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William J. Firth

Publications and source records attributed to William J. Firth.

10 recordsLinked to original sources
arXiv2025

Theory and Application of Cavity Solitons in Photonic Devices

Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity dispersion are balanced by the nonlinear interaction with the medium while cavity losses balance the input energy. The history, properties, physical interpretation and wide application of cavity solitons are reviewed. Cavity solitons in the plane perpendicular to light propagation find application in optical information processing, while cavity solitons in the longitudinal direction produce high quality frequency combs with applications in optical communications, frequency standards, optical clocks, future GPS, astronomy and quantum technologies.

physics.optics↗
arXiv2021

Self-Organization in Cold Atoms Mediated by Diffractive Coupling

This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincar{é} sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.

nlin.PS↗
arXiv2021

Analytic instability thresholds in folded Kerr resonators of arbitrary finesse

We present analytic threshold formulae applicable to both dispersive (time-domain) and diffractive (pattern-forming) instabilities in Fabry-Perot Kerr cavities of arbitrary finesse. We do so by extending the gain-circle technique, recently developed for counter-propagating fields in single-mirror-feedback systems, to allow for an input mirror. In time-domain counter-propagating systems walk-off effects are known to suppress cross-phase modulation contributions to dispersive instabilities. Applying the gain-circle approach with appropriately-adjusted cross-phase couplings extends previous results to arbitrary finesse, beyond mean-field approximations, and describes Ikeda instabilities.

nlin.PS↗
arXiv2013

Optomechanical self-structuring in cold atomic gases

The rapidly developing field of optomechanics aims at the combined control of optical and mechanical (solid-state or atomic) modes. In particular, laser cooled atoms have been used to exploit optomechanical coupling for self-organization in a variety of schemes where the accessible length scales are constrained by a combination of pump modes and those associated to a second imposed axis, typically a cavity axis. Here, we consider a system with many spatial degrees of freedom around a single distinguished axis, in which two symmetries - rotations and translations in the plane orthogonal to the pump axis - are spontaneously broken. We observe the simultaneous spatial structuring of the density of a cold atomic cloud and an optical pump beam. The resulting patterns have hexagonal symmetry. The experiment demonstrates the manipulation of matter by opto-mechanical self-assembly with adjustable length scales and can be potentially extended to quantum degenerate gases.

physics.atom-ph↗
arXiv1999

Frequency selection by soliton excitation in nondegenerate intracavity downconversion

We show that soliton excitation in intracavity downconversion naturally selects a strictly defined frequency difference between the signal and idler fields. In particular, this phenomenon implies that if the signal has smaller losses than the idler then its frequency is pulled away from the cavity resonance and the idler frequency is pulled towards the resonance and {\em vice versa}. The frequency selection is shown to be closely linked with the relative energy balance between the idler and signal fields.

physics.optics↗
arXiv1999

Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch the rings break up into filaments which move radially to initial ring. For sufficient negative mismatches rings are found to coalesce with central peak, forming a single oscillating filament.

patt-sol↗
arXiv1999

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.

patt-sol↗
arXiv1999

Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schröedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.

patt-sol↗
arXiv1999

Stability of multi-hump optical solitons

We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the experimental results reported by M. Mitchell, M. Segev, and D. Christodoulides [Phys. Rev. Lett. v. 80, p. 4657 (1998)].

patt-sol↗