This work demonstrates an improved method to simulate long-distance femtosecond pulse propagation in highcontrast nanowaveguides. Different from typical beam propagation methods, the foundational tool here is capable of simulating strong spatiotemporal waveform reshaping and extreme spectral dynamics. Meanwhile, the ability to fully capture effects due to index contrast in the transverse direction is retained, without requiring a decomposition of the electric field in terms of waveguide modes. These simulations can be computationally expensive, however, so cost is reduced in the improved method by considering only the waveguide core. Fields in the cladding are then properly accounted for through a boundary condition suitable for the case of total internal reflection.
@article{bwmeta1.element.doi-10_2478_nsmmt-2013-0010,
author = {Jonathan Andreasen and Miroslav Kolesik},
title = {Efficient simulation of unidirectional pulse propagation in high-contrast nonlinear nanowaveguides},
journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},
volume = {2},
year = {2013},
pages = {157-165},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_nsmmt-2013-0010}
}
Jonathan Andreasen; Miroslav Kolesik. Efficient simulation of unidirectional pulse propagation in high-contrast nonlinear nanowaveguides. Nanoscale Systems: Mathematical Modeling, Theory and Applications, Tome 2 (2013) pp. 157-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_nsmmt-2013-0010/
[1] J. Andreasen and M. Kolesik, Nonlinear propagation of light in structured media: Generalized unidirectional pulse propagation equations. Phys. Rev. E, 86(3), 036706, (2012). [WoS][Crossref]
[2] J. Andreasen and M. Kolesik, Midinfrared femtosecond laser pulse filamentation in hollow waveguides: A comparison of simulation methods. Phys. Rev. E, 87(5), 053303, (2013). [WoS][Crossref]
[3] C. L. Arnold, S. Akturk, M. Franco, A. Couairon, and A. Mysyrowicz, Compression of ultrashort laser pulses in planar hollow waveguides: a stability analysis. Opt. Express, 17(13), 11122–11129, (2009). [WoS][Crossref][PubMed]
[4] C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers. New J. Phys., 12(7), 073015, (2010). [WoS][Crossref]
[5] L Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Ultrashort filaments of light in weakly ionized optically transparent media. Rep. Prog. Phys., 70(10), 1633–1713, (2007). [Crossref][WoS]
[6] L. Caspani, D. Duchesne, K. Dolgaleva, S. J. Wagner, M. Ferrera, L. Razzari, et al., Optical frequency conversion in integrated devices. J. Opt. Soc. Am. B, 28(12), A67–A82, (2011). [Crossref]
[7] S. L. Chin, Femtosecond Laser Filamentation. Springer, New York, (2009).
[8] A. Couairon and A. Mysyrowicz, Femtosecond filamentation in transparent media. Phys. Rep., 441(2-4), 47–189, (2007). [Crossref]
[9] A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramírez-Góngora, and M. Kolesik, Practitioner’s guide to laser pulse propagation models and simulation. Eur. Phys. J. Special Topics, 199(1), 5–76, (2011). [WoS]
[10] C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments. Phys. Plasmas, 8(7), 3445–3456, (2001). [Crossref]
[11] D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, et al., Supercontinuum generation in a high index doped silica glass spiral waveguide. Opt. Express, 18(2), 923–930, (2010). [Crossref]
[12] M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Broad-band optical parametric gain on a silicon photonic chip. Nature, 441(7096), 960–963, (2006).
[13] M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, Nonlinear optics in photonic nanowires. Opt. Express, 16 (2), 1300–1320, Jan (2008). [PubMed][Crossref]
[14] M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides. Opt. Express, 15(20), 12949–12958, (2008).
[15] X. Gai, D.-Y. Choi, S. Madden, Z. Yang, R. Wang, and B. Luther-Davies, Supercontinuum generation in the midinfrared from a dispersion-engineered As2S3 glass rib waveguide. Opt. Lett., 37(18), 3870–3872, (2012). [WoS][Crossref]
[16] J. H. Greene and A. Taflove, General vector auxiliary differential equation finite-difference time-domain method for nonlinear optics. Opt. Express, 14(18), 8305–8310, (2006). [PubMed][Crossref]
[17] R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, Ultrabroadband supercontinuum generation in a CMOS-compatible platform. Opt. Lett., 37(10), 1685–1687, (2012). [Crossref]
[18] R. J. Hawkins, Propagation properties of single-mode dielectric waveguide structures: a path integral approach. Appl. Opt., 26(7), 1183–1188, (1987). [PubMed][Crossref]
[19] S. T. Hendow and S. A. Shakir, Recursive numerical solution for nonlinear wave propagation in fibers and cylindrically symmetric systems. Appl. Opt., 25(11), 1759–1764, (1986). [PubMed][Crossref]
[20] P. Kinsler, Optical pulse propagation with minimal approximations. Phys. Rev. A, 81(1), 013819, (2010). [Crossref][WoS]
[21] P. Kinsler, Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses. Phys. Rev. A, 81(2), 023808, (2010). [Crossref][WoS]
[22] M. Kolesik and J. V. Moloney, Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations. Phys. Rev. E, 70(3), 036604, (2004). [Crossref]
[23] M. Kolesik, J. V. Moloney, and M. Mlejnek, Unidirectional optical pulse propagation equation. Phys. Rev. Lett., 89 (28), 283902, (2002). [PubMed][Crossref]
[24] M. Kolesik, P. T. Whalen, and J. V. Moloney, Theory and simulation of ultrafast intense pulse propagation in extended media. IEEE J. Sel. Top. Quantum Electron., 18(1), 494–506, (2012). [WoS][Crossref]
[25] H. M. Masoudi and M. S. Akond, Efficient iterative time-domain beam propagation methods for ultra short pulse propagation: Analysis and assessment. J. Lightwave Technol., 29(16), 2475–2481, (2011). [WoS][Crossref]
[26] Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, Octave-spanning frequency comb generation in a silicon nitride chip. Opt. Lett., 36(17), 3398–3400, (2011). [Crossref]
[27] J. V. Roey, J. van der Donk, and P. E. Lagasse, Beam-propagation method: analysis and assessment. J. Opt. Soc. Am., 71,803–810, (1981). [Crossref]
[28] K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, et al., Modelocking and femtosecond pulse generation in chip-based frequency combs. Opt. Express, 21(1), 1335–1343, (2013). [Crossref]
[29] J. Shibayama, M. Muraki, J. Yamauchi, and H. Nakano, Comparative study of several time-domain methods for optical waveguide analyses. J. Lightwave Technol., 23(7), 2285, (2005). [Crossref]
[30] G. Tempea and T. Brabec, Theory of self-focusing in a hollow waveguide. Opt. Lett., 23(10), 762–764, (1998). [Crossref]
[31] D. Yevick and B. Hermansson, New formulations of the matrix beam propagation method: Application to rib waveguides. IEEE J. Quantum Electron., 25(2), 221–229, (1989). [Crossref]
[32] L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, and A. E. Willner, On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses. Opt. Express, 19(12), 11584–11590, (2011). [Crossref]