Photorefractive Feedback System Research Articles

Self-organization and Fourier selection of optical patterns in a nonlinear photorefractive feedback system

The formation of patterns in two transverse dimensions in photorefractive two-wave mixing with a single feedback mirror is investigated theoretically. We perform numerical simulations of the full (3+1)-dimensional nonlinear model equations, displaying the breakup of the unstable annulus of active modes into hexagonal spots. Analytically we derive amplitude equations of the Landau type for patterns with rhombic- and hexagonal-mode interaction and discuss the stability and coexistence of transverse planforms in the photorefractive feedback system. A strong renormalization for the hexagon amplitude is determined, and its consequences for pattern formation using Landau formalism are discussed. In particular, the stability of regular substructures of a dodecagonal spot arrangement is investigated and square-hexagon competition is predicted. We use an invasive Fourier-filtering technique for the selection of unstable patterns, such as stripes and squares. The longitudinal propagation of the critical and higher-order modes of the self-organized structures and the impact of a Fourier filter on the mode propagation within a nonlinear bulk photorefractive medium is studied in detail.

Multiple-pattern stability in a photorefractive feedback system

We report on the observation of a multiple-pattern stability region in a photorefractive single-feedback system. Whereas hexagonal patterns are predominant for feedback with positive diffraction length we show that a variety of stable non-hexagonal patterns are generated for certain negative diffraction lengths. For the same values of the control parameters square, rectangular, or squeezed hexagonal patterns are found alternating in time. Besides these pure states, we found a number of different mixed-pattern states. We review the linear stability analysis for this system and show that the special shape of the threshold curves in the investigated parameter region gives a first explanation for the occurrence of a multiple-pattern region.

Selecting optical patterns with spatial phase modulation

Optical pattern selection by use of spatial phase modulation is investigated experimentally in a photorefractive feedback system. A feedback mirror with spatially periodic phase modulation is used for selection of different spatial patterns. Local phase modulation is used to create patterns with coexisting spatial symmetries. The experimental results are consistent with numerical simulations based on a model with a cubicly nonlinear medium.

Origin and Control of Dynamics of HexagonalPatterns in a Photorefractive Feedback System

We investigate the origin of dynamics of hexagonal pattern formation in aphotorefractive single feedback system. By introducing an asymmetry, we induced differentcomplex motion behaviours. A visualization method is presented and means to control thedynamics in the case of fixed external parameters are discussed.

Stabilization, manipulation and control of transverse optical patterns in a photorefractive feedback system

We present an experimental realization of an almost non-invasive stabilization and manipulation method of coexisting and unstable states of pattern forming systems. In a photorefractive single feedback system, a control path is used to realize amplitude and phase-sensitive Fourier-plane filtering, utilizing only a few per cent of the system's intensity. By that means, we were able to stabilize desired but not predominantly excited patterns in parameter space regions where several patterns are present as coexisting or underlying solutions. Changing the phase of the control signal allows one to switch between different pattern states.

Pattern dynamics and competition in a photorefractive feedback system

We investigate the temporal dynamics of transverse optical patterns spontaneously formed in a photorefractive single-feedback system with a virtual feedback mirror. The linear stability analysis for the system is reviewed and extended to the region of larger propagation lengths. The stationary patterns obtained experimentally are classified as a function of feedback reflectivity and feedback mirror position. Inserting masks into the feedback path permits pattern selection and control by Fourier filtering. When an asymmetry that is due to noncollinear pump beams is introduced, the otherwise stationary hexagons show several complex but periodic rotationlike motions. Furthermore, the competition of hexagonal and square patterns can be observed by the appropriate choice of feedback mirror position and coupling strength. The origin of this behavior is discussed. The temporal evolution of the patterns is illustrated by a method based on unfolding the angular distribution of the spots in the far field.