diffraction gratings and does - Breault Research Organization, Inc.

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DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical ElementsEquation 4Here, m is the diffraction order, T is the grating period, and :(EQ 4)Equation 5(EQ 5)where n is the refractive index of the grating, d is the blaze thickness, and is thewavelength of light. From the grating equation and these equations, we determinethat the diffraction angles and efficiencies are highly dependent on wavelength andblaze thickness.Light from large bandwidth sources will be diffracted into many orders. This is atype of scatter, but it is deterministic scatter since its direction and diffraction orscatter efficiency can be exactly computed with the above equations.NOTE Deterministic scatter is different from the surface scatter dueto random surface variations that are covered in the ASAPtechnical guide, Scattering.The concept of the linear grating in this context can be used to develop a simplebut useful physical model of random scatter. You can consider a random scatteringsurface as being composed of many randomly oriented linear gratings, whosecombined grating spacing and orientation yield the surface scatter pattern.Phase functionBlazed gratings—and, in fact, other types of optical elements such as apertures,prisms, lenses and mirrors—can be described in terms of a transmittance function.The transmittance function describes how the optical element changes the16 ASAP Technical Guide
DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical Elements. . . . .amplitude and phase of a wavefront propagating through the component. We learnlater that we must know the phase function of a diffractive optical element tomodel it in ASAP.Generally, the transmittance function is defined as,Equation 6A(x,y) is the amplitude function and (x,y) is the phase function of the element.(EQ 6)The simplest transmittance function is perhaps that of a one-dimensional aperturewhose transmittance function is one inside the aperture and zero outside of theaperture. Mathematically,Equation 7A prism has a transmittance function equal to,(EQ 7)Equation 8(EQ 8)Here, we assumed that phase is changed, but the amplitude was unalteredpropagating through the prism. k is the wave number whose physical effect is toconvert the linear dimension of the phase function into a fraction of an oscillatorycycle measured in radians. o is a constant term of the phase function.A blazed grating has a transmittance function equal to,Equation 9(EQ 9)ASAP Technical Guide 17
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diffraction gratings and does - Breault Research Organization, Inc.

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