Transmission function of diffraction grating aperture

• FiberOptix
In summary, the conversation discusses an aperture with vertical opaque strips and open spaces separated by a width of 2a. The overall width of the aperture is 19a. The main topic of discussion is the transmission function for this aperture and the field distribution when irradiated by a plane wave in the Fraunhofer zone. The speaker is having trouble finding a clear expression for the transmission function and is seeking help or references. They suggest referencing a derivation for the single-slit to figure out how the phase contributions from the openings combine to produce a pattern.
FiberOptix
Homework Statement

The aperture has vertical opaque strips of width, a, separated by open spaces of width 2a. The width of the overall aperture is L = 19a.

a) Write a transmission function for this aperture.

b) What would the field distribution be, at a plane in the Fraunhofer zone, if the aperture was
irradiated by a plane wave directed along the normal of the aperture? Draw a sketch of the
irradiance pattern along the X and Y axes of the far field plane.

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Despite searching through some notes and several textbooks I still cannot find a clear expression for a transmission function that includes the specifics of this question. If someone can help or make some useful references that would be very helpful, thank you.

This looks like a pretty specialized, so I doubt you'll find a final formula for it.

They are probably expecting you to figure out how the phase contributions from all the openings combine to produce a pattern. Not sure off the top of my head how to do that, but do you have a derivation for the single-slit you can refer to? That would probably illustrate how to proceed for this case.

1. What is the transmission function of a diffraction grating aperture?

The transmission function of a diffraction grating aperture refers to the mathematical representation of how much light is transmitted through the grating at different spatial frequencies or wavelengths.

2. How is the transmission function of a diffraction grating aperture calculated?

The transmission function can be calculated by taking the Fourier transform of the grating's amplitude or phase profile.

3. Why is the transmission function important in diffraction grating design?

The transmission function is important because it determines the efficiency and spectral properties of the diffraction grating, which are crucial for its performance in applications such as spectrometry and wavelength selection.

4. How does the number of grating lines affect the transmission function?

The number of grating lines affects the transmission function by determining the spatial frequency range over which the transmission function is non-zero. A higher number of lines results in a wider range of spatial frequencies being transmitted.

5. Can the transmission function be modified or optimized for specific applications?

Yes, the transmission function can be modified or optimized by changing the grating parameters such as the number of lines, period, and groove profile. This allows for tailoring the grating's performance for specific applications.

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