(3+1)-dimensional optical soliton dragging logic

A review of the varieties of optical solitons and their possible interactions, combined with the requirements for a robust digital logic gate motivate the use of (3+1)-dimensional optical solitons (light bullets) as information carriers and soliton dragging gates as switches. Soliton dragging is the asymmetric interaction between two initially overlapping, orthogonally polarized solitons propagating at different angles so that a weak signal soliton can drag a strong pump out of a spatial aperture, thereby implementing a phase-insensitive, high-contrast, logical switch with gain. Light bullets may be an ideal choice for use in these soliton dragging gates but are unstable in Kerr media, but stable (for sufficient pulse energy) in materials with physically reasonable saturating or negative ${\mathit{n}}_4$ ${\mathit{I}}^2$ nonlinearities. An efficient technique for the propagation of spherically symmetric (3+1)-dimensional field envelopes is developed and used to verify the theoretical stability predictions. A split-step numerical algorithm that models the propagation and phase-independent interaction of arbitrary (3+1)-dimensional, vector e.m. fields in anisotropic media with up to sixth-order tensor nonlinearities is developed and used to demonstrate the features of the gates. NOT and single-stage, two- and four-input NOR light-bullet dragging logic gates are simulated and their performance over a range of operating parameters is presented. It is shown that, with material parameters in the range of those currently available from highly nonlinear organic crystals, high-contrast, all-optical, soliton logic gates with a clock rate greater than 1 THz, latency of a few picoseconds, and switching energy of 25 pJ may be possible.