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Application of a Parabolic Wave Equation to Sub-Micron Thermal Radiation Analysis

[+] Author Affiliations
James S. Hammonds, Jr.

City College of the City University of New York, New York, NY

Paper No. HT2003-47262, pp. 353-359; 7 pages
  • ASME 2003 Heat Transfer Summer Conference
  • Heat Transfer: Volume 1
  • Las Vegas, Nevada, USA, July 21–23, 2003
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 0-7918-3693-2 | eISBN: 0-7918-3679-7
  • Copyright © 2003 by ASME


Coordinate transformation of the homogeneous Helmholtz equation is applied such that, upon invoking the paraxial wave approximation, a parabolic wave equation is derived that is independent of the propagation vector, in the limit of wave transmission over very short distances. Thus, similarity solutions applicable to wavelengths in the UV and IR range can be calculated using this approach. This work proposes that these solutions are appropriate for analysis of thermal radiation at sub-micron distances from a surface, as interference effects are captured by this method. Furthermore, by employing a source tensor as the boundary condition, surface wave effects can also be accounted for. In this paper, the method is applied to a case where surface wave propagation is limited to one direction. The solution of the normalized amplitude field is shown to be equivalent to the Green function for thermal emission.

Copyright © 2003 by ASME



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