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Laser Physics EAL 501 Lecture 6 Power & Frequency

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

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

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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

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Higher order modes are given by

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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

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

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Gain Saturation We drive the rate equations

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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

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

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Solution above threshold in the case of two levels without pumping

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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

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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

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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

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

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1.3 Cavity modes Axial modes λ = 2d / n ν = nc / 2d n = 2d / λ

1.3 Cavity modes Axial modes λ = 2d / n ν = nc / 2d n = 2d / λ

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