diffraction gratings and does - Breault Research Organization, Inc.

DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical Elements. . . . .FUNDAMENTALS OF DIFFRACTIVE OPTICALELEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Two common approaches exist for calculating the diffraction patterns from DOEs:vector calculation and scalar calculation.Using vector diffraction theory, we can calculate the directions of propagation ofthe various reflected and transmitted orders of a beam after interacting with theDOE as well as the fractional power contained in each order. The fractional powerdiffracted into each order is called the diffraction efficiency, and is determined bythe diffractive surface profile. This complicated calculation involves not only theDOE structural data, but also the physical and electromagnetic properties of theDOE. ASAP does not perform this type of calculation.Using scalar diffraction theory, we can calculate the idealized directions ofpropagation of the various reflected and transmitted orders of a beam afterinteracting with a diffractive element. The scalar diffraction theory technique isvalid if the grating period is larger than the wavelength of the diffracting light.Swanson notes that the scalar approximation can be used in Maxwell’s equations ifthe grating period is approximately five times the wavelength of the diffractinglight. The diffraction orders are selected by adjusting the direction cosines of theexiting beams according to the grating equation. The diffraction efficienciescannot be generally or easily calculated with this method since this is a scalartechnique. Most optical design and analysis software programs, including ASAP,use this technique since it is adaptable to ray tracing.The grating equation can also be derived from the Huygens-Fresnel principle. Thisis, perhaps, a more physically intuitive derivation than one from scalar diffractiontheory, yet mathematically less rigorous. Therefore, we use Huygens-Fresnelprinciple to derive the grating equation.Huygens-Fresnel principleChristian Huygens proposed a theory of diffraction based upon primary andsecondary wavefronts. A wavefront is a mathematical surface of constant phase. Ina contemporary, geometrical sense, wavefronts are mathematical surfaces overwhich the optical path lengths from rays of a point source have the same length.Huygens proposed that every point on a primary wavefront can be considered asource of secondary wavelets (or sources), each with the same frequency andvelocity, such that at a later time, the primary wavefront is the envelope of theASAP Technical Guide 9