This paper shows structural optimal design of optical waveguide components utilizing an efficient 3D frequency-domain and 2D time-domain beam propagation method (BPM) with an alternating direction implicit (ADI) scheme. Usual optimal design procedure is based on iteration of numerical simulation, and total computational cost of the optimal design mainly depends on the efficiency of numerical analysis method. Since the system matrices are tridiagonal in the ADI-based BPM, efficient analysis and optimal design are available. Shape and topology optimal design shown in this paper is based on optimization of density distribution and sensitivity analysis to the density parameters. Computational methods of the sensitivity are shown in the case of using the 3D semi-vectorial and 2D time-domain BPM based on ADI scheme. The validity of this design approach is shown by design of optical waveguide components: mode converters, and a polarization beam splitter.

We propose a new design approach to improve the computational efficiency of an optimal design of optical waveguide devices utilizing coupled mode theory (CMT) and a neural network (NN). Recently, the NN has begun to be used for efficient optimal design of optical devices. In this paper, the eigenmode analysis required in the CMT is skipped by using the NN, and optimization with an evolutionary algorithm can be efficiently carried out. To verify usefulness of our approach, optimal design examples of a wavelength insensitive 3dB coupler, a 1 : 2 power splitter, and a wavelength demultiplexer are shown and their transmission properties obtained by the CMT with the NN (NN-CMT) are verified by comparing with those calculated by a finite element beam propagation method (FE-BPM).

The process of designing analogue circuits is formulated as a controlled dynamic system. For analysis of such system's properties it is suggested to use the concept of Lyapunov's function for a dynamic system. Various forms of Lyapunov's function are suggested. Analyzing the behavior of Lyapunov's function and its first derivative allowed us to determine significant correlation between this function's properties and processor time used to design the circuit. Numerical results prove the possibility of forecasting the behavior of various designing strategies and processor time based on the properties of Lyapunov's function for the process of designing the circuit.

Various trajectories of design, arising from the new methodology of analog network design, are analyzed. Several major criteria suggested for optimal selection of initial approximation to the design process permit the minimization of computer time. The initial approximation point is selected with regard to the previously revealed effect of acceleration of the design process. The concept of separatrix is defined making it possible to determine the optimal position of the initial approximation. The numerical results obtained for passive and active networks prove the possibility of optimal choice of the initial point in design process.

A novel digital redesign methodology based on evolutionary programming (EP) is introduced to find the 'best' digital controller for optimal tracking design of hybrid uncertain multi-input/ multi-output (MIMO) input-delay systems with constraints on states and controls. To deal with these multivariable concurrent specifications and system restrictions, instead of conventional interval methods, the proposed global optimization scheme is able to practically implement optimal digital controller for constrained uncertain hybrid systems with input time delay. Further, an illustrative example is included to demonstrate the efficiency of the proposed method.

This paper provides a review on the optimal design of photonic bandgap structures by inverse problem techniques. An overview of inverse problems techniques is given, with a special focus on topology design methods. A review of first applications of inverse problems techniques to photonic bandgap structures and waveguides is given, as well as some model problems, which provide a deeper insight into the structure of the optimal design problems.

This paper presents the design consideration of a polarization-transformation transmission filter, which is composed of a multilayered chiral slab. The optimal material parameters and thickness of each layer of the slab can be determined by using a genetic algorithm (GA). Substituting the constitutive relations for a chiral medium into Maxwell's equations, the electromagnetic field in the medium is obtained. A chain-matrix formulation is used to derive the relationship between the components of the incident, the reflected, and the transmitted electric fields. The cross- and co-polarized powers carried by the transmitted and reflected waves are represented in terms of their electric field components. The procedure proposed for the design of a polarization-transformation filter is divided into two stages. An ordinary filter without polarization-transformation and a polarization-transformation filter for the transmitted wave are designed with a multilayered non-chiral slab and a multilayered chiral slab at the first and the second stages, respectively. According to the specifications of the filters, two functionals are defined with the transmitted and reflected powers. Thus the optimal design of a polarization-transformation filter with the multilayered chiral slab is reduced to an optimization problem where the material parameters and thickness of each chiral layer are found by maximizing the functionals. Applying the GA to the maximization of the functionals, one can obtain the optimal material parameters and thicknesses of the multilayered chiral slab. Numerical results are presented to confirm the effectiveness of the two-stage design procedure. For three types of multilayered chiral slabs, optimal values of refractive indices, thicknesses, and chiral admittances are obtained. It is seen from the numerical results that the proposed procedure is very effective in the optimal design of polarization-transformation filters for the transmitted wave.