Whispering-gallery exciton polaritons in submicron spheres

C. E. Platts, M. A. Kaliteevski, S. Brand, R. A. Abram, I. V. Iorsh, and A. V. Kavokin

Phys. Rev. B 79, 245322 – Published 23 June 2009

Abstract

We show that a semiconductor sphere with a radius comparable with the wavelength of light at the exciton resonance frequency can behave as a high-quality three-dimensional microcavity or “polariton dot.” We obtain numerical results for gallium arsenide submicron spheres and demonstrate that, in contrast to a larger sphere or planar microcavity, they can simultaneously possess both large quality factor and high finesse. In the strong-coupling regime the Rabi splitting approaches the bulk polariton splitting.

Received 17 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.245322

Authors & Affiliations

C. E. Platts, M. A. Kaliteevski, S. Brand, and R. A. Abram

Department of Physics, Durham University, DH1 3LE Durham, United Kingdom

I. V. Iorsh

Ioffe Institute, Polytechnicheskaya 26, 194021 St. Petersburg, Russia

A. V. Kavokin^*

Department of Physics, University of Rome II, 1 via della Ricerca Scientifica, Rome 00133, Italy

^*On leave from the University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.

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Vol. 79, Iss. 24 — 15 June 2009

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Images

Figure 1
(Color online) Power reflection coefficients of TE and TM outgoing spherical waves with $l = 1$ , 2, and 3 incident on a spherical interface of radius $r$ . The refractive indices of the sphere and the surrounding medium are 3.7 (appropriate to GaAs) and 1.0, respectively.Reuse & Permissions
Figure 2
(Color online) (a) Dependence on $l$ of the minimum radius of a GaAs sphere at which a particular mode exists. The photon energy of the first mode with specific $l$ and radial quantum number $N = 0$ ( $TE l 0$ , $TM l 0$ ) is chosen to be 1.515 eV. Open (solid) symbols correspond to the value obtained for the TM (TE) polarization using Eqs. (6, 7). The lines show the results obtained using the simplified Eq. (10) (dashed line) and Eq. (11) (solid line) for the eigenfrequencies of the cavity modes for the TM (upper/red) and TE (lower/green) polarizations. (b) Dependence on $l$ of the radiative decay rate of the first mode ( $N = 0$ , photon $energy = 1.515 eV$ ). Open (solid line) symbols correspond to the value obtained for the TM (TE) polarization using Eqs. (6, 7). The lines show the results obtained using the simplified Eq. (13) for the TM (upper/red) and TE (lower/green) polarizations. The horizontal solid line indicates the threshold between the weak-coupling and strong-coupling regimes.Reuse & Permissions
Figure 3
(Color online) The radiative decay rate of the optical eigenmodes of a GaAs sphere as a function of the sphere radius for those modes with the real part of their eigenenergy equal to 1.515 eV for different values of $l$ . The open (solid) squares correspond to the TM (TE) polarization, respectively. The index of the mode $(l N)$ is shown to the left of each symbol. The horizontal line indicates the threshold between the weak-coupling and strong-coupling regimes.Reuse & Permissions
Figure 4
(Color online) Cross section of the electric field squared for the TM20 mode (sphere radius $r_{0} = 192 nm$ and $eigenenergy = 1.515 - 0.028 i eV$ ) and the TE30 mode ( $r_{0} = 199 nm$ and $eigenenergy = 1.515 - 0.0027 i eV$ ). The azimuthal number $m = 0$ for both modes. Dark areas (blue) correspond to zero field and light areas (red) to high field.Reuse & Permissions
Figure 5
(Color online) The real part of the photon energy of the first polariton modes of a GaAs sphere as a function of its radius. Within the interval of the radii considered only two bare optical modes exist: TM20 and TE30 (shown by solid lines). The vertical bars show the values of $γ$ for the modes. The horizontal line shows the energy of the exciton resonance.Reuse & Permissions

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