# 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 [1] 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 [1] 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 [2] + +
+
[[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 [1] 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

(1)

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 :

(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 [2]

(3)

where