Cui Xudong

Efficient procedures for the optimization of defects in photonic crystal structures.

Seven different stochastic binary optimizers--based on the concepts of genetic algorithms and evolutionary strategies--are developed, applied to determine defect locations in several photonic crystal structures that serve as test cases, and compared by extensive statistical analysis. In addition to the stochastic optimizers, a quasi-deterministic optimizer based on an algorithm inspired by hill-climbing algorithms was implemented. The test cases include the prominent 90 degrees photonic crystal waveguide bend and a photonic crystal power divider. The analysis of the results shows that many different photonic crystal structures with high transmission may be found for any operating frequency. All of the eight optimizers outperform standard codes-because they maintain an incomplete fitness table-and find the global optima with a high probability even when the number of fitness evaluations is much smaller than the number of potential solutions contained in the discrete search space. Based on the incomplete fitness table, an algorithm to estimate bit-fitness values is presented. The bit-fitness values are then used to improve the performance of some algorithms. The four best algorithms-an extended microgenetic algorithm, two mutation-based algorithms, and the quasi-deterministic algorithm inspired by hill-climbing algorithms-are considered to be of high value for the optimization of defects in photonic crystals and for similar binary optimization problems.

Model-based parameter estimation (MBPE) for metallic photonic crystal filters

An efficient method for the accurate computation of the response of photonic crystal filters is obtained when model-based parameter estimation (MBPE) is combined with accurate field solvers. In this paper, MBPE is combined with MMP and MAS and the results are compared with results obtained from a commercial field solver. When metals are present in photonic crystal filters, strong material dispersion at optical frequencies causes nonlinearity of the filter response. It is demonstrated that MBPE is still useful although it is originally designed for linear systems.

Design of ultra-compact metallo-dielectric photonic crystal filters

Filter characteristics of metallo-dielectric photonic crystal slabs are analyzed using the Multiple Multipole Program combined with the Model-Based Parameter Estimation technique. This approach takes losses and material dispersion into account and provides highly accurate results at short computation time. Starting from this analysis, different ultra-compact band pass filters for telecommunication wavelengths are designed. The filters consist of five silver wires embedded in a waveguide structure. By applying stochastic and deterministic techniques the filter structures are optimized to obtain the desired characteristics.

Sharp trench waveguide bends in dual mode operation with ultra-small photonic crystals for suppressing radiation

A sharp 90 degree bend in a dual mode trench waveguide is analyzed by means of the MMP method. Through evolutionary strategy optimization, different configurations with low reflection, low radiation, low mode conversion, and therefore high transmission for the dominant mode are obtained. Three different types of bends are analyzed and compared: mirror-based structures, resonator-based structures, and structures with a small photonic crystal in the bend area. The local photonic crystal helps not only suppressing radiation but also provides solutions with fewer fabrication tolerance problems.

Model-based parameter estimation (MBPE) for solving non-linear eigenvalue problems

The model-based parameter estimation (MBPE) for the computation of the band structure of photonic crystals (PhCs) is presented. The analysis of the band structure of a periodic structure is a very useful starting point for the PhCs design. PhCs made with metallic wires that have strong dispersion properties in the optical range are currently intensively studied. The calculation of band diagrams of such structures requires the efficient solution of non-linear eigenvalue problems. In this paper, MBPE is combined with two semi-analytic field solvers working in the frequency domain, the multiple multipole program (MMP) and the method of auxiliary sources (MAS). From this combination, two efficient and highly accurate numerical methods for the band structure calculation of PhCs are obtained

Parameters extraction from inhomogeneous metamaterials with model based parameter estimation

Numerical extraction of effective material parameters of metamaterials is limited by data noise that may be caused by inaccurate field solvers as well as by inaccurate measurements. In some areas, the extraction formulas strongly amplify the noise, which results in useless results. This paper demonstrates that these noise-related problems may be overcome when the model based parameter estimation technique is used for fitting the frequency dependence of S parameters

Resolution of negative-index slabs

Different definitions of the resolution of negative-index-material (NIM) slabs and classical optical lenses with magnification 1 are presented and evaluated for both cases. Several numerical codes--based on domain and boundary discretizations and working in the time and frequency domains--are applied and compared. It is shown that superresolution depends very much on the definition of resolution and that it may be obtained not only for NIM slabs but also for highly refracting classical lenses when the distances of the image and source points from the surface of the lens or slab are shorter than the wavelength.

Efficient field solvers for the analysis of photonic crystal filters

An efficient method for the accurate conputation of the response of photonic crystal filters is obtained from a combination of the Model-Based Parameter Estimation (MBPE) technique with accurate field solvers such as the Multiple Multipole Program (MMP) or the Method of Auxiliary Sources (MAS). When metals are present in such filters, strong material dispersion at optical frequencies causes nonlinearity of the filter respose. It is demonstrated that the technique remains accurate when the frequency range is subdivided into pieces with moderate dispersion. Excellent agreement of MMP-MBPE and MAS-MBPE with a commercial time domain solver is demonstrated

Surface impedance boundary conditions for the simulation of metallic photonic crystals

The surface impedance boundary conditions (SIBC) approximation is applied to the analysis of metallic photonic crystals. It is demonstrated that this approximation is highly valuable and sufficiently accurate even at optical frequencies where metals cannot be characterized by a high conductivity. As a simple test case, the band diagrams of a metallic photonic crystal consisting of circular silver wires are computed with the SIBC and with the perfect electric conductor (PEC) approximations and compared with a highly accurate multiple multipole (MMP) solution.

Metallic photonic crystal filters design with MMP methods

An ultra-compact metallic photonic crystal filter for telecommunication wavelength is designed using the multiple multipole program combined with the model-based parameter estimation technique. Material loss is taken into account and measured data is employed to make this design more realistic. Finally, deterministic optimization techniques are applied for obtaining the desired filter characteristics.