A Note on the Guided Complex Wave Supported by a Slightly Random Surface
Summary :
This paper describes an open question in a mathematical formulation of the guided complex wave supported by a slightly random surface. In case of the TM wave propagating over a randomly reactive plane surface, a formal wave solution is obtained and is shown to have an equivalent network representation. It is pointed out, however, that such a formal solution has no physical significance, because the effective surface impedance in the transverse resonance condition determining the complex propagation constant is not an analytic function on the complex wavenumber plane and because the formal solution gives a diverging variance of the guided complex wave. It is concluded that it is still an open problem to have a correct mathematical formulation for the guided wave over a random surface. Finally suggestions are given for obtaining a correct mathematical formulation.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E66-E No.3 pp.202-206
- Publication Date
- 1983/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Electromagnetic Theory
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Junichi NAKAYAMA, "A Note on the Guided Complex Wave Supported by a Slightly Random Surface" in IEICE TRANSACTIONS on transactions,
vol. E66-E, no. 3, pp. 202-206, March 1983, doi: .
Abstract: This paper describes an open question in a mathematical formulation of the guided complex wave supported by a slightly random surface. In case of the TM wave propagating over a randomly reactive plane surface, a formal wave solution is obtained and is shown to have an equivalent network representation. It is pointed out, however, that such a formal solution has no physical significance, because the effective surface impedance in the transverse resonance condition determining the complex propagation constant is not an analytic function on the complex wavenumber plane and because the formal solution gives a diverging variance of the guided complex wave. It is concluded that it is still an open problem to have a correct mathematical formulation for the guided wave over a random surface. Finally suggestions are given for obtaining a correct mathematical formulation.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e66-e_3_202/_p
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@ARTICLE{e66-e_3_202,
author={Junichi NAKAYAMA, },
journal={IEICE TRANSACTIONS on transactions},
title={A Note on the Guided Complex Wave Supported by a Slightly Random Surface},
year={1983},
volume={E66-E},
number={3},
pages={202-206},
abstract={This paper describes an open question in a mathematical formulation of the guided complex wave supported by a slightly random surface. In case of the TM wave propagating over a randomly reactive plane surface, a formal wave solution is obtained and is shown to have an equivalent network representation. It is pointed out, however, that such a formal solution has no physical significance, because the effective surface impedance in the transverse resonance condition determining the complex propagation constant is not an analytic function on the complex wavenumber plane and because the formal solution gives a diverging variance of the guided complex wave. It is concluded that it is still an open problem to have a correct mathematical formulation for the guided wave over a random surface. Finally suggestions are given for obtaining a correct mathematical formulation.},
keywords={},
doi={},
ISSN={},
month={March},}
Copy
TY - JOUR
TI - A Note on the Guided Complex Wave Supported by a Slightly Random Surface
T2 - IEICE TRANSACTIONS on transactions
SP - 202
EP - 206
AU - Junichi NAKAYAMA
PY - 1983
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E66-E
IS - 3
JA - IEICE TRANSACTIONS on transactions
Y1 - March 1983
AB - This paper describes an open question in a mathematical formulation of the guided complex wave supported by a slightly random surface. In case of the TM wave propagating over a randomly reactive plane surface, a formal wave solution is obtained and is shown to have an equivalent network representation. It is pointed out, however, that such a formal solution has no physical significance, because the effective surface impedance in the transverse resonance condition determining the complex propagation constant is not an analytic function on the complex wavenumber plane and because the formal solution gives a diverging variance of the guided complex wave. It is concluded that it is still an open problem to have a correct mathematical formulation for the guided wave over a random surface. Finally suggestions are given for obtaining a correct mathematical formulation.
ER -
English
