“Mathematical Methods for Optics and Photonics”
Spring Semester (Wednesday, January 11 – Wednesday, May 3) 2023
This course covers the basic mathematics needed for an in-depth understanding of the science and technology of fiber-optical communication systems. Every mathematical tool/technique developed in this course will first be motivated by the relevant application. The students are not expected to have a broad-based prior knowledge of the topics covered in this course, but they should generally be familiar with the basics of algebra, Euclidean geometry, trigonometry, integral and differential calculus, simple differential equations, and the rudiments of complex number analysis. The course will cover complex analysis, Fourier transform theory, stationary-phase approximation (in the context of optical diffraction), vector algebra, linear algebra, ordinary and partial differential equations (e.g., Maxwell’s electrodynamics, wave equation, diffusion equation), special functions (e.g., Bessel functions needed to study the guided modes of optical fibers), and probability theory (needed for understanding various sources of noise in communication systems, photodetection theory, digital communication via noisy channels, Information theory, etc.).