Optical Physics and Lasers

OPTI 511R, Spring 2012

Instructor: Prof. R. Jason Jones, College of Optical Sciences

HW#3 posted below, due in class next Thurs.Feb 9.

     Location: room 307, T-Th, 2:00 - 3:15 PM

    Instructor:
        Prof. R. Jason Jones (link to faculty web page)
        Office:        Meinel 625
        Phone:        520-626-4634
        email:          rjjones at optics.arizona.edu

Office Hours: 12-1 Tues. and Friday

TA:
Chih Yu Huang (Office hours Wed 3-4 in 8th floor conference room)

email: chuang@optics.arizona.edu

OSC official OPTI511R course webpage: http://www.optics.arizona.edu/classes/Opti_511R.htm

Class Notes

A copy of the ClassNotes is required for this course and available from the University of Arizona bookstore

Textbooks (recommended)

The books listed below are recommended as references but not required, each covering a portions of the material covered in 511R.

Introduction to Quantum Mechanics, by David J. Griffiths (highly recommended if you have no other QM text)

Lasers, by Peter W. Milonni and Joseph H. Eberly

Fundamentals of Photonics, by B.E.A. Saleh and M.C. Teich

Atomic Physics, by C.J. Foot

Grading structure:

Midterm Exam (40%)
Final Exam (40%)
Homework (20%)

Handouts and Misc. Material

Course Description

Course description
OPTI 511 is an introduction to basic concepts of optical physics and the interaction between light and matter. This course is designed to give optics students a broad understanding of the generation and absorption of light by matter, and how light can be used to manipulate properties of matter and be manipulated by matter. In this course, basic ideas from quantum mechanics will be introduced and used to develop the concepts of atom/light interaction, and the quantum nature of atoms and optical fields will be explored. The basic properties of lasers will be briefly discussed in a few lectures near the end of the semester.
While previous courses in physics would indeed be helpful, this course is designed to be accessible to students who have a general science or engineering background and basic familiarity with using complex numbers, matrices, and differential equations. Previous courses in quantum mechanics are NOT needed.

Course emphasis
Because this is an introductory course covering many topics, this course will not develop detailed exploration of the subjects that will be covered. If you have further interest in any of the course topics, other specialized classes cover the subjects in detail. In this respect, OPTI 511R covers material that is fundamental to many other Optics courses in quantum optics and photonics. In OPTI 511R, an emphasis will be placed on the learning of new concepts, rather than detailed mathematical derivation of all of the subjects. Many of the concepts of quantum mechanics and quantum optics may seem strange and non-intuitive. For some of these concepts, an initial (perhaps tentative) acceptance will be needed until they become more familiar. The math used in this course is generally not difficult. However, learning the mathematical formalism and the application of the mathematical tools can be tricky and confusing. Many simple tricks and approximations exist to solve problems, some of which we will explore.
The language of optical physics and quantum mechanics can also be confusing at times. Previously familiar words take on new meanings or new mathematical formalism, and a single concept can have various mathematical representations or notations on paper. As in most scientific disciplines, different authors and instructors use different symbols to represent identical concepts. In this course, it is the concept that is of primary importance; given a symbol or a problem, you must interpret the expression or method to solve the problem, and extract the relevant concepts.

Recommended texts:
    This class does not have a required textbook.
    The recommended textbook is "Introduction to Quantum Mechanics" by David Griffiths. Either edition (first or second) is suitable. This book will be paralleled for about half of the semester as the concepts of quantum mechanics are introduced and developed, and until the basic properties of light/matter interaction have been introduced. If you have never had a course in QM, and are serious about learning this topic, this is an excellent book for learning the basics of QM. If you have had a QM course, you will probably find that the class notes or other QM reference books are fine. Thus, this is not a required textbook. Please note that while many subjects, notations, and problems in the book and in the lectures will be similar or identical, it will be each student's option to follow along in the book, find and read the relevant sections, and work example problems as needed.

