A nice view of modern optics has it that the subject of optics began afresh with the invention of the laser. We'll take the laser as a pivot-point, and look backwards from its invention to the classical optics needed to understand how the laser tailors light, and forward to the quantum optics explosion that has followed. We'll study: basic optics, diffraction theory, gaussian beams, laser resonators, semiclassical laser theory, and ultrafast pulse generation. In group presentations, we'll also review a selection from the remarkable range of currently active research topics: laser cooling, photonic bandgap structures, extreme optics, quantum information and other topics.
The course should be considered a subject of basic physics literacy, particularly in optics.
Basic information (see also course handout)- Textbook
- Recommended purchase (in general, also for other courses!)
(2002 printing ~$23 Amazon.ca, cheaper than 1995 printing)
- Other recommended texts (regular use in library probably sufficient)
Other reference material is described in the course handout
- Lectures: T, R 3pm MP137
Lecturer- Prof. Robin Marjoribanks
- marj
physics.utoronto.ca - Office: MP1104C
- office hours: Wednesdays 2-3 pm
MarkersPS #1, 2
- ZHOU Jing
- jzou
lphys.chem.utoronto.ca - Office: MP039
- McKINNEY, Luke
- mckinney
physics.utoronto.ca - Office: MP021 (MP092 while MP021 under construction)
The recommended texts are on reserve in the Physics Library, and at Gerstein Science Library.
Special Dates*Double-check dates at Faculty of Arts & Science*
September 8 - Fall term classes begin in F and Y section code courses
September 21 - Last day to add courses with F and Y section codes
October 17 - Examination timetable for F section code courses posted
November 3 - Last day to drop courses with F section codes from academic record and GPA. After this deadline a mark is recorded for each course, whether course work is completed or not (a "0" is assigned for incomplete work), and calculated into the GPA.
December 5 - Fall classes end
Problem Sets & Midterm Dates (links will work once items are posted)Problem sets are handed in to the Drop Box (#25 PHY485/1485, Jing Zou), basement floor stairwell opposite elevators, by 5pm on the day due. Please keep a photocopy of anything handed in.
PS#1 - out 18 September, due 6 October 2008 Solutions to PS#1 Solutions to PS#1-missing materials
PS#2 - out 7 October, due 23 October 2008 (extended), Solutions to PS#2
Midterm Test: (now confirmed) Friday 31 October 2008, 4-6pm, room BA-2139 (Bahen building); Midterm2008; Solutions to MT 2008
PS#3 - out 30 October, due 13 November 2008 TA-Solutions to PS#3
PS#4 - out 20 November, due 4 December 2008 (note: Faculty rules prohibit extensions beyond last day of term) DRAFT Solutions to PS#4 (RSM); TA Solutions to PS#4 (revised)
Seminar Day: Saturday 29 November, 10am-5pm, MP137
New Postings:Diffraction Demo (Java applet; open “index.html” in your Java-aware browser) This gives quite a good ‘feel’ for diffraction.
Dispersion Primer (sent by email)
Resonance Demo (Mac)/(Wintel)
Polarization Demo (Mac)/(Wintel)
Note that these require downloading the FREE LabVIEW 7.1 Runtime Engine from National Instruments. This means you don’t have to own LabVIEW 7.1; you need a different engine for Windows/Mac OS X/Linux.
