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Low Threshold Lasing in Photonic Liquid Crystals
V.A. Belyakov
L. D. Landau Institute for Theoretical Physics, Kosygin str.2, 119334 Moscow, Russia
e-mail: bel@landau.ac.ru

A brief survey of the recent experimental and theoretical results on the low threshold distributed feedback (DFB) lasing in chiral liquid crystals (CLC) and new original theoretical results on the localized optical modes [1] (edge (EM) [2] and defect (DM) modes [3]) are presented. It is shown that EM and DM not only ensure a low DFB lasing threshold in the photonic LCs but efficiently reveal themselves also in some other optical phenomena. An analytic theory of EM and DM is developed and applied to the DFB lasing in CLC. The properties of the EM and DM are investigated. The dispersion equations for EM and DM are found, analysed, solved analytically for some limiting cases, and solved numerically for the typical values of the related parameters. The expressions determining the decay rate for these modes are presented. Lasing thresholds at the frequencies corresponding to the spatially localized EM and DM in a CLC layer occur to be much lower than the ones for conventional lasing. The options for a further reduction of the lasing thresholds connected with the pumping at the EM and DM frequencies are predicted (and partially experimentally observed [4]). It is demonstrated that the analytic approach applied to the DFB lasing allows to reveal some qualitative effects escaped from the researchers employing the numerical methods and to predict new options for a low threshold lasing. Namely, the effect of anomalously strong absorption at the DM frequency, a direct analogue of the corresponding effect at the EM frequency [5], is predicted [3]. It is shown also that the localized EM and DM reveal themselves in an enhancement of some inelastic and nonlinear optical processes in photonic LCs. As examples the corresponding experimentally observed effects for the enhancement of nonlinear optical second harmonic generation [6] and lowering of the lasing threshold [4] in photonic LCs are presented. New options for the EM and DM application to the lasing in CLCs are discussed.
Acknowledgment: This work was supported by the RFBR grants 09-02-90417-Ukr_f_a and 10-02-92103-Jpf_a.

1. I. Kopp, Z.-Q. Zhang, and A. Z. Genack, Prog. Quant. Electron. 2003, 27(6), 369.
2.V.A.Belyakov and S.V.Semenov, JETP, 2009, 109, 687.
3. V.A.Belyakov, MCLC, 2008, 494, 127.
4. Y.Matsuhisa, Y.Huang, Y.Zhou et al., Appl.Phys.Lett., 2007, 90, 091114.
5. V.A.Belyakov, A.A.Gevorgian, O.S.Eritsian and N.V.Shipov, Zhurn.Tekhn.Fiz., 1987, 57, 1418 [Sov. Phys. Technical Physics, 1987, 32 (n7), 843-845, English translation].
6. K.Shin, H.Hoshi, D.Chang, K.Ishikawa and H.Takezoe, Optics Lett., 2002, 27, 128.

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