diffraction gratings and does - Breault Research Organization, Inc.

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DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical ElementsIf the phase difference between lines P 1 P 2 and P 3 P 4 is an integer number ofmultiple wavelengths , all the waves from the secondary wavelets are in phase inthe direction corresponding to m . Operationally, this is,Equation 3The above equation is called the grating equation, and m is called the grating ordiffraction order. Note that the grating equation is independent of the refractiveindex of the slab substrate. This can be easily validated with Snell’s law. Thegrating equation is the same, even in the case of the phase reflection grating.(EQ 3)The grating equation is the same as the equation that describes the maximumorders for Young’s double slit experiment. However, there are some fundamentalphysical differences in the diffraction patterns for each situation:• The diffraction or interference pattern from Young’s double-slit experiment isdue to an amplitude transmission grating. It is also more diffuse or less sharpthan that from the phase diffraction grating. This is primarily due to the largersize of the apertures in Young’s double slit experiment as compared to therelatively small line sources in the diffraction grating. In Young’s experiment,different points across the two apertures, other than the center points, can be inphase with each other and constructively interfere at slightly different locationsthan the center points causing a broadening of the diffraction pattern in thatorder.• The linear phase transmission grating behaves more like a Fabry-Perot etalon orfilter.Blazed gratingsIn many applications that use linear diffraction gratings, we are not interested inthe light in the zeroth order. This light is often wasted. It is useful to transfer lightout of the zeroth order and into another order or arbitrary direction other than thespecular direction. Many modern diffraction gratings, especially phase reflectiongratings are blazed to accomplish this task.John William Strutt Rayleigh, or Lord Rayleigh suggested a clever way to transferenergy out of the zeroth order into other orders. This involved changing the angle14 ASAP Technical Guide
DIFFRACTION GRATINGS AND DOESFundamentals of Diffractive Optical Elements. . . . .of or tilting the surfaces that the specular light sees in between the grating lines.Such a grating is called a blazed grating.The key to a blazed grating is that the angular direction of the non-zero diffractionorders are a function of the grating spacing d, the wavelength of the incident light, and the angle of incidence i . However, m and i are measured from thegrating plane and not the blazed (tilted) surface. If we tilt the specular surfaces inbetween the grating lines, we change the direction of the specular output, but notthe higher diffraction grating orders. Figure 3.Blazed GratingdGratingPeriodBlaze AngleGrating has RefractiveIndex nFigure 3 Blazed transmission gratingThe diffraction efficiency of a given order for regular and blazed linear phasegratings can be calculated using scalar diffraction theory. Swanson, for example,gives the result for diffraction efficiencies as,ASAP Technical Guide 15
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