Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media

Abstract

We introduce a Hamiltonian formulation of electromagnetic fields in dispersive and absorptive structured media of arbitrary dimensionality; the Kramers-Kronig relations are satisfied by construction. Our method is based on an identification of the photonic component of the polariton modes of the system. Although the medium degrees of freedom are introduced in an oscillator model, only the susceptibility of the medium appears in the derived eigenvalue equation for the polaritons; the theory is applicable to both classical and quantum optics. A discrete polariton spectrum is obtained in the transparent regime below the absorption cutoff frequency, and the normalization condition contains the material dispersion in a simple way. In the absorptive regime, a continuous polariton spectrum is obtained. The expressions for the full electromagnetic field of the system can be written in terms of the modes of a limiting, nondispersive, nonabsorptive system, so the theory is well suited to studying the effect of dispersion or absorption on photonic dispersion relations and mode structure. Available codes for dispersive photonic modes can easily be leveraged to obtain polariton modes in both the transparent and absorptive regimes.

Atom–light interactions in photonic crystals

“…By optimizing the power and detuning of the E 1 trap mode, we should be able to achieve stable atomic trapping and ground state cooling 41,50,51 . By applying continuous on-site cooling to Nc1 atoms, we expect to create a 1D atomic lattice with single atoms trapped in unit cells along the APCW, thus opening new opportunities for studying novel quantum transport and many-body phenomena [5][6][7][8][9][10][11][12][13][14][15][16][17][18] .…”

“…L ocalizing arrays of atoms in photonic crystal waveguides (PCW) with strong atom-photon interactions could provide new tools for quantum networks [1][2][3] and enable explorations of quantum many-body physics with engineered atom-photon interactions [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . Bringing these scientific possibilities to fruition requires creation of an interdisciplinary 'toolkit' from atomic physics, quantum optics and nanophotonics for the control, manipulation and interaction of atoms and photons with a complexity and scalability not currently possible.…”

Dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media

“…In Refs. [45][46][47][49][50][51] general proofs were given for the formal equivalence between the Huttner Barnett model and the Langevin noise approach.…”

Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium

“…It is central to observe that the DLN approach is a direct development of the historical works by Rytov and others [53][54][55][56] which, based on some considerations about the standard fluctuation dissipation theorem for electric currents [57], was used for justifying Casimir and thermal forces (for recent developments of such phenomenological 'fluctuational electrodynamics' techniques in the context of nanotechnology see [58][59][60][61][62][63]). Few years ago, it was proposed that the equivalence between the Hamiltonian and DLN approaches should finally be rigorous [64][65][66][67][68][69][70]. However, we recently showed [71][72][73] that a full Hamiltonian description, generalizing the Huttner-Barnett results [14][15][16][17][18][19][20] and valid for any inhomogeneous dielectric systems, must not only include the material oscillator degrees of freedom, i.e., like in the DLN method, but also add the previously omitted quantized photonic degrees of freedom associated with fluctuating optical waves coming from infinity and scattered by the inhomogeneities of the medium [72].…”