Module 8 : Laser- II
Lecture   : Rate equations for Lasers
 

Note that at the resonance, i.e., when $ kL=m\pi$, the transmission intensity is maximum. The FWHM of the intensity pattern can be obtained by looking at any of the peaks since the shape of intensity function repeats itself. Consider the peak near $ kL=0$. For large values of $ R$, the peak is very sharp and we may replace $ \sin kL$by $ kL$itself. Thus FWHM is given by

$\displaystyle \frac{1}{1+R(kL)^2}=\frac{1}{2}$

which gives $ kL=\pm 1/\sqrt F$, so that FWHM is $ 2/\sqrt F$.
A Fabry-Perot cavity can, therefore, be used to select wavelength by suitably adjusting the mirror separation, the wavelengths at which resonances occur are given by

$\displaystyle \lambda^{\rm max} = \frac{2L}{m}$

where $ m$are integers. As $ m$increases, the wavelengths decrease. Using the speed of light in the medium to be $ c/\mu$, where $ \mu$is the refractive index of the medium, the resonance frequencies are

$\displaystyle \nu^{\rm max} = \frac{cm}{2\mu L}$

which are eqi-spaced. Each possible standing wave satisfying the above is called a cavity mode $ m$being the mode number .

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