# Phase diffraction grating Phase diffraction grating | Diffraction gratings are perhaps the simplest of diffractive optical elements. In diffractive optical elements, the wave nature of light is the dominant effect as the feature sizes in the element are in the range of tens of micrometers. This gives rise to diffraction effects that by their very nature cannot be explained or simulated by geometrical optics, that is, with ray-tracing techniques. Thus, the design and simulation of a diffractive optical element are based around solutions and simplifications of the diffraction integral which treats the incoming beam as a complex and, usually, continuous function.

Classical transmission diffraction gratings are made by printing opaque lines on a glass substrate. The line spacing is usually defined in line pairs per micrometer. A beam traversing this diffractive structure will experience constructive interference on a set of discrete angular positions which are referred to as diffraction orders. These orders are labeled with numbers that can be either positive or negative. In relevant applications for diffraction gratings, such as spectroscopy or beam steering, the interest resides in the first orders, that is, the plus one or the minus first order.

Now, when calculating the radiance after passing through the diffraction grating, the mathematical formulae for diffractive optics predict a power distribution in which the zeroth-order takes most of it, around 80%. The zeroth-order is the part of the beam that passes through the diffraction grating unaffected, just as if there was nothing there. Thus, if the interest resides in the first diffraction orders, having a transmission diffraction grating made from clear and opaque lines will result in low light efficiency.

To overcome this hindrance the diffraction grating is modified in a way that the amplitude of the passing beam is unaltered, and it is only the phase of the beam that is modulated by the diffractive element. A grating that behaves like this is known as a phase diffraction grating. The opaque and clear lines are replaced by purely transparent lines with the added characteristic that every other line has an extra step of transparent material, so the beam experiences a longer optical path along that strip. Thus, the output beam is said to be phase modulated.

With a phase diffraction grating, the power on the zeroth-order can be, in theory, completely suppressed for a specific wavelength. This in turn results in much power being allocated to the first diffraction orders.

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