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arxiv: 2604.15476 · v1 · submitted 2026-04-16 · ⚛️ physics.optics

Quantum-Well-Metasurface to Maximize Nonlinear Polarization

Pith reviewed 2026-05-10 09:49 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords nonlinear opticsmetasurfacequantum wellsecond-order nonlinearityGaAs heterostructurefrequency conversioninterband transitiondielectric metasurface
0
0 comments X p. Extension

The pith

A metasurface patterned on an engineered GaAs/AlGaAs heterostructure boosts the effective second-order nonlinearity to about 14 nm/V.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that combining bandstructure engineering in a quantum-well heterostructure with a dielectric metasurface can produce large effective nonlinearities for frequency conversion. A reader would care because weak nonlinear responses currently hinder compact devices needed for telecommunications and quantum technologies. The approach first creates a resonant interband transition yielding 1.6 nm/V, then uses the metasurface to make this accessible in free space and enhance it to roughly 14 nm/V. This simultaneously tailors the material response and optimizes the internal electromagnetic field, offering a path to efficient miniaturized nonlinear photonic components.

Core claim

By engineering a resonant interband transition in a GaAs/AlGaAs heterostructure, a second-order nonlinear tensor element of 1.6 nm/V is realized at 1.57 um wavelength. Patterning a high quality factor dielectric metasurface on the material makes the nonlinearity free-space-accessible and increases the effective nonlinearity to approximately 14 nm/V. The proof-of-concept shows that interband transition engineering combined with metasurfaces can deliver giant effective nonlinearities in the near-infrared to visible range, addressing constraints in nonlinear photonics.

What carries the argument

The resonant interband transition in the bandstructure-engineered GaAs/AlGaAs heterostructure, made accessible and enhanced by a high-Q dielectric metasurface that optimizes the electromagnetic field within the structure.

If this is right

  • Compact and efficient nonlinear frequency converters become feasible for near-infrared and visible wavelengths.
  • Scalable fabrication of devices that overcome miniaturization barriers in nonlinear photonics.
  • Access to otherwise unusable nonlinear tensor elements through metasurface patterning.
  • Potential for integration into telecommunications and quantum computation systems with reduced size and power requirements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar engineering could extend to other semiconductor heterostructures for different operating wavelengths.
  • The technique might enable lower thresholds for nonlinear processes, reducing required input powers in applications.
  • Integration with photonic circuits could follow if the metasurface pattern is compatible with waveguide designs.
  • Further optimization of the quality factor or pattern geometry could yield even larger enhancements.

Load-bearing premise

The observed increase in effective nonlinearity to 14 nm/V results primarily from the designed metasurface field enhancement and the engineered interband transition rather than from fabrication imperfections, material losses, or unaccounted experimental variables.

What would settle it

Detailed measurements of the local field intensity enhancement inside the heterostructure under the metasurface, or a control experiment without the metasurface pattern showing no such boost, or full error bars demonstrating the 14 nm/V value is within uncertainty of the base 1.6 nm/V.

Figures

Figures reproduced from arXiv: 2604.15476 by Amberly Ricks, Christina M. Sp\"agele, Federico Capasso, Hyunseung Jung, Igal Brener, Irene Occhiodori, Marcus Ossiander, Moaz Waqar, Patrick Devaney, Pernille Undrum Fathi, Rithvik Ramesh, Seth R. Bank, Theodore P. Letsou, Xiaoqing Pan, Yiwei Ju.

Figure 1
Figure 1. Figure 1: Tailoring all components of the second-order polarization. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: GaAs/AlGaAs heterostructure properties. a [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Metasurface design and device simulations. a [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Measured nonlinear device response. a Experimental pump-incidence-angle-resolved second har￾monic spectra measured at a pump power of 41 mW. The second harmonic maxima follow the angular evolution of the GMR branches (compare with [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Characterization of the substrate transferred heterostructure. a [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Schematic of the optical setup for device characterization. [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Incidence angle-resolved transmission spectra of the metasurface for x-polarized illumi [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Nonlinear response of the metasurface/heterostructure sample and the bare heterostruc [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Substrate transfer. The sample is grown via molecular beam epitaxy and subsequently flip-chip bonded to a 500-µm thick sapphire substrate using 353ND EPO-TEK epoxy resin. Mechanical lapping is used for the first stage of the GaAs substrate removal, followed by a wet etch removal of the remaining GaAs substrate and the etch-stop layers. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Metasurface fabrication. Positive-tone E-Beam resist is spin coated on the surface of the het￾erostructure and exposed using electron beam lithography. The exposed resist is removed using developer and the gaps are filled with TiO2 by atomic layer deposition. The overgrown TiO2 is removed by reactive ion etching, and the remaining resist is removed [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Measured and modeled sum-frequency spectra. [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
read the original abstract

