Physics Masters

MASTERS PROGRAMS

Master of Science - Physics
The Master of Science degree prepares students optimally for further continuation to a Ph.D. program in physics. It is awarded after completion of 30 credits of graduate coursework which include the following required courses:

• PEP 510 Modern Optics Lab

  The course is designed to familiarize students with a range of optical instruments and their applications. Included will be the measurement of aberrations in optical systems, thin-film properties, Fourier transform imaging systems, nonlinear optics, and laser beam dynamics. Fall term.  This course may sometimes be offered in the spring term if space
  

• PEP 528 Mathematical Methods of Science and Engineering II

  Vector and Tensor Fields: transformation properties, algebraic and  differential operators and identities, geometric interpretation of tensors,  integral theorems.  Dirac delta-function and Green's function technique for  solving linear inhomogeneous equations.  N-dimensional complex space:  rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation,  similarity transformations and diagonalization, Schmidt orthogonalization.  Introduction to functions of a complex variable: analyticity, Cauchy's  theorem, Taylor and Laurent expansions, analytic continuation, multiple-  valued functions, residue theorem, contour integration, asymptotics.  As  techniques are developed, they are applied to examples in mechanics,  electromagnetism and/or transport theory.         Fall semester.

• PEP 554 Quantum Mechanics II

  Basic concepts of quantum mechanics, states, operators; time development of  Schrödinger and Heisenberg pictures; representation theory; symmetries;  perturbation theory; systems of identical particles, L-S and j-j coupling;  fine and hyperfine structure; scattering theory; molecular structure.        Spring semester.    Typical texts: Gottfried, Quantum Mechanics, Schiff, Quantum Mechanics.

• PEP 555 Statistical Physics and Kinetic Theory

  Kinetic theory: ideal gases, distribution functions, Maxwell-Boltzmann distribution, Boltzmann equation, H-theorem and entropy, and simple transport theory. Thermodynamics: review of first and second laws, thermodynamic potentials, Legendre transformation, and phase transitions. Elementary statistical mechanics: introduction to microcanonical, canonical, and grand canonical distributions, partition functions, simple applications, including ideal Maxwell-Boltzmann, Einstein-Bose, and Fermi-Dirac gases, paramagnetic systems, and blackbody radiation. Typical text: Reif, Statistical and Thermal Physics.Fall semester.

• PEP 642 Mechanics

  Lagrangian and Hamiltonian formulations of mechanics, rigid body motion, elasticity, mechanics of continuous media, small vibration theory, special relativity, canonical transformations, and perturbation theory. Typical text: Goldstein, Classical Mechanics.

• PEP 643 Electricity and Magnetism I

  Electrostatics, boundary value problems, Green’s function techniques, methods of image, inversion, and conformal mapping; multipole expansion. Magnetostatics, vector potential. Maxwell’s equations and conservation laws. Electromagnetic wave propagation in media. Crystal optics. Fall semester. Typical texts: Jackson, Classical Electrodynamics; Landau and Lifshitz, Electrodynamics in Continuous Media.

• PEP 644 Electricity and Magnetism II

  Interaction of electromagnetic waves with matter, dispersion, waveguides and resonant cavities, radiating systems, scattering and diffraction, covariant electromagnetic theory, motion of relativistic particles in electromagnetic fields, relativistic radiation theory, radiation damping, and self-fields. Spring semester. Typical texts: Jackson, Classical Electrodynamics and Landau and Lifshitz, The Classical Theory of Fields, Electrodynamics in Continuous Media.

• One 600-level advanced quantum mechanics course
• and two additional elective courses, chosen in consultation with an academic advisor.

These courses may be used to conduct research to graduate with an MS Thesis (PEP 900.) Courses with material already covered in undergraduate preparation must be replaced in consultation with an academic advisor.

