ls2_unit_6

ls2_unit_6 - THE INTERACTION OF RADIATION AND MATTER...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
THE INTERACTION OF RADIATION AND MATTER: SEMICLASSICAL THEORY PAGE 62 R. Victor Jones, March 16, 2000 62 VI. SEMICLASSICAL LASER THEORY 23 L ASER S ELF -C ONSISTENCY E QUATIONS Lamb's theory of laser operation provides a very powerful means for interpreting and predicting complex time dependent behavior without invoking all the intricacy of a full quantum mechanical theory. It is semiclassical, self-consistent theory in the following sense: statistic summation macroscopic Maxwell theory quantum theory self-consistency Suppose that the field in the laser is represented in the form E z , t ( ) = 1 2 E n t ( ) exp i ω n t + φ n t ( ) ( ) [ ] U n z ( ) n + c . c . [ VI-1 ] where, for example, in a simple a cavity laser U n z ( ) sin k n z = sin n π L z Λ Ν Ξ Π standing wave [ VI-2a ] and in a ring laser U n z ( ) exp i k n z ( ) = exp i n 2 π L z Λ Ν Ξ Π traveling wave [ VI-2b ] 23 An adaptation or interpretation of Lamb's "semiclassical" or "self-consistent" laser theory as first presented in Phys. Rev. 134 , A1429 (1964) and refined in countless other treatments. In these lecture notes we drawn extensively on M. Sargent III, M. O. Scully and W. E. Lamb, Jr., Laser Physics , Addison-Wesley (1974) and P. Meystre and M. Sargent III, Elements of Quantum Optics , Springer-Verlag (1992).
Background image of page 1

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

View Full DocumentRight Arrow Icon
THE INTERACTION OF RADIATION AND MATTER: SEMICLASSICAL THEORY PAGE 63 R. Victor Jones, March 16, 2000 63 With this representation for the field the induced polarization can be expressed as P z , t ( ) = 1 2 P n t ( ) exp i ω n t + φ n t ( ) ( ) [ ] U n z ( ) n + c.c. [ VI-3 ] where P n t ( ) is the complex, slowly varying component of the polarization of the n th mode. If we take the wave equation in the form 24 −∇ 2 v E o v J t + 1 c 2 2 v E t 2 = μ o 2 v P t 2 [ VI-4 ] where second term is included as a means to account for cavity losses. From Equation [ VI-1 ] assuming that E n , P n , and ˙ φ n are slowly varying functions of time 25 −∇ 2 v E ⇒− 2 E z , t ( ) z 2 = 1 2 E n exp i ω n t + φ n ( ) [ ] 2 U n z 2 n + c . c . = 1 2 c 2 Ω n 2 E n exp i ω n wt + φ n ( ) [ ] U n n + c . c . [ VI-5a ] where Ω n = c k n are the eigenfrequencies of the cold resonator eigenmodes. v E t E z , t ( ) t = 1 2 ˙ E n i E n ω n + ˙ φ n ( ) { } exp i ω n t + φ n ( ) [ ] U n z ( ) n + c . c . [ VI-5b ] 24 In this formulation we are assuming that v v P 0 . 25 The so called slowly-varying amplitude and phase approximation (SVAP) is used extensively in treating problems in laser dynamics. In the SVAP approximation it is assumed that z ln E n ; z ln P n ; z φ n Χ Ψ ± Ϋ ά έ << k n and t ln E n ; t ln P n ; t φ n Χ Ψ ± Ϋ ά έ << Ω n
Background image of page 2
THE INTERACTION OF RADIATION AND MATTER: SEMICLASSICAL THEORY PAGE 64 R. Victor Jones, March 16, 2000 64 μ o v J t μ
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/29/2012 for the course PHYSICS 216 taught by Professor Staff during the Fall '11 term at BU.

Page1 / 20

ls2_unit_6 - THE INTERACTION OF RADIATION AND MATTER...

This preview shows document pages 1 - 4. Sign up to view the full document.

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