Modeling the optical properties of transparent and absorbing dielectrics by means of symbolic regression.

In this contribution we explore the possibilities and limitations of symbolic regression as an alternative to the approaches currently used to characterize the dispersive behavior of a given material. To this end, we make use of genetic programming to retrieve, from either ellipsometric or spectral data, closed-form expressions that model the optical properties of the materials studied. In a first stage we consider transparent dielectrics for our numerical experiments. Next we increase the complexity of the problem and consider absorbing dielectrics, which not only require the use of complex functions to model their dielectric function, but also imply a supplementary constraint imposed by the verification of the causality principle.

Meta-model-based multi-objective optimization for robust color reproduction using hybrid diffraction gratings.

We propose an efficient and versatile optimization scheme, based on the combination of multi-objective genetic algorithms and neural-networks, to reproduce specific colors through the optimization of the geometrical parameters of metal-dielectric diffraction gratings. To illustrate and assess the performance of this approach, we tailor the chromatic response of a structure composed of three adjacent hybrid V-groove diffraction gratings. To be close to the experimental situation, we include the feasibility constraints imposed by the fabrication process. The strength of our approach lies in the possibility to simultaneously optimize different contradictory objectives, avoiding time-consuming electromagnetic calculations.

Metamodeling of high-contrast-index gratings for color reproduction.

We propose a metamodel-based optimization technique to tailor the chromatic response of high-contrast-index gratings. The algorithm, which couples a population-based metaheuristic with a neural network, is used to retrieve the optimal geometrical parameters of a grating to reproduce a prescribed color. By means of some examples, we assess the possibilities and limitations of our optimization scheme. The numerical evidence found shows that the metamodel approach offers an alternative to traditional metaheuristic techniques that not only provides the best solution for a given geometry and a material but also significantly improves the computing time required for the optimization process.

Optimization of all-dielectric structures for color generation.

In this work, we propose an inversion scheme to tailor the chromatic response of an all-dielectric structure. To this end, we couple, through a previously defined objective functional involving the concept of color difference, a forward solver with an optimization algorithm. The former is based on the differential method, whereas the latter is based on particle swarm optimization. The optimal geometrical parameters of the structure that generates a specific color are obtained through the solution of an approximation problem. We illustrate the performance of our inversion scheme through examples and discuss its limitations and potential applications.

Determination of the spectral-dependent refractive index of a single layer in a natural multilayer system: comparison of different approaches.

By means of heuristic optimization techniques, we estimate the unknown refractive index of one layer of a periodic natural multilayer system from far-field reflectance data. To take into account the dispersive characteristics of the material, we employ two different strategies. The first is based on the retrieval of Lorentz model-related parameters, to describe the unknown dielectric permittivity within a specific spectral range. The second strategy, based on a wavelength-by-wavelength approach, takes into account the reflectance values for each wavelength at a time. Through some examples, we compare the performance of both strategies when they look for the best estimates and analyze the error involved in each case. The applicability of both approaches to the case of noisy reflectance spectra is also explored.

Characterization of the iridescence-causing multilayer structure of the Ceroglossus suturalis beetle using bio-inspired optimization strategies.

We investigate the iridescence exhibited by Ceroglossus suturalis beetles, which mostly live endemically in the southern end of South America. Two differently colored specimens have been studied. We observed and characterized the samples by different microscopy techniques, which revealed a multilayer structure within their cuticle. Using measured reflectance spectra as input data, we applied heuristic optimization techniques to estimate the refractive index values of the constituent materials, to be introduced within the theoretical model. The color of the samples was calculated for different incidence angles, showing that multilayer interference is the mechanism responsible for the observed iridescence.

Retrieval of relevant parameters of natural multilayer systems by means of bio-inspired optimization strategies.

Natural photonic structures exhibit remarkable color effects such as metallic appearance and iridescence. A rigorous study of the electromagnetic response of such complex structures requires to accurately determine some of their relevant optical parameters, such as the refractive indices of the materials involved. In this paper, we apply different heuristic optimization strategies to retrieve the real and imaginary parts of the refractive index of the materials comprising natural multilayer systems. Through some examples, we compare the performances of the inversion methods proposed and show that these kinds of algorithms have a great potential as a tool to investigate natural photonic structures.

Biomechanical characterization of the passive response of the thoracic aorta in chronic hypoxic newborn lambs using an evolutionary strategy.

The present study involves experiments and modelling aimed at characterizing the passive structural mechanical behavior of the chronic hypoxic lamb thoracic aorta, whose gestation, birth and postnatal period were carried at high altitude (3600 masl). To this end, the mechanical response was studied via tensile and pressurization tests. The tensile and pressurization tests measurements were used simultaneously to calibrate the material parameters of the Gasser-Holzapfel-Ogden (GHO) hyperelasctic anisotropic constitutive model through an analytical-numerical optimization procedure solved with an evolutionary strategy that guarantees a stable response of the model. The model and procedure of calibration adequately adjust to the material behavior in a wide deformation range with an appropriate physical description. The results of this study predict the mechanical response of the lamb thoracic aorta under generalized loading states like those that can occur in physiological conditions and/or in systemic arterial hypertension. Finally, the novel use of the evolutionary strategy, together with the set of experiments and tools used in this study, provide a robust alternative to validate biomechanical characterizations.

Application of evolution strategies for the solution of an inverse problem in near-field optics.

We introduce an inversion procedure for the characterization of a nanostructure from near-field intensity data. The method proposed is based on heuristic arguments and makes use of evolution strategies for the solution of the inverse problem as a nonlinear constrained-optimization problem. By means of some examples we illustrate the performance of our inversion method. We also discuss its possibilities and potential applications.

Inverse scattering with a wave-front-matching algorithm.

We propose and study a numerical procedure for the reconstruction of surface profiles from far-field scattering data. The algorithm, based on wave-front-matching principles, is used to reconstruct one-dimensional surface profiles from amplitude scattering data calculated by using rigorous techniques. The study is complemented by the development of a sampling strategy and considerations of the tolerance of the algorithm to noise in the data.