PHGN-570 Spring-2016

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Course Information

Professor: Chip Durfee

Office: Timberline trailer #1, room 15

Meeting Times: Monday, Wednesday 4:30-5:45.

Room: Alderson 340


1 Mar: HW3 clarifications: More clarifications:

Problems 3-7 are all for the same experimental situation.

For problem 3c, assume the beam is in the lowest order, 11 mode. Keep in mind, that in contrast to the example I worked in class, the core of the waveguide is glass (you can use fused silica), so you need to modify the dispersion expression to include the dispersion of that material.

For problem 4, set the wavelength to 800nm and the window length 1mm. problem 1: First set up the calculation so you can look at the pulse in the time domain for a given input Taylor series spectral phase. Then you vary the amount of the different phase orders (phi2, phi3, phi4) until the FWHM is about 3x the original pulse. This is to give a feel for what order of magnitude of these parameters makes a difference.

Problem 2: There was a typo and an important missing line of explanation. The corrected version is re-posted as of now (10:30am tuesday).

Also, to help you out, I've posted in the Mathematica demo section below the exercise in pulse propagation and compression that we worked on last week. This version has working code and plots.

24 Feb: Today we will meet at 4pm in CTLM 231 for some hands-on computer work.

17 Feb: Homework 3 is posted. It will be due in class, 2 March. There are a number of problems, so don't hold off on working on it, and come see me for help if you need it.

1 Feb: Homework 2 is posted. work on problems 3 and 5 before class on Wednesday, so you can ask questions in class. I am still waiting for confirmation, but we should be meeting in CTLM room B56 Wednesday at 4pm, where they will have computers we can use.

27 Jan: In class today, I discussed an alternate approach to understanding the Kramers-Kronig relations without contour integration. Here is a link to a nice document that explains it well. link Understanding the Kramers-Kronig Relation Using A Pictorial Proof by Colin Warwick

26 Jan: Homework 1 notes:

You can have 2 more days to do the homework, now due by 5pm Friday in my mailbox.

for problem 1 the Theta function is the Heaviside step function, or UnitStep[ ] in Mathematica.

In problem 3, I had the inequality backwards, it should be T << t_1, so that the separation is greater than the width of the pulses.

Both of these are corrected in the currently posted version.

For wednesday, we will start at 4pm. Please bring a laptop that can run Mathematica.

25 Jan: We will meet at the regular time today, but think about starting earlier at 4 on wednesday. Also, in class today, can you let me know if you each have a laptop that can run mathematica? If so, we could do some computational exercises in class.

19 Jan: HW 1 is posted below.

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

For Monday's class, please go over transform pairs for Gaussian and Dirac delta functions, as well as linearity, shift and scale theorems, Parseval's theorem, and symmetry properties of Fourier transforms. We'll do in-class exercises with these.

I don't have any other travel planned for the semester yet, but this upcoming week, I have a meeting in DC for a project that is just starting up. The meeting is all day thursday and friday, and I can't get a flight out later than 4:30. This means that I will have to miss that class (01/20). On monday we'll discuss how to make that up.

Office hours

Office hours:

Tentative: Monday 1-4, Wed 1-3

Course Material

Syllabus and Reading List

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
HW 1: due Wednesday 27 Jan in class
HW 2: due Wednesday 10 Feb in class
HW 3: due Wednesday 2 March in class. This version was re-posted to fix some typo's in problem 2.

Lecture Notes

This list is from 2016

Pdf.png These downloads require Adobe Acrobat Reader
Class 1: intro to Fourier optics
Class 2: FT pairs, theorems
Class 3: Parseval, Convolution
Class 4: Linear systems
Class 5: classical dispersion theory, Fabry-Perot transfer function and impulse response
pulse propagation and compression
sampling theory notes
pulse characterization, derivation of the nonlinear Schroedinger equation
foundations of diffraction theory

This list below is from 2014. New notes will be posted above this.

Pdf.png These downloads require Adobe Acrobat Reader
Class 1: intro to Fourier optics, transform pairs
Class 2: FT IDs and symmetry relations
Class 3: examples, Parseval and convolution theorem. See ListConvolve.nb below
Class 4: convolution examples, linear systems introduction
Class 5: impulse response and transfer functions, spectral interferometry
Class 6: MMA demonstration of quasi-monochromatic waves ( .nb file, use "save link as..."). Run file to see all the graphics.
Class 7: review of EM waves, calculation of intensity, Michelson interferometer, autocorrelation thm and Fourier transform spectroscopy
Class 8: slides for Fabry-Perot resonator as a linear system
Class 8: array theorem and sampling theory notes. See also fft demo code below in mathematica demo section
Class 9: review of classical oscillator model of dispersion theory
Class 10: dispersive pulse propagation, gaussian pulse stretching
Class 11: pulse compression
Class 12: Gerchberg-Saxton algorithm for phase optimization and pulse shaping. Download .nb file and evaluate entire notebook to see output.
Class 13: self-phase modulation, continuum generation
Class 14: derivation of the Nonlinear Schrodinger eqn
Class 16: derivation of diffraction integral
diffraction, angular spectrum, fresnel to fraunhofer approx, fraunhofer examples, diffraction gratings.

For class 3: Online demonstration of convolution of various functions. See other tabs on this webpage for notes about convolutions.

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. (9.0.1 is the current version)

Pdf.png These downloads require Adobe Acrobat Reader
Fft_and_listconvolve.nb: demonstrate numerical Fourier transforms (FFT) and convolutions. Updated 2014-02-04.
List convolve demo.nb: demonstrate both analytical and numerical convolutions
pulse propagation and compression exercises - working code

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

Spectral interferometry

sample link - more to come...

  • 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

Signals and Systems | MIT OpenCourseWare

JavaOptics: a nice collection of optics-related demonstrations

Fabry-Perot demonstration some nice optics demos

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