Abstract

Nearly all thermal radiation phenomena involving materials with linear response can be accurately described via semi-classical theories of light. Here, we go beyond these traditional paradigms to study a nonlinear system that, as we show, requires quantum theory of damping. Specifically, we analyze thermal radiation from a resonant system containing a χ(2) nonlinear medium and supporting resonances at frequencies ω1 and ω2 ≈ 2ω1, where both resonators are driven only by intrinsic thermal fluctuations. Within our quantum formalism, we reveal new possibilities for shaping the thermal radiation. We show that the resonantly enhanced nonlinear interaction allows frequency-selective enhancement of thermal emission through upconversion, surpassing the well-known blackbody limits associated with linear media. Surprisingly, we also find that the emitted thermal light exhibits non-trivial statistics (g(2)(0) ≠ ~2) and biphoton intensity correlations (at two distinct frequencies). We highlight that these features can be observed in the near future by heating a properly designed nonlinear system, without the need for any external signal. Our work motivates new interdisciplinary inquiries combining the fields of nonlinear photonics, quantum optics and thermal science.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Quantum effects of thermal radiation in a Kerr nonlinear blackbody

Ze Cheng
J. Opt. Soc. Am. B 19(7) 1692-1705 (2002)

Phonon effects in quantum dot single-photon sources

Emil V. Denning, Jake Iles-Smith, Niels Gregersen, and Jesper Mork
Opt. Mater. Express 10(1) 222-239 (2020)

References

  • View by:
  • |
  • |
  • |

  1. D. Chang, V. Vuletić, and M. Lukin, “Quantum nonlinear optics–photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
    [Crossref]
  2. S. Fan, “Thermal photonics and energy applications,” Joule 1(2), 264–273 (2017).
    [Crossref]
  3. E. Tervo, E. Bagherisereshki, and Z. Zhang, “Near-field radiative thermoelectric energy converters: a review,” Front. Energy 12(1), 5–21 (2018).
    [Crossref]
  4. C. Khandekar, A. Pick, S. Johnson, and A. Rodriguez, “Radiative heat transfer in nonlinear kerr media,” Phys. Rev. B 91(11), 115406 (2015).
    [Crossref]
  5. C. Khandekar, Z. Lin, and A. Rodriguez, “Thermal radiation from optically driven kerr (χ (3)) photonic cavities,” Appl. Phys. Lett. 106(15), 151109 (2015).
    [Crossref]
  6. C. Khandekar and A. Rodriguez, “Near-field thermal upconversion and energy transfer through a kerr medium,” Opt. Express 25(19), 23164–23180 (2017).
    [Crossref]
  7. C. Khandekar, R. Messina, and A. Rodriguez, “Near-field refrigeration and tunable heat exchange through four-wave mixing,” AIP Adv. 8(5), 055029 (2018).
    [Crossref]
  8. R. W. Boyd, Nonlinear optics (Elsevier, 2003).
  9. S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
    [Crossref]
  10. H. Schmidt and A. Imamoglu, “Giant kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996).
    [Crossref]
  11. H. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University, 2002).
  12. L. Landau and E. Lifshitz, “Course of theoretical physics, volume 5,” Publ. Butterworth-Heinemann 3 (1980).
  13. C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
    [Crossref]
  14. S. Rytov, “Theory of electric fluctuations and thermal radiation,” AFCRC-TR 59, 162 (1959).
  15. C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
    [Crossref]
  16. L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
    [Crossref]
  17. A. Karalis and J. Joannopoulos, “Temporal coupled-mode theory model for resonant near-field thermophotovoltaics,” Appl. Phys. Lett. 107(14), 141108 (2015).
    [Crossref]
  18. M. Scully and M. Zubairy, Quantum optics (AAPT, 1999).
  19. G. Agarwal, “Quantum theory of second harmonic generation,” Opt. Commun. 1(3), 132–134 (1969).
    [Crossref]
  20. P. Drummond and M. Hillery, The quantum theory of nonlinear optics (Cambridge University, 2014).
  21. M. Kozierowski and R. Tanaś, “Quantum fluctuations in second-harmonic light generation,” Opt. Commun. 21(2), 229–231 (1977).
    [Crossref]
  22. M. Dykman and M. Krivoglaz, “Spectral distribution of nonlinear oscillators with nonlinear friction due to a medium,” Phys. Status Solidi B 68(1), 111–123 (1975).
    [Crossref]
  23. S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
    [Crossref]
  24. V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
    [Crossref]
  25. D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
    [Crossref]
  26. J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
    [Crossref]
  27. K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
    [Crossref]
  28. O. D. Miller, A. G. Polimeridis, M. H. Reid, C. W. Hsu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to optical response in absorptive systems,” Opt. Express 24(4), 3329–3364 (2016).
    [Crossref]
  29. S. Buddhiraju, P. Santhanam, and S. Fan, “Thermodynamic limits of energy harvesting from outgoing thermal radiation,” Proc. Natl. Acad. Sci. 115(16), E3609–E3615 (2018).
    [Crossref]
  30. S. Molesky, W. Jin, P. Venkataram, and A. Rodriguez, “Bounds on absorption and thermal radiation for arbitrary objects,” arXiv:1907.04418 (2019).
  31. S. Molesky, P. Venkataram, W. Jin, and A. Rodriguez, “Fundamental limits to radiative heat transfer: theory,” arXiv:1907.03000 (2019).
  32. J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
    [Crossref]
  33. W. Li and S. Fan, “Nanophotonic control of thermal radiation for energy applications,” Opt. Express 26(12), 15995–16021 (2018).
    [Crossref]
  34. D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
    [Crossref]
  35. H. Soo and M. Krüger, “Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium,” Phys. Rev. B 97(4), 045412 (2018).
    [Crossref]
  36. J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic crystals: Molding the flow of light (Princeton University, 2011).
  37. J. Bravo-Abad, S. Fan, S. Johnson, J. Joannopoulos, and M. Soljacic, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25(9), 2539–2546 (2007).
    [Crossref]
  38. A. Rodriguez, M. Soljačić, J. Joannopoulos, and S. Johnson, “χ (2) and χ (3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
    [Crossref]
  39. L.-P. Yang and Z. Jacob, “Engineering first-order quantum phase transitions for weak signal detection,” arXiv preprint arXiv:1905.07420 (2019).
  40. L.-P. Yang and Z. Jacob, “Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions,” Opt. Express 27(8), 10482–10494 (2019).
    [Crossref]
  41. S.-A. Biehs and G. Agarwal, “Dynamical quantum theory of heat transfer between plasmonic nanosystems,” J. Opt. Soc. Am. B 30(3), 700–707 (2013).
    [Crossref]
  42. A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77(8), 1413–1415 (1996).
    [Crossref]
  43. D. Walls and G. Milburn, Quantum optics (Springer, 2008).
  44. W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
    [Crossref]
  45. K. Rivoire, Z. Lin, F. Hatami, W. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22609–22615 (2009).
    [Crossref]
  46. Z.-F. Bi, A. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ (2) microring resonators,” Opt. Express 20(7), 7526–7543 (2012).
    [Crossref]
  47. Z. Lin, X. Liang, M. Lončar, S. Johnson, and A. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3(3), 233–238 (2016).
    [Crossref]
  48. P. Campagnola and L. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003).
    [Crossref]
  49. T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
    [Crossref]
  50. J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
    [Crossref]
  51. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
    [Crossref]
  52. N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
    [Crossref]
  53. S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
    [Crossref]
  54. L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
    [Crossref]
  55. M. Minkov, D. Gerace, and S. Fan, “Doubly resonant χ(2) nonlinear photonic crystal cavity based on a bound state in the continuum,” Optica 6(8), 1039–1045 (2019).
    [Crossref]
  56. C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
    [Crossref]
  57. J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
    [Crossref]
  58. D. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. 114(17), 4336–4341 (2017).
    [Crossref]
  59. L. Zhu, Y. Guo, and S. Fan, “Theory of many-body radiative heat transfer without the constraint of reciprocity,” Phys. Rev. B 97(9), 094302 (2018).
    [Crossref]
  60. C. Khandekar and Z. Jacob, “Thermal spin photonics in the near-field of nonreciprocal media,” New J. Phys. 21(10), 103030 (2019).
    [Crossref]
  61. W. Jin, A. Polimeridis, and A. Rodriguez, “Temperature control of thermal radiation from composite bodies,” Phys. Rev. B 93(12), 121403 (2016).
    [Crossref]
  62. C. Khandekar and Z. Jacob, “Circularly polarized thermal radiation from nonequilibrium coupled antennas,” Phys. Rev. Appl. 12(1), 014053 (2019).
    [Crossref]
  63. F. Moss and P. McClintock, Noise in nonlinear dynamical systems, vol. 2 (Cambridge University, 1989).
  64. N. Van Kampen, Stochastic processes in physics and chemistry, vol. 1 (Elsevier, 1992).

