Simmulations of sommerfeld and brillouin precursors in the medium with frequency dispersion using numerical method of solving wave equations
E.S. Kozlova , V.V. Kotlyar

PDF, 1415 kB

Full text of article: Russian language.

DOI: 10.18287/0134-2452-2013-37-2-146-154

Pages: 146-154.

Abstract:
The wave equation (2 +1) taking into account the frequency dispersion of the material for TE polarization is written in a form in which the second time derivative included under the sign of the convolution integral describing the electric induction. An algorithm for solving such equations using explicit finite difference scheme is developed. The solution of the wave equation, describing the propagation of ultrashort pulse duration of 3.36 fs (in the spectral range 274-806 nm) in a planar waveguide made of quartz glass at the center wavelength of 532 nm, is different from solutions of this equation without dispersion for 3% and from solutions of Maxwell's equations derived by FDTD-method in the program FullWAVE, for 6%. A detailed analysis of the obtained solutions for a femtosecond pulse with a sharp initial front resulted in the discovery of precursors, which come to the observation point before the main pulse and the intensity is 100 times smaller. Moreover, the calculated time delay Sommerfeld precursor differs from the theoretical to 20%, And the Brillouin precursor of 3%.

Key words:
wave equation, permettivety, explicit finite-difference scheme, numerical simulation, ultrashort pulse, the optical precursor.

References:

