Classical and quantum electromagnetic momentum in anisotropic optical waveguides

The guided modes supported by dielectric channel waveguides act as individual carriers of momentum. We show this by proving that the modes satisfy an orthogonality condition which relates to the momentum of the optical electromagnetic field, with a link to the more familiar power (energy) orthogonality. This result forms the basis for a rigorous, self-consistent procedure for the quantization of broadband guided electromagnetic fields in the typical channels used in integrated photonic circuits. Our work removes the existing theoretical gap between the classical solution of the Maxwell equations for guided fields and the intuitive understanding of photons in waveguides. The presented approach is valid for straight, lossless, and potentially anisotropic, dielectric waveguides of general shape, in the linear regime, and including material dispersion. Examples for the hybrid modes of a thin film lithium niobate strip waveguide are briefly discussed.