2019 (5)

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

L.-P. Yang and Z. Jacob, “Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions,” Opt. Express 27(8), 10482–10494 (2019).
[Crossref]

M. Minkov, D. Gerace, and S. Fan, “Doubly resonant χ(2) nonlinear photonic crystal cavity based on a bound state in the continuum,” Optica 6(8), 1039–1045 (2019).
[Crossref]

C. Khandekar and Z. Jacob, “Thermal spin photonics in the near-field of nonreciprocal media,” New J. Phys. 21(10), 103030 (2019).
[Crossref]

C. Khandekar and Z. Jacob, “Circularly polarized thermal radiation from nonequilibrium coupled antennas,” Phys. Rev. Appl. 12(1), 014053 (2019).
[Crossref]

2018 (12)

C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
[Crossref]

L. Zhu, Y. Guo, and S. Fan, “Theory of many-body radiative heat transfer without the constraint of reciprocity,” Phys. Rev. B 97(9), 094302 (2018).
[Crossref]

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref]

H. Soo and M. Krüger, “Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium,” Phys. Rev. B 97(4), 045412 (2018).
[Crossref]

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

S. Buddhiraju, P. Santhanam, and S. Fan, “Thermodynamic limits of energy harvesting from outgoing thermal radiation,” Proc. Natl. Acad. Sci. 115(16), E3609–E3615 (2018).
[Crossref]

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
[Crossref]

W. Li and S. Fan, “Nanophotonic control of thermal radiation for energy applications,” Opt. Express 26(12), 15995–16021 (2018).
[Crossref]

E. Tervo, E. Bagherisereshki, and Z. Zhang, “Near-field radiative thermoelectric energy converters: a review,” Front. Energy 12(1), 5–21 (2018).
[Crossref]

C. Khandekar, R. Messina, and A. Rodriguez, “Near-field refrigeration and tunable heat exchange through four-wave mixing,” AIP Adv. 8(5), 055029 (2018).
[Crossref]

2017 (4)

C. Khandekar and A. Rodriguez, “Near-field thermal upconversion and energy transfer through a kerr medium,” Opt. Express 25(19), 23164–23180 (2017).
[Crossref]

S. Fan, “Thermal photonics and energy applications,” Joule 1(2), 264–273 (2017).
[Crossref]

N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
[Crossref]

D. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. 114(17), 4336–4341 (2017).
[Crossref]

2016 (4)

2015 (4)

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

C. Khandekar, A. Pick, S. Johnson, and A. Rodriguez, “Radiative heat transfer in nonlinear kerr media,” Phys. Rev. B 91(11), 115406 (2015).
[Crossref]

