Skip to main content
Log in

Quasi-Phase-Matching Generation of the Second Optical Harmonic under the Pendulum Effect Conditions in Photonic Crystals

  • NONLINEAR OPTICAL PHENOMENA
  • Published:
Bulletin of the Lebedev Physics Institute Aims and scope Submit manuscript

Abstract

The generation of the second optical harmonic in one-dimensional photonic crystals under the pendulum effect conditions is considered for the dynamic Bragg diffraction in the Laue geometry. It is shown that in photorefractive photonic crystals as well as in photonic crystals with photoinduced quadratic nonlinearity, a new direction of quasi-phase-matching generation of the second harmonic appears due to the inclusion of the additional reciprocal lattice vector into the quasi-phase-matching condition. This vector appears due to the formation of a 2D spatial intensity lattice at the pumping field frequency under the pendulum effect. In such structures, effective quasi-phase-matchings generation of the second-harmonic waves, which are not collinear to the Bormann or anti-Bormann pumping modes, is observed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. Joannopoulos, J.D., Johnson, S.G., Winn, J.N., and Meade, R.D., Photonic Crystals: Molding the Flow of Light, Princeton: Univ. Press, 2008.

    MATH  Google Scholar 

  2. Mantsyzov, B.I., Kogerentnaya i nelineinaya optika fotonnykh kristallov (Coherent and Nonlinear Optics of Photonic Crystals), Moscow: Fizmatlit, 2009.

  3. Kartashov, Y.V., Malomed, B.A., and Torner, L., Solitons in nonlinear lattices, Rev. Mod. Phys., 2011, vol. 83, p. 247. https://doi.org/10.1103/RevModPhys.83.247

    Article  ADS  Google Scholar 

  4. Busch, K., Von Freymann, G., Linder, S., Mingaleev, S., Tkeshelashvili, L., and Wegener, M., Periodic nanostructures for photonics, Phys. Rep., 2007, vol. 444, no. 3–6, p. 101–202. https://doi.org/10.1016/j.physrep.2007.02.011

    Article  ADS  Google Scholar 

  5. Bykov, V.P., Spontaneous emission in a periodic structure, Sov. Phys. JETP, 1972, vol. 35, p. 369.

    Google Scholar 

  6. David, A., Benisty, H., and Weisbuch, C., Photonic crystal light-emitting sources, Rep. Prog. Phys., 2012, vol. 75, p. 126501. https://doi.org/10.1088/0034-4885/75/12/126501

  7. Ghebrebrhan, M., Ibanescu, M., Johnson, S., Soljacic, M., and Joannopoulos, J., Distinguishing zero-group-velocity modes in photonic crystals, Phys. Rev. A, 2007, vol. 76, no. 6, p. 063810. https://doi.org/10.1103/PhysRevA.76.063810

  8. Skorynin, A.A., Bushuev, V.A., and Mantsyzov, B.I., Dynamical Bragg diffraction of optical pulses in photonic crystals in the Laue geometry: Diffraction-induced splitting, selective compression, and focusing of pulses, J. Exp. Theor. Phys., 2012, vol. 115, pp. 56–67. https://doi.org/10.1134/S1063776112060167

    Article  ADS  Google Scholar 

  9. Svyakhovskiy, S.E., Skorynin, A.A., Bushuev, V.A., Chekalin, S.V., Kompanets, V.O., Maydykovskiy, A.I., Murzina, T.V., and Mantsyzov, B.I., Experimental demonstration of selective compression of femtosecond pulses in the Laue scheme of the dynamical Bragg diffraction in 1D photonic crystals, Opt. Express, 2014, vol. 22, pp. 31002–31007. https://doi.org/10.1364/OE.22.031002

    Article  ADS  Google Scholar 

  10. Novikov, V.B. and Murzina, T.V., Borrmann effect in photonic crystals, Opt. Lett., 2017, vol. 42, pp. 1389–1392. https://doi.org/10.1364/OL.42.001389

    Article  ADS  Google Scholar 

  11. Feng, L., Xu, Y., Fegadolli, W.S., Lu, M., Oliveira, J.E., Almaida, V.R., Chen, Y., and Scherer, A., Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies, Nat. Mater, 2012, vol. 12, pp. 108–113. https://doi.org/10.1038/nmat3495

    Article  ADS  Google Scholar 

  12. Bushuev, V.A., Dergacheva, L.V., and Mantsyzov, B.I., Asymmetric pendulum effect and transparency change of PT-symmetric photonic crystals under dynamical Bragg diffraction beyond the paraxial approximation, Phys. Rev. A, 2017, vol. 95, p. 033843. https://doi.org/10.1103/PhysRevA.95.033843

  13. Tsvetkov, D.M., Bushuev, V.A., Konotop, V.V., and Mantsyzov, B.I., Broadband quasi-PT-symmetry sustained by inhomogeneous broadening of the spectral line, Phys. Rev. A, 2018, vol. 98, p. 053844. https://doi.org/10.1103/PhysRevA.98.053844

