Cross-Sectional Optimization of Whispering-Gallery Mode Sensor With High Electric Field Intensity in the Detection Domain

Abstract

Optimal cross-sectional shapes for whisperinggallery mode sensors with prescribed emission wavelengths and resonance modes are generated through topology optimization based on the finite element method. The sensor is assumed to detect the state of the domain surrounded by the sensor. We identified the integral of the square of the electric field intensity over the detection domain and the quality factor (Q factor), which should be maximized, as key values for the sensor sensitivity, representing the detection limit for the relative permittivity change of the test object. Based on this, the integral of the square of the electric field intensity over the detection domain and the Q factor are studied as the optimization targets. In our numerical study, their optimal configuration characteristics are identified and analyzed. The resulting device has a small radius, a small detection domain and a concave shape with a center located next to the detection domain. We also succeeded in performing simultaneous optimization of the integral of the square of the electric field intensity over the detection domain and the Q factor.

Topology optimization of surface flows

“…Optimization of structural topology was investigated as early as 1904 for trusses by Michell [5]. Material distribution method for topology optimization was pioneered by Bendsøe and Kikuchi for elasticity [6], and this method has been extended to a variety of areas, e.g., acoustics, electromagnetics, fluid dynamics and thermodynamics [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Several other methods also have been proposed and developed for the implementation of topology optimization, e.g., the level set method [21,22], the evolutionary techniques [23][24][25], the evolutionary structural optimization method [26,27], the method of moving morphable components [28,29] and the phase field method [30].…”

Sensitivity analysis and optimization of eigenmode localization in continuum systems

“…For the eigenmode optimization problem, some researchers use eigenmode sensitivity analysis of matrices, which are derived by the finite element method (FEM) discretization of the original problem (Fox and Kapoor 1968;Nelson 1976;Wang 1991;Maeda et al 2006). In the continuum form, sensitivity analysis is used for eigenmode optimization problems (Inzarulfaisham and Azegami 2004;Zhang et al 2014;Takezawa and Kitamura 2012;Takezawa et al 2014). Inzarulfaisham and Azegami (2004) evaluate the shape gradient for the boundary shape optimization problem with optimality conditions obtained by the adjoint variable method, the Lagrange multiplier method, and the formula for the material derivative.…”

“…Takezawa and Kitamura (2013) obtain the derivative of the objective function including the k-th eigenmode and the adjoint variable, which avoids the computation of higher order eigenfrequencies and eigenmodes. This idea is applied into the cross-sectional shape optimization of whisperinggallery mode resonators with prescribed emission wavelength and resonance mode (Takezawa and Kitamura 2012;Takezawa et al 2014), where the electric field is calculated as an eigenmode of the eigenvalue problem. Zhang et al (2014) propose a penalty optimization algorithm based on the derivative of the objective function including the k-th eigenvalue and the k-th eigenmode and the adjoint variable.…”