Abstract
Small-scale self-focusing is mostly caused by spatial diffraction modulation. It is the major factor for degradation of the laser pulse quality and the maximum output power. We investigate diffraction modulation evolution from a knife-edge for small-scale self-focusing through numerical calculation and experiment. We find that the effect of diffraction modulation weakens and the effect of small-scale self-focusing strengthens with the decrease of the truncation parameter. As the truncation parameter decreased continually, the effect of small-scale self-focusing strengthens sequentially,the laser begins split. In addition, the position of new growth for small-scale self-focusing is increasingly far away from the diffraction modulation peak and the diffraction fringes are broadened with the increment of the propagation distance. Our experimental results are in good agreement with an approximate theoretical analysis.
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Bespalov, V.I., Talanov, V.I.: Filamentary structure of light beams in nonlinear liquids. ZhETF Pisma Redaktsiiu 3, 471 (1966)
Bliss, E.S.: Propagation of a high-intensity laser pulse with small-scale intensity modulation. Appl. Phys. Lett. 25, 448–450 (2003)
Campillo, A.J., Shapiro, S.L., Suydam, B.R.: Periodic breakup of optical beams due to self-focusing. Appl. Phys. Lett. 23, 628–630 (1973)
Canabarro, A.A., Santos, B., Gleria, I., Lyra, M.L., Sombra, A.S.B.: Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses. JOSA. B. 27, 1878–1885 (2010)
Chekalin, S.V., Kandidov, V.P.: From self-focusing light beams to femtosecond laser pulse filamentation. Phys. Usp. 56, 123–140 (2013)
Chu, W., Li, G.H., Xie, H.Q., Ni, J.L., Yao, J.P., Zeng, B., Zhang, H.S., Jing, C.R., Xu, H.L., Cheng, Y., Xu, Z.Z.: A self-induced white light seeding laser in a femtosecond laser filament. Laser Phys. Lett. 11, 015301 (2014)
Cook, K., Kar, A., Lamb, R.A.: White-light filaments induced by diffraction effects. Opt. Express 13, 2025–2031 (2005)
Deng, Y.B., Fu, X.Q., Tan, C., Yang, H., Deng, S.G., Xiong, C.X., Zhang, G.F.: Experimental investigation of spatiotemporal evolution of femtosecond laser pulses during small-scale self-focusing. Appl. Phys. B. 114, 449–454 (2014)
Dulkeith, E., Vlasov, Y.A., Chen, X., Panoiu, N.C., Osgood Jr, R.M.: Self-phase-modulation in submicron silicon-on-insulator photonic wires. Opt. Express 14, 5524–5534 (2006)
Freund, I.: Nonlinear diffraction. Phys. Rev. Lett. 21, 1404–1406 (1968)
Gattass, R.R., Mazur, E.: Femtosecond laser micromachining in transparent materials. Nat. Photonics 2, 219–225 (2008)
Hao, Z., Stelmaszczyk, K., Rohwetter, P., Nakaema, W.M., Woeste, L.: Femtosecond laser filament-fringes in fused silica. Opt. Express 19, 7799–7806 (2011)
Jia, H., Xu, B., Wang, F., Zhou, L.: Small-scale self-focusing in a tapered optical beam. Appl. Opt. 51, 6089–6994 (2012)
Kandidov, V.P., Kosareva, O.G., Golubtsov, I.S., Liu, W., Becker, A., Akozbek, N., Bowden, C.M., Chin, S.L.: Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation). Appl. Phys. B. 77, 149–165 (2003)
Manela, O., Segev, M.: Nonlinear diffractive optical elements. Opt. Express 15, 10863–10868 (2007)
Mendez, C., De Aldana, J.V., Torchia, G.A., Roso, L.: Optical waveguide arrays induced in fused silica by void-like defects using femtosecond laser pulses. Appl. Phys. B. 86, 343–346 (2007)
Mendoza-Yero, O., et al.: Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment. Opt. Express 18, 20900–20911 (2010)
Mironov, S., Khazanov, E., Lozhkarev, V., Ginzburg, V., Mourou, G.: Small-Scale Self-Focusing Suppression at Intense Laser Beams in Mediums with Quadratic and Cubic Nonlinearity. In High Intensity Lasers and High Field Phenomena. Optical Society of America p. HWC6 (2011)
Mironov, S., Lozhkarev, V., Luchinin, G., Shaykin, A., Khazanov, E.: Suppression of small-scale self-focusing of high-intensity femtosecond radiation. Appl. Phys. B. 113, 147–151 (2013)
Ngo, Q.M., Le, K.Q., Lam, V.D.: Optical bistability based on guided-mode resonances in photonic crystal slabs. JOSA B 29, 1291–1295 (2012)
Nolte, S., Will, M., Burghoff, J., Tuennermann, A.: Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics. Appl. Phys. A 77, 109–111 (2003)
Rohwetter, P., Queisser, M., Stelmaszczyk, K., Fechner, M., Woste, L.: Laser multiple filamentation control in air using a smooth phase mask. Phys. Rev. A 77, 013812 (2008)
Schweinsberg, A., Kuper, J., Boyd, R.W.: Loss of spatial coherence and limiting of focal plane intensity by small-scale laser-beam filamentation. Phys. Rev. A 84, 053837 (2011)
Semak, V.V., Shneider, M.N.: Effect of power losses on self-focusing of high-intensity laser beam in gases. J. Phys. D Appl. Phys. 46, 185502 (2013)
Shim, B., Schrauth, S.E., Gaeta, A.L.: Filamentation in air with ultrashort mid-infrared pulses. Opt. Express 19, 9118–9126 (2011)
Sun, H.B., Xu, Y., Matsuo, S., Misawa, H.: Microfabrication and characteristics of two-dimensional photonic crystal structures in vitreous silica. Opt. Rev. 6, 396–398 (1999)
Velchev, I., Pattnaik, R., Toulouse, J.: Two-beam modulation instability in non-instantaneous nonlinear media. Phys. Rev. Lett. 91, 093905 (2003)
Wan, W., Jia, S., Fleischer, J.W.: Dispersive superfluid-like shock waves in nonlinear optics. Nat. Phys. 3, 46–51 (2007)
Wan, W.J., et al.: Diffraction from an edge in a self-focusing medium. Opt. Lett. 35, 2819–2821 (2010)
Acknowledgments
This work was supported in part by the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110161110012), the Department of Science and Technology of Hunan Province (2013FJ2018).
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Wang, N., Tan, C. & Fu, X. Diffraction modulation evolution from a knife-edge for small-scale self-focusing. Opt Quant Electron 47, 2697–2707 (2015). https://doi.org/10.1007/s11082-015-0156-8
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DOI: https://doi.org/10.1007/s11082-015-0156-8