CoChat
Sign Up
Cited by 16Photorefractive and Nonlinear OpticsStrong Light-Matter InteractionsQuantum optics and atomic interactions

Purcell enhancement of the parametric down-conversion in two-dimensional nonlinear materials

Open access
Tokman, Mikhail, Long, Zhongqu, AlMutairi, Sultan, Wang, Yongrui, Vdovin, Valery, Belkin, Mikhail, Belyanin, Alexey·2019·APL Photonics
DOI 10.1063/1.5044539
Open this paper in CoChat — free accountOpen PDF

Abstract

Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads to a strong Purcell enhancement of the nonlinear processes and compensates for a small interaction volume. The generic feature of such devices which makes them especially challenging for analysis is strong dissipation of both the nonlinear polarization and highly confined modes of a subwavelength cavity. Here we solve a quantum-electrodynamic problem of the spontaneous and stimulated parametric down-conversion in a nonlinear quasi-2D waveguide or cavity. We develop a rigorous Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. Within a relatively simple model, we take into account the nonlinear coupling of the quantized cavity modes, their interaction with a dissipative reservoir and the outside world, amplification of thermal noise and zero-point fluctuations of the electromagnetic field, and other relevant effects. We derive closed-form analytic results for relevant quantities such as the spontaneous parametric signal power and the threshold for parametric instability. We find a strong reduction in the parametric instability threshold for 2D nonlinear materials in a subwavelength cavity and provide a comparison with conventional nonlinear photonic devices.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1063/1.5044539

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • All-dielectric metasurfaces exhibit much lower loss and higher damage thresholds compared to plasmonic counterparts.

    “all-dielectric metasurfaces exhibit much lower loss and higher damage thresholds”

    From Inverse Design of an All-Dielectric Nonlinear Polaritonic Metasurface. (2025) · cites this paper as [9]

    Section IV describes a plasmonic nanocavity as having high radiative and absorption losses and says bulk transparent nonlinear devices have lower dissipation than ultracompact structures. This lends support to the loss comparison, but it does not establish that all-dielectric metasurfaces specifically have much lower loss than plasmonic metasurfaces. The paper does not compare their damage thresholds. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

No references could be resolved yet.

