Dark modes, slow modes, and coupling in multimode systems

H. Benisty

doi:10.1364/JOSAB.26.000718

Journal of the Optical Society of America B
Vol. 26,
Issue 4,
pp. 718-724
(2009)
•https://doi.org/10.1364/JOSAB.26.000718

Dark modes, slow modes, and coupling in multimode systems

H. Benisty

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H. Benisty, "Dark modes, slow modes, and coupling in multimode systems," J. Opt. Soc. Am. B 26, 718-724 (2009)

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Abstract

We present general aspects of coupling among two or more families of modes with a view to deepen the insight on so-called “dark modes.” We first review the relationship of dark modes, “coherent population trapping,” “rotating wave approximation,” “coupled-mode theory,” and a few related concepts. The approach we emphasize is related either to inhomogeneous light–matter strong coupling or to the variety of multimode coupled systems designed for slowing down light or for filtering light. Some semantic caveats are discussed, notably down to what can be termed “dark” and “bright” in as simple a system as a distributed Bragg reflector case. A generic “ $N - F$ ” classification simply states that whatever the total number N of modes, the key point is the number $N_{F}$ of “prediagonal” families, since the number $N_{b}$ of bright modes is simply $N_{F}$ leaving $N_{d} = N - N_{F}$ dark modes.

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Domain^a	References	Comments^b
Coherent population trapping	[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]	Initially for archetypal systems such as Λ and V three-levels configurations, with two strong laser beams.
		Dark states are those dressed states formed through transitions that, in the presence of the second beam, do not absorb the first beam; bright states are the remaining radiating transitions.
Electromagnetically induced transparency	[14, 15, 16, 17, 18]	Derived from CPT but one beam has low power and behaves as a linear probe; can be seen as nonlinear resonant index changes. Here, dark states are also dressed states that do not absorb the incoming energy whereas their constituent states would, in the low power linear regime. Bright states are the other dressed states.
Superradiance, Dicke states	[21, 22]	Coherent interaction of, e.g., emitting two-level atoms. Bright states are the fully symmetrical states of an ensemble of identical atoms (e.g., two-level atoms, not all in the same state). Other linear combinations give rise to various degrees of radiant states. There are notably subradiant states. The less radiant are termed dark states, notably in quantum optics and quest for best possible qubits.
Excitons	[19, 20, 23]	In [23] a microcavity mode couples to nearly degenerate exciton subsets, only two bright modes arise, the rest are dark.
Transition of complex excited state	[26, 27, 28, 29, 30, 31]	Between molecular energy surfaces in the Franck–Condon picture, or in highly excited molecules, [28] is specific of Rydberg atom.
Plasmonics	[33, 38, 39, 40]	Plasmonic modes poorly coupled to the outside are called dark.
Waveguide dark mode	[34, 35]	Combination of waveguide modes does not interact with cavity and can be termed dark, for example.
Domains not relevant
Dark Hamiltonian	[32]	Dark states refer to Hamiltonian of particles without interaction with light, hence a kinetic term $p^{2}$ and not ${(p - q A)}^{2}$ .
Degraded molecules	(no reference given)	Generally chemically reacted, not directly relevant here. Some cases may, however, correspond to the transition of complex excited states, but the material aspect dominates over its internal level couplings

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Journal of the Optical Society of America B