Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions

Abstract

Intersubband transitions in n-doped multi-quantum-well semiconductor heterostructures make it possible to engineer one of the largest known nonlinear optical responses in condensed matter systems—but this nonlinear response is limited to light with electric field polarized normal to the semiconductor layers1,2,3,4,5,6,7. In a different context, plasmonic metasurfaces (thin conductor–dielectric composite materials) have been proposed as a way of strongly enhancing light–matter interaction and realizing ultrathin planarized devices with exotic wave properties8,9,10,11. Here we propose and experimentally realize metasurfaces with a record-high nonlinear response based on the coupling of electromagnetic modes in plasmonic metasurfaces with quantum-engineered electronic intersubband transitions in semiconductor heterostructures. We show that it is possible to engineer almost any element of the nonlinear susceptibility tensor of these structures, and we experimentally verify this concept by realizing a 400-nm-thick metasurface with nonlinear susceptibility of greater than 5 × 104 picometres per volt for second harmonic generation at a wavelength of about 8 micrometres under normal incidence. This susceptibility is many orders of magnitude larger than any second-order nonlinear response in optical metasurfaces measured so far12,13,14,15. The proposed structures can act as ultrathin highly nonlinear optical elements that enable efficient frequency mixing with relaxed phase-matching conditions, ideal for realizing broadband frequency up- and down-conversions, phase conjugation and all-optical control and tunability over a surface.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Nonlinear metasurface structure.
Figure 2: Simulations and predicted performance of the metasurface geometry.
Figure 3: Characterization of processed metasurface.
Figure 4: Nonlinear response from the metasurface.

References

  1. 1

    Fejer, M. M. et al. Observation of extremely large quadratic susceptibility at 9.6–10.8 μm in electric-field-biased AlGaAs quantum wells. Phys. Rev. Lett. 62, 1041–1044 (1989)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Rosencher, E., Bois, P., Nagle, J. & Delaitre, S. Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs. Electron. Lett. 25, 1063–1065 (1989)

    Article  Google Scholar 

  3. 3

    Capasso, F., Sirtori, C. & Cho, A. Y. Coupled-quantum-well semiconductors with giant electric-field tunable nonlinear-optical properties in the infrared. IEEE J. Quantum Electron. 30, 1313–1326 (1994)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Rosencher, E. et al. Quantum engineering of optical nonlinearities. Science 271, 168–173 (1996)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Gmachl, C. et al. Optimized second-harmonic generation in quantum cascade lasers. IEEE J. Quantum Electron. 39, 1345–1355 (2003)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Belkin, M. A. et al. Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation. Nature Photon. 1, 288–292 (2007)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Vijayraghavan, K. et al. Broadly tunable terahertz generation in mid-infrared quantum cascade lasers. Nature Commun. 4, 2021 (2013)

    ADS  Article  Google Scholar 

  8. 8

    Liu, X. L. et al. Taming the blackbody with infrared metamaterials as selective thermal emitters. Phys. Rev. Lett. 107, 045901 (2011)

    ADS  Article  Google Scholar 

  9. 9

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

    ADS  CAS  Article  Google Scholar 

  10. 10

    Ni, X. J. et al. Broadband light bending with plasmonic nanoantennas. Science 335, 427 (2012)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Monticone, F., Estakhri, N. M. & Alu, A. Full control of nanoscale optical transmission with a composite metascreen. Phys. Rev. Lett. 110, 203903 (2013)

    ADS  Article  Google Scholar 

  12. 12

    Klein, M. W., Enkrich, C., Wegener, M. & Linden, S. Second-harmonic generation from magnetic metamaterials. Science 313, 502–504 (2006)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Feth, N. et al. Second-harmonic generation from complementary split-ring resonators. Opt. Lett. 33, 1975–1977 (2008)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Fan, W. J. et al. Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array. Opt. Express 14, 9570–9575 (2006)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Niesler, F. B. P. et al. Second-harmonic generation from split-ring resonators on a GaAs substrate. Opt. Lett. 34, 1997–1999 (2009)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Fang, N., Lee, H., Sun, C. & Zhang, X. Sub-diffraction-limited optical imaging with a silver superlens. Science 308, 534–537 (2005)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  19. 19

    Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  20. 20

    Chen, P. Y., Soric, J. & Alu, A. Invisibility and cloaking based on scattering cancellation. Adv. Mater. 24, Op281–Op304 (2012)

    CAS  PubMed  Google Scholar 

  21. 21

    Pendry, J. B. Time reversal and negative refraction. Science 322, 71–73 (2008)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  22. 22

    Rose, A. & Smith, D. R. Overcoming phase mismatch in nonlinear metamaterials. Opt. Mater. Express 1, 1232–1243 (2011)

    ADS  Article  Google Scholar 

  23. 23

    Argyropoulos, C. et al. Nonlinear plasmonic cloaks to realize giant all-optical scattering switching. Phys. Rev. Lett. 108, 263905 (2012)

    ADS  Article  Google Scholar 

  24. 24

    Hugi, A. et al. Mid-infrared frequency comb based on a quantum cascade laser. Nature 492, 229–233 (2012)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Vodopyanov, K. L. et al. Phase-matched second harmonic generation in asymmetric double quantum wells. Appl. Phys. Lett. 72, 2654–2656 (1998)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Vurgaftman, I., Meyer, J. R. & RamMohan, L. R. Optimized second-harmonic generation in asymmetric double quantum wells. IEEE J. Quantum Electron. 32, 1334–1346 (1996)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Boyd, R. W. Nonlinear Optics (Academic, 2008)