Nonlinear frequency conversion unlocks technologies ranging from telecommunications to quantum computation; however, weak nonlinearities and architectures that resist miniaturization currently limit devices. Here, we combine a bandstructure-engineered GaAs/AlGaAs heterostructure with a high quality factor dielectric metasurface to simultaneously tailor the intrinsic nonlinear susceptibility and optimize the electromagnetic field within the heterostructure. By engineering a resonant interband transition, we realize a large second-order nonlinear tensor element, 1.6 nm/V at 1.57 um wavelength. We then make it free-space-accessible and boost the effective nonlinearity to ~ 14 nm/V using a metasurface patterned on the material. Our proof-of-concept experiment establishes that interband transition engineering and metasurfaces accessing otherwise unusable nonlinear tensor elements enable giant effective nonlinearities in the near-infrared to visible spectrum. This addresses material and device-level constraints in nonlinear photonics, providing a scalable route to compact, efficient devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that by engineering a resonant interband transition in a GaAs/AlGaAs quantum-well heterostructure, a large second-order nonlinear tensor element of 1.6 nm/V is realized at 1.57 μm; patterning a high-Q dielectric metasurface on the material then renders this response free-space accessible and boosts the effective nonlinearity to ~14 nm/V, as demonstrated in a proof-of-concept experiment.

Significance. If the reported values and their attribution to the combined interband engineering plus metasurface enhancement hold after detailed verification, the work would offer a scalable route to giant effective nonlinearities in the near-IR/visible range, directly addressing miniaturization and efficiency limits in nonlinear photonics devices.

major comments (2)
  1. [Abstract] Abstract: the central experimental claims (1.6 nm/V intrinsic and ~14 nm/V effective) are stated without any supporting data, figures, error bars, or methods details, so the support for the claims cannot be assessed.
  2. [Results/Methods] Results/Methods (conversion from SHG): the extraction of d_eff ~14 nm/V relies on simulated local-field enhancement, mode overlap, and Q-factor without reported reference SHG measurements on unpatterned regions of the same wafer, error propagation, or sensitivity analysis to discrepancies between simulated and actual field distributions; this leaves open alternative explanations such as fabrication variations or calibration offsets.
minor comments (2)
  1. [Abstract] Abstract: wavelength notation alternates between '1.57 um' and '1.57 μm'; standardize throughout.
  2. [Throughout] Throughout: clarify whether the reported tensor element is d or χ^(2) and confirm the unit conversion (nm/V is used but is 1000× larger than typical pm/V values).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments identify opportunities to improve the clarity of our central claims and the rigor of our data analysis. We address each point below and describe the revisions we will implement.

read point-by-point responses
  1. Referee: [Abstract] Abstract: the central experimental claims (1.6 nm/V intrinsic and ~14 nm/V effective) are stated without any supporting data, figures, error bars, or methods details, so the support for the claims cannot be assessed.

    Authors: We agree that the abstract, being a concise summary, does not itself contain the supporting data or references. The full manuscript includes the relevant SHG spectra, metasurface characterization, and extraction procedures in the Results and Methods sections. To address the concern directly, we will revise the abstract to include brief references to the key figures and supplementary sections that present the experimental data, error estimates, and methods supporting the reported values of 1.6 nm/V and ~14 nm/V. revision: yes

  2. Referee: [Results/Methods] Results/Methods (conversion from SHG): the extraction of d_eff ~14 nm/V relies on simulated local-field enhancement, mode overlap, and Q-factor without reported reference SHG measurements on unpatterned regions of the same wafer, error propagation, or sensitivity analysis to discrepancies between simulated and actual field distributions; this leaves open alternative explanations such as fabrication variations or calibration offsets.