Master of Engineering - Engineering Physics
The Master of Engineering - Engineering Physics degree program has three options. Students enrolled in a particular option develop a course of study in conjunction with their academic advisor. In contrast to the Master of Science in physics, the Master of Engineering option is intended to provide the student with deeper insight into the specific area of their choice - which may even be interdisciplinary. Students wanting to continue their education towards a doctoral degree will be optimally prepared for interdisciplinary Physics research, yet may have to take several additional courses to fulfill the requirements for a Ph.D. in Physics.

The Engineering Physics option in Applied Optics seeks to extend and broaden training in those areas pertinent to the field of applied optics or optical engineering. A bachelor's degree in either science or engineering from an accredited institution is required.

Core Courses in Engineering Physics (Applied Optics)

• PEP 509 Intermediate Waves and Optics

  The general study of field phenomena; scalar and vector fields and waves; dispersion phase and group velocity; interference, diffraction and polarization; coherence and correlation; geometric and physical optics. Typical text: Hecht and Zajac, Optics. Spring semester.

• PEP 510 Modern Optics Lab

  The course is designed to familiarize students with a range of optical instruments and their applications. Included will be the measurement of aberrations in optical systems, thin-film properties, Fourier transform imaging systems, nonlinear optics, and laser beam dynamics. Fall term.  This course may sometimes be offered in the spring term if space
  

• PEP 515 Photonics I

  This course will cover topics encompassing the fundamental subject matter for the design of optical systems. Topics will include optical system analysis, optical instrument analysis, applications of thin-film coatings and opto-mechanical system design in the first term. The second term will cover the subjects of photometry and radiometry, spectrographic and spectrophotometric systems, infrared radiation measurement and instrumentation, lasers in optical systems and photon-electron conversion. Typical texts: Military Handbook 141 (U.S. Govt. Printing Office); S.P.I.E Reprint Series (Selected Issues); W.J. Smith, Modern Optical Engineering .

• PEP 516 Photonics II

  This course will cover topics encompassing the fundamental subject matter for the design of optical systems. Topics will include optical system analysis, optical instrument analysis, applications of thin-film coatings and opto-mechanical system design in the first term. The second term will cover the subjects of photometry and radiometry, spectrographic and spectrophotometric systems, infrared radiation measurement and instrumentation, lasers in optical systems and photon-electron conversion. Typical texts: Military Handbook 141 (U.S. Govt. Printing Office); S.P.I.E Reprint Series (Selected Issues); W.J. Smith, Modern Optical Engineering .

• PEP 527 Mathematical Methods of Science and Engineering I

  Fourier series, Bessel functions, and Legendre polynomials as involved in the  solution of vibrating systems; tensors and vectors in the theory of  elasticity; applications of vector analysis to electrodynamics; vector  operations in curvilinear coordinates; numerical methods of interpolation and  of integration of functions and differential equations.

• PEP 542 Electromagnetism

  Electrostatics; Coulomb-Gauss law; Poisson-Laplace equations; boundary value problems; image techniques;dielectric media; magnetostatics; multipole expansion; electromagnetic energy; electromagnetic induction; Maxwell’s equations; electromagnetic waves, radiation, waves in bounded regions, wave equations and retarded solutions; simple dipole antenna radiation theory; transformation law of electromagnetic fields. Spring semester. Typical text: Reitz, Milford and Christy, Foundation of Electromagnetic Theory.

• PEP 553 Quantum Mechanics and Engineering Applications

   This course is meant to serve as an introduction to formal quantum mechanics  as well as to apply the basic formalism to several generic and important  applications.

• PEP 554 Quantum Mechanics II

  Basic concepts of quantum mechanics, states, operators; time development of  Schrödinger and Heisenberg pictures; representation theory; symmetries;  perturbation theory; systems of identical particles, L-S and j-j coupling;  fine and hyperfine structure; scattering theory; molecular structure.        Spring semester.    Typical texts: Gottfried, Quantum Mechanics, Schiff, Quantum Mechanics.