    Google Scholar 

  28. 28

    Todorov, Y. et al. Ultrastrong light-matter coupling regime with polariton dots. Phys. Rev. Lett. 105, 196402 (2010)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Benz, A. et al. Strong coupling in the sub-wavelength limit using metamaterial nanocavities. Nature Commun. 4, 2882 (2013)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Ellenbogen, T., Seo, K. & Crozier, K. B. Chromatic plasmonic polarizers for active visible color filtering and polarimetry. Nano Lett. 12, 1026–1031 (2012)

    ADS  CAS  Article  Google Scholar 

  31. 31

    Zhao, Y. & Alu, A. Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates. Nano Lett. 13, 1086–1091 (2013)

    ADS  CAS  Article  Google Scholar 

  32. 32

    Balanis, C. A. Advanced Engineering Electromagnetics (Wiley, 1989)

    Google Scholar 

  33. 33

    Vodopyanov, K. L. et al. Intersubband absorption saturation study of narrow III–V multiple quantum wells in the λ = 2.8–9 μm spectral range. Semicond. Sci. Technol. 12, 708–714 (1997)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by NSF EAGER grant no. 1348049 (to M.A.B. and A.A.), AFOSR YIP award no. FA9550-10-1-0076 (M.A.B.), AFOSR YIP award no. FA9550-11-1-0009 (A.A.), and ONR MURI grant no. N00014-10-1-0942 (A.A.). The Walter Schottky Institute group acknowledges support from the Excellence Cluster ‘Nano Initiative Munich (NIM)’. Sample fabrication was carried out in the Microelectronics Research Center at the University of Texas at Austin, which is a member of the National Nanotechnology Infrastructure Network.

Author information

Affiliations

Authors

Contributions

J.L. designed the semiconductor heterostructure, calculated physical parameters and performed all fabrication and experimental measurements; M.T., C.A. and P.-Y.C. performed theoretical computations and structure optimization; F.L. assisted in experimental measurements; F.D., G.B. and M.-C.A. performed the semiconductor heterostructure growth; M.A.B. conceived the concept and the experiment; M.A.B. and A.A. developed the concept and planned and directed the research; and J.L., M.T., C.A., A.A. and M.A.B. wrote the manuscript.

Corresponding author

Correspondence to Mikhail A. Belkin.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Intersubband absorption measurement.

Intersubband absorption spectrum of the wafer used in our experiments after background correction. Bottom y axis, wavenumber ( = 1/λ); top y axis, energy ( = ). Inset, measurement geometry.

Extended Data Figure 2 Structures with plasmonic resonances detuned from intersubband transition frequencies.

a, Linear absorption spectrum of a metasurface in which plasmonic resonances were not well-overlapped spectrally with intersubband transitions of the MQW structure for fundamental and SH frequencies. b, SH peak power (left axis) or intensity (right axis) as a function of FF peak power squared (bottom axis) or peak intensity squared (top axis) for different input/output polarization combinations (yyy and so on, see key) at FF pump wavenumber 1/λpump = 1,310 cm−1 and SH wavenumber 2,620 cm−1 both in resonance with the plasmonic absorption peaks. SH response was close to the noise limit of our setup. Inset, SEM image of the metasurface. c, SH peak power output as a function of FF peak power squared (bottom axis) or peak intensity squared (top axis) for different input/output polarization combinations at FF wavenumber 1,240 cm−1 and SHG wavenumber of 2,480 cm−1, both away from plasmonic resonances of the metasurface but in resonance with intersubband transitions in the MQW structure.

Extended Data Figure 3 Nonlinear response saturation mechanism.

a, SH peak power output as a function of FF peak power squared (bottom axis) or peak intensity squared (top axis) at FF wavenumber 1,240 cm−1. Black curve, data for the pump laser operating with 400 ns pulses (same as used in the main text); red curve, data for the pump laser operating with 60 ns pulses. A slight difference in the SHG power for 60 ns and 400 ns FF input is attributed to slight changes in the pulse shape and detector response for 400 ns and 60 ns pulses. b, SH conversion efficiency versus FF peak power (bottom axis) or peak intensity (top axis) for FF wavenumber 1,240 cm−1 (red) and 1,280 cm−1 (blue). Straight lines show expected linear dependence of SH conversion efficiency on FF power for the cases in the absence of intensity saturation.

Extended Data Figure 4 SHG at oblique incidence.

a, Optical set-up for metasurface characterization at 45° incidence angle. LP and SP are long- and short-pulse filters, respectively. HWP is a half-wave plate for FF polarization control. Directions of S- and P-polarizations and orientation of the metasurface are indicated. Inset, SEM image of the metasurface with x and y axes shown. b, Measured SH peak power output as a function of FF peak power squared (bottom axis) or peak intensity squared (top axis) at FF wavenumber 1,240 cm−1 for different input/output polarization combinations (SSS and so on, see key). c, Simulated absorption spectrum of the metasurface at 45° incidence for different input light polarizations.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lee, J., Tymchenko, M., Argyropoulos, C. et al. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature 511, 65–69 (2014). https://doi.org/10.1038/nature13455

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.