Nonradiating current configurations attract attention of physicists for many years as possible models of stable atoms in the field theories. One intriguing example of such a nonradiating source is known as anapole (which means without poles in Greek)
, and it was originally proposed by Yakov Zeldovich in nuclear physics. Recently, an anapole was suggested as a model of elementary particles describing dark matter in the Universe. Classically, an anapole mode can be viewed as a composition of electric and toroidal dipole moments, resulting in destructive interference of the radiation fields due to similarity of their far-field scattering patterns. Here we demonstrate experimentally that dielectric nanoparticles can exhibit a radiationless anapole mode in visible. We achieve the spectral overlap of the toroidal and electric dipole modes through a geometry tuning, and observe a highly pronounced dip in the far-field scattering accompanied by the specific near-field distribution associated with the anapole mode. The anapole physics provides a unique playground for the study of electromagnetic properties of nontrivial excitations of complex fields, reciprocity violation, and Aharonov-Bohm like phenomena at optical frequencies.
Through a particularly chosen coordinate transformation, we propose an optical carpet cloak that only requires homogeneous anisotropic dielectric material. The proposed cloak could be easily imitated and realized by alternative layers of isotropic di
electrics. To demonstrate the cloaking performance, we have designed a two-dimensional version that a uniform silicon grating structure fabricated on a silicon-on-insulator wafer could work as an infrared carpet cloak. The cloak has been validated through full wave electromagnetic simulations, and the non-resonance feature also enables a broadband cloaking for wavelengths ranging from 1372 to 2000 nm.
Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $DD_infty:= {{bf x}in [0,1]^N: sum_{ige 1} x_i=1}$ with GEM distribution as the rever
sible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence to the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract space $S$. This provides a reasonable alternative to the Fleming-Viot process which does not satisfy the log-Sobolev inequality when $S$ is infinite as observed by W. Stannat cite{S}.
