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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences.

David G Voelz¹, Michael C Roggemann

¹New Mexico State University, Klipsch School of Electrical and Computer Engineering, Las Cruces, New Mexico 88003, USA. davvoelz@nmsu.edu

|November 12, 2009

Summary

Accurate optical diffraction simulations depend on sampling the phase chirp function. Non-ideal sampling in FFT-based methods reduces simulation accuracy and available support sizes, impacting Fresnel propagation analysis.

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Area of Science:

Computational optics and electromagnetics.
Numerical simulation of wave propagation.

Background:

Accurate simulation of scalar optical diffraction is crucial for various optical system designs.
Fresnel diffraction calculations involve a phase chirp function that requires careful sampling.

Purpose of the Study:

To analyze the impact of sampling regimes on Fast Fourier Transform (FFT)-based Fresnel propagation methods.
To define conditions and consequences of nonideal sampling in optical diffraction simulations.

Main Methods:

Investigated three sampling regimes: ideally sampled, oversampled, and undersampled.
Analyzed three FFT-based Fresnel propagation approaches: angular spectrum, single FFT, and two-step methods.
Examined the discrete transforms of sampled chirp functions and their impact on simulation accuracy.

Main Results:

Nonideal sampling (under- or oversampling) reduces source plane support size, source bandwidth, or observation support size.
Ideal sampling offers the most accurate results but is challenging to implement practically.
Demonstrated the relationships between different methods under ideal sampling and the consequences of nonideal sampling.

Conclusions:

Proper sampling of the phase chirp function is critical for accurate FFT-based optical diffraction simulations.
Understanding sampling limitations is essential for selecting appropriate propagation methods and parameters.
The analysis extends to the sampling constraints of the Rayleigh-Sommerfeld diffraction solution.