6.974 / 6.097 Fundamentals of Photonics: Quantum Electronics

Spring 2006

Octave Spanning, 5 Femtosecond Ti:sapphire Laser.Octave Spanning, 5 Femtosecond Ti:sapphire Laser. MIT - Ultrafast Optics Laboratory. (Image courtesy of Richard Ell. Used with permission.)

Course Highlights

This course features a complete set of lecture notes. Quizzes and the final exam are also available in the exams section.

Course Description

This course explores the fundamentals of optical and optoelectronic phenomena and devices based on classical and quantum properties of radiation and matter culminating in lasers and applications. Fundamentals include: Maxwell's electromagnetic waves, resonators and beams, classical ray optics and optical systems, quantum theory of light, matter and its interaction, classical and quantum noise, lasers and laser dynamics, continuous wave and short pulse generation, light modulation; examples from integrated optics and semiconductor optoelectronics and nonlinear optics.


A list of topics covered in the course is available in the calendar.


6.003, 6.013 or 8.07.


The course will have 10 Problem Sets, 2 Quizzes, and Final Exam.

Grading Policy

The grade will be decided based on the results of two quizzes and final exam. The homework will or will not count towards the final grade, depending on the option you choose at the beginning of classes. The table below gives the emphasis that will be given to homework, quizzes, and the final exam in determining the final grade. Note that once you have chosen one of these two options, you will not be allowed to change your mind afterward.

"Homework" Option"No Homework" Option
Final Exam40%50%

Homework Policies

The class will have 10 problem sets which will be distributed during the lecture. Normally the solutions are due in the following week. If for some reason you cannot hand in the solution on time, please contact the teaching assistant before the solution is due. Solutions to the problems will usually be distributed at the next recitation.

As explained above, you will have a "no homework" option, in which case you will not have to solve problem sets. Note however that not doing homework is a bad idea because the homework is necessary to understand the material properly and also prepares you for the quizzes and the final.

Collaboration on problem sets is encouraged. However, you must write your own solutions to the problems rather then copying solutions from somebody else. Please cite all people with whom you have collaborated.

The problem set on which you get the lowest grade will not be counted towards the final grade. Only the top 9 graded problem sets out of the 10 problem sets you have to submit will count towards your final grade.

The grades for homework will depend not only on the correctness of the final result, but also on the ideas used in solution. If the idea is correct but there was some mathematical error during solution you still have a good chance of getting a good grade. It is a good idea to check the final result for physical consistency; if your answer is obviously wrong your grade will be low even if the initial ideas were correct.

The solution must have adequate explanations which demonstrate your approach towards the solution. This does not mean that you need to explain each equation you are writing. Doing so will provide us valuable feedback on your understanding of the concepts. Solutions without adequate explanations will be graded lower.

If you solve problems numerically, please always submit the code together with the results.

Quizzes and Final Exam

The class will have two quizzes and the final exam. The quizzes will be 1.5 hours long, the final exam will be 3 hours long. The problems in the quizzes and final exam are of the similar type than your homework.

Quizzes and final exam will be closed book, i.e. no books, class notes, or other materials are allowed. However, you may take one double-sided page of notes to the first quiz, two pages to the second, and three to the final exam. Using calculators is allowed. Cooperation of any kind is not permitted.


2Maxwell's Equations of Isotropic Media (Review)Problem set 1 out
3Electromagnetic Waves and Interfaces I (Review)
4Electromagnetic Waves and Interfaces IIProblem set 1 due

Problem set 2 out
5Mirrors, Interferometers and Thin-Film StructuresProblem set 2 due

Problem set 3 out
6Gaussian Beams and Paraxial Wave Equation
7Ray Optics and Optical SystemsProblem set 3 due
8Optical Resonators
9Integrated Optics: WaveguidesQuiz 1 week

Problem set 4 out
10Integrated Optics: Coupled Mode Theory
11Optical FibersProblem set 4 due

Problem set 5 out
12Anisotropic Media: Crystal Optics and Polarization
13Quantum Nature of Light and MatterProblem set 5 due

