Continuous control of the nonlinearity phase for harmonic generations

Nature Materials volume 14, pages607–612(2015)Cite this article

Subjects

Abstract

The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

Rent or Buy

All prices are NET prices.

Figure 1: Illustration of geometric-phase-controlled nonlinear metamaterials.
Figure 2: Experimental verification of the nonlinear phase with nonlinear phase gratings.
Figure 3: Diffraction of the fundamental wave on metasurfaces with linear phase gradients.
Figure 4: THG signals from metasurfaces with a phase gradient of the nonlinearity.

References

  1. 1

    Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962).

    CAS  Article  Google Scholar 

  2. 2

    Fejer, M. M., Magel, G. A., Jundt, D. H. & Byer, R. L. Quasi-phase-matched second harmonic generation: Tuning and tolerances. IEEE J. Quantum Electron. 28, 2631–2654 (1992).

    Article  Google Scholar 

  3. 3

    Zhang, X. et al. Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light. Nature Phys. 3, 270–275 (2007).

    CAS  Article  Google Scholar 

  4. 4

    Ellenbogen, T., Voloch-Bloch, N., Ganany-Padowicz, A. & Arie, A. Nonlinear generation and manipulation of Airy beams. Nature Photon. 3, 395–398 (2009).

    CAS  Article  Google Scholar 

  5. 5

    Xu, P. & Zhu, S. N. Quasi-phase-matching engineering of entangled photons. AIP Adv. 2, 041401 (2012).

    Article  Google Scholar 

  6. 6

    Zhu, S. N. et al. Harmonic generation in a Fibonacci optical superlattice of LiTaO3 . Phys. Rev. Lett. 78, 2752–2755 (1997).

    CAS  Article  Google Scholar 

  7. 7

    Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. 392, 45–57 (1984).

    Article  Google Scholar 

  8. 8

    Bhandari, R. Phase jumps in a QHQ phase shifter—some consequences. Phys. Lett. A 204, 188–192 (1995).

    CAS  Article  Google Scholar 

  9. 9

    Gori, F. Measuring Stokes parameters by means of a polarization grating. Opt. Lett. 24, 584–586 (1999).

    CAS  Article  Google Scholar 

  10. 10

    Bomzon, Z., Kleiner, V. & Hasman, E. Pancharatnam-Berry phase in space-variant polarization state manipulations with subwavelength gratings. Opt. Lett. 26, 1424–1426 (2001).

    CAS  Article  Google Scholar 

  11. 11

    Gorodetski, Y., Niv, A., Kleiner, V. & Hasman, E. Observation of the spin-based plasmonic effect in nanoscale structures. Phys. Rev. Lett. 101, 043903 (2008).

    CAS  Article  Google Scholar 

  12. 12

    Yu, N. et al. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science 334, 333–337 (2011).

    CAS  Article  Google Scholar 

  13. 13

    Ni, X., Emani, N. K., Kildishev, A., Boltasseva, V. A. & Shalaev, V. M. Broadband light bending with plasmonic nanoantennas. Science 335, 427 (2012).

    CAS  Article  Google Scholar 

  14. 14

    Chen, X. et al. Dual-polarity plasmonic metalens for visible light. Nature Commun. 3, 1198 (2012).

    Article  Google Scholar 

  15. 15

    Huang, L. L. et al. Three-dimensional optical holography using a plasmonic metasurface. Nature Commun. 4, 2808 (2013).

    Article  Google Scholar 

  16. 16

    Li, G. X. et al. Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light. Nano Lett. 13, 4148–4151 (2013).

    CAS  Article  Google Scholar 

  17. 17

    Yin, X. B., Ye, Z. L., Rho, J., Wang, Y. & Zhang, X. Photonic spin Hall effect at metasurfaces. Science 339, 1405–1407 (2013).

    CAS  Article  Google Scholar 

  18. 18

    Burns, W. K. & Bloembergen, N. Third-harmonic generation in absorbing media of cubic or isotropic symmetry. Phys. Rev. B 4, 3437–3450 (1971).

    Article  Google Scholar 

  19. 19

    Bhagavantam, S. & Chandrasekhar, P. Harmonic generation and selection rules in nonlinear optics. Proc. Indian Acad. Sci. A 76, 13–20 (1972).

    CAS  Article  Google Scholar 

  20. 20

    Konishi, K. et al. Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry. Phys. Rev. Lett. 112, 135502 (2014).

    Article  Google Scholar 

  21. 21

    Chen, S. M. et al. Symmetry selective third harmonic generation from plasmonic metacrystals. Phys. Rev. Lett. 113, 033901 (2014).

    Article  Google Scholar 

  22. 22

    Kauranen, M. & Zayats, A. V. Nonlinear plasmonics. Nature Photon. 6, 737–748 (2012).

    CAS  Article  Google Scholar 

  23. 23

    Kujala, S., Canfield, B. K., Kauranen, M., Svirko, Y. & Turunen, J. Multipole interference in the second-harmonic optical radiation from gold nanoparticles. Phys. Rev. Lett. 98, 167403 (2007).

