## Dispersion of nonlinearity in subwavelength waveguides: derivation of pulse propagation equation and frequency conversion effects |

JOSA B, Vol. 30, Issue 4, pp. 812-820 (2013)

http://dx.doi.org/10.1364/JOSAB.30.000812

Enhanced HTML Acrobat PDF (724 KB)

### Abstract

Description of pulse propagation in waveguides with subwavelength features and high refractive index contrasts requires an accurate account of the dispersion of nonlinearity due to the considerable mode profile variation with the wavelength. The corresponding model derived from asymptotic expansion of Maxwell equations contains a complicated network of interactions between different harmonics of the pulse, and therefore is not convenient for analysis. We demonstrate that this model can be reduced to the generalized nonlinear Schrödinger-type pulse propagation equation under the assumption of factorization of the four-frequency dependence of nonlinear coefficients. We analyze two different semiconductor waveguide geometries and find that the factorization works reasonably well within large wavelength windows. This allows us to utilize the pulse propagation equation for the description of a broadband signal evolution. We study the mechanism of modulational instability induced by the dispersion of nonlinearity and find that the power threshold predicted by the simple model with three interacting harmonics is effectively removed when using pulses, while the efficiency of this process grows for shorter pulse durations. Also, we identify the effects of geometrical and material dispersion of nonlinearity on spectral broadening of short pulses in semiconductor waveguides.

© 2013 Optical Society of America

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(130.4310) Integrated optics : Nonlinear

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(190.4223) Nonlinear optics : Nonlinear wave mixing

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 27, 2012

Revised Manuscript: January 29, 2013

Manuscript Accepted: February 4, 2013

Published: March 6, 2013

**Citation**

Xuesong Zhao, Andrey V. Gorbach, and Dmitry V. Skryabin, "Dispersion of nonlinearity in subwavelength waveguides: derivation of pulse propagation equation and frequency conversion effects," J. Opt. Soc. Am. B **30**, 812-820 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-4-812

Sort: Year | Journal | Reset

### References

- R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I.-W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires,” Adv. Opt. Photon. 1, 162–235 (2009). [CrossRef]
- J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010). [CrossRef]
- J. Meier, W. S. Mohammed, A. Jugessur, L. Qian, M. Mojahedi, and J. S. Aitchison, “Group velocity inversion in AlGaAs nanowires,” Opt. Express 15, 12755–12762 (2007). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
- Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007). [CrossRef]
- A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79, 053812 (2009). [CrossRef]
- 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. Express 17, 2298–2318 (2009). [CrossRef]
- T. X. Tran and F. Biancalana, “An accurate envelope equation for light propagation in photonic nanowires: new nonlinear effects,” Opt. Express 17, 17934–17949 (2009). [CrossRef]
- A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Self-focusing and spatial plasmon-polariton solitons,” Opt. Express 17, 21732–21737 (2009). [CrossRef]
- D. V. Skryabin, A. V. Gorbach, and A. Marini, “Surface-induced nonlinearity enhancement of TM modes in planar subwavelength waveguides,” J. Opt. Soc. Am. B 28, 109–114 (2011). [CrossRef]
- A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in subwavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011). [CrossRef]
- N. C. Panoiu, X. Liu, and J. Osgood, “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. 34, 947–949 (2009). [CrossRef]
- A. V. Gorbach, X. Zhao, and D. V. Skryabin, “Dispersion of nonlinearity and modulation instability in subwavelength semiconductor waveguides,” Opt. Express 19, 9345–9351 (2011). [CrossRef]
- P. Kinsler and G. H. C. New, “Few-cycle soliton propagation,” Phys. Rev. A 69, 013805 (2004). [CrossRef]
- S. Amiranashvili, U. Bandelow, and N. Akhmediev, “Dispersion of nonlinear group velocity determines shortest envelope solitons,” Phys. Rev. A 84, 043834 (2011). [CrossRef]
- Z. Xu, B. Maes, X. Jiang, J. D. Joannopoulos, L. Torner, and M. Soljacić, “Nonlinear photonic crystals near the supercollimation point,” Opt. Lett. 33, 1762–1764 (2008). [CrossRef]
- Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063(2007). [CrossRef]
- J. Gomez-Gardeñes, B. A. Malomed, L. M. Flora, and A. R. Bishop, “Solitons in the Salerno model with competing nonlinearities,” Phys. Rev. E 73, 036608 (2006). [CrossRef]
- W. Ding, O. K. Staines, G. D. Hobbs, A. V. Gorbach, C. de Nobriga, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. J. Strain, and M. Sorel, “Modulational instability in a silicon-on-insulator directional coupler: role of the coupling-induced group velocity dispersion,” Opt. Lett. 37, 668–670 (2012). [CrossRef]
- D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]
- I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15, 15242–15249 (2007). [CrossRef]
- A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82, 041802 (2010). [CrossRef]
- Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 21111 (2007). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Fig. 1. |
Fig. 2. |
Fig. 3. |

Fig. 4. |
Fig. 5. |
Fig. 6. |

Fig. 7. |
Fig. 8. |
Fig. 9. |

Fig. 10. |
Fig. 11. |
Fig. 12. |

Fig. 13. |
||

« Previous Article | Next Article »

OSA is a member of CrossRef.