Power distribution follows Bessel function in the scaler region.
T ≈ λ for transmission.
T ≈ λ/4 for reflection.
Easily replicated or deep etch can yield higher efficiency.
Square, rectangle
Max D.E. ~ 40% ± 1 order.
Power distributions favors odd orders.
Pi phase shift typical.
Classic binary grating.
T ≈ λ for transmission.
T ≈ λ/4 for reflection.
Blazed, sawtooth
Max D.E ~ 98%
Reflection Case:
λ = 2 d sin a
T = λ/2 ± 10%
Transmission Case:
λ = d sin b
a ≈ 2b
T = λ/(n-1) ± 10%
Surface shadows reduce D.E. by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textstyle \frac{\lambda^2}{n d^2}}
Wavelength changes reduce D.E. by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle \left(\frac{\pi\Delta\lambda}{b\lambda}\right)^2}
Holographic Deflectors (hologons)
N = θD/(1.4λ)
N = number of resolvable spots
θ = full scan angle in radians
D = beam diameter in microns
λ = wavelength
Φ = wedge angle of glass
Special case of linear scan and near wobble invariance a ~ b ~ 45° max straight scan angle ~ 36°
Dynamic wobble Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle \simeq \Delta\Omega/128}