Laser Physics EAL 501
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Transcript of Laser Physics EAL 501
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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?
nLc2
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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 (x1,y1,z1) 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 BeamsThe 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 factorRayleigh range
Beam waist
Radius of curvature
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Gain Saturation
We drive the rate equations
))(()( 12
12 NggNg
)1(21..
)1(21)1ln(
21
1
21
2121
221
rrL
lossescavity
rrLrrL
g
err
t
Lgt
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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)(N2-N1) then we can write
)()(1
)()(
sat
o
II
gg
)(2)(
)()(
21
21
21
PhI
NPPg
sat
To
Problem : find small signal gain and saturation intensity for 4 level laser
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Hole burning1. Spatial hole burning2. 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 rapidly2- 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
tgrrl
g )1(21)( 21
tsat
o gII
gg
/1)()(
It2
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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