Lecture 17

Lecture 17 - Lecture 17 Lecture 17 Gaussian beams Plane...

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

View Full Document Right Arrow Icon
Lecture 17 1 © Jeffrey Bokor, 2000, all rights reserved Lecture 17 Gaussian beams Plane waves: . Another solution to Maxwell’s equations: – Paraxial approximation: variation with is slow compared to variation. – Plug this form into Maxwell’s equations. Use paraxial approximation. The resulting solution is: The transverse amplitude profile of the beam is Gaussian: Exyz   E 0 e ik z t = E 0 xyz e z t = transverse beam profile varies slowly with z z xy EE 0 w 0 ikz i z +  exp wz ---------------------------------------------------- x 2 y 2 + w 2 z ---------------- x 2 y 2 + 2 Rz exp = Exy E o e x 2 y 2 + w 2 ------------------------ = : transverse beam radius w 0 1 zz R 2 + 12 / = : spherical wavefront radius of beam R 2 z + = z : phase shift of plane wave phase z tan 1 R = z z R w 0 “waist” z = 0
Background image of page 1

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

View Full DocumentRight Arrow Icon
Lecture 17 2 © Jeffrey Bokor, 2000, all rights reserved Lasers can be made to generate this Gaussian beam (in most cases) Use one or two curved mirrors Given , there is one unique Gaussian beam (transverse mode) that fits into the laser resona- tor. Gaussian beam curvature must
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 09/05/2010.

Page1 / 4

Lecture 17 - Lecture 17 Lecture 17 Gaussian beams Plane...

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