diffraction gratings and does - Breault Research Organization, Inc.

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DIFFRACTION GRATINGS AND DOESSimulating Diffractive Optical Elements in ASAPWe can equate the above equations, rearrange, and integrate to yield,Equation 23(EQ 23)Our results can be extended to rotationally symmetric systems or to threedimensions without loss of generality. If f(y) and f’ are determined in this manner,f’ is commonly set equal to one, and the exponent term of the MULITIPLEcommand is not needed normally.If you choose to, you can derive the grating line equation directly. In this case, youmust derive f(x,y,z) and determine f’ and the exponent p of the j term.Alternatively, ASAP can calculate f’ such that the distance from a point (x,y,z) onthe original surface to the first sheet is d. It does this by evaluating the expression,Equation 24(EQ 24)This second expression is most useful for diffractive optical elements, such aslinear gratings that have equally spaced grating lines. You are not specifying thephase function, but rather the direction in which parallel replications of the originalsurface are generated. At each distance d along the original surface’s normal,38 ASAP Technical Guide
DIFFRACTION GRATINGS AND DOESSimulating Diffractive Optical Elements in ASAP. . . . .computed from the gradient of f(x,y,z), you get a replicated version of the originalsurface. In the case of a plane, resulting planes are stacked on top of each other butspaced at a distance d apart. In the case of cylinders, resulting concentric cylindersare spaced a distance d apart. This special spacing is the grating line spacing.Note the similarity of the above equation to the special case of the MULTIPLEcommand, when the grating lines are equally spaced.Equation 25(EQ 25)Before we examine several DOE examples, we must learn about the necessaryoptions of the INTERFACE command for assigning a diffractive optical interfaceto an object.ASAP Technical Guide 39
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