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:<math>\psi = \int_{-\infty}^{\infty} \phi(k_\rho) e^{i k_\rho \rho} dk_\rho </math> |
:<math>\psi = \int_{-\infty}^{\infty} \phi(k_\rho) e^{i k_\rho \rho} dk_\rho </math> |
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For three-dimensional layered media, lateral waves have the asymptotic form: |
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:<math>\psi ~ \sim \frac{e^{i k_2 \rho }}{\rho^2}</math> |
:<math>\psi ~ \sim \frac{e^{i k_2 \rho }}{\rho^2}</math> |
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Latest revision as of 14:05, 26 September 2025
In electromagnetics, acoustics and seismology, lateral waves or head waves are localized waves that are launced at or near grazing incidence with respect to the interface of two different media with different physical properties, such as permittivity, acoustic impedance or slowness. While lateral waves are often classified as surface waves, they are distinct from conventional surface waves such as surface plasmon polaritons in optics or surface acoustic waves in acoustics.
Lateral waves play a role in various different physical phenomena, such as radio propagation at large distances,[1] extraordinary optical transmission[2] and total internal reflection.[3] In exploration seismology and geophysics, lateral waves constitute the basis of the seismic refraction method.[4]
Mathematical formulation
[edit]
For three-dimensional layered media, lateral waves have the asymptotic form:
- ^ a b Tamir, T. (1967). “On radio-wave propagation in forest environments”. IEEE Transactions on Antennas and Propagation. 15 (6): 806–817. doi:10.1109/TAP.1967.1139054.
- ^ a b Nevels, Robert D.; Michalski, Krzysztof A. (2014). “On the Behavior of Surface Plasmons at a Metallo-Dielectric Interface”. Journal of Lightwave Technology. 32 (19): 3299–3305. doi:10.1109/JLT.2014.2343018.
- ^ a b Tamir, T.; Oliner, A. A. (1969). “Role of the Lateral Wave in Total Reflection of Light”. Journal of the Optical Society of America. 59 (8): 942–949. doi:10.1364/JOSA.59.000942.
- ^ a b Červený, Vlastislav; Ravindra, Ravi (1971). Theory of Seismic Head Waves. Toronto: University of Toronto Press. ISBN 978-1442639034.
- ^ Felsen, L. B. (15 November 1965). Lateral Waves (PDF) (Report). Bedford, Massachusetts: Air Force Cambridge Research Laboratories. PIBMRI-1303-65.
- ^ Heelan, Patrick A. (1953). “On the Theory of Head Waves”. Geophysics. 18 (4): 871–893. doi:10.1190/1.1437941.
- ^ King, R. W. P.; Brown, M. F. (1984). “Lateral electromagnetic waves along plane boundaries: A summarizing approach”. Proceedings of the IEEE. 72 (5): 595–611. doi:10.1109/PROC.1984.12898.
- ^ King, Ronold W. P.; Owens, Margaret; Wu, Tai Tsun (1992). Lateral Electromagnetic Waves: Theory and Applications to Communications, Geophysical Exploration, and Remote Sensing. New York: Springer Science+Business Media. ISBN 978-1-4613-9176-0.
- ^ Tamir, T.; Felsen, L. (1965). “On lateral waves in slab configurations and their relation to other wave types”. IEEE Transactions on Antennas and Propagation. 13 (3): 410–422. doi:10.1109/TAP.1965.1138420.
