ECE615_Lecture04

ECE615_Lecture04 - Lecture 4 Nonlinear Susceptibility of an...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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.

Page1 / 9

ECE615_Lecture04 - Lecture 4 Nonlinear Susceptibility of an...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online