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 layers. 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 properties. 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 × 10(4) 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 far. 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.

Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions

Thanks to the recent progresses in epitaxy techniques, it is now possible to grow alternating layers of semiconductors with different band gap energies with a thickness control down to one atomic layer. It is now well established that these systems behave, as far as the electron motion is concerned, as a succession of potential barriers and wells. If the width of the potential well is less than the deBroglie wavelength of the electrons in the material (e.g. less than ≈15 nm in GaAs), the motion of the electrons may be considered, at sufficiently low temperature, as quantized in the direction normal to the growth axis1. The electrons are quantized into subbands where their wavefunctions in the growth direction have the form of envelope functions with an extension equal to the well width, i.e. in the few nanometer range. Electromagnetic waves may induce electronic transitions between these subbands. The dipole matrix elements associated to these intersubband transitions (ISBT) have the same order of magnitude as the quantum well width leading to extremely large absorption. These large absorptions have been observed for the first time in GaAs/AlGaAs multiquantum wells (MQW) by West and Eglash2.

Model system for optical nonlinearities: Asymmetric quantum wells.

Second-order optical nonlinearities in materials are of paramount importance for optical wavelength conversion techniques, which are the basis of new high-resolution spectroscopic tools. Semiconductor technology now makes it possible to design and fabricate artificially asymmetric quantum structures in which optical nonlinearities can be calculated and optimized from first principles. Extremely large second-order susceptibilities can be obtained in these asymmetric quantum wells. Moreover, properties such as double resonance enhancement or electric field control will open the way to new devices, such as fully solid-state optical parametric oscillators.

https://science.sciencemag.org/content/sci/271/5246/168.full.pdf

Quantum Engineering of Optical Nonlinearities

We study the effects of excitons in nonlinear optical rectification in one-dimensional semiparabolic quantum dots. We consider the cases that the electron and the hole are confined in semiparabolic potentials (i) with the same oscillator frequency and (ii) with the same width. In the first case we present approximate analytical results in the strong confinement regime and find a closed-form relation between the nonlinear optical rectification coefficient of an exciton and the nonlinear optical rectification coefficient when only one electron exists in the structure. In the second case we use the Hartree-Fock approximation and the potential morphing method and present results for the nonlinear optical rectification coefficient in all confinement regimes.

Effects of excitons in nonlinear optical rectification in semiparabolic quantum dots

The potential energy profile in semiconductor heterostructures can now be controlled in a fascinating way that could barely be dreamed of twenty years ago 1. When dealing with interband optical transitions, additional features related to electron-hole interactions (see for instance exciton descriptions in this book) are coming into play and the one-electron wavefunctions and energy levels may fail to describe or predict experimental results. Moreover, the quantization energy is usually small compared to the forbidden band gap, so that typical interband transitions always occur in the same energy range for a given materials pair. On the contrary, intersubband transitions (ISBT) are very sensitive to the exact potential profile and transitions have been observed at wavelengths between lμm and 100μm. In addition, they can be quantitatively described by a simple formalism based on one-electron approaches and many-body effects usually appear as small corrections only. Since 19852, many devices have been designed according to this quantum engineering and have shown unsurpassed properties3. Various materials have been successfully used for these quantum well (QW) heterostructures: GaAs/AlGaAs, InP/InGaAs/InAlAs, Si/SiGe, D/VI compounds…We will focus here on the GaAs/AlGaAs system which has been the most widely studied. First, the calculation of the ISBT matrix element will evidence two major characteristic properties: the optical transitions take advantage of giant dipoles but must verify in the same time a rather drastic selection rule. Then, examples will be given in different fields of application: detection, modulation and emission. Some interesting aspects of coupling and propagation in these structures involve a photon mode density alteration. Finally, a detailed study of second order non linearities will exemplify the beauty of quantum engineering for improving optical properties.

Intersubband transitions in quantum wells

We report the first experimental evidence of second harmonic generation due to inter-subband transitions in compositionally asymmetrical multiquantum wells using a continuous CO2 laser. The extremely large value of the second-order susceptibility (χ(2)2ω ~ 7.6×10−7m/V) is ingood agreement with theoretical predictions.

Second harmonic generation by intersub-band transitions in compositionally asymmetrical MQWs

We report on the first observation of sum frequency generation using intersubband transitions. The quantum well structure was specially designed to enhance the second-order nonlinear coefficient. Using two CO 2 lasers, sum frequency generation was achieved in step quantum wells via intersubband transition processes. The power from each cw CO 2 laser was kept low such that the total power onto the sample was below 2 W. The experimentally determined and calculated second-order susceptibility values are in reasonable agreement.

Sum frequency generation by intersubband transition in step quantum wells

Summary form only given. The authors present evidence of nonlinear optical rectification in compositionally asymmetrical GaAs/AlGaAs MQWs (multi-quantum wells). The structure consisted of 12 periods of 30-AA GaAs-65-AA Al/sub 0.2/Ga/sub 0.8/As wells separated by 500-AA Al/sub 0.4/Ga/sub 0.6/As barriers, epitaxially grown on a 3*10/sup 18/ cm/sup -3/ Si-doped GaAs wafer. The GaAs well is 3*10/sup 17/ cm/sup -3/ Si doped, while the rest of the wells and barriers are nonintentionally doped. A 3000-AA 10/sup 18/-cm/sup -3/ Si-doped GaAs contact layer is grown. The optical rectification is measured at 77 K as a bias appearing at the diode electrodes (with no photocurrent) when it is illuminated by a 10.6- mu m CO/sub 2/ laser. An optical rectification coefficient chi ( omicron = omega - omega ) of 5*10/sup -6/ m/V for each well was determined that is an effective electrooptical coefficient of 4.5*10/sup -9/ m/V in the whole structure. This value of chi ( omicron = omega - omega ) is more than three orders of magnitude higher than in a natural nonlinear medium such as GaAs or InP at 10.6 mu m. This structure can thus be used as a highly effective electrooptic medium in infrared waveguides. >

J. Nagle

Papers

Second harmonic generation by intersub-band transitions in compositionally asymmetrical MQWs

Sum frequency generation by intersubband transition in step quantum wells

Non-linear optical rectification at 10.6 mu m in compositionally asymmetrical GaAs/AlGaAs multi-quantum wells