Open AccessWave-mechanical phenomena in optical coupled-mode structures
Author(s) -
Konstantin G. Zloshchastiev
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1400/4/044028
Subject(s) - hamiltonian (control theory) , physics , eigenvalues and eigenvectors , hilbert space , classical mechanics , maxwell's equations , boundary value problem , operator (biology) , quantum mechanics , mathematics , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene
We derive a formal mapping between Schrödinger equations and certain classes of Maxwell equations describing the classical electromagnetic wave’s propagation inside coupled-modes waveguides. This mapping reveals a phenomenon, which is not visible in the original form of Maxwell equations: multiple solutions occur which satisfy same boundary conditions but correspond to different eigenvalues of a certain operator; the latter is analogous to Hamiltonian operators which occur in quantum systems. If one deals with normalized state vectors then a proper analogy with the conventional wave mechanics is established: solutions form a Hilbert space which is somewhat similar to that in the quantum mechanics. Therefore, coupled-mode configurations should possess certain wave-mechanical features, which can be formally studied using a formalism of quantum mechanics or, at least, its mathematical part. We notice also that the occurring Hamiltonian operators always possess a skew-adjoint part if one deals with normalized state vectors – even if permittivity and permeability are real-valued. This leads to the “dressing” effect of propagation constants, which indicates presence of additional gain or loss processes in the coupled-mode systems.