# Applied Physics (APh) Graduate Courses (2020-21)

APh 100.
Advanced Work in Applied Physics.
Units in accordance with work accomplished:
.
Special problems relating to applied physics, arranged to meet the needs of students wishing to do advanced work. Primarily for undergraduates. Students should consult with their advisers before registering. Graded pass/fail.

Ae/APh/CE/ME 101 abc.
Fluid Mechanics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: APh 17 or ME 11 abc, and ME 12 or equivalent, ACM 95/100 or equivalent (may be taken concurrently).
Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli's equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics.
Instructors: Dimotakis, Pullin.

Ae/APh 104 abc.
Experimental Methods.
9 units (3-0-6) first term; (0-6-3) second, third terms:
first, second, third terms.
Prerequisites: ACM 95/100 ab or equivalent (may be taken concurrently), Ae/APh/CE/ME 101 abc or equivalent (may be taken concurrently).
Lectures on experiment design and implementation. Measurement methods, transducer fundamentals, instrumentation, optical systems, signal processing, noise theory, analog and digital electronic fundamentals, with data acquisition and processing systems. Experiments (second and third terms) in solid and fluid mechanics with emphasis on current research methods. Ae/APh 104 a offered 2020-21.

APh/MS 105 abc.
States of Matter.
9 units (3-0-6):
first, second, third terms.
Prerequisites: APh 17 abc or equivalent.
Thermodynamics and statistical mechanics, with emphasis on gases, liquids, materials, and condensed matter. Effects of heat, pressure, and fields on states of matter are presented with both classical thermodynamics and with statistical mechanics. Conditions of equilibrium in systems with multiple degrees of freedom. Applications include ordered states of matter and phase transitions. The three terms cover, approximately, thermodynamics, statistical mechanics, and phase transitions. APh/MS 105ab not offered 2020-21. APh/MS 105c
Instructor: Falson.

APh/EE 109.
Introduction to the Micro/Nanofabrication Lab.
9 units (0-6-3):
first, second, third terms.
Introduction to techniques of micro-and nanofabrication, including solid-state, optical, and microfluidic devices. Students will be trained to use fabrication and characterization equipment available in the applied physics micro- and nanofabrication lab. Topics include Schottky diodes, MOS capacitors, light-emitting diodes, microlenses, microfluidic valves and pumps, atomic force microscopy, scanning electron microscopy, and electron-beam writing.
Instructors: Troian, Ghaffari.

APh 110.
Topics in Applied Physics.
2 units (2-0-0):
first, second terms.
A seminar course designed to acquaint advanced undergraduates and first-year graduate students with the various research areas represented in the option. Lecture each week given by a different member of the APh faculty, who will review his or her field of research. Graded pass/fail.
Instructor: Bellan.

APh 114 abc.
Solid-State Physics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 125 abc or equivalent.
Introductory lecture and problem course dealing with experimental and theoretical problems in solid-state physics. Topics include crystal structure, symmetries in solids, lattice vibrations, electronic states in solids, transport phenomena, semiconductors, superconductivity, magnetism, ferroelectricity, defects, and optical phenomena in solids.
Instructors: Nadj-Perge, Schwab.

APh/Ph 115.
Physics of Momentum Transport in Hydrodynamic Systems.
9 units (3-0-6):
second term.
Prerequisites: ACM 95 or equivalent.
Contemporary research in many areas of physics requires some knowledge of the principles governing hydrodynamic phenomena such as nonlinear wave propagation, symmetry breaking in pattern forming systems, phase transitions in fluids, Langevin dynamics, micro- and optofluidic control, and biological transport at low Reynolds number. This course offers students of pure and applied physics a self-contained treatment of the fundamentals of momentum transport in hydrodynamic systems. Mathematical techniques will include formalized dimensional analysis and rescaling, asymptotic analysis to identify dominant force balances, similitude, self-similarity and perturbation analysis for examining unidirectional and Stokes flow, pulsatile flows, capillary phenomena, spreading films, oscillatory flows, and linearly unstable flows leading to pattern formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods will be taught in class as needed.
Instructor: Troian.

APh/Ph/Ae 116.
Physics of Thermal and Mass Transport in Hydrodynamic Systems.
9 units (3-0-6):
third term.
Prerequisites: ACM 95 or equivalent and APh/Ph 115 or equivalent.
Contemporary research in many areas of physics requires some knowledge of how momentum transport in fluids couples to diffusive phenomena driven by thermal or concentration gradients. This course will first examine processes driven purely by diffusion and progress toward description of systems governed by steady and unsteady convection-diffusion and reaction-diffusion. Topics will include Fickian dynamics, thermal transfer in Peltier devices, Lifshitz-Slyozov growth during phase separation, thermocouple measurements of oscillatory fields, reaction-diffusion phenomena in biophysical systems, buoyancy driven flows, and boundary layer formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods such as singular perturbation, Sturm-Liouville and Green's function analysis will be taught in class as needed.
Instructor: Troian.

