Optical computation of the Laplace operator using phase-shifted Bragg grating

Area of Science:

• Optics and Photonics
• Computational Electromagnetics

Background:

• Diffraction of optical beams is fundamental to light manipulation.
• Phase-shifted Bragg gratings (PSBG) offer unique optical properties.
• Spatial operators are crucial for analyzing electromagnetic fields.

Purpose of the Study:

• To investigate the diffraction of 3D optical beams on multilayer PSBG.
• To demonstrate the optical computation of the spatial Laplace operator using PSBG.
• To explore the transformation of Gaussian beams into Laguerre-Gaussian modes.

Main Methods:

• Theoretical analysis of 3D optical beam diffraction.
• Numerical simulations of light interaction with multilayer PSBG.
• Investigation of normal incidence reflection configurations.

Main Results:

• PSBG enables optical computation of the spatial Laplace operator for electromagnetic fields.
• The computation is achieved in reflection at normal incidence.
• A specific PSBG design transforms a Gaussian beam into a Laguerre-Gaussian mode (1,0).

Conclusions:

• PSBG are effective for all-optical computation of the spatial Laplace operator.
• The proposed method demonstrates high-quality Laplacian computation.
• The formation of Laguerre-Gaussian modes is confirmed, paving the way for all-optical data processing.