Mikaelian Lens Research Articles

Morse lens [Invited

In this Letter, we find that Morse potential (proposed about 90 years ago) could be connected to Coulomb potential (or Newton potential) and harmonic potential (or Hooke potential) by conformal mappings. We thereby design a new conformal lens from Morse potential, Eaton lens, and Luneburg lens and propose a series of generalized Eaton/Luneburg lenses. We find that this Morse lens is a perfect self-focusing asymmetric lens that differs from a Mikaelian lens. Our theory provides a new insight to Morse potential and other traditional potentials, and revisits their classical applications on designing lenses.

Two-Dimensional Problem of Electromagnetic Scattering by Mikaelian Lens, Two Methods of Solution, and Some Features of Focusing

Two-Dimensional Problem of Electromagnetic Scattering by Mikaelian Lens, Two Methods of Solution, and Some Features of Focusing

Maxwell's fish-eye lenses under Schwartz-Christoffel mappings

In this paper, we designed Maxwell's fish-eye lens in a square shape from a conformal mapping and constructed it into a waveguide and a photonic crystal. We studied the unidirectional self-imaging effect from both geometric optics and wave optics. Ray tracing and full-wave simulations were performed to validate this effect. Specifically, the designed waveguide is of a finite width while having the same imaging properties as the ideal infinite waveguide---the Mikaelian lens, the refractive index profile of which is 1/cosh ($x$) [Mikaelian and Prokhorov, Prog. Opt. 17, 279 (1980)].

Conformally Mapped Multifunctional Acoustic Metamaterial Lens for Spectral Sound Guiding and Talbot Effect.

We demonstrate a conformally mapped multifunctional acoustic metamaterial Mikaelian lens. Mikaelian lens is a gradient medium with a hyperbolic secant refractive index profile that can realize functions like beam self-focusing. Unlike the conventional design approaches, with a conformal transformation method, only isotropic material parameters with gradient refractive index profiles are required for the construction of such lens. To realize desired gradient index distribution, we carefully design a new type of cross-channel-shaped acoustic metamaterial, whose refractive index can be effectively modulated by simply changing the slit opening size. The distinct capabilities of the metamaterial Mikaelian lens in manipulating acoustic waves are experimentally verified with the fabricated sample. Simultaneous sound guiding and Talbot effects, which normally require respective geometrical and wave acoustic approximations, are observed in simulations and experiments. Furthermore, those effects of shaping acoustic wave propagations were validated within a relatively wide frequency range. Our study reveals how the conformal transformation method can help to bridge the ray acoustics with wave acoustics. It offers opportunities to the development of novel multifunctional acoustic devices for various applications, such as sound and particle manipulations.

Imaging along conformal curves

In this article, we prove that conformal transformation optics could be used to construct absolute instruments. The Mikaelian lens, whose refractive index profile is $1/cosh(\mathrm{x})$ [A. Mikaelian and A. Prokhorov, Progress in Optics 17, 279 (1980)], are of imaging functionalities along lines and will be used as a generic lens. Under a conformal mapping, it can be transformed to another lens, where imaging or self-imaging happens along predesigned curves. Ray tracing simulations are performed to confirm the imaging functionalities.

Compact Mikaelian Lens Synthesized by Metasurfaces

Synthesized using metasurfaces, we propose the implementation of the rectangular Mikaelian lens, one that is not only just flat but now also thin, thus enabling impingent wavefronts to converge at focal points over shorter distances, a feature that no other contemporary types of circularly shaped lenses are able to achieve. The subsequent savings of space and weight afforded by this unique property could be invaluable. By further postprocessing of the fields extracted from the simulations, the degree of focusing attained by the lens is also quantitatively characterized, thus offering insights beyond mere visual inspection of field patterns. The phenomenon of power concentration has been successfully demonstrated with simulations that are well corroborated by results of measurements carried out on a manufactured prototype.

Analysis of a conformal invisible device

We perform a semi-analytical calculation of the field distributions of a conformal invisible device via mode expansions. For a discrete set of frequencies in the regime of wave optics, the conformal invisible device is perfectly transparent, which stems from the special conformal mapping and the refractiveindex profile of the Mikaelian lens.

Planar anisotropic Mikaelian lens on the basis of EBG-structure

The problem on the synthesis of a planar Mikaelian lens in the form of layered metal−dielectric waveguide with a nonuniform anisotropic dielectric layer is solved. The problem is reduced to solution of the dispersion equations for E and H modes of a homogeneous layered waveguide. As an example of implementation of the solution obtained, the synthesis and analysis of the Mikaelian lens is carried out on the basis of the EBG structure in the form of a planar corrugated open and closed layered metal−dielectric waveguide. For a special case of the closed waveguide, the solution of the problem of synthesis for both polarizations is obtained explicitly.

