Laser-II

Module 8 : Laser- II

Lecture : Rate equations for Lasers

	In the presence of light, the steady state solution to equation (A) is obtained by equating the right hand side of (A) to zero. The steady state population of the upper level is given by $\displaystyle N_u = \frac{N_u^0}{1+\sigma\tau S}$ We may rewrite the above as $\displaystyle N_u = \frac{N_u^0}{1+ S/S_{\rm sat}}\equiv\frac{N_u^0}{1+I/I_{\rm sat}}$ where $I_{\rm sat}$ is the saturation intensity, which is equal to the intensity for which the gain is reduced by a factor of 2.
2.13	Properties of Laser Beam:
	Laser beams are characterized by the following special properties :
	Coherence: Laser beam is highly coherent, i.e, different parts of the beam maintain a phase relationship bfor a long time. this results in interference effect. When a laser beam reflects off a surface, the reflected light can be seen to have bright regions separated by dark regions. Temporal Coherence: One can define a coherence time $\Delta\tau$ after which the phase correlation between two waves which were initially in phase ( or between two points in the same wave which had a known phase difference) drops significantly. The reason for loss of coherence is than an optical source does not emit a continuous wave for all time to come. Thermal sources, for instance, have a typical life time of $\Delta t=10^{-7}$ seconds so thata wave which seems continuous, actually consists of a sequence of waves which are typically $c\Delta t\simeq 0.3$ m long which no phase correlation between parts of one wave train and another. Temporal coherence is essentially a measure of monochromaticity of the beam. To see this consider a wave train which is emitted for a finite duration. Let the wave disturbance be represented by