Accelerating and Airy beams are of great interest in a variety of applications as they remain diffraction free while experiencing a transverse quadratic shift along propagation, transporting intensity in the transverse plane over a straight line and describing an overall parabolic trajectory in space. This work presents optical fields that transport intensity in the transverse plane over a continuum of directions arranged over a semi-circle, creating transverse intensity fluxes with a variety of shapes. We construct these beams via a superposition of a nondiffracting beam with a strong carrier wave that reproduces phase variations of the former field over the resultant intensity distribution, generating profiles with a finite and well defined propagation period. The on-demand light patterns presented here are expected to find diverse applications as Airy beams and nondiffracting beams have previously found.
We present a simplified model for describing the propagation of optical solitons through optical lattices. A pair
of second order differential equations for the transverse coordinates of the intensity centroid of the soliton are
deduced from the nonlinear Schr¨odinger equation. As an advantage over the quasiparticle approach we avoid the
need of integrating algebraically the soliton intensity profile over the lattice. This allows modeling soliton motion
even for non-symmetric lattice potentials, as that presented by an outer ring of a modulated Bessel lattice . We
discuss in detail the range of applicability of our model and use it to predict the soliton motion in optical lattices
generated by plane-waves, Bessel beams, and others.
We introduce and discuss the shaping properties of a novel optical lattice that we call dynamic parabolic optical
lattice (DPOL). While the transverse structure of the DPOL is characterized by a suitable superposition of
parabolic nondiffracting beams with different transverse wave numbers, its longitudinal structure exhibits a
controlled periodic modulation. We address the existence and the controlled stability of two-dimensional solitons
in DPOLs and characterize its propagation. An efficient numerical method for constructing nondiffracting
parabolic beams and DPOLs is presented as well.
We investigate optical solitons propagating through a nondiffracting Bessel photonic lattice. The transverse
intensity pattern of the lattice can be adjusted through a shape parameter, inducing and changing an azimuthal
modulation. We study how this modulation can stabilize transversal motion around a light ring of the lattice
and characterize the different dynamics of motion.
We study the problem of shaping the transverse propagation invariant intensity pattern of an optical beam to
induce a photonic lattice for trapping and propagating spatial optical solitons in a stable elliptic motion with
varying rotation rate. The transverse pattern is described by a suitable superposition of helical Mathieu beams,
the natural family of nondiffracting beams in elliptic cylindrical coordinates. We discuss the properties of the
lattice and the novel dynamics of propagation allowed by it.