The Fabry Perot Resonator

Abstract

Whether a steady state radiation field can be established in an optical resonator depends on the wavelength of the radiation and on the mirror spacing. Steady state means that both the amplitude and the phase reproduce themselves after one round trip. It is easy to understand that both conditions can only be accomplished if the resonator length is an integral multiple of half the wavelength. Only in this case can we obtain standing waves inside the resonator with nodal intensity points on the mirror surfaces (Fig. 4.1). The preceding statement is always true as long as the field is not confined laterally by means of apertures. Hence, for a given mirror spacing L ₀ and a medium with index of refraction n between the mirrors, we will find steady state field distributions for all wavelengths λ _q for which the following condition holds:

$${\lambda _q} = \frac{{2L}}{q}$$

((4.1))

with:

$$ \begin{array}{l} \lambda q:wavelength\,in\,vacuum \\ L = {L_0}n:optical\,path\,length\,between\,mirrors \\ {L_0}:geomatrical\,path\,langth\,betweenmirrors \\ n:index\,of\,refraction \\ \end{array} $$