Nonlinear Optics

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Course Information

Professor: Chip Durfee

Office: Meyer Hall 330

Meeting Times: Monday, Wednesday 11:00-12:15

Room: Hill Hall 211

Office hours: - TBA

Announcements

7 March: Homework 4 comments:

Problem 1: Assume chi(3) is the same in the glass and in the water. You can set your coordinate system such that z = 0 is at the beam waist, and the interface is at some other z position, zI. Then you'll be looking at two integrals, from -infinity to zI through water, then from zI to plus infinity. Note that the spot size is connected to the f/number: w = (2/π) λ f/number.

Problem 2: δ is a measure of the ellipticity of the state. It is a function of Aplus and Aminus, so you should be able to express Aplus and Aminus in terms of δ. From there, you can then calculate the Δn.

2 March: Homework 4 will be due next wednesday instead of monday, since some of you have an EM project due on Monday.

1 March: Homework 4 is posted, due next monday at the end of the day. Solutions to HW3 are available - come by my office to pick them up.

14 Feb: Homework 3 is due a week from Tuesday instead of Monday since there is no class that monday. Lecture notes are all scanned and posted.

12 Feb: Homework 3 is posted, due a week from Monday.

2 Feb: Caught up with notes scanning. Homework 2 is posted, due next wednesday.

If you are new to Mathematica, try doing the Wolfram screencast introduction, which you can find at http://url.wolfram.com/4enrnS/ 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.

12 Jan: Welcome to the new Wiki page for Nonlinear Optics! The syllabus is posted below. You'll see an old sections for Lecture Notes with some scans of notes from previous years. Note that the '07 version is in Gaussian units. I've scanned and posted the notes for our first lecture. The first homework will be posted soon.

Office hours

Office hours:

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

Course Material

Syllabus and Reading List

These downloads require Adobe Acrobat Reader Syllabus for the course

Homework Assignments

These downloads require Adobe Acrobat Reader Fourier transform ID sheet, t-omega domains LiIO3 datasheet. This has the dispersion information in it. Homework 1, due wednesday 21 Jan 2011. End of day (5pm) in my mailbox is OK. Homework 2, due wednesday 9 Feb 2011. Homework 3, due wednesday 21 Feb 2011. Homework 4, due Monday 7 March 2011.

Lecture Notes 2011

These downloads require Adobe Acrobat Reader Lecture 1: intro, define NL polarization Lecture 2: classical oscillator model Lecture 2: slides Lecture 3: tensor symmetries Lecture 3: slides Lecture 4: time-dependent chi, mixing propagation equations Lecture 5: polarization, birefringence, waveplates Lecture 6: index ellipsoid, birefringent phase matching Lecture 7: electro-optics, quasi-phasematching Lecture 8: beam crossing, pulse autocorrelation Lecture 9: NL index, tensor chi3, polarization gating and NL ellipse rotation

Lecture Notes 2009

These downloads require Adobe Acrobat Reader Lecture 13: perturbation theory in quantum Lecture 12: viewgraphs on dispersion in ultrafast optics (courtesy R. Trebino, GaTech Lecture 12: viewgraphs on guided wave NLO research (from a talk I gave a few years ago Lecture 11: linear propagation of wide bandwidth light using Fourier transforms. Includes more on Gaussian pulses than covered in class. Lecture 11 chirped pulses. Also includes a bit on the impulse response of dielectric materials, which loosely follows Jackson 7.10 2nd edition Lecture 10: guided waves, time-freq domain Lecture 9: crossed-beam mixing Lecture 9: gaussian beams Lecture 9: walkoff Lecture 8: quasiphasematching Lecture 8: solution of mixing equations Notes for Lecture 7: Birefringence and the index ellipsoid. Some derivations here that weren't in class) Reading for Lecture 7: Birefringence and the index ellipsoid.) Lecture 6: Slides discussing OPA paper. (As we work through this, I'll be filling in and revising this.) Lecture 6: phase mismatch, start of birefringence Lecture 5: NL propagation equations Lecture 4: symmetries and NL chi Lecture 3:classical oscillator model of nonlinear electron response Lecture 2: definition of the NL chi Lecture 1: handwritten notes for introduction Lecture 1: introduction (slides courtesy R. Trebino, GaTech, see link below)

Lecture Notes 2007

These will be revised as we go along. Note that they are in Gaussian units, not SI. It looks like I had scanned just past halfway through the course. I'll see if I can find someone to help scan the rest.