Perfect conformal invisible device with feasible refractive indexes

Optical conformal mapping has been used to construct several isotropic devices with novel functionalities. In particular, a conformal cloak could confer omnidirectional invisibility. However, the maximum values of the refractive indexes needed for current designs are too large to implement, even in microwave experiments. Furthermore, most devices designed so far have had imperfect impedance matching and therefore incomplete invisibility functionalities. Here we describe a perfect conformal invisible device with full impedance matching everywhere. The maximum value of refractive index required by our device is just about five, which is feasible for microwave and terahertz experiments using current metamaterial techniques. To construct the device, we use a logarithmic conformal mapping and a Mikaelian lens. Our results should enable a conformal invisible device with almost perfect invisibility to be made soon.

Design and characterization of a foam-based Mikaelian lens antennas in millimeter waves

The design principles and radiation performances of Mikaelian lens antennas are presented. The ways to manufacture gradient index lenses are briefly reviewed. An innovative technique based on the variation of the foam density is described and applied to the Mikaelian lenses. This yields low cost and lightweight gradient index lenses. The focusing properties of Mikaelian lenses are compared numerically to Luneburg lenses. A foam-based planar Mikaelian lens antenna is manufactured and its radiation performances are characterized at 60 GHz. With its flat shape in contact to the primary source, the cylindrical Mikaelian lens turns out to be, for focusing purposes, an interesting alternative to the well-known Luneburg lens.

Photonic Crystal Mikaelian Lenses and Their Potential Use as Transverse Focusing Elements in Microstructured Fibers

We numerically studied the focusing properties of a special type of graded index photonic crystal media, i.e., the so-called photonic crystal Mikaelian lenses (PCMLs). We considered PCMLs with a varying air hole diameter and with a varying air hole pitch in hexagonal and rectangular lattices, and we compared their frequency response and polarization dependence. Our eventual objective is to design microstructured optical fibers equipped with a PCML in their cladding region adapted to allow for more efficient femtosecond laser grating inscription. Therefore, we have also evaluated the possibility of using such lenses as transverse focusing elements in microstructured optical fibers.

Super-thin Mikaelian’s lens of small index as a beam compressor with an extremely high compression ratio

Based on a focusing Mikaelian's lens with small refraction index (0<n<<1), an optical device is designed as a super-thin optical beam compressor (e.g., thickness = 3λ0) with an extremely high beam compression ratio (more than 19:1). This device can also be used as a beam collimator or a cylindrical-to-plane wave convertor with a much higher transmissivity than a zero-index metamaterial slab. The output beam shows good directionality in both near field and far field. A metamaterial structure is also designed to realize this device and verify its performance with finite element method (FEM).

Subwavelength focusing with a Mikaelian planar lens

We show that an arbitrary TE-polarized light field propagating in a Mikaelian secant (MS) planar lens can be decomposed into modes described by the Jacobi polynomials. This light field will be periodically repeated at the Talbot length and focused with a half-Talbot length period. An analytical expression for the width of the focal spot has been obtained. The MS lens allows obtaining a focal spot of width equal to the diffraction limit in the medium. The MS lens has been fabricated as a planar photonic crystal lens in a silicon film for wavelength 1.55 μm, and its focusing properties have been demonstrated by visible light (532 nm) interference fringes.

Three-dimensional simulation of a nanophotonics device with use of fullwave software

Using the FullWAVE software (www.rsoftdesign.com) that implements the finite-difference FDTD-method of solving Maxwell’s equations, we simulate the performance of a three-dimensional nanophotonics device comprising a sub-wavelength diffraction grating, a wide and a narrow planar waveguide, and a photonic crystal (PhC) Mikaelian lens located in a thin silicon film coated on a substrate containing a three-period Bragg mirror, with each period made up of silicon + silica layer. The device is intended to couple a focused laser beam with the focal spot of 3 × 4.6 μm2 and wavelength 1.55 μm into a planar waveguide of width 500 nm, resulting in a 125-fold “compression” of the input beam cross-section. The modeling has shown that the coupling efficiency amounts to 32% of the energy of the linearly polarized elliptic Gaussian beam focused onto the grating and 52% when a plane wave segment is incident onto the grating. For comparison, the grating-unaided coupling of light into the same device by the butt-coupling of light into the wide waveguide’s silicon film gives the efficiency as low as 8%.

Photonic crystal Mikaelian lens

A mode solution in the form of a hyperbolic secant for a two-dimensional gradient medium with the refractive index also in the form of hyperbolic secant is derived. A photonic crystal analogue of the cylindrical Mikaelian lens is found and comparative numerical simulation of plane wave diffraction by both micro-lenses with the help of the two-dimensional FDTD-method is performed.