J. Eur. Opt. Society-Rapid Publ. 2025, 21, 35 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2025032 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Generation of nondiffracting radial carpet-lattice beams by using an extended Durnin’ s setup
Ning Gong 1, 2, Bo Zhang 2, Youxiang Ye 1, Changjiang Fan 2, Yefeng Liu 2, and Zhijun Ren 2,*
1 College of Modern Science and Technology, China Jiliang University, Jinhua, Zhejiang, 321004, PR China 2 Key Laboratory of Optical Information Detecting and Display Technology, Zhejiang Normal University, Jinhua, Zhejiang, 321004,
PR China
Received 16 April 2025 / Accepted 3 July 2025
Abstract. In the past, the researchers have generated radial carpet beams, a type of 2D optical lattice with polar symmetry. However, the classical radial carpet beams expand slowly as they propagate, that is, they are not nondiffracting beams. By introducing an extended Durnin’ s experimental setup equipped with an amplitude-type spatial light modulator loaded with the angular spectrum of a radial grating function, which is distributed along narrow annular pupils, we generated and demonstrated a type of nondiffracting radial carpet-lattice beam. Different from classical radial carpet beams that slowly expand during propagation, the generated nondiffracting radial carpet-lattice beams are propagation-invariant, hence termed nondiffracting radial carpet-lattice beams.
Keywords: Radial carpet-lattice beams, Radial gratings, Durnin’ s experimental setup, Amplitude-type spatial light modulator.
1 Introduction
In 2018, Rasouli and his research team introduced an important class of lattice beams, named combined halfinteger Bessel-like beams [ 1 ]. These lattice beams are generated based on the near-field diffraction of radial gratings. By utilizing different radial gratings, several types of combined half-integer Bessel beams – including radial carpet beams, petal-like beams, and annular vortex beams are generated successively. Among them, radial carpet beams [ 2 – 4 ] exhibit unprecedented 2D optical lattices with polar symmetry. Here, we term the carpet beams featuring a radial lattices optical structure as carpet-lattice beams. Nondiffracting or propagation-invariant optical fields do not present spreading or change in their transverse intensity distribution as they propagate within a finite distance determined by the optical setup. However, classical radial carpet beams expand slowly during propagation. Hence, although their optical structure is maintained, they are not strictly propagation-invariant and thus do not qualify as nondiffracting beams.
The defining characteristic of a nondiffracting beam is the presence of a single longitudinal wavenumber. This implies that nondiffracting beams possess a cone-like angular spectrum that can be mathematically described
* Corresponding author: renzhijun @ zjnu. cn by the Dirac delta function d( v – v 0). In 1987, Durnin proposed and generated the first practical nondiffracting beams: zero-order Bessel beam [ 5 ]. Bessel beams are exact solutions to the scalar Helmholtz equation in cylindrical coordinates, with their amplitude governed by the Bessel function of the first kind. To generate these beams, Durnin and coworkers placed an annular slit in the front focal plane of a lens. This configuration modulated the incident diffracting wavefront, converting it into a conical wave. Subsequently, researchers generate other nondiffracting beams, such as high-order Bessel beams [ 6, 7 ], Mathieu beams [ 8 – 10 ] and parabolic beams [ 11, 12 ], using Durnin’ s setup.
In our scheme, we extend Durnin’ s original setup by creating an annular pupil aperture in the Fourier plane. This aperture incorporates arbitrary azimuthal amplitude components to generate nondiffracting radial carpet-lattice beams. An amplitude-type spatial light modulator( SLM) serves as the key component for angular pupil modulation. In modern optics, SLMs are important modulation element widely used to dynamically generate nondiffracting beams with complex profiles [ 13 – 15 ]. Building upon this principle, an extended version of Durnin’ s experimental setup can be constructed. By loading the spectral information of radial gratings onto the annular slit, we generate a family of nondiffracting radial carpet-lattice beams in the plane after the Fourier transform lens.
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