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Milti -wave interaction in metamaterials

ω. 2 ω. Milti -wave interaction in metamaterials. Ildar Gabitov , Zhaxylyk Kudyshev, Andrei Maimistov. Broad spectrum. Multi-wave interaction. Nonlinear phenomena in negative index materials. Nonlinearity in negative index materials. What is new?. Two general cases:.

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Milti -wave interaction in metamaterials

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  1. ω 2ω Milti-wave interaction in metamaterials Ildar Gabitov, Zhaxylyk Kudyshev, Andrei Maimistov SCT'12 Novosibirsk, June 4-8, 2012

  2. Broad spectrum Multi-wave interaction Nonlinear phenomena in negative index materials Nonlinearity in negative index materials. What is new? Two general cases: Frequency interface SCT'12 Novosibirsk, June 4-8, 2012

  3. Three wave interaction: slowly varying amplitude approximation SCT'12 Novosibirsk, June 4-8, 2012

  4. Simplest case of three wave interaction: Second harmonic generation A. Zakhidov, Agranovich Yu. Kivshar et. al. Popov, V. Shalaev M. Scalora et. al. Zh. Kudyshev et. al. D. Smith, et. al. SCT'12 Novosibirsk, June 4-8, 2012

  5. Second Harmonics generation: Classical Case N. Blombergen SCT'12 Novosibirsk, June 4-8, 2012

  6. ω 2ω Second harmonic generation -- boundary conditions SCT'12 Novosibirsk, June 4-8, 2012

  7. Classical Case • If fields are periodically oscillating. SCT'12 Novosibirsk, June 4-8, 2012

  8. Here: Maimistov, Kudyshev, I.G. SCT'12 Novosibirsk, June 4-8, 2012

  9. From the first two equations follows the modified M-R relation: • In conventional case we have conservation of energy. • In negative index material - conservation of total flux of the energy. Popov, Shalaev SCT'12 Novosibirsk, June 4-8, 2012

  10. Energy of pump wave decay with z, therefore the phase difference is equal to . • Exact solutions general formulae: Here and Important: m1 is unknown! SCT'12 Novosibirsk, June 4-8, 2012

  11. Boundary conditions together with M-R relation lead to the implicit equation for : Here e10 is an amplitude of the pump wave. This transcendental equation can be solved numerically and it has multiple branches. SCT'12 Novosibirsk, June 4-8, 2012

  12. Solution of transcendental equation Spatial field profiles Physical branch: Irrelevant branches: Field is singular in between of these branches SCT'12 Novosibirsk, June 4-8, 2012

  13. “Physical” branch shows saturation of output power of electric field at fundamental frequency with increase of input power. This indicates that with the increase of input power all excessive energy of pump signal converts to the energy of second harmonic signal. SCT'12 Novosibirsk, June 4-8, 2012

  14. Second harmonic generation in presence of phase mismatch Two integrals: SCT'12 Novosibirsk, June 4-8, 2012

  15. Second harmonic generation in presence of phase mismatch -- critical mismatch SCT'12 Novosibirsk, June 4-8, 2012

  16. “Exact” solutions Equation for the power of second harmonic field: - is the Weierstrass function SCT'12 Novosibirsk, June 4-8, 2012

  17. Numerical solution SCT'12 Novosibirsk, June 4-8, 2012

  18. Second harmonic generation in presence of phase mismatch SCT'12 Novosibirsk, June 4-8, 2012

  19. Second harmonic generation in presence of phase mismatch If then second harmonic does not radiate outside. Therefore, sample becomes transparent for fundamental mode. The conversion efficiency of pump wave to second harmonic is limited by the value: SCT'12 Novosibirsk, June 4-8, 2012

  20. Conversion efficiency Jump SCT'12 Novosibirsk, June 4-8, 2012

  21. Multi-stability SCT'12 Novosibirsk, June 4-8, 2012

  22. Second harmonic generation in presence of losses SCT'12 Novosibirsk, June 4-8, 2012

  23. SCT'12 Novosibirsk, June 4-8, 2012

  24. Parametric amplification: SCT'12 Novosibirsk, June 4-8, 2012

  25. Two additional integrals SCT'12 Novosibirsk, June 4-8, 2012

  26. Full system consideration Numerical solution of transcendental equation SCT'12 Novosibirsk, June 4-8, 2012

  27. If there is non-zero output signal value corresponding to zero input signal then such branch is non physical. Popov, Shalaev regime SCT'12 Novosibirsk, June 4-8, 2012

  28. Spatial distribution of intensities: example SCT'12 Novosibirsk, June 4-8, 2012

  29. Conclusions SCT'12 Novosibirsk, June 4-8, 2012

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