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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.

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

Syllabi