This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Lecture 4 Nonlinear Susceptibility of an Anharmonic Oscillator Approach:- Lorentz (harmonic) oscillator: A good approximation of the linear response of an atom to an incident electric field.- Add additional nonlinear restoring force term => Differential equation for electron displacement (not directly solvable) 1- Employ perturbation analysis to obtain approximate solution. Lorentz Harmonic Oscillator (1) where is the applied field add nonlinear term (2) damping force is directed against restoring force is ( 29 2 2 ( ) x x x E t e m γ ϖ + + = - ɺɺ ɺ ɶ ɶ ɶ ɶ ( ) E t ɶ ( 29 2 2 2 ( ) x x x ax E t e m γ ϖ + + + = - ɺɺ ɺ ɶ ɶ ɶ ɶ ɶ 2 m x γ- ɺ ɶ x ɺ ɶ 2 2 restoring F m x max ϖ = - + ɶ ɶ Potential energy is integral of restoring force over displacement (3) Note- potential is not symmetric in => implies noncentrosymmetric medium (for centrosymmetric media, must hold, so only even powers of appear.)- Symmetric potential of Lorentz is a parabola.- Nonlinear potential is asymmetric. ssume incident field 2 2 3 1 1 2 3 r U F dx m x max ϖ = - = + ∫ ɶ ɶ ɶ ɶ x ɶ x ɶ x ɶ ˆ ˆ ( ) ( ) U x U x =- 2 Assume incident field and solve for displacement of (2) for For a small applied field, then and (2) can be solved using a perturbation expansion....
View Full Document
This note was uploaded on 01/10/2011 for the course ECE 615 taught by Professor Shalaev during the Fall '10 term at Purdue.
- Fall '10