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Electromagnetic theory of light. Fresnel
reflection and refraction. Polarization and crystal optics.
Metallic and dielectric waveguides.

**Learning Outcomes:**

Upon completing this course, the students will:

- Know the electromagnetic foundation of optics and the need for an electromagnetic description of light, as opposed to scalar waves or rays.
- Know the basics of polarization optics and the difference between different states of polarization (linear, circular or elliptical).
- Know how reflection at a boundary can change polarization.
- Be able to design simple systems that control the polarization of light.
- Know how reflection at a boundary can change polarization.
- Know the concept of surface and evanescent waves.
- Know the difference between guided waves in metallic and in dielectric planar waveguides.
- Know the concept of guided modes and cut-off conditions in waveguides.

**Topics:****Vector Analysis: (3 lectures)**

- Vector algebra, coordinate systems, vector representation, and vector coordinate transformation
- Vector integration: The divergence theorem and Stoke's theorem
- Vector differentiation: Gradient of scalar function, divergence of vector field, curl of vector function, Laplacian of a scalar function, and vector Laplacian of vector function

**Electromagnetic Theory and Maxwell's Equations: (3 lectures)**

- Electric and magnetic fields - permittivity and permeability of free-space
- Lorentz force equation
- Gauss's, Ampere's, and Faraday's Laws; displacement current
- Maxwell's equations in integral form
- Maxwell's equations in differential form
- Continuity equation and the displacement current
- The Poynting's theory and electromagnetic power
- Time harmonic fields and their representations
- Time harmonic Maxwell's equations

**Electromagnetic Fields in Materials: (3 lectures)**

- Electromagnetic properties of materials:
- Conductor and conduction current - Conductivity
- Dielectric materials and their polarization - Permittivity
- Magnetic materials and their magnetization and Permeability

- The constitutive relations between the field intensity and the flux density in materials
- Maxwell's equations in material regions
- The concept of complex permittivity
- Electromagnetic field boundary conditions at the interface between two layers

**Review and First Midterm: (2 lectures)****Plane Wave Propagation in Materials: (4 lectures)**

- The wave equation in source free region
- The time harmonic wave (Helmholtz) equation in source free region
- Plane wave solution of the Helmholtz equation

- Plane wave propagation in materials
- The concept of refractive index
- Characteristics of planes waves: Propagation vector, phase velocity, wavelength, the concept of refractive index, relationship between the propagation vector and electric and magnetic fields

- The Poynting's theory and electromagnetic power for a plane wave
- Polarization of plane waves: Linear, circular, elliptical

**Normal Incidence Plane Wave Reflection and Transmission at Planar Boundaries: (2 lectures)**

- Normal incidence plane wave reflection and transmission at plane boundary between two media
- Normal incidence plane wave reflection at perfectly conducting plane

- Reflection and Transmission at multiple interfaces
- Quarter and half-wave transformers
- Applications include anti-reflection coating

**Oblique Incidence Plane Wave Reflection and Transmission at Planar Boundaries: (3 lectures)**

- Oblique incidence plane wave reflection and transmission at plane boundary between two media
- Parallel (TM) and perpendicular (TE) polarizations
- Reflection and transmission coefficients
- Brewster angle and total transmission, the critical angle and total reflection
- Surface and evanescent waves

- Oblique incidence plane wave reflection at a perfectly conducting plane

**Review and Second Midterm: (2 lectures)****Crystal Optics: (2 lectures)**

- Anisotropic media such as crystals
- Propagation of light through anisotropic media
- Retardation and retardation plates

- Polarization devices - wave plates, polarization rotators, amplitude modulators
- Application: Liquid crystal displays

**Metallic and dielectric planar waveguides: (4 lectures)**

- Guide modes in metallic waveguides
- TEM modes in two plate planar waveguides and cut-off condition
- TM and TE modes in rectangular waveguides and cut-off condition
- Guided modes and cut-off condition

- Guide modes in dielectric waveguides
- Symmetric waveguides
- TM and TE modes in rectangular waveguides - cut-off condition
- Single mode waveguides
- Asymmetric waveguides

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