    Authors: We acknowledge that the current presentation of the d_eff extraction would benefit from additional validation steps. In the revised manuscript we will add reference SHG measurements performed on unpatterned regions of the identical wafer to establish a direct experimental baseline. We will also incorporate a full error-propagation analysis and a sensitivity study that quantifies the effect of plausible deviations between simulated and measured local-field distributions, Q-factors, and mode overlaps. These additions will allow us to assess and exclude alternative explanations such as fabrication variations or calibration offsets, thereby strengthening the attribution of the observed enhancement to the metasurface. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental claims rest on measurements, not self-referential derivations

full rationale

The paper reports fabrication and optical characterization of a GaAs/AlGaAs quantum-well heterostructure patterned with a dielectric metasurface. Its central claims (realization of 1.6 nm/V intrinsic nonlinearity at 1.57 µm via interband engineering, followed by an effective ~14 nm/V via metasurface enhancement) are presented as direct experimental outcomes from second-harmonic generation measurements. No derivation chain, predictive equations, or first-principles calculations are described that reduce by construction to fitted inputs, self-citations, or ansatzes; the results are obtained from physical samples and are subject to external verification or falsification. Self-citations, if present, are not load-bearing for the reported values.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard principles of semiconductor bandstructure engineering and electromagnetic metasurface design from prior literature, with no new free parameters, axioms beyond domain standards, or invented entities introduced.

axioms (2)
  • standard math Established models of second-order nonlinear susceptibility in III-V semiconductors and resonant interband transitions
    The paper invokes known physics of GaAs/AlGaAs heterostructures and nonlinear optics without deriving them.
  • domain assumption High-Q dielectric metasurfaces can enhance local fields without prohibitive losses in the near-IR
    Assumed for the field optimization step.

pith-pipeline@v0.9.0 · 5524 in / 1360 out tokens · 54696 ms · 2026-05-10T09:49:20.549631+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages

  1. [1]

    P., Vaskin, A., Reno, J

    Liu, S., Vabishchevich, P. P., Vaskin, A., Reno, J. L., Keeler, G. A., Sinclair, M. B., Staude, I. & Brener, I. An all-dielectric metasurface as a broadband optical frequency mixer. Nature Communi- cations 9, 2507. doi: 10.1038/s41467-018-04944-9 (2018)

  2. [2]

    & Meng, H

    Wu, Q., Peng, L., Huang, Z., Liu, X., Luo, M., Gao, D. & Meng, H. Advancements in ultrafast photonics: confluence of nonlinear optics and intelligent strategies. Light: Science & Applications 14, 97. doi: 10.1038/s41377-024-01732-7 (2025)

  3. [3]

    & Van, V

    Saghaei, H. & Van, V. Broadband mid-infrared supercontinuum generation in dispersion-engineered silicon-on-insulator waveguide. Journal of the Optical Society of America B 36, A193. doi:10.1364/ JOSAB.36.00A193 (2019)

  4. [4]

    & Fejer, M

    Jankowski, M., Langrock, C., Desiatov, B., Lončar, M. & Fejer, M. M. Supercontinuum generation by saturated second-order nonlinear interactions. APL Photonics 8, 116104. doi: 10.1063/5.0158926 (2023)

  5. [5]

    & Bowers, J

    Chang, L., Liu, S. & Bowers, J. E. Integrated optical frequency comb technologies. Nature Photonics 16, 95–108. doi: 10.1038/s41566-021-00945-1 (2022)

  6. [6]

    & Dai, D.-X

    Pan, B.-C., Liu, H.-X., Xu, H.-C., Huang, Y.-S., Li, H., Yu, Z.-J., Liu, L., Shi, Y.-C. & Dai, D.-X. Ultra-compact lithium niobate microcavity electro-optic modulator beyond 110 GHz. Chip 1, 100029. doi:10.1016/j.chip.2022.100029 (2022)

  7. [7]

    Quantum Pair Generation in Nonlinear Metasurfaces with Mixed and Pure Photon Polarizations

    Noh, J., Santiago-Cruz, T., Sultanov, V., Doiron, C. F., Gennaro, S. D., Chekhova, M. V. & Brener, I. Quantum Pair Generation in Nonlinear Metasurfaces with Mixed and Pure Photon Polarizations. Nano Letters 24, 15356–15362. doi: 10.1021/acs.nanolett.4c04398 (2024)

