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We present a new math-physics modeling approach, called canonicalquantization with numerical mode-decomposition, for capturing the physics ofhow incoming photons interact with finite-sized dispersive media, which is notdescribable by the previous Fano-diagonalization methods. The main procedure isto (1) study a system where electromagnetic (EM) fields are coupled tonon-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2)derive a generalized Hermitian eigenvalue problem for conjugate pairs incoordinate space, (3) apply computational electromagnetics methods to find acountably/finite set of time-harmonic eigenmodes that diagonalizes theHamiltonian, and (4) perform the subsequent canonical quantization withmode-decomposition. Moreover, we provide several numerical simulations thatcapture the physics of full quantum effects, impossible by classical Maxwell'sequations, such as non-local dispersion cancellation of an entangled photonpair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.

Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD)