# Diffraction grating: arbitrary incident angle

• anandr
In summary, the conversation discusses diffraction on a 1D grating and how it is typically covered in physics books. The simple case of incident light coming along the normal to the grating is usually presented, but there is also a more complicated case where the light is tilted in the plane perpendicular to the stripes. The question is raised about how to handle diffraction when the incident light comes from an arbitrary direction. One person mentions their experience with a Laser printed grating and how the variable d changes with the angle of incidence i. They also mention rotating the grating to change the angle of incidence for ease.
anandr
Diffraction on 1D grating is covered in many physics books. Usually they cover simple case when incident light is coming along the normal to the grating. Sometimes they present slightly more complicated case when incident light is tilted in the plane perpendicular to the stripes (left case on the image below).
Does anybody have an idea how to treat diffraction on a grating when incident light comes from arbitrary direction ( gamma ≠ 0 and i ≠ 0 , right case on the image below )?

I tried to split the incident wave vector k in two components: kx and kyz.
First part (kx) should diffract same way as in case of normal incidence (diffracted maxima will be symmetrically placed around the k across the grating stripes with diffraction angles Θ defined by d*sin(Θ)=n*λ ).
Second part (kyz) seems to be the case presented in left part of the image (these maxima are also symmetrically placed around the k but this time incident angle i is taken into account so d*(sin(Θ)+sin(i))=n*λ ). After that I just added the resulting diffracted wave vectors for each n to get the final diffracted wave vectors. Is this approach correct?

I just played with a Laser printed grating few days ago.

For the Kx part there should be no change with i.
For the Ky part the only variable that changes with i is d. That should look like:
d*cos(i)*sin(Θ)=n*λ
Now i did suppose that the angle of incidence is changed by rotating the grating along the x and y-axis for ease.

## 1. What is a diffraction grating?

A diffraction grating is a device used to separate light into its component wavelengths by causing it to diffract as it passes through closely spaced parallel slits or lines. It is commonly used in scientific experiments and in various optical instruments.

## 2. How does a diffraction grating work?

A diffraction grating works by causing interference of light waves as they pass through the narrow slits or lines on its surface. This interference results in the separation of light into different wavelengths, with longer wavelengths being diffracted at larger angles than shorter wavelengths.

## 3. What is an arbitrary incident angle?

An arbitrary incident angle refers to the angle at which light is shone onto the diffraction grating. It can be any angle, as opposed to specific angles such as 0 degrees (normal incidence) or 90 degrees (grazing incidence).

## 4. How does the incident angle affect diffraction?

The incident angle affects diffraction by determining the angle at which different wavelengths of light are separated. A smaller incident angle will result in a larger separation between wavelengths, while a larger incident angle will result in a smaller separation between wavelengths.

## 5. What are some applications of diffraction gratings?

Diffraction gratings have a wide range of applications, including spectroscopy, optical communications, and laser technology. They are also used in various scientific experiments to study the properties of light and to measure the wavelengths of different sources of light.

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