VHOE Relationships

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Key
a = input angle in air b = output angle in air an = input angle in medium
bn = output angle in medium f0 = spatial frequency = 1/d λ = wavelength
n = index of refraction Δn = index modulation D.E. = diffraction efficiency
φ = The half angle d = grating period T = thickness of medium
ρ = regime factor Q = quality factor B = fringe tilt angle
0, +1, -1, +2, -2 = diffraction orders possible f = focal length f# = f number


Grating equation, transmission
f0λ = sin a + sin b
D.E. ~ sin2 [Δn T / (λ cos φ)] < 99.9%


Plane grating, slanted fringes, +3 order is TIR, Δn is asymmetric
Fig1.gif


Grating equation, reflection


Uniform tilted reflector, also has weak transmission grating at surface.

Fig3.gif


Last modified on 9/29/97