Problem set 6 out
14Schrödinger Equation and Stationary States
15Harmonic Oscillator and Hydrogen AtomProblem set 6 due

Problem set 7 out
16Wave Mechanics
17Dirac Formalism and Matrix MechanicsProblem set 7 due
18Harmonic Oscillator RevisitedQuiz 2 week

Problem set 8 out
19Coherent States
20Interaction of Light and Mater the Two-Level Atom: Rabi-OscillationsProblem set 8 due

Problem set 9 out
21Density Matrix, Energy and Phase Relaxation
22Rate Equations, Dispersion, Absorption and GainProblem set 9 due

Problem set 10 out
23Optical Amplifiers and Lasers
24Homogenous and Inhomogenous Broadening and Related EffectsProblem set 10 due
25Q-Switching and Mode Locking
26Electro- and Acousto-Optic Modulation


Amazon logo Help support MIT OpenCourseWare by shopping at! MIT OpenCourseWare offers direct links to to purchase the books cited in this course. Click on the book titles and purchase the book from, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.

Required Text

Class notes, available in the lecture notes section.

Recommended Texts

Saleh, B. E. A., and M. C. Teich. Fundamentals of Photonics. New York, NY: John Wiley and Sons, 1991. ISBN: 0471839655.

Hecht, E., and A. Zajac. Optics. 3rd ed. Reading, MA: Addison-Wesley, 1997. ISBN: 0201838877.

Griffiths, D. Introduction to Quantum Mechanics. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1995. ISBN: 0131118927.

Cohen-Tannoudji, C., B. Diu, and F. Laloe. Quantum Mechanics I. New York, NY: John Wiley and Sons, 1992. ISBN: 0471569526.

Additional Texts

Yariv, A. Optical Electronics in Modern Communications. 5th ed. New York, NY: Oxford University Press, 1997. ISBN: 0195106261.

Svelto, O. Principles of Lasers. New York, NY: Springer-Verlag, 2004. ISBN: 0306457482.

Haus, H. A. Waves and Fields in Optoelectronics. Upper Saddle River, NJ: Prentice Hall, 1983. ISBN: 0139460535.

Allen, L., and J. H. Eberly. Optical Resonance and Two-Level Atoms. New ed. New York, NY: Dover, 1987. ISBN: 0486655334.

Liu, Jia-Ming. Photonic Devices. Cambridge, UK: Cambridge University Press, 2005. ISBN: 0521551951.

Meystre, P., and M. Sargent, III. Elements of Quantum Optics. 3rd ed. New York, NY: Springer-Verlag, 1986. ISBN: 354064220X.

Lecture Notes

This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.


Maxwell's Equations of Isotropic Media (Review)

Electromagnetic Waves and Interfaces I (Review)

Electromagnetic Waves and Interfaces II

Mirrors, Interferometers and Thin-Film Structures

Gaussian Beams and Paraxial Wave Equation

Ray Optics and Optical Systems

Optical Resonators

Integrated Optics: Waveguides

Integrated Optics: Coupled Mode Theory

Optical Fibers

Anisotropic Media: Crystal Optics and Polarization

(PDF - 2.5 MB)#
13Quantum Nature of Light and Matter(PDF)#
14-16Schrödinger Equation and Stationary States

Harmonic Oscillator and Hydrogen Atom

Wave Mechanics
17-19Dirac Formalism and Matrix Mechanics

Harmonic Oscillator Revisited

Coherent States
20-22Interaction of Light and Mater the Two-Level Atom: Rabi-Oscillations

Density Matrix, Energy and Phase Relaxation

Rate Equations, Dispersion, Absorption and Gain
23-26Optical Amplifiers and Lasers

Homogenous and Inhomogenous Broadening and Related Effects

Q-Switching and Mode Locking

Electro- and Acousto-Optic Modulation


This section contains the quizzes and final exam given in the course.

Quiz 1 (PDF)

Quiz 2 (PDF)

Final Exam (PDF)



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