Fourier Optics

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Course Information

Professor: Chip Durfee (John Scales and Jeff Squier will be teaching sections of the course.)

Office: Meyer Hall 330

Meeting Times: Wednesday 9:00-10:30. This may change as we see what works for everyone.

Room: 1st 3 weeks: Green 281. Rest of semester: Meyer physics library

Office hours: - TBA


5 Mar: Homework 5 (? I think John S. gave you one HW) is posted. We might add one problem on the eikonal/ray equation, but what is posted will get you started. I'll be around for questions...

1 Feb: Reminder: class meets this week in the physics library. On Feb 9th, class will be back in Green 281, but after that, all classes will be in the Physics library. Tomorrow, we can work on some programming of pulse propagation and compression. Bring your computers if you can.

Homework 3 is posted (the one I emailed to you), along with notes from last class. Tomorrow, we'll talk about pulse compression and shaping, then go over 2D FT in the spatial domain. We're now on the Goodman book, so you can go through ch 2 if you haven't already.

20 Jan: Homework 2 is posted, due next week in class. For next class, read about sampling theory - both in Goodman ch2 and in my posted notes.

19 Jan: Notes, ListConvolve.nb posted. The last section of notes are on sampling theory and the FFT. Please read those and also review linear dispersion. In week 3 (next week), we'll talk about pulse propagation, spectral and temporal phase, and pulse compression. I'll post some exercises for next week soon.

12 Jan: Reading and work for the second week: I have posted a complete set of notes related to Fourier transform pairs, IDs and theorems. Please be sure to work through the transform ID's and theorems on your own, making sure you see how to derive each of them - shift, scale, ... The Gaskill and Bracewell books on reserve are also good references for these (especially if my notes don't have enough detail for you). The better you understand them, the easier it is to identify when to use them.

Homework 1 is posted - due in class next week. Just 3 problems.

If you all can go through these, we can use our limited class time more productively by working realistic examples.

If you are new to Mathematica, try doing the Wolfram screencast introduction, which you can find at I haven't tried this myself, but it's probably worth the time to help you get started. After going through that, feel free to come by during office hours to ask questions about working with Mathematica.

8 Jan: Welcome to the new Wiki page for Fourier Optics! The syllabus is posted below.

Office hours

Office hours:

tentative times - M12:30-3:30, W12:30-2:30.

Course Material

Syllabus and Reading List

Tentative reading list is posted - I'll make changes as we go along, but this will give you an idea of what parts of the book we'll go through.

Pdf.png These downloads require Adobe Acrobat Reader
Syllabus for the course

Fourier Transform ID sheets and other reference material

Note that the conventions (sign, 2 pi, ...) are different for the t-omega and x-fx domains.

Pdf.png These downloads require Adobe Acrobat Reader
Fourier transform ID sheet, t-omega domains

Homework Assignments

Pdf.png These downloads require Adobe Acrobat Reader
Homework 1, due in class 19 Jan
Homework 2, due in class 26 Jan
Homework 3, due in class 2 Feb
Homework 5, due friday, 11 March

Lecture Notes

Pdf.png These downloads require Adobe Acrobat Reader
Week 1: intro to Fourier optics, transform IDs and theorems
Week 2: some illustrations of convolution (see also listconvolve.nb below
Week 2: examples, linear systems, sampling theory
Week 3: sampling theory (better version), FFT's and dispersive pulse propagation
Week 4: pulse compression (today we also talked about dispersive propagation/role of group delay

Mathematica Demos

You can use these as a template for programming you want to do. I would like you to attribute me when you do though.

These aren't actually pdf's. Do a "save link as" to save these to your computer, then open with Mathematica. In most cases the output has been deleted to save server space, so you have to run the code to see the output.

Please note that thee is a bug in the Fourier[ ] routine (FFT) in v7.0.0. This does not show in earlier versions, and was fixed in 7.0.1 and later. (8.0.0 is the current version)

Pdf.png These downloads require Adobe Acrobat Reader
List convolve demo.nb: demonstrate numerical convolutions
fft demo.nb: demonstrate numerical Fourier transforms (FFT)

some older files (written in v5.2. These will be updated soon and posted above.)

Pdf.png These downloads require Adobe Acrobat Reader
NL prop code

Links to literature in Fourier optics

Each one of you should add references you think would be of general interest to this list - a minimum of one every other week.

Click 'edit' at the right to add references. Include a short description, make a new category if it makes sense. Links only - don't upload actual pdf's please. Put your last name and posting date along with the citation.

Feel free to add to the list of database and journal sites. The list below is old - let me know if any of the links are dead.

Journal Database pages

Use these to go to papers where you know the reference, or for searching for related papers

Scitation: American Institute of Physics journals search

Optics Infobase: Optical Society of America journal search

CSM link to physics-related databases. In particular, try Web of Science (online Science Citation Index). This is the best resource for finding papers that are related to each other. I think our access goes back 10 years from present.

Google Scholar

Journal pages

You can go to these to browse current issues or to look up specific references.These journal are (mostly) European journals not indexed through Scitation or Optics Infobase. Go to OpticsInfoBase for Optics Letters, Josa A and B, Optics Express, Applied Optics, etc.

Applied Physics B

Journal of Physics B

Optics Communications

Journal Articles

Development of the theory, historical

this is a sample link

  • Midwinter et al, British J. Applied Phys v16 p1135 (1965) "The effects of phase matching method and of uniaxial crystal symmetry on the polar distribution of second-order non-linear optical polarization" Derivation of the variation of dEff in nonlinear crystals with beam direction. (Durfee 1/12/2007) Midwinter (1965)

Other course Links

JavaOptics: a nice collection of optics-related demonstrations

Lectures from GaTech (Rick Trebino): a very useful collection of graphics and worked examples in optics. One of the courses he has taught is in ultrafast optics - relevant for this course.

Fabry-Perot demonstration some nice optics demos

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