# Nonlinear Waves and Turbulence in Photonics 2022 - Abstract

**Giudici, Massimo**

*Temporal Localized Patterns in VECSELs*

We investigate spatially-extended self-imaging VECSELs in the regime localized mode-locking and we report on the observation of pulsating patterns which can be individually addressed. The characteristics of the patterns depends on the sign of the B and C coefficients of the ABCD round-trip matrix describing the propagation in the external cavity. While B controls the diffraction coefficient, C introduces a quadratic mask phase profile on the near field which may have a focusing (C<0) or defocusing effect (C>0). For C<0 0 the patterns observed consist of a combination of an axial plane-wave with a set of tilted waves having a nearly hexagonal arrangement in the Fourier space. These plane waves are locked in phase and their interference gives birth to a honeycomb profile in near-field. For C>0 the patterns observed consist of a set of counterpropagating tilted waves with opposite transverse wavevectors. These wavevectors share the same modulus and they draw a circle in the far field profile. When the rotational symmetry is broken by some anisotropy in the cavity, only two spots are observed in the far field and a roll pattern appears in the near-field.