**Speaker:** Oscar P. Bruno, CalTech

**Title:** Numerical Simulation of Propagation and Scattering of Electromagnetic Waves: time-domain transients, pure frequencies, and the Fourier transform.]

**Abstract:** After a brief review of classical numerical methods for the differential equations of physics and, in particular, electromagnetism, we will consider electromagnetic waves with harmonic temporal dependence (ie, "pure" radio waves, or light waves, or rays). X, etc.) We will use the fundamental solution of the harmonic electromagnetic problem to construct numerical solutions to problems involving highly complex electromagnetic structures. As an illustration of these ideas, we will present applications to the design and optimization of photonic devices (such as cameras, circuits, and optical fibers). We will also mention an intriguing observation, according to which it is possible to obtain in a very effective way the arbitrary temporal dependence (not necessarily harmonic) of the electromagnetic fields and other observables in physics on the basis of solutions with harmonic temporal dependence for a fixed set of frequencies of oscillation.

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