jan 2001afosr san antonio meeting inverse source problem a.j. devaney and mei-li, “the inverse...
TRANSCRIPT
Jan 2001 AFOSR 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. DevaneyDepartment of Electrical and Computer Engineering
Northeastern UniversityBoston, MA 02115
[email protected] , [email protected]
Research supported by Delaware MURI
Jan 2001 AFOSR San Antonio Meeting
Inverse Source Problem
j(r,), (r,)
E (r,), H (r,) Determine charge current distribution thatradiates a prescribed field
j(r,), (r,)
E (r,), H (r,)
Radome
Determine charge current distribution thatradiates a prescribed field in presence of
known background structure and subject to “energy” constraints
Non-unique due to N.R. charge-current distributions
Jan 2001 AFOSR San Antonio Meeting
Jan 2001 AFOSR San Antonio Meeting
Radiation Problem
Radiation Condition
Background potential
Jan 2001 AFOSR 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 2001 AFOSR San Antonio Meeting
Non-uniqueness-N.R. Sources
Pseudo-inverse: Minimize “source energy”
Minimum energy source
Jan 2001 AFOSR San Antonio Meeting
Free-space Case
Jan 2001 AFOSR San Antonio Meeting
Multipole Expansion
Jan 2001 AFOSR San Antonio Meeting
Free-space I.S.P.
Jan 2001 AFOSR San Antonio Meeting
Source Energy
Eigenvalues tend to zero exponentially fast when l>k0a
Stable source possible only if L k0a
Jan 2001 AFOSR San Antonio Meeting
Jan 2001 AFOSR San Antonio Meeting
Jan 2001 AFOSR San Antonio Meeting
Jan 2001 AFOSR San Antonio Meeting
Jan 2001 AFOSR 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 2001 AFOSR San Antonio Meeting
Scattering Wave States
Jan 2001 AFOSR San Antonio Meeting
Spherically Symmetrical Backgrounds
Same as free space case with spherical Bessel functionsreplaced with the radial wave functions
Jan 2001 AFOSR San Antonio Meeting
Inverse Problem
Same as free space case with spherical Bessel functionsreplaced with the radial wave functions
Jan 2001 AFOSR San Antonio Meeting
Minimum Energy Source
Same as free space case with spherical Bessel functionsreplaced with the radial wave functions
Jan 2001 AFOSR San Antonio Meeting
Piece-wise Constant Backgrounds
Jan 2001 AFOSR San Antonio Meeting
Eigenvalues
Jan 2001 AFOSR San Antonio Meeting
Source Energy
Eigenvalues tend to zero exponentially fast when l>k0a
Stable source possible only if L k0a
Jan 2001 AFOSR San Antonio Meeting
Jan 2001 AFOSR San Antonio Meeting
Source Energy
Jan 2001 AFOSR San Antonio Meeting
Future Work
• Include source-field interaction constraints• Full EM case• Other examples• Planar backgrounds