Course outline
With the advent of spatial light modulators the field of wave optics has never been more exciting.
Applications in science harness the force of light to manipulate microparticles. These include 'tweezers', bright light spots that allow for the manipulation of tiny articles, even organelles within living cells. Superpositions of plane wave laser light beams can form artificial crystals of light which are widely used in atomic physics.
Other tricks with light are possible: evanescent waves form mirrors that reflect atoms; funnels and bottles can be realized through superpositions of fundamental laser modes synthesized with spatial light modulators; crossed beam configurations allow for wide atom beam lenses, and beams with orbital angular momentum can form bright and dark helices of light.
After a brief introduction of wave optics, the physics of optical forces and potentials is introduced. Many examples and applications from contemporary research will be presented, and analyzed by the students. This course makes extensive use of Maple programs for 'handson' modelling throughout the course. No prior knowledge of Maple is required.
Topics
 Optical Lattices:
 Interference of plane waves
 Symmetries
 Introduction to Maple
 Symmetries continued, such as:
 ^{*} Cubic, tetragonal,
 ^{*} Fivefold Lattice Symmetry.
 Interference of Gaussian beams
 ^{*} Harmonically modulated Sinusoidal Lattice
 Fermi Surfaces  experimental results of expanding atom clouds
 Feshbach Resonances  experimental results Fermionic  BCS transitions
 ^{*} Atomic Conveyor belt
 Tunneling studies
 Evanescent Waves:
 ^{*} Tunneling exp(I*k) > exp(k)
 Scaling Laws:
 Surface to Volume
 Pushing Atoms with Light
 ^{*} Scaling of Gradient (Equal Intensity across beam)
 Optical Trapping:
 Optical Dipole Force (from Maxwell's equations)
 ^{*} Bead in Gaussbeam (Determine Force)
 Scattering Force
 ^{*} Determine Laser Power for Atomic Fountain (given detuning, pulse length....)
 Laser Cooling
 Scattering Rates
 Zeeman Slower
 BECs
 ^{*} Recoil Limit Temperature
 Spatial Laser Modes:
 Helmholtz Eq
 ^{*} Derive Paraxial Wave Eq
 TEM modes
 LGmodes
 ^{*} connection between
 ^{*} Paraxial Wave Eq Equivalence with QHOSC
 Gouy's Phase
 Intensity Inversion
 Squeezed Beams on the Rebound (Bottle Beam)
 ^{*} Intensity > Gradients / Force profile
 Optical Potential Patterns:
 Funnels
 Conveyor Belt
 Atom Optics
 ^{*} Wide Lenses (remove higher order terms)
 Thin Lenses with Large Numerical Aperture
 Optical Helices
 Orbital Angular Momentum
 ^{*} Superposition of Laguerre Gauss Beams
 Bright Helices
 possible waveguides
 Dark Helices
 ^{*} going below the diffraction limit
Above, possible homework problems are indicated by the (^{*}) symbol
Course format
The format of this course is very unusual, but hopefully you will find it stimulating.
Formal lectures will be held during two weeks during the term, and homework problems will be assigned in the interim periods. Lectures will be 4 hours, the exact time and format to be worked out.
 Week 1 February 11,12,15,16,17
 Week 2 April 5,6,7,8,9
Semiregular teleconferences will be had with Prof. Steurnagel to answer questions regarding the homework and to discuss the projects. These times have been tenetivly scheduled for Tuesdays at 9 AM St.Catharines' time.
Marking scheme
Component 
Worth 
Comments 
Homework 
60% 
There will be approximately 3 assignments before Week 1, a nightly problem during the lecture weeks, and another few assignments in the interim. 
Term project 
40% 
In lieu of a final exam, you will present an individual project report to be presented in class on April 9,
and as a HTML web project. Project topics will appear on this webpage shortly. 
