Nonlinear Planar Waveguides Research Articles

Power-Dependent Coupling Characteristics of a Butt Joint between a Single-Mode Planar Waveguide and a Nonlinear Planar Waveguide with Different Film Thickness

An efficient coupling scheme between single-mode planar waveguides with different film thickness is proposed. The configuration consists of a tapered waveguide with nonlinear cladding. Power-dependent coupling efficiency of the configuration is analyzed by the beam propagation method. The numerical results show that this configuration has high coupling efficiency and is less sensitive to the offset between coupled waveguides when the input power is properly selected.

Amplification of nonlinear waves in a symmetric planar waveguide.

The gain process of modes of a nonlinear symmetric planar waveguide is investigated. It is shown using numerical simulations that the gain process is adiabatic at low values of gain factor and that the wave envelope changes slowly, remaining close to the shape of the stable nonlinear mode. The representative point of the wave on the plane (energy integral, propagation constant) moves continuously along the stable branches of dispersion curves. When the representative point achieves the region of instability, the spatial solitons are split off from the guided mode. This process is repeated periodically due to the gain. We considered a number of typical cases of guided-wave propagation with symmetric as well as asymmetric initial conditions.

Simple model for spatial optical solitons in planar waveguides

We use a variational method to develop a simple model for the steady-state behavior of self-trapped beams that have recently been observed in nonlinear planar waveguides. The model allows us to study the transition from two-dimensional to three-dimensional self-trapping as power levels increase and also to investigate the effect of saturation on these beams.

Computations of the diffraction effect and the nonlinear effect on spatial solitons in nonlinear planar waveguides

The nonlinear effect and the diffraction effect on a spatial soliton are isolated by rewriting the nonlinear Schrödinger equation into a form of the linear Schrödinger equation with a nonlinear potential. Numerical results on these effects are obtained for a fundamental spatial soliton, a second-order spatial soliton, and two coupled solitons in a parallel-plate waveguide. The effects of waveguide loss are also included.

Externally controlled TE-TM mode coupling in nonlinear planar waveguides

The coupling of a TE-polarized weak waveguide mode with a TM-polarized one by means of two strong orthogonally polarized bulk waves falling from outside on a nonlinear thin film is discussed. In dependence on the parameters of the external bulk waves (intensities, phase difference, incident angles) the state of polarization of the guided fields can be externally controlled.

Emission of spatial solitons from nonlinear waveguides

One of the unique features of nonlinear planar waveguides is that spatial solitons can be emitted into a self-focussing cladding medium. In this paper we discuss this phenomenon for a variety of models for the nonlinear medium, and show that soliton emission persists even when nonideal media are employed. We discuss the conditions for the emission and trapping of such solitons.

Nonlinear all-optical beam scanner

An all-optical integrated optics beam-scanning device is analyzed. It consists of a surface relief grating used to couple both a control and a signal beam into and out of a nonlinear planar waveguide, respectively. Varying the control beam power tunes the signal beam out-coupling angle. Both local and diffusive nonlinearities are considered, and various design parameters are discussed. The theoretical results are compared to experimental data from ZnS waveguides for the thermal diffusive case.

Stripe nonlinear waves in a symmetrical planar structure

A three-dimensional stationary problem of the bound modes in a symmetrical planar nonlinear waveguide is considered. Modes limited in two directions, and propagation in the third direction (“stripe” modes)are obtained for saturable selffocusing films bounded by linear media in “antiwaveguiding” and “waveguiding” geometry.

TM waves guided by nonlinear planar waveguides

A numerical method is given for calculating the dispersion relations and field distributions of stationary, nonlinear transverse magnetic (TM) waves guided by optical planar waveguides with intensity-dependent permittivities. The method can treat arbitrary linear permittivity profiles and arbitrary types of the nonlinearity, since it is based on a numerical integration of the nonlinear wave equation. Numerical results for TM waves guided by symmetric nonlinear film with linear claddings and the three-layer waveguide with a nonlinear cover are presented for different mechanisms of the nonlinearity and compared with those for transverse electric (TE) waves. The treated waveguide is weakly guiding and the nonlinearity is of the Kerr type. It is shown that under these assumptions, the dispersion relations for TM waves are similar to those for TE waves except for the power levels required for operation. The behavior of TM waves is little affected by the nonlinear mechanism. These features can be derived from the fact that the longitudinal electric-field component is fairly small compared with the transverse component. >

A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide

A simple matrix approach, which involves multiplication of 2*2 transfer matrices, is developed to study the propagation characteristics of a nonlinear planar waveguide. Numerical results for some nonlinear structures are presented and compared with the exact and previously published numerical results. It is shown that results obtained by the present approach are very accurate. In addition, the present method can be applied to arbitrary refractive index profiles with arbitrary nonlinear dependence. >

Stable self-trapping of laser beams: Observation in a nonlinear planar waveguide

Stable self-trapping is demonstrated of laser beams inside a nonlinear planar waveguide, due to the dependence of the refractive index on the optical power density. The spatial distortions of the observed self-trapped beams look like first and higher orders soliton beam propagations.

Computer analysis of general nonlinear planar waveguides

We present a numerical method for analyzing stationary nonlinear TE waves guided by general planar waveguides consisting of optical Kerr media. The nonlinear wave equation is directly solved by using a numerical integration. The numerical results for dispersion relations of several nonlinear waveguides with linear step and gaussian permittivity profiles have been presented and the comparison among them has been made. The numerical results for dispersion relations of non-Kerr-like nonlinear waveguides have also been presented. This method is a powerful and versatile approach which can treat arbitrary linear permittivity profiles, arbitrary nonlinearities, and TM wave solutions.

Saturation of guided wave index with power in nonlinear planar waveguides

Coupled mode theory is used to derive analytical formulae for the variation in the guided wave effective index with power in nonlinear media exhibiting saturation.

Spatial hysteresis and switching waves in a nonlinear planar waveguide

An experimental investigation was made of the transformation of the intensity profile of a spatially confined light beam reflected from a nonlinear planar waveguide. It was found that when the system exhibited optical bistability, a hysteresis of the intensity profile was observed and it was due to the formation and propagation of a switching wave in the waveguide layer. A hysteresis was also observed when a switching wave crossed the unilluminated part of the waveguide layer.

Instability of standing waves in nonlinear optical waveguides

A new mathematical instability technique is presented and applied to determine the stability properties of a physically important class of standing waves in nonlinear planar optical waveguides. The method is illustrated by a case where soliton perturbation techniques or variational methods are inapplicable.