Control of spatially rotating structures in diffractive Kerr cavities.

Area of Science:

• Nonlinear optics
• Optical cavity dynamics
• Pattern formation

Background:

• Turing patterns are self-organized structures arising from reaction-diffusion systems.
• Nonlinear optical cavities exhibit complex dynamics, including pattern formation.
• Orbital angular momentum (OAM) in light beams offers unique properties for optical manipulation.

Purpose of the Study:

• To investigate the rotation dynamics of Turing patterns in nonlinear optical cavities.
• To explore the influence of orbital angular momentum (OAM) on pattern rotation.
• To demonstrate control over pattern angular velocity using different light beam configurations.

Main Methods:

• Theoretical modeling of Turing patterns in 1D and 2D optical cavity models.
• Simulation of systems pumped by Laguerre-Gaussian, top-hat, cylindrical vector beams, and Poincaré beams with varying OAM.
• Analysis of pattern angular velocity (ω) as a function of OAM (m) and ring radius (R).

Main Results:

• Turing patterns rotate with an angular velocity ω = 2m/R² on rings of radius R.
• Full control over rotation speed, from -2m/R² to 2m/R², achieved using cylindrical vector beams.
• Poincaré beams with differing OAM result in tunable angular velocities (ω = (mL + mR)/R²).
• Concentric, counter-rotating Turing patterns observed with low mode overlap, creating an 'optical peppermill'.

Conclusions:

• Orbital angular momentum dictates the rotation of Turing patterns in nonlinear optical cavities.
• Precise control over pattern rotation is achievable through tailored light beam properties.
• Potential applications include particle manipulation, atom trapping, and circular transport of cold atoms and BECs.