Diffraction efficiency

Diffraction efficiency (engl. Diffraction efficiency ) or short efficiency is a characteristic of diffractive optical elements (DOE), in particular optical grating .

It is defined as the ratio of the intensity that is bent by a DOE into a certain solid angle to the intensity incident on the element.

Optical grating

In particular, for optical gratings, the diffraction efficiency is defined as the proportion of the incident intensity that is diffracted into the 1st order of diffraction . As a formula:

${\displaystyle \eta ={\frac {I_{1}}{\sum _{m_{\text{min}}}^{m_{\text{max}}}I_{m}}},}$

with the intensity in the mth order. ${\displaystyle I_{m}}$

In the case of a simple amplitude transmission grating with grating line spacing d and slot width d / 2 , d. H. a grating which does not generate any phase differences between the individual light waves at each of its grating lines, but only weakens them in their amplitudes, the intensity in the m. Order (in the far field )

${\displaystyle I_{m}\propto \left|{\frac {d}{2}}\mathrm {sinc} (\pi m/2)\right|^{2}.}$

This leads to a maximum efficiency of approx. 10%. Phase gratings , such as a blaze grating , are used to achieve higher efficiencies . Blaze gratings ideally achieve efficiencies of 100%, but only for small wavelength ranges.

Individual evidence

1. ^ Jürgen Jahns: Photonics: Basics, Components and Systems . Oldenbourg Verlag, 2001, p. 166 ( limited preview in Google Book search).
2. ^ Joseph W. Goodman: Introduction To Fourier Optics . Roberts and Company Publishers, 2005 ( limited preview in Google Book Search).
3. ^ Ariel Lipson, Stephen G. Lipson, Henry Lipson: Optical Physics . Cambridge University Press, 2010 ( limited preview in Google Book Search).