Waveguide array simulation of the Dirac equation for even potentials

Abstract

In this work, we consider a single unitary transformation that enables us to diagonalize the Dirac Hamiltonian with an even potential. Its diagonal matrix elements are translated to the optical domain, which leads to a direct mapping onto a lattice with interactions to second neighbours. Consequently, Bloch oscillations arise naturally, if we consider a quadratic potential.

Keywords

• Dirac equation
• Waveguide arrays
• Quantum–classical analogies