• PEP 577 Laser Theory and Design

   An introductory course to the theory of lasers; treatment of spontaneous and  stimulated emission, atomic rate equations, laser oscillation conditions,  power output and optimum output coupling; CW and pulsed operation, Q  switching, mode selection, and frequency stabilization; excitation of lasers,  inversion mechanisms, and typical efficiencies; detailed examination of  principal types of lasers, gaseous, solid state, and liquid; chemical lasers,  dye lasers, Raman lasers, high power lasers, TEA lasers, gas dynamic lasers.  Design considerations for GaAlAs, argon ion, helium neon, carbon dioxide,  neodymium YAG and pulsed ruby lasers.      Fall semester.         Typical text: Yariv, Optical Electronics.

• PEP 578 Laser Applications and Advanced Optics

  Integrated optics, nonlinear optics, Pockels effect, Kerr effect, harmonic generation, parametric devices, phase conjugate mirrors, and phase matching. Coherent and incoherent detection, Fourier optics, image processing and holography, and Gaussian optics. Detection of light, signal to noise, PIN and APD diodes, and optical communication. Scattering of light, Rayleigh, Mie, Brillouin, Raman, and Doppler shift scattering. Spring semester.

• PEP 678 Physics of Optical Communication Systems

  This course explains the physics behind modern optical communication systems at high data rates. The first half of this course covers information theory and light propagation over fiber optic waveguide channels; semiconductor laser sources and detectors; high speed digital optic links; and dense wavelength division multiplexing methods and devices. The second half of this course covers quantum optical information theory; coherent systems and quantum correlations; optical solition-based communication; squeezed light and noise limitations; de-phasing and de-coherence; teleportation and secure communication system protocols; and cryptography and chaotic optics.

The Engineering Physics option in Solid State Physics seeks to extend and broaden training in those areas pertinent to the field of solid state device engineering. A bachelor's degree in either science or engineering from an accredited institution is required.

Core Courses in Engineering Physics (Solid State Physics)

• EE 619 Solid State Devices

  Operating principle, modeling and fabrication of solid state devices for modern optical and electronic system implementation; recent developments in solid state devices and integrated circuits; devices covered include bipolar and MOS diodes and transistors, MESFET, MOSFET transistors, tunnel, IMPATT and BARITT diodes, transferred electron devices, light emitting diodes, semiconductor injection and quantum-well lasers, PIN and avalanche photodetectors.

• PEP 503 Introduction to Solid State Physics

  Description of simple physical models which account for electrical conductivity and thermal properties of solids. Basic crystal lattice structures, X-ray diffraction and dispersion curves for phonons and electrons in reciprocal space. Energy bands, Fermi surfaces, metals, insulators, semiconductors, superconductivity and ferromagnetism. Fall semester. Typical text: Kittel, Introduction to Solid State Physics.

• PEP 510 Modern Optics Lab

  The course is designed to familiarize students with a range of optical instruments and their applications. Included will be the measurement of aberrations in optical systems, thin-film properties, Fourier transform imaging systems, nonlinear optics, and laser beam dynamics. Fall term.  This course may sometimes be offered in the spring term if space
  

• PEP 527 Mathematical Methods of Science and Engineering I

  Fourier series, Bessel functions, and Legendre polynomials as involved in the  solution of vibrating systems; tensors and vectors in the theory of  elasticity; applications of vector analysis to electrodynamics; vector  operations in curvilinear coordinates; numerical methods of interpolation and  of integration of functions and differential equations.

• PEP 538 Introduction to Mechanics

  Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations.

• PEP 542 Electromagnetism

  Electrostatics; Coulomb-Gauss law; Poisson-Laplace equations; boundary value problems; image techniques;dielectric media; magnetostatics; multipole expansion; electromagnetic energy; electromagnetic induction; Maxwell’s equations; electromagnetic waves, radiation, waves in bounded regions, wave equations and retarded solutions; simple dipole antenna radiation theory; transformation law of electromagnetic fields. Spring semester. Typical text: Reitz, Milford and Christy, Foundation of Electromagnetic Theory.