    Article  Google Scholar 

  24. 24

    Zhang, Y., Grady, N. K., Ayala-Orozco, C. & Halas, N. J. Three-dimensional nanostructures as highly efficient generators of second harmonic light. Nano Lett. 11, 5519–5523 (2011).

    CAS  Article  Google Scholar 

  25. 25

    Cai, W., Vasudev, A. P. & Brongersma, M. L. Electrically controlled nonlinear generation of light with plasmonics. Science 333, 1720–1723 (2011).

    CAS  Article  Google Scholar 

  26. 26

    Aouani, H. et al. Multiresonant broadband optical antennas as efficient tunable nanosources of second harmonic light. Nano Lett. 12, 4997–5002 (2012).

    CAS  Article  Google Scholar 

  27. 27

    Utikal, T. et al. Towards the origin of the nonlinear response in hybrid plasmonic systems. Phys. Rev. Lett. 106, 133901 (2011).

    Article  Google Scholar 

  28. 28

    Renger, J., Quidant, R., Van Hulst, N. & Novotny, L. Surface-enhanced nonlinear four-wave mixing. Phys. Rev. Lett. 104, 046803 (2010).

    Article  Google Scholar 

  29. 29

    Rose, A., Powell, D. A., Shadrivov, I. V., Smith, D. R. & Kivshar, Y. S. Circular dichroism of four-wave mixing in nonlinear metamaterials. Phys. Rev. B 88, 195148 (2013).

    Article  Google Scholar 

  30. 30

    Suchowski, H. et al. Phase mismatch-free nonlinear propagation in optical zero-index materials. Science 342, 1223–1226 (2013).

    CAS  Article  Google Scholar 

  31. 31

    Kruk, K. S. et al. Spin-polarized photon emission by resonant multipolar nanoantennas. ACS Photon. 1, 1218–1223 (2014).

    CAS  Article  Google Scholar 

  32. 32

    Berger, V. Nonlinear photonic crystals. Phys. Rev. Lett. 81, 4136–4139 (1998).

    CAS  Article  Google Scholar 

  33. 33

    Broderick, N. G. R., Ross, G. W., Offerhaus, H. L., Richardson, D. J. & Hanna, D. C. Hexagonally poled lithium niobate: A two-dimensional nonlinear photonic crystal. Phys. Rev. Lett. 84, 4345–4348 (2000).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

This work was partly supported by EPSRC (EP/J018473/1). T.Z. and S.Z. acknowledge financial support by the European Commission under the Marie Curie Career Integration Program. N.P., B.R. and T.Z. acknowledge the financial support by the DFG Research Center TRR142 ‘Tailored nonlinear photonics’. K.W.C. and E.Y.B.P. acknowledge the support by the Research Grant Council of Hong Kong under Projects HKUST2/CRF/11G and AoE/P-02/12. G.L. acknowledges support from the High Performance Cluster Computing Centre, Hong Kong Baptist University. S.Z. acknowledges financial support from the National Science Foundation of China (grant no. 61328503) and Leverhulme Trust (grant no. RPG-2012-674).

Author information

Author notes

  1. Guixin Li and Shumei Chen: These authors contributed equally to this work.

Affiliations

  1. School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK

    Guixin Li, Shumei Chen & Shuang Zhang

  2. Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Guixin Li, Shumei Chen & Kok Wai Cheah

  3. Department of Physics, University of Paderborn, Warburger Straße 100 D-33098 Paderborn, Germany

    Nitipat Pholchai, Bernhard Reineke & Thomas Zentgraf

  4. Department of Industrial Physics and Medical Instrumentation, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road, Bangkok 10800, Thailand

    Nitipat Pholchai

  5. Lasers and Optics Research Group, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road Bangkok 10800, Thailand

    Nitipat Pholchai

  6. Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong

    Polis Wing Han Wong & Edwin Yue Bun Pun

  7. State Key Laboratory of Millimeter Waves, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong

    Edwin Yue Bun Pun

Authors
  1. Guixin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shumei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nitipat Pholchai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bernhard Reineke
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Polis Wing Han Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Edwin Yue Bun Pun
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Kok Wai Cheah
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Thomas Zentgraf
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Shuang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.Z. and T.Z. conceived the idea and experiment. B.R., P.W.H.W. and E.Y.B.P. fabricated the samples. G.L., S.C., N.P., K.W.C. and T.Z. performed the measurements. S.C. performed the simulation. G.L., S.Z. and T.Z. wrote the paper. All authors participated in discussions.

Corresponding authors

Correspondence to Kok Wai Cheah or Thomas Zentgraf or Shuang Zhang.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 804 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, G., Chen, S., Pholchai, N. et al. Continuous control of the nonlinearity phase for harmonic generations. Nature Mater 14, 607–612 (2015). https://doi.org/10.1038/nmat4267

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing