Self-defocusing Case Research Articles

Jackiw-Rebbi states in interfaced binary waveguide arrays with Kerr nonlinearity

We systematically investigate the optical analogs of quantum relativistic Jackiw-Rebbi states in binary waveguide arrays in the presence of Kerr nonlinearity with both self-focusing and self-defocusing cases. The localized profiles of these nonlinear Jackiw-Rebbi states can be calculated exactly by using the shooting method. We show that these nonlinear Jackiw-Rebbi states have a very interesting feature which is totally different from all other well-known nonlinear localized structures, including optical solitons. Namely, the profiles of nonlinear JR states with higher peak amplitudes can totally envelope the ones with lower peak amplitudes. We demonstrate that media with the positive nonlinear coefficient can support stable Jackiw-Rebbi states for a wide range of peak amplitudes, whereas media with the negative nonlinear coefficient are only able to support Jackiw-Rebbi states with low peak amplitudes. A general rule for the detuning of nonlinear Jackiw-Rebbi states in binary waveguide arrays is found.

Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m×m matrix nonlinear Schrödinger-type equation which, in the case m=2, has been proposed as a model to describe hyperfine spin F=1 spinor Bose–Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann–Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

Modulational instability in a [formula omitted]-symmetric vector nonlinear Schrödinger system

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier–Floquet–Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet–Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μc for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μc. In the self-defocusing case, solitons exist only when μ < μc. Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.

Surface lattice solitons in diffusive nonlinear media with spatially modulated nonlinearity.

Two families of gap and twisted surface lattice solitons in diffusive nonlinear periodic media with spatially modulated nonlinearity are reported. It is shown that the existence and stability of such solitons are extremely spatially modulated nonlinearity sensitive. For self-focusing nonlinearity, gap surface solitons belonging to the semi-infinite gap are stable in whole existence domain, twisted surface solitons are also linearly stable in low modulated strength region and a very narrow unstable region near the upper cutoff appears in high modulated strength region. In the self-defocusing case, surface gap solitons belonging to the first gap can propagate stably in whole existence domain except for an extremely narrow region close to the Bloch band, twisted solitons belonging to this gap are unstable in the entire existence domain.

P-polarized nonlinear surface polaritons near the surface of an epsilon-near-zero metamaterial with saturable permittivity

We study p-polarized nonlinear surface polaritons (NLSP) propagating along the interface of an epsilon-near-zero metamaterial with saturable nonlinearity, very small negative linear permittivity and an optically linear medium. On the basis of the exact solution of Maxwell's equations, we investigate the relationship between the NLSP propagation constant and the NLSP energy flux for self-focusing and self-defocusing cases. In both cases, for the chosen value of propagation constant, calculations due to Kerr model lead to the lowest NLSP energy flux compared with the energy flux for metamaterial with saturable permittivity.

Switch between the Types of the Symmetry Breaking Bifurcation in Optically Induced Photorefractive Rotational Double-Well Potential

We study the possibility of switching the types of symmetry breaking bifurcation (SBB) in the cylinder shell waveguide with helical double-well potential along propagation direction. This model is described by the one-dimensional nonlinear Schrödinger (NLS) equation. The symmetry- and antisymmetry-breakings can be caused by increasing the applied voltage onto the waveguide in the self-focusing and -defocusing cases, respectively. In the self-focusing case, the type of SBB can be switched from supercritical to subcritical. While in the self-defocusing case, the type of SBB can not be switched because only one type of SBB is found.

Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes

Transverse Anderson localization of light in one-dimensional waveguide arrays with both width and position disorders of individual waveguide has been studied and characterized quantitatively in the viewpoint of transverse localization of eigen modes of the disordered arrays. With the increase in the disorder of the waveguide arrays, more and more eigen modes become localized near the band edges of the finite-sized waveguide arrays in the linear regime. Such a disorder-induced light localization is more effective in waveguide arrays with the width disorder than those with the position disorder. It is shown that, a self-focusing nonlinearity results in an increase of the inverse participation ratio of the nonlinear disordered modes originating from Anderson modes near the edge of the semi-infinite bandgap, therefore, tends to enhance the transverse localization of light. On the other hand, with the increase of the self-defocusing nonlinearity, the inverse participation ratio first increases to a maximum and then decreases for the nonlinear disordered modes originating from Anderson modes near the edge of the first bandgap. The delocalization effect in the self-defocusing case is mainly the result of the joint effects of the normal diffraction near the second band edge and the resonant interaction between the nonlinear disordered modes and the eigen modes in the second band of the waveguide array.