• PEP 553 Quantum Mechanics and Engineering Applications

   This course is meant to serve as an introduction to formal quantum mechanics  as well as to apply the basic formalism to several generic and important  applications.

• PEP 554 Quantum Mechanics II

  Basic concepts of quantum mechanics, states, operators; time development of  Schrödinger and Heisenberg pictures; representation theory; symmetries;  perturbation theory; systems of identical particles, L-S and j-j coupling;  fine and hyperfine structure; scattering theory; molecular structure.        Spring semester.    Typical texts: Gottfried, Quantum Mechanics, Schiff, Quantum Mechanics.

• PEP 555 Statistical Physics and Kinetic Theory

  Kinetic theory: ideal gases, distribution functions, Maxwell-Boltzmann distribution, Boltzmann equation, H-theorem and entropy, and simple transport theory. Thermodynamics: review of first and second laws, thermodynamic potentials, Legendre transformation, and phase transitions. Elementary statistical mechanics: introduction to microcanonical, canonical, and grand canonical distributions, partition functions, simple applications, including ideal Maxwell-Boltzmann, Einstein-Bose, and Fermi-Dirac gases, paramagnetic systems, and blackbody radiation. Typical text: Reif, Statistical and Thermal Physics.Fall semester.

• PEP 680 Quantum Optics

  This course explores the quantum mechanical aspects of the theory of electromagnetic radiation and its interaction with matter. Topics covered include Einstein’s theory of emission and absorption, Planck’s law, quantum theory of light-matter interaction, classical fluctuation theory, quantized radiation field, photon quantum statistics, squeezing, and nonlinear interactions. Offered in alternate years. Typical text: Loudon, Quantum Theory of Light.

Courses with material already covered in undergraduate preparation must be replaced in consultation with an academic advisor.

Nanotechnology Concentration - Masters Engineering Physics
The Engineering Physics option in Nanotechnology seeks to extend and broaden training in a largely interdisciplinary learning environment with a focus on fundamentals and applications of Nanotechnology. A bachelor degree in either science or engineering from an accredited institution is required. The M.E. degree in nanotechnology will be awarded after completion of 30 credits of graduate coursework with the following requirements:

Core Courses in Engineering Physics (Nanotechnology)

• NANO 600 Nanoscale Science and Technology

  This course deals with the fundamentals and applications of nanoscience and nanotechnology. Size-dependent phenomena, ways and means of designing and synthesizing nanostructures, and cutting-edging applications will be presented in an integrated and interdisciplinary manner.

• NANO 625 Techniques of Surface and Nanostructure Characterization

  Lectures, demonstrations, and laboratory experiments, selected from among the following topics, depending on student interest: vacuum technology; thin-film preparation; scanning electron microscopy; infrared spectroscopy and ellipsometry; electron spectroscopy; Auger, photoelectron, and LEED; ion spectroscopies; SIMS, IBS, and field emission; surface properties-area, roughness, and surface tension.

• PEP 503 Introduction to Solid State Physics

  Description of simple physical models which account for electrical conductivity and thermal properties of solids. Basic crystal lattice structures, X-ray diffraction and dispersion curves for phonons and electrons in reciprocal space. Energy bands, Fermi surfaces, metals, insulators, semiconductors, superconductivity and ferromagnetism. Fall semester. Typical text: Kittel, Introduction to Solid State Physics.

• PEP 538 Introduction to Mechanics

  Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations.

• PEP 542 Electromagnetism

  Electrostatics; Coulomb-Gauss law; Poisson-Laplace equations; boundary value problems; image techniques;dielectric media; magnetostatics; multipole expansion; electromagnetic energy; electromagnetic induction; Maxwell’s equations; electromagnetic waves, radiation, waves in bounded regions, wave equations and retarded solutions; simple dipole antenna radiation theory; transformation law of electromagnetic fields. Spring semester. Typical text: Reitz, Milford and Christy, Foundation of Electromagnetic Theory.

