## Near-field radiative transfer between two unequal sized spheres with large size disparities |

Optics Express, Vol. 22, Issue 12, pp. 14473-14492 (2014)

http://dx.doi.org/10.1364/OE.22.014473

Enhanced HTML Acrobat PDF (1730 KB)

### Abstract

We compute near-field radiative transfer between two spheres of unequal radii *R*_{1} and *R*_{2} such that *R*_{2} ≲ 40*R*_{1}. For *R*_{2} = 40*R*_{1}, the smallest gap to which we have been able to compute radiative transfer is *d* = 0.016*R*_{1}. To accomplish these computations, we have had to modify existing methods for computing near-field radiative transfer between two spheres in the following ways: (1) exact calculations of coefficients of vector translation theorem are replaced by approximations valid for the limit *d* ≪ *R*_{1}, and (2) recursion relations for a normalized form of translation coefficients are derived which enable us to replace computations of spherical Bessel and Hankel functions by computations of ratios of spherical Bessel or spherical Hankel functions. The results are then compared with the predictions of the modified proximity approximation.

© 2014 Optical Society of America

**OCIS Codes**

(030.5620) Coherence and statistical optics : Radiative transfer

(240.6690) Optics at surfaces : Surface waves

(260.2160) Physical optics : Energy transfer

(290.4020) Scattering : Mie theory

(290.4210) Scattering : Multiple scattering

(290.6815) Scattering : Thermal emission

**ToC Category:**

Physical Optics

**History**

Original Manuscript: March 24, 2014

Manuscript Accepted: May 27, 2014

Published: June 5, 2014

**Citation**

Karthik Sasihithlu and Arvind Narayanaswamy, "Near-field radiative transfer between two unequal sized spheres with large size disparities," Opt. Express **22**, 14473-14492 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-12-14473

