OPTI 553

8/08

Opti 553. Elements of Nonlinear Optics (2) I. Second-order nonlinear optics, second-harmonic generation, parametric processes; third-order nonlinear optics, Kerr-type nonlinearities, four-wave mixing; self-focusing collapse, critical power, spatial solitons; temporal solitons in optical fibers, space-time collapse, optical breakdown; stimulated Raman and Rayleigh wing scattering, two beam coupling; current topics in nonlinear optics.
P,  OPTI 501.
 

Course Outline (50-minute lectures)

The course introduces the student to the zoology of phenomena produced by optical nonlinearities for very intense laser fields propagating in dielectric media.  The treatment is centered on the classical Lorentz electron oscillator, but a quantum perspective is also given for many of the phenomena discussed.  The class project requires students to have some computational skills.

1. Review

          Linear optical properties, Maxwell's equations, plane-wave solutions,       
          paraxial wave equation and Gaussian beam propagation, Lorentz            
          electron oscillator model in the time and frequency domains, crystal       
          optics basics.

2. Introduction

          Introduction to nonlinear optics, nonlinear response function and optical
          susceptibility, classes of nonlinear optical interactions, tensorial      
          description properties of the nonlinear susceptibility.

3. Second-order Nonlinear Optics

          Second-harmonic generation, sum and frequency generation,   
          propagation effects, phase matching methods eg. quasi-phase matching,
          parametric processes, parametric amplifiers and oscillators.

4.   Third-order Nonlinear Optics

          Third-harmonic generation, Kerr-type nonlinearitites and self-phase        
          modulation, two-photon absorption, four-wave mixing.  Applications  
          including supercontinuum or white light generation, nonlinear pulse        
          compression, and optical phase-conjugation.

5.  Self-focusing collapse and optical solitons

          The nonlinear Schrodinger equation, modulational instability of a plane-  
          wave, self-focusing collapse in a bulk nonlinear medium, abberationless  
          approximation and the critical power, spatial solitons in one-dimensional
          waveguides, higher- order solitons, cascaded nonlinearities in second-          order media, spatial solitons in second-order nonlinear media.

6.  Optical breakdown in transparent materials

          Multi-photon ionization and avalanche ionization, optical limiting.

7.   Temporal solitons and space-time collaps

          Group velocity dispersion in optical fibers, temporal optical solitons,      
          space-time collapse in transparent dielectric media, collapse arrest   
          mechanisms including pulse-splitting due to group velocity  
          dispersion, multi-photon absorption an optical breakdown.

8.  Stimulated Scattering

          Stimulated Raman and Rayleigh wing scattering, two-wave coupling,       
          Raman amplification and oscillation. 

9.  Current topics in nonlinear optic

          Potential topics include long distance propagation, high-harmonic
          generation, attosecond pulse generation, extreme nonlinear optics,
          and vacuum nonlinear optics.

Recommended Text:

R. W. Boyd: Nonlinear Optics (Academic Press)

Grading Criteria:

Grading will be based on a combination of three assignments: The first assignment will be a report based on an assigned seminal paper on nonlinear optics (25 %), and the second assignment will be a similar report on a paper to be mutually agreed upon by the student and instructor (35 %).  This second assignment will allow the student more flexibility to explore an area of direct interest to them.  The third assignment will be a project based on a mutually agreed upon topic that is intended to give the student some calculational experience in nonlinear optics (40 %).  The class project will require the student to have some computational skills.