  8. [8]

    D., Mitrofanov, O., Addamane, S., Reno, J., Brener, I

    Santiago-Cruz, T., Gennaro, S. D., Mitrofanov, O., Addamane, S., Reno, J., Brener, I. & Chekhova, M. V. Resonant metasurfaces for generating complex quantum states. Science 377, 991–995. doi:10. 1126/science.abq8684 (2022)

  9. [9]

    & Guo, G.-C

    Zhang, C., Huang, Y.-F., Liu, B.-H., Li, C.-F. & Guo, G.-C. Spontaneous Parametric Down-Conversion Sources for Multiphoton Experiments. Advanced Quantum Technologies 4, 2000132. doi: 10.1002/ qute.202000132 (2021)

  10. [10]

    & Tang, H

    Yang, F., Lu, J., Shen, M., Yang, G. & Tang, H. X. Symmetric second-harmonic generation in sub-wavelength periodically poled thin film lithium niobate. Optica 11, 1050–1055. doi: 10.1364/ OPTICA.527236 (2024)

  11. [11]

    & Lončar, M

    Wang, C., Xiong, X., Andrade, N., Venkataraman, V., Ren, X.-F., Guo, G.-C. & Lončar, M. Second harmonic generation in nano-structured thin-film lithium niobate waveguides. Optics Express 25, 6963–6973. doi: 10.1364/OE.25.006963 (2017)

  12. [12]

    B., Schurig, D

    Pendry, J. B., Schurig, D. & Smith, D. R. Controlling Electromagnetic Fields. Science 312, 1780–

  13. [13]

    doi: 10.1126/science.1125907 (2006)

  14. [14]

    and Aieta, Francesco and Tetienne, Jean-Philippe and Capasso, Federico and Gaburro, Zeno , month = oct, year =

    Yu, N., Genevet, P., Kats, M. A., Aieta, F., Tetienne, J.-P., Capasso, F. & Gaburro, Z. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction. Science 334, 333–337. doi: 10.1126/science.1210713 (2011)

  15. [15]

    & Capasso, F

    Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 13, 139–150. doi: 10. 1038/nmat3839 (2014)

  16. [16]

    T., Zhu, A

    Chen, W. T., Zhu, A. Y. & Capasso, F. Flat optics with dispersion-engineered metasurfaces. Nature Reviews Materials 5, 604–620. doi: 10.1038/s41578-020-0203-3 (2020). 15

  17. [17]

    & Rho, J

    Jung, C., Lee, E. & Rho, J. The rise of electrically tunable metasurfaces. Science Advances 10, eado8964. doi: 10.1126/sciadv.ado8964 (2024)

  18. [18]

    Abdelraouf, O. A. M., Wang, Z., Liu, H., Dong, Z., Wang, Q., Ye, M., Wang, X. R., Wang, Q. J. & Liu, H. Recent Advances in Tunable Metasurfaces: Materials, Design, and Applications. ACS Nano 16, 13339–13369. doi: 10.1021/acsnano.2c04628 (2022)

  19. [19]

    & Belkin, M

    Lee, J., Tymchenko, M., Argyropoulos, C., Chen, P.-Y., Lu, F., Demmerle, F., Boehm, G., Amann, M.-C., Alù, A. & Belkin, M. A. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature 511, 65–69 (2014)

  20. [20]

    & De Angelis, C

    Carletti, L., Locatelli, A., Stepanenko, O., Leo, G. & De Angelis, C. Enhanced second-harmonic generation from magnetic resonance in AlGaAs nanoantennas. Optics Express 23, 26544. doi: 10. 1364/OE.23.026544 (2015)

  21. [21]

    F., Carletti, L., Locatelli, A., Rocco, D., Finazzi, M., Ghirardini, L., Favero, I., Gomez, C., Lemaître, A., Celebrano, M., De Angelis, C

    Gili, V. F., Carletti, L., Locatelli, A., Rocco, D., Finazzi, M., Ghirardini, L., Favero, I., Gomez, C., Lemaître, A., Celebrano, M., De Angelis, C. & Leo, G. Monolithic AlGaAs second-harmonic nanoantennas. Optics Express 24, 15965. doi: 10.1364/OE.24.015965 (2016)

  22. [22]

    A., Solntsev, A

    Camacho-Morales, R., Rahmani, M., Kruk, S., Wang, L., Xu, L., Smirnova, D. A., Solntsev, A. S., Miroshnichenko, A., Tan, H. H., Karouta, F., Naureen, S., Vora, K., Carletti, L., De Angelis, C., Jagadish, C., Kivshar, Y. S. & Neshev, D. N. Nonlinear Generation of Vector Beams From AlGaAs Nanoantennas. Nano Letters 16, 7191–7197. doi: 10.1021/acs.nanolett.6...

