Related papers: Negative refractive index, Perfect Lens and Ces\`a…
Here we re-examine one of the most basic quantities in optics: the refractive index. Considering propagation in a plane, we first develop a general formalism for calculating the direction dependent refractive index in a general…
We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to…
New propagation regimes for light arise from the ability to tune the dielectric permittivity to extremely low values. Here we demonstrate a universal approach based on the low linear permittivity values attained in the epsilon-near-zero…
We study the inverse seesaw mechanism for neutrino masses and phenomenological consequences in the context of conformal electro-weak symmetry breaking. The main difference to the usual case is that all explicit fermion mass terms including…
Coherent perfect absorber (CPA) was proposed as the time-reversed counterpart to laser: a resonator containing lossy medium instead of gain medium can absorb the coherent optical fields completely. Here, we exploit a monolayer graphene to…
In this paper we perform a detailed analysis of Riemann's hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation $\zeta(s) = 2^{s}\pi^{s-1}\sin{(\displaystyle \pi…
In this article we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The…
We found that a single negative material has a character of zero-refraction in near field, and point out that the mechanism of a metal superlens to image with the resolution exceeding the diffraction limitation is different from that of a…
In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind…
We present drawings on the complex plane of the lines Im(zeta(s))=0 and Re(zeta(s))=0. This allow to illustrate many properties of the zeta function of Riemann. This is an expository paper. It does not pretend to prove any new result about…
This paper is a summary of the general approach outlined in my previous papers toward proving the riemann hypothesis. Numerical and graphical proof of the Riemann Hypothesis is presented with analytical arguments although more work needs…
With the emergence of super-resolution lenses such as superlens and hyperlens, coupled with advancements in metamaterials, the diffraction limit of approximately half wavelength is no longer unbreakable. However, superlenses are easily…
We provide a description of the far-field encountered in the diffraction problem resulting from the interaction of a monochromatic plane-wave and a right-angled no-contrast penetrable wedge. To achieve this, we employ a two-complex-variable…
Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin-1/2 particle. Here…
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a…
We examine the Seidel aberrations of thin spherical lenses composed of media with refractive index not restricted to be positive. We find that consideration of this expanded parameter space allows reduction or elimination of more…
The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann zeta function which are sufficiently strong to break the density hypothesis in a nontrivial part of the critical strip. Apart from…
Cylinder-shaped perfect lens deduced from the coordinate transformation method is proposed. The previously reported perfect slab lens is noticed to be a limiting form of the cylindrical lens when the inner radius approaches infinity with…
We discuss the feasibility of negative refraction with reduced absorption in coherently driven atomic media. Coherent coupling of an electric and a magnetic dipole transition by laser fields induces magneto-electric cross-coupling and…