• PEP 553 Quantum Mechanics and Engineering Applications

   This course is meant to serve as an introduction to formal quantum mechanics  as well as to apply the basic formalism to several generic and important  applications.

• PEP 555 Statistical Physics and Kinetic Theory

  Kinetic theory: ideal gases, distribution functions, Maxwell-Boltzmann distribution, Boltzmann equation, H-theorem and entropy, and simple transport theory. Thermodynamics: review of first and second laws, thermodynamic potentials, Legendre transformation, and phase transitions. Elementary statistical mechanics: introduction to microcanonical, canonical, and grand canonical distributions, partition functions, simple applications, including ideal Maxwell-Boltzmann, Einstein-Bose, and Fermi-Dirac gases, paramagnetic systems, and blackbody radiation. Typical text: Reif, Statistical and Thermal Physics.Fall semester.

In addition to the core courses, the student has to complete three additional courses out of the PEP or NANO program (elective courses) selected in consultation with the advisor. As an option, candidates may choose to execute a Master thesis in the realm of nanotechnology in consultation with an academic advisor for up to six credits to be counted towards the degree in replacement of elected courses. 

* Students with a background in Quantum Mechanics should take directly PEP/NANO554 after consultation with the advisor.

For more information, visit the Nanotechnology Graduate Program site.

Interdisciplinary Master- Concentration Microelectronics and Photonics and Technology

The Physics and Engineering Physics program offers, jointly with Electrical and Computer Engineering (ECE) and Materials Engineering, a unique interdisciplinary concentration in Microelectronics and Photonics Science and Technology. Intended to meet the needs of students and of industry in the areas of design, fabrication, integration, and applications of microelectronic and photonic devices for communications and information systems, the program covers fundamentals, as well as state-of-the-art industrial practices. Designed for maximum flexibility, the program accommodates the background and interests of students with either a master's degree or graduate certificate.

Core course required:

• PEP 507 Introduction to Microelectronics and Photonics

  An overview of Microelectronics and Photonics Science and Technology.  It provides the student who wishes to specialize in the application, physics or fabrication with the necessary knowledge of how the different aspects are interrelated.  It is taught in three modules: design and applications, taught by EE faculty; operation of electronic and photonic devices, taught by Physics faculty; fabrication and reliability, taught by the
  Materials faculty.

Six electives are required from the courses offered below by Materials Engineering, Physics and Engineering Physics, and Electrical Engineering. Three of these courses must be from Physics and Engineering Physics and at least one must be from each of the other two departments. Ten courses are required for the degree.

Required Concentration Electives:

• CPE 690 Introduction to VLSI Design

  This course introduces students to the principles and design techniques of very large scale integrated circuits (VLSI). Topics include: MOS transistor characteristics, DC analysis, resistance, capacitance models, transient analysis, propagation delay, power dissipation, CMOS logic design, transistor sizing, layout methodologies, clocking schemes, case studies. Students will use VLSI CAD tools for layout and simulation. Selected class projects may be sent for fabrication.

• EE 585 Physical Design of Wireless Systems

  Physical design of wireless communication systems, emphasizing present and next generation architectures. Impact of non-linear components on performance; noise sources and effects; interference; optimization of receiver and transmitter architectures; individual components (LNAs, power amplifiers, mixers, filters, VCOs, phase-locked loops, frequency synthesizers, etc.); digital signal processing for adaptable architectures; analog-digital converters; new component technologies (SiGe, MEMS, etc.); specifications of component performance; reconfigurability and the role of digital signal processing in future generation architectures; direct conversion; RF packaging; minimization of power dissipation in receivers.

• EE 626 Optical Communication Systems

  Components for and design of optical communication systems; propagation of optical signals in single mode and multimode optical fibers; optical sources and photodetectors; optical modulators and multiplexers; optical communication systems: coherent modulators, optical fiber amplifiers and repeaters; transcontinental and transoceanic optical telecommunication system design; optical fiber LANs.