Metallic nonlinear magnetooptical nonreciprocal isolator

In advanced optical fiber communication systems where reflection light might cause degradation of the signal quality, optical waveguide isolators play an important role. The effect of a metal layer with negative permittivity on the behavior of nonlinear-magnetooptic isolator is studied. The isolator consists of metal film, nonlinear cladding, and magnetooptic substrate. It is found that difference between forward and backward propagation for TM 0 mode increases with increasing the absolute value of the tuning parameter which is the permittivity of the metal film, ɛ f . It is also found that the maximum cut-off thickness of the isolator occurs in self-defocusing case around η = 0.65 and at the highest assumed value of ɛ f = −8. These results are helpful in fabricating an isolator with high performance.

Spatial pump-meter quantum correlations in a vectorial Kerr-medium model

We consider a vectorial Kerr-medium model including transverse spatial effects. We analyze cases in which, immediately above the threshold of the spatial instability, the homogeneous pump wave gives rise to two tilted waves corresponding to a stripe pattern in the near field. We analyze both the self-focusing and the selfdefocusing case and we point out the existence of anti-correlations between the quantum fluctuations of the intensity of the pump and the sum of the intensities of the two tilted waves creating the transverse pattern in the near field. We also evaluate the efficiency of this scheme as a quantum nondemolition~QND! scheme which uses the tilted waves as a ‘‘meter’’ to measure the intensity fluctuations of the pump. Our results show the posibility of a QND measurement in the self-defocusing case. In this case, and for a linearly polarized pump, the output pump beam ~uniform in the transverse plane! and the pattern have orthogonal polarization and could be easily separated experimentally. @S1050-2947~99!06402-1#

Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping

Beam shaping processes, such as self-lensing, strongly influence many experiments in nonlinear optics. Concentrating on the self-defocusing case, we present a detailed experimental and theoretical investigation of the lens-like behavior of an atomic vapor optically pumped by a Gaussian laser beam and discuss the validity of a description of the vapor as a thin, “ideal” lens. Through comparison between experimental results and theoretical predictions, we show how the simultaneous presence of “local” effects (saturation) and “nonlocal” effects (atomic and radiation diffusion) contribute to the radial distribution of the index of refraction in the vapor. The separate contributions of atomic and radiation diffusion are experimentally identified by measurements with different buffer gases. A good qualitative agreement between the experimental results and the theoretical predictions is obtained, although hyperfine and propagation effects are neglected.

All-optical Switching in a Nonlinear Resonator

In this paper we consider some features of all-optical switching in a unidirectional ring cavity which is partially filled with a fast and saturably nonlinear medium. A comparative study of cross-talk for both signs of nonlinearity, in a two pixel (whole-beam switching) configuration, is made. A particular interaction modulation is discovered for two beams in the self-defocusing case. For self-focusing media, results are extended by consideration of large (part-beam switched) solitary arrays. Prescribed binary patterns may be stably encoded in a single cavity transit which is in sharp contrast to the hundreds of transits required for spontaneous stabilisation. These patterns are seen to be stable over thousands of transits.

P-polarized nonlinear surface polaritons in materials with intensity-dependent dielectric functions.

We investigate the properties of p-polarized nonlinear surface polaritons (NLSP) propagating along the interfaces of optically nonlinear materials. We show that Maxwell's equations for the NLSP can be solved exactly in quadratures for optically isotropic media with dielectric functions which can be an arbitrary function of the field intensity. The required boundary conditions can be imposed readily, and a form of the dispersion relation for the NLSP is obtained without the need to solve for the field profile first. The general results are then applied to a specific model in which the material has a nonlinear dielectric function proportional to the electric field intensity. Both the self-focusing and self-defocusing cases are studied, as well as different values of the linear dielectric functions inside and outside the material. The physically allowed regions in parameter space and the nonlinear surface-plasmon resonance conditions are examined. The field profile in each region is also investigated.