A general scattering theorem for chiral Herglotz functions. (7th August 2013)

• Record Type: Journal Article
• Authors: Athanasiadis, Christodoulos E.; Dimitroula, Sotiria; Barbatis, Gerassimos; Stratis, Ioannis
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 2(2014:Jan. 30)
• Page Start: 187
• Page End: 193
• Publication Date: 2013-08-07
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2944
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2944-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2944-para-0001">A chiral electric Herglotz pair is an incident upon a scatterer that is a perfect conductor. First, we define appropriate tangential subspaces of <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4t700md9" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2944:mma2944-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi mathvariant="script">L</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo class="MathClass-open">(</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo class="MathClass-close">)</mml:mo></mml:math></alternatives> that satisfy the conditions of the left circularly and right circularly polarization, and we prove that they are complete and orthogonal spaces. Then, we define integral operators on these spaces that compose the chiral far‐field operator. We prove a general scattering theorem that connects chiral Herglotz functions with the chiral far‐field operator, which covers known results in the achiral case. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>