Propagation of truncated Gaussian beams and their application in modeling sharp-edge diffraction

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Gaussian beams are fundamental in optics.
• Conventional methods struggle with sharp edges in diffraction.
• Accurate modeling of diffraction from apertures is crucial.

Purpose of the Study:

• Introduce novel truncated Gaussian beams (half and quarter).
• Develop analytical propagation formulas for these beams.
• Enhance Gaussian beam decomposition for arbitrary hard apertures.

Main Methods:

• Defined half and quarter Gaussian beams using the Heaviside unit step function.
• Derived exact analytical propagation formulas via the generalized Collins integral.
• Combined truncated Gaussian beams with a modified Gaussian beam decomposition method.

Main Results:

• Successfully represented sharp edges of fields after hard apertures.
• Developed a method to calculate diffraction from arbitrary hard apertures.
• Demonstrated improved accuracy, especially in the near field.

Conclusions:

• The modified Gaussian beam decomposition method accurately models diffraction from hard apertures.
• Truncated Gaussian beams offer a powerful tool for analyzing complex diffraction phenomena.
• This work overcomes limitations in modeling fields with sharp edges.