# 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