Laser Physics EAL 501 Lecture 6 Power & Frequency

We said that there are two types of cavities 1- Ring cavities

Standing wave cavities 1- Longitudenal modes due to standing waves Do ring lasers have longitudenal modes?

2-Transversal modes [Gaussian beams] The electric field distribution in the x-y plane Satisfy the wave eq. The Fresnel-Kirchoff’s theory states that “if we know the field distribution at a plan 1 (x 1,y 1,z 1 ) then the distribution at any plane (x,y,z) is given by We can write Where The solution is

Higher order modes are given by

Gaussian Beams The solution of wave equation can be plane waves But it is not real q(z) is the complex beam parameter of the beam

Amplitude factor Transverse phase factor Longitudenal phase factor Rayleigh range Beam waist Radius of curvature

Gain Saturation We drive the rate equations

The steady state solution of the rate equation in the case I=0 gives us the threshold condition The steady state solution of the rate equation in the case after the threshold can be shown to be

Steady state under threshold solution is In case of 3 level laser In case of 4 level laser

Solution above threshold in the case of two levels without pumping

Solution above threshold in the case of 3levels with pumping Since g(ν)=σ(v)(N 2 -N 1 ) then we can write Problem : find small signal gain and saturation intensity for 4 level laser

Hole burning 1.Spatial hole burning 2.Spectral hole burning 1- Spatial hole burning in the case of standing wave cavity there are points of zero intensity and points of max. intensity which depletes the gain much more rapidly 2- Spectral hole burning in the case of inhomogeneous broadening the atoms that feed the laser modes will be depleted much more rapidly

Output power Usually only one mirror produces output and if the mirror reflection is high Where s is the scattering losses The condition of steady state lasing

It is easy to find the value of transmission t to get the maximum output So the optimum output intensity is