Planar immersion lens with metasurfaces

John S. Ho, Brynan Qiu, Yuji Tanabe, Alexander J. Yeh, Shanhui Fan, and Ada S. Y. Poon

Phys. Rev. B 91, 125145 – Published 30 March 2015

Abstract

The solid immersion lens is a powerful optical tool that allows light entering material from air or a vacuum to focus to a spot much smaller than the free-space wavelength. Conventionally, however, the lenses rely on semispherical topographies and are nonplanar and bulky, which limits their integration in many applications. Recently, there has been considerable interest in using planar structures, referred to as metasurfaces, to construct flat optical components for manipulating light in unusual ways. Here, we propose and demonstrate the concept of a planar immersion lens based on metasurfaces. The resulting planar device, when placed near an interface between air and dielectric material, can focus electromagnetic radiation incident from air to a spot in the material smaller than the free-space wavelength. As an experimental demonstration, we fabricate an ultrathin and flexible microwave lens and further show that it achieves wireless energy transfer in material mimicking biological tissue.

Received 15 September 2014
Revised 5 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.125145

Authors & Affiliations

John S. Ho¹, Brynan Qiu², Yuji Tanabe¹, Alexander J. Yeh¹, Shanhui Fan¹, and Ada S. Y. Poon^1,*

¹Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
²Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA

^*adapoon@stanford.edu

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Issue

Vol. 91, Iss. 12 — 15 March 2015

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Images

Figure 1
Refraction at a planar interface between air and high-index material. (a) Ordinary refraction. Light cannot be refracted beyond the critical angle $θ_{critical}$ since the corresponding beam is trapped by total internal reflection (dashed red line). (b) Refraction with an immersion lens. The lens enables light to both enter (black line) and escape (dashed red line) material at a forbidden angle. Light can thus be focused to $\sim λ / n$ , where $n$ is the material refractive index. (c) Refraction with a metasurface. The metasurface changes the amplitude and phase of light, enabling it to refract at a forbidden angle.
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Figure 2
Refraction at forbidden angles with a metasurface. (a) Metasurface consisting of metallic strips reactively loaded with impedances varying in the $x$ direction. The strips, separated by a distance of $s = λ / 20$ , are periodic in the $y$ direction and impart a phase gradient of $π / 0.55 λ$ on incident $s$ -polarized radiation. (b) Magnetic field amplitude $| Re (H_{x}) |$ below the metasurface in the air gap and material ( $n = 2$ ) for a plane wave at $θ_{inc} = 30^{\circ}$ . (c) Magnetic field in air when the material volume is removed. (d) Contour plot of the angular spectrum of the refracted beam as a function of the angle of incidence. The solid white line is the angle of refraction predicted by the generalized Snell law and the solid purple line ordinary refraction.
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Figure 3
Focusing across an interface with a metasurface. (a) Metasurface lens above a material with refractive index $n = 2$ . The strips are assumed to be periodic in the $y$ direction. (b) Magnetic field intensity in material for incident $s$ -polarized radiation. The focal plane (dashed line) is $4 λ / n$ from the lens. (c) Intensity profile at the focal plane for a plane wave at normal incidence. The spot width is $0.42 λ$ FWHM for the lens (dark shading) and $λ$ for the grating (light shading). The grating consists of metal strips without passive elements.
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Figure 4
Optimal focusing across an interface. (a) Focusing in material with an optimized current sheet (contour plot of $| Re (H_{x}) |$ shown). The material is 0.5% saline water ( $n = 8.8 + i 0.9$ at 1.5 GHz). The focal plane (dashed white line) is located $2.3 λ / n$ (wavelength in material) from the current sheet. (b) Magnetic field intensity profile and (c) angular spectrum at the (1) source, (2) interface, and (3) focal planes. The shaded region in (b) denotes the width of the focal spot $λ / 11$ (FWHM). Shaded regions in (c) show the propagating wave vectors $1 < | k_{x} / k_{0} | < 8.8$ supported by material.
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Figure 5
Planar immersion lens with concentric rings. (a) Metasurface lens consisting of concentric rings for focusing an incident plane wave. The rings are loaded with passive elements. The lens is positioned $λ / 15$ above saline water. (b) Phase profile of the magnetic field ( $H_{x}$ ) exiting the lens along the $x$ axis. The phase response of the lens matches the profile derived from the optimization procedure within the aperture. (c) Contour plot of the magnetic field intensity. The focal plane is located $2.3 λ / n$ (wavelength in material) away from the lens. Simulations are performed at 1.6 GHz.
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Figure 6
Focusing in a dielectric liquid using a coaxial-excited lens. (a) Focusing in a 0.5% saline solution with a metasurface lens. The lens is excited across the center gap (white circles) at 1.6 GHz by a coaxial cable. Separation between the lens and interface, 1 cm; focal plane and lens, 5 cm. (b) Photograph of the lens. (c) Magnetic field intensity profile at the focal spot. The theory curve is calculated using the refractive index $n = 8.8 + i 0.9$ . (d) Energy transfer to a 2-mm device as a function of distance. Inset images show the brightness of a light-emitting diode on the device. The output power is 500 mW. Scale bar, 1 cm.
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