We introduce the basic properties of solitons in elliptical photonic lattices induced optically by a superposition of Mathieu beams. Owing to the modulation of the intensity along its elliptical rings, these lattices allow novel dynamics of propagation, being possible, for the first time to our knowledge, to propagate solitons in an elliptic motion with varying rotation rate.
We present an unexplored non-interferometric approach for wavefront measurement of vortex beams based on the transport of intensity equation (TIE). By exploiting the symmetries of vortexes we are able to simplify the TIE to a reduced expression not reported before in the context of phase imaging. This reduced model can be solved to measure the phase profile of vortexes via one-dimensional operations only without the complexities pertaining the regular TIE. We also use the axial symmetry exhibited by the intensity profile of vortexes to build a noise filtering scheme exclusive to circularly symmetric images and thus address electronic noise in digital imaging systems. We present a series of numerical experiments both to clarify how to apply our proposal step by step and to prove its overall functionality.
Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Their unique characteristics have opened the door to applications that range from optical micromanipulation and plasma-channel generation to laser micromachining. Here, we demonstrate, theoretically and experimentally, that accelerating beams can be generated with a variety of arbitrarily chosen transverse shapes. We present a general method to construct such beams in the paraxial and nonparaxial regime and demonstrate experimentally their propagation in the paraxial case. The key ingredient of our method is the use of the spectral representation of the accelerating beams, which offers a unique and compact description of these beams. The on-demand accelerating light patterns described here are likely to give rise to new applications and add versatility to the current ones.
We address the existence and the controlled stability of two-dimensional solitons in modulated Bessel lattices (MBL) induced by a superposition of nondiffracting Bessel beams. We show that variation of the modulation parameter of the lattice and the initial transverse momentum of the soliton significantly modify the behavior of the solitons. We find that, under suitable and well-identified conditions, solitons propagating in the MBL exhibit six regimes of transverse mobility: stationary, oscillatory, rotating, unbounded or escape, transitional, and unstable. These results report propagating solitons that can develop these dynamics of transverse motion.
We present optical fields formed by superposing nondiffracting parabolic beams with distinct longitudinal wave-vector components, generating light profiles that display intensity fluxes following parabolic paths in the transverse plane. Their propagation dynamics vary depending on the physical mechanism originating interference, where the possibilities include constructive and destructive interference between traveling parabolic beams, interference between stationary parabolic modes, and combinations of these. The dark parabolic region exhibited by parabolic beams permits a straightforward superposition of intensity fluxes, allowing formation of a variety of profiles, which can exhibit circular, elliptic, and other symmetries.
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