diffraction gratings and does - Breault Research Organization, Inc.

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DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical ElementsGenerally, phase gratings are more efficient at diffracting monochromatic lightthan amplitude gratings, and surface relief phase gratings are more efficient atdiffracting broadband light than volume phase gratings. Theoretically, a phasegrating can diffract 100% of incident monochromatic light into a single diffractionorder. A surface relief phase grating has higher diffraction efficiencies than avolume phase grating operating over the same bandwidth. An amplitude gratingcannot diffract 100% of the incident monochromatic light into a single diffractionorder, because some of the incident light is reflected, absorbed, and so on, by thegrating mask.The simplest type of surface relief—phase transmission diffraction grating—is alinear phase transmission grating embossed on a flat, slab substrate. We can gainan intuitive understanding of more complicated diffraction gratings fromexamining the linear grating. A linear grating is a series of regularly arrayed linesor scratches embossed in a transmissive material known as the substrate. Phasetransmission gratings are usually replicated from a master on a plastic substrate.The master is quite often a series of regularly arrayed lines or scratches carved oretched onto a glass substrate.As a simple physical model, the regularly arrayed lines can be consideredscratches, troughs, or humps in the substrate. In the case of scratches, each lineacts like a linear scattering center. In the case of troughs or humps, each line actslike a very short radius of curvature, highly divergent cylindrical lens. In bothcases, the effect is to produce equivalent linear or line sources.Each effective line source is illuminated by the same, or more correctly, differentparts of the same wavefront. Therefore, each line source resembles the secondarysources or wavelets of the Huygens-Fresnel principle. See Figure 1Their superposition at a later time or, equivalently, a later position, will determinethe optical field at that point in time or position.A constructive interference of all the wavelets in a particular direction leads todiffraction orders. Some of the light is not scattered or diverged in transmittingthrough the diffraction grating. This occurs in between the grating lines. This light,basically unperturbed from the specular direction, is called the zeroth order. Inother words, the zeroth order of the diffraction grating is specular direction of theincident light.We have constructed a simple graphical model of the Huygens-Fresnel principle asapplied to linear phase transmission and reflection gratings in Figure 2.12 ASAP Technical Guide
DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical Elements. . . . .P 4 mDiffraction Orders mPhase Transmission GratingPhase Reflection GratingDiffraction Orders mSpecular - Zeroth OrderP 2P i m3 d iP 1 mP 3P 2P 4 idSpecular - Zeroth Order iP 1Figure 2 Transmission and reflection gratingsFor the linear phase transmission illustration, note that the trigonometric sine ofthe incident angle is,Equation 1(EQ 1)Here d is the grating line spacing. Similarly, note that the trigonometric sine of thediffracted order angle is,Equation 2(EQ 2)ASAP Technical Guide 13
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