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OSE3053 - Electromagnetic Waves for Photonics

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

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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