What is Nonlinear Optics?
Atoms and molecules and solids are bound by electrostatic fields, and when light shines on them the E-field of the EM wave adds in and changes things, driving a response in the system. Quite typically, light with twice as much intensity drives twice as much response — things are linear. But if the light is intense enough, the E-field obviously can rip everything apart. So linearity can’t be a general rule.
When, and why, does optics become nonlinear? What happens then? And how do we describe it physically and mathematically? Can new relationships lead to new techniques, or new technologies?
This course should be considered a subject of basic literacy in optics, and an important path to many exceptionally useful methods and phenomena in condensed matter physics, plasma physics, astrophysics, atomic and molecular physics, ultrafast optics and laser physics.

Syllabus Description This course offers an introduction to the concepts underlying nonlinear optical phenomena. Topics include: overview of basic formalism and classification  of nonlinear optical processes; non-phase matched processes (e.g. rectification, Kerr effect, soliton  generation, Pockels  effect, two-photon absorption,  degenerate 4-wave mixing, phase conjugation); phase-matched processes (e.g. parametric up and down conversion; THz generation, 2nd  and 3rd harmonic generation); slow nonlinear optics (e.g. photorefraction, optical Drude effects, and other fluence dependent phenomena); spontaneous and stimulated Brillouin and Raman scattering; microscopic (quantum) origins of nonlinear susceptibilities.

Recommended preparation:

PHY 1485 - "Modern Optics"



Basic information (see also course handout)
  • Textbook
“Nonlinear Optics” 3rd edition (Academic Press, 2008) by Robert W. Boyd; the U of T Bookstore has stocked some copies. This book is also available as a free eBook in downloadable PDF from the U of T Libraries, using your UTORid.

  • Other useful texts
“The Principles of Nonlinear Optics” by Y.R. Shen (Wiley-Interscience). 
Perhaps the other most standard text, it has a different style some might prefer and find useful. It is not required.
 
  • Lectures: First lecture Wednesday 7 January 1pm, MP408 -- double-check this with notices posted by elevators

Lecturer
  • Prof. Robin Marjoribanks
  • marjphysics.utoronto.ca
  • Office: MP1104C
  • office hours: Fridays 2–3pm (or by appointment for the couple of people who had conflicts)

Marker
  • Ahmad Golaraei
  • problem sets handed in to dropbox #43 by 5pm on day due
If you have concerns about marking, first see the marker.
The recommended texts are on reserve in the Physics Library, and at Gerstein Science Library.

First Lecture Organizational Topics
  • To sign up for course email, send me an email WITH THE SUBJECT LINE:
PHY2208 SIGNUP

Q: what is a good day & time to set for any make-up lectures?


Special Dates
*Double-check all important dates with the Graduate Office or Faculty of Arts & Science*
January 5 - Lectures begin for Arts & Science; the graduate office asks that we follow their schedule.
January 7 - First lecture; also organizational -- we’ll discuss changing lecture times (may not be possible) and times for any make-up lectures; please bring your personal schedulers/calendars --
double-check this with notices posted by elevators
February 16-20 - Reading Week - no lecture
April 2 - Winter classes end in Arts & Science.

Seminars

Date for Student Seminars: Monday 30 March 2015, 3–6pm (confirmed), room TBD
Download all 2015 presentations (password on request, after presentations given)
This is part of the course, and examinable at some appropriate level. As discussed in class, one mark per group, shared by all members. Normally by PowerPoint or similar, let me know if you need speakers or other needs. Your aim should be to bring ideas and information to your classmates; evaluation will be based on:
• course-related content (nonlinear optics) [relevance and quality of information presented, internet-harvesting not usually sufficient at this level];
• technical preparation [slides easily readable, clear and effective communication, appropriate references];
• presentation [audible, address/engage audience; you don’t want to read out from a page];
• answering questions from class [clear? correct? concise? Better to say so, if you cannot answer -- marks off for bluffing ;-D];
• participation, asking questions of other presentations.
Because groups share one mark, which should be explained, I’ll send comments favorable :-) and unfavorable :-(, and constructive criticism, about each member’s presentation to all members of your group (only).  Please contact me in advance if you have concerns about this approach.

Final Exam

TBD
Similar format to midterm, including definitions, probably a derivation, probably a question closely related to problem-sets. Students are permitted a two-sided hand-prepared aid sheet, no photocopy-reduction or microfilm allowed... more details in class.


Problem Sets & Midterm Dates (dead links will work once items are posted)

Problem sets will be posted two weeks before they’re due. Problem sets are handed in dropbox #43 by 5pm on the day they’re due. Please keep a photocopy/scan/photo of anything handed in, for your protection.
(The following pre-made links will not work until the hand-out dates, or solution-posting dates.)

PS#1 - due 6 February Solutions to PS#1
(you may be interested in this related research paper, which is not particularly useful for your solutions:
S. Banerjee, A. R. Valenzuela, R. C. Shah, A. Maksimchuk, and D. Umstadter, "High-harmonic generation in plasmas from relativistic laser-electron scattering"
J. Opt. Soc. Am. B/Vol. 20, No. 1/January 2003)

PS#2 - due 27 February, Solutions to PS#2
Midterm Test:
Wednesday 4 March 6–8 pm (confirmed) room MP257; Midterm2011; Solutions to MT 2015
PS#3 - due 20 March Solutions to PS#3
PS#4 - due 1 April Solutions to PS#4
Seminar Day: Monday 30 March 2015, 3–6pm (confirmed), room TBD
Final Exam:
(TBD)
 


New Postings:

Lectures & Reading for 2015:
7 January
9 & 14 January-role of polarization response We’ll recap the connection between the applied EM field, the polarization response of the material, its radiated field, and the new net response -- that’s how the phase speed in media changes, which is basically the index of refraction. The polarization can be considered a source term added to the homogeneous wave equation (free space, epsilon-0 and mu-0), or the polarization can be folded into the material field, to make a homogeneous wave equation for propagation in the material (epsilon, and mu, in the material). When we consider nonlinear effects, we can create new light at a new wavelength in the material -- then we’ll really treat the nonlinear polarization as a source term of a new inhomogeneous wave equation.
14 January-dimensionless milestones
21 January-tourofNLO

Useful Boyd reference on optical materials & nonlinear optics:
http://www.optics.rochester.edu/workgroups/boyd/assets/pdf/publications/nlomater.pdf

Boyd writes in his preface:
I am sometimes asked for my advice on extracting the essential material from the book—that is, in determining which are topics that everyone should know. This question often arises in the context of determining what material students should study when preparing for qualifying exams. My best response to questions of this sort is that the essential material is as follows: Chapter 1 in its entirety; Sections 2.1–2.3, 2.4, and 2.10 of Chapter 2; Subsection 3.5.1 of Chapter 3; Sections 4.1, 4.6, and 4.7 of Chapter 4; Chapter 7 in its entirety; Section 8.1 of Chapter 8; and Section 9.1 of Chapter 9.



Collection of illustrations - 2015

movie of indicatrix ellipsoid for phase-matching


Collection of some student questions, and answers -2015

Q: any questions?

A:
Not yet -- waiting for enquiries from folks in lecture or by email...
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Last revised: 4 March 2015 -- © 2015 R.S. Marjoribanks