C. Khandekar, Z. Lin, and A. Rodriguez, “Thermal radiation from optically driven kerr (χ (3)) photonic cavities,” Appl. Phys. Lett. 106(15), 151109 (2015).
[Crossref]

A. Karalis and J. Joannopoulos, “Temporal coupled-mode theory model for resonant near-field thermophotovoltaics,” Appl. Phys. Lett. 107(14), 141108 (2015).
[Crossref]

2014 (3)

C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
[Crossref]

D. Chang, V. Vuletić, and M. Lukin, “Quantum nonlinear optics–photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

2013 (3)

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

S.-A. Biehs and G. Agarwal, “Dynamical quantum theory of heat transfer between plasmonic nanosystems,” J. Opt. Soc. Am. B 30(3), 700–707 (2013).
[Crossref]

2012 (3)

W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
[Crossref]

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Z.-F. Bi, A. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ (2) microring resonators,” Opt. Express 20(7), 7526–7543 (2012).
[Crossref]

2009 (1)

2007 (2)

2004 (1)

C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
[Crossref]

2003 (1)

P. Campagnola and L. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003).
[Crossref]

1996 (3)

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

H. Schmidt and A. Imamoglu, “Giant kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996).
[Crossref]

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77(8), 1413–1415 (1996).
[Crossref]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

1982 (1)

T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
[Crossref]

1977 (1)

M. Kozierowski and R. Tanaś, “Quantum fluctuations in second-harmonic light generation,” Opt. Commun. 21(2), 229–231 (1977).
[Crossref]

1975 (1)

M. Dykman and M. Krivoglaz, “Spectral distribution of nonlinear oscillators with nonlinear friction due to a medium,” Phys. Status Solidi B 68(1), 111–123 (1975).
[Crossref]

1969 (1)

G. Agarwal, “Quantum theory of second harmonic generation,” Opt. Commun. 1(3), 132–134 (1969).
[Crossref]

1959 (1)

S. Rytov, “Theory of electric fluctuations and thermal radiation,” AFCRC-TR 59, 162 (1959).

Agarwal, G.

Alu, A.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Alù, A.

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Amann, M.-C.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Argyropoulos, C.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Bagherisereshki, E.

E. Tervo, E. Bagherisereshki, and Z. Zhang, “Near-field radiative thermoelectric energy converters: a review,” Front. Energy 12(1), 5–21 (2018).
[Crossref]

Baranov, D.

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Belkin, M.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Ben-Abdallah, P.

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

Berger, V.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Bi, Z.-F.

Biehs, S.-A.

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

S.-A. Biehs and G. Agarwal, “Dynamical quantum theory of heat transfer between plasmonic nanosystems,” J. Opt. Soc. Am. B 30(3), 700–707 (2013).
[Crossref]

Boehm, G.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Bois, P.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Bouchon, P.

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

Bravo-Abad, J.

Breuer, H.

H. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University, 2002).

Brucoli, G.

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
[Crossref]

Buddhiraju, S.

S. Buddhiraju, P. Santhanam, and S. Fan, “Thermodynamic limits of energy harvesting from outgoing thermal radiation,” Proc. Natl. Acad. Sci. 115(16), E3609–E3615 (2018).
[Crossref]

Campagnola, P.

P. Campagnola and L. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003).
[Crossref]

Carletti, L.

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref]

Chang, D.

D. Chang, V. Vuletić, and M. Lukin, “Quantum nonlinear optics–photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

Chen, C.

T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
[Crossref]

Chen, G.

C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
[Crossref]

Chen, P.-Y.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Cuevas, J.

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

Cui, L.

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

De Angelis, C.

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref]

DeLacy, B. G.

Demmerle, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Drummond, P.

P. Drummond and M. Hillery, The quantum theory of nonlinear optics (Cambridge University, 2014).

Du, W.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Duchesne, D.

Dykman, M.

M. Dykman and M. Krivoglaz, “Spectral distribution of nonlinear oscillators with nonlinear friction due to a medium,” Phys. Status Solidi B 68(1), 111–123 (1975).
[Crossref]

Fan, S.

M. Minkov, D. Gerace, and S. Fan, “Doubly resonant χ(2) nonlinear photonic crystal cavity based on a bound state in the continuum,” Optica 6(8), 1039–1045 (2019).
[Crossref]

L. Zhu, Y. Guo, and S. Fan, “Theory of many-body radiative heat transfer without the constraint of reciprocity,” Phys. Rev. B 97(9), 094302 (2018).
[Crossref]

S. Buddhiraju, P. Santhanam, and S. Fan, “Thermodynamic limits of energy harvesting from outgoing thermal radiation,” Proc. Natl. Acad. Sci. 115(16), E3609–E3615 (2018).
[Crossref]

W. Li and S. Fan, “Nanophotonic control of thermal radiation for energy applications,” Opt. Express 26(12), 15995–16021 (2018).
[Crossref]

S. Fan, “Thermal photonics and energy applications,” Joule 1(2), 264–273 (2017).
[Crossref]

D. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. 114(17), 4336–4341 (2017).
[Crossref]

C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
[Crossref]

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

J. Bravo-Abad, S. Fan, S. Johnson, J. Joannopoulos, and M. Soljacic, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25(9), 2539–2546 (2007).
[Crossref]

Feist, J.

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Fernández-Domínguez, A.

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

Fernández-Hurtado, V.

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Fiore, A.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Fu, Y.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

García-Vidal, F.

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Gerace, D.

Gieseler, J.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

Gong, S.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Greffet, J.-J.

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
[Crossref]

Guo, Y.

