Abstract

We propose a beam propagation method variant, which only requires the computational grid to span the core region of a waveguiding structure. Optical fields outside are accounted for through semitransparent boundary conditions. The method is fast, simple to implement, and accurate over a wide range of wavelengths. It is applicable to both guiding and leaky structures, with sufficiently strong contrast between refractive indices in the core, substrate, and cladding.

© 2013 IEEE

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  1. J. Shibayama, M. Muraki, J. Yamauchi, and H. Nakano, “Comparative study of several time-domain methods for optical waveguide analyses,” J. Lightwave Technol., vol. 23, no. 7, pp. 2285–2293, 2005.
  2. N.-N. Feng, G.-R. Zhou, W.-P. Huang, "An efficient split-step time-domain beam-propagation method for modeling of optical waveguide devices," J. Lightwave Technol. 23, (pp. 2186–2191, 2005).
  3. H. M. Masoudi, "A novel nonparaxial time-domain beam-propagation method for modeling ultrashort pulses in optical structures," J. Lightwave Technol. 25, 3175-3184 (2007).
  4. K. Q. Le, T. Benson, P. Bienstman, "Application of modified Padé approximant operators to time-domain beam propagation methods," J. Opt. Soc. Amer. B 26, 2285-2289 (2009).
  5. H. M. Masoudi, M. S. Akond, "Efficient iterative time-domain beam propagation methods for ultra short pulse propagation: Analysis and assessment," J. Lightwave Technol. 29 , 2475-2481 (2011 ).
  6. L. Yin, Q. Lin, G. P. Agrawal, "Soliton fission and supercontinuum generation in silicon waveguides," Opt. Lett. 32 , 391-393 (2007 ).
  7. M. Kolesik, E. Wright, J. Moloney, "Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers," Appl. Phys. B 79, 293-300 (2004).
  8. S. Afshar V. and T. M. Monro, "A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures Part I: Kerr nonlinearity," Opt. Exp. 17, 2298-2318 (2009).
  9. J. Andreasen, M. Kolesik, "Nonlinear propagation of light in structured media: Generalized unidirectional pulse propagation equations," Phys. Rev. E 86, 036706-1-036706-9 (2012).
  10. J. Andreasen, M. Kolesik, "Midinfrared femtosecond laser pulse filamentation in hollow waveguides: A comparison of simulation methods," Phys. Rev. E 87, 053303-1-053303-7 (2013).
  11. A. Couairon, A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 ( 2007).
  12. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media ," Rep. Prog. Phys. 70, 1633-1713 (2007).
  13. A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, M. Kolesik, "Practitioner’s guide to laser pulse propagation models and simulation," Eur. Phys. J. Spec. Topics 199, 5 -76 (2011).
  14. M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, "Nonlinear optics in photonic nanowires ," Opt. Exp. 16, 1300-1320 (2008).
  15. X. Gai, D.-Y. Choi, S. Madden, Z. Yang, R. Wang, B. Luther-Davies, "Supercontinuum generation in the mid-infrared from a dispersion-engineered As2S3 glass rib waveguide," Opt. Lett. 37, 3870-3872 (2012).
  16. R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, A. L. Gaeta, "Ultrabroadband supercontinuum generation in a CMOS-compatible platform," Opt. Lett. 37, 1685-1687 (2012).
  17. L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, A. E. Willner, "On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses," Opt. Exp. 19, 11 584-11 590 (2011).
  18. L. Zhang, Q. Lin, A. Agarwal, L. Kimerling, and J. Michel, “On-chip sub-cycle pulse generation via a two-octave supercontinuum from visible to mid-infrared wavelengths,” presented at the Conference on Lasers and Electro-Optics 2012, ser. OSA Technical Digest [Online], 2012, Paper CTu3G.4..
  19. D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Lgar, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, "Supercontinuum generation in a high index doped silica glass spiral waveguide," Opt. Exp. 18, 923-930 (2010).
  20. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, "Modelocking and femtosecond pulse generation in chip-based frequency combs," Opt. Exp. 21, 1335-1343 (2013).
  21. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, A. L. Gaeta, "Octave-spanning frequency comb generation in a silicon nitride chip," Opt. Lett. 36, 3398-3400 (2011).
  22. L. Caspani, D. Duchesne, K. Dolgaleva, S. J. Wagner, M. Ferrera, L. Razzari, A. Pasquazi, M. Peccianti, D. J. Moss, J. S. Aitchison, R. Morandotti, "Optical frequency conversion in integrated devices [invited]," J. Opt. Soc. Amer. B 28, A67-A82 (2011).
  23. C. L. Arnold, S. Akturk, M. Franco, A. Couairon, A. Mysyrowicz, "Compression of ultrashort laser pulses in planar hollow waveguides: A stability analysis ," Opt. Exp. 17, 11 122-11 129 (2009).
  24. S. Akturk, C. L. Arnold, B. Zhou, A. Mysyrowicz, "High-energy ultrashort laser pulse compression in hollow planar waveguides," Opt. Lett. 34, 1462-1464 (2009).
  25. S. Chen, A. Jarnac, A. Houard, Y. Liu, C. L. Arnold, B. Zhou, B. Forestier, B. Prade, A. Mysyrowicz, "Compression of high-energy ultrashort laser pulses through an argon-filled tapered planar waveguide," J. Opt. Soc. Amer. B 28, 1009-1012 (2011).
  26. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzyls, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, "Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers," Science 336, 1287-1291 (2012).
  27. T. V. Yioultsis, G. D. Ziogos, E. E. Kriezis, "Explicit finite-difference vector beam propagation method based on the iterated Crank–Nicolson scheme," J. Opt. Soc. Amer. A 26, 2183 -2191 (2009).
  28. R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, 1973).
  29. E. Marcatili, R. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers.," Bell Syst. Tech. J. 43, 1783 -1809 (1964).

