This paper analytically formulates both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform. The two-dimensional morphological Haar wavelet transform has been proposed as a nonlinear wavelet transform. It has been anticipated for application to nonlinear transform coding. To utilize a transformation to transform coding, both the optimal quantization noise allocation ratio and the coding gain of the transformation should be derived beforehand regardless of whether the transformation is linear or nonlinear. The derivation is crucial for progress of nonlinear transform image coding with nonlinear wavelet because the two-dimensional morphological Haar wavelet is the most basic nonlinear wavelet. We derive both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform by introducing appropriate approximations to handle the cumbersome nonlinear operator included in the transformation. Numerical experiments confirmed the validity of formulations.

It is found that the supercontinuum spectrum is generated from cross-phase modulated soliton pulses which are propagated through a dispersion-flattened/decreasing fiber with low birefringence. The cross-phase modulation is achieved by exciting two orthogonally polarized modes in a birefringent fiber and the effect of input azimuth of linearly polarized pulses is discussed theoretically and numerically.

This paper proposes an optical power limiter composed of serially connected two tapered velocity couplers consisting partly of nonlinear material. The method of device designing is explained and it is exemplified that the optical output can be regulated stably to a prescribed value over a wide range of optical input. The device performance is simulated by means of FD-BPM algorithm.

Optical logic gates for OR, AND, NOT, and NOR operations in waveguides consisting of nonlinear material are numerically investigated by means of FD-BPM (Finite Difference Beam Propagation Method). The proposed devices are designed utilizing the self-routing characteristics of nonlinear X-crossing structures when they are operated with one input beam or two. The numerical simulations show that the proposed structures can favorably be applied to optical data processing and computing as fundamental logic gates.

A three-dimensional beam propagation method based on a finite element scheme is described for the analysis of second harmonic generation devices. For the wide-angle beam propagation analysis, the Pade approximation is applied to the differential operator along the propagation direction. In order to avoid spurious reflection from the computational windows edges, the transparent boundary condition is introduced. Numerical results are shown for quasi-phase matched second harmonic generation devices using periodically domain-inverted LiNbO3 and LiTaO3 waveguides. The influences of the shape of domain-inverted regions and the inversion width on the conversion efficiencies are investigated in detail.

In this paper, the stress wave propagation in a coupled pendulum system with friction force is discussed experimentally and numerically. The coupled system is analogous to the one dimensional fault dynamics model in seismicity. However, we will not intend to discuss about the geophysical feature of the system. The system has rich characteristics of the spatio-temporal stress wave propagation effected by nonlinear friction force. The relation between the wave propagation and the vibration of the pendulum is mainly discussed on the standpoint of nonlinear coupled system.

We examine crossing waveguides with three channels consisting of nonlinear material by means of FD-BPM (Finite Difference Beam Propagation Method). Specifically, we investigate how the insertion of a multimode waveguide into the crossing section of both 13 and 23 structures influences the switching characteristics of output power. We then confirm that these structures can be favorably applied to a wide variety of all-optical devices for integrated optics such as intensity-dependent optical switches, optical power distributors and so on.

We investigate a three-waveguide tapered velocity coupler which consists of a uniform linear, tapered linear and tapered nonlinear slab waveguide. The coupling characteristics depending on the gap width between the waveguides and sloping angle of the tapered waveguides are analyzed by means of the finite difference method. The numerical results show that with realistic structural parameters flat output power characteristics can be obtained over a wide range of input power. It is found that it is possible to use the present structure as a power limiter.

A beam adaptive frame for finite-element beam-propagation analysis is proposed. The width of the frame can be adapted itself to either the guiding structure or the propagating beam in optical circuits, so the size of the computational window can be reduced.

The propagation characteristics of nonlinear TE waves guided by planar optical waveguide whose guiding region has arbitrary inhomogeneous refractive-index profile are investigated theoretically by using the WKB method. The effects of inhomogeneous index profile of a guided region on the propagation characteristics such as the propagation constant and the field distribution are estimated numerically.