OPTI 310

04/08

OPTI 310. Physical Optics I  (3). Review of math concepts, waves, and EM theory, Maxwell’s equations and the wave equation, plane-wave solution and properties, Lorentz oscillator model of optical properties, reflection and refraction at a dielectric interface,  Fabry-Perot, multilayer films, polarization optics, Jones calculus, Fraunhofer diffraction, single and double slit diffraction, Airy disk for a circular aperture. P, PHYS 241, MATH 223, MATH 254 and OPTI 280.

Course Outline:

  1. Math Review

  • Scalars, vectors in Cartesian and polar coordinates, vector addition, scalar and cross products.

  • Scalar and vector fields.

  • Differential vector calculus, gradient, divergence, curl, vector identities.

  • Integral vector calculus, Gauss’s divergence theorem and Stokes’ theorem.

  • Complex variables, basic notion of complex numbers and representation in the Argand plane, Euler formula, modulus and phase.

  1. One-dimensional (1D) Waves

  • Physical examples of 1D traveling waveforms.

  • The one-dimensional wave equation.

  • Harmonic waves, wavelength, frequency, phase, and phase velocity.

  • The superposition principle and interference, examples.

  • Complex representation of harmonic waves, phasor addition of complex amplitudes.

  1. Three-dimensional (3D) Waves

  • 3D harmonic waves, complex plane-wave representation,  wave-vectors and wavefronts, dispersion relation, direction cosines, synthesis of waveforms using plane-waves.

  • Spherical waves in polar coordinates.

  1. Review of Electromagnetism

  • Experimental underpinnings of electromagnetic theory.

  • Lorentz law for forces on charged particles.

  • Time varying magnetic fields and Faraday’s law.

  • Gauss’s law for electric and magnetic fields.

  • Dielectric constant.

  • Time-varying electric fields and Ampere’s law.

  • Maxwell’s equations in integral form.

  1. Maxwell’s equation and the Wave Equation

  • Maxwell’s equations in differential form.

  • Wave equations in free-space.

  • Speed of light in a medium and vacuum, refractive-index.

  1. Electromagnetic Waves

  • Transverse electromagnetic wave solution.

  • Complex representation of the plane-wave solution.

  • Poynting vector and energy flow.

  • Time averaged flow and irradiance.

  • Wavefronts and rays.

  • Radiation pressure and momentum.

  • Photons.

  1. Light-matter Interaction

  • Lorentz electron oscillator model for matter.

  • Electric polarization.

  • Refractive-index and dispersion.

  • Birefringence in crystals.

  1. Reflection and refraction at a Dielectric Interface

  • Internal and external reflection.

  • Laws of reflection and refraction.

  • The Fresnel equations for TE waves, examples.

  • Fresnel’s equations for TM waves, examples.

  • Reflectance and transmittance.

  • Total internal reflection.

  • Critical angle and evanescent waves.

  • Brewster’s angle and law for TM waves.

  1. Fabry-Perot Interferometer

  • The two-mirror Fabry-Perot, division of amplitude.

  • Transmission and the Airy function, coefficient of finesse.

  • Fabry-Perot interferometer, fringes of equal inclination.

  • Normal incidence, free-spectral range.

  • Longitudinal modes and cavity finesse

  • Scanning Fabry-Perot, resolving power.

  • Multilayer films, transfer matrix approach.

  • Anti-reflection coatings, high-pass and low-pass filters.

  1. Polarization

  • Linear polarization.

  • Circular and elliptical polarizations.

  • Jones vector representation.

  • Polarization elements, polarizers, Malus’s law, wave plates.

  • Jones calculus, transformation of polarization, examples.

  1. Fraunhofer diffraction

  • Huygens-Fresnel principle of secondary wavelets.

  • Fraunhofer versus Fresnel diffraction.

  • Fraunhofer diffraction from a single slit.

  • Double slit interference, division of wavefront.

  • Fraunhofer diffraction for a rectangular aperture.

  • Airy disk for a circular aperture.

  • Inclusion of a lens, diverging versus converging wavefront.

Grading Criteria:

  • Homework/attendance 20%
  • Midterm exam 1  25%
  • Midterm exam 2  25% 
  • Final exam 30%

Textbooks:

  • Hecht, Optics (4th Edition).
  • Fowles, Introduction to Modern Optics (2nd Edition).