Sort: Year | Journal | Reset

### References

- A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82, 3544–3546 (2003). [CrossRef]
- S. Basu, Z. M. Zhang, and C. J. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33(13), 1203–1232 (2009). [CrossRef]
- O. Ilic, M. Jablan, J. D. Joannopoulos, I. Celanovic, and M. Soljačić, “Overcoming the black body limit in plasmonic and graphene near-field thermophotovoltaic systems,” Opt. Express 20(103), A366–A384 (2012). [CrossRef] [PubMed]
- M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. Appl. Phys. 100(6), 063704 (2006). [CrossRef]
- C. Otey, W.-T. Lau, and S. Fan, “Thermal rectification through vacuum,” Phys. Rev. Lett. 104(15), 154301 (2010). [CrossRef] [PubMed]
- B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Confinement of infrared radiation to nanometer scales through metallic slit arrays,” J. Quant. Spectrosc. Radiat. Transfer 109(4), 608–619 (2008). [CrossRef]
- W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. J. Gokemeijer, and Y. T. Hsia, “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. Photon. 3(4), 220–224 (2009). [CrossRef]
- Y. D. Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006). [CrossRef] [PubMed]
- B. Guha, C. Otey, C. B. Poitras, S. Fan, and M. Lipson, “Near-field radiative cooling of nanostructuresm,” Nano Lett. 12(9), 4546–4550 (2012). [CrossRef] [PubMed]
- S. M. Rytov, “Theory of electric fluctuations and thermal radiation,” Air Force Cambridge Research Center, Bedford, MA (1959).
- D. Polder and M. V. Hove, “Theory of radiative heat transfer between closely spaced bodies,” Phys. Rev. B 4, 3303–3314 (1971). [CrossRef]
- J. J. Loomis and H. J. Maris, “Theory of heat transfer by evanescent electromagnetic waves,” Phys. Rev. B 50, 18517–18524 (1994). [CrossRef]
- E. G. Cravalho, C. L. Tien, and R. P. Caren, “Effect of small spacings on radiative transfer between two dielectrics,” J. Heat Transfer 89, 351–358 (1967). [CrossRef]
- J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative transfer at nanometric distances,” Microscale Thermophys. Eng. 6, 209–222 (2002). [CrossRef]
- J. B. Pendry, “Radiative exchange of heat between nanostructures,” J. Phys.: Condens. Matter 11, 6621 (1999).
- C. H. Park, H. A. Haus, and M. S. Weinberg, “Proximity-enhanced thermal radiation,” J. Phys. D: Appl. Phys 35(21), 2857–2863 (2002). [CrossRef]
- A. I. Volokitin and B. N. J. Persson, “Radiative heat transfer between nanostructures,” Phys. Rev. B 63, 205404 (2001). [CrossRef]
- G. Domingues, S. Volz, K. Joulain, and J.-J. Greffet, “Heat transfer between two nanoparticles through near-field interaction,” Phys. Rev. Lett. 94(8), 085901 (2005). [CrossRef] [PubMed]
- J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Nanoscale radiative heat transfer between a small particle and a plane surface,” Appl. Phys. Lett. 78, 2931–2933 (2001). [CrossRef]
- A. Narayanaswamy and G. Chen, “Thermal near-field radiative transfer between two spheres,” Phys. Rev. B 77(7), 075125 (2008). [CrossRef]
- C. Otey and S. Fan, “Numerically exact calculation of electromagnetic heat transfer between a dielectric sphere and plate,” Phys. Rev. B 84, 245431 (2011). [CrossRef]
- M. Krüger, T. Emig, and M. Kardar, “Nonequilibrium electromagnetic fluctuations: Heat transfer and interactions,” Phys. Rev. Lett. 106(21), 210404 (2011). [CrossRef] [PubMed]
- A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries,” Phys. Rev. B 86(22), 220302 (2012). [CrossRef]
- R. Messina and M. Antezza, “Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies,” Phys. Rev. A 84(4), 042102 (2011). [CrossRef]
- A. Narayanaswamy and Y. Zheng, “A Green’s function formalism of energy and momentum transfer in fluctuational electrodynamics,” J. Quant. Spectrosc. Radiat. Transfer 132, 12–21 (2014). [CrossRef]
- P. Ben-Abdallah, S. Biehs, and K. Joulain, “Many-body radiative heat transfer theory,” Phys. Rev. Lett., 107(11), 114301 (2011). [CrossRef] [PubMed]
- S. Shen, A. Narayanaswamy, and G. Chen, “Surface phonon polaritons mediated energy transfer between nanoscale gaps,” Nano Lett. 9(8), 2909–2913 (2009). [CrossRef] [PubMed]
- E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, “Radiative heat transfer at the nanoscale,” Nat. Photon. 3(9), 514–517 (2009). [CrossRef]
- P. J. van Zwol, L. Ranno, and J. Chevrier, “Tuning near field radiative heat flux through surface excitations with a metal insulator transition,” Phys. Rev. Lett. 108(23), 234301 (2012). [CrossRef] [PubMed]
- S. Shen, A. Mavrokefalos, P. Sambegoro, and G. Chen, “Nanoscale thermal radiation between two gold surfaces,” Appl. Phys. Lett. 100(23), 233114 (2012). [CrossRef]
- A. Narayanaswamy, S. Shen, and G. Chen, “Near-field radiative heat transfer between a sphere and a substrate,” Phys. Rev. B 78(11), 115303 (2008). [CrossRef]
- W. M. Hirsch, A. Kraft, M. T. Hirsch, J. Parisi, and A. Kittel, “Heat transfer in ultrahigh vacuum scanning thermal microscopy,” J. Vac. Sci. Technol. A 17(4), 1205–1210 (1999). [CrossRef]
- A. Kittel, W. Müller-Hirsch, J. Parisi, S. A. Biehs, D. Reddig, and M. Holthaus, “Near-field heat transfer in a scanning thermal microscope,” Phys. Rev. Lett. 95(22), 224301 (2005). [CrossRef] [PubMed]
- L. Worbes, D. Hellmann, and A. Kittel, “Enhanced near-field heat flow of a monolayer dielectric island,” Phys. Rev. Lett. 110(13), 134302 (2013). [CrossRef] [PubMed]
- A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68(2), 248–263 (1980). [CrossRef]
- R. E. Collin, Field Theory of Guided Waves (IEEE Press, 1991), Vol. 2.
- L. Landau, E. M. Lifšic, J. B. Sykes, J. S. Bell, M. J. Kearsley, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1960).
- R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29(1), 255 (1966). [CrossRef]
- U. M. B. Marconi, A. Puglisi, L. Rondoni, and A. Vulpiani, “Fluctuation–dissipation: response theory in statistical physics,” Phys. Rep. 461(4), 111–195 (2008). [CrossRef]
- J. H. Bruning and Y. T. Lo, “Multiple scattering by spheres,” Antenna Laboratory Report No.69(5) (1969).
- W. C. Chew, “Derivation of the vector addition theorem,” Microwave Opt. Technol. Lett. 3, 256–260 (1990). [CrossRef]
- W. C. Chew, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Wave 7, 651–665 (1993). [CrossRef]
- K. Sasihithlu and A. Narayanaswamy, “Proximity effects in radiative heat transfer,” Phys. Rev. B 83(16), 161406 (2011). [CrossRef]
- J. Błocki, J. Randrup, W. J. Światecki, and C. F. Tsang, “Proximity forces,” Ann. Phys. 105(2), 427–462 (1977). [CrossRef]
- S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6 to 6μm range,” Phys. Rev. Lett. 78, 5–8 (1997). [CrossRef]
- H. Gies and K. Klingmüller, “Casimir effect for curved geometries: Proximity-force-approximation validity limits,” Phys. Rev. Lett. 96(22), 220401 (2006). [CrossRef] [PubMed]
- V. Golyk, M. Krüger, A. P. McCauley, and M. Kardar, “Small distance expansion for radiative heat transfer between curved objects,” Europhys. Lett. 101(3), 34002 (2013). [CrossRef]
- M. Abramowitz and I. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (Dover, 1965).
- K. Sasihithlu and A. Narayanaswamy, “Convergence of vector spherical wave expansion method applied to near-field radiative transfer,” Opt. Express 19(S4), A772–A785 (2011). [CrossRef] [PubMed]
- W. C. Chew, “Recurrence relations for three-dimensional scalar addition theorem,” J. Electromagn. Wave 6, 133–142 (1992). [CrossRef]
- A. Cuyt, Handbook of Continued Fractions for Special Functions (Springer, 2008).
- E. J. Rothwell, “Computation of the logarithm of bessel functions of complex argument,” Commun. Numer. Methods Eng. 21(10), 597–605 (2005). [CrossRef]
- W. C. Chew, “A derivation of the vector addition theorem,” Microwave Opt. Tech. Lett. 3(7), 256–260 (1990). [CrossRef]
- R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor and Francis, 2002).
- N. H. Juul, “Investigation of approximate methods for calculation of the diffuse radiation configuration view factor between two spheres,” Lett. Heat Mass Transfer 3(6), 513–521 (1976). [CrossRef]
- B. E. Sernelius, Surface Modes in Physics (Wiley-Vch, 2011).
- N. Gu, K. Sasihithlu, Y. Zheng, and A. Narayansawamy, “Proximity approximation and radiative transfer between sub-wavelength spheres and planar surfaces,” under review (2013).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.