William J. Firth

Overview of transverse effects in nonlinear-optical systems

Beams of light interacting with nonlinear-optical materials naturally form complex transverse profiles. Self-focusing, filamentation, modulational instabilities, spontaneous pattern formation and symmetry breaking, nonlinear waveguiding, and transverse mode excitation are but some of the many phenomena that are observed in lasers, in optical bistability, and in the free interaction of beams. As an introduction to a special issue of the Journal of the Optical Society of America B on transverse effects in nonlinear-optical systems, we provide this overview of history and current work.

Spatial Instabilities in a Kerr Medium with Single Feedback Mirror

Abstract This Letter predicts the occurrence of spontaneous spatial patterns and dynamic instabilities in an unusually simple optical system.

Realization of a semiconductor-based cavity soliton laser.

The realization of a cavity soliton laser using a vertical-cavity surface-emitting semiconductor gain structure coupled to an external cavity with a frequency-selective element is reported. All-optical control of bistable solitonic emission states representing small microlasers is demonstrated by injection of an external beam. The control scheme is phase insensitive and hence expected to be robust for all-optical processing applications. The mobility of these structures is also demonstrated.

Pattern formation in a passive Kerr cavity

Analytic and numerical investigations of a cavity containing a Kerr medium are reported. The mean field equation with plane-wave excitation and diffraction is assumed. Stable hexagons are dominant close to threshold for a self-focusing medium. Bistable switching frustrates pattern formation for a self-defocusing medium. Under appropriate parametric conditions that we identify, there is coexistence of a homogeneous stationary solution, of a hexagonal pattern solution and of a large (in principle infinite) number of localized structure solutions which connect the homogeneous and hexagonal state. Further above threshold, the hexagons show defects, and then break up with apparent turbulence. For Gaussian beam excitation, the different symmetry leads to polygon formation for narrow beams, but quasihexagonal structures appear for broader beams.

Transverse modulational instabilities for counterpropagating beams in Kerr media

Continuous-wave and oscillatory transverse instabilities are predicted for counterpropagating waves in Kerr media for both focusing and defocusing nonlinearities. Neither a cavity nor a finite response time is required. Computed Gaussian-beam results agree well with analytic plane-wave calculations that straddle Raman-Nath and Bragg regimes.

Fundamentals and Applications of Spatial Dissipative Solitons in Photonic Devices

We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐localized optical excitations sitting on a uniform, or quasi‐uniform, background in a dissipative environment like a nonlinear optical cavity. Indeed, in optics they are often termed “cavity solitons.” We discuss their dynamics and interactions in both ideal and imperfect systems, making comparison with experiments. SDS in lasers offer important advantages for applications. We review candidate schemes and the tremendous recent progress in semiconductor‐based cavity soliton lasers. We examine SDS in periodic structures, and we show how SDS can be quantitatively related to the locking of fronts. We conclude with an assessment of potential applications of SDS in photonics, arguing that best use of their particular features is made by exploiting their mobility, for example in all‐optical delay lines.

All-optical delay line using semiconductor cavity solitons

An all-optical delay line based on the lateral drift of cavity solitons in semiconductor microresonators is proposed and experimentally demonstrated. The functionalities of the device proposed as well as its performance is analyzed and compared with recent alternative methods based on the decrease of group velocity in the vicinity of resonances. We show that the current limitations can be overcome using broader devices with tailored material responses.

Transverse instabilities due to counterpropagation in Kerr media

Counterpropagation of optical beams in Kerr media is shown to be unstable against transverse modulation. This is true for both focusing and defocusing media. Numerical studies show metastability, hysteresis, symmetry breaking, oscillations, and probable chaos. Transverse effects are likely to lower thresholds for known plane-wave counterpropagation instabilities. Similar effects can be expected in saturable media and lasers.

Two-dimensional clusters of solitary structures in driven optical cavities

Interaction between localized structures in the transverse plane of a passive optical cavity containing a saturable medium is studied analytically and numerically. Stability properties of clusters of localized structures and their spontaneous motion are described.

Dynamical properties of two-dimensional Kerr cavity solitons

We present the results of our study of the dynamics of two-dimensional Kerr cavity solitons. The solitons are absolutely stable over a substantial parameter domain. We analyze their dynamics beyond the instability boundary, finding regions of stable oscillation and of fivefold or sixfold azimuthal instability. The Hopf oscillation is surprisingly robust, owing to the influence of a lower-amplitude unstable soliton.