The Optics PhD Qualifying Examination is an oral exam based on material covered by the four courses on the fundamentals of Optics:

- OSE 5115 – Interference, Diffraction & Coherence
- OSE 5312 – Light Matter Interaction
- OSE 6111 – Optical Wave Propagation
- OSE 6211 – Imaging and Optical Systems

Note: OSE 5525 – Laser Engineering is a required PhD core class, but is not part of the Qualifying Examination.

A detailed list of topics covered by the PhD qualifying exam is given below. Students are required to take the Qualifying Exam at the first opportunity after all of the above listed courses have been taken. Those students failing on the first attempt must retake the exam at the very next attempt. Failure to take the exam at the required time will be regarded as equivalent to a failure of the exam. The examination committee may, in exceptional circumstances, use a brief oral exam to help them obtain information necessary to reach a decision on a student who has marginally failed the exam at the second attempt.

The exam is waived for students earning an average GPA of 3.5 or higher in the four core courses. Students must have a minimum GPA of 3.0 in the four core courses to take the exam.

#### Foundations of Optical Wave Propagation

**Electromagnetic Field Theory:**

- Electromagnetic fields
- Time varying and Harmonic Maxwell’s equations
- Boundary condition
- Power Flow

**Wave Equation in Linear Isotropic Homogenous Media:**

- Uniform plane waves in unbounded lossless media
- Non-uniform plane waves in lossy media
- Phase and group velocity
- Polarization, linear, circular, and elliptical
- Reflection and refraction at planar boundaries of lossless – Brewster angle, critical angle, total internal reflection and associated phase shifts
- Reflection and refraction at planar single and multi-layered lossless and lossy media

**Electromagnetic Propagation in Anisotropic Media:**

- Dielectric tensor classification of anisotropic media, plane wave propagation in anisotropic media – the dispersion relation
- Light propagation in uniaxial and biaxial media
- Power flow in anisotropic media
- Refraction and reflection at anisotropic interface
- Index ellipsoid
- Optical activities, Faraday rotation
- Jones’s Calculus, retardation plates, polarizers

**Optical Propagation in Periodic Media:**

- Periodic field spatial harmonics
- Generalized phased matching and the grating equation
- Conical and planar diffraction in one-dimensional periodic structures
- Spherical diffraction in two-dimensional periodic structures
- Propagation and evanescent diffracted orders

**Planar Dielectric Waveguides**

- TE and TM guided modes in planar waveguides
- Symmetric and asymmetric dielectric planar waveguides
- Cut-off conditions and single mode waveguide
- Field distribution in planar waveguides
- Power flow in waveguides
- Mode orthogonally and mode excitation

#### Optical Interference, Diffraction and Coherence

- Fourier transforms
- Interference
- Superposition
- Optical path difference
- Plane and spherical waves
- Spatial frequencies & angular spectrum of plane waves
- Young’s double slit
- Huygens wavelets and Rayleigh-Sommerfeld diffraction integral
- Transition from Fresnel to Fraunhofer
- Fraunhofer calculations (circle, slit, edge, multiple slits)
- Fresnel zones & Fresnel calculations (circle, slit, edge)
- Dual-Beam Interferometers
- Newton’s fringes (Fizeau)
- Michelson, Twyman-Green interferometers
- Multiple-Beam interferometers
- Thin-film filters
- AR & HR
- Fabry-Perot (Airy fringe shape, finesse, FSR)
- Coherence, temporal & spatial coherence
- Visibility
- VanCittert-Zernike Theorem
- Diffraction Gratings
- Amplitude & phase gratings
- Grating equations
- Diffraction efficiency

#### Light Matter Interaction

**Maxwell’s Equations and the Dielectric Function:**

- Free charge
- Vacuum displacement
- Meaning of susceptibility and polarization response
- Bound electron polarization
- Causality and Kramers-Kronig relations

**Optical Properties of Solids, Liquids, and Gases:**

- Molecules
- Liquids
- Metals
- Insulators
- Semiconductors

**Classical Treatment of Light-Matter Interaction:**

- Lorentz oscillator, Drude model, Debye model, calculation of susceptibility and complex refractive index
- Sellmeier equations and Abbe number
- Molecular rotational/vibrational transitions in molecules
- Dipole-active and Raman-active modes
- Phonons in solids, acoustic modes, optical modes

**Quantum mechanical description of light matter interaction:**

- Operators, eigenfunctions, orthonormal complete sets, Dirac notation
- Wavefunctions, observables, commutation
- Ensemble averages, energy Eigenfunctions
- Time independent Schrödinger equation, infinite and finite wells, barriers
- Time dependent Schrödinger equation, time dependent perturbation theory
- Fermi Golden Rule, expectation value of Polarization, susceptibility
- Oscillator strength, dopants / impurities in dielectric hosts
- Kronig-Penney Model and Energy bands, Band gaps
- Excitons, impurities (n- and p-type)
- Blackbody radiation
- Einstein coefficients
- Thermal distributions (Bose-Einstein, Fermi-Dirac, Maxwell-Boltzmann)

#### Imaging and Optical Systems

- Introduction to linear system theory
- Discrete systems and their matrix description, transforms, and modes
- Application to polarization devices, optical resonators, and coupled waveguides
- One-dimensional continuous linear systems and integral transforms
- Impulse response function and transfer function
- Application to pulse propagation in dispersive media
- Two-dimensional linear systems and integral transforms
- Application to optical propagation, diffraction, spatial filtering, and coherent imaging
- Introduction to random signals and systems
- Applications to imaging with incoherent light
- Point spread function and optical transfer function of gazing and scanning imaging systems