  23. [23]

    & Zentgraf, T

    Li, G., Zhang, S. & Zentgraf, T. Nonlinear photonic metasurfaces. Nature Reviews Materials 2, 1–14. doi:10.1038/natrevmats.2017.10 (2017)

  24. [24]

    & Alù, A

    Krasnok, A., Tymchenko, M. & Alù, A. Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Materials Today 21, 8–21. doi: 10.1016/j.mattod.2017.06.007 (2018)

  25. [25]

    J., Steinert, M., Geiss, R., Pertsch, T., Staude, I

    Fedotova, A., Younesi, M., Sautter, J., Vaskin, A., Löchner, F. J., Steinert, M., Geiss, R., Pertsch, T., Staude, I. & Setzpfandt, F. Second-Harmonic Generation in Resonant Nonlinear Metasurfaces Based on Lithium Niobate. Nano Letters 20, 8608–8614. doi: 10 . 1021 / acs . nanolett . 0c03290 (2020)

  26. [26]

    Nobel Lecture: Quasielectric fields and band offsets: teaching electrons new tricks

    Kroemer, H. Nobel Lecture: Quasielectric fields and band offsets: teaching electrons new tricks. Reviews of Modern Physics 73, 783–793. doi: 10.1103/RevModPhys.73.783 (2001)

  27. [27]

    & Tsu, R

    Esaki, L. & Tsu, R. Superlattice and Negative Differential Conductivity in Semiconductors. IBM Journal of Research and Development 14, 61–65. doi: 10.1147/rd.141.0061 (1970)

  28. [28]

    M., Yoo, S

    Fejer, M. M., Yoo, S. J. B., Byer, R. L., Harwit, A. & HarrisJr., J. S. Observation of extremely large quadratic susceptibility at 9.6 - 10.8 um in electric-field-biased AlGaAs quantum wells. Physical Review Letters 62, 1041–1044. doi: 10.1103/PhysRevLett.62.1041 (1989)

  29. [29]

    L., Chu, S

    Sirtori, C., Capasso, F., Sivco, D. L., Chu, S. N. G. & Cho, A. Y. Observation of large second order susceptibility via intersubband transitions at ￿￿10 um in asymmetric coupled AlInAs/GaInAs quantum wells. Applied Physics Letters 59, 2302–2304. doi: 10.1063/1.106050 (1991)

  30. [30]

    & Cho, A

    Capasso, F., Sirtori, C. & Cho, A. Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared. IEEE Journal of Quantum Electronics 30, 1313–

  31. [31]

    doi: 10.1109/3.303697 (1994)

  32. [32]

    B., Belkin, M

    Sarma, R., Xu, J., de Ceglia, D., Carletti, L., Campione, S., Klem, J., Sinclair, M. B., Belkin, M. A. & Brener, I. An All-Dielectric Polaritonic Metasurface with a Giant Nonlinear Optical Response. Nano Letters 22, 896–903. doi: 10.1021/acs.nanolett.1c03325 (2022). 16

  33. [33]

    A., Goh, H

    Mann, S. A., Goh, H. & Alù, A. Inverse Design of Nonlinear Polaritonic Metasurfaces for Second Harmonic Generation. ACS Photonics 10, 993–1000. doi: 10.1021/acsphotonics.2c01342 (2023)

  34. [34]

    F., Jollivet, A., Wang, D., Cheng, J

    Quach, P., Liu, S. F., Jollivet, A., Wang, D., Cheng, J. Y., Isac, N., Pirotta, S., Bouville, D., Sheng, S. S., Imran, A., Chen, L., Li, D., Zheng, X. T., Wang, Y. X., Qin, Z. X., Tchernycheva, M., Julien, F. H., Shen, B. & Wang, X. Q. A GaN/AlN quantum cascade detector with a broad response from the mid-infrared (4.1 um) to the visible (550 nm) spectral ...

