Convergence of Vector Spherical Wave Expansion Method Applied to Near-field Radiative Transfer References and Links

Near-field radiative transfer between two objects can be computed using Rytov's theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green's function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green's function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax/d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.

[1]  John B. Pendry,et al.  Radiative exchange of heat between nanostructures , 1999 .

[2]  G. Mie.  Contributions to the optics of turbid media, particularly of colloidal metal solutions , 1976 .

[3]  M. Hove,et al.  Theory of Radiative Heat Transfer between Closely Spaced Bodies , 1971 .

[4]  Gang Chen,et al.  Surface modes for near field thermophotovoltaics , 2003 .

[5]  Gang Chen,et al.  DIRECT COMPUTATION OF THERMAL EMISSION FROM NANOSTRUCTURES , 2005 .

[6]  Philippe Ben-Abdallah,et al.  Fundamental limits for noncontact transfers between two bodies , 2010 .

[7]  A. Kittel,et al.  Near-field thermal imaging of nanostructured surfaces , 2008, 1103.3059.

[8]  Jean-Jacques Greffet,et al.  Radiative heat transfer at the nanoscale , 2009 .

[9]  S. Kawata,et al.  Plasmonics for near-field nano-imaging and superlensing , 2009 .

[10]  J. Popp,et al.  Surface-enhanced Raman spectroscopy , 2009, Analytical and bioanalytical chemistry.

[11]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[12]  D. Mackowski.  Electrostatics analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot particles. , 1995, Applied optics.

[13]  Gang Chen,et al.  Thermal near-field radiative transfer between two spheres , 2008, 0909.0765.

[14]  W. Wiscombe,et al.  Mie Scattering Calculations: Advances in Technique and Fast, Vector-speed Computer Codes , 1979 .

[15]  M. Pinar Mengüç,et al.  Near-field radiative heat transfer enhancement via surface phonon polaritons coupling in thin films , 2008 .

[16]  Gang Chen,et al.  Surface phonon polaritons mediated energy transfer between nanoscale gaps. , 2009, Nano letters.

[17]  Gang Chen,et al.  Near-field radiative heat transfer between a sphere and a substrate , 2008, 0909.0784.

[18]  S. Stein.  ADDITION THEOREMS FOR SPHERICAL WAVE FUNCTIONS , 1961 .

[19]  M. Quinten,et al.  Scattering and extinction of evanescent waves by small particles , 1999 .

[20]  O. Cruzan.  Translational addition theorems for spherical vector wave functions , 1962 .

[21]  Ceji Fu,et al.  Review of near‐field thermal radiation and its application to energy conversion , 2009 .

[22]  R. Carminati,et al.  Near-field thermophotovoltaic energy conversion , 2006 .

[23]  Lu Hu,et al.  Near-field Thermal Radiation Between Two Closely Spaced Glass Plates Exceeding Planck’s Blackbody Radiation Law , 2008 .

[24]  C. M Hargreaves,et al.  Anomalous radiative transfer between closely-spaced bodies , 1969 .

[25]  W. Denk,et al.  Optical stethoscopy: Image recording with resolution λ/20 , 1984 .

[26]  Y. Lo,et al.  Scattering by Two Spheres , 1966 .

[27]  Milton Kerker,et al.  The Scattering of Light and Other Electromagnetic Radiation ~Academic , 1969 .

[28]  Shanhui Fan,et al.  Numerically exact calculation of electromagnetic heat transfer between a dielectric sphere and plate , 2011 .

[29]  J. Greffet,et al.  Mesoscopic description of radiative heat transfer at the nanoscale. , 2010, Physical review letters.

[30]  Ludmilla Kolokolova,et al.  Light scattering by cometary dust numerically simulated with aggregate particles consisting of identical spheres , 2006 .

[31]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[32]  D B Tanner,et al.  Near-field radiative heat transfer between macroscopic planar surfaces. , 2011, Physical review letters.

[33]  R. Carminati,et al.  Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field , 2005, physics/0504068.

[34]  M. Pinar Mengüç,et al.  Role of fluctuational electrodynamics in near-field radiative heat transfer , 2007 .

[35]  A. Maradudin,et al.  Nano-optics of surface plasmon polaritons , 2005 .

[36]  Gang Chen,et al.  Breakdown of the Planck blackbody radiation law at nanoscale gaps , 2009 .

[37]  Jean-Jacques Greffet,et al.  Thermal radiation scanning tunnelling microscopy , 2006, Nature.

[38]  Y. Lo,et al.  Multiple scattering of EM waves by spheres part I--Multipole expansion and ray-optical solutions , 1971 .

[39]  W. Chew.  A derivation of the vector addition theorem , 1990 .

[40]  Weng Cho Chew,et al.  Efficient way to compute the vector addition theorem , 1993 .

[41]  Ramani Duraiswami,et al.  Computation of scattering from N spheres using multipole reexpansion. , 2002, The Journal of the Acoustical Society of America.

[42]  U. Dürig,et al.  Near‐field optical‐scanning microscopy , 1986 .

[43]  Jean-Jacques Greffet,et al.  ENHANCED RADIATIVE HEAT TRANSFER AT NANOMETRIC DISTANCES , 2002, Proceeding of Heat Transfer and Transport Phenomena in Microscale.

[44]  W. Barnes,et al.  Surface plasmon subwavelength optics , 2003, Nature.

[45]  N. Vitanov,et al.  Spontaneous emission of a two-level atom placed within clusters of metallic nanoparticles , 2007 .