• MT 562 Solid State Electronics for Engineeing II

  This course introduces operating principles and develops models of modern semiconductor devices that are useful in the analysis and design of integrated circuits. Topics covered include: charge carrier transport in semiconductors; diffusion and drift, injection and lifetime of carriers; p-n junction devices; bipolar junction transistors; metal-oxide-semiconductor field effect transistors; metal-semiconductor field effect transistors and high electron mobility transistors; microwave devices; light emitting diodes, semiconductor lasers and photodetectors; integrated devices.

• MT 595 Reliability and Failure of Solid State Devices

  This course deals with the electrical, chemical, environmental and mechanical driving forces that compromise the integrity and lead to the failure of electronic materials and devices. Both chip and packaging level failures will be modeled physically and quantified statistically in terms of standard reliability mathematics. On the packaging level, thermal stresses, solder creep, fatigue and fracture, contact relaxation, corrosion and environmental degradation will be treated.

• MT 596 Microfabrication Techniques

  Deals with aspects of the technology of processing procedures involved in the fabrication of microelectronic devices and microelectromechanical systems (MEMS). Students will become familiar with various fabrication techniques used for discrete devices, as well as large-scale integrated thin film circuits. Students will also learn that MEMS are sensors and actuators that are designed using different areas of engineering disciplines, and they are constructed using a microlithographically-based manufacturing process in conjunction with both semiconductor and micro-machining microfabrication technologies.

• PEP 503 Introduction to Solid State Physics

  Description of simple physical models which account for electrical conductivity and thermal properties of solids. Basic crystal lattice structures, X-ray diffraction and dispersion curves for phonons and electrons in reciprocal space. Energy bands, Fermi surfaces, metals, insulators, semiconductors, superconductivity and ferromagnetism. Fall semester. Typical text: Kittel, Introduction to Solid State Physics.

• PEP 515 Photonics I

  This course will cover topics encompassing the fundamental subject matter for the design of optical systems. Topics will include optical system analysis, optical instrument analysis, applications of thin-film coatings and opto-mechanical system design in the first term. The second term will cover the subjects of photometry and radiometry, spectrographic and spectrophotometric systems, infrared radiation measurement and instrumentation, lasers in optical systems and photon-electron conversion. Typical texts: Military Handbook 141 (U.S. Govt. Printing Office); S.P.I.E Reprint Series (Selected Issues); W.J. Smith, Modern Optical Engineering .

• PEP 516 Photonics II

  This course will cover topics encompassing the fundamental subject matter for the design of optical systems. Topics will include optical system analysis, optical instrument analysis, applications of thin-film coatings and opto-mechanical system design in the first term. The second term will cover the subjects of photometry and radiometry, spectrographic and spectrophotometric systems, infrared radiation measurement and instrumentation, lasers in optical systems and photon-electron conversion. Typical texts: Military Handbook 141 (U.S. Govt. Printing Office); S.P.I.E Reprint Series (Selected Issues); W.J. Smith, Modern Optical Engineering .

• PEP 561 Solid State Electronics for Engineering I

  This course introduces fundamentals of semiconductors and basic building blocks of semiconductor devices that are necessary for understanding semiconductor device operations. It is for first-year graduate students and upper-class undergraduate students in electrical engineering, applied physics, engineering physics, optical engineering and materials engineering, who have no previous exposure to solid state physics and semiconductor devices. Topics covered will include description of crystal structures and bonding; introduction to statistical description of electron gas; free-electron theory of metals; motion of electrons in periodic lattice-energy bands; Fermi levels; semiconductors and insulators; electrons and holes in semiconductors; impurity effects; generation and recombination; mobility and other electrical properties of semiconductors; thermal and optical properties; p-n junctions; metal-semiconductor contacts.