  35. [35]

    E., Ma, Q., Tao, A

    Qian, H., Li, S., Chen, C.-F., Hsu, S.-W., Bopp, S. E., Ma, Q., Tao, A. R. & Liu, Z. Large optical nonlinearity enabled by coupled metallic quantum wells. Light: Science & Applications 8, 13. doi:10. 1038/s41377-019-0123-4 (2019)

  36. [36]

    C., Xiong, W

    Chen, C.-F., Tian, F., Zhou, J., Wagner, J. C., Xiong, W. & Liu, Z. Giant optical second- and third- order nonlinearities at a telecom wavelength. Optics Letters 49, 3725. doi: 10 . 1364 / OL . 528340 (2024)

  37. [37]

    Second‐order susceptibility of asymmetric coupled quantum well structures

    Khurgin, J. Second‐order susceptibility of asymmetric coupled quantum well structures. Applied Physics Letters 51, 2100–2102. doi: 10.1063/1.98960 (1987)

  38. [38]

    Second-order nonlinear effects in asymmetric quantum-well structures

    Khurgin, J. Second-order nonlinear effects in asymmetric quantum-well structures. Physical Review B 38, 4056–4066. doi: 10.1103/PhysRevB.38.4056 (1988)

  39. [39]

    M., Meng, Q., Wen, K

    Ramesh, R., Hsieh, T., Skipper, A. M., Meng, Q., Wen, K. C., Shafiei, F., Wistey, M. A., Downer, M. C., Khurgin, J. B. & Bank, S. R. Interband second-order nonlinear optical susceptibility of asymmetric coupled quantum wells. Applied Physics Letters 123, 251111. doi: 10.1063/5.0168596 (2023)

  40. [40]

    Ramesh, R., Brown, M., Ricks, A., Esfahani, S., Devaney, P., Wen, K., Waqar, M., Sakotic, Z., Mann, S., Hsieh, T., Skipper, A., Meng, Q., Jung, H., Cotrufo, M., Shafiei, F., Downer, M., Shakkottai, S., Wistey, M., Brener, I., Pan, X., Alu, A., Wasserman, D., Khurgin, J. B. & Bank, S. R. Enhanced Interband Optical Nonlinearities from Coupled Quantum Wells....

  41. [41]

    D., Winn, J

    Fan, S., Joannopoulos, J. D., Winn, J. N., Devenyi, A., Chen, J. C. & Meade, R. D. Guided and defect modes in periodic dielectric waveguides. Journal of the Optical Society of America B 12, 1267. doi:10.1364/JOSAB.12.001267 (1995)

  42. [42]

    and Jin, R

    Huang, L., Jin, R., Zhou, C., Li, G., Xu, L., Overvig, A., Deng, F., Chen, X., Lu, W., Alù, A. & Miroshnichenko, A. E. Ultrahigh-Q guided mode resonances in an All-dielectric metasurface. Nature Communications 14, 3433. doi: 10.1038/s41467-023-39227-5 (2023)

  43. [43]

    J., Kamboj, A., Mansfield, N

    Muhowski, A. J., Kamboj, A., Mansfield, N. C. & Wasserman, D. Mid-infrared rainbow light- emitting diodes. Applied Physics Letters 121, 261105. doi: 10.1063/5.0129196 (2022)

  44. [44]

    S., Kim, G

    Bark, H. S., Kim, G. J. & Jeon, T.-I. Transmission characteristics of all-dielectric guided-mode resonance filter in the THz region. Scientific Reports 8, 13570. doi: 10.1038/s41598-018-31931-3 (2018)

  45. [45]

    & Miller, B

    David, A. & Miller, B. in Quantum Dynamics of Simple Systems (eds Oppo, G.-L., Barnett, S. M., Riis, E. & Wilkinson, M.) 1st ed., 239–266 (CRC Press, Boca Raton, FL, 2020). doi: 10 . 1201 / 9781003072973-9

  46. [46]

    Quantum Cascade Lasers (Oxford University Press, Oxford, U.K., 2013)

    Faist, J. Quantum Cascade Lasers (Oxford University Press, Oxford, U.K., 2013)

  47. [47]

