Diffraction Gratings

Izentis LLC designs and builds a variety of diffraction gratings. We mostly make gratings with nanoscale periods (often referred to as pitches) for x-ray spectroscopy, which are challenging to fabricate. We have fabricated larger periods, and are happy to fabricate those for our customers.  At present we offer both transmission and reflection gratings with periods ranging from 200 nanometers to 5 microns.

Gratings geometrically disperse light in a way that is analogous to prisms. Prisms refract light according to Snell’s law  and gratings utilize diffraction.

prismsA simple explanation of the physics behind gratings is as follows. Suppose a grating just had two slits and is exposed to spatially coherent monochromatic light from a distant source. As the light passes through the two slits it emanates as two cylindrical waves with the electric fields superimposed on each other. If the peak of one wave intersects the peak of the other, it doubles the electric field creating a bright region. Alternatively when the peak of one wave intersects the trough of another it is cancelled creating a dark region. See figure below for a graphical depiction of double-slit interference.

diffraction

What is particularly interesting is that the regions of interference depend on both the wavelength and distance between the slits. In order to have constructive interference, the optical path length difference between each slit must be an integer multiple of the wavelength of the light. Alternatively the darkest regions occur where the optical path difference is an integer and a half of a wavelength. Since the distance between the slits is fixed, the interference pattern will be a function of the wavelength. As a result, the bright regions will be in different regions of space depending on the wavelength.

This is the basis for grating wavelength-dispersive spectroscopy. If the intensity is measured downstream of the grating, the relative intensity of the various wavelengths in the original source can be calculated. Unfortunately with just two slits, the interference pattern will have a gradual irradiance pattern between the brightest and dark regions, and distinguishing wavelengths is nearly impossible. Gratings for spectroscopy have thousands of slits, which widens the dark regions and narrows the bright regions. Ideally, the only light is where all of the slits contribute an integer multiple in optical path length difference of the wavelength. Anywhere outside of these regions will have destructive interfere from adjacent, and more importantly, non-adjacent slits. Hypothetically, if the light from slits n and n + 25 is destructive, then the slits n + 1 and n + 26 will also be destructive in the same spot, etc. The same could be true for another region in space for light from slits spaced 30 periods, etc. This results in very broad dark regions and narrow spots where there is constructive interference from all of the slits.

The bright regions are referred to as diffraction orders. Since the diffraction orders are very narrow, different wavelengths will be separated and can be measured. This can be visually observed when a grating of micron-scale (μm) period is illuminated with white light generating a rainbow of colors. Soft x-rays have wavelength on the order of a nanometer (nm), and require gratings with nm-scale periods for spectroscopy.

 

 

 

 

 

 

 

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