Theory of Bloch cavity solitons

Abstract

We present a detailed study of light dynamics in passive nonlinear resonators with shallow intracavity periodic modulation of the refractive index in both longitudinal and transverse directions of the resonator. Specifically, we concentrate on the nonlinear envelopes of dissipative Bloch modes, localized in the transverse plane of the resonator, the so-called Bloch cavity solitons, predicted recently in K. Staliunas et al. [Phys. Rev. Lett. 101, 153903 (2008)]. Bloch cavity solitons, being dissipative structures, are attractors, therefore they can be excited from a wide range of initial conditions (the attractor basin) depending on the system's parameters. A unique property of Bloch cavity solitons is that they are envelopes of waves with tailored diffraction. Using the round-trip model for forward- and backward-propagating waves we reveal different types of Bloch cavity solitons supported by both focusing (at normal diffraction) and defocusing (at anomalous diffraction) nonlinearities. We show also the coexistence of solitons bifurcating from different Bloch wave dispersion branches. In order to analyze the properties of Bloch cavity solitons and to obtain an analytical access we develop a modified mean-field model and prove its validity. In particular, we demonstrate substantial narrowing of Bloch cavity solitons near the zero-diffraction regime.