Transverse oscillation arising from spatial soliton formation in nonlinear optical cavities

Abstract

A new type of transverse instability in dispersively nonlinear optical cavities, called the optical whistle, is discussed. This instability occurs in the mean field, soliton forming limit when the cavity is driven with a finite width Gaussian beam, and gives rise to oscillation, period doubling, and chaos. It is also seen that bistability is strongly affected due to the oscillation within the upper transmission branch. The phenomenon is interpreted as a mode mismatch in the soliton formation process and is believed to have broad applicability.

Dynamics of atom-mediated photon-photon scattering

“…However, as shown in Fig. 16, the narrow resonance associated with R (1) 2 contributes the linear response of the medium. The nonlinear response, which has the same resonance character as the "ladder" process, is not limited in this way because R (3) 2 does not depend upon the output photon energies.…”

“…Recently there has been experimental and theoretical interest in the nonlinear optics of confined light [1]. A medium possessing an optical Kerr nonlinearity and confined within a planar or cylindrical Fabry-Perot resonator gives rise to new nonlinear optical phenomena such as soliton filtering and bilateral symmetry breaking [2,3].…”

Dynamics of frequency conversion of an optical pulse in a microcavity

“…We begin with a Kerr nonlinear microcavity whose transverse length is much greater than its longitudinal length a, and fitted with mirrors to ensure perfect reflection of the longitudinal component of the electromagnetic field within the cavity [2,3,10]. Then the longitudinal component of the wave vector k takes discrete values of which the lowest, and only one of interest to us, is k ʈ0 = / a.…”

“…If x represents the single transverse degree of freedom and t the time, we may assume the slowly varying envelope approximation ͑x , t͒cos k z ze it for the total electric field inside the cavity (we are also assuming that there is no significant dynamics in the ỹ direction). Then one finds that the cavity's internal field envelope obeys the Lugiato-Lefever equation [10,11] *Email address: jcmartin@nie.edu.sg…”

Observation of a nonlinear mode in a cylindrical Fabry–Perot cavity

“…The most important dynamics are in the x-dimension, where the field is determined by the combined effects of self-(de)focusing and diffraction. The field envelope within the cavity, in the mean field limit, evolves according to a damped, driven version of the nonlinear Schrödinger equation [10,11] …”