L. Zhu, Y. Guo, and S. Fan, “Theory of many-body radiative heat transfer without the constraint of reciprocity,” Phys. Rev. B 97(9), 094302 (2018).
[Crossref]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Hashemi, H.

Hatami, F.

He, S.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Heinz, T.

T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
[Crossref]

Hillery, M.

P. Drummond and M. Hillery, The quantum theory of nonlinear optics (Cambridge University, 2014).

Hsu, C. W.

Imamoglu, A.

H. Schmidt and A. Imamoglu, “Giant kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996).
[Crossref]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Jacob, Z.

L.-P. Yang and Z. Jacob, “Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions,” Opt. Express 27(8), 10482–10494 (2019).
[Crossref]

C. Khandekar and Z. Jacob, “Thermal spin photonics in the near-field of nonreciprocal media,” New J. Phys. 21(10), 103030 (2019).
[Crossref]

C. Khandekar and Z. Jacob, “Circularly polarized thermal radiation from nonequilibrium coupled antennas,” Phys. Rev. Appl. 12(1), 014053 (2019).
[Crossref]

L.-P. Yang and Z. Jacob, “Engineering first-order quantum phase transitions for weak signal detection,” arXiv preprint arXiv:1905.07420 (2019).

Jeong, W.

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Jin, W.

C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
[Crossref]

W. Jin, A. Polimeridis, and A. Rodriguez, “Temperature control of thermal radiation from composite bodies,” Phys. Rev. B 93(12), 121403 (2016).
[Crossref]

S. Molesky, W. Jin, P. Venkataram, and A. Rodriguez, “Bounds on absorption and thermal radiation for arbitrary objects,” arXiv:1907.04418 (2019).

S. Molesky, P. Venkataram, W. Jin, and A. Rodriguez, “Fundamental limits to radiative heat transfer: theory,” arXiv:1907.03000 (2019).

Joannopoulos, J.

N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
[Crossref]

A. Karalis and J. Joannopoulos, “Temporal coupled-mode theory model for resonant near-field thermophotovoltaics,” Appl. Phys. Lett. 107(14), 141108 (2015).
[Crossref]

J. Bravo-Abad, S. Fan, S. Johnson, J. Joannopoulos, and M. Soljacic, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25(9), 2539–2546 (2007).
[Crossref]

A. Rodriguez, M. Soljačić, J. Joannopoulos, and S. Johnson, “χ (2) and χ (3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
[Crossref]

C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
[Crossref]

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic crystals: Molding the flow of light (Princeton University, 2011).

Joannopoulos, J. D.

Johnson, S.

Johnson, S. G.

Jones, A.

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Kaminer, I.

N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
[Crossref]

Karalis, A.

A. Karalis and J. Joannopoulos, “Temporal coupled-mode theory model for resonant near-field thermophotovoltaics,” Appl. Phys. Lett. 107(14), 141108 (2015).
[Crossref]

Kats, M.

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Khandekar, C.

C. Khandekar and Z. Jacob, “Circularly polarized thermal radiation from nonequilibrium coupled antennas,” Phys. Rev. Appl. 12(1), 014053 (2019).
[Crossref]

C. Khandekar and Z. Jacob, “Thermal spin photonics in the near-field of nonreciprocal media,” New J. Phys. 21(10), 103030 (2019).
[Crossref]

C. Khandekar, R. Messina, and A. Rodriguez, “Near-field refrigeration and tunable heat exchange through four-wave mixing,” AIP Adv. 8(5), 055029 (2018).
[Crossref]

C. Khandekar and A. Rodriguez, “Near-field thermal upconversion and energy transfer through a kerr medium,” Opt. Express 25(19), 23164–23180 (2017).
[Crossref]

C. Khandekar, Z. Lin, and A. Rodriguez, “Thermal radiation from optically driven kerr (χ (3)) photonic cavities,” Appl. Phys. Lett. 106(15), 151109 (2015).
[Crossref]

C. Khandekar, A. Pick, S. Johnson, and A. Rodriguez, “Radiative heat transfer in nonlinear kerr media,” Phys. Rev. B 91(11), 115406 (2015).
[Crossref]

Kim, K.

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Kivshar, Y.

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref]

Koshelev, K.

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref]

Kozierowski, M.

M. Kozierowski and R. Tanaś, “Quantum fluctuations in second-harmonic light generation,” Opt. Commun. 21(2), 229–231 (1977).
[Crossref]

Krasnok, A.

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Krivoglaz, M.

M. Dykman and M. Krivoglaz, “Spectral distribution of nonlinear oscillators with nonlinear friction due to a medium,” Phys. Status Solidi B 68(1), 111–123 (1975).
[Crossref]

Krüger, M.

H. Soo and M. Krüger, “Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium,” Phys. Rev. B 97(4), 045412 (2018).
[Crossref]

Landau, L.

L. Landau and E. Lifshitz, “Course of theoretical physics, volume 5,” Publ. Butterworth-Heinemann 3 (1980).

Lee, J.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Lee, W.

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Li, W.

Liang, X.

Lifshitz, E.

L. Landau and E. Lifshitz, “Course of theoretical physics, volume 5,” Publ. Butterworth-Heinemann 3 (1980).

Lin, Z.

C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
[Crossref]

Z. Lin, X. Liang, M. Lončar, S. Johnson, and A. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3(3), 233–238 (2016).
[Crossref]

C. Khandekar, Z. Lin, and A. Rodriguez, “Thermal radiation from optically driven kerr (χ (3)) photonic cavities,” Appl. Phys. Lett. 106(15), 151109 (2015).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22609–22615 (2009).
[Crossref]

Loew, L.

P. Campagnola and L. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003).
[Crossref]

Loncar, M.

Lu, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Lukin, M.

D. Chang, V. Vuletić, and M. Lukin, “Quantum nonlinear optics–photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

Luo, C.

C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
[Crossref]

Ma, Y.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Mao, L.

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Marquier, F.

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
[Crossref]

Masselink, W.

McArdle, P.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

McClintock, P.

F. Moss and P. McClintock, Noise in nonlinear dynamical systems, vol. 2 (Cambridge University, 1989).

Meade, R.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic crystals: Molding the flow of light (Princeton University, 2011).

Messina, R.

C. Khandekar, R. Messina, and A. Rodriguez, “Near-field refrigeration and tunable heat exchange through four-wave mixing,” AIP Adv. 8(5), 055029 (2018).
[Crossref]

Meyhofer, E.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Milburn, G.

D. Walls and G. Milburn, Quantum optics (Springer, 2008).

Miller, D.

D. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. 114(17), 4336–4341 (2017).
[Crossref]

Miller, O. D.

Minkov, M.

Mittapally, R.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

Molesky, S.

S. Molesky, P. Venkataram, W. Jin, and A. Rodriguez, “Fundamental limits to radiative heat transfer: theory,” arXiv:1907.03000 (2019).

S. Molesky, W. Jin, P. Venkataram, and A. Rodriguez, “Bounds on absorption and thermal radiation for arbitrary objects,” arXiv:1907.04418 (2019).

Moss, F.

F. Moss and P. McClintock, Noise in nonlinear dynamical systems, vol. 2 (Cambridge University, 1989).

Nagle, J.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Narayanaswamy, A.

C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
[Crossref]

Nechepurenko, I.

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Novotny, L.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

Otey, C.

C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
[Crossref]

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

Peres, A.

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77(8), 1413–1415 (1996).
[Crossref]

Pernice, W.

W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
[Crossref]

Petruccione, F.

H. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University, 2002).

Pick, A.

C. Khandekar, A. Pick, S. Johnson, and A. Rodriguez, “Radiative heat transfer in nonlinear kerr media,” Phys. Rev. B 91(11), 115406 (2015).
[Crossref]

Polimeridis, A.

W. Jin, A. Polimeridis, and A. Rodriguez, “Temperature control of thermal radiation from composite bodies,” Phys. Rev. B 93(12), 121403 (2016).
[Crossref]

Polimeridis, A. G.

Qazilbash, M. M.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

Quidant, R.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

Reddy, P.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Reid, M.

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Reid, M. H.

Ricard, D.

T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
[Crossref]

Rivera, N.

N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
[Crossref]

Rivoire, K.

Rodriguez, A.

C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
[Crossref]

C. Khandekar, R. Messina, and A. Rodriguez, “Near-field refrigeration and tunable heat exchange through four-wave mixing,” AIP Adv. 8(5), 055029 (2018).
[Crossref]

C. Khandekar and A. Rodriguez, “Near-field thermal upconversion and energy transfer through a kerr medium,” Opt. Express 25(19), 23164–23180 (2017).
[Crossref]

W. Jin, A. Polimeridis, and A. Rodriguez, “Temperature control of thermal radiation from composite bodies,” Phys. Rev. B 93(12), 121403 (2016).
[Crossref]

Z. Lin, X. Liang, M. Lončar, S. Johnson, and A. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3(3), 233–238 (2016).
[Crossref]

C. Khandekar, Z. Lin, and A. Rodriguez, “Thermal radiation from optically driven kerr (χ (3)) photonic cavities,” Appl. Phys. Lett. 106(15), 151109 (2015).
[Crossref]

C. Khandekar, A. Pick, S. Johnson, and A. Rodriguez, “Radiative heat transfer in nonlinear kerr media,” Phys. Rev. B 91(11), 115406 (2015).
[Crossref]

Z.-F. Bi, A. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ (2) microring resonators,” Opt. Express 20(7), 7526–7543 (2012).
[Crossref]

A. Rodriguez, M. Soljačić, J. Joannopoulos, and S. Johnson, “χ (2) and χ (3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
[Crossref]

S. Molesky, W. Jin, P. Venkataram, and A. Rodriguez, “Bounds on absorption and thermal radiation for arbitrary objects,” arXiv:1907.04418 (2019).

S. Molesky, P. Venkataram, W. Jin, and A. Rodriguez, “Fundamental limits to radiative heat transfer: theory,” arXiv:1907.03000 (2019).

Rosencher, E.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Rosolen, G.

N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
[Crossref]

Rytov, S.

S. Rytov, “Theory of electric fluctuations and thermal radiation,” AFCRC-TR 59, 162 (1959).

Sadat, S.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

Sandhu, S.

C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
[Crossref]

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

Santhanam, P.

S. Buddhiraju, P. Santhanam, and S. Fan, “Thermodynamic limits of energy harvesting from outgoing thermal radiation,” Proc. Natl. Acad. Sci. 115(16), E3609–E3615 (2018).
[Crossref]

Schmidt, H.

Schuck, C.

W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
[Crossref]

Scully, M.

M. Scully and M. Zubairy, Quantum optics (AAPT, 1999).

Shan Luk, T.

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

Shen, Y.

T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
[Crossref]

Sinclair, M.

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

Sitawarin, C.

C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
[Crossref]

Soljacic, M.

Song, B.

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Soo, H.

H. Soo and M. Krüger, “Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium,” Phys. Rev. B 97(4), 045412 (2018).
[Crossref]

Su, Y.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Tanas, R.

M. Kozierowski and R. Tanaś, “Quantum fluctuations in second-harmonic light generation,” Opt. Commun. 21(2), 229–231 (1977).
[Crossref]

Tang, H.

W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
[Crossref]

Tervo, E.

E. Tervo, E. Bagherisereshki, and Z. Zhang, “Near-field radiative thermoelectric energy converters: a review,” Front. Energy 12(1), 5–21 (2018).
[Crossref]

Thompson, D.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

Tymchenko, M.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Van Kampen, N.

N. Van Kampen, Stochastic processes in physics and chemistry, vol. 1 (Elsevier, 1992).

Venkataram, P.

S. Molesky, P. Venkataram, W. Jin, and A. Rodriguez, “Fundamental limits to radiative heat transfer: theory,” arXiv:1907.03000 (2019).

S. Molesky, W. Jin, P. Venkataram, and A. Rodriguez, “Bounds on absorption and thermal radiation for arbitrary objects,” arXiv:1907.04418 (2019).

Vinter, B.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Vuckovic, J.

Vuletic, V.

D. Chang, V. Vuletić, and M. Lukin, “Quantum nonlinear optics–photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

Walls, D.

D. Walls and G. Milburn, Quantum optics (Springer, 2008).

Wang, K.-M.

Winn, J.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic crystals: Molding the flow of light (Princeton University, 2011).

Wu, S.

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Xiao, Y.

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Xing, Z.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

Xiong, C.

W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
[Crossref]

Xu, X.

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Yang, J.

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Yang, L.-P.

L.-P. Yang and Z. Jacob, “Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions,” Opt. Express 27(8), 10482–10494 (2019).
[Crossref]

L.-P. Yang and Z. Jacob, “Engineering first-order quantum phase transitions for weak signal detection,” arXiv preprint arXiv:1905.07420 (2019).

Yao, W.

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Zhang, C.

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Zhang, Z.

E. Tervo, E. Bagherisereshki, and Z. Zhang, “Near-field radiative thermoelectric energy converters: a review,” Front. Energy 12(1), 5–21 (2018).
[Crossref]

Zhu, L.

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

L. Zhu, Y. Guo, and S. Fan, “Theory of many-body radiative heat transfer without the constraint of reciprocity,” Phys. Rev. B 97(9), 094302 (2018).
[Crossref]

D. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. 114(17), 4336–4341 (2017).
[Crossref]

C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
[Crossref]

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

Zubairy, M.

M. Scully and M. Zubairy, Quantum optics (AAPT, 1999).

AFCRC-TR (1)

S. Rytov, “Theory of electric fluctuations and thermal radiation,” AFCRC-TR 59, 162 (1959).

AIP Adv. (1)

C. Khandekar, R. Messina, and A. Rodriguez, “Near-field refrigeration and tunable heat exchange through four-wave mixing,” AIP Adv. 8(5), 055029 (2018).
[Crossref]

Appl. Phys. Lett. (4)

C. Khandekar, Z. Lin, and A. Rodriguez, “Thermal radiation from optically driven kerr (χ (3)) photonic cavities,” Appl. Phys. Lett. 106(15), 151109 (2015).
[Crossref]

L. Zhu, S. Sandhu, C. Otey, S. Fan, M. Sinclair, and T. Shan Luk, “Temporal coupled mode theory for thermal emission from a single thermal emitter supporting either a single mode or an orthogonal set of modes,” Appl. Phys. Lett. 102(10), 103104 (2013).
[Crossref]

A. Karalis and J. Joannopoulos, “Temporal coupled-mode theory model for resonant near-field thermophotovoltaics,” Appl. Phys. Lett. 107(14), 141108 (2015).
[Crossref]

W. Pernice, C. Xiong, C. Schuck, and H. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012).
[Crossref]

Front. Energy (1)

E. Tervo, E. Bagherisereshki, and Z. Zhang, “Near-field radiative thermoelectric energy converters: a review,” Front. Energy 12(1), 5–21 (2018).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

C. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transfer 132, 3–11 (2014).
[Crossref]

Joule (1)

S. Fan, “Thermal photonics and energy applications,” Joule 1(2), 264–273 (2017).
[Crossref]

Nano Lett. (1)

S. Wu, L. Mao, A. Jones, W. Yao, C. Zhang, and X. Xu, “Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene,” Nano Lett. 12(4), 2032–2036 (2012).
[Crossref]

Nat. Biotechnol. (1)

P. Campagnola and L. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003).
[Crossref]

Nat. Commun. (1)

J. Yang, W. Du, Y. Su, Y. Fu, S. Gong, S. He, and Y. Ma, “Observing of the super-planckian near-field thermal radiation between graphene sheets,” Nat. Commun. 9(1), 4033 (2018).
[Crossref]

Nat. Mater. (1)

D. Baranov, Y. Xiao, I. Nechepurenko, A. Krasnok, A. Alù, and M. Kats, “Nanophotonic engineering of far-field thermal emitters,” Nat. Mater. 18(9), 920–930 (2019).
[Crossref]

Nat. Photonics (1)

D. Chang, V. Vuletić, and M. Lukin, “Quantum nonlinear optics–photon by photon,” Nat. Photonics 8(9), 685–694 (2014).
[Crossref]

Nat. Phys. (1)

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

Nature (3)

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

D. Thompson, L. Zhu, R. Mittapally, S. Sadat, Z. Xing, P. McArdle, M. M. Qazilbash, P. Reddy, and E. Meyhofer, “Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit,” Nature 561(7722), 216–221 (2018).
[Crossref]

K. Kim, B. Song, V. Fernández-Hurtado, W. Lee, W. Jeong, L. Cui, D. Thompson, J. Feist, M. Reid, F. García-Vidal, E. Meyhofer, and P. Reddy, “Radiative heat transfer in the extreme near field,” Nature 528(7582), 387–391 (2015).
[Crossref]

New J. Phys. (1)

C. Khandekar and Z. Jacob, “Thermal spin photonics in the near-field of nonreciprocal media,” New J. Phys. 21(10), 103030 (2019).
[Crossref]

Opt. Commun. (2)

M. Kozierowski and R. Tanaś, “Quantum fluctuations in second-harmonic light generation,” Opt. Commun. 21(2), 229–231 (1977).
[Crossref]

G. Agarwal, “Quantum theory of second harmonic generation,” Opt. Commun. 1(3), 132–134 (1969).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Optica (2)

Photonics Res. (1)

C. Sitawarin, W. Jin, Z. Lin, and A. Rodriguez, “Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion,” Photonics Res. 6(5), B82–B89 (2018).
[Crossref]

Phys. Rev. Appl. (1)

C. Khandekar and Z. Jacob, “Circularly polarized thermal radiation from nonequilibrium coupled antennas,” Phys. Rev. Appl. 12(1), 014053 (2019).
[Crossref]

Phys. Rev. B (6)

W. Jin, A. Polimeridis, and A. Rodriguez, “Temperature control of thermal radiation from composite bodies,” Phys. Rev. B 93(12), 121403 (2016).
[Crossref]

L. Zhu, Y. Guo, and S. Fan, “Theory of many-body radiative heat transfer without the constraint of reciprocity,” Phys. Rev. B 97(9), 094302 (2018).
[Crossref]

C. Khandekar, A. Pick, S. Johnson, and A. Rodriguez, “Radiative heat transfer in nonlinear kerr media,” Phys. Rev. B 91(11), 115406 (2015).
[Crossref]

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

V. Fernández-Hurtado, A. Fernández-Domínguez, J. Feist, F. García-Vidal, and J. Cuevas, “Super-planckian far-field radiative heat transfer,” Phys. Rev. B 97(4), 045408 (2018).
[Crossref]

H. Soo and M. Krüger, “Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium,” Phys. Rev. B 97(4), 045412 (2018).
[Crossref]

Phys. Rev. Lett. (5)

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77(8), 1413–1415 (1996).
[Crossref]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

C. Luo, A. Narayanaswamy, G. Chen, and J. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. 93(21), 213905 (2004).
[Crossref]

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref]

T. Heinz, C. Chen, D. Ricard, and Y. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48(7), 478–481 (1982).
[Crossref]

Phys. Rev. X (1)

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local kirchhoff law,” Phys. Rev. X 8(2), 021008 (2018).
[Crossref]

Phys. Status Solidi B (1)

M. Dykman and M. Krivoglaz, “Spectral distribution of nonlinear oscillators with nonlinear friction due to a medium,” Phys. Status Solidi B 68(1), 111–123 (1975).
[Crossref]

Proc. Natl. Acad. Sci. (3)

S. Buddhiraju, P. Santhanam, and S. Fan, “Thermodynamic limits of energy harvesting from outgoing thermal radiation,” Proc. Natl. Acad. Sci. 115(16), E3609–E3615 (2018).
[Crossref]

N. Rivera, G. Rosolen, J. Joannopoulos, I. Kaminer, and M. Soljačić, “Making two-photon processes dominate one-photon processes using mid-ir phonon polaritons,” Proc. Natl. Acad. Sci. 114(52), 13607–13612 (2017).
[Crossref]

D. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. 114(17), 4336–4341 (2017).
[Crossref]

Science (1)

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271(5246), 168–173 (1996).
[Crossref]

Other (12)

F. Moss and P. McClintock, Noise in nonlinear dynamical systems, vol. 2 (Cambridge University, 1989).

N. Van Kampen, Stochastic processes in physics and chemistry, vol. 1 (Elsevier, 1992).

S. Molesky, W. Jin, P. Venkataram, and A. Rodriguez, “Bounds on absorption and thermal radiation for arbitrary objects,” arXiv:1907.04418 (2019).

S. Molesky, P. Venkataram, W. Jin, and A. Rodriguez, “Fundamental limits to radiative heat transfer: theory,” arXiv:1907.03000 (2019).

D. Walls and G. Milburn, Quantum optics (Springer, 2008).

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic crystals: Molding the flow of light (Princeton University, 2011).

L.-P. Yang and Z. Jacob, “Engineering first-order quantum phase transitions for weak signal detection,” arXiv preprint arXiv:1905.07420 (2019).

P. Drummond and M. Hillery, The quantum theory of nonlinear optics (Cambridge University, 2014).

M. Scully and M. Zubairy, Quantum optics (AAPT, 1999).

H. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University, 2002).

L. Landau and E. Lifshitz, “Course of theoretical physics, volume 5,” Publ. Butterworth-Heinemann 3 (1980).

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. We rigorously analyze thermal radiation from a resonant system depicted in the inset. It is comprised of two resonators of frequencies $\omega _1$ and $\omega _2\approx 2\omega _1$ , and contains a $\chi ^{(2)}$ nonlinear medium. The resonantly enhanced nonlinear interaction will modify the Planck’s blackbody distribution, potentially allowing enhancement of thermal emission at wavelengths where it is otherwise exponentially suppressed.
Fig. 2.
Fig. 2. Steady state mean photon numbers ( $\langle n_{\omega _j} \rangle$ ) of nonlinearly coupled resonators ( $\kappa \neq 0$ ) are equal to equilibrium mean photon numbers ( $\bar {n}_{\omega _j,T}$ ) of bath oscillators ( $T_d =T_e =T$ ) irrespective of nonlinear coupling, decay rates and temperatures (higher or lower mean photon numbers). The steady state density matrix is diagonal and same as in the linear regime given by Eq. (11). The inset demonstrates all energy flux rates that balance each other at thermal equilibrium.
Fig. 3.
Fig. 3. (a) Far-field thermal emission from a doubly resonant nanophotonic system at temperature $T_d=600$ K into external environment at temperature $T_e=0$ K. Various decay/coupling channels are shown as arrows with their directionalities indicating the flow of energy in the regime $T_d \gg T_e$ . Red arrows indicate favorable channels for nonlinear-upconversion-induced enhancement of thermal emission at $\omega _2$ . We consider representative normalized decay rates shown in the table (assuming $\gamma = 10^{-5}\omega _1$ , same as in Fig. 2) to explore thermal-radiation features in (b,d,e). Figures in (b) demonstrate the nonlinear-upconversion-induced enhancement of thermal emission at $\omega _2$ (left figure) and the associated suppression of thermal emission at $\omega _1$ (right figure), as anticipated by the schematic of this mechanism in Fig. 1. Figure(c) compares the maximum achievable enhancements in linear versus nonlinear regimes, demonstrating an enhancement factor of 4 beyond the standard blackbody limit for linear systems. Figure (d) shows that the statistics of intensity fluctuations characterized by $g^{(2)}(0)$ are modified at frequencies $\omega _2$ (left figures) and $\omega _1$ (right figures).(e) Because of the nonlinear coupling, the resulting thermal emission also exhibits correlations between the intensities [ $I(\omega )$ ] collected at frequencies $\omega _1$ and $\omega _2$ . The figures indicate that these nonlinear effects are large when the favorable channels $\gamma _{1d},\gamma _{2e},\kappa$ (red arrows) dominate the spurious channels $\gamma _{1e},\gamma _{2d}$ (black arrows).
Fig. 4.
Fig. 4. Steady state mean photon numbers $\langle n_j \rangle$ obtained using semi-classical coupled mode theory are compared with the quantum theory for the exact same system parameters as analyzed in Fig. 2 of the main text. Evidently, the semi-classical theory leads to significant deviation from thermal equilibrium for finite nonlinear coupling and despite perfect frequency matching ( $\omega _2=2\omega _1$ ).

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

H sys = ω 1 a 1 a 1 + ω 2 a 2 a 2 + ( κ a 1 2 a 2 + κ a 1 2 a 2 )
H = H sys + k , l = [ d , e ] j = [ 1 , 2 ] g k , l , j [ b k , l a j + b k , l a j ] + ω k b k , l b k , l
ρ ˙ = i [ H sys , ρ ] + l = [ d , e ] j = [ 1 , 2 ] [ γ j , l ( n ¯ ω j , T l + 1 ) [ 2 a j ρ a j a j a j ρ ρ a j a j ] + γ j , l n ¯ ω j , T l [ 2 a j ρ a j a j a j ρ ρ a j a j ] ]
d d t a 1 a 1 = 2 [ i κ a 1 2 a 2 i κ a 1 2 a 2 ] l = [ d , e ] 2 γ 1 , l [ a 1 a 1 n ¯ ω 1 , T l ]
d d t a 2 a 2 = [ i κ a 1 2 a 2 i κ a 1 2 a 2 ] l = [ d , e ] 2 γ 2 , l [ a 2 a 2 n ¯ ω 2 , T l ]
P j l = 2 γ j , l ω j [ a j a j n ¯ ω j , T l ]
P 1 2 = 2 ω 1 [ i κ a 1 2 a 2 i κ a 1 2 a 2 ]
P 2 1 = ω 2 [ i κ a 1 2 a 2 i κ a 1 2 a 2 ]
P j far-field = 2 γ j , e ω j [ a j a j n ¯ ω j , T e ]
| ρ ) = n 1 = 0 m 1 = 0 n 2 = 0 m 2 = 0 ρ n 1 , m 1 ; n 2 , m 2 | n 1 , m 1 ; n 2 , m 2 )
ρ n , m ; n , m = n ¯ ω 1 , T n n ¯ ω 2 , T m ( n ¯ ω 1 , T + 1 ) n + 1 ( n ¯ ω 2 , T + 1 ) m + 1
a ˙ 1 = [ i ω 1 γ 1 ] a 1 i β 1 a 2 a 1 + D 1 ξ 1 d + 2 γ 1 e ξ 1 e
a ˙ 2 = [ i ω 2 γ 2 ] a 2 i β 2 a 1 2 + D 2 ξ 2 d + 2 γ 2 e ξ 2 e
ξ j l ( ω ) ξ j l ( ω ) = Θ ( ω j , T l ) δ ( ω ω )
β 1 = ω 1 2 ϵ 0 E i ( ω 1 ) χ i j k ( 2 ) [ E j ( ω 2 ) E k ( ω 1 ) + E j ( ω 1 ) E k ( ω 2 ) ] ( ϵ ω ) ω | E ( ω 2 ) | 2 ( ( ϵ ω ) ω | E ( ω 1 ) | 2 ) β 2 = ω 2 2 ϵ 0 E i ( ω 2 ) χ i j k ( 2 ) E j ( ω 1 ) E k ( ω 1 ) ( ϵ ω ) ω | E ( ω 2 ) | 2 ( ( ϵ ω ) ω | E ( ω 1 ) | 2 )
P 1 2 = i β 1 a 2 a 1 2 i β 1 a 2 a 1 2
P 2 1 = i β 2 a 2 a 1 2 i β 2 a 2 a 1 2
κ = β ω 1 2
d P d t = j = [ 1 , 2 ] a j K a j P a j K a j P + 1 2 2 a 1 a 1 K a 1 a 1 P
K a 1 = [ i ω 1 γ 1 ] a 1 i β a 2 a 1 , K a 1 = K a 1 K a 2 = [ i ω 2 γ 2 ] a 2 i β a 1 2 , K a 2 = K a 2 K a j a j = K a j a j = D j 2 Θ ( ω j , T d ) + 2 γ j e Θ ( ω j , T e ) , K a j a j = K a j a j = 0 , cross terms K a 1 a 2 = K a 2 a 1 = K a 1 a 2 = K a 2 a 1 = 0

Metrics