Abstract
Analytical expressions derived for dispersion relations and fields are used to obtain analytical predictions for the performance of modulators fabricated in second-order \((\upchi ^{2})\) and third-order \((\upchi ^{3})\) nonlinear materials filled into waveguide slot of silicon-on-insulator waveguides. Analytical expressions are used to model the electron-optical modulation and Kerr effect on slot waveguides for the theoretical modeling. The results obtained for slot waveguides with second-order nonlinearities are compared with those obtained under the planar-waveguide approximations reported as in earlier work. Also, exhaustive solutions are obtained for third-order nonlinear slot waveguides. This work employs long standing and reliable mathematical methods to develop the computational modal of photonics integrated devices. Moreover, the present work allows one a new perspective on design of various optical devices based on low-index sub-wavelength nonlinear slot waveguides.
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Acknowledgements
Prof. Vishnu Priye, who was exchange scholar at University of Colorado, Boulder, USA (June 1, 2013, to August 31, 2013) acknowledges financial support from Indian Institute of Technology (Indian School Of Mines), Dhanbad, University of Colorado, Boulder, and Lightwave Logic, USA.
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Appendices
Appendix I
1.1 Terms of second-order nonlinear propagation constant
We provide here the expressions for the constants that appear in Eq. (16):
Appendix II
1.1 Third-order nonlinear propagation constant terms
We provide here the expressions for the constants that appear in Eq. (23):
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Priye, V., Malviya, N. & Mickelson, A. Analytical predictions for nonlinear optical processes in silicon slot waveguides. J Comput Electron 17, 857–865 (2018). https://doi.org/10.1007/s10825-018-1150-8
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DOI: https://doi.org/10.1007/s10825-018-1150-8