Effect of the Cavity Q on Power Broadening

The Quality Factor Q is variously described, but most usefully in this context 

The energy stored cannot increase ad infinitum, so ultimately the power input to the cavity must equal the sum of the power dissipated resistively and lost by other mechanisms diffraction losses, coupling into the circuit etc. The power lost in the steady state is thus the input power Pin. 

The electric field strength in the cavity E is not a singular quantity, it varies around the structure at resonance both spatially and temporally, but can be represented by a mean value E, and is related to the energy stored by 

Rcav is the effective cavity volume that is occupied by the electric field. The electric field in a Fabry-Perot cavity operating in TMqo mode is largely confined to a cylindrical element of radius (Al/2 r)i and length L equal to the mirror spacing (Section 2.1). The term cEqE equates to the power density term P in the Karplus and Schwinger equation. The power broadening contribution in that equation therefore becomes for a Fabry-Perot cavity 

In applying Equation 1.44 to power saturation it needs to be remembered that Bmn is proportional to 1 — M / J +1) for each M component. This means that states of high M are both less intense and less readily saturated than those near M = 0. Although no simple formula can be applied to extract the resulting line profile, it is probably a good approximation to use the most intense component as a signal of the onset of power saturation. 

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