Ph/APh/EE/BE 118 abc.
Physics of Measurement.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 127, APh 105, or equivalent, or permission from instructor.
This course focuses on exploring the fundamental underpinnings of experimental measurements from the perspectives of responsivity, noise, backaction, and information. Its overarching goal is to enable students to critically evaluate real measurement systems, and to determine the ultimate fundamental and practical limits to information that can be extracted from them. Topics will include physical signal transduction and responsivity, fundamental noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlations. The first term will cover the essential fundamental underpinnings, while topics in second term will include examples from optical methods, high-frequency and fast temporal measurements, biological interfaces, signal transduction, biosensing, and measurements at the quantum limit. Part c not offered in 2020-21.
Instructor: Roukes.

EE/APh 120.
Physical Optics.
9 units (3-0-6):
second term.
Prerequisites: Intermediate-level familiarity with Fourier transforms and linear systems analysis. Basic familiarity with Maxwell's electromagnetic theory (EE40 and EE44, or equivalent).
Course focuses on applying linear systems analysis on propagation of light waves. Contents begin with a review of Electromagnetic theory of diffraction and transitions to Fourier Optics for a scalar-wave treatment of propagation, diffraction, and image formation with coherent and incoherent light. In addition to problems in imaging, the course makes connections to a selected number of topics in optics where the mathematics of wave phenomena plays a central role. Examples include propagation of light in multilayer films and meta surfaces, Gaussian beams, Fabry-Pérot cavities, and angular momentum of light. Areas of application include modern imaging, display, and beam shaping technologies.
Instructor: Mirhosseini.

MS/APh 122.
Diffraction, Imaging, and Structure.
9 units (0-4-5):
third term.
Prerequisites: MS 132, may be taken concurrently.
Experimental methods in transmission electron microscopy of inorganic materials including diffraction, spectroscopy, conventional imaging, high resolution imaging and sample preparation. Weekly laboratory exercises to complement material in MS 132. Not Offered 2020-21.
Instructor: Ahn.

EE/APh 123.
Advanced Lasers and Photonics Laboratory.
9 units (1-3-5):
first term.
Prerequisites: none.
This course focuses on hands-on experience with advanced techniques related to lasers, optics, and photonics. Students have the opportunity to build and run several experiments and analyze data. Covered topics include laser-based microscopy, spectroscopy, nonlinear optics, quantum optics, ultrafast optics, adaptive optics, and integrated photonics. Limited enrollment. Not offered 2020-21.
Instructor: Marandi.

APh/EE 130.
Electromagnetic Theory.
9 units (3-0-6):
first term.
Electromagnetic fields in vacuum: microscopic Maxwell's equations. Monochromatic fields: Rayleigh diffraction formulae, Huyghens principle, Rayleigh-Sommerfeld formula. The Fresnel-Fraunhofer approximation. Electromagnetic field in the presence of matter, spatial averages, macroscopic Maxwell equations. Helmholtz's equation. Group-velocity and group-velocity dispersion. Confined propagation, optical resonators, optical waveguides. Single mode and multimode waveguides. Nonlinear optics. Nonlinear propagation. Second harmonic generation. Parametric amplification. Not offered 2020-21.

EE/APh 131.
Light Interaction with Atomic Systems-Lasers.
9 units (3-0-6):
second term.
Prerequisites: APh/EE 130.
Light-matter interaction, spontaneous and induced transitions in atoms and semiconductors. Absorption, amplification, and dispersion of light in atomic media. Principles of laser oscillation, generic types of lasers including semiconductor lasers, mode-locked lasers. Frequency combs in lasers. The spectral properties and coherence of laser light. Not offered 2020-21.
Instructor: Yariv.

APh/EE 132.
Special Topics in Photonics and Optoelectronics.
9 units (3-0-6):
third term.
Interaction of light and matter, spontaneous and stimulated emission, laser rate equations, mode-locking, Q-switching, semiconductor lasers. Optical detectors and amplifiers; noise characterization of optoelectronic devices. Propagation of light in crystals, electro-optic effects and their use in modulation of light; introduction to nonlinear optics. Optical properties of nanostructures. Not offered 2020-21.