2013 (2)

J. Andreasen, M. Kolesik, "Midinfrared femtosecond laser pulse filamentation in hollow waveguides: A comparison of simulation methods," Phys. Rev. E 87, 053303-1-053303-7 (2013).

K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, "Modelocking and femtosecond pulse generation in chip-based frequency combs," Opt. Exp. 21, 1335-1343 (2013).

2012 (4)

X. Gai, D.-Y. Choi, S. Madden, Z. Yang, R. Wang, B. Luther-Davies, "Supercontinuum generation in the mid-infrared from a dispersion-engineered As2S3 glass rib waveguide," Opt. Lett. 37, 3870-3872 (2012).

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzyls, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, "Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers," Science 336, 1287-1291 (2012).

J. Andreasen, M. Kolesik, "Nonlinear propagation of light in structured media: Generalized unidirectional pulse propagation equations," Phys. Rev. E 86, 036706-1-036706-9 (2012).

R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, A. L. Gaeta, "Ultrabroadband supercontinuum generation in a CMOS-compatible platform," Opt. Lett. 37, 1685-1687 (2012).

2011 (5)

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, A. L. Gaeta, "Octave-spanning frequency comb generation in a silicon nitride chip," Opt. Lett. 36, 3398-3400 (2011).

L. Caspani, D. Duchesne, K. Dolgaleva, S. J. Wagner, M. Ferrera, L. Razzari, A. Pasquazi, M. Peccianti, D. J. Moss, J. S. Aitchison, R. Morandotti, "Optical frequency conversion in integrated devices [invited]," J. Opt. Soc. Amer. B 28, A67-A82 (2011).

L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, A. E. Willner, "On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses," Opt. Exp. 19, 11 584-11 590 (2011).

S. Chen, A. Jarnac, A. Houard, Y. Liu, C. L. Arnold, B. Zhou, B. Forestier, B. Prade, A. Mysyrowicz, "Compression of high-energy ultrashort laser pulses through an argon-filled tapered planar waveguide," J. Opt. Soc. Amer. B 28, 1009-1012 (2011).

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, M. Kolesik, "Practitioner’s guide to laser pulse propagation models and simulation," Eur. Phys. J. Spec. Topics 199, 5 -76 (2011).

2010 (1)

D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Lgar, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, "Supercontinuum generation in a high index doped silica glass spiral waveguide," Opt. Exp. 18, 923-930 (2010).

2009 (5)

C. L. Arnold, S. Akturk, M. Franco, A. Couairon, A. Mysyrowicz, "Compression of ultrashort laser pulses in planar hollow waveguides: A stability analysis ," Opt. Exp. 17, 11 122-11 129 (2009).

S. Akturk, C. L. Arnold, B. Zhou, A. Mysyrowicz, "High-energy ultrashort laser pulse compression in hollow planar waveguides," Opt. Lett. 34, 1462-1464 (2009).

T. V. Yioultsis, G. D. Ziogos, E. E. Kriezis, "Explicit finite-difference vector beam propagation method based on the iterated Crank–Nicolson scheme," J. Opt. Soc. Amer. A 26, 2183 -2191 (2009).

K. Q. Le, T. Benson, P. Bienstman, "Application of modified Padé approximant operators to time-domain beam propagation methods," J. Opt. Soc. Amer. B 26, 2285-2289 (2009).

S. Afshar V. and T. M. Monro, "A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures Part I: Kerr nonlinearity," Opt. Exp. 17, 2298-2318 (2009).

2008 (1)

M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, "Nonlinear optics in photonic nanowires ," Opt. Exp. 16, 1300-1320 (2008).

2007 (2)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media ," Rep. Prog. Phys. 70, 1633-1713 (2007).

H. M. Masoudi, "A novel nonparaxial time-domain beam-propagation method for modeling ultrashort pulses in optical structures," J. Lightwave Technol. 25, 3175-3184 (2007).

2004 (1)

M. Kolesik, E. Wright, J. Moloney, "Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers," Appl. Phys. B 79, 293-300 (2004).

1964 (1)

E. Marcatili, R. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers.," Bell Syst. Tech. J. 43, 1783 -1809 (1964).

Appl. Phys. B (1)

M. Kolesik, E. Wright, J. Moloney, "Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers," Appl. Phys. B 79, 293-300 (2004).

