Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions


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.

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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.


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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




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.

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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.

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

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