Multiple Subset Problem as an encryption scheme for communication

Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as finding a subset of integers from a given set, whose sum is equal to a specified integer. The classic SSP has various variants, one of which is the multiple-subset problem (MSSP). In the MSSP, the goal is to select items from a given set and distribute them among multiple bins, en-suring that the capacity of each bin is not exceeded while maximizing the total weight of the selected items. This approach addresses a related problem with a different perspective. Here a related different kind of problem is approached: given a set of sets A={A1, A2..., An}, find an integer s for which every subset of the given sets is summed up to, if such an integer exists. The problem is NP-complete when considering it as a variant of SSP. However, there exists an algorithm that is relatively efficient for known pri-vate keys. This algorithm is based on dispensing non-relevant values of the potential sums. In this paper we present the encryption scheme based on MSSP and present its novel usage and implementation in communication

Nonlinear diffraction from a virtual beam

We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating. We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual beam propagating along the bisector of the two pump beams. The observed diffraction phenomena is a purely nonlinear effect that has no analogue in linear diffraction

Spatial quadratic solitons guided by narrow layers of a nonlinear material

We report analytical solutions for spatial solitons supported by layers of a quadratically nonlinear material embedded into a linear planar waveguide. A full set of symmetric, asymmetric, and antisymmetric modes pinned to a symmetric pair of the nonlinear layers is obtained. The solutions describe a bifurcation of the subcritical type, which accounts for the transition from the symmetric to asymmetric modes. The antisymmetric states (which do not undergo the bifurcation) are completely stable (the stability of the solitons pinned to the embedded layers is tested by means of numerical simulations). Exact solutions are also found for nonlinear layers embedded into a nonlinear waveguide, including the case when the uniform and localized nonlinearities have opposite signs (competing nonlinearities). For the layers embedded into the nonlinear medium, stability properties are explained by comparison to the respective cascading limit.Comment: J. Opt. Soc. Am. B, in pres

Efficient optical energy harvesting in self-accelerating beams

We report the experimental observation of energetically confined self-accelerating optical beams propagating along various convex trajectories. We show that, under an appropriate transverse compression of their spatial spectra, these self-accelerating beams can exhibit a dramatic enhancement of their peak intensity and a significant decrease of their transverse expansion, yet retaining both the expected acceleration profile and the intrinsic self-healing properties. We found our experimental results to be in excellent agreement with the numerical simulations. We expect further applications in such contexts where power budget and optimal spatial confinement can be important limiting factors

Optimal compression and energy confinement of optical Airy bullets

We report on an approach to generate non-diffractive and non dispersive Airy3 bullets with enhanced spatio-temporal energy confinement. By appropriately reshaping the initial spectral components in the Fourier domain, the resulting optical bullets show a significant enhancement of their central lobe intensity while exhibiting a reduced spatio-temporal outspread of the surrounding sub-lobes - typical of Airy3 bullets. Numerically, we demonstrate that when propagating in dispersive media within a linear regime, such optimized Airy3 bullets maintain the peculiar properties of their “standard” counterparts, including curved trajectories, non-spreading features and self-healing. We foresee direct applications in novel and non-disruptive optical techniques for imaging, tomography and spatio-temporally resolved spectroscopy

On the asymptotic evolution of finite energy Airy wavefunctions

In general, there is an inverse relation between the degree of localization of a wavefunction of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wavepackets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyse the asymptotic properties of finite energy Airy wavefunctions using the stationary phase method. We obtain one dominant contribution to the long term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased

Cherenkov radiation control via self-accelerating wave-packets

Cherenkov radiation is a ubiquitous phenomenon in nature. It describes electromagnetic radiation from a charged particle moving in a medium with a uniform velocity larger than the phase velocity of light in the same medium. Such a picture is typically adopted in the investigation of traditional Cherenkov radiation as well as its counterparts in different branches of physics, including nonlinear optics, spintronics and plasmonics. In these cases, the radiation emitted spreads along a “cone”, making it impractical for most applications. Here, we employ a self-accelerating optical pump wave-packet to demonstrate controlled shaping of one type of generalized Cherenkov radiation - dispersive waves in optical fibers. We show that, by tuning the parameters of the wave-packet, the emitted waves can be judiciously compressed and focused at desired locations, paving the way to such control in any physical system