Advertisement

An Extensive Finite-Difference Time-Domain Formalism for Second-Order Nonlinearities Based on the Faust-Henry Dispersion Model: Application to Terahertz Generation

  • B. N. CarnioEmail author
  • A. Y. Elezzabi
Article

Abstract

A nonlinear finite-difference time-domain (FDTD) formalism is developed to model dispersive second-order nonlinear effects in photonic arrangements and optical devices. The dispersion of the second-order nonlinear susceptibility, χ(2), is based on the Faust-Henry model, which makes no implicit assumption on the relationship between the linear and nonlinear dispersion. Unlike other models for χ(2) dispersion, the Faust-Henry model accurately describes a broad range of crystal classes, including the \( \overline{4}3m \) crystal class, which is essential to generating radiation in the terahertz frequency regime. As such, the developed formalism based on the Faust-Henry dispersion model overcomes limitations imposed by previous FDTD methods for modelling second-order nonlinear effects.

Keywords

Finite-difference time-domain Nonlinear optics Numerical models Optical sources 

Notes

Acknowledgements

The authors are grateful for the support provided by Optiwave Systems Inc., especially Scott Newman, Ahmad Atieh, and Kevin Chu, and for the access to Optiwave’s OptiFDTD simulation software platform.

Funding Information

This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC). This work was performed under NSERC’s Engage grant program in collaboration with Optiwave Systems Inc.

References

  1. 1.
    D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron.24, 184–197 (1988).CrossRefGoogle Scholar
  2. 2.
    R. L. Aggarwal and B. Lax, “Optical mixing of CO2 lasers in the far-infrared” in Nonlinear Infrared Generation, edited by Y.-R. Shen, Topics in Applied Physics16 (Springer, 1977), pp. 19–80.Google Scholar
  3. 3.
    A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. I. χ (2) near ionic resonance,” Phys. Rev. B33, 6954–6961 (1986).CrossRefGoogle Scholar
  4. 4.
    W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, "Generalized miller formulæ," Opt. Express18, 6613–6620 (2010).CrossRefGoogle Scholar
  5. 5.
    M. Bell, “Frequency dependence of Miller's Rule for nonlinear susceptibilities,” Phys. Rev. B6, 516–521 (1972).CrossRefGoogle Scholar
  6. 6.
    C. Garrett and F. Robinson, “Miller's phenomenological rule for computing nonlinear susceptibilities,” IEEE J. Quantum Electron.2, 328–329 (1966).CrossRefGoogle Scholar
  7. 7.
    R. C. Miller, “Optical second harmonic generation in piezoelectric crystals," Appl. Phys. Lett.5, 17–19 (1964).CrossRefGoogle Scholar
  8. 8.
    W. L. Faust and Charles H. Henry, “Mixing of visible and near-resonance infrared light in GaP,” Phys. Rev. Lett.17, 1265–1268 (1966).CrossRefGoogle Scholar
  9. 9.
    S. Casalbuoni, H. Schlarb, B. Schmidt, P. Schmüser, B. Steffen, and A. Winter, “Numerical studies on the electro-optic detection of femtosecond electron bunches,” Phys. Rev. Accel. Beams11, 072802 (2008).CrossRefGoogle Scholar
  10. 10.
    Y. J. Ding, "Efficient generation of high-frequency terahertz waves from highly lossy second-order nonlinear medium at polariton resonance under transverse-pumping geometry," Opt. Lett.35, 262–264 (2010).CrossRefGoogle Scholar
  11. 11.
    M. Cherchi, A. Taormina, A. C. Busacca, R. L. Oliveri, S. Bivona, A. C. Cino, S. Stivala, S. R. Sanseverino, and C. Leone, “Exploiting the optical quadratic nonlinearity of zinc-blende semiconductors for guided-wave terahertz generation: a material comparison,” IEEE J. Quantum Electron. 46, 368–376 (2010).CrossRefGoogle Scholar
  12. 12.
    D.E. Thompson and P.D. Coleman, “Step-tunable far infrared radiation by phase matched mixing in planar-dielectric waveguides,” IEEE Trans. Microw. Theory Tech.22, 995–1000 (1974).CrossRefGoogle Scholar
  13. 13.
    C. M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, and R. K. Lee, "Nonlinear finite-difference time-domain method for the simulation of anisotropic, χ (2), and χ (3) optical effects," J. Lightwave Technol.24, 624–634 (2006)CrossRefGoogle Scholar
  14. 14.
    B. N. Carnio and A. Y. Elezzabi, "Second harmonic generation in metal-LiNbO3-metal and LiNbO3 hybrid-plasmonic waveguides," Opt. Express26, 26283–26291 (2018).CrossRefGoogle Scholar
  15. 15.
    B. N. Carnio and A. Y. Elezzabi, "A modeling of dispersive tensorial second-order nonlinear effects for the finite-difference time-domain method," Opt. Express27, 23432–23445 (2019).CrossRefGoogle Scholar
  16. 16.
    B. E. Schmidt, P. Lassonde, G. Ernotte, M. Clerici, R. Morandotti, H. Ibrahim, and F. Légaré, “Decoupling frequencies, amplitudes and phases in nonlinear optics,” Sci. Rep. 7, 7861 (2017).CrossRefGoogle Scholar
  17. 17.
    I. Wilke and S. Sengupta, “Nonlinear optical techniques for terahertz pulse generation and detection-optical rectification and electrooptic sampling” in Terahertz Spectroscopy: Principles and Applications, edited by S. L. Dexheimer, 1st edn. (CRC Press, 2007), pp. 41–72.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of AlbertaEdmontonCanada

Personalised recommendations