    Boyd, R. W. Nonlinear optics 4th ed. (Academic Press, San Diego, 2019)

  48. [48]

    & Petukhov, A

    Roke, S., Bonn, M. & Petukhov, A. V. Nonlinear optical scattering: The concept of effective suscep- tibility. Physical Review B 70, 115106. doi: 10.1103/PhysRevB.70.115106 (2004). 17

  49. [49]

    Yarykin, J

    Rose, A., Powell, D. A., Shadrivov, I. V., Smith, D. R. & Kivshar, Y. S. Circular dichroism of four- wave mixing in nonlinear metamaterials. Physical Review B 88, 195148. doi:10.1103/PhysRevB.88. 195148 (2013)

  50. [50]

    R., Lee, I.-H., Maier, S

    Noor, A., Damodaran, A. R., Lee, I.-H., Maier, S. A., Oh, S.-H. & Ciracì, C. Mode-Matching Enhancement of Second-Harmonic Generation with Plasmonic Nanopatch Antennas. ACS Photonics 7, 3333–3340. doi: 10.1021/acsphotonics.0c01545 (2020)

  51. [51]

    Nonlinear Optics (World Scientific, Singapore, 1996)

    Bloembergen, N. Nonlinear Optics (World Scientific, Singapore, 1996)

  52. [52]

    & Vogl, P

    Birner, S., Zibold, T., Andlauer, T., Kubis, T., Sabathil, M., Trellakis, A. & Vogl, P. nextnano: General Purpose 3-D Simulations. IEEE Transactions on Electron Devices 54, 2137–2142. doi: 10. 1109/TED.2007.902871 (2007)

  53. [53]

    Inverse Design of Lightweight Broadband Reflector for Relativistic Lightsail Propulsion , volume=

    Jin, W., Li, W., Orenstein, M. & Fan, S. Inverse Design of Lightweight Broadband Reflector for Rel- ativistic Lightsail Propulsion. ACS Photonics 7, 2350–2355. doi: 10.1021/acsphotonics.0c00768 (2020)

  54. [54]

    C., Nordland, W

    Miller, R. C., Nordland, W. A. & Bridenbaugh, P. M. Dependence of Second‐Harmonic‐Generation Coefficients of LiNbO3 on Melt Composition. Journal of Applied Physics 42, 4145–4147. doi: 10 . 1063/1.1659746 (1971)

  55. [55]

    Nikogosyan, D. N. Nonlinear Optical Crystals: A Complete Survey doi:10.1007/b138685 (Springer- Verlag, New York, 2005)

  56. [56]

    J., Hu, Y., Holzgrafe, J., Ghosh, S., Shams- Ansari, A., Puma, E., Sinclair, N., Reimer, C., Zhang, M

    Zhu, D., Shao, L., Yu, M., Cheng, R., Desiatov, B., Xin, C. J., Hu, Y., Holzgrafe, J., Ghosh, S., Shams- Ansari, A., Puma, E., Sinclair, N., Reimer, C., Zhang, M. & Lončar, M. Integrated photonics on thin-film lithium niobate. Advances in Optics and Photonics 13, 242–352. doi:10.1364/AOP.411024 (2021)

  57. [57]

    Miller, R. C. Optical second harmonic generation in piezoelectric crystals. Applied Physics Letters 5, 17–19. doi: 10.1063/1.1754022 (1964)

  58. [58]

    Takeshi, R

    Shoji, I., Kondo, T., Kitamoto, A., Shirane, M. & Ito, R. Absolute scale of second-order nonlinear- optical coefficients. Journal of the Optical Society of America B 14, 2268–2294. doi:10.1364/JOSAB. 14.002268 (1997)

  59. [59]

    Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions

    Roberts, D. Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions. IEEE Journal of Quantum Electronics 28, 2057–

  60. [60]

    doi: 10.1109/3.159516 (1992)

  61. [61]

    & Crespo, H

    Miranda, M., Fordell, T., Arnold, C., L’Huillier, A. & Crespo, H. Simultaneous compression and characterization of ultrashort laser pulses using chirped mirrors and glass wedges. Optics Express 20, 688–697. doi: 10.1364/OE.20.000688 (2012). 18 Supplementary Information for Quantum-Well-Metasurface to Maximize Nonlinear Polarization Pernille Undrum Fathi 1...