Finite-element solution of nonlinear TM waves inmultiple-quantum-well waveguides

Intensity-dependent characteristics for TM-polarized optical waves guided by multiple-quantum-well (MQW) waveguides with arbitrary nonlinear media are numerically analyzed by the finite element method. In this approach, self-consistent solutions are obtained through a simple iterative procedure. The power-dependent dispersion relations and magnetic-field (H_x) as well as two electric-field ( E_y and E_z) profiles for nonlinear TM waves in MQW waveguides with three different nonlinear mechanisms are presented. It is shown that, for the waveguides with molecular orientational mechanism, a distinct power limiting action for nonlinear TM modes exists     

Nonlinear slab-guided waves in non-Kerr-like media

Guided waves with unique, power-dependent properties arise when one or more of the media bounding a guiding film exhibits an intensity-dependent refractive index. Previous theoretical work on this problem has been based formalism-limited to Kerr-type nonlinear media in which the change in refractive index is quadratic in the optical field. In this paper, a formalism recently reported by Langbein et al. is used to investigate nonlinear guided wave solutions in more realistic material systems. It is shown numerically that saturation of the optically induced change in the refractive index can dramatically alter, and in some cases eliminate, the more interesting power-dependent features of the solutions. Nonlinear wave solutions are also investigated for a larger class of media characterized by refractive indexes which depend on the optical field raised to some arbitrary power.     

Finite-element analysis of topographic waveguides for acoustic surface waves using approximate analytical solutions

An efficient finite-element program utilising approximate analytical solutions is described for the analysis of topographic waveguides for acoustic surface waves. The results obtained agree well with the earlier theoretical and experimental results.     

General formalism for the study of nonlinear pulse propagation in optical fibres

A general formalism for the study of nonlinear pulse propagation in optical fibres is presented. It is then applied to study the time evolution of a Gaussian laser pulse in a fibre with cubic and fifth-order nonlinearity in the index of refraction. The results are presented and discussed.     

Measurements on nonlinear space-charge waves

Results of measurements on the nonlinear ac currents in a velocity modulated confined electron beam are reported. The test vehicle is a two cavity klystron type device with an axially movable demodulator. The ac beam currents at the fundamental and at the two lowest harmonic frequencies have been measured as functions of the distance along the beam for various modulation levels and dc beam currents. The work provides experimental data in the transition range between linear space-charge wave-type and ballistic-type behavior of the ac beam current. The experimental results are in good agreement with the nonlinear space-charge wave theory.     

Maxwell Garnett formalism for weakly nonlinear,bianisotropic, dilute,particulate composite media

The homogenization of a composite medium formed by randomly dispersing electrically small, weakly nonlinear, bianisotropic, ellipsoidal inclusions in a linear bianisotropic host medium is considered. The effective constitutive properties of the homogenized composite medium (HCM) are estimated using the Maxwell Garnett formalism. The linear and nonlinear properties of the HCM are estimated separately because the nonlinearity of the inclusions is weak and the composite medium is dilute. Whereas previously available results were confined to simple dielectric media and spherical inclusions, the reach of the presented formalism is vast and can be significant for numerous technological applications.     

Finite-element analysis for fused couplers

By using the finite-element method we show that the polarisation beam splitting property of realistic fused optical couplers is well modelled by an elliptical cross-section, but differs substantially from a rectangular cross-section.     

Optically nonlinear waves in thin films

A new treatment of the behavior of TE nonlinear waves in an optically nonlinear film is given. The new mathematical results are expressed in terms of the physical parameters of the system and represent a straightforward way to introduce the necessary Jacobian elliptic functions. The optical nonlinearity is of the Kerr type and the numerical calculations are performed for a self-focusing medium. Dispersion curves labeled with optical power density at the lower film boundary, detailed plots of the variation of electric field amplitude as the wave number changes, and details of the power distribution across the guide are given. Since two values of a wave number can exist for the same power level and power thresholds exist, the system is of device interest in the area of optical switching.     

Finite-element method for waveguide problems

A numerical method is presented from which it is possible to calculate the propagation coefficients of waveguides with arbitrary boundaries and dielectric fillings.     

Spinor formalism for waveguides

The authors first prove that there exists a close relationship between the spinor fields and the electromagnetic transverse fields TE, TM.Then the spinor formalism is applied to the waveguide theory and explicit formulae are given for waveguides with rectangular or circular cross section. An interesting feature of the spinor formalism is to require only two components.     

