Ultra-compact, high-numerical-aperture achromatic multilevel diffractive lens via metaheuristic approach

Abstract

Recently, the multilevel diffractive lenses (MDLs) have attracted considerable attention mainly due to their superior wave focusing performance; however, efforts to correct the chromatic aberration are still in progress. Here, we demonstrate the numerical design and experimental demonstration of high-numerical aperture (NA) (~0.99), diffraction-limited achromatic multilevel diffractive lens (AMDL) operating in microwave range 10 GHz-14 GHz. A multi-objective differential evolution (MO-DE) algorithm is incorporated with the three-dimensional finite-difference time-domain (3D FDTD) method to optimize both the heights and widths of each concentric ring (zone) of the AMDL structure. In this study, the desired focal distance ( d F  ) is treated as an optimization parameter in addition to the structural parameters of the zones for the first time. In other words, MO-DE diminishes the necessity of predetermined focal distance and center wavelength by also providing an alternative method for phase profile tailoring. The proposed AMDL can be considered as an ultra-compact, the radius is 3.7 c  where c  is the center wavelength (i.e., 12 GHz frequency), and flat lens which has a thickness of . c The numerically calculated full-width at half-maximum (FWHM) values are below 0.554λ and focusing efficiency values are varying between 28% and 45.5%. To experimentally demonstrate the functionality of the optimized lens, the AMDL composing of polylactic acid material (PLA) polymer is fabricated via 3D-printing technology. The numerical and experimental results are compared, discussed in detail and a good agreement between them is observed. Moreover, the verified AMDL in microwave regime is scaled down to the visible wavelengths to observe achromatic and diffraction-limited focusing behavior between 380 nm -620 nm wavelengths.

Revolutionary meta-imaging: from superlens to metalens

“…21(j)] or at several discrete wavelengths with the same interval [red line in Fig. 21(j)] [185][186][187][188][189][190][191][192][193][194][195][196][197] . The free-form MDL is designed by inverse design as introduced in Section 3.4.…”

“…To further increase the DoF in design, a new class of diffractive lenses, denoted free-form MDLs, has been proposed in recent years [185][186][187][188][189][190][191][192][193][194][195][196][197] . The height profile of the free-form MDL is irregular and quite different from that of conventional diffractive lenses, as shown in Fig.…”

“…More details about other FoMs, such as the difference between real and ideal light intensity distributions at the focal plane or the difference between real and ideal phase profiles at lens surfaces, are presented in Refs. [185,190,191].…”

“…Other algorithms such as brute-force search or gradient-descent are also applied to solve Eq. (24) in some related works [190,191] . It should be mentioned that almost all of these methods are local optimization algorithms and cannot achieve the optimal height profile by just one trial.…”

“…(g) Broadband AMDL over the long-wave infrared region (8–12 µm) with NA=0.45 and diameter equal to 15.2 mm [28] . (h) Broadband AMDL over the microwave region (10–14 GHz) with NA=0.99 and diameter equal to 186 mm [191] .…”