arXiv subjects

Jonathan M. Silver

Publications and source records attributed to Jonathan M. Silver.

11 recordsLinked to original sources

arXiv2021

Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling

We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can therefore be used as a foundation for describing any phenomenon resulting from any combination of linear coupling, scattering and Kerr nonlinearity, such as bending and surface roughness losses, geometric backscattering, self- and cross-phase modulation, four-wave mixing, third-harmonic generation and Kerr frequency comb generation. The theory is then applied to a translationally symmetric waveguide in order to calculate the evanescent coupling strength to the modes of a microresonator placed nearby, as well as the Kerr self- and cross-phase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetry-breaking dynamics of two counterpropagating modes of a loop resonator and prove that cross-phase modulation is exactly twice as strong as self-phase modulation only in the case that the two counterpropagating modes are otherwise identical.

physics.optics↗

arXiv2021

Kerr-Nonlinearity-Induced Mode-Splitting in Optical Microresonators

The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high-Q microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counter-intuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy scheme that allows us to measure power dependent resonance splittings of up to 35 cavity linewidths (corresponding to 52 MHz) at 10 mW of pump power. The required power to split the resonance by one cavity linewidth is only 286$μ$W. In addition, we demonstrate threefold resonance splitting when taking into account four-wave mixing and two counterpropagating probe lasers. These Kerr splittings are of interest for applications that require two resonances at optically controlled offsets, eg. for opto-mechanical coupling to phonon modes, optical memories, and precisely adjustable spectral filters.

physics.optics↗

arXiv2021

Coherent suppression of backscattering in optical microresonators

As light propagates along a waveguide, a fraction of the field can be reflected by Rayleigh scatterers. In high-quality-factor whispering-gallery-mode microresonators, this intrinsic backscattering is primarily caused by either surface or bulk material imperfections. For several types of microresonator-based experiments and applications, minimal backscattering in the cavity is of critical importance, and thus, the ability to suppress backscattering is essential. We demonstrate that the introduction of an additional scatterer into the near field of a high-quality-factor microresonator can coherently suppress the amount of backscattering in the microresonator by more than 30 dB. The method relies on controlling the scatterer position such that the intrinsic and scatterer-induced backpropagating fields destructively interfere. This technique is useful in microresonator applications where backscattering is currently limiting the performance of devices, such as ring-laser gyroscopes and dual frequency combs, which both suffer from injection locking. Moreover, these findings are of interest for integrated photonic circuits in which back reflections could negatively impact the stability of laser sources or other components.

physics.optics↗

arXiv2020

Logic Gates based on Interaction of Counterpropagating Light in Microresonators

Optical logic has the potential to replace electronics with photonic circuits in applications for which optic-to-electronic conversion is impractical and for integrated all-optical circuits. Nonlinear optics in whispering gallery mode resonators provides low power, scalable methods to achieve optical logic. We demonstrate, for the first time, an all-optical, universal logic gate using counterpropagating light in which all signals have the same operating optical frequency. Such a device would make possible the routing of optical signals without the need for conversion into the electronic domain, thus reducing latency. The operating principle of the device is based on the Kerr interaction between counter-propagating beams in a whispering gallery mode resonator which induces a splitting between the resonance frequencies for the two propagating directions. Our gate uses a fused silica microrod resonator with a \textit{Q}-factor of $\SI{2e8}{}$. This method of optical logic gives a practical solution to the on-chip routing of light.

physics.optics↗

arXiv2020

A Nonlinear Enhanced Microresonator Gyroscope

We demonstrate a novel optical microresonator gyroscope whose responsivity to rotation is enhanced by a factor of around $10^4$ by operating close to the critical point of a spontaneous symmetry breaking transition between counterpropagating light. We present a proof-of-principle rotation measurement using a resonator with a diameter of 3 mm. In addition, we characterise the dynamical response of the system to a sinusoidally varying rotation, and show this to be well described by a simple theoretical model. We observe the universal critical behaviors of responsivity enhancement and critical slowing down, both of which are beneficial in an optical gyroscope.

physics.optics↗

arXiv2019

Critical Dynamics of an Asymmetrically Bidirectionally Pumped Optical Microresonator