General Course syllabus and topics list

        Quantum Mechanics
                1.       Introduction to quantum mechanics, wave/particle duality, uncertainty principle
                2.       Quantum mechanics of free and bound particles, wave packets
                3.       Schrödinger equation, wave functions, eigenvalue equations
                4.       Postulates of quantum mechanics
                5.       Measurements in quantum mechanics, expectation values
                6.       Quantum harmonic oscillator
                7.    Dirac notation, matrix formulation of quantum mechanics
                8.       Hydrogen atom, quantum mechanics of the real hydrogen atom
                9.       Spin angular momentum, Pauli exclusion principle

        Optical Physics
                10.   Hamiltonian for light/matter interaction, time-dependent probability amplitudes
                11.   Electric dipole approximation, Rotating wave approximation
                12.   Two-level atom approximation, Rabi oscillations
                13.   Collisional decay and spontaneous emission, rate equations
                14.   Blackbody radiation, Einstein A and B coefficients
                15.   Steady-state absorption coefficient, saturation
                16.   Inhomogeneous line broadening, absorption lineshapes
                17. Quantization of the electromagnetic field, vacuum field fluctuations, photon statistics

        Lasers
                18. Optical resonators, resonator stability
                19. Population inversion
                20. Threshold gain and steady-state laser operation
                21. Laser output characteristics and output control
                22. Pulsed lasers, Q-switching, mode locking
                23. Survey of lasers and output characteristics (if time permits)

Prereqs: OPTI 501 and basic linear algebra
        Particularly, it is assumed that the following concepts will be familiar:
            1. Wave equation and complex representation of EM waves
            2. Lorentz oscillator model, absorption, and refractive index
            3. Basic operations with vectors and complex variables
            4. Manipulation of matrices
            5. Eigenvalues and eigenvectors/eigenfunctions in algebraic and matrix forms.
            6. Basic properties of Fourier transforms
            7. Separation of variables method of solving partial differential equations
        Topics 1-5 above are especially important. If you are weak in any of these areas, you may need to do some extra work during the course of OPTI 511. Some key ideas will be reviewed, but these topics will not be taught from scratch.
        Again, previous courses in physics will be helpful, but are not required. This course is designed to be accessible to students without a physics background.

Homework

Homework assignments are due weekly. Distance learning students may send in assignments to Cindy Robertson by midnight of the due day. Once posted, late assignments will not be accepted.

HW#1 (Due Jan 26th)

HW#2 (Due Feb. 2nd)

HW#3 (Due Feb. 9th)

References

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Some relevant wikipedia pages and other internet sites are listed below for convenient reference. Caution: I have not read all of these pages, or verified that the material is either correct or follows the same sign conventions as used in class. You will need to judge for yourself if the material conforms to OPTI 511R topics and terminology, or if it these web pages are even useful to you.

Internet

-APP WITH HYDROGEN ATOM WAVEFUNCTIONS: http://www.falstad.com/mathphysics.html (Also used in class for infinite square well)

- Link to University of Colorado Applets. (Used in class for free particle wavepacket and scattering)

Wikipedia
- Optical Resonators, cavity stability, cavity modes, resonator types: http://en.wikipedia.org/wiki/Laser_cavity
- Longitudinal modes: http://en.wikipedia.org/wiki/Longitudinal_mode
- Transverse modes: http://en.wikipedia.org/wiki/Transverse_mode
- Eigenvalue, eigenvector: http://en.wikipedia.org/wiki/Eigenvalue
- Gaussian beams: http://en.wikipedia.org/wiki/Gaussian_beam

- Wave particle duality, milestones in QM development: http://en.wikipedia.org/wiki/Wave-particle_duality
- Wavefunction normalization: http://en.wikipedia.org/wiki/Normalisable_wavefunction
- QM expectation values: http://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)
- Mathematical formulation of QM, postulates: http://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics
- Quantum Harmonic Oscillator, including ladder operators: http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

Miscellaneous

Double slit
- Dr Quantum - double slit experiment movie (animated): http://www.youtube.com/watch?v=DfPeprQ7oGc
- REAL double slit experiment movie: http://www.hqrd.hitachi.co.jp/em/doubleslit.cfm

Spherical Harmonics
- a good, quick viewer of spherical harmonics: http://www.bpreid.com/applets/poasDemo.html
- spherical harmonics applet: http://www.quantum-physics.polytechnique.fr/en/ (needs Java, slow to load)

Other applets
- 2D infinite square well eigenfunctions: http://www.bpreid.com/applets/squareDemo.html