Efficient matrix approach to optical wave propagation and Linear Canonical Transforms.

Area of Science:

• Optics and Photonics
• Computational Physics
• Wave Propagation

Background:

• The Fresnel diffraction integral and Linear Canonical Transforms (LCT) are fundamental to modeling optical wave propagation.
• Fast Fourier Transform (FFT) based methods are widely used but have limitations regarding aliasing and boundary conditions.
• Independent control over sampling and window sizes in input/output planes is desirable for computational efficiency.

Purpose of the Study:

• To reformulate optical wave propagation, including Fresnel diffraction and LCT, into a matrix transformation framework.
• To develop a computationally efficient and analytically versatile tool for wave propagation analysis.
• To overcome limitations of existing FFT-based methods, particularly in aliasing, boundary conditions, and sampling flexibility.

Main Methods:

• Representing optical wave propagation via Fresnel diffraction integrals and Linear Canonical Transforms (LCT) as matrix transformations.
• Leveraging efficient matrix multiplication algorithms for computational implementation.
• Developing a method that allows independent sampling and window sizes for input and output planes.

Main Results:

• The matrix transformation approach is computationally competitive with FFT-based methods.
• This method demonstrates improved performance regarding aliasing and transparent boundary conditions.
• Significant speed advantages are observed for calculations requiring only specific output points (e.g., Strehl or power-in-the-bucket metrics).

Conclusions:

• Matrix transformation of LCT offers a powerful and flexible alternative for optical wave propagation.
• The method provides enhanced accuracy and efficiency, especially for targeted output calculations.
• This approach represents a significant advancement in computational optics, offering practical benefits over traditional FFT methods.