Research works printed but not linked: 39

  1. E. M. Purcell, H. C. Torrey, and R. V. Pound, Phys. Rev. 69, 37 (1946). · DOI
  2. H.-B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994). · DOI
  3. P. Bermel, A. Rodriguez, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. Lett. 99, 053601 (2007). · DOI
  4. P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, Nano Lett. 10, 4880 (2010). · DOI
  5. M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737 (2012). · DOI
  6. M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, Rev. Mod. Phys. 86, 1093 (2014). · DOI
  7. J. Lee et al., Nature 511, 65 (2014). · DOI
  8. J. Lee et al., Adv. Opt. Mater. 4, 664 (2016). · DOI
  9. D. Smirnova and Y. S. Kivshar, Optica 3, 1241 (2016). · DOI
  10. A. R. Davoyan and H. A. Atwater, Optica 5, 608 (2018). · DOI
  11. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, Phys. Rev. Lett. 105, 097401 (2010). · DOI
  12. X. Yao and A. Belyanin, Phys. Rev. Lett. 108, 255503 (2012). · DOI
  13. X. Yao, M. D. Tokman, and A. Belyanin, Phys. Rev. Lett. 112, 055501 (2014). · DOI
  14. Y. Wang, M. Tokman, and A. Belyanin, Phys. Rev. B 94, 195442 (2016). · DOI
  15. L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, and A. M. de Paula, Phys. Rev. B 87, 201401 (2013). · DOI
  16. H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, Nat. Phys. 13, 262 (2016). · DOI
  17. P. Alonso-Gonzlez et al., Nat. Nanotechnol. 12, 31 (2016). · DOI
  18. Y. Ye, Z. Wong, X. Lu, X. Ni, H. Zhu, X. Chen, Y. Wang, and X. Zhang, Nat. Photonics 9, 733 (2015). · DOI
  19. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
  20. C. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, Berlin, Heidelberg, 2004).
  21. M. Erukhimova and M. Tokman, Phys. Rev. A 95, 013807 (2017). · DOI
  22. L. Davidovich, Rev. Mod. Phys. 68, 127 (1996). · DOI
  23. M. Tokman, X. Yao, and A. Belyanin, Phys. Rev. Lett. 110, 077404 (2013). · DOI
  24. M. Erukhimova and M. Tokman, Opt. Lett. 40, 2739 (2015). · DOI
  25. M. Tokman and M. Erukhimova, J. Lumin. 137, 148 (2013). · DOI
  26. M. Tokman, Z. Long, S. AlMutairi, Y. Wang, M. Belkin, and A. Belyanin, Phys. Rev. A 97, 043801 (2018). · DOI
  27. V. M. Fain and Ya. I. Khanin, Quantum Electronics (The MIT Press, Cambridge, MA, 1969), Vol. 1.
  28. M. D. Tokman, M. A. Erukhimova, and V. V. Vdovin, Ann. Phys. 360, 571 (2015). · DOI
  29. M. Tokman, Y. Wang, I. Oladyshkin, A. R. Kutayiah, and A. Belyanin, Phys. Rev. B 93, 235422 (2016). · DOI
  30. Yu. A. Illinskii and L. V. Keldysh, Electromagnetic Response of Material Media (Springer, New York, 1994).
  31. M. D. Tokman and M. A. Erukhimova, Phys. Rev. E 84, 056610 (2011). · DOI
  32. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, Hoboken, NJ, 2003).
  33. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Oxford, 1984).
  34. T. Low, A. Chaves, J. D. Caldwell, A. Kumar1, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, Nat. Mater. 16, 182 (2016). · DOI
  35. G. M. Akselrod, T. Ming, C. Argypoulos, T. B. Hoang, Y. Lin, X. Ling, D. R. Smith, J. Kong, and M. H. Mikkelsen, Nano Lett. 15, 3578 (2015). · DOI
  36. Y. Li, Y. Rao, K. F. Mak, Y. You, S. Wang, C. R. Dean, and T. F. Heinz, Nano Lett. 13, 3329 (2013). · DOI
  37. M. L. Trolle, Y.-C. Tsao, K. Pedersen, and T. G. Pedersen, Phys. Rev. B 92, 161409(R) (2015). · DOI
  38. J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). · DOI
  39. V. O. Martynov, V. A. Mironov, and L. A. Smirnov, J. Phys. B: At., Mol. Opt. · DOI

Cited by

Sorted by citations

Authors
Tokman, M., Long, Z., AlMutairi, S., Wang, Y., Vdovin, V., Belkin, M., & Belyanin, A.
Affiliations
  • Institute of Applied Physics (RU)
  • Texas A&M University (US)
  • The University of Texas at Austin (US)
ORCID
Venue
APL Photonics
Publisher
AIP Publishing
Published
2018-12-11
Volume
4
Issue
3
ISSN
2378-0967 (ISSN-L)
DOI
10.1063/1.5044539
OpenAlex
W2900645057
Cited by
16
References
0
Citations by year
2025: 1 · 2024: 1 · 2023: 2 · 2022: 4 · 2021: 1 · 2020: 3 · 2019: 4
FWCI
0.92
Type
journal article
Language
en
Open access
Licence
Locations
  • APL Photonics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Figshare (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • Russian Foundation for Basic Research (17-02-00387)
  • Air Force Office of Scientific Research (FA9550-15-1-0153, FA9550-17-1-0341)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photorefractive and Nonlinear Optics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
Keywords
Purcell effect, parametric down-conversion, subwavelength cavities, nonlinear waveguides, energy dissipation, thermal noise, vacuum fluctuations, spontaneous parametric down-conversion, quantum electrodynamics, nonlinear optical devices

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review