http://zone.ni.com/reference/en-XX/help/lv/71/lvhelp/Using_the_LV_Run_Time_Eng/
Topics and sections of Hecht for first half of course:
Meaning of Index of Refraction
-Maxwell's equations and wave equations in vacuum; speed of light from epsilon and mu
-the same in media
-closure by the constitutive relations
-characterizing how the constitutive relations (esp. electric susceptibility) contain all info about interaction
-non-locality in time for electric susceptibility
-how this is much simplified in frequency space; equivalence of harmonic representation, for our linear equations
-dielectric function, leading to index of refraction
-interpretation of real, imaginary parts
Impact of Index of Refraction
-connection to Lorentz model, reasonableness of this phenomenological model
-connection between real, imaginary parts; Kramers-Kronig relation
-relation of field and oscillator phase, from driven, damped SHO
-radiated field from Lorentz model adds to incident field; the sum of fields leads to net field at shifted phase
-thus propagating wave sees different phase speed
-simple dispersion (and connection to non-locality in time)
-group-velocity dispersion, propagation of energy and information
-frequency-chirped pulses and spreading of pulses
Anisotropic Index of Refraction
-electric susceptibility generally a tensor; anisotropic crystals, nanostructured materials
-leads to index, phase-speed difference according to direction of E-field for a single k (polarization)
-different states of polarization, connection to Lissajous figures; amplitude and phase contributions
-birefringence (e.g., calcite crystal)--> discrimination of x and y directions of E
-optical activity (e.g., sugar solution) --> discrimination of right and left helicities (handedness) of E
-manipulation of polarization by waveplates (QWP, HWP)
-Jones calculus formalism for manipulation of polarization
Reading
Sections of Hecht are relevant to what we've been studying: here's what I see when I scan through relevant material in Hecht (which is organized a little differently than our plan). Note that the class is a diverse mix of grads and undergrads in Physics, Chemistry and Engineering, and folks’ backgrounds are therefore quite varied; I've marked below the sections that the course, at this level, assumes you already know.
Ch 1: introductory
Ch 2: expected you already know this...
Ch 3: to 3.3.1, you should already know...
3.3.2 Irradiance
3.3.3 mostly you already know
3.3.4 radiation pressure
3.4 you mostly already know
3.5 Light in Bulk matter, directly relevant
3.6, 3.7 interesting but not specifically discussed in our course
Ch 4: to 4.2.2 not yet discussed
4.2.3 as discussed in lecture
4.3-4.7 future lectures, not covered in first half
4.8 Optical properties of metals, but we haven't begun discussion of reflection yet
4.9 onwards, not covered
Ch 5, 6: not yet covered (we will in second half)
Ch 7: 7.1, 7.2 expected you already know
7.2.2 group velocity, at a lower level than we've done -- but discussions very informative
7.2, 7.4 expected you already know
7.4.2 coherence length -- not yet done in our course, but we will do in deeper detail
Ch 8: to 8.4.2 inclusive, covered
8.5, 8.6 not yet covered
8.7 - 8.11.2 inclusive; we haven't done 8.11.3 yet but we will
8.12 liquid crystals
8.13 Jones Calculus, not Müller matrices
Chapters of Hecht, and other material, for second half of course:
Ch 4.3-4.7 reflection, Fresnel equations (having already done 4.8)
Ch 5 Geometrical Optics - but using ray-matrices
Ch 6 More on Geometrical Optics - this chapter ‘lite’ (a reading understanding), but attention to aberrations
Ch 9 Interference
Ch 12 Basic CoherenceTheory
Ch 10 Diffraction (emphasis on Fraunhofer diffraction)
Gaussian beams (connection to Fraunhofer -- Fourier transform of gaussian is gaussian in far-field; paraxial wave equation, Gaussian solution in all fields; complex beam parameter q; transformation of Gaussian beams uses ABCD matrix elements, but in fractional-linear transformation)
laser-cavity stability (Fabry-Perot; stable cavity eigenmodes q = T(q) )
introduction to lasers
Hecht discusses many interesting and edifying things, one big reason we're using his book, and I encourage you to use those new concepts and applications to make things relevant to your own individual interests! He discusses many more ramifications and illustrations than we can deal with in class, though.
Lecture NotesMany parts of these notes are adapted or taken from materials made available by Professor Rick Trebino at Georgia Tech -- he's done a wonderful service! Please don't distribute these notes further, they are © R Trebino, used by permission.
Lectures for 2008 are now complete. All materials not from Professor Trebino are © RS Marjoribanks, 2003-2008.
