Optimization of a single defect photonic crystal laser cavity

Abstract

Using nonlinear programing and the geometry projection method, the quality factor of the monopole mode of a single defect photonic crystal laser cavity is improved from 38 000 to 87 000. Beginning with a design that considers only round air holes shifted away from the cavity, the radius of the nearest neighbor and of the surrounding air holes are optimized while satisfying a constraint on the resonant frequency. The total reflectivity of the photonic crystal laser structure is then defined, and it is shown that this quantity correlates strongly to the total quality factor. The reflectivity of the structure is improved by altering the shape of the holes immediately surrounding the cavity, thus leading to an improvement in quality factor. The geometry projection method is used to define the shape of the holes and the finite element and adjoint methods are used to compute the objective function and sensitivities required by the optimizer. This work demonstrates one way to optimize the Q factor of a photonic crystal laser by altering the hole shape.

Scalable numerical approach for the steady-stateab initiolaser theory

“…Our solution strategy proceeds by a direct discretization using First, it is now possible to study lasing in much more complex geometries than could previously be readily simulated, offering the possibility of discovering geometries that induce unexpected new lasing phenomena. Going one step further, future computations could search a huge space of lasing structures via large-scale optimization ("inverse design"), which has already been applied to the design of linear microcavities [55][56][57]. Since our approach is only more expensive than the solution of linear cavity modes by a small constant factor (e.g., the number of modes and the number of Newton iterations) it will be the ideal tool for this purpose.…”

Topology optimization for nano‐photonics

“…For the level set approach the boundaries of the design are given as zero-level contour and design updates are based on boundary sensitivity analysis and updates using Hamilton-Jacobi based update formulations. This concept was first applied to topology optimization problems in mechanics [86,87] and has since then in different forms been applied to problems in nano-photonics [57,[88][89][90][91].…”

Transverse-electric and transverse-magnetic mode slow light propagation in a two-dimensional photonic crystal waveguide

“…In this paper, the finite element method (FEM) and geometry projection method (GPM) [18,19] are combined to optimize a two-dimensional (2D) PCW structure for both TE and TM propagations. GPM is an alternative approach that has the unique ability to deal with 2D structure problems.…”

“…And it can avoid some drawbacks of parameter and topology optimization methods, such as low computing efficiency and accuracy, intermediate dielectrics, and being captive to multiple local optimums. Recently, it has been successfully used in PC structure design [20], PCW optimization, and PC cavity problems [19]. In our previous publication, we have used this method to design a flat-band 2D PCW and achieved ultraslow light propagation with the minimum n g around 2335 for the TM mode [21].…”