Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is usually not given attention. The aim of this work is to demonstrate the work of the proposed the algorithm in the framework of geometrical approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters. The methods of differential geometry are used for effective metrics construction for isotropic and anisotropic media. For effective metric space ray trajectories are obtained in the form of geodesic curves. The introduced algorithm is applied to well-known objects - Maxwell and Luneburg lenses. The similarity of results obtained by classical and geometric approach is demonstrated.
Super-resolution imaging is vital for optical applications, such as high capacity information transmission, real-time bio-molecular imaging and nanolithography. Technology and method of super-resolution imaging have attracted much attention. In recent years, different kinds of novel lens, from the superlens to the super-oscillatory lens, has been designed and fabricated to break out the diffraction limit. However, the effect of the super-resolution imaging in these lenses is not satisfactory due to intrinsic loss, aberration, bigger sidebands and single super-resolution imaging. In this resear…
The imaging properties of the Maxwell's fisheye (MFE) lens makes it a viable candidate to implement power coupling between different types of waveguides. A coupler based on the MFE lens is designed to couple a square lattice photonic crystal to a triangular lattice one. The MFE lens is implemented as ring-based multilayer and graded photonic crystal (GPC) structures. The performance of the ring-based MFE lens is better than the GPC-based one in the C-band of optical communication. The proposed ring-based MFE coupler has a footprint of $3.62\times 3.62μm$ and covers the entire C and U bands. Th…
Comment on 'Perfect drain for the Maxwell fish eye lens'
已经提出了非磁损耗材料（2011 New J.Phys.13 023038）来模拟麦克斯韦鱼接目镜（MFL）中的无源完美漏极。在这篇评论中，我们认为，这种被动介质只能被视为一个完美的吸收体，可以完全吸收所有入射辐射，而不被它散射，但它不能模仿一个完美的焦点。因此，这种被动介质不能帮助实现MFL的完美聚焦。
In this paper, we report two new kinds of absolute optical instruments that can make stigmatically images for geometric optics in two dimensional space. One is called the duplex Mikaelian lens, which is made by splicing two half Mikaelian lenses with different periods. The other is exponential conformal transformer of duplex Mikaelian lens with the ratio of different periods of its two half Mikaelian lenses a rational number, which we call duplex Maxwell's fish eye lens. Duplex Mikaelian lenses have continuous translation symmetry with arbitrary real number, while duplex Maxwell's fish eye len…
The Maxwell's fisheye (MFE) lens, due to its focusing properties, is an interesting candidate for implementing the crossing of multiple waveguides. The MFE lens is implemented by two different structures: concentric cylindrical multilayer and radially diverging gourd-shaped rods. Realization of the refractive index profile of the lens is achieved by controlling the thickness ratio of the alternating Si and SiO2 layers determined by effective medium theory. Both structures are optimized to cover the entire C-band in the single mode implementation. The transmission efficiency of the ring-based s…
The number of waveguides crossing an intersection increases with the development of complex photonic integrated circuits. Numerical simulations are presented to demonstrate that Maxwell's fish-eye (MFE) lens can be used as a multiband crossing medium. In previous designs of waveguide intersection, bends are needed before and after the intersection to adjust the crossing angle resulting in a larger footprint. The presented design incorporates the waveguide bends into the intersection which saves footprint. In this paper, 4x4 and 6x6 intersections based on ideal and graded photonic crystal (GPC)…
Broadband super-resolution imaging is important in optical field. To achieve super-resolution imaging, various lenses from superlens to solid immersion lens have been designed and fabricated in recent years. However, the imaging is unsatisfactory due to low work efficiency and narrow band. In this work, we propose a solid immersion square Maxwell's fish-eye lens which realizes broadband (7-16GHz) achromatic super-resolution imaging with full width at half maximum around 0.2 wavelength based on transformation optics at microwave frequencies. In addition, a super-resolution information transmiss…
