In this lecture, we give a broad introduction to the concept of computational design in photonics. We show how simulation and mathematical optimization can be combined to analyze and design photonic devices effectively.

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.

In this lecture, we show how to use the previously introduced “adjoint variable method” to perform gradient-based optimization of a focusing lens. We set up a simple device based on a pixellated array of permittivity values, compute the gradient of this array with respect to the focusing strength of our lens, and then perform an optimization to achieve a final device that focuses light successfully.

In this lecture, we will discuss the need for fabrication constraints in inverse design optimization. We describe one approach to this and demonstrate it by optimizing a Silicon photonics mode converter.

In this lecture, we introduce a method to optimize your device with respect to a geometric parameterization using inverse design and the adjoint method. As an example, we demonstrate the inverse design of a 90 degree waveguide bend by shifting the boundaries of the device.

In this lecture, we introduce a method to optimize your device using a level set parameterization using inverse design and the adjoint method. As an example, we demonstrate the inverse design of a waveguide splitter.