The Gaussian beam models laser beams - index 高斯光束模式，激光束-指数.ppt

The Gaussian beam models laser beams - index 高斯光束模式，激光束-指数
Ray Optics
We'll define "light rays" as directions in sate away from the laser.
The beam has a waist at z = 0, where the spot size is w0. It then
expands to w = w(z) with distance z away from the laser.
The beam radius of curvature, R(z), also increases with distance far away.
But lasers are Gaussian Beams, not rays.
Gaussian Beam Math
The expression for a real laser
beam's electric field is given by:
where:
w(z) is the spot size vs. distance from the waist,
R(z) is the beam radius of curvature, and
y(z) is a phase shift.
This equation is the solution to the wave equation when we require that the beam be well localized at some point (., its waist).
Gaussian Beam Spot, Radius, and Phase
The expressions for the spot size,
radius of curvature, and phase shift:
where zR is the Rayleigh Range (the distance over which the beam remains about the same diameter), and it's given by:
Twice the Rayleigh range is the
distance over which the beam
remains about the same size,
that is, remains “collimated.”
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.225 cm km km

cm km 5 km
cm 30 km 500 km
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Tightly focused laser beams expand quickly.
Weakly focused beams expand less quickly, but still expand.
As a result, it's very difficult to shoot down a missile with a laser.
Gaussian Beam Collimation
Collimation Collimation
Waist spot Distance Distance
size w0 l = µm l = µm
Longer wavelengths expand faster than shorter ones.
Gaussian Beam Divergence
Far away from the waist, the
spot size of a Gaussian beam will be:
The beam 1/e divergence half angle is then w(z) / z as z ® ¥ :

The smaller the waist and the larger the wavelength, the larger
the divergence angle.
Focusi