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Timestamp: 2019-04-26 00:50:29+00:00

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We design plano–concave silicon lenses with coupled gradient-index plasmonic metacoatings for ultrawide apertured focusing utilizing a reduced region of ∼20λ2. The anomalous refraction induced in the planar input side of the lens and in the boundary of the wavelength-scale focal region boosts the curvature of the emerging wavefront, thus significantly enhancing the resolution of the tightly focused optical wave. The formation of a light tongue with dimensions approaching those of the concave opening is here evidenced. This scheme is expected to have potential applications in optical trapping and detection.
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Fig. 1. Schematics based on optical rays of the focusing action of plano–concave dielectric lenses. (a) Transparent dielectrics with an index of refraction higher than unity lead to a diverging configuration. (b) An epsilon-near-zero metamaterial enables us to focus light at the center of curvature of the concave surface. (c) An increased numerical aperture is attained by using negative-index metamaterials. (d) Our proposal based on coupled metacoatings set at the entrance and exit surfaces of a transparent dielectric thick lens. A focused beam of semiaperture angle Ω will be generated by passing through the gradient-index flat metasurface. The converging wave field propagating inside the lens will be refocused at F ′ by means of the active curved metacoating, having an increased semiaperture angle Ω ′ .
Fig. 2. (a) Intensity distribution | H | 2 generated by a nonuniform surface current with modulated phase distribution given by Eq. (3) and set at the front surface of a plano–concave Si lens (sketched in white solid line), mimicking the effect of the designer metacoating. In (b) we set the surface current with phase distribution given by Eq. (4) at the back surface of the Si lens. Normalized intensity of the magnetic field in the focal volume of the flat (cylindrical) surface current, represented in green solid lines (red dashed lines) as measured along (c) the x -axis and (d) the y -axis. On-axis resolution critically improves with an active cylindrical surface while transverse resolution does not change significantly.
Fig. 3. Effective index of refraction evaluated with Eq. (5) for a gold-silicon periodic medium at a wavelength of λ = 800 nm . Silicon layers are set with a fixed width w d = 15 nm . The metal filling fraction is governed by the Au films width w m .
Fig. 4. Phase shift gained by a TM-polarized plane wave traversing through an Au-Si metacoating of thickness d = 100 nm , as set in an air/silicon plane interface. For simplicity, we represent the phase shift in an interval ranging from − π to π . The slit width of the periodic nanostructure is fixed at w d = 15 nm and we vary the metal width w m . In (a) the beam impinges from air, and in (b) from silicon. The red dashed line establishes the phase shift measured for an all-dielectric coating ( w m = 0 ). Red squares illustrate that metamaterials with w m = 9 , 15, and 23 nm producing incremental phase shifts of approximately π / 2 rad with respect to a nonconducting film.
Fig. 5. Transmittance (T), reflectance (R), and absorptance (A) calculated for Au-Si metacoatings as described in Fig. 4, varying the width w m of the metallic wires. The beam impinges from (a) air and from (b) Si.
Fig. 6. Transmittance of metallic nanostructures with different Au wire width w m as a function of thickness d of the metacoating, calculated at a wavelength λ = 800 nm . Here we set w d = 15 nm .
Fig. 7. FEM-based numerical simulations showing the intensity of the magnetic field when a monochromatic TM-polarized plane wave passes through a Si plano–concave lens of radius R = 3 μm and vertex distance of 200 nm: (a) without metacoatings, (b) including a single metacoating set on the flat front surface, and (c) with coupled metacoatings lying on the front and back surfaces of the lens. (d) Close-up of patterned Au nanoslit arrays in the flat (top) and concave (bottom) surfaces of the Si lens.
Fig. 8. Intensity distribution produced in the focal region of a Si plano–concave lens including metacoatings with different arrangements of elementary metal–dielectric gratings. (a) A metallic grating of period Λ 3 = 38 nm is used at the central zone of both metacoatings. Alternatively, we use an all-dielectric central zone for one metacoating and a metallic grating of period Λ 3 in the center of (b) the cylindrical metacoating, and (c) the front flat metacoating. In (d) we reproduce Fig. 7(c), where the central zone of both metacoatings has no metallic components, but here using the same color map of previous subfigures.
Fig. 9. Intensity distribution of focal waves produced by tilted TM-polarized plane waves with angles (a) θ = 5 ° , (b) 10°, and (c) 15°, all measured with respect to the optical axis y = 0 .
Fig. 10. Intensity of the magnetic field in the focal region of a metacoated Si plano–concave lens of radius R = 2 μm , setting the focal shift parameter as a = 1 μm .
(6) t = τ 12 τ 23 exp ( i k n eff d ) 1 − ρ 21 ρ 23 exp ( 2 i k n eff d ) .

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