Optical analogue of the Aharonov–Bohm effect using anisotropic media

We show that in the context of paraxial optics, which can be analyzed through a wave equation similar to the non-relativistic Schrödinger equation of quantum mechanics but replacing time t by spatial coordinate z  , the existence of a vector potential A⊥A⊥ mimicking the magnetic vector potential in quantum mechanics is allowed by specific gauge symmetries of the optical field in a medium with anisotropic refractive index. In this way, we use Feynmanʼs path integral to demonstrate an optical analogue of the quantum-mechanical Aharonov–Bohm effect, encouraging the search for another optical systems with analogies with more complex quantum field theories.

► The optical analogue of the Aharonov–Bohm effect is demonstrated using anisotropic media. ► It follows from the gauge principle applied to the optical field in the paraxial regime. ► Feynmanʼs path integral formalism is used to obtain the main result, leading directly from geometric to physical optics.