepacket can be selectively created where otherwise dispersion is far too large for KIS to be experimentally feasible. Since a unique group velocity for both colors exists thanks to cross-phase modulation, the repetition rate disciplining of the secondary color wavepacket through its KIS automatically translates into the DKS microcomb control. We first investigate this color-KIS phenomenon theoretically, and then experimentally demonstrate its control and tuning of the soliton microcomb repetition rate. As a consequence, we demonstrate optical frequency division that is uncoupled from the main pump that generates the DKS.

physics.optics↗

arXiv2024

AC-Josephson Effect and Sub-Comb Mode-Locking in a Kerr-Induced Synchronized Cavity Soliton

Kerr-induced synchronization (KIS) [1] involves the capture of a dissipative Kerr soliton (DKS) microcomb [2] tooth by a reference laser injected into the DKS resonator. This phase-locking behavior is described by an Adler equation whose analogous form describes numerous other physical systems [3], such as Josephson junctions [4]. We present an AC version of KIS whose behavior is similar to microwave-driven Josephson junctions, where periodic synchronization occurs as so-called Shapiro steps. We demonstrate consistent results in the AC-KIS dynamics predicted by the Adler model, Lugiato-Lefever equation, and experimental data from a chip-integrated microresonator system. The (integer) Shapiro steps in KIS can simply be explained as the sideband created through the reference laser phase modulation triggering the synchronization. Notably, our optical system allows for easy tuning of the Adler damping parameter, enabling the further observation of fractional-Shapiro steps, where the synchronization happens at a fraction of the driving microwave frequency. Here, we show that the comb tooth is indirectly captured thanks to a four-wave mixing Bragg-scattering process, leading to sub-comb mode-locking, and we demonstrate this experimentally through noise considerations. Our work opens the door to the study of synchronization phenomena in the context of microresonator frequency combs, synthesis of condensed-matter state analogues with DKSs, and the use of the fractional Shapiro steps for flexible and tunable access to the KIS regime.

physics.optics↗

arXiv2023

Two-Dimensional Nonlinear Mixing Between a Dissipative Kerr Soliton and Continuous Waves for a Higher-Dimension Frequency Comb

Dissipative Kerr solitons (DKSs) intrinsically exhibit two degrees of freedom through their group and phase rotation velocity. Periodic extraction of the DKS into a waveguide produces a pulse train and yields the resulting optical frequency comb's repetition rate and carrier-envelope offset, respectively. Here, we demonstrate that it is possible to create a system with a single repetition rate but two different phase velocities by employing dual driving forces. By recasting these phase velocities into frequencies, we demonstrate, experimentally and theoretically, that they can mix and create new phase-velocity light following any four-wave mixing process, including both degenerately pumped and non-degenerately pumped effects. In particular, we show that a multiple-pumped DKS may generate a two-dimensional frequency comb, where cascaded nonlinear mixing occurs in the phase velocity dimension as well as the conventional mode number dimension, and where the repetition rate in each dimension differs by orders of magnitude.

physics.optics↗