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Modeling of spontaneous emission modification in nanostructured elements

Light emission in OLED is a relaxation process in single molecule. This process is defined by radiative recombination rate. This rate depends strongly on dielectric surrounding as well as chemical properties of a molecule 1). Radiative recombination rate is defined by local photonic density of states (LDOS) 2).

The correspondence principle

The radiative recombination rate of a dipole emitter in a given environment is proportional to the power radiated by the classical dipole source placed in the same environment 3). Below listed are the examples of this approach to the calculation of the radiative decay rates for a number of cases. -Modeling of Eu3+ complexes placed in the vicinity of the metallic surface 4) 5) 6). The correspondence principle that is used allows to separate radiative and nonradiative recombination rates as well quantum yield.

  • Dipole near or inside a dielectric sphere 7) 8).
  • Dipole near or inside a multilayered sphere 9)

The method of Green's functions

This method is based on the calculation of the local density of states (LDOS) via the classical Green’s dyadic 10). The decay rate of the emitter depends on its frequency, position, as well as its orientation. So the control over the orientation is of crucial importance for the purpose of manipulating spontaneous emission. It turns out one does not need to sample the decay rate for a large set of emitter orientations in order to adequately describe the orientational dependence of the rate. In 11) a method is described, which allows modeling the spontaneous emission rate surfaces (that is, the decay rate as a function of the emitter orientation) for a given emitter position, frequency based calculating the rates at the fewest possible orientations (less than 10). By making special use of symmetry properties of the Green’s function in a given environment, three principal axes can be derived for the given emitter position and frequency, and the corresponding principal rates can be calculated. The approach provides a clear physical picture of emission rate dependencies in an arbitrary nanostructured environment. The authors also show how control over the emitter orientation opens up new possibilities of switching emission from inhibited to enhanced and vice versa.

The knowledge of the principal rates and axes is a key to proper interpretation of dynamics of orientational dipole ensembles 12) 13) 14) 15).

Decay of such ensembles is a sum of single exponentials with a rate distribution given by the emission rate surface. Therefore, any observable derived from time-resolved decay beyond the orientation-averaged rate – requires knowledge of the principal rates, which is thus relevant to many physical situations in nanophotonics.

1) Surface enhanced fluorescence, E. Fort, S. Grésillon, J. Phys. D: Appl. Phys. – 2008. – V. 41. – P. 013001
2) Optical emission in periodic dielectrics, R. Sprik, B. A. van Tiggelen, and A. Lagendijk, Europhys. Lett. – 1996. – V. 35. – P. 265–270.
3) A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere, Annals of Physics – 2005. – V. 315. – P. 352–418
4) Lifetime of an emitting molecule near a partially reflecting surface, R. R. Chance, A. Prock, and R. Silbey, J. Chem. Phys. – 1974. – V. 60. – P. 2744–2748
5) Comments on the classical theory of energy transfer, R. R. Chance, A. Prock, and R. Silbey, J. Chem. Phys. – 1975. – V. 62. – P. 2245–2253
6) Decay of an emitting dipole between two parallel mirrors, R. R. Chance, A. Prock, and R. Silbey, J. Chem. Phys. – 1975. – V. 62. – P. 771–772
7) Transition rates of atoms near spherical surfaces, J. Chem. Phys. – 1987. – V. 87. – P. 1355–1360
8) Radiation and lifetimes of atoms inside dielectric particles. Phys. Rev. A. – 1988. – V. 38. – P. 3410–3416
9) A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere, Annals of Physics. – 2005. – V. 315. – P. 352–418.
10) Dyadic Green Functions in Electromagnetic Theory, 2nd ed, New York: IEEE. – 2003
11) Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment, W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, Phys. Rev. A. – 2009. – V. 80. – P. 053802-1–053802-7
12) Enhanced Spontaneous Emission by Quantum Boxes in a Monolithic Optical Microcavity, J.-M.Gérard, B.Sermage, B.Gayral, B.Legrand, E.Costard, and V.Thierry-Mieg, Phys. Rev. Lett. – 1998. – V. 81. – P. 1110–1113
13) Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals, P.Lodahl, A. F.van Driel, I. S.Nikolaev, A.Irman, K.Overgaag, D.Vanmaekelbergh, and W. L. Vos, Nature. – 2004. – V. 430. – P. 654–657
14) Strong Enhancement of the Radiative Decay Rate of Emitters by Single Plasmonic Nanoantennas, O. L.Muskens, V.Giannini, J. A.Sánchez-Gil, and J. Gómez Rivas, Nano Lett. – 2007. – V. 7. – P. 2871–2875
15) Simulation of Light Extraction from OLEDS using FDTD Solutions, H.Greiner and J. Pond, NFO9 (September 2006), Lausanne, Switzerland. – 2006
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