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130 4 Optical Rotor
tW(z)

q W(z)

tW 0
W
z=z f
0

l

z
Fig. 4.10. Ray optics model for a focused laser beam considering beam waist. The
ray of tW(z)passes tW 0 at the beam waist (z = z f )where 0 ≤ t ≤ 1

where W 0 is the minimum waist radius, z f is the minimum waist position and
2Z 0 corresponds to the depth of focus. An arbitrary point on the ray, angle θ
in the xy plane, can be described as

{W(z)cos θ, W(z)sin θ, z} . (4.12)

Ray vector I of tW(z) that passes through tW 0 (0 ≤ t ≤ 1) on the beam
waist (z = z f ) plane can be expressed as

I = {tW (z)cos θ, tW (z)sin θ, z} , (4.13)
where W (z)isthe z derivative of W(z). Reflected ray vector l r and refracted

ray vector l t on the incident plane can be written, usingvector I of the incident
tW(z)ray as
I r = I − 2(I • n) n, (4.14)

tan (θ 2 )

I t = I +(I • n) − 1 n, (4.15)
tan (θ 1 )
where n defines the vector normal to the interface, θ 1 is the angle of incidence
and θ 2 is the angle of refraction. The optical forces at each point are calculated
usingthese ray vectors as follows.
We traced the rays until they hit the bottom surface and computed the
optical pressure on each surface. The light reflected from the bottom causes
an error in the optical pressure. The ratios of such light power to the input