Loss of coherence of exciton polaritons in inhomogeneous organic microcavities

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 16, 2006, Pages

  Litinskaya, Marina ^a,b   Reineker, Peter ^b  

^a INSTITUTE OF SPECTROSCOPY   (Russian Federation)

^b UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750157372     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.165320     Document Type: Article

References (30)

1. For a review see D. G. Lidzey, in Thin Films and Nanostructures, edited by, V. M. Agranovich, and, F. Bassani, (Elsevier, New York, 2003), Vol. 31, Chap..
2. (a) D. G. Lidzey, D. D. C. Bradley, T. Virgili, A. Armitage, M. S. Skolnick, and S. Walker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 82.3316 82, 3316 (1999);
3. (b) A. I. Tartakovskii, M. Emam-Ismail, D. G. Lidzey, M. S. Skolnick, D. D. C. Bradley, S. Walker, and V. M. Agranovich, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.121302 63, 121302 (R) (2001);
4. (c) P. Schouwink, J. M. Lupton, H. von Berlepsch, L. Daehne, and R. F. Mahrt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.081203 66, 081203 (R) (2002);
5. (d) N. Takada, T. Kamata, and D. D. C. Bradley, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1559950 82, 1812 (2003);
6. (e) J. H. Song, Y. He, A. V. Nurmikko, J. Tischler, and V. Bulovic, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.235330 69, 235330 (2004).
7. V. M. Agranovich, M. Litinskaia, and D. G. Lidzey, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.085311 67, 085311 (2003).
8. P. Michetti and G. C. La Rocca, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.115320 71, 115320 (2005).
9. The discussion of the difference between the scattering processes in one and two dimensions for inorganic microcavities can be found in D. M. Whittaker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.4791 80, 4791 (1998).
10. H. Zoubi and G. C. La Rocca, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.235316 71, 235316 (2005).
11. F. Tassone, F. Bassani, and L. C. Andreani, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.6023 45, 6023 (1992).
12. I. M. Lifshitz and L. N. Rozenzweig, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 16, 967 (1946);
13. I. M. Lifshitz, M. I. Kaganov, and V. M. Tzukernik in Selected Works of I. M. Lifshitz (Nauka, Moscow, 1987), p. 337.
14. We have obtained the same dispersion equation for each of the two polarizations, since we have neglected the difference in the factors standing in the coupling constants Tjλ (q) [compare Eqs. 6 4]. If this difference is taken into account, the dispersion for s and p modes will be slightly different at large q [where Ecav (q) differs considerably from Ec].
15. L. C. Andreani, G. Panzarini, A. V. Kavokin, and M. R. Vladimirova, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.57.4670 57, 4670 (1998);
16. G. Malpuech, A. Kavokin, and G. Panzarini, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.16788 60, 16788 (1999).
17. U. Fano, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.124.1866 124, 1866 (1961).
18. It is easy to show by elementary integration that P= 0 πa d q1 q1 D0 (E*, q1) - Δ2 + Δ2 R (z*) Lc a R, so that P∼πR (a is the mean distance between the molecules). In reality, P is even less than the above estimate, if one takes into account the term proportional to the second power of the vector potential 2 in the Hamiltonian, as it is usually done far from the resonance [W. Heitler, The Quantum Theory of Radiation (Oxford University Press, Oxford, 1954)].
19. In the case of large negative detuning u= Ec - E0 one has to replace in this estimate Δ3 by Δ2 u. This however plays no role for the following discussion.
20. We suppose that the molecules are distributed homogeneously in the plane of the cavity and in its growth direction, so that S(N Lc2) (a Lc) 3.
21. It follows from Eq. 16 that R(E)= -d Ei Ei - E0 Ei -E ρ (Ei, E0; σ), and it is clear that Im[R(E)]ρ(E, E0; σ).
22. We use [β2 (q) is defined in Eq. 25]: D(E,q) E E= E(0) = Δ2 β2 (q) (E(0) - E0).
23. M. Litinskaia and I. M. Kaganova, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00571-5 275, 292 (2000).
24. A convenient representation of this equation for numerical simulations is (Ref.) [E* - Ecav (q)]=-i Δ2 π σ e- z*2 erfc(-i z*).
25. M. Litinskaya, P. Reineker, and V. M. Agranovich, Phys. Status Solidi A PSSABA 0031-8965 10.1002/pssa.200304067 201, 646 (2004).
26. The factors C1 and C2 appear as a result of the summation over the number j of the in-plane layers of the crystalline slab j cos2 π z j Lc = C1 Lc 2 a, j cos4 π z jLc = 3 C2 Lc 8 a.
27. Small anisotropic corrections appear at large wave vectors if one takes into account the proper dependence of the coupling constants on the factors Ec Ecav (q) [compare Eqs. 4 6].
28. M. Litinskaia, G. C. La Rocca, and V. M. Agranovich, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.165316 64, 165316 (2001).
29. M. S. Skolnick, T. A. Fisher, and D. M. Whittaker, Semicond. Sci. Technol. SSTEET 0268-1242 10.1088/0268-1242/13/7/003 13, 645 (1998).
30. G. Panzarini, L. C. Andreani, A. Armitage, D. Baxter, M. S. Skolnick, V. N. Astratov, J. S. Roberts, A. V. Kavokin, M. R. Vladimirova, and M. A. Kaliteevski, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.5082 59, 5082 (1999).