Transmission function of diffraction grating aperture

Click For Summary
SUMMARY

The discussion centers on deriving the transmission function for a diffraction grating aperture characterized by vertical opaque strips of width 'a' and open spaces of width '2a', with an overall width of 'L = 19a'. Participants emphasize the need to understand how phase contributions from each opening combine to create the field distribution in the Fraunhofer zone when illuminated by a plane wave. A reference to the single-slit diffraction derivation is suggested as a foundational approach to tackle this problem.

PREREQUISITES
  • Understanding of diffraction principles, specifically Fraunhofer diffraction.
  • Familiarity with transmission functions in optics.
  • Knowledge of phase contributions in wave interference.
  • Basic skills in sketching irradiance patterns in optical systems.
NEXT STEPS
  • Study the derivation of the single-slit diffraction pattern to understand phase contributions.
  • Research the mathematical formulation of transmission functions for periodic apertures.
  • Explore the application of Fourier transforms in analyzing diffraction patterns.
  • Investigate software tools for simulating diffraction patterns, such as MATLAB or Python libraries.
USEFUL FOR

Students and professionals in optics, physicists focusing on wave phenomena, and anyone involved in the design and analysis of diffraction gratings.

FiberOptix
Messages
12
Reaction score
0
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.

---------------------------------------------------------

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.
 
Physics news on Phys.org
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.
 

Similar threads

Aperture function of Diffraction Grating
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad How Can One Derive the Diffraction Pattern Formula from a 1D Aperture?
  • · Replies 2 ·
Replies
2
Views
2K
Diffraction grating with slits out of phase
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Fraunhofer diffraction and convolution of two aperture functions
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Diffraction Definition & Common Examples
  • · Replies 1 ·
Replies
1
Views
5K
Graduate How Does a Circular Aperture Affect Light Diffraction?
  • · Replies 1 ·
Replies
1
Views
4K
Can Diffraction Gratings Resolve Close Wavelengths in Visible Light Spectrum?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad 'Diffraction' or 'Interference' gratings ?
  • · Replies 5 ·
Replies
5
Views
8K
Graduate Voltage and current waves in a transmission line
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Abbe theory: diffraction pattern to primary image
  • · Replies 12 ·
Replies
12
Views
3K