These downloads require Adobe Acrobat Reader Fourier transform sheet: t and omega Lecture 1: survey slides (courtesy R. Trebino, GaTech (see link below), with changes to units to gaussian Lecture 2: part 1, nonlinear wave equation and NL effects Lecture 2: part 2, linear and NL classical model Lecture 3: symmetries in chi Lecture 4: time-freq representations Lecture 5: HHG and NL wave mixing equations Lecture 6: NL wave mixing solutions Lecture 7: Birefringence and phase matching Lecture 8: quasi-phase matching and NLO with focused Gaussian beams Lecture 9: notes on guided-wave NLO Lecture 9: talk slides on cascaded guided wave frequency mixing Lecture 10: Time dependent perturbation theory, QM calc of chi Lecture 11: Transition rates, Intro to NL refractive index Lecture 12: NL refr index, NL ellipse rotation Lecture 13: mechanisms for n2: electronic, molecular, thermal, relativistic filamentation and phase conjugation dispersive pulse propagation: linear and nonlinear split step spatial propagation

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)

2011 files (these have been updated to run in v8.)

These downloads require Adobe Acrobat Reader Nonpert_nlo_response.nb: classical model of time dependent nonlinear response (3rd order), solved with NDSolve. Includes FFT to show harmonic structure chi2map.nb: using classical NL model, map of chi2 vs input frequencies, showing resonance locations Crystal_symmetries.nb: demonstrate effect of crystal symmetries, calculate angular dependence of deff. This has some examples of working with vectors and matrices in Mathematica. Phase_match_KDP.nb: Phase matching program for KDP crystals Mixing_solutions.nb: solutions of simultaneous NL eqns for doubling fft demo.nb: demonstrate numerical Fourier transforms (FFT)

2007 files (written in v5.2, but can be read into v6 or v7 and updated)

These downloads require Adobe Acrobat Reader NL prop code List convolve demo.nb: demonstrate numerical convolutions Hhg_simple_model.nb: kinetic model of electron motion in high-order harmonic generation

Links to literature in nonlinear optics

Feel free to add to the list of database and journal sites

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. Good for Optics Letters, Optics Express, Applied Optics, JOSA A and B, etc

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 journals are European journals that are not indexed through Scitation or Optics Infobase.

Applied Physics B

Journal of Physics B

Optics Communications

Journal Articles

Each one of you should add references you think would be of general interest to this list. We will have a rotating schedule for when it will be your turn. (Please note that this will be part of your grade...)

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.

Development of the theory, historical

• 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)

Optical parametric amplifiers

• Brida, et al. Optics Express V15 p15035 (2007) "Generation of broadband mid-infrared pulses from an optical parametric amplifier" Brida OPA 1 (Durfee 1/19/09)-This is the paper we are working through in class as an example of an ultrafast OPA.

High-order harmonic generation

• Corkum, Physical Review Letters V71 p1994 (1993) "Plasma Perspective on strong-field multiphoton ionization" Corkum (1993) (Durfee 1/22/07)-This is one of the first papers with a simple, semi-classical model of high-order harmonic generation and other strong-field effects that take place during tunneling ionization.

• Kapteyn, Henry: slides from a talk at LLBL (2005) "Coherent XUV Radiation: High-harmonic generation" Kapteyn HHG talk (Durfee 1/23/07) - This is a nice summary of the high-order harmonic generation process and some of the recent developments of the field.

Self-focusing, spatial solitons

• Neshev et al, Optics Letters V28 p710 (2003) "Spatial solitons in optically induced gratings" On Campus Link (Murrell 1/16/07)-Interesting Paper on a nonlinear optics application from the first lecture.

