Semiclassical theory of the Hyperlens

Abstract

We study ray dynamics inside the Hyperlens, a device recently demonstrated as capable of sub-diffraction-limited far-field imaging.The obtained semiclassical result of spiraling rays is confirmed by numerical simulations of gaussian beam scattering from the hyperlens.A conventional lens cannot construct the image of an object with resolution better than λ/2, where λ is the wavelength of the illuminating wave. This is because the conventional lens brings to focus only the propagating waves emanating from the object while the evanescent waves decay away exponentially and are lost in the far field. Such an apparent loss of information gives rise to the diffraction limit of λ/2. It is therefore highly desirable for many practical applications, such as biological imaging, to be able to construct images with feature sizes much below the wavelength of the illuminating light [1].Recently it was proposed that a hollow core cylinder or half-cylinder made of materials with a strongly anisotropic dielectric response [2,3] can function as a far-field imaging device capable of resolution beyond the diffraction limit [4]. The object is placed inside the hollow core and the magnified image is projected into the farfield which can be processed by conventional optics. The local wavelength at the core of the device, where the object to be imaged is placed, is below the free space wavelength and this leads to the subwavelength resolution [4,5]. The hyperbolic dispersion in strongly anisotropic materials (materials with dielectric permitivitties of opposite signs in two perpendicular directions) is the key to achieving the wavelength compression in the Optical Hyperlens.The advantages of semiclassical approach are two-fold. First, the connection to the underlying ray optics uncovers the physical origin of light propagation and imaging in the device. Second, as opposed to 'brute-force' numerical methods that are computationally intensive and suffer from instabilities when treating evanescent fields, the semiclassical approach while quantitatively accurate, is both numerically inexpensive and stable.The accuracy of the semiclassical approach in the hyperlens is due to the wavelength compression in this device. As the light approaches the core of the hyperlens, due to the hyperbolic dispersion relation the radial and tangential momentum increase, leading to substantial suppression of wavelength. Fig. 1 (a) Schematic of the hyperlens (hollow inner core) with alternating layers of metal and dielectric to achieve ε r <0 and ε θ >0 (b) path of 2 rays (shown in red) with different impact parameters impinging from vacuum onto a homogeneous medium with cylindrical anisotropy ε r = -1 and ε θ = 1 calculated using eq. (1) (c) path of the ray calculated using eq. (1) for ε r = -0.01 and ε θ = 1. Note that the rays spiral towards the center. a2032_1.pdf JWA2.pdf ©OSA 1-55752-834-9

Advances in the hyperlens

“…coined, concentrates on the curved surfaces appearing in a cylindrically symmetric geometry and expounds on the fundamental theory of why and how a hyperlens works [12]. Additional work by this group led to a ray optics approach to the understanding of the hyperlens [20].…”

“…Additional theory regarding the ray optics of the cylindrical hyperlens was developed based on the eikonal/ Hamiltonian approach [20]. A major result of this study is the understanding of the profound scattering that occurs due to a combination of rays following a spiral-like path through the hyperlens and the large reflections at the hyperlens surfaces, as shown in Figure 3(a).…”

“…Two-dimensional field plots are also shown for the internal (c) and external (d) matching conditions. Reprinted with permission from[20,22].…”

Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe

“…We remark that in Ref. [17] both trajectories given by Eqs. (77) and (82) were obtained through numerical simulations in a scattering experiment in a hyperlens system.…”

Image quality deterioration due to phase fluctuation in layered superlens

“…Therefore, the operating wavelength can be tuned by adjusting a rather than the dielectric medium of the surroundings [4,6]. Furthermore, hyperlens-like structures based on layered structure are supposed to magnify subwavelength images beyond the diffraction limit [17][18][19][20][21].…”