Holographic solitons

Parametric self-trapping in the presence of randomized quasi phase matching

We report on experimental evidence of parametric spatial solitons in a quadratic crystal with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams.

Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit

This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

Counterpropagating spatial solitons in reflection gratings with a longitudinally modulated Kerr nonlinearity

We investigate quasi-Bragg-matched counterpropagating spatial solitons in a reflection grating in the presence of a longitudinally modulated Kerr nonlinearity. The physical interplay of linear reflection and Kerr self-focusing with the modulation in the nonlinearity yields a variety of elaborate self-action mechanisms. We first analytically predict the existence of symmetric soliton pairs supported by a pure Kerr-like effective nonlinearity. We then analytically derive two families of solitons, associated with the linear grating eigenmodes, supported by an effective "incoherent" Kerr-like coupling arising from the exact balance between the modulation in the nonlinearity and the Kerr interaction due to beam interference.

Helmholtz-Manakov solitons

A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.

Transverse and soliton instabilities due to counterpropagation through a reflection grating in Kerr media

Transverse instabilities are shown to accompany counterpropagation of optical beams through reflection gratings in Kerr media. The instability threshold of continuous waves is analytically derived, and it is shown that the presence of the grating broadens and narrows the stability region of plane waves in focusing and defocusing media, respectively. Furthermore, counterpropagating soliton stability is numerically investigated and compared with the transverse modulation instability analysis, revealing an underlying physical link.

Counterpropagating spatial Kerr soliton in reflection gratings

We analytically predict the existence of both spatial bright and dark counterpropagating solitons in a reflection grating in the presence of the Kerr nonlinearity. The basic trapping mechanism consists of a twofold balance where diffraction is compensated by self-focusing and reflection is altered by the nonlinear-induced interferometric grating. We find that, whenever the spectral soliton profile lies within the grating stop band, bright and dark solitons exist only if the mutual phase of the counterpropagating solitons is pi or 0, respectively.

Counterpropagating self-trapped beams in optical photonic lattices

Dynamical properties of counterpropagating (CP) mutually incoherent self-trapped beams in optically induced photonic lattices are investigated numerically. A local model with saturable Kerr-like nonlinearity is adopted for the photorefractive media, and an optically generated two-dimensional fixed photonic lattice introduced in the crystal. Different incident beam structures are considered, such as Gaussians and vortices of different topological charge. We observe spontaneous symmetry breaking of the head-on propagating Gaussian beams as the coupling strength is increased, resulting in the splitup transition of CP components. We see discrete diffraction, leading to the formation of discrete CP vector solitons. In the case of vortices, we find beam filamentation, as well as increased stability of the central vortex ring. A strong pinning of filaments to the lattice sites is noted. The angular momentum of vortices is not conserved, either along the propagation direction or in time, and, unlike the case without lattice, the rotation of filaments is not as readily observed.

Dynamics of counterpropagating multipole vector solitons

Dynamical behavior of counterpropagating (CP) mutually incoherent vector solitons in a 5 x 5 x 23 mm SBN:60Ce photorefractive crystal is investigated. Experimental study is carried out, displaying rich dynamics of three-dimensional CP solitons and higher-order multipole structures, and a theory formulated that is capable of capturing such dynamics. We find that our numerical simulations agree well with the experimental findings for various CP beam structures. Linear stability analysis is also performed, predicting a threshold for the modulational instability of CP beams, and an appropriate control parameter is identified. We attempt at utilizing these results to CP solitons, but find only qualitative agreement with the numerical simulations and experimental findings. However, when broader hyper-Gaussian CP beams are used in simulations, an improved agreement with the theory is obtained.

Spatial Thirring-type solitons via electromagnetically induced transparency

We show that the giant Kerr nonlinearity in the regime of electromagnetically induced transparency in vapor can give rise to the formation of Thirring-type spatial solitons, which are supported solely by cross-phase modulation that couples the two copropagating light beams.

Counterpropagating optical vortices in photorefractive crystals

We present a comprehensive numerical study of (2+1)D counterpropagating incoherent vortices in photorefractive crystals, in both space and time. We consider a local isotropic dynamical model with Kerr-type saturable nonlinearity, and identify the corresponding conserved quantities. We show, both analytically and numerically, that stable beam structures conserve angular momentum, as long as their stability is preserved. As soon as the beams loose stability, owing to radiation or non-elastic collisions, their angular momentum becomes non-conserved. We discover novel types of rotating beam structures that have no counterparts in the copropagating geometry. We consider the counterpropagation of more complex beam arrangements, such as regular arrays of vortices. We follow the transition from a few beam propagation behavior to the transverse pattern formation dynamics.

Holographic solitons in photorefractive dissipative systems

A new kind of holographic soliton is proposed for a photorefractive dissipative system consisting of a biased photorefractive crystal and a strong pump beam with a uniform spatial distribution in both transverse dimensions. The self-trapping beam in the system can evolve into a spatial soliton when it couples coherently with the pump beam by two-wave mixing. Unlike the holographic solitons recently proposed by Cohen et al. [Opt. Lett. 27, 2031 (2002)], the most unique features of the present solitons are that they have a fixed amplitude and width that are determined completely by the system parameters and that their existence conditions are independent of the polarity of the bias field. Numerical simulations show that these solitons are stable relative to small perturbations.

Existence and stability of rigid photovoltaic solitons in an open-circuit amplifying or absorbing photovoltaic medium

A different type of photovoltaic soliton is predicted for open-circuit photovoltaic media with a gain provided by two-wave mixing. Such solitons are a result of a double balance, i.e., loss is balanced by gain and diffraction is balanced by nonlinearity that is due to both, photovoltaic effects and two-wave mixing. Exact bright and dark analytical solutions are obtained under the condition that the signal beam is much weaker than the pump beam. Such solitons have fixed amplitude and width for the fixed values of the system parameters and hence are named rigid photovoltaic solitons. When the pump beam is switched to a background illumination, rigid photovoltaic solitons can become previously observed photovoltaic solitons. Numerical simulations show that rigid photovoltaic solitons are stable against small perturbations.

Spatial optical solitons supported by mutual focusing

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both single- and two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic nonlinear crystals.