A dual-functionality metalens to shape a circularly polarized optical vortex or a second-order cylindrical vector beam
Introduction
The trend towards the miniaturization of optical elements has generated interest in optical metasurfaces, which are ultrathin-film optical elements that enable the amplitude, phase, and polarization of light to be controlled simultaneously. The most widely used optical elements – lenses based on metasurfaces, were proposed in Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], in which the desired characteristics were attained by using metalenses containing optical antennae. For example, antennae in the form of elliptical cylinders [2] and L-shaped antennae [4] have been proposed. Another way to control characteristics of a light field is through the use of subwavelength diffraction gratings: with the subwavelength grating being anisotropic, TE-and TM-waves will have different phases and amplitudes after passing through it. Based on this effect, analogs of conventional polarization converters and wave plates can be designed [10]. In particular, in a number of earlier papers, we experimentally characterized optical metasurfaces intended to generate a subwavelength focal spot. For instance, in Ref. [11], using a 16-sector metalens, linearly polarized incident light was converted into an azimuthally polarized optical vortex and focused into a subwavelength focal spot whose size was less than the diffraction limit. Obtaining focal spots of size below the diffraction limit is not the only remarkable effect that can be observed. Other recently discovered effects include multi-segmented light tunnels [12], [13], optical chains [14], [15], and flat-top foci [16], [17]. Previously, we have theoretically shown that by focusing light with a carefully selected polarization state and phase it is possible to generate tight-focus regions where the Poynting vector is directed oppositely to the incident light [18], [19], [20].
The latest advances in the development of high-efficiency, high-NA metalenses have been set forth in Refs. [21], [22], [23], [24], [25], [26], [27], which deal with multifocus metalenses. Such metalenses are capable of generating an array of foci along the optical axis or in a transverse plane. In this work, rather than studying the multifocal properties of the metalens, we aim at demonstrating multi-functionality. Depending on the type of the illuminating beam, the metalens under study is able to generates in the focus a beam with either phase or polarization singularity.
In an earlier work [28], we reported on the design of a similar metalens, theoretically showing it to form a reverse energy flow at the focus and presenting a prototype metalens, which proved to be of inferior quality, preventing us from its detailed experimental characterization. Here, we report on the fabrication of a high-quality metalens, enabling an optical experiment to be conducted and results that prove the generation of the reverse energy flow in the tight focus to be obtained. The high quality of the metalens under analysis is corroborated by the good agreement between the results of the experiment and the rigorous numerical simulation. The use of a metalens with high NA enables the magnitude of the reverse energy flow to be increased.
Below, we discuss the fabrication and characterization of a metalens intended to generate a reverse energy flow in the focus. The metalens under study combines a spiral Fresnel zone plate with 633 nm focus and a 16-sectored polarization converter based on subwavelength binary diffraction gratings of period 220 nm and depth 120 nm. The multi-sectored polarizer converts an incident linearly polarized Gaussian beam into a cylindrical second-order vector beam, being also able to convert a right-hand circularly polarized Gaussian incident beam into a right-hand circularly polarized optical vortex with topological charge m = –2 and a left-hand circularly polarized Gaussian beam into a left-hand circularly polarized optical vortex with m = +2. Unlike our previous works dealing with metalenses based on subwavelength diffraction gratings [11], [28], this work reports on the fabrication and experimental characterization of a metalens specifically designed to create a reverse energy flow in the strong focus. A distinctive feature of the fabricated metalens is that after passing it, an arbitrary input beam with uniform polarization generates an on-axis near-focus reverse energy flow. It would be possible to generate similar intensity distributions with a combination of a 2nd-order liquid crystal q-plate [29] and a focusing microlens (100х, NA = 0.95), as reported in Ref. [30]. Meanwhile, in this work, we propose using a single metalens capable of successfully replacing the 'q-plate plus microlens' combination. Therefore, the major finding of this work is that, through transverse intensity measurements, we have proven that the metalens generates either a circularly polarized optical vortex or a vortex-free cylindrically polarized optical beam. Besides, we have shown that in both cases, a reverse energy flow occurs in the focus.
Section snippets
Theoretical background
The operation of a spiral optical metasurface [28] can be schematically defined by the Jones matrix , which describes the polarization vector rotation by a polar angle φ. When illuminated by a TE-wave (projection Ex of the incident E-field), the metasurface R(φ) with m = 2 produces the output second-order radial polarization:
When illuminated by a TM-wave (projection Ey of the incident E-field), at the output is an azimuthally
Design, fabrication, and relief measurements of a metalens
Fig. 1а depicts the metalens of interest. A detailed description of the design of such a metalens can be found in Ref. [28]. The metalens combines a sectored wave-plate and a spiral Fresnel zone plate of focal length f = λ = 633 nm (numerical aperture: NA≈1). The wave-plate serves as a polarization converter of incident light, which is described by a Jones matrix , where φ is the polar angle in the metalens plane.
The metalens under study was synthesized in amorphous
FDTD-aided numerical simulation of the metalens
The FDTD-aided numerical simulation implemented using the FullWave software [42] has shown that the metalens generates a reverse energy flow when illuminated by light of an arbitrary polarization, be it linear, right- or left-handed circular polarization. The computations were conducted for a λ/30 mesh along all three axes, with the initial field containing 601х601 pixels for an 8 × 8 μm area. Fig. 3 depicts the arguments (phases) of the transverse E-vector projections Ex and Ey (Fig. 3а and b)
Experiment
While being unable to directly measure the reverse energy flow, we are still able to demonstrate experimentally its presence in a certain region. In this work, aiming to detect a reverse energy flow near the optical metasurface, we utilized a hollow metal pyramid probe with a 100 nm nanohole in its tip. The probe was placed in the region where the reverse energy flow was expected, and scanning performed with a 35 nm step. We note that such a probe measures a transverse intensity and not an
Conclusion
A high-NA metalens synthesized in a thin-film amorphous silicon and intended to generate a reverse energy flow in the strong focus of laser light has been experimentally characterized. Such a metalens has been synthesized and characterized for the first time. Its unique feature is that when illuminated by an arbitrary beam with homogeneous (linear, right-or left-handed circular) polarization, the metalens generates an on-axis near-focus reverse energy flow. The 30 µm metalens combined a spiral
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The work was partly funded by the Russian Federation Ministry of Science and Higher Education within a government project of the FSRC “Crystallography and Photonics” of the RAS, the Russian Science Foundation under grant 18-19-00595 (experiment), the Russian Foundation for Basic Research under grant # 18–29-20003 (numerical simulation), EU H2020 Marie Skłodowska-Curie TERRIFIC grant agreement no. 749143, and the European Union's Horizon 2020 Research and Innovation Programme via ASCENT Access
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