How to Build a Laser Death Ray
Stimulated Scattering Notes
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How to Build a Laser Death RayStimulated Scattering Notes |
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Uniform beam radius R, beam diamater D, power P, gain g, intensity I = P/(π R2), distance z.
Stimulated scattering Is increases by
dIs = g I Is dz
Solution for constant I
Is(z) = Is(0) exp(g I z)
For stimulated Raman scattering off rotational modes of N2, get runaway amplification of scattered beam when spontaneous Raman amplified by approximately a factor of 1011, or
g I z ≈ 25.
For beam of constant power P focusing from initial beam diameter D to spot of diameter S at distance z0.
d = D (zf - z)/zf.
Stimulated scattering Is increases by
dIs = g (P/(π d2/4)) Is dz
Solution
= 4 g P Is (zf2/(π D2)) (dz/(zf - z)2)
dIs/Is = d(ln(Is))
Assuming runaway still occurs when scattered light is amplified by 1011, we have condition
=4 g P (zf2/(π D2)) (dz/(zf - z)2) = 4 g P (zf2/(π D2)) d(1/(zf - z)) ln(Is(z)/Is(0)) = 4 g P (zf2/(π D2)) [1/(zf - z) - 1/zf] = (4 g P/(π D2)) [z/(1-z/zf)] Is(z) = Is(0) exp((4 g P/(π D2)) [z/(1-z/zf)])
(4 g P/(π D2)) [z/(1-z/zf)] = 25.
Runaway scattering occurs at
z = 1/((4 g P)/(25 π D2) + (1-S/D)/z0).
To avoid runaway scattering at desired spot, we need z ≥ z0.
z0 ≤ 25 π S D / (4 g P).
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