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A quantum theory of retarded surface plasmons on a metal–vacuum interface is formulated, by analogy with the well-known and widely exploited theory of exciton-polaritons. The Hamiltonian for mutually interacting instantaneous surface plasmons and transverse electromagnetic modes is diagonalized with recourse to a Hopfield–Bogoljubov transformation, in order to obtain a new family of modes, to be identified with retarded plasmons. The interaction with nearby dipolar emitters is treated with a full quantum formalism based on a general definition of modal effective volumes. The illustrative cases of a planar surface and of a spherical nanoparticle are considered in detail. In the ideal situation of absence of dissipation, as an effect of the conservation of in-plane wavevector, retarded plasmons on a planar surface represent true stationary states (which are usually called surface plasmon polaritons), whereas retarded plasmons in a spherical nanoparticle, characterized by frequencies that overlap with the transverse electromagnetic continuum, become resonances with a finite radiative broadening. The theory presented constitutes a suitable full quantum framework for the study of nonperturbative and nonlinear effects in plasmonic nanosystems.

@article{alpeggiani_quantum_2014, title = {Quantum {Theory} of {Surface} {Plasmon} {Polaritons}: {Planar} and {Spherical} {Geometries}}, volume = {9}, issn = {1557-1955, 1557-1963}, shorttitle = {Quantum {Theory} of {Surface} {Plasmon} {Polaritons}}, url = {http://link.springer.com/article/10.1007/s11468-014-9703-6}, doi = {10.1007/s11468-014-9703-6}, abstract = {A quantum theory of retarded surface plasmons on a metal–vacuum interface is formulated, by analogy with the well-known and widely exploited theory of exciton-polaritons. The Hamiltonian for mutually interacting instantaneous surface plasmons and transverse electromagnetic modes is diagonalized with recourse to a Hopfield–Bogoljubov transformation, in order to obtain a new family of modes, to be identified with retarded plasmons. The interaction with nearby dipolar emitters is treated with a full quantum formalism based on a general definition of modal effective volumes. The illustrative cases of a planar surface and of a spherical nanoparticle are considered in detail. In the ideal situation of absence of dissipation, as an effect of the conservation of in-plane wavevector, retarded plasmons on a planar surface represent true stationary states (which are usually called surface plasmon polaritons), whereas retarded plasmons in a spherical nanoparticle, characterized by frequencies that overlap with the transverse electromagnetic continuum, become resonances with a finite radiative broadening. The theory presented constitutes a suitable full quantum framework for the study of nonperturbative and nonlinear effects in plasmonic nanosystems.}, language = {en}, number = {4}, urldate = {2014-08-26TZ}, journal = {Plasmonics}, author = {Alpeggiani, Filippo and Andreani, Lucio Claudio}, month = aug, year = {2014}, keywords = {Biochemistry, general, Biophysics and Biological Physics, Biotechnology, Quantum plasmonics, Radiative broadening, Surface plasmon polaritons, nanotechnology}, pages = {965--978} }

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