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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].

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laser physics eal 501

Laser Physics EAL 501

Lecture 6

Power & Frequency

slide5

Standing wave cavities

  • 1- Longitudenal modes

due to standing waves

Do ring lasers have longitudenal modes?

2 transversal modes gaussian beams
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 (x1,y1,z1) then the distribution at any plane (x,y,z) is given by

We can write

Where

The solution is

slide9

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

slide11

Amplitude factor

Longitudenal phase factor

Transverse phase factor

Rayleigh range

Beam waist

Radius of curvature

slide14

Gain Saturation

We drive the rate equations

slide15

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
slide16

Steady state under threshold solution is

In case of 3 level laser

In case of 4 level laser

slide18

Solution above threshold in the case of 3levels with pumping

Since g(ν)=σ(v)(N2-N1) then we can write

Problem : find small signal gain and saturation intensity for 4 level laser

slide19

Hole burning

Spatial hole burning

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

slide20

Output power

Usually only one mirror produces output and if the mirror reflection is high

The condition of steady state lasing

Where s is the scattering losses

slide21

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

So the optimum output intensity is