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Theorem Concerning Reflection From a Plane Stratified Medium
Author(s) -
Booker Henry G.,
Fejer Jules A.,
Lee Kai Fong
Publication year - 1968
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1002/rds196833207
Subject(s) - mathematics , reflection (computer programming) , complex plane , mathematical analysis , plane (geometry) , refractive index , function (biology) , analytic function , gravitational singularity , optics , wavelength , reflection coefficient , angle of incidence (optics) , geometry , physics , evolutionary biology , computer science , biology , programming language
Let a plane electromagnetic wave of wavelength λ be incident in free space at an angle of incidence i upon a medium that is stratified in horizontal planes. Let the squared complex refractive index be an analytic function of height, and consider height as a complex variable. By sliding the contour map of the analytic function parallel to the imaginary height axis a family of refractive index profiles is obtained along the real height axis. Let one member of the family correspond to a nonabsorbing medium, and let another typical member of the family be obtained by displacing the contour map of the analytic function a distance b in the direction of the negative imaginary height axis. Then the amplitude reflection coefficient of the stratified medium is exp and the phase change on reflection is independent of b . This is true regardless of the precise form of the analytic function specifying the refractive index profiles. A function with singularities may be used, provided that the range of b is restricted to use only a region of the complex plane where the function is analytic.