Week of 9/17

Download amplitude and phase spectrum of a single resonance.

9/21/07: More on the Fabry-Perot etalon

$E_t = (E_0 t^2) e^{i \omega L/c} + r^2 (E_0 t^2) e^{i \omega 3L/c} + r^4 (E_0 t^2) e^{i \omega 5L/c} .... \,$

or

$E_t = (E_0 t^2) e^{i \omega L/c}\left[ 1 + r^2 e^{i \omega 2L/c} + r^4 e^{i \omega 4L/c} ...\right]$

Hence

$E_t = (E_0 t^2) e^{i \omega L/c} \frac{ 1 - r^2m e^{i \omega 2mL/c}} {1 - r^2m e^{i \omega 2L/c}}$

Take the limit as the number of bounces goes to infinity, then take | E_t | ² and We get:

$I_t/I_i = \frac{1}{1+ K \sin^2(L \omega/c)}$

where K = 2r / (1 − r)² and r is the reflectivity of the mirror.

For more details see the tutorial on spectroscopy and interferometry

Download Amplitude spectrum of a Fabry-Perot etalon

Download how matrices arise in the coupled oscillator problem