Lecture 0
Lecture 1
Lecture 2
Lecture 3 (plus blackboard lecture)
(up to around here covered in Hecht Ch. 2)
EM Spectrum Survey (show-and-tell) [16.5MB]
Lecture 4 (+ blackboard lecture, cf. Hecht Ch. 3)
Lecture 5 (+ blackboard lecture, cf. Hecht Ch. 3.5-->)
Lecture 6 (finish slides from Lecture 5, + blackboard lecture, cf. Hecht section 3.5)
Lecture 7
Lecture 8 (blackboard & materials from Lecture 7 slides)
Lecture 9 (blackboard & materials from Lecture 7 slides)
Lecture 10 (Polarization I)
missed lecture (21 October)
Lecture 11 (Polarization II - 23 October)
Lecture 12 (Polarization, Optical Activity - 28 October)
Lecture 13 (Stokes (cnt’d), Fresnel - 30 October)
Lecture 14 (Fresnel (cnt’d), 4 November ‘makeup’)
Lecture 15 (4 November regular; geometrical optics)
Lecture 16 (geometrical optics, materials from Lecture 15 slides)
Lecture 17 (11 November ‘makeup’: ray matrices, materials from Lecture 15 slides)
Lecture 18 (11 November ‘regular’: ray matrices, aberrations, materials from Lecture 15 slides)
Lecture 19 (13 November; coherence)
Lecture 20 (18 November; coherence & interference -- mostly blackboard)
Lecture 21 (20 November; coherence & interference, Fabry Perot)
Lecture 22 (25 November; more interference, begin diffraction)
Lecture 23 (27 November; diffraction -- also demo of Fresnel diffraction)
Lecture 24 (2 December; blackboard lecture -- Fraunhofer diffraction, Gaussian beams; NB: not responsible for the extra content of this set of slides, FYI)
Lecture 25 (4 December; blackboard lecture -- paraxial wave equation, Gaussian beams, intro to resonator)
Extra material: links, illustrations and commentsRemember that you are permitted ONLY the aid sheet attached to this year's exam, as discussed in lecture. You are NOT permitted your own aid sheet. Suggest you review the one below, checking for what you think may be missing, and memorize the small balance of any materials.
AidSheet2006
Final Exam from PHY485/1860F in 2004
AidSheet for final exam PHY485/1860F in 2004
Final Exam from PHY485/1860F in 2003 AidSheet2003
Midterm Exam from PHY485/1860F in 2007 Solutions to MT2007
Collection of some student questions, and answersQ: In Problem Set #1, Question 2 ( c ), is the “1 / c” term, in the first equation, correct? The equation does not seem to be dimensionally consistent.
And the second equation also seems to be dimensionally inconsistent in that “-e.(v X B) “ has units of force or momentum/sec, not energy per second.
A: The difference is what system of units one is in -- these formulae on the problem set are in cgs, pretty standard with theorists. In class we've been using SI (~MKS), more common among experimentalists and engineers.
Physicists switch back and forth pretty commonly, and it's good to be able to recognize what 'dialect' is being used. In fact, there are several additional systems that are fairly commonly used, convenient to different particular applications like atomic physics, and in those systems certain constants like 'c' may take the value of 1.
In class I mentioned that this can come up, and wrote on the board a very useful reference:
J.D. Jackson, "Classical Electrodynamics"
See the appendices for different systems of units for electrodynamics.
For those who don't have Jackson or who want more, it's great that *most* information in Wikipedia is pretty reliable, and there's some side-by-side comparison in this article:
http://en.wikipedia.org/wiki/Maxwell's_equations
Early courses in physics sometimes try to spare you this diversity, but you will want to be able to recognize and work in either system, in fourth year or above.
Q: What's the connection between short-wave radio reflecting from the ionosophere and total internal reflection, going from inside a piece of glass towards the air outside? Where does a mirror reflection fit in this picture?
A: Reflection from a plasma is ALWAYS total internal reflection, basically... At the plasma resonance, if there is no damping/collisions, the dielectric function goes to *zero*, that is, the index of refraction in a plasma is less than 1. What happens in detail is actually that there's a gradient-index as one approaches the critical density; if the beam approaches at some oblique angle to the slab, really the beam will be refracted and turned before reaching the critical density. But rays directly incident will also suffer total internal reflection, because where the dielectric function goes to zero the critical angle for TIR goes to zero.
A metallic mirror is really a high-density plasma -- the electrons are free to move, and most wavelengths will reflect. Gold and other metallic coatings can even be used to make x-ray mirrors: the change in the index of refraction is not very large, but for grazing angles of incidence (around a degree or less), even kilovolt-energy x-rays will reflect by total internal reflection.
Last revised: 6 December 2008 -- © 2007, 2008 R.S. Marjoribanks