This course discusses the fundamentals properties of light propagation in free space and inside various technologically relevant materials, as well as the effect of materials interfaces on light propagation. The covered propagation modes include plane waves, Gaussian beams, and Floquet modes. Isotropic, anisotropic (uniaxial, biaxial), and periodic (1D, 2D) media are covered.

Credit Hours:

• 3 hours (3,0)

Prerequisite:

• Graduate standing or consent of instructor

Suggested Reading:

• Any text book on fundamentals of applied electromagnetism particularly on Maxwell's equations and plane wave propagation.

List of topics

Review of Vector Analysis

• Vector Representation and vector coordinate transformations
• Dot product and cross products
• Differential vector operations
• Integral vector theorems

Electromagnetic Field Theory

• Electromagnetic fields
• Integral and differential time varying Maxwell’s equations
• Constitutive relationships and electric permittivity, magnetic permeability, and electrical conductivity
• Boundary conditions
• Power and Energy
• Fourier series and Fourier transforms in linear systems
• Complex time harmonic Maxwell’s equations

Electromagnetic Propagation in Linear Isotropic Homogenous Media

• Wave propagation in linear homogenous isotropic (LHI) media
• The wave equation and Helmholtz equation
• The Poynting’s theory and power flow density
• Electromagnetic field polarization, linear, circular, and elliptical

Reflection and Refraction at Planar Interfaces

• Reflection and refraction at planar boundaries
• Phase Matching
• E and TM polarizations
• Brewster angle, critical angle, total internal reflection
• Reflection/refraction in multi-layered media
• Quarter-wave stack and applications in thin film coatings

Electromagnetic Propagation in Anisotropic Media

• Dielectric tensor classification of anisotropic media
• Dispersion relation and light propagation in uniaxial and biaxial media
• Power flow in anisotropic media
• Index ellipsoid
• Refraction and reflection at anisotropic interface
• Jones's calculus and retardation plates

Gaussian Beam Propagation

• Scalar wave equation approximation
• Propagation of Gaussian beams and beam divergence
• Limitation of the paraxial approximation
• Transformation of Gaussian beams and the ABCD bilinear transformation
• Applications to simple resonators
• Plane wave decomposition for finite beam propagation

Optical Propagation in Periodic Media

• Periodic field spatial harmonics
• Generalized phased matching condition and the grating equation
•  Propagation and evanescent diffracted orders
• Interferometric formation of volume gratings
• Bragg condition for volume gratings