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 'hands-on' modelling throughout the course. No prior knowledge of Maple is required.

  • 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 Gauss-beam (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
    • LG-modes
    • * 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

Semi-regular 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.