On the evanescent fields and the causality of the focus wave modes

Amr M. Shaarawi, Richard W. Ziolkowski, Ioannis M. Besieris

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


The diverging and converging field components of the source-free focus wave modes are studied within the framework of both the Whittaker and Weyl plane wave expansions. It is shown that, in the Weyl picture, the evanescent fields associated with the diverging and converging components of the focus wave mode solution cancel each other identically. The source-free focus wave modes are, hence, composed solely of backward and forward propagating components of the Whittaker type. It will also be shown that no evanescent fields are associated with the causal excitation of an aperture by an initial focus wave mode field. The diverging field, however, is composed solely of causal components that propagate away from the aperture. With a specific choice of parameters, the field generated by the aperture is a very good approximation to the source-free solution. Under the same conditions, the original focus wave mode solution is composed predominantly of causal forward propagating fields.

Original languageEnglish (US)
Pages (from-to)5565-5587
Number of pages23
JournalJournal of Mathematical Physics
Issue number10
StatePublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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