We investigate the dynamic effect of nonlinearity on lasing in disordered medium. The third-order nonlinearity not only changes frequency and size of lasing mode, but also modifies laser emission intensity and laser pulse width

Cao, Hui

Ling, Y.

Liu, B.

Xu, J. Y.

Yamilov, Alexey

English

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

Missouri University of Science and Technology Scholars' Mine Physics Faculty Research & Creative Works Physics 01 Jan 2003 Dynamic Nonlinear Effect on Lasing in Random Media B. Liu Alexey Yamilov Missouri University of Science and Technology, yamilov@mst.edu Y. Ling J. Y. Xu et. al. For a complete list of authors, see https://scholarsmine.mst.edu/phys_facwork/277 Follow this and additional works at: https://scholarsmine.mst.edu/phys_facwork  Part of the Physics Commons Recommended Citation B. Liu et al., "Dynamic Nonlinear Effect on Lasing in Random Media," Postconference Digest of Quantum Electronics and Laser Science, 2003. QELS, Institute of Electrical and Electronics Engineers (IEEE), Jan 2003. The definitive version is available at https://doi.org/10.1109/QELS.2003.237953 This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Physics Faculty Research & Creative Works by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu. QThG3 Dynamic Nonlinear Effect on Lasing in Random Media H. Cao, B. Liu, A. Yamilov, Y. Ling, J .  Y. Xu Department of Physacs and Astronomy, Northwestern Unaversaty, Evanston, IL 60208 Tel: 847-467-5452, Fax: 84 7-491-9982, h-cao @northwestern. edu Abstract: We investigate the dynamic effect of nonlinearity on lasing in disordered medium. The* third-order nonlinearity not only changes frequency and size of lasing mode, but also mod- ifies laser emission intensity and laser pulse width. @ 2002 Optical Society of America OCIS codes: (290.4210) Multiple scattering; (190.3270) Kerr effect Recent studies illustrate that adding gain to a disordered medium leads to lasing in the long-lived eigenmodes. [l, 2, 31 Despite the modes with long lifetime are preferably amplified, their wavefunctions are not modified by the presence of gain. However, nonlinearity can change the eigenmodes of a disordered system. In random lasers nonlinearity is large due to  high intensity and resonance enhancement. We first present the experimental evidence of the change of lasing modes by nonlinearity. As the pump intensity increases, the frequencies of lasing modes shift in the opposite direction of the gain spectrum. This phenomenon indicates the spectral shift of lasing modes is caused not by cavity pulling but by nonlinearity. The time-resolved measurement of lasing spectra reveals the temporal shift of lasing frequencies caused by dynamic change of the refractive index. To understand the nonlinear effect on random lasing, we carry out numerical simulation of a model system. The algorithm is based on the finite-difference time-domain (FDTD) solution to Maxwell equations cou- pled with the rate equations of electronic populations. Third-order nonlinearity with finite-time response is incorporated into the Maxwell equations. Our calculation results demonstrate that nonlinearity shifts the frequency and modify the size of the eigenmode of a disordered system. Figure l(a) plots the spatial size of a random lasing mode in both linear and nonlinear cases under pulsed pumping. The laser emission intensity and laser pulse width of a random laser are also changed by third-order non- linearity ~ ( ~ 1 .  Such changes are sensitive to the nonlinear response time TO. Figure l(b) plots the total laser emission energy for the same ~ ( ~ 1  but different TO. The effect of nonlinearity on laser pulse intensity and width depends on the relative magnitude of the nonlinear response time TO and the mode lifetime T,. When 70 is longer than T,, the change of laser pulse intensity and width is related to the size change of the lasing mode. If the size of the lasing mode decreases (or increases) in the presence of nonlinearity, light confinement gets better (or worse). The decrease (or increase) of light leakage is equivalent to an increase (or decrease) of the quality factor of the random cavity. Hence, lasing lasts longer (or shorter), and laser emission is stronger (or weaker). When TO is shorter than T,, the change of laser output depends only on the sign of ~ ( ~ 1 ,  i.e., positive (or negative) nonlinearity always extract more (or less) laser emission from the random medium at the same pumping rate. When the nonlinear response is much faster than the buildup of the lasing mode, the lasing mode cannot response fast enough to the nonlinear refractive index change. The phase of scattered light changes quickly due to rapid change of refractive index with intensity. The absence of constant phase relations among light waves scattered by different particles undermines the interference effect. Hence, the effect of single particle scattering becomes dominant over the collective effect of many particle scattering. For x ( ~ )  > 0 (or ~ ( ~ 1  < 0 ) ,  the refractive index contrast of the binary layers increases (or decreases) as the laser intensity increases. Light scattering of a single particle becomes stronger (or weaker). The increase (or decrease) of scattering strength results in more (or less) efficient lasing, i.e., higher (or lower) laser intensity and longer (or shorter) lasing period. References 1. C. Vanneste and P. Sehbah, Phys. Rev. Lett. 87, 183903 (2001). 2. X. Jiang and C.M. Soukoulis, Phys. Rev. E 65, R25601 (2002). 3. H. Cao, Y. Ling, J.Y. Xu, and A.L. Burin, Phys. Rev. E 66, R25601 (2002). QThG3 2.0- 1.5- = ? .  E - 1.0- v 5 .  0.5 - Cao et.nl., 1)ynamic Nonlinear Uffect on Lasing ill Random Media 0.0) J I , , . 5 . I . I , 20 25 30 35 40 t (PSI 5 

Dynamic Nonlinear Effect on Lasing in Random Media

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Dynamic Nonlinear Effect on Lasing in Random Media

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