A rigorous vectorial formulation of the surface diffractive optics of plasmon polaritons is derived using the Green’s function formalism. Theoretical predictions for several 2D plasmonic scenarios, i.e. plasmonic single-and double-slit diffraction, are exemplified and compared with published experimental observations. The importance, in near field diffraction, of all vectorial components of pla...

The maximum absolute value of integral weights sufficient to represent any linearly separable Boolean function is investigated. It is shown that upper bounds exhibited by Muroga (1971) for rational weights satisfying the normalized System of inequalities also hold for integral weights. Therewith, the previous best known upper bound for integers is improved by approximately a factor of 1/2.

In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n + 1)⌉ NO...

We elucidate a ray picture of coherence for vectorial electromagnetic waves by using the Stokes parameters for light rays defined by the optical Wigner function. Paraxial propagation is formulated as a complementary Huygens principle. We show that the degrees of coherence are averages of the phase difference where the weights are the Stokes parameters for light rays. We analyze the van Cittert–...

In this paper, several methods for constructing substitution boxes (S-boxes) with good cross-correlation properties are proposed. We firstly analyze the cross-correlation properties of bent functions and derive a sufficient condition that the absolute indicator f ,g of two bent functions f and g achieve its lowest possible value 2 n/2. More precisely, it is sufficient that f + g is also a bent ...

Two boolean functions f, g : {0, 1} → {0, 1} are isomorphic if they are identical up to relabeling of the input variables. We consider the problem of testing whether two functions are isomorphic or far from being isomorphic with as few queries as possible. In the setting where one of the functions is known in advance, we show that the non-adaptive query complexity of the isomorphism testing pro...