We consider the propagation of polarized light in the medium with Maxwell fish eye refraction index profile. We show that polarization violates the additional symmetries of medium, so that ray trajectories no longer remain closed. Then we suggest a modified, polarization-dependent Maxwell fish eye refraction index which restores all symmetries of initial profile and yields closed trajectories of polarized light. Explicit expressions for the polarization dependent integrals of motion and the solutions of corresponding ray trajectories are presented.
Graphene quantum dot with Maxwell fish eye potential energy profile is studied. A quasiclassical approximation is used given that potential energy is a slowly varying function of coordinates. Near the zero energy the spectrum of electron macroscopically degenerates. All the electron trajectories are closed circles that are classified by angular momentum and an additional integral of motion. Provided the complete filling of the lower Dirac zone, a universal value for Hall conductivity is found.
Alternative construction of the closed form of the Green's function for the wavized Maxwell fish-eye problem
在最近的论文[J.物理学\ A 44（2011）065203]，我们已经得到了描述标量波在$N$维（$N\geqslant2$）麦克斯韦鱼眼介质中的传播的偏微分算子的格林函数的闭合形式表达式。推导是基于鱼眼波方程在超球面反演下的独特变换性质。在这篇文章中，我们沿着不同的路线得到了鱼眼格林函数的相同表达式。我们在这里提出的替代推导利用的事实是，有一个密切的数学关系，通过球极投影，在$\mathbb{R}^{N}$和标量波的传播问题之间的波动鱼眼问题的表面上的$N$维超球面。
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。
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…
The design of compact optical systems with large field of view has been difficult due to the requirement of many elements or a curved focal plane to reduce off-axis aberration. We propose a multi-aperture lens design to effectively resolve these issues. Metagrating-based deflectors are placed near entrance pupils of multi-aperture lens array to enhance field of view. A systematic design method is given in details. In design examples, a $\pm$80$^\circ$ field of view using only two planar optical elements is achieved. Also, the system is extremely compact with total track lengths an order of mag…
Radiation from a charged particle moving in a medium with Maxwell fish eye refraction index profile is considered. It is shown that the radiation spectrum has a discrete character. The main emitted wavelength is proportional to the refractive profiles radius and has a dipole character in a regular medium. Cherenkov like threshold velocity is established. A cardinal rearrangement of angular distribution in a lossless medium is predicted. This behavior is caused by the total internal reflection in a lossless medium as opposed to photons attenuated total reflection in the regular medium. Lossless…
Motion-induced radiation from electrons moving in Maxwell's fish-eye
在uCerenkov辐射和跃迁辐射中，由带电粒子运动产生的倏逝波相干地转变为辐射。然而，这种耗散的运动感应辐射要求粒子在介质中运动得比光快，或者遇到速度跃迁以泵送能量。受Zhang { \itshape et al.}通过观察快速移动的电子束团穿过斗篷的辐射来探测斗篷的方法的启发，研究了电子与麦克斯韦鱼眼球相互作用产生的电子感应辐射。计算结果表明，该辐射是uCerenkov辐射和跃迁辐射的组合，这为研究将倏逝波转换为辐射的新方案奠定了基础。
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…
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）
