RESEARCH PAPERS: Radiative Heat Transfer

Energy Transmission by Photon Tunneling in Multilayer Structures Including Negative Index Materials

[+] Author and Article Information
C. J. Fu

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

Z. M. Zhang1

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USAzzhang@mail.me.gatech.edu

D. B. Tanner

Department of Physics, University of Florida, Gainesville, Florida 32611, USA


Corresponding author.

J. Heat Transfer 127(9), 1046-1052 (Jan 26, 2005) (7 pages) doi:10.1115/1.2010495 History: Received August 12, 2004; Revised January 26, 2005

The phenomenon of photon tunneling, which depends on evanescent waves for radiative transfer, has important applications in microscale energy conversion devices and near-field optical microscopy. In recent years, there has been a surge of interest in the so-called negative index materials (NIMs), which have simultaneously negative electric permittivity and negative magnetic permeability. The present work investigates photon tunneling in multilayer structures consisting of positive index materials (PIMs) and NIMs. Some features, such as the enhancement of radiative transfer by the excitation of surface polaritons for both polarizations, are observed in the predicted transmittance spectra. The influence of the number of layers on the transmittance is also examined. The results suggest that the enhanced tunneling transmittance by polaritons also depends on the NIM layer thickness and that subdividing the PIM/NIM layers to enhance polariton coupling can reduce the effect of material loss on the tunneling transmittance.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 7

The transmittance and absorptance of multilayer structures, with different number of layers, versus the incidence angle θ1. (a) s polarization and (b) p polarization. The configurations are the same as corresponding ones in Fig. 6 and the frequency is fixed at ω=0.665ωp.

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Figure 6

The transmittance spectra of multilayer structures with different numbers of layers at an incidence angle θ1=60deg: (a) s polarization and (b) p polarization. Parameters for calculating ε(ω) and μ(ω) of the NIM are the same as those used for Fig. 5. In each multilayer structure a VG and a NIM layer of the same thickness are alternately placed between the two end layers. The total thickness of the VGs is the same as the total thickness of the NIM layers and is set to 0.85λp, the same as in Figs.  35.

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Figure 3

Spectral transmittance of a four-layer structure at 45deg incidence angle: (a) s polarization and (b) p polarization. For the dielectrics: ε1=ε4=2.25 and μ1=μ4=1; medium 2 is vacuum: ε2=μ2=1; for the NIM: ε3 and μ3 are calculated from Eqs. 1,2 with ω0∕ωp=0.5, F=0.875, and with different values of γ. The vacuum gap (VG) width and the NIM layer thickness are both taken to be 0.85λp. The transmittance without a NIM layer (d3=0) is also shown for comparison.

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Figure 5

The transmittance spectra of a five-layer structure for γ=0.0025ωp. In (a) and (b), the VG is equally divided into two layers sandwiching the NIM layer. The total thickness of the VGs and the thickness of the NIM layer are the same as in Fig. 4, i.e., 0.85λp. In (c) and (d), the NIM layer is equally divided into two layers that sandwich the VG.

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Figure 4

Peak transmittance of the four-layer structure versus the thickness of the NIM for incidence angle of 45deg, when d2 is fixed at 0.85λp: (a) s polarization and (b) p polarization.

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Figure 2

Schematic illustration of a N-layer structure

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Figure 1

Refractive index n and extinction coefficient κ of a NIM, calculated from Eqs. 1,2,3 as functions of the dimensionless frequency ω∕ωp. The dashed line shows the κ values multiplied by 100.



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