Diffractive elements with multi-ring spectra

Abstract We introduce pure amplitude almost periodic structures (APSs) with multi-ring spatial spectra, characterized by four degrees of freedom in the spectral domain: the number of rings, the number of impulses on each ring, the radius of each ring, and the angular positions of the impulses within a ring. A comprehensive mathematical framework is developed to describe the diffraction of arbitrary optical beams by such structures. This framework is theoretically validated and experimentally verified through the analysis of diffraction patterns produced under Gaussian beam illumination. The method is systematically tested on various APS configurations, including structures with one, two, three, and four rings, as well as different impulse arrangements within these rings, demonstrating its robustness and adaptability. Notably, each APS achieves a high diffraction efficiency, transferring approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>N</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>N</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> of the transmitted beam power to each impulse, where 2 N represents the total number of impulses excluding the zero-diffraction order. This efficiency is significantly superior to that of conventional spatial light modulators. Additionally, a detailed comparison between theoretical predictions and experimental measurements of power ratios for the diffraction orders confirms the accuracy and reliability of our approach. The versatility of APS makes them highly suitable for a range of applications, including optical communications, optical tweezing, multi-particle trapping, screening, micro-manipulation, and microscopy. For example, APS-enhanced Gaussian lattice beams can improve imaging speed in fluorescence microscopy. Furthermore, their ability to enable three-dimensional optical multiple trapping and beam splitting positions APS as a powerful tool for advancing laser and optical research.