diffraction gratings and does - Breault Research Organization, Inc.

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DIFFRACTION GRATINGS AND DOESSimulating Diffractive Optical Elements in ASAPIf MULTIPLE is used to define a diffraction grating, the value of n is irrelevant,and can even be zero. ASAP automatically knows how to use the multiple surfacein the case of a diffractive optical element because of its special reference on theINTERFACE command where j specifies the diffractive order numbers.Depending upon the nature of the surface, the value of the exponent p, and theadditive constant f' to the original surface, the sheets may not be equally spaced.The exponent p is defaulted to 1, but can be used, for example, to get evenlyspaced cylinders or spheres (p=2). The zeroth sheet is just the original surface.What is the function f(x,y,z) when used with the first syntax of MULTIPLE tosimulate a diffractive optical element? It is an equation describing the grating linespacing. You can derive this equation from the phase function, or you can computeit directly. To derive f(x,y,z) from the phase function, we must understand that it isa normalized form of the phase function that we described in the section,“Fundamentals of Diffractive Optical Elements” on page 9.Recall that the phase function, in general, describes how the phase of an incidentwave is altered by an optical element. A modulo 2 phase function is the phasefunction of a diffractive optical element.NOTE The function f(x,y,z) is the function obtained when the phasefunction of a given order m is divided by 2m uniquely specifiesthe grating line equation.The grating line spacing is a physical spacing, which does not change for otherorders. Other orders are diffracted according to this spacing. In other words, aphysical grating line is obtained whenever a specific phase goes though 2. Ingeneral, the function f(x,y,z) on the MULTIPLE command, as well as its otherterms, can be obtained from an arbitrary phase function by dividing the phasefunction by 2m or where m is the order number corresponding to that phasefunction.We can mathematically demonstrate this relationship by re-examining Figure 2“Transmission and reflection gratings” on page 13. The local phase change withina specific period in one dimension is,36 ASAP Technical Guide
DIFFRACTION GRATINGS AND DOESSimulating Diffractive Optical Elements in ASAP. . . . .Equation 21But the difference in sine terms is equal to(EQ 21)Equation 22(EQ 22)Note here that d(y) indicates that the local spatial period may, in general, change asa function of position, and n(y) is a spatial frequency denoting the number of localgrating lines per unit length.ASAP Technical Guide 37
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diffraction gratings and does - Breault Research Organization, Inc.

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