Turing patterns in semiconductor microcavities : formation and optical control

Turing pattern formation in nonlinear systems attracts great interest in fields as varied as biology, chemistry and physics [1,2]. Here, we show that patterns can also be formed in semiconductor microcavities operated in the optical parametric oscillation (OPO) regime [3,4]. The basic process involved is the very efficient polariton-polariton scattering, induced mostly by the Coulomb interaction that induces strong resonant χ (3) nonlinearities [3]. In this context, coupled planar microcavities [4] offer a unique test-bed for studying the formation of patterns. The sample design allows engineering multiple polariton modes that can be tuned at will [4]. The system can be resonantly pumped at normal incidence inducing interbranch energy-degenerate OPO. With respect to other studied patterns (e.g. in hydrodynamics or in conventional OPOs), the originality relies here with: (i) the excitation and emitted beams wave-vectors can be easily accessed and controlled; (ii) the particular role played by the polarization of light and the polariton spin; (iii) the perspective given to use such semiconductor nanostructures to realize fast optical- switches. Here, we demonstrate the formation of hexagonal patterns observed in the OPO far-field emission as well as in the real space. We then prove that these patterns can be optically controlled by changing the pump wave-vector as well as by modifying the polarization of the pump beam. Finally an all-optical switch is demonstrated. 1] M.C. Cross and P. Hohenberg, Rev. Mod. Phys. 65,851 (1993). [2] A. Turing,Phil. Trans.. R. Soc. Lonf. B 237, 37 (1952). [3] P. G. Savvidis, J. J. Baumberg, R. M. Stevenson, M. S. Skolnick, D. M. Whittaker, J. S. Roberts, Phys. Rev. Lett. 84, 1547 (2000). [4] C. Diederichs, J. Tignon, G. Dasbach, C. Ciuti, A. Lemaitre, J. Bloch, Ph. Roussignol, C. Delalande , Nature 410, 904 (2006).