Bell Syst. Tech. J. (1)

E. Marcatili, R. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers.," Bell Syst. Tech. J. 43, 1783 -1809 (1964).

Eur. Phys. J. Spec. Topics (1)

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, M. Kolesik, "Practitioner’s guide to laser pulse propagation models and simulation," Eur. Phys. J. Spec. Topics 199, 5 -76 (2011).

J. Lightwave Technol. (1)

N.-N. Feng, G.-R. Zhou, W.-P. Huang, "An efficient split-step time-domain beam-propagation method for modeling of optical waveguide devices," J. Lightwave Technol. 23, (pp. 2186–2191, 2005).

J. Lightwave Technol. (1)

H. M. Masoudi, "A novel nonparaxial time-domain beam-propagation method for modeling ultrashort pulses in optical structures," J. Lightwave Technol. 25, 3175-3184 (2007).

J. Lightwave Technol. (1)

H. M. Masoudi, M. S. Akond, "Efficient iterative time-domain beam propagation methods for ultra short pulse propagation: Analysis and assessment," J. Lightwave Technol. 29 , 2475-2481 (2011 ).

J. Opt. Soc. Amer. B (1)

L. Caspani, D. Duchesne, K. Dolgaleva, S. J. Wagner, M. Ferrera, L. Razzari, A. Pasquazi, M. Peccianti, D. J. Moss, J. S. Aitchison, R. Morandotti, "Optical frequency conversion in integrated devices [invited]," J. Opt. Soc. Amer. B 28, A67-A82 (2011).

J. Opt. Soc. Amer. B (1)

K. Q. Le, T. Benson, P. Bienstman, "Application of modified Padé approximant operators to time-domain beam propagation methods," J. Opt. Soc. Amer. B 26, 2285-2289 (2009).

J. Opt. Soc. Amer. A (1)

T. V. Yioultsis, G. D. Ziogos, E. E. Kriezis, "Explicit finite-difference vector beam propagation method based on the iterated Crank–Nicolson scheme," J. Opt. Soc. Amer. A 26, 2183 -2191 (2009).

J. Opt. Soc. Amer. B (1)

S. Chen, A. Jarnac, A. Houard, Y. Liu, C. L. Arnold, B. Zhou, B. Forestier, B. Prade, A. Mysyrowicz, "Compression of high-energy ultrashort laser pulses through an argon-filled tapered planar waveguide," J. Opt. Soc. Amer. B 28, 1009-1012 (2011).

Opt. Exp. (6)

C. L. Arnold, S. Akturk, M. Franco, A. Couairon, A. Mysyrowicz, "Compression of ultrashort laser pulses in planar hollow waveguides: A stability analysis ," Opt. Exp. 17, 11 122-11 129 (2009).

S. Afshar V. and T. M. Monro, "A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures Part I: Kerr nonlinearity," Opt. Exp. 17, 2298-2318 (2009).

M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, "Nonlinear optics in photonic nanowires ," Opt. Exp. 16, 1300-1320 (2008).

L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, A. E. Willner, "On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses," Opt. Exp. 19, 11 584-11 590 (2011).

D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Lgar, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, "Supercontinuum generation in a high index doped silica glass spiral waveguide," Opt. Exp. 18, 923-930 (2010).

K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, "Modelocking and femtosecond pulse generation in chip-based frequency combs," Opt. Exp. 21, 1335-1343 (2013).

Opt. Lett. (1)

X. Gai, D.-Y. Choi, S. Madden, Z. Yang, R. Wang, B. Luther-Davies, "Supercontinuum generation in the mid-infrared from a dispersion-engineered As2S3 glass rib waveguide," Opt. Lett. 37, 3870-3872 (2012).

Opt. Lett. (4)

Phys. Rep. (1)

A. Couairon, A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 ( 2007).

Phys. Rev. E (2)

J. Andreasen, M. Kolesik, "Nonlinear propagation of light in structured media: Generalized unidirectional pulse propagation equations," Phys. Rev. E 86, 036706-1-036706-9 (2012).

J. Andreasen, M. Kolesik, "Midinfrared femtosecond laser pulse filamentation in hollow waveguides: A comparison of simulation methods," Phys. Rev. E 87, 053303-1-053303-7 (2013).

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media ," Rep. Prog. Phys. 70, 1633-1713 (2007).

Science (1)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzyls, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, "Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers," Science 336, 1287-1291 (2012).

Other (3)

R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, 1973).

J. Shibayama, M. Muraki, J. Yamauchi, and H. Nakano, “Comparative study of several time-domain methods for optical waveguide analyses,” J. Lightwave Technol., vol. 23, no. 7, pp. 2285–2293, 2005.

L. Zhang, Q. Lin, A. Agarwal, L. Kimerling, and J. Michel, “On-chip sub-cycle pulse generation via a two-octave supercontinuum from visible to mid-infrared wavelengths,” presented at the Conference on Lasers and Electro-Optics 2012, ser. OSA Technical Digest [Online], 2012, Paper CTu3G.4..

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