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# Physics of linear and nonlinear optical waveguides

## Overview

Optical waveguide is a physical structure that guides electromagnetic waves and it is the most important component of integrated optical circuits. This course is intended to describe the theoretical basis of optical waveguides. In this course we learn the principal of light guidance by understanding the light-matter interaction in linear and nonlinear regime. We will also discuss different optical components based on waveguides that are used extensively in communication and sensing. This course is mostly self-contained with very basic prerequisites like knowledge of elementary algebra and calculus. The course is prepared for the senior graduate and M.Sc. students having a prior knowledge of electromagnetic theory. The course is also useful to the junior PhD students and M-Tech students whose research interest is related to Photonics. The exam of this course will be based on multiple choice questions and each week the descriptive type practice-assignments will be given to the students as home work.
INTENDED AUDIENCE :
3rd year B. Sc Physics , M. Sc Physics , M-Tech (Applied Optics),PREREQUISITES : Basic calculus, Algebra, Basic complex numbers, Basic concept of electrodynamicsINDUSTRIES SUPPORT :None

## Syllabus

### COURSE LAYOUT

Week 1:Linear and nonlinear optical waveguides & Brief history, Maxwell’s equation, Plane wave, Wave equation, Snell’s Law, Total Internal Reflection, Concept of core and claddingWeek 2:Numerical Aperture (NA), V-parameter, Cut off wavelength, Ray propagation in optical fibers, Meridonial rays, Skew ray, Concept of discrete ray propagation inside waveguidesWeek 3:Waveguide characteristics: Loss mechanism, Modal dispersion, Ray Equation, Ray path for step-index waveguideWeek 4:Ray equation continue: Ray path for triangular-index waveguide, Ray path for parabolic index waveguide, Transit Time
Week 5:Material Dispersion, Group delay, Pulse broadening, Concept of zero dispersion, Birefringence waveguidesWeek 6:Modes: TE & TM Modes, Modes in slab waveguide, Symmetric and anti-symmetric mode, Calculation of propagation constantWeek 7:Modes: Step index optical fibers, Bassel function, Recursion relation, LPlm modesWeek 8:Optical waveguide components: Directional coupler, Optical switching, Power coupler, Wavelength Division Multiplexing (WDM), Couple Mode Theory
Week 9:Fiber Bragg Grating (FBG), Bragg wavelength, Reflectivity calculation, Linear waveguide arrayWeek 10:Nonlinear Waveguides, Kerr nonlinearity, EM wave propagation under Kerr nonlinearityWeek 11:Nonlinear Susceptibility, Second Harmonic Generation (SHG), Third Harmonic Generation (THG), Phase MatchingWeek 12:Self Phase Modulation (SPM), Nonlinear absorption, Optical Soliton, Supercontinuum Generation

### Taught by

Prof. Samudra Roy

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