The speed of light ( c ) in a vacuum is independent the choice frames to describe propagation, according theory relativity. We consider how characterised material, where different from that due finite dielectric constant. phase velocity material smaller than , such moving frame can be larger velocity, move faster material. Consequently, an unusual Doppler effect expected, and wavelength changes...

We investigate the transmission and reflection properties at the interfaces between the lossy positive-index materials (PIM) and negative-index materials (NIM) with graded permittivity and permeability. We present an exact analytical solution to Helmholtz’ equation for the oblique incidence on profile with the graded real parts of permittivity and permeability profile changing according to a hy...

We successfully obtained a high-bandwidth (1 GHz km) and low-loss (90 dB/km at 0.572 µm of wavelength) graded-index polymer optical fiber by using the interfacial-gel polymerization technique, in which we used an unreactive component to obtain the quadratic refractive-index distribution. This high-bandwidth graded-index polymer optical fiber makes it possible to transmit a high-speed optical si...

Let A be a graded C∗-algebra. We characterize Kasparov’s K-theory group K̂0(A) in terms of graded ∗-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded Hilbert modules. An application to the index theory of elliptic differential operators on smooth closed manifolds and asymptotic morphisms is discussed.