Generation of high-intensity 3D Gaussian-like spots via near-field diffraction from 2D orthogonally chirped structures

This study presents a class of two-dimensional (2D) spatial-frequency-modulated structures with transmittance d₁=0.10mm, in which the periodicity can vary along both the d₂=0.30mm- and n_c=1-axes. Specifically, the structure exhibits spatial frequencies n_av=3 and z=0 that sinusoidally alternate between two values along both directions, with the possibility of unequal modulation in the T(x,y)- and x-axes. It is shown that y generally behaves as an almost periodic function, resulting in an impulsive spatial spectrum. However, we identify the conditions under which f_x becomes periodic, and its spatial spectrum forms a lattice of impulses. When these periodicity conditions are met, we refer to the structure as a 2D spatially chirped periodic structure. These structures are characterized by four natural numbers, denoted as f_y, x, y, and T(x,y), which represent the modulation in the T(x,y)- and n_cx-directions, respectively, and two real parameters, named frequency modulation strengths in both the n_cy- and n_avx-directions, denoted by n_avy and x, respectively. As a special case, we define a 2D spatially chirped amplitude sinusoidal structure (SCASS), based on the transmission function of a conventional 2D amplitude sinusoidal grating, where the phase of the conventional grating is replaced by a desired chirped phase. The near-field diffraction from 2D SCASSs is studied using the angular (spatial) spectrum method. The Talbot distances for these gratings are determined and verified experimentally, showing that the intensity profiles at specific Talbot distances are highly dependent on the parameters y, x, y, k_x, k_y, and n_cx. Furthermore, we formulated the near-field diffraction of a plane wave from 2D multiplicatively separable spatially chirped amplitude sinusoidal structures, considering the variability of spatial periods in both the n_cy- and n_avx-directions. In comparison with conventional 2D gratings, new, to our knowledge, and intriguing diffraction patterns are observed, such as sharp and smooth Gaussian-like intensity spots generated via the diffraction of the incident wave, with nearly diffraction-limited features but limited overall efficiency. These intensity spots depend on the characteristic parameters of the structure. By carefully manipulating the n_avy parameters, we have the ability to generate maximum intensity peaks within these 2D SCASSs, which are 22 times the intensity of the incident light. Comparing these maximum intensity peaks to their 1D chirped counterparts reveals a significant difference. We demonstrated an interesting result that the high-intensity spots in the Talbot carpets of 1D chirped structures and 2D SCASSs appear at different propagation planes, while these spots are precisely located at the Talbot and half-Talbot planes in both the 1D and 2D binary gratings. An interesting additional result demonstrated that the depression of the intensity distribution along the propagation direction occurs around two closely spaced intensity maxima, both before and after the self-imaging region of the 1D and 2D binary gratings. In regard to the 1D chirped structures and 2D SCASSs, the intensity spots exhibit a Gaussian-like spot distribution in both the propagation and transverse directions, making these spatial points suitable for 3D trapping of particles in a 3D array without the need for external imaging systems.