Module 8 : Laser- II
Lecture   : Rate equations for Lasers
  \includegraphics{laser19.eps}
 

In addition, if the wave vector of the field is $ k$, the wave suffers a phase change $ 2kL$(this is in addition to the phase change due to reflection) If $ t_1$and $ t_2$are the transmission coefficients of the mirror, the transmitted amplitude is given by

$\displaystyle E_t$

$\displaystyle =$

$\displaystyle t_1t_2E_i + t_1t_2r_1r_2E_ie^{2ikL} + t_1t_2(r_1r_2)^2E_ie^{4ikL}+\ldots$

 

 

$\displaystyle =$

$\displaystyle t_1t_2E_i\frac{1}{1-r_1r_2e^{2ikL}}$

 


The transmitted intensity is given by

$\displaystyle I_t = \mid E_t\mid^2$

$\displaystyle =$

$\displaystyle \mid t_1t_2\mid^2E_i^2\frac{1}{1-r_1r_2e^{2ikL}} \frac{1}{1-r_1r_2e^{-2ikL}}$

 

 

$\displaystyle =$

$\displaystyle I_0 T_1T_2\frac{1}{(1-r_1r_2)^2+4r_1r_2\sin^2kL}$

 

1