Diffraction Efficiency
Diffraction efficiency (DE) is the fraction of incident optical power that a periodic structure—typically a diffraction grating, hologram, or other diffractive optical element—sends into a chosen diffraction order.
In lasers and photonics it is the main figure of merit for how well a grating or holographic element “steers” light rather than reflecting, transmitting, absorbing, or scattering it into unused orders.
For incident power P/inc and power Pm leaving in order m,
ηm = Pm
Pinc
This is absolute efficiency.
Relative efficiency instead compares Pm to the power that would be reflected (or transmitted) by a mirror or window with the same coating, so it isolates diffraction losses from coating losses.
For LCOS spatial light modulators a common lab definition is first-order intensity divided by the average zero-order intensity when a blazed (or multi-level) grating is displayed.
Technical points:
Orders and the grating equation. Period Λ, wavelength λ, and incidence angle determine which orders exist. High DE into one order usually requires a period small enough that only the desired order (often m=−1) plus the specular (m=0) order can propagate. Remaining light is then forced into that single order if the groove profile is correct.
Profile / modulation.
Surface-relief (ruled or holographic) gratings use groove depth, duty cycle and blaze angle.
Volume (Bragg) holograms use refractive-index modulation Δn and thickness. Kogelnik coupled-wave theory gives, at Bragg resonance for a lossless unslanted transmission grating:
η = sin2 (κd/cosθ)
where κ∝Δn/λ. Reflection volume gratings follow a tanh2 form and can also approach 100 %.
Scalar vs rigorous models. Multi-level (quantized-blaze) scalar theory predicts first-order efficiencies of ~40.5 % (binary), ~81 % (4 levels), ~95 % (8 levels), approaching 100 % for a continuous blaze. When feature sizes approach λ, polarization, evanescent orders and guided-mode resonances appear; those cases need rigorous coupled-wave analysis (RCWA) or modal methods.
Loss channels. Absorption (especially in metal coatings), scattering, residual zero-order, higher orders, and polarization mismatch all reduce η. Multilayer-dielectric (MLD) gratings minimize absorption and routinely exceed 99 % over tens of nanometers. Gold gratings typically sit in the 90–95 % range because of metal loss.
Dependencies. Wavelength, incidence angle (Littrow vs non-Littrow), polarization (TE vs TM), and fabrication errors all move the efficiency curve. Volume holograms add strong angular and spectral Bragg selectivity.
Typical practical values:
MLD reflection gratings for femtosecond lasers: >99 % over 30–70 nm bands.
Volume phase holograms (VPH) and well-designed transmission gratings: 90–99 % at design wavelength.
Photopolymer volume holograms: 90 %+ is common; >99 % has been shown in optimized materials.
Applications:
Chirped-pulse amplification (CPA) and pulse compression. High-DE, high-damage-threshold gratings (often MLD) stretch and compress ultrashort pulses; even a few percent loss per pass becomes costly at petawatt scale.
Spectrometers, monochromators and Raman systems. High DE improves signal-to-noise when the source is weak.
Laser wavelength selection. External-cavity diode lasers and tunable sources use gratings in Littrow or Littman–Metcalf mounts; high first-order DE lowers threshold and improves efficiency.
Spectral beam combining of high-power laser arrays.
Holographic optical elements (HOEs) and volume Bragg gratings: beam combiners, notch filters, AR/VR waveguides, solar concentrators, and multiplexed data storage. Diffraction efficiency sets how many holograms can be superimposed before each becomes too weak (1/M2) scaling for conventional multiplexed volume holograms).
Spatial light modulators and beam shaping. LCOS and MEMS devices are characterized by first-order DE of the displayed grating or hologram.
Precision interferometry and all-reflective cavities. Near-100 % DE gratings act as low-loss beam splitters or output couplers, reducing thermal lensing.
Diffraction efficiency tells you how much of the laser power actually ends up where the optical design intends it to go.
Modern dielectric and holographic designs routinely push that number above 95–99 % at the design wavelength and polarization, which is why they dominate high-power ultrafast lasers, spectroscopy, and compact holographic optics.