Nonlinear Optical Eigenmodes; Perturbative approach

摘要

In linear optics, the concept of a mode is well established. Often these modes correspond to a set of fields that aremutually orthogonal with intensity profiles that are invariant as they propagate through an optical medium. Moregenerally, one can define a set of orthogonal modes with respect to an optical measure that is linear in intensityor quadratic/Hermitian in the fields using the method of Optical Eigenmodes (OEi). However, if the intensity ofthe light is large, the dipole response of an optical medium introduces nonlinear terms to Maxwell's equations.In this nonlinear regime such terms inuence the evolution of the fields and the principle of superposition isno longer valid and consequently, the method of Optical Eigenmodes breaks down. In this work, we defineOptical Eigenmodes in the presence of these nonlinear source terms by introducing small perturbation fieldsonto a nonlinear background interaction and show how this background interaction inuences the symmetriesassociated with the eigenmodes. In particular, by introducing orbital angular momentum (OAM) to the Hilbertspace of the perturbation and background fields, we observe conservation laws and symmetries for which wederive associated operators.