• Chin "et al", Can. J. Phys. 83:863-905 (2005) "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges" [1] (A. Meier 4/27/11)-A review of filamentation.

Ultrafast Nonlinear Optics

• S. Zhang, et al, Optics Letters V30 p2852-2854 (2005) "Passive mode locking at harmonics of the free spectral range of the intracavity filter in a fiber ring laser," On Campus Link (Murrell 1/29/07)-An experimental writeup on a passivly mode locked ring laser via polarization controllers in the cavity.

• opticsinfobase & osa Dan Adams (2/22) These articles describes the process of measuring ultrashort light pulses by using a frequency resolved optical gate that consists of a nonlinear crystal. Many types of this device exist and have been cited in class.

• T. Brabec, et al, Optics Letters, Vol. 17, Issue 18, pp. 1292-1294 (1992) "Kerr lens mode locking" opticsinfobase (B. Galloway 1/25/2011). An article describing an optical system in a laser oscillator to allow passive mode locking using a Kerr lens and an aperture. Aspects like dependence of gain on intracavity power and the stability parameter are included in the analysis.

• H. Hirori, et al, "Single Cycle THz Pulses with amplitudes exceeding 1MV/cm generated by optical rectification in LiNbO3" arxiv (K. Strovink 2/14/2011). Describes a method for creating coherent, ultrashort pulses at 1THz.

Imaging with Harmonic Generation

• J. Squier, M. Muller, Applied Optics V38 p5789-5794 (1999) "Third-Harmonic generation imaging of laser-induced breakdown in glass," On Campus Link (Hrin 1/31/07)-A description of how harmonic generation can be used to image sub-micron structures and features.

• Kuang Yao Lo, Juh Tzeng Lue, Physical Review B V 51 (4) p2467-2472 (1995) "Quantum size effect on optical second-harmonic generation in small metal particles," On Campus Link (Hrin 2/21/07)-Theoretical and experimental work looking at SHG from quantum confined systems

Stimulated Brillouin Scattering

• V. I. Kovalev and R. G. Harrison, Opt. Lett. 30, 3389-3391 (2005) "Origin of temporally stable continuous-wave Stokes emission in stimulated Brillouin scattering: evidence of spectral self-phase conjugation," Kovalev & Harrison (2005) (Hoffman 2/27/07)- Useful Article talking about SBS and phase conjugation.

• A. A. Fotiadi, P. Mégret, and M. Blondel, Opt. Lett. 29, 1078-1080 (2004) "Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror," Fotiadi, Mégret, & Blondel (2004) (Hoffman 2/27/07)- Interesting Article using SBS to Q-switch a fiber laser.

Nonlinear Surface Plasmons

• D. Sarid, Appl. Phys. Lett. 39, 889 (1981) "The nonlinear propagation constant of a surface plasmon," Sarid (1981) (Perzinski 3/29/2007)-A description for an expression for the change in the propagation constant.

• D. Sarid, R. T. Deck, and J. J. Fasano, J. Opt. Soc. Am. 72, 1345- (1982) "Enhanced nonlinearity of the propagation constant of a long-range surface-plasma wave," Sarid (1982) (Perzinski 3/29/2007)-A description of the propagation constant as a function of the thickness of the metal film bounded by a nonlinear semiconductor.

• H. J. Simon, D. E. Mitchell, and J. G. Watson, Phys. Rev. Lett. 33, 1531 - 1534 (1974), "Optical Second-Harmonic Generation with Surface Plasmons in Silver Films," Simon (1974) (Perzinski 3/29/2007)-First experimental investigation of coupling SHG to surface plasmons on silver films.

Misc cool papers

• M. McCall, A. Favaro, P. Kinsler and A. Boardman, J. Opt. v13, 024003 (2011) "A spacetime cloak, or a history editor." McCall (2011) (Durfee 1/19/2011)-How to hide from a time-machine?

• R.W. Boyd and D. Gauthier, Science, 326,1074-1077 (2009) "Controlling the Velocity of Light Pulses," Boyd (2009) (Lemmon, 5/12/2011) -Nice review of slow and fast light techniques and applications

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

Falstad.com: some nice optics demos