OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 13014–13029

Pseudospectral mode solver for analyzing nonlinear optical waveguides

Chia-Chien Huang  »View Author Affiliations

Optics Express, Vol. 20, Issue 12, pp. 13014-13029 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1346 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Numerical mode solver using a pseudospectral scheme is developed for solving various nonlinear dielectric and plasmonic waveguides with arbitrary nonlinear media. Two nonlinear iterative approaches that use this scheme are implemented; these approaches assign the mode power and effective index as extracted eigenvalues. However, to obtain the complete power dispersion curve including the stable and unstable modal solutions, assigning the mode power as an eigenvalue for a given effective index is required. Moreover, the biaxial feature of the nonlinear refractive index is considered for solving the transverse magnetic (TM) modes in materials of practical interest. Furthermore, the proposed scheme solves the problem of nonlinear surface plasmons guided by a thin metal film with nonlinear cladding, and the mode characteristics of long- and short-range surface plasmon polaritons are analyzed. We also apply the proposed scheme to a 2D strip waveguide with a nonlinear saturation substrate.

© 2012 OSA

OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(230.7380) Optical devices : Waveguides, channeled
(240.4350) Optics at surfaces : Nonlinear optics at surfaces

ToC Category:
Nonlinear Optics

Original Manuscript: April 9, 2012
Revised Manuscript: May 20, 2012
Manuscript Accepted: May 20, 2012
Published: May 24, 2012