Ph/APh 137 abc.
Atoms and Photons.
9 units (3-0-6):
first, second terms.
Prerequisites: Ph 125 ab or equivalent, or instructor's permission.
This course will provide an introduction to the interaction of atomic systems with photons. The main emphasis is on laying the foundation for understanding current research that utilizes cold atoms and molecules as well as quantized light fields. First term: resonance phenomena, atomic/molecular structure, and the semi-classical interaction of atoms/molecules with static and oscillating electromagnetic fields. Techniques such as laser cooling/trapping, coherent manipulation and control of atomic systems. Second term: quantization of light fields, quantized light matter interaction, open system dynamics, entanglement, master equations, quantum jump formalism. Applications to cavity QED, optical lattices, and Rydberg arrays. Third term [not offered 2020-21]: Topics in contemporary research. Possible areas include introduction to ultracold atoms, atomic clocks, searches for fundamental symmetry violations, synthetic quantum matter, and solid state quantum optics platforms. The emphasis will be on reading primary and contemporary literature to understand ongoing experiments.
Instructors: Hutzler, Endres.

APh/Ph 138 ab.
Quantum Hardware and Techniques.
9 units (3-0-6):
second and third terms.
Prerequisites: Ph 125 abc or Ph 127 abc or Ph 137 ab or instructor's permission.
This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into three-week modules covering: applications of near-term quantum computers, superconducting qubits, trapped atoms and ions, topological quantum matter, solid state quantum bits, tensor-product states. APh/Ph 138a will not be offered 2020-21. APh/Ph 138b
Instructors: Endres, Faraon, Hsieh, Painter.

EE/APh 149.
Frontiers of Nonlinear Photonics.
9 units (3-0-6):
second term.
This course overviews recent advances in photonics with emphasis on devices and systems that utilize nonlinearities. A wide range of nonlinearities in the classical and quantum regimes is covered, including but not limited to second- and third-order nonlinear susceptibilities, Kerr, Raman, optomechanical, thermal, and multi-photon nonlinearities. A wide range of photonic platforms is also considered ranging from bulk to ultrafast and integrated photonics. The course includes an overview of the concepts as well as review and discussion of recent literature and advances in the field. Not Offered 2020-21.
Instructor: Marandi.

APh 150.
Topics in Applied Physics.
Units and terms to be arranged:
.
Content will vary from year to year, but at a level suitable for advanced undergraduate or beginning graduate students. Topics are chosen according to the interests of students and staff. Visiting faculty may present portions of this course.

APh 156 abc.
Plasma Physics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 106 abc or equivalent.
An introduction to the principles of plasma physics. A multitiered theoretical infrastructure will be developed consisting of the Hamilton-Lagrangian theory of charged particle motion in combined electric and magnetic fields, the Vlasov kinetic theory of plasma as a gas of interacting charged particles, the two-fluid model of plasma as interacting electron and ion fluids, and the magnetohydrodynamic model of plasma as an electrically conducting fluid subject to combined magnetic and hydrodynamic forces. This infrastructure will be used to examine waves, transport processes, equilibrium, stability, and topological self-organization. Examples relevant to plasmas in both laboratory (fusion, industrial) and space (magneto-sphere, solar) will be discussed.
Instructor: Bellan.

EE/APh 158.
Quantum Electrical Circuits.
9 units (3-0-6):
third term.
Prerequisites: advanced-level familiarity with Maxwell's electromagnetic theory and quantum mechanics (EE 151 and Ph 125 abc, or equivalent).
Course focuses on superconducting electrical systems for quantum computing. Contents begin with reviewing required concepts in microwave engineering, quantum optics, and superconductivity, and proceeds with deriving quantum mechanical description of superconducting linear circuits, Josephson qubits, and parametric amplifiers. The second part of the course provides an overview of integrated nano-mechanical, piezo-electric and electro-optical systems and their applications in transducing quantum electrical signals in conjunction with superconducting qubits.
Instructor: Mirhosseini.

BE/APh 161.
Physical Biology of the Cell.
12 units (3-0-9):
second term.
Prerequisites: Ph 2 ab and ACM 95/100 ab, or background in differential equations and statistical and quantum mechanics, or instructor's written permission.
Physical models applied to the analysis of biological structures ranging from individual proteins and DNA to entire cells. Topics include the force response of proteins and DNA, models of molecular motors, DNA packing in viruses and eukaryotes, mechanics of membranes, and membrane proteins and cell motility.
Instructor: Phillips.

MS/APh 171.
Inelastic Scattering of Materials, Molecules, and Condensed Matter.
9 units (3-0-6):
third term.
Prerequisites: EE/APh 131 or MS 132 or equivalent.
Review of Patterson function and memory function for space or time correlations. Van Hove function for correlated dynamics in space and time, especially for materials with thermal energy. Dynamical structure factors for coherent scattering from solids and liquids. Measurements of energy and momentum of dispersive excitations in crystals using neutrons, x-rays, and electrons. Additional topics to be selected from the following list: incoherent inelastic scattering and the thermodynamic partition function, transport of thermal energy, fluctuation-dissipation theorem, quasielastic scattering, sideband information in coherent inelastic scattering, transition from quantum to classical scattering.
Instructor: Fultz.