An optical ring resonator with third-order, or Kerr, nonlinearity will exhibit symmetry breaking between the two counterpropagating circulating powers when pumped with sufficient power in both the clockwise and counterclockwise directions. This is due to the effects of self- and cross-phase modulation on the resonance frequencies in the two directions. The critical point of this symmetry breaking exhibits universal behaviors including divergent responsivity to external perturbations, critical slowing down, and scaling invariance. Here we derive a model for the critical dynamics of this system, first for a symmetrically-pumped resonator and then for the general case of asymmetric pumping conditions and self- and cross-phase modulation coefficients. This theory not only provides a detailed understanding of the dynamical response of critical-point-enhanced optical gyroscopes and near-field sensors, but is also applicable to nonlinear critical points in a wide range of systems.

physics.optics↗

arXiv2018

Universal Symmetry Breaking Dynamics for the Kerr Interaction of Counter-Propagating Light in Dielectric Ring Resonators

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr-interaction of counter-propagating light in a dielectric ring resonator. In particular, we study discontinuous behaviour in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realise, for example, highly sensitive near-field or rotation sensors. We then generalise to a time-dependent model, which predicts new types of dynamical behaviour, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarisation in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.

physics.optics↗

arXiv2018

Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

Optically induced breaking of symmetries plays an important role in nonlinear photonics, with applications ranging from optical switching in integrated photonic circuits to soliton generation in ring lasers. In this work we study for the first time the interplay of two types of spontaneous symmetry breaking that can occur simultaneously in optical ring resonators. Specifically we investigate a ring resonator (e.g. a fiber loop resonator or whispering gallery microresonator) that is synchronously pumped with short pulses of light. In this system we numerically study the interplay and transition between regimes of temporal symmetry breaking (in which pulses in the resonator either run ahead or behind the seed pulses) and polarization symmetry breaking (in which the resonator spontaneously generates elliptically polarized light out of linearly polarized seed pulses). We find ranges of pump parameters for which each symmetry breaking can be independently observed, but also a regime in which a dynamical interplay takes place. Besides the fundamentally interesting physics of the interplay of different types of symmetry breaking, our work contributes to a better understanding of the nonlinear dynamics of optical ring cavities which are of interest for future applications including all-optical logic gates, synchronously pumped optical frequency comb generation, and resonator-based sensor technologies.

physics.optics↗

arXiv2018

Microresonator Isolators and Circulators Based on the Intrinsic Nonreciprocity of the Kerr Effect

Nonreciprocal light propagation is important in many applications, ranging from optical telecommunications to integrated photonics. A simple way to achieve optical nonreciprocity is to use the nonlinear interaction between counterpropagating light in a Kerr medium. Within a ring resonator, this leads to spontaneous symmetry breaking, with the result that light of a given frequency can circulate in one direction, but not in both directions simultaneously. In this work, we demonstrate that this effect can be used to realize optical isolators and circulators based on a single ultra- high-Q microresonator. We obtain isolation of more than 24 dB and develop a theoretical model for the power scaling of the attainable nonreciprocity.

physics.optics↗

arXiv2017

Kerr Superoscillator Model for Microresonator Frequency Combs

Microresonator-based optical frequency combs, or "microcombs", have attracted lots of attention in the last few years thanks to their promising applications in telecommunications, spectroscopy and optical clocks. The process of comb generation in microresonators can be modelled in the frequency domain using coupled mode equations, and has also recently been successfully described in the time domain using a nonlinear Schrödinger equation known as the Lugiato-Lefever equation. Though time-domain approaches have brought many interesting insights for the understanding of microcombs, an intuitive frequency-domain model has not yet been established. In this work we present a frequency-domain model of microcombs that describes the overall structure of the spectra in terms of a few collective excitations of groups of neighboring comb lines, which we term "superoscillators". This approach ties in nicely with the recently-developed time-domain model based on soliton crystals, and links the microcomb generation process with frequency response theory.

physics.optics↗

arXiv2016

Symmetry Breaking of Counter-Propagating Light in a Nonlinear Resonator

Light is generally expected to travel through isotropic media independent of its direction. This makes it challenging to develop non-reciprocal optical elements like optical diodes or circulators, which currently rely on magneto-optical effects and birefringent materials. Here we present measurements of non-reciprocal transmission and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) light waves to circulate in the resonator. Equivalently, the symmetry breaking can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. This effect is expected to take place in any dielectric ring-resonator and might constitute one of the most fundamental ways to induce optical non-reciprocity. Our findings pave the way for a variety of applications including all optical switching, nonlinear-enhanced rotation sensing, optically controllable circulators and isolators, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.

physics.optics↗