Chia-Chien Huang, "Pseudospectral mode solver for analyzing nonlinear optical waveguides," Opt. Express 20, 13014-13029 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Vach, C. T. Seaton, G. I. Stegeman, and I. C. Khoo, “Observation of intensity-dependent guided waves,” Opt. Lett.9, 238–240 (1984). [CrossRef] [PubMed]
  2. I. Bennion, M. J. Goodwin, and W. J. Stewart, “Experimental nonlinear optical waveguide device,” Electron. Lett.21(1), 41–42 (1985). [CrossRef]
  3. F. Lederer, U. Langbein, and H. E. Ponath, “Nonlinear waves guided by a dielectric slab: I. TE polarization,” Appl. Phys. B31(2), 69–73 (1983). [CrossRef]
  4. F. Lederer, U. Langbein, and H. E. Ponath, “Nonlinear waves guided by a dielectric slab: II. TM–polarization,” Appl. Phys. B31(3), 187–190 (1983). [CrossRef]
  5. D. J. Robbins, “TE modes in a slab waveguide bounded by nonlinear media,” Opt. Commun.47(5), 309–312 (1983). [CrossRef]
  6. G. I. Stegeman, C. T. Seaton, J. Chilwell, and S. D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett.44(9), 830–832 (1984). [CrossRef]
  7. C. T. Seaton, J. D. Valera, B. Svenson, and G. I. Stegeman, “Comparison of solutions for TM-polarized nonlinear guided waves,” Opt. Lett.10(3), 149–150 (1985). [CrossRef] [PubMed]
  8. C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. Chilwell, and S. D. Smith, “Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media,” IEEE J. Quantum Electron.21(7), 774–783 (1985). [CrossRef]
  9. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A35(3), 1159–1164 (1987). [CrossRef] [PubMed]
  10. R. I. Joseph and D. N. Christodoulides, “Exact field decomposition for TM waves in nonlinear media,” Opt. Lett.12(10), 826–828 (1987). [CrossRef] [PubMed]
  11. G. I. Stegeman, E. M. Wright, C. T. Seaton, J. V. Moloney, T. P. Shen, A. A. Maradudin, and R. F. Wallis, “Nonlinear slab-guided waves in non-Kerr-like media,” IEEE J. Quantum Electron.22(6), 977–983 (1986). [CrossRef]
  12. K. Hayata, M. Nagai, and M. Koshiba, “Finite-element formalism for nonlinear slab-guided waves,” IEEE Trans. Microw. Theory Tech.36(7), 1207–1215 (1988). [CrossRef]
  13. K. Hayata and M. Koshiba, “Full vectorial analysis of nonlinear-optical waveguides,” J. Opt. Soc. Am. B5(12), 2494–2501 (1988). [CrossRef]
  14. K. Ogusu, “TM waves guided by nonlinear planar waveguides,” IEEE Trans. Microw. Theory Tech.37(6), 941–946 (1989). [CrossRef]
  15. M. R. Ramadas, R. K. Varshney, K. Thyagarajan, and A. K. Ghatak, “A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide,” J. Lightwave Technol.7(12), 1901–1905 (1989). [CrossRef]
  16. B. M. A. Rahman, J. R. Souza, and J. B. Davies, “Numerical analysis of nonlinear bistable optical waveguides,” IEEE Photon. Technol. Lett.2(4), 265–267 (1990). [CrossRef]
  17. R. D. Ettinger, F. A. Fernandez, B. M. A. Rahman, and J. D. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett.3(2), 147–149 (1991). [CrossRef]
  18. Q. Y. Li, R. A. Sammut, and C. Pask, “Variational and finite element analyses of nonlinear strip optical waveguides,” Opt. Commun.94(1-3), 37–43 (1992). [CrossRef]
  19. A. P. Zhao and S. R. Cvetkovic, “Finite-element solution of nonlinear TM waves in multiple-quantum-well waveguides,” IEEE Photon. Technol. Lett.4(11), 1231–1234 (1992). [CrossRef]
  20. X. H. Wang and G. K. Cambrell, “Full vectorial simulation of bistability phenomena in nonlinear-optical channel waveguides,” J. Opt. Soc. Am. B10(6), 1090–1095 (1993). [CrossRef]
  21. T. Rozzi and L. Zappelli, “Modal analysis of nonlinear propagation in dielectric slab waveguide,” J. Lightwave Technol.14(2), 229–235 (1996). [CrossRef]
  22. J. G. Ma and Z. Chen, “Numerically determining the dispersion relations of nonlinear TE slab-guided waves in non-Kerr-like media,” IEEE Trans. Microw. Theory Tech.45(7), 1113–1117 (1997). [CrossRef]
  23. R. K. Varshney, I. C. Goyal, and A. K. Ghatak, “A simple and efficient numerical method to study propagation characteristics of nonlinear optical waveguides,” J. Lightwave Technol.16(4), 697–702 (1998). [CrossRef]
  24. S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikati, “Full vectorial finite–element solution of nonlinear bistable optical waveguides,’,” IEEE J. Quantum Electron.38(8), 1120–1125 (2002). [CrossRef]
  25. C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, “Analyzing multilayer optical waveguide with all nonlinear layers,” Opt. Express15(5), 2499–2516 (2007). [CrossRef] [PubMed]
  26. S. Roy and P. Roy Chaudhuri, “Analysis of nonlinear multilayered waveguides and MQW structures: a field evolution approach using finite–difference formulation,” IEEE J. Quantum Electron.45(4), 345–350 (2009). [CrossRef]
  27. T. H. Wood, “Multiple quantum well (MQW) waveguide modulators,” J. Lightwave Technol.6(6), 743–757 (1988). [CrossRef]
  28. S. Radic, N. George, and G. P. Agrawal, “Optical switching in λ/4-shifted nonlinear periodic structures,” Opt. Lett.19(21), 1789–1791 (1994). [CrossRef] [PubMed]
  29. Y. D. Wu, “New all-optical wavelength auto-router based on spatial solitons,” Opt. Express12(18), 4172–4177 (2004). [CrossRef] [PubMed]
  30. T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B23(4), 684–691 (2006). [CrossRef]
  31. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear plasmonic slot waveguides,” Opt. Express16(26), 21209–21214 (2008). [CrossRef] [PubMed]
  32. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express17(22), 20063–20068 (2009). [CrossRef] [PubMed]
  33. I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett.36(17), 3374–3376 (2011). [CrossRef] [PubMed]
  34. I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B84(11), 113409 (2011). [CrossRef]
  35. J. R. Salgueiro and Y. S. Kivshar, “Nonlinear plasmonic directional couplers,” Appl. Phys. Lett.97(8), 081106 (2010). [CrossRef]
  36. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett.105(11), 116804 (2010). [CrossRef] [PubMed]
  37. A. Degiron and D. R. Smith, “Nonlinear long-range plasmonic waveguides,” Phys. Rev. A82(3), 033812 (2010). [CrossRef]
  38. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Springer–Verlag, 2001).
  39. C.-C. Huang, C.-C. Huang, and J.-Y. Yang, “A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles,” IEEE J. Sel. Top. Quantum Electron.11(2), 457–465 (2005). [CrossRef]
  40. P.-J. Chiang, C.-L. Wu, C.-H. Teng, C.-S. Yang, and H.- Chang, “Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations,” IEEE J. Quantum Electron.44(1), 56–66 (2008). [CrossRef]
  41. C. C. Huang, “Simulation of optical waveguides by novel full-vectorial pseudospectral-based imaginary-distance beam propagation method,” Opt. Express16(22), 17915–17934 (2008). [CrossRef] [PubMed]
  42. J. B. Xiao and X. H. Sun, “Full-vectorial mode solver for anisotropic optical waveguides using multidomain spectral collocation method,” Opt. Commun.283(14), 2835–2840 (2010). [CrossRef]
  43. C. C. Huang, “Numerical investigation of mode characteristics of nanoscale surface plasmon-polaritons using a pseudospectral scheme,” Opt. Express18(23), 23711–23726 (2010). [CrossRef] [PubMed]
  44. C. C. Huang, “Solving the full anisotropic liquid crystal waveguides by using an iterative pseudospectral-based eigenvalue method,” Opt. Express19(4), 3363–3378 (2011). [CrossRef] [PubMed]
  45. G. I. Stegeman and C. T. Seaton, “Nonlinear surface plasmons guided by thin metal films,” Opt. Lett.9(6), 235–237 (1984). [CrossRef] [PubMed]
  46. J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by meal films,” J. Appl. Phys.58(7), 2460–2466 (1985). [CrossRef]
  47. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,” Phys. Rev. B63(12), 125417 (2001). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited