Parametric polariton solitons in coherently pumped semiconductor microcavities

O. A. Egorov, D. V. Skryabin, and F. Lederer

Phys. Rev. B 84, 165305 – Published 4 October 2011

Abstract

We demonstrate the existence of parametric solitons due to four-wave mixing in a coherently pumped semiconductor microcavity operating in the strong-coupling regime. These spatial solitons are localized in the direction perpendicular to the pump momentum and form periodic trains of pulses in the direction parallel to it. The parametric solitons constitute a family continuously parameterized by the energies and momenta of the signal and idler components. They also play a profound role in the formation of two-dimensional polariton solitons.

Received 6 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.165305

Authors & Affiliations

O. A. Egorov^1,*, D. V. Skryabin², and F. Lederer¹

¹Institute of Condensed Matter Theory and Solid State Optics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany
²Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom

^*Corresponding author: oleg.egorov@uni-jena.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 84, Iss. 16 — 15 October 2011

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Sketch of the microcavity driven by a coherent optical pump. The semiconductor quantum well (QW) is sandwiched between two Bragg mirrors (BM). (b) Dispersion of the lower polaritons (LP). $Ω_{p}$ , $Ω_{s}$ , and $Ω_{i}$ are the frequencies of the pump, signal, and idler polaritons, respectively.Reuse & Permissions
Figure 2
(a) Maxima of the pump component of parametric polariton solitons for different detunings of the signal component: (1) $Δ_{s} = 0.15$ , (2) $Δ_{s} = 0.25$ , (3) $Δ_{s} = 0.35$ , (4) $Δ_{s} = 0.45$ , (5) $Δ_{s} = 0.55$ , (6) $Δ_{s} = 0.65$ , and (7) $Δ_{s} = 0.75$ . The dotted (black) line marks the unstable pump-only bright soliton (BS), which bifurcates from the pump-only homogeneous solutions (HS). (b) Amplitude profile of the unstable pump-only BS. (c) Pump, signal, and idler components of the parametric polariton soliton close to the bifurcation point. Other parameters: $Δ_{p, i} = 0.25$ , $D_{p} = 0.23$ , $D_{s} = 0.5$ , and $D_{i} = 0.03$ .Reuse & Permissions
Figure 3
(a) Branches of homogeneous solution (HS), unstable bright soliton (BS), and parametric polariton soliton (PPS). Dashed lines represent unstable solutions. The thick dotted line shows the slightly unstable PPS (see text). PT represents the parametric threshold point given by Eq. (10). (b) Frequency shift ( $δ$ ) between signal and idler components of the parametric polariton soliton vs the external pump amplitude. Amplitude profiles of (c) stable fundamental PPS for $W = 0.0505$ and (d) stable second-order PPS for $W = 0.051$ . Other parameters: $Δ_{p, i} = 0.25$ , $Δ_{s} = 0.35$ .Reuse & Permissions
Figure 4
Evolution dynamics of an unstable PPS. (a) Destabilization due to an asymmetric eigenmode with $λ = 0.0018$ for the pump amplitude $W = 0.0511$ . (b) Destabilization due to an symmetric eigenmode with $λ = 0.00014 \pm i 0.015$ for the pump amplitude $W = 0.0517$ (b). Parameters: $Δ_{p, i} = 0.25$ , $Δ_{s} = 0.35$ .Reuse & Permissions
Figure 5
(a)-(c) 2D profiles of the parametric polariton soliton calculated in the original model, (1), for (a) $E_{p} = 0.136$ and $k_{seed} = 0$ , (b) $E_{p} = 0.140$ and $k_{seed} = - 0.4138$ , and (c) $E_{p} = 0.138$ and $k_{seed} = 0.7448$ . (d) Profile of a moving 2D cavity polariton soliton for $E_{p} = 0.1375$ and $k_{seed} = 0.4966$ . The (red) arrow shows the direction of pattern motion. For all calculations, $Ω_{p} = - 0.25$ and the optical pump momentum is $k_{p} = 1.2$ .Reuse & Permissions
Figure 6
(a) Effective detuning of the signal polariton versus the seed pulse momentum ( $Ω_{seed} = - 0.5$ ). (b) Families of parametric polariton solitons as a function of the seed pulse momentum ( $k_{seed}$ ) calculated in the original model, (1), for different amplitudes of the pump beam: (1) $E_{p} = 0.1355$ , (2) $E_{p} = 0.136$ , (3) $E_{p} = 0.137$ , (4) $E_{p} = 0.138$ , (5) $E_{p} = 0.139$ , and (6) $E_{p} = 0.140$ . For all calculations, $Ω_{p} = - 0.25$ and the optical pump momentum is $k_{p} = 1.2$ .Reuse & Permissions

Physical Review B

covering condensed matter and materials physics