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PhD Qualifying Exam Topics After Fall 2010
The Optics PhD Qualifying Examination is a written exam based on material covered by the six courses on the fundamentals of Optics:
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, which for full time students starting in the Fall, means in August of the next year. For part time students, this rule means that the exam must be taken at the next opportunity after all of the above listed these 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.
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.
Gaussian Beam Propagation: Gaussian beams in homogeneous media, · Plane wave decomposition for finite beam propagation, · Scalar wave equation approximation, · The electric and magnetic fields of Gaussian beam, · Non-planar phase fronts and beam divergence, · Limitation of the paraxial approximation, · Transformation of Gaussian beams and the ABCD bilinear transformation, · Applications to simple resonators etc., Plane wave decomposition for finite beam propagation.
Propagation of Optical Pulses: Pulse propagation equation, · Group velocity and group velocity dispersion, · Time delay and pulse spreading, · Gaussian Pulse Propagation, · Frequency chirp.
Optical Propagation in Periodic Media: Periodic field spatial harmonics, · Floquet theorem, · 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, · Periodic layered media.
Foundations of Optical Interference, Diffraction & 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 & 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 and magnetization; causality & 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).
Geometrical Optics and Imaging Science
Foundations of Image Formation: Huygens’s Principle, Wavefronts and Rays, Malus Theorem, Fermat's Principle, Law of Reflection, Vectorial Law of Refraction and Snell's Law, Critical Angle and TIR, Dispersion, Optical Materials, Plane Mirrors and Prisms, Diffraction Effects in Imaging Systems, Define Coherent, Partially Coherent, and Incoherent Imaging, Linear Systems Approach to Image Formation (OTF/MTF, PSF) (point to list of other criteria).
Geometrical Theory of Image Formation: Gaussian Image Formation, Cardinal Points, Graphical Ray Tracing, Imaging Eqs. of Newton and Descartes, Transverse and Longitudinal Magnification, Angular Magnification and the Helmholtz Invariant. Paraxial Ray Tracing, Stops and Pupils (Vignetting), Marginal and Chief Rays (the Lagrange Invariant). Numerical Aperture, Focal Ratio or F#, Front and Rear Effective F# (working F#). Real Ray Trace Procedure, Geometrical Aberrations, Spot Diagrams, Diffraction-limited Resolution.
Basic Optical Devices and Instruments: The Simple Magnifier, Projector, Compound Microscope, The Camera, Telescopes, The Eye, Afocal Systems, Field Lenses and Relay Systems, Radiometer and Detector Optics, Fiber Optics. Non imaging systems, Adaptive Optics, and Synthetic Aperture / Lenslet Arrays.
Radiometry and Flux Transfer in Imaging Systems: Radiometric Terminology and Nomenclature, The Inverse Square Law. Radiant Power Transfer, Lambert's Cosine Law, The Brightness Theorem (Optical Throughput or Etendue). Radiometry of Images, Cosine-fourth Illumination Fall-off, Limits in Detection of Light.
Introduction to Aberration Theory: The Wavefront Aberration Function, Relationship of Ray Aberrations to Wavefront Aberrations. The Effect of Lens Shape and Stop Position, Symmetrical Principle, The Seidel Aberrations, Structural Aberration Coefficients, Comparison of 3rd-order Aberration Theory with Real Ray Trace Data. Effect of Aberrations of MTF, PSF, Detector Effects, Post-detection Processing.
Fundamental of Photonics
Guided Wave Optics: Planar slab waveguides, Waveguide modes, field distribution, and group velocity, Rectangular channel, Coupled-mode theory, Optical coupling between waveguides, Single and multi-mode optical fibers, Propagation constants and velocities, Waveguide, material and modal dispersion, Pulse propagation.
Electro-optics and Acousto-Optics: Light propagation in anisotropic media, Linear electro-optic effect and the electro-optic tensor, Longitudinal and transverse modulators, Amplitude modulation, phase modulation, Longitudinal and transverse modulators, Mach-Zehnder modulators, Acousto-optic interaction and Bragg diffraction, The photoelastic effect, Acousto-optic modulators, deflectors, and scanners.
Optoelectronics: Semiconductor laser amplifier: gain, pumping, heterostructures. Semiconductor injection lasers: Amplification, feedback, oscillation, power, spectral and spatial distribution, mode selection. Properties of semiconductor photoconductors: Quantum efficiency, responsively, response time. Photodiodes: p-n and p-i-n, hetero structure photodiodes. Photodetector noise: Thermal and Shot noise.
Principles of Lasers: Absorption, Spontaneous & Stimulated Emission, Einstein coefficients; Line Broadening Mechanisms; Optical gain and loss, two level system; Rate equations: Three and four level systems. Amplification threshold; Saturation - Homogeneous and Inhomogeneous lines; Amplified Spontaneous Emission. Vibronic transitions in solids, liquids and gases, Molecular transitions in gases; Semiconductor and quantum well laser media; The simple CW laser oscillator, Laser oscillation threshold, CW output power. Resonator stability, ray matrices; Properties of Resonators, longitudinal and transverse modes; Gaussian Beams, modes, ABCD matrices; Unstable resonators; Coherence and divergence; Relaxation oscillations; Q-switching; Mode-locking and ultrafast pulses. Nonlinear susceptibility and second order wave mixing (SHG, SFG, DFG); Harmonic generation efficiency; Parametric generation and oscillation.
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