Optical patterns with different wavelengths

Nonvariational real Swift-Hohenberg equation for biological, chemical, and optical systems

We derive asymptotically an order parameter equation in the limit where nascent bistability and long-wavelength modulation instabilities coalesce. This equation is a variant of the Swift-Hohenberg equation that generally contains nonvariational terms of the form psinabla(2)psi and /nablapsi/(2). We briefly review some of the properties already derived for this equation and derive it on three examples taken from chemical, biological, and optical contexts. Finally, we derive the equation on a general class of partial differential systems.

Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities

Taking up to fourth-order dispersion effects into account, we show that fiber resonators become stable for a large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for an arbitrary small but nonzero fourth-order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and open the way to experimental implementation.

Modulated optical structures over a modulationally stable medium

Evidence of modulated dissipative structures with an intrinsic wavelength in a nonlinear optical system devoid of Turing instability is given. They are found in the transverse field distribution of an optical cavity containing a liquid crystal light valve. Their existence is related to a transition from flat to modulated fronts connecting the unstable middle branch of a bistability cycle and either of the two stable uniform states. We first analyze the cavity in the limit of nascent bistability, where a modified Swift-Hohenberg equation is derived. This allows for a simple analytical expression of the threshold associated with the transition as well as the wavelength of the emerging structure. Numerical simulations show development of ring-shaped modulated fronts and confirm analytical predictions. We then turn to the full model and find the same transition, both analytically and numerically, proving that this transition in not limited to nascent bistability regimes.

Bouncing localized structures in a liquid-crystal light-valve experiment

Experimental evidence of bouncing localized structures in a nonlinear optical system is reported. Oscillations in the position of the localized states are described by a consistent amplitude equation, which we call the Lifshitz normal form equation, in analogy with phase transitions. Localized structures are shown to arise close to the Lifshtiz point, where nonvariational terms drive the dynamics into complex and oscillatory behaviors.