EE/APh 180.
Nanotechnology.
6 units (3-0-3):
first term.
This course will explore the techniques and applications of nanofabrication and miniaturization of devices to the smallest scale. It will be focused on the understanding of the technology of miniaturization, its history and present trends towards building devices and structures on the nanometer scale. Examples of applications of nanotechnology in the electronics, communications, data storage and sensing world will be described, and the underlying physics as well as limitations of the present technology will be discussed.
Instructor: Scherer.

APh/EE 183.
Physics of Semiconductors and Semiconductor Devices.
9 units (3-0-6):
third term.
Principles of semiconductor electronic structure, carrier transport properties, and optoelectronic properties relevant to semiconductor device physics. Fundamental performance aspects of basic and advanced semiconductor electronic and optoelectronic devices. Topics include energy band theory, carrier generation and recombination mechanisms, quasi-Fermi levels, carrier drift and diffusion transport, quantum transport.
Instructor: Nadj-Perge.

APh 190 abc.
Quantum Electronics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 125 or equivalent.
Generation, manipulations, propagation, and applications of coherent radiation. The basic theory of the interaction of electromagnetic radiation with resonant atomic transitions. Laser oscillation, important laser media, Gaussian beam modes, the electro-optic effect, nonlinear-optics theory, second harmonic generation, parametric oscillation, stimulated Brillouin and Raman scattering. Other topics include light modulation, diffraction of light by sound, integrated optics, phase conjugate optics, and quantum noise theory. APh 190c not offered 2020-21. APh 190 ab
Instructor: Vahala.

APh 200.
Applied Physics Research.
Units in accordance with work accomplished:
.
Offered to graduate students in applied physics for research or reading. Students should consult their advisers before registering. Graded pass/fail.

Ae/ME/APh 218.
Statistical Mechanics.
9 units (3-0-6):
third term.
Prerequisites: Ae/ME 118, or equivalent.
Overview of probability and statistics, and the Maxwell-Boltzmann distribution. Overview and elements of Quantum Mechanics, degenerate energy states, particles in a box, and energy-state phase space. Statistics of indistinguishable elementary particles, Fermi-Dirac and Bose-Einstein statistics, partition functions, connections with classical thermodynamics, and the Law of Equipartition. Examples from equilibrium in fluids, solid-state physics, and others. Not offered 2020-21.

Ph/APh 223 ab.
Advanced Condensed-Matter Physics.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 135 or equivalent, or instructor's permission.
Advanced topics in condensed-matter physics, with emphasis on the effects of interactions, symmetry, and topology in many-body systems. Ph/Aph 223a covers second quantization, Hartree-Fock theory of the electron gas, Mott insulators and quantum magnetism, bosonization, quantum Hall effects, and symmetry protected topological phases such as topological insulators. Ph/APh 223b will continue with BCS theory of superconductivity, Ginzburg-Landau theory, elements of unconventional and topological superconductors, theory of superfluidity, Bose-Hubbard model and bosonic Mott insulators, and some aspects of quantum systems with randomness.
Instructors: Alicea, Kitaev.

APh 250.
Advanced Topics in Applied Physics.
Units and term to be arranged:
.
Content will vary from year to year; topics are chosen according to interests of students and staff. Visiting faculty may present portions of this course.
Instructor: Staff.

APh/MS 256.
Computational Solid State Physics and Materials Science.
9 units (3-3-3):
third term.
Prerequisites: Ph125 or equivalent and APh114ab or equivalent.
The course will cover first-principles computational methods to study electronic structure, lattice vibrations, optical properties, and charge and heat transport in materials. Topics include: Theory and practice of Density Functional Theory (DFT) and the total-energy pseudopotential method. DFT calculations of total energy, structure, defects, charge density, bandstructures, density of states, ferroelectricity and magnetism. Lattice vibrations using the finite-difference supercell and Density Functional Perturbation Theory (DFPT) methods. Electron-electron interactions, screening, and the GW method. GW bandstructure calculations. Optical properties, excitons, and the GW-Bethe Salpeter equation method. Ab initio Boltzmann transport equation (BTE) for electrons and phonons. Computations of heat and charge transport within the BTE framework. If time permits, selected advanced topics will be covered, including methods to treat vander Waals bonds, spin-orbit coupling, correlated materials, and quantum dynamics. Several laboratories will give students direct experience with running first-principles calculations. Not offered 2020-21.

APh 300.
Thesis Research in Applied Physics.
Units in accordance with work accomplished:
.
APh 300 is elected in place of APh 200 when the student has progressed to the point where his or her research leads directly toward a thesis for the degree of Doctor of Philosophy. Approval of the student's research supervisor and department adviser or registration representative must be obtained before registering. Graded pass/fail.

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The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics.