Jan 2001AFOSR San Antonio Meeting Inverse Source Problem A.J. Devaney and Mei-Li, “The inverse source problem in non-homogeneous background media”, accepted to JOSA A A.J. Devaney Department of Electrical and Computer Engineering Northeastern University Boston, MA Research supported by Delaware MURI

Jan 2001AFOSR San Antonio Meeting Inverse Source Problem j(r,  ),  (r,  ) E (r,  ), H (r,  ) Determine charge current distribution that radiates a prescribed field j(r,  ),  (r,  ) E (r,  ), H (r,  ) Radome Determine charge current distribution that radiates a prescribed field in presence of known background structure and subject to “energy” constraints Non-unique due to N.R. charge-current distributions

Jan 2001AFOSR San Antonio Meeting

Jan 2001AFOSR San Antonio Meeting Radiation Problem Radiation Condition Background potential

Jan 2001AFOSR San Antonio Meeting Inverse Source Problem Determine the source that generates a prescribed field everywhere outside the source region Determine the source that generates a prescribed radiation pattern Determine the source that generates a prescribed set of multipole moments Radiation pattern multipole expansion

Jan 2001AFOSR San Antonio Meeting Non-uniqueness-N.R. Sources Pseudo-inverse: Minimize “source energy” Minimum energy source

Jan 2001AFOSR San Antonio Meeting Free-space Case

Jan 2001AFOSR San Antonio Meeting Multipole Expansion

Jan 2001AFOSR San Antonio Meeting Free-space I.S.P.

Jan 2001AFOSR San Antonio Meeting Source Energy Eigenvalues tend to zero exponentially fast when l>k 0 a Stable source possible only if L  k 0 a

Jan 2001AFOSR San Antonio Meeting

Jan 2001AFOSR San Antonio Meeting

Jan 2001AFOSR San Antonio Meeting

Jan 2001AFOSR San Antonio Meeting

Jan 2001AFOSR San Antonio Meeting I.S.P. In a Non-Homogeneous Background Motivation: Most antennas include passive structures that can be modeled this way The radiation patterns generated by such “composite” sources may have interesting properties Field dependent “effective” source

Jan 2001AFOSR San Antonio Meeting Scattering Wave States

Jan 2001AFOSR San Antonio Meeting Spherically Symmetrical Backgrounds Same as free space case with spherical Bessel functions replaced with the radial wave functions

Jan 2001AFOSR San Antonio Meeting Inverse Problem Same as free space case with spherical Bessel functions replaced with the radial wave functions

Jan 2001AFOSR San Antonio Meeting Minimum Energy Source Same as free space case with spherical Bessel functions replaced with the radial wave functions

Jan 2001AFOSR San Antonio Meeting Piece-wise Constant Backgrounds

Jan 2001AFOSR San Antonio Meeting Eigenvalues

Jan 2001AFOSR San Antonio Meeting Source Energy Eigenvalues tend to zero exponentially fast when l>k 0 a Stable source possible only if L  k 0 a

Jan 2001AFOSR San Antonio Meeting

Jan 2001AFOSR San Antonio Meeting Source Energy

Jan 2001AFOSR San Antonio Meeting Future Work Include source-field interaction constraints Full EM case Other examples Planar backgrounds