# Near-field radiative energy transfer between sphere-sphere and sphere-flat surfaces

(Difference between revisions)
 Revision as of 09:19, 1 March 2012 (view source)Kpark75 (Talk | contribs)m ← Older edit Revision as of 08:09, 3 March 2012 (view source)Kpark75 (Talk | contribs) Newer edit → Line 1: Line 1: - Near-field thermal radiation between two spheres was first reported by Volokitin and Persson  by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are ''ε1''  and ''ε2'' , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as + Near-field thermal radiation between two spheres was first reported by Volokitin and Persson  by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are ''ε1''  and ''ε2'' , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as + +
+
[[File:Sphereee.jpg|center|EQ1]]
+ (1) +
+ + + + where x2 is the position of the particle 2 and ${\alpha _2} = {4 \pi R^3 (\epsilon_2 -1) / (\epsilon_2 +2)}$ is the polarizability of a sphere of radius ''R'' having the relative permittivity of ε2. The electric field incident on the particle 2, Einc(x2,''ω''), is created by the thermal fluctuating dipole of particle 1 at Temperature ''T1'' : +
+
[[File:Sphere2.jpg|center|EQ2]]
+ (2) +
+ + + where $\rm \overline {\overline G}_e (x_2,x_1,\omega)$ is the electric dyadic Green’s function between two dipoles in vacuum and expressed as  + +
+
[[File:Sphereuc.jpg|center|EQ3]]
+ (3) +
+ + + + + where

## Revision as of 08:09, 3 March 2012

Near-field thermal radiation between two spheres was first reported by Volokitin and Persson  by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are ε1 and ε2 , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as

where x2 is the position of the particle 2 and α2 = 4πR32 − 1) / (ε2 + 2) is the polarizability of a sphere of radius R having the relative permittivity of ε2. The electric field incident on the particle 2, Einc(x2,ω), is created by the thermal fluctuating dipole of particle 1 at Temperature T1 :

where $\rm \overline {\overline G}_e (x_2,x_1,\omega)$ is the electric dyadic Green’s function between two dipoles in vacuum and expressed as 

where