  1. Hecht, J. Spectral Broadening Advances Quest for Single-Cycle Pulses / J. Hecht // Laser Focus World. – 2011. – V. 47(8). – P. 65-70.
  2. Fourmaux, S. Laser Pulse Contrast Ratio Cleaning in 100 TW Scale Ti: Sapphire Laser Systems / S. Fourmaux, S. Payeur, Ph. Lassonde, J.C. Kieffer and F. Martin // Laser Systems for Applications. – 2011. – P. 139-154.
  3. Block, М. Few-cycle high-contrast vortex pulses / M. Block, J. Jahns and R. Grunwald // Optics Letters. – 2012. – V. 37(18). – P. 3804-3806.
  4. Povolotskiy, A. 2D and 3D laser writing for integrated optical elements creation / A. Povolotskiy, A. Shimko, A. Manshina // Mondello Proceedings of WFOPC2005: Elioticinese Service Point srl. – 2005. – V. 4. – P. 196-202.
  5. Cheng, Ya. Microfabrication of 3D hollow structures embedded in glass by femtosecond laser for Lab-on-a-chip applications / Ya. Cheng, K. Sugioka, K. Midorikawa // Applied Surface Science. – 2005. – V. 248 – P. 172-176.
  6. Liu, X. Laser ablation and micromachining with ultrashort laser pulses / X. Liu, D. Du, G. Mourou // IEEE Quantum Electron. – 1997. – V. 38. – P. 1706.
  7. Krukov, P.G. Lasers of ultrafast pulses and it’s application / P.G. Krukov. – Dolgoprudniy: “Intellekt” Publishing House, 2012. – 248 p. – (In Russian).
  8. Bohkarev, N.N. The interaction of femtosecond laser pulses with biological substance / N.N. Bockarev [et al.]. – Tomsk: “TPU” Publishing, 2007. – 121 p. – (In Russian).
  9. Liu, Z. Ultraviolet conical emission produced by high-power femtosecond laser pulse in transparent media / Z. Liu, X. Lu, Q. Liu, S. Sun, L. Li, X. Liu, B. Ding, B. Hu // Appl. Phys. B. – 2012. – V. 108 – P. 493-500.
  10. Piglosiewicz, B. Ultrasmall bullets of light-focusing few-cycle light pulses to the diffraction limit / B. Piglosiewicz, D. Sa­diq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa and C. Lie­nau // Optics Express. – 2011. – V. 19(15) – P. 14451-14463.
  11. Ahmanov, S.А. Optics of Femtosecond Laser Pulses / S.A. Ahmanov, V.A. Vislouh, A.S. Chirkin. – Moscow: “Nauka” Publisher, 1988. – 312 p. – (In Russian).
  12. Oughstun, K.E. Electromagnetic pulse propagation in causial dielectrics / K.E. Oughstun, G.C. Sherman. – Springer-Verlag, 1994. – 465 p.
  13. Li, C. Approach to accurately measuring the speed of optical precursors / C. Li, Z. Zhou, H. Jeong, G. Guo // Phys. Rev. A. – 2011. – V. 84 – P. 043803.
  14. Safian, R. Joint time-frequency and FDTD analysis of precursor fields in dispersive media / R. Safian, C.D. Sarris, M. Mojahedi // Phys. Rev. E. – 2006.– V. 73.– P. 066602.
  15. Jeong, H. Evolution of Sommerfeld and Brillouin precursors in intermediate spectral regimes / H. Jeong, U.L. Osterberg, T. Hansson // J. Opt. Soc. Am. B. – 2009. – V. 26. –P. 2455-2460.
  16. Macke, B. From Sommerfeld and Brillouin forerunners to optical precursors / B. Macke and B. Segard // Phys. Rev. A. – 2013. – V. 87 – P. 043830.
  17. Macke, B. Simle asymptotic forms for Sommerfelod and Brillouin precursore / B. Macke and B. Segard // Phys. Rev. A. – 2012. – V. 86 – P. 013837.
  18. Luebbers, R.J. A frequency-depended finite-difference time-domain formulation for dispersive materials / R.J. Luebbers, F.P. Hunsberger, K.S. Kunz, R.B. Standler and M. Schneider // IEEE Trans. Electromagn. Compat. – 1990. –V. 32. – P. 222-227.
  19. Luebbers, R.J. FDTD for Nth-order dispersive media / R.J. Luebbers and F.P. Hunsberger // IEEE Trans. Antennas. Propagat. – 1992. –V. 40. – P. 1297-1301.
  20. Bui, M.D. Propagation of transients in dispersive dielectric me­dia / M.D. Bui, S.S. Stuchly and G.I. Costache // IEEE Trans. Microwve Theory Technol. – 1991. – V. 39 – P. 1165-1171.
  21. Hawkins, R.J. Linear electronic dispersion and finite-difference time-domain calculations: a simple approach / R.J. Hawkins and J.S. Kallman // J. Lightwave Technol. – 1993. – V. 11 – P. 1872-1874.
  22. Kelley, D.F. Piecewise linear recursive convolution for dispersive media using FDTD / D.F. Kelley and R.J. Luebbers – IEEE Trans. Antennas. Propagat. – 1996. –V. 44. – P. 792-797.
  23. Kashiwa, T. A treatment by the FD-TD method of the dispersive characteristics associated with electronic polarizaion / T. Kashiwa and I. Fukai // Microwave Opt. Technol. Lett. – 1990. – V. 3(5) – P. 203-205.
  24. Kashiwa, T. A finite-difference time-domain formulation for transient propagation in dispersive media associated with Cole-Cole’s circular arc law / T. Kashiwa, Y. Ohtomo and I. Fukai // Microwave Opt. Technol. Lett. – 1990. – V. 3(12) – P. 16-419.
  25. Joseph, R.M. Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses / R.M. Joseph, S.C. Hagness and A. Taflove // Opt. Lett. – 1991. – V. 16. – P. 1412-1414.
  26. Gandhi, O.P. A frequency-depended finite-difference time-domain formulation for general dispersive media / O.P. Gandhi, B.-Q. Gao and J.Y. Chen // IEEE Trans. Microwve Theory Technol. – 1993. – V. 41. – P. 658-664.
  27. Korner, T.O. Auxiliary differential equation: efficient implementation in the finite-difference time-domain method / T.O. Korner and W. Fichtner // Opt. Lett. – 1997. – V. 22(21) – P. 1586-1588.
  28. Liu, Y. Formulation of the finite-difference time-domain method for the analysis of axially symmetric metal nanodevices / Y. Liu and W. Yu // Journal of Modern Optics. – 2012. – V. 59(16) – P. 1439-1447.
  29. Sullivan, D.M. Frequency-depended FDTD methods using Z transform / D.M. Sullivan // IEEE Trans. Antennas. Propagat. – 1992. –V. 40. – P. 1223-1230.
  30. Ilin, V.A. Mathematical analysis. P.1. / V.A. Ilin, V.A. Sadovnishii, Bl.H. Sendov. – Мoscow: “MSU Press” Publisher, 1985. – 663 p. – (In Russian).
  31. Couairon, A. Filamentation and damage in fused silica indu­ced by tightly focused femtosecond laser pulses / A. Cou­airon, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz // Phys. Rev. B. – 2005. – V. 71. – P. 125435-125441.
  32. Kozlova, E.S. Simulation of ultrafast 2D light pulse / E.S. Kozlova, V.V. Kotlyar // Computer Optics. – 2012. – V. 36(2) – P. 158-164. – (In Russian).
© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20