Printed circuit antennas have been used for the detection of electromagnetic radiation at a wide range of frequencies that go from radio frequencies (RF) up to optical frequencies. The design of printed antennas at optical frequencies has been done by using design rules derived from the radio frequency domain which do not take into account the dispersion of material parameters at optical frequencies. This can make traditional RF antenna design not suitable for optical antenna design. This work presents the results of using a genetic algorithm (GA) for obtaining an optimized geometry (unconventional geometries) that may be used as optical regime antennas to capture electromagnetic waves. The radiation patterns and optical properties of the GA generated geometries were compared with the conventional dipole geometry. The characterizations were conducted via finite element method (FEM) computational simulations.
Printed circuit antennas which have been extensively used in the radio frequency (RF) spectrum have also been used to detect electromagnetic radiation at optical and infrared frequencies. The use of these types of antennas at optical frequencies provides several advantages over traditional optical and infrared detectors; among these advantages are low profile, low cost, faster response times, compatibility with integrated circuit technology, and wavelength and polarization selectivity [
Even though several RF antenna designs have been successfully used at optical and infrared frequencies [
Evolutionary algorithms imitate nature, where all living organisms possess specific genetic material which contains information about each organism that can be transferred to new generations via reproduction. The other organism involved in reproduction also transfers some of its characteristics [
These evolutionary processes can be used to optimize the solution of nonanalytical problems assuming that the environment is defined based on known values and characteristics. The evolved individual or the whole evolved population can constitute the potential solution to a given problem [
An adequate mathematical function must be chosen to define the fitness of any given individual representing how well adapted they are to their environment. Exchange of genetic materials and mutations will occur during the genetic crossover process. Thus, an optimal solution will be created that best suits a given environment.
These algorithmic techniques allow the exploration of unconventional geometries or combination of materials that can be used in the design of nanophotonic circuits and devices for diverse applications [
In this work, a genetic algorithm (GA) is used to obtain the geometry that optimally concentrates the electromagnetic field of a dipole-type nanoantenna at a resonance frequency of 500 THz, which can be varied based on the nanostructure dimensions. The nanoantenna radiation pattern was obtained via computational simulations and compared to a classical dipole geometry.
The most basic and general type of genetic algorithm called “Holland Genetic Algorithm” proposed by Henry Holland [
Flow diagram of the genetic algorithm.
Various studies, such as [
(a) Top: reference classical dipole. Bottom: geometry generated by the genetic algorithm. (b) Efficiency comparison between the reference antenna and that generated by the genetic algorithm, taken from [
Figure
The authors assume a specific preestablished antenna area based on the desired resonance frequency. The geometry is then modified using the evolutionary algorithm as a malleable material. No empty regions are added, and a solid shape is sought which achieves a maximum electromagnetic field concentration at the center of the nanostructure.
This algorithm has been successfully applied to multiple problems; the results show that the resulting optimized geometries are different from classical RF antennas [
The genetic algorithm was programmed in MATLAB where a link was made to COMSOL Multiphysics where the electromagnetic simulations were performed and the results were returned to MATLAB where the fitness function was evaluated. Iterative changes or adjustments are then made to optimize the solution, and the new proposed nanostructure is analyzed using COMSOL until a fixed number of iterations was achieved.
The genetic algorithm performs the nanostructure analysis required to suggest a geometry that approaches the optimal design conditions, assuming a (two-dimensional) flat nanostructure. The solution space is constrained to dimensions near the optical wavelength for an antenna irradiated by a normal incident electromagnetic wave. The main parameters required by the genetic algorithm, such as the dimensions of the simulation space (maximum size of the antenna), number of chromosomes (number of individuals to be analyzed), chromosome resolutions (quality), overlap between generations (mortality index), mutation rate (as a percentage), and mating rules, must be input by the user.
Figure
Flow diagram of the application process, noting the links between the COMSOL and MATLAB software packages.
The Bézier curve control points, which are modeled as chromosomes, are used to obtain the optimized geometry of the dipole-type nanoantenna. A total of 10 lines are set, including 4 with two Bézier control points, 4 with only one, and 2 straight lines with no control points. The lines with no control points represent the section where the electromagnetic field is applied to the nanoantenna. The algorithm execution stops if the average loss in the electric field is zero or if the iterative limit is reached, which is based on the number of generations [
The fitness function [
A geometric model with 12 Bézier curve control points, plus 11 fixed points which represent the geometry limits (noting the first point is also the last one to have a closed geometry), is found during the first iteration, based on steady-state initial conditions, 100 chromosomes, a 50% intergeneration overlap, and a 1% mutation rate. In addition, a single crossover point was used, which can occur between any pair of segments in the chromosome with equal probability. Figure
Lines demonstrating the geometry modification process due to mutations when applying the genetic algorithm.
(a) Plot showing the trend toward zero of the electromagnetic field loss after each new population generation. (b) Data trends for a zoomed portion of the main plot.
The geometry obtained at the end of the genetic algorithm execution is shown in Figure
(a) Geometry obtained after the genetic algorithm optimization function application. (b) Finite element method simulation of the nanostructure electromagnetic radiation pattern.
According to the results obtained by [
Many studies use analogies between nanostructure geometries and conventional radiofrequency macroscopic antenna geometries based on the assumption that their behaviors can be extrapolated to optical frequencies as in [
Electromagnetic field concentration comparison according to the geometry. Panel (a) shows a classical dipole; (b) shows the first iteration of the genetic algorithm; and (c) shows the final geometry, which is based on the maximum electromagnetic field concentration at the center of the nanostructure.
Figure
Electromagnetic field concentration comparison between the classical dipole geometry and that generated by the genetic algorithm.
The classical or conventional dipole-type antenna geometries (in the radiofrequency regime) do not encompass the maximum electromagnetic field concentration (in the optical regime). This is due to the intrinsic differences between electron and photon behaviors. In addition, many macroscopic antenna assumptions and simplifications are not applicable for nanoscale optical frequency regimes because the electromagnetic wavelength is comparable to or even shorter than the antenna dimensions. Thus, a new refractive index function is introduced which defines the electromagnetic field behavior at such frequencies.
The proposed alternative genetic algorithm was applied to improve dipole geometry while accounting for the nanoscopic scale properties of these structures. Our results demonstrate that the final nanoantenna shape is significantly different than the classical case in the context of providing the optimal electromagnetic field concentration.
The results of this study will be used in future nanostructure fabrication and characterization studies using two materials with different Seebeck coefficients (one positive and one negative). The materials will generate maximum heating in the region of interest, producing a direct electric current [
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the “