Garuda Fujii

Level set based topology optimization for optical cloaks

This letter presents a level set-based topology optimization method that provides discrete cloaking configurations with superior performance. In some cases, the amount of light scattered around the two-dimensional cloaking structures is less than one-tenth that obtained in previous studies. Optimal configurations that express different geometrical characteristics can be obtained by adjusting a regularization parameter. The obtained configurations are free from grayscales, areas of intermediate density between that of dielectric materials or air, and the use of a level set method provides clear structural boundaries. The level set functions are given on grid points and the dielectric boundaries are interpreted as lines on the iso-surface of the level set functions. The finite element method is used for light scattering analyses, computations of the adjoint variable field, and when updating the level set functions.

Study on transition from photonic-crystal laser to random laser.

The dependence of the lasing threshold on the amount of positional disorder in photonic crystal structures is newly studied by means of the finite element method, not of the finite difference time domain method usually used. A two-dimensional model of a photonic crystal consisting of dielectric cylinders arranged on a triangular lattice within a circular region is considered. The cylinders are assumed to be homogeneous and infinitely long. Positional disorder of the cylinders is introduced to the photonic crystals. Optically active medium is introduced to the interspace among the cylinders. The population inversion density of the optically active medium is modeled by the negative imaginary part of dielectric constant. The ratio between radiative power of electromagnetic field without amplification and that with amplification is computed as a function of the frequency and the imaginary part of the dielectric constant, and the threshold of the imaginary part, namely population inversion density for laser action is obtained. These analyses are carried out for various amounts of disorder. The variation of the lasing threshold from photonic-crystal laser to random laser is revealed by systematic computations with numerical method of reliable accuracy for the first time. Moreover, a novel phenomenon, that the lasing threshold have a minimum against the amount of disorder, is found. In order to investigate the properties of the lasing states within the circular system, the distributions of the electric field amplitudes of the states are also calculated.

Topology Optimization for a Dielectric Optical Cloak Based on an Exact Level Set Approach

This paper proposes a topology optimization method for a dielectric optical cloak that provides results that are perfectly free from intermediate materials, based on a level set boundary expression and the Finite Element Method. The finite element mesh is re-generated to fit the iso-surface of the level set function at every iterative step, to remove intermediate materials, so that the obtained optimal structure consists of only two materials, the dielectric material and air. First, the level set-based topology optimization is formulated and a topology optimization algorithm is proposed for the exact level set approach. Next, design requirements for the dielectric optimal cloak device are clarified and an objective functional for the design is formulated. The proposed method is then applied to a simple numerical problem to illustrate its effectiveness.

Finite-element analysis of lasing modes within photonic random media

We investigated several types of random lasing modes against frequency and the excitation of active medium. Random lasing occurring from multiple light scatterings and the interference effect of the scattered light has various complex lasing states in disordered structures, in which light waves are localized in various forms. Modes of random lasing are generally classified into localized, extended and transition modes based on their localization types. Numerical methods are used for analysing such complex phenomena. In this paper, a finite-element method is used to investigate the relationship among lasing modes, frequency and population inversion density of active medium for random lasing. Light amplification defined as the ratio of radiative powers between excited and non-excited states of the active medium is computed by changing both the frequency and the population inversion density of the active medium, which is modelled by the negative imaginary part of relative permittivity. The distributions of random lasing modes is strongly influenced by the lasing frequency. We also found that the localized modes that are strongly confined lasing modes in disordered structures do not appear in the frequency ranges in which mean free paths are approximately equal to the half-wavelength.

Topology-optimized multiple-disk resonators obtained using level set expression incorporating surface effects.

Topology-optimized designs of multiple-disk resonators are presented using level-set expression that incorporates surface effects. Effects from total internal reflection at the surfaces of the dielectric disks are precisely simulated by modeling clearly defined dielectric boundaries during topology optimization. The electric field intensity in optimal resonators increases to more than four and a half times the initial intensity in a resonant state, whereas in some cases the Q factor increases by three and a half times that for the initial state. Wavelength-scale link structures between neighboring disks improve the performance of the multiple-disk resonators.

