Research ArticlePHYSICS

Giant optical nonlinearity interferences in quantum structures

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Science Advances  04 Oct 2019:
Vol. 5, no. 10, eaaw7554
DOI: 10.1126/sciadv.aaw7554
  • Fig. 1 Resonant nonlinear frequency mixing and QCL band structure.

    (A) Schematic diagram showing difference (left) and sum (right) frequency generation in a resonant excitation geometry and the corresponding spectrum. The green, red, and orange arrows represent the THz, NIR, and mixing beams, respectively. Inset: Case used for resonant excitation, with the external NIR polarization in the plane of the semiconductor QW layers. (B) Moduli squared of the relevant wave functions, shown with corresponding energies for electronic levels in the conduction band potential and for light hole (LH) levels (left) and heavy hole (HH) levels (right), respectively, in the valence band potential. The main electron and hole levels contributing to large interband dipoles are plotted in colors. The electric field applied to the structure for these simulations is 10 kV/cm.

  • Fig. 2 Minima in the second-order nonlinear susceptibility.

    (A) Modulus squared of the second-order susceptibility |χ(2)|2 as a function of sum energy calculated taking into account HH-el transitions only (red curve) and LH-el transitions only (blue curve) and calculated for a combination of LH-el and HH-el transitions (orange curve), according to selection rules in reflection geometry. (B) Real part (top) and imaginary part (bottom) of calculated χ(2) for SFG process, considering LH-el only (blue curves), HH-el only (red curves), and combined (orange curves) as a function of energy. The energy minima in the |χ(2)|2 combined spectrum are indicated as green dashed lines and highlight the energies where both real and imaginary total parts (orange) are, or are close to, 0.

  • Fig. 3 Sum frequency generation in reflection geometry.

    (A) Schematic diagram of the experimental geometry implemented to excite the QCL. Two slits were etched into the top gold surface of the QCL to let the NIR pump excite the QW structure. (B) Propagation of the pump and generated sum beams through the layered structure. The SFG could be generated during either forward or backward path of the pump. (C) Example of SFG spectrum around 1.529 eV for a pump excitation near 1.517 eV.

  • Fig. 4 SFG intensity from experimental data and theoretical model.

    SFG intensity (black squares, right axis) measured in the reflection geometry with NIR excitation through the top slits, as a function of sum energy. Modulus squared F.|χ(2)|2 (red line, left axis) calculated for the same geometry, taking into account the appropriate combination of LH-el and HH-el, and the absorption factor. The term without interference of the LH and HH contributions F.|χno int (2)|2 is also plotted (green curve). All plots are presented with the same logarithmic scale increment.

  • Fig. 5 Susceptibility minima origins.

    (A) Interband dipole strength of both HH-el (red) and LH-el (black) transitions [only dipoles with absolute strength >0.01 arbitrary units (a.u.) are shown]. (B) Modulus squared |χ(2)|2 calculated in reflection geometry for both HH-el and LH-el transitions, taking into account all states (orange curve) and only the first-order confined states (purple curve). Minima previously discussed are indicated by green dashed lines.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaaw7554/DC1

    Fig. S1. Simuations of THz mode confinement in a double-metal QCL with one (left) and two (right) apertures in the top metal layer.

    Fig. S2. Photoluminescence (PL) spectrum measured in reflection on a QCL facet when the QCL is biased at the threshold voltage.

    Fig. S3. Modulus squared |χ(2)|2 calculated in reflection geometry for different electric fields applied to the structure, from 7 to 12 kV/cm, as a function of energy.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Simuations of THz mode confinement in a double-metal QCL with one (left) and two (right) apertures in the top metal layer.
    • Fig. S2. Photoluminescence (PL) spectrum measured in reflection on a QCL facet when the QCL is biased at the threshold voltage.
    • Fig. S3. Modulus squared |χ(2)|2 calculated in reflection geometry for different electric fields applied to the structure, from 7 to 12 kV/cm, as a function of energy.

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