Leveraging Continuous Material Averaging for Inverse Electromagnetic Design

Inverse electromagnetic design has emerged as a way of efficiently designing active and passive electromagnetic devices. This maturing strategy involves optimizing the shape or topology of a device in order to improve a figure of merit--a process which is typically performed using some form of steepest descent algorithm. Naturally, this requires that we compute the gradient of a figure of merit which describes device performance, potentially with respect to many design variables. In this paper, we introduce a new strategy based on smoothing abrupt material interfaces which enables us to efficiently compute these gradients with high accuracy irrespective of the resolution of the underlying simulation. This has advantages over previous approaches to shape and topology optimization in nanophotonics which are either prone to gradient errors or place important constraints on the shape of the device. As a demonstration of this new strategy, we optimize a non-adiabatic waveguide taper between a narrow and wide waveguide. This optimization leads to a non-intuitive design with a very low insertion loss of only 0.041 dB at 1550 nm.Comment: 20 pages, 9 figure

Intermediate Mirrors to Reach Theoretical Efficiency Limits of Multi-Bandgap Solar Cells

Creating a single bandgap solar cell that approaches the Shockley-Queisser limit requires a highly reflective rear mirror. This mirror enhances the voltage of the solar cell by providing photons with multiple opportunities for escaping out the front surface. Efficient external luminescence is a pre-requisite for high voltage. Intermediate mirrors in a multijunction solar cell can enhance the voltage for each cell in the stack. These intermediate mirrors need to have the added function of transmitting the below bandgap photons to the next cell in the stack. In this work, we quantitatively establish the efficiency increase possible with the use of intermediate selective reflectors between cells in a tandem stack. The absolute efficiency increase can be up to ~6% in dual bandgap cells with optimal intermediate and rear mirrors. A practical implementation of an intermediate selective mirror is an air gap sandwiched by antireflection coatings. The air gap provides perfect reflection for angles outside the escape cone, and the antireflection coating transmits angles inside the escape cone. As the incoming sunlight is within the escape cone, it is transmitted on to the next cell, while most of the internally trapped luminescence is reflected

Light Trapping Textures Designed by Electromagnetic Optimization for Sub-Wavelength Thick Solar Cells

Light trapping in solar cells allows for increased current and voltage, as well as reduced materials cost. It is known that in geometrical optics, a maximum 4n^2 absorption enhancement factor can be achieved by randomly texturing the surface of the solar cell, where n is the material refractive index. This ray-optics absorption enhancement limit only holds when the thickness of the solar cell is much greater than the optical wavelength. In sub-wavelength thin films, the fundamental questions remain unanswered: (1) what is the sub-wavelength absorption enhancement limit and (2) what surface texture realizes this optimal absorption enhancement? We turn to computational electromagnetic optimization in order to design nanoscale textures for light trapping in sub-wavelength thin films. For high-index thin films, in the weakly absorbing limit, our optimized surface textures yield an angle- and frequency-averaged enhancement factor ~39. They perform roughly 30% better than randomly textured structures, but they fall short of the ray optics enhancement limit of 4n^2 ~ 50