Numerical study on the structural color of blue birds by a disordered porous photonic crystal model

It has been observationally confirmed that the color of birds, such as kingfisher and red-flanked bluetail, is a structural color owing to the interference of the light within a sponge structure inside a barb. In this study, we consider the air rod photonic crystal to which disorder is introduced into the translation vectors and the radius as a model of the structural color of red-flanked bluetail; the optical property of the model is numerically analyzed and is compared with that of the structural color.

Exploring optimal topology of thermal cloaks by CMA-ES

This paper presents topology optimization for thermal cloaks expressed by level-set functions and explored using the covariance matrix adaptation evolution strategy (CMA-ES). Designed optimal configurations provide superior performances in thermal cloaks for the steady-state thermal conduction and succeed in realizing thermal invisibility, despite the structures being simply composed of iron and aluminum and without inhomogeneities caused by employing metamaterials. To design thermal cloaks, a prescribed objective function is used to evaluate the difference between the temperature field controlled by a thermal cloak and when no thermal insulator is present. The CMA-ES involves searches for optimal sets of level-set functions as design variables that minimize a regularized fitness involving a perimeter constraint. Through topology optimization subject to structural symmetries about four axes, we obtain a concept design of a thermal cloak that functions in an isotropic heat flux.

Topology optimized design of carpet cloaks based on a level set approach

This paper presents topology optimized designs of carpet cloaks made of dielectrics modeled by a level set boundary expression. The objective functional, evaluating the performance of the carpet cloaks, is defined as the integrated intensity of the difference between electric field reflected by the flat plane and that controlled by a carpet cloak covering a bump. The dielectric structures of carpet cloak are designed to minimize the objective functional value and, in some cases, the value reach 0.34% of that when a bare bump exists. Dielectric structures of carpet cloaks are expressed by level set functions given on grid points. The function becomes positive in dielectrics, negative in air and zero on air-dielectric interfaces and express air-dielectric interfaces explicitly.

A study on optical properties of photonic crystals consisting of hollow rods

Photonic crystals have been receiving a lot of attentions in recent years and have been applied to some electromagnetic devices as lasers, filters, etc. We present some new photonic crystal structures which comprise hollow rods being periodically arrayed and forming two dimensional triangular lattices. Firstly, dispersion relations for the solid rods with round, hexagonal, and square cross sections are computed by changing sizes of the rods in order to seek the most suitable rod size producing the widest bandgaps. Next, we compute bandgaps for hollow rod structures to study the effect of the hollow portion of the rods to the bandgaps. We also investigate a dual periodic photonic structure consisting of solid and hollow rods. The band calculations demonstrate that, for solid rod structures, the increase of the rod size causes the drops of bandgap positions. For hollow rod structure and dual periodic structure consisting of solid and hollow rods, the bandgaps in high frequency region are shown to disappear once and appear again on further increase of the hollow portions.

Direct-current electric invisibility through topology optimization

Based on the covariance matrix adaptation evolution strategy (CMA-ES), advanced designs of direct-current (DC) electric cloaks composed of bulk isotropic materials are presented through a topology optimization using a level set method. The designed DC electric cloaks succeed in providing DC electric invisibility of an electrical insulator in DC flow; specifically, an electric potential distribution is found that closely reproduces a distribution when no insulator is present. To produce this invisibility, we minimized the difference between distributions for the DC electric cloak and one without insulating obstacles as the objective function. CMA-ES explores optimal sets of level set functions as design variables that minimize the objective function with a perimeter constraint. In the best case in our simulation, the minimized objective function under cloaking reaches 0.00194% of that in the absence of cloaking. Toward multidirectional DC electric cloaks, a topology optimization subject to four-axial structural symmetries is demonstrated.Based on the covariance matrix adaptation evolution strategy (CMA-ES), advanced designs of direct-current (DC) electric cloaks composed of bulk isotropic materials are presented through a topology optimization using a level set method. The designed DC electric cloaks succeed in providing DC electric invisibility of an electrical insulator in DC flow; specifically, an electric potential distribution is found that closely reproduces a distribution when no insulator is present. To produce this invisibility, we minimized the difference between distributions for the DC electric cloak and one without insulating obstacles as the objective function. CMA-ES explores optimal sets of level set functions as design variables that minimize the objective function with a perimeter constraint. In the best case in our simulation, the minimized objective function under cloaking reaches 0.00194% of that in the absence of cloaking. Toward multidirectional DC electric cloaks, a topology optimization subject to four-axial struc...