Abstract
A solution has been obtained for the spherical or the three-dimensional Luneberg lens. The paper starts with a general discussion of the vector wave functions which can be used to represent the electromagnetic field in a radially stratified medium. It is then applied specifically to the Luneberg lens. Four essential vector wave functions are defined in terms of two scalar wave functions. One of them contains the confluent hypergeometric function, and the other involves a “generalized” confluent hypergeometric function. The latter satisfies a differential equation which can be obtained by a proper confluence of three regular singularities of an equation with five regular singularities. The confluence differs from the confluences employed to obtain the differential equations commonly encountered in certain branches of mathematical physics. It is, therefore, concluded that the “generalized” confluent hypergeometric function is an entirely new function which is not simply related to other well-known functions. The paper finally presents a number of important formulae pertinent to the problem. The solution to another class of stratified lenses is briefly discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
