Inverse Design in Photonics Lecture 2: Adjoint Method

In this lecture, we derive the adjoint variable method for computing the gradient of the figure of merit of a photonic device. We derive this gradient from first principles, starting from the solution of Maxwell’s equations in the frequency domain. Using a simple example of focusing electromagnetic field intensity at a single position, we derive the relevant terms in the gradient and give physical interpretation. We discuss how this method provides gradient information with only two simulations, regardless of the number of design parameters, and how this enables inverse design optimization.

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