  14. Fejer, M.M., Magel, G.A., Jundt, D.H., and Byer, R.L., Quasi-phase-matched second harmonic generation: tuning and tolerances, IEEE J. Quantum Electron., 1992, vol. 28, no. 11, p. 2653. https://doi.org/10.1109/3.161322

    Article  Google Scholar 

  15. Russell, P.St.J., Bragg resonance of light in optical superlattices, Phys. Rev. Lett., 1986, vol. 56, p. 596. https://doi.org/10.1103/PhysRevLett.56.596

    Article  ADS  Google Scholar 

  16. Calvo, M., Cheben, P., Martinez-Matos, O., del Monte, F., and Rodrigo, J.A., Experimental detection of the optical pendellösung effect, Phys. Rev. Lett., 2006, vol. 97, p. 084801. https://doi.org/10.1103/PhysRevLett.97.084801

  17. Novikov, V.B., Svyakhovskiy, S.E., Maydykovskiy, A.I., Murzina, T.V., and Mantsyzov, B.I., Optical pendulum effect in one-dimensional diffraction-thick porous silicon based photonic crystals, J. Appl. Phys., 2015, vol. 118, p. 193101. https://doi.org/10.1063/1.4935635

  18. Mayer, A.A. and Sukhorukov, A.P., Synchronous nonlinear interaction of waves during Bragg diffraction in media with periodic structures, Sov. Phys. JETP, 1979, vol. 50, p. 4.

    Google Scholar 

  19. Shwartz, S., Fuchs, M., Hastings, J.B., Inubushi, Y., Ishikawa, T., Katayama, T., Reis, D.A., Sato, T., Tono, K., Yabashi, M., Yudovich, S., and Harris, S.E., X-ray second harmonic generation, Phys. Rev. Lett., 2014, vol. 112, p. 163901. https://doi.org/10.1103/PhysRevLett.112.163901

  20. Kopylov, D.A., Svyakhovskiy, S.E., Dergacheva, L.V., Bushuev, V.A., Mantsyzov, B.I., and Murzina, T.V., Observation of optical second-harmonic generation in porous-silicon-based photonic crystals in the Laue diffraction scheme, Phys. Rev. A, 2016, vol. 93, p. 053840. https://doi.org/10.1103/PhysRevA.93.053840

  21. Novikov, V.B., Maydykovskiy, A.I., Mantsyzov, B.I., and Murzina, T.V., Laue diffraction in one-dimensional photonic crystals: The way for phase-matched second-harmonic generation, Phys. Rev. B, 2016, vol. 93, p. 235420. https://doi.org/10.1103/PhysRevB.93.235420

  22. Petrov, M.P., Stepanov, S.I., and Khomenko, A.V., Photorefractive Crystals in Coherent Optical Systems, Berlin: Springer, 2013.

    Google Scholar 

  23. Bloch, J., Mihaychuk, J.G., and van Driel, H.M., Electron photoinjection from silicon to ultrathin SiO2 films via ambient oxygen, Phys. Rev. Lett., 1996, vol. 77, p. 920.

    Article  ADS  Google Scholar 

  24. Marka, Z., Pasternak, R., Rashkeev, S., Jiang, Y., Pantelides, S., Tolk, N., Roy, P., and Kozub, J., Band offsets measured by internal photoemission-induced second-harmonic generation, Phys. Rev. B, 2003, vol. 67, p. 045302. https://doi.org/10.1103/PhysRevB.67.045302

  25. Choi, J., Bellec, M., Royon, A., Bourhis, K., Papon, G., Cardinal, T., Canioni, L., and Richardson, M., Three-dimensional direct femtosecond laser writing of second-order nonlinearities in glass, Opt. Lett., 2012, vol. 37, pp. 1029–1031. https://doi.org/10.1364/OL.37.001029

    Article  ADS  Google Scholar 

  26. Dianov, E.M. and Starodubov, D.S., Photoinduced generation of the second harmonic in centrosymmetric media, Quantum Electron., 1995 vol. 25, p. 395. https://doi.org/10.1070/QE1995v025n05ABEH000371

    Article  ADS  Google Scholar 

  27. Nitiss, E., Hu, J., Stroganov, A., and Bres, C.-S., Optically reconfigurable quasi-phase-matching in silicon nitride microresonators, Nat. Photonics, 2022, vol. 16, pp. 134–141. https://doi.org/10.1038/s41566-021-00925-5

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors are grateful to D.A. Kopylov and T.V. Murzina for fruitful discussions of results.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. I. Mantsyzov.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Translated by N. Wadhwa

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dergacheva, L.V., Mantsyzov, B.I. Quasi-Phase-Matching Generation of the Second Optical Harmonic under the Pendulum Effect Conditions in Photonic Crystals. Bull. Lebedev Phys. Inst. 50 (Suppl 1), S25–S35 (2023). https://doi.org/10.3103/S1068335623130031

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068335623130031

Keywords:

Navigation