Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices

Abstract

The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, nonintuitive structures with superior performance. Among various methods, large-scale, gradient-based optimization techniques have been one of the most important ways to design a structure containing a vast number of degrees of freedom. These techniques are made possible by the adjoint method, in which the gradient of an objective function with respect to all design degrees of freedom can be computed using only two full-field simulations. However, this approach has so far mostly been applied to linear photonic devices. Here, we present an extension of this method to modeling nonlinear devices in the frequency domain, with the nonlinear response directly included in the gradient computation. As illustrations, we use the method to devise compact photonic switches in a Kerr nonlinear material, in which low-power and high-power pulses are routed in different directions. Our technique may lead to the development of novel compact nonlinear photonic devices.

Forward-Mode Differentiation of Maxwell’s Equations

“…(7) may be expressed in the form of Maxwell's equations. To show this, we define du dφj (t) ≡ [h j (t), e j (t)] T as the 'derivative' fields for parameter φ j and evaluate the other terms using (2) and (3), giving 8) or in the form of Maxwell's equations,…”

“…We now compare the computation of dF dφ through the adjoint and FMD methods. To do this, following a treatment given in [8], we apply the chain rule to obtain…”

MetaNet: a new paradigm for data sharing in photonics research

“…These collective efforts have given rise to new classes of high-performance photonic design technologies based on freeform layouts [24,[32][33][34]. However, these research efforts have been uncoordinated, and many algorithms and device layouts remain unshared.…”

Controlling the minimal feature sizes in adjoint optimization of nanophotonic devices using b-spline surfaces

“…Adjoint method has become a very useful tool in the inverse design of photonics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and among other optimization methods such as genetic algorithms [17], swarm optimization [18], or nonlinear optimization [19], adjoint method is particularly efficient as it computes the gradient of a cost function w.r.t. a large number of design parameters.…”