Optically nonlinear s-polarized waves in dielectric superlattices

We study theoretically the s-polarized electromagnetic waves in two-component superlattices, in which one component has a Kerr-type nonlinear dielectric constant. Numerical results are obtained for the effective refractive index (and hence the dispersion relation) of these modes as a function of an effective nonlinear coefficient and the geometric parameters of the structure. Attention is focused on determining both edges of the nonlinear wave subbands, which are shown to form a rich spectrum in these periodic structures. A more than double-valued relation between the effective refractive index and the electric field intensity is obtained in some cases, contrasting with the situation in structures having a single nonlinear layer. This property offers a potential application to non resonant multi stable devices     

Shock waves in a nonlinear delay line

The shock-wave behaviour of a nonlinear `square-root? delay line, assumed lossless, is investigated. Analytical expressions are obtained for shock-wave formation and propagation velocity. It is shown that in this line shock waves, in addition to continuous waves, do not suffer reflections. A number of experimental results are given.     

TM-polarized nonlinear guided waves in multilayer systems

The ability of various multilayer systems to support TM-polarized nonlinear guided waves is studied. A flexible numerical technique which includes the proper consideration of the nonlinear crossing conditions is used to calculate the field profiles and derive the dispersion relations. The fundamentals of the model are described, and the algorithm is applied to several nonlinear film configurations. For the sake of comparison with the finite-element method, a single linear film, embedded between two nonlinear materials, is treated. A three-film unit cell, consisting of a high-index linear film, sandwiched between two low-index nonlinear, ones is considered. This is the elementary unit cell of a composite geometry, a ten-unit-cell superlattice, which is then studied. It is found that unlike TE-polarized nonlinear guided waves in multilayer systems, the TM waves reveal a distinct power maximum. The inclusion of saturation effects in the analysis is straightforward     

Light waves mixing in nonlinear anisotropic media

A recent method for the solution of problems at the boundary of nonlinear electromagnetic media is extended to the anisotropic case for the purpose of studying the mixing between two strong electromagnetic waves in crystals. The general solution for the wave at the beat frequency is first derived for an unbounded medium on the hypothesis of weak harmonic generation. The boundary conditions at the plane surface of a nonlinear dielectric are then considered and the polarization characteristics of the fundamental waves are examined with the aim of obtaining a more efficient mixing.     

Instability regions of nonlinear planar guided waves

The authors use the method described by N.N. Akhmediev et al. (1988) to investigate the stability of modes of general asymmetric planar guides with linear cores. Regions of instability in terms of the V waveguide parameter are calculated for some particular modes which might prove useful for practical purposes. The authors briefly summarize the analysis method. The stability results are discussed together with comments on the efficiency of the analytic method and some possible device implications     

Guided waves in nonlinear saturable self-focusing thin films

Novel features of nonlinear guided waves in saturable thin-film waveguides are obtained. It is shown that the presence of saturation can strongly modify the behavior of TE waves in comparison to films having a Kerr-like nonlinearity. The fundamental mode index is seen to become bounded by limits determined by the saturation level. The example of symmetric waveguide is analyzed and the dispersion plots of symmetric and asymmetric solutions are obtained. It is shown that only the symmetric solution can be followed at high film interface intensity and that the asymmetric solution becomes absent at low saturation levels.     

Some problems of asymptotic theory of nonlinear waves

Asymptotic methods developed recently in the nonlinear wave theory and applicable to the analysis of nonsinusoidal processes are discussed. These methods are based on the assumption of sufficiently slow space-time modulation of wave parameters (shortwave approximation). The intention of this paper is neither to review all problems of asymptotic wave theory nor to give a complete bibliography. Its purpose is to show the main ideas of the methods and to present concrete procedures for the construction of the approximate solutions that correspond to the "nonlinear geometrical optics" for various types of waves. A brief classification of these processes is also given in this paper. The following questions are considered: a) the asymptotic method for quasi-stationary waves; b) a modification of this method describing slowly varying aperiodic waves (shocks and solitary waves); c) the derivation of "averaged variational principle" and its generalization for dissipative systems; d) the method of reduction of a system of equations close to the linear hyperbolic ones which is valid for nonstationary waves propagating along the characteristics; and e) the concrete problem of cylindrical finite-amplitude electromagnetic wave propagation in isotropic dielectrics.     

Finite-element coupling matrices

Finite-element coupling matrices are given for hybrid-mode problems in waveguide structures. The matrices refer to Nth-order polynomial expansions of the field, where N = 1, 2, 3, 4 and are antisymmetric and independent of the shape of the element triangle.     

Evaluation of loss factor of multilayered inhomogeneous waveguidesfor magnetostatic waves using efficient finite element formalism

An efficient finite-element solution procedure is developed for calculating propagation losses of magnetostatic waves in multilayered inhomogeneous waveguides. The final matrix equation is reduced to a standard complex eigenvalue problem whose eigenvalue corresponds to the complex phase constant itself. Thus, iteration procedures are not necessary and the phase and attenuation constants can be directly obtained by solving a standard eigenvalue equation. The validity of the method is confirmed by calculating propagation losses of magnetostatic surface waves in a single yttrium-iron-garnet (YIG)-film structure. Numerical results for a triple-layered YIG film structure are also presented. It is found that, in the triple-layered structure, propagation losses are highly dependent on the linewidth of the film in which the magnetostatic potential is well confined