in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

Chiral spoof surface plasmon polaritons in the terahertz region, resulting from a coherent superposition of TM and HE modes, can be generated by normally exciting helically corrugated metal wire with a linearly polarized Gaussian light. The handedness of the chiral SPP depends on the handedness of the helical groove. The chirality of the surface wave causes a spiral spatial extent of average po...

The resonant optical modes of a high permittivity dielectric prism with an equilateral triangular cross section are discussed. Eigenmode solutions of the scalar Helmholtz equation with Dirichlet boundary conditions, appropriate to a conducting boundary, are applied for this purpose. The particular plane wave components present in these modes are analyzed for their total internal reflection beha...

By means of (1.2) and (1.3) each matrix S ∈ SL(2,C) is associated with some matrix S ∈ SO(1, 3,R) so that we can write S = φ(S), see [1], [2], and [3] for detailed description of this construction. Let M be a space-time manifold, i. e. a four-dimensional orientable manifold equipped with a pseudo-Euclidean Minkowski-type metric g and carrying a special smooth geometric structure which is called...

Based on the total internal reflection (TIR) under second Bragg incidence angle, polarization-independent two-port beam splitter grating etched in fused silica is described for the usual duty cycle of 0.5. There are three diffraction orders in the reflection: –2nd order, –1st order, and 0th order. The grating depth and period are optimized using the rigorous coupled-wave analysis (RCWA) in orde...

In this article, an ultrathin penta-band polarization-insensitive metamaterial absorber has been presented, which consists of an array of a closed ring embedded in a tetra-arrow resonator. The proposed ultrathin (~k0/18 corresponding to the highest absorption frequency) structure exhibits five distinct absorption peaks at 3.4, 8.34, 9.46, 14.44, and 16.62 GHz with peak absorptivities of 98.6%, ...

We report negative-index imaging at near infrared wavelengths using a photonic crystal PC with an effective index matched closely to air as the incident medium. A tapered waveguide is used to generate a point-sourcelike object field; and to probe the focusing behavior of the PC, an array of 500 nm wide photonic wire waveguides is placed in the backplane of the PC lens. This represents a samplin...