We investigate the quantum optical properties of Maxwell's two-dimensional fish eye lens at the single-photon and single-atom level. We show that such a system mediates effectively infinite-range dipole-dipole interactions between atomic qubits, which can be used to entangle multiple pairs of distant qubits. We find that the rate of the photon exchange between two atoms, which are detuned from the cavity resonances, is well described by a model, where the photon is focused to a diffraction-limited area during absorption. We consider the effect of losses on the system and study the fidelity of …
We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including \emph{reconfigurable} lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and {\emph{widely separated}} multi-wavelength lenses ($λ= 1\,μ$m and $10\,μ$m). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths…
Multimode waveguide crossings are crucial components for novel mode-division-multiplexing systems. One of the challenges of multimode waveguide routing in MDM systems is decreasing the inter-mode crosstalk and mode leakage of waveguide crossings. In this work, we present the intersections of three and four waveguides based on polygonal Maxwell's fisheye lens via transformation optics. The designed lenses are implemented by mapping their refractive index to the thickness of guiding Si layer. The three-dimensional finite-difference time-domain simulations are used to evaluate the performance of …
Intersection of two or more silicon slot waveguides is inevitable in modern optical integrated circuits based on silicon on insulator (SOI) platform. In this article, we design a Maxwell's fisheye lens as the crossing medium for three Si slot waveguides and numerically investigate its characteristics such as insertion loss, crosstalk and bandwidth. For the 3$\times$3 slot waveguide crossing, the average insertion loss of 1.2 dB and crosstalk levels lower than -15.1 dB are achieved in an ultra-wideband wavelength range of 415 nm covering the entire O, E, S, C, L, and U bands of optical communic…
Mode-division multiplexing (MDM) is an emerging large-capacity data communication technology utilizing orthogonal guiding modes as independent data streams. One of the challenges of multimode waveguide routing in MDM systems is decreasing the mode leakage of waveguide crossings. In this article, a square Maxwell's fish-eye lens as waveguide crossing medium based on quasi-conformal transformation optics is designed and implemented on the silicon-on-insulator platform. Two approaches were taken to realize the designed lens: graded photonic crystal and varying the thickness of Si slab waveguide. …
A Maxwell Fish-Eye Lens in a Bose-Einstein Condensate
Kirchhoff-Institut für Physik, Universität Heidelberg（海德堡大学基尔霍夫物理研究所）；Department of Physics and Astronomy, McMaster University（麦克马斯特大学物理与天文系）；Physikalisches Institut, Universität Heidelberg（海德堡大学物理研究所）
Centre de Nanosciences et Nanotechnologies, CNRS, UMR 9001, Université Paris-Sud, Université Paris-Saclay（纳米科学与技术中心）；École Centrale de Lyon, INSA Lyon, CNRS, Université Lyon 1, CPE Lyon, INL（里昂中央理工学院）
It has been shown that negative refraction makes a perfect lens. However, with little loss, the imaging functionality will be strongly compromised. Later on, it was proved that positive refraction from Maxwell's fish-eye lens can also makes a perfect lens. However, strong debating happens on the introduced drain problem at the imaging position. In this work, we for the first time find that a solid immersion Maxwell's fish-eye lens could be used for super-resolution imaging. We find that it is due to the perfect focusing and total reflection at the outer interface, such that a super-resolution …
The absolute instruments like the Maxwell's fisheye (MFE) lens with aberration-free imaging properties have found interesting applications such as waveguide crossing. The flat wavefront of an optical wave in the waveguide does not match with the circular wavefront of the circular MFE lens at its edge, hence, we design and study the performance of a square MFE lens as photonic crystal waveguide crossing medium. We also have truncated the square MFE lens to a cross-shaped lens to squeeze it inside the crossing waveguides, therefore, practically no extra footprint is consumed by the truncated MFE…
Media with symmetric inhomogeneity have been of great interest due to numerous effects which occur when electromagnetic waves propagate through such media. In general, the inhomogeneity of a certain medium means that the refraction index of the medium is not constant and has some sort of spatial dependency. These types of media are called gradient index (GRIN) media. Different optical effects related to GRIN media are described by GRIN optics. GRIN optics examines different phenomena related to the gradient of the refractive index of the medium and/or the material. Electromagnetic waves propag…
