19.巴俾涅原理(13-0).docVIP

19. Babinet’s Principle A. Statement of Babilet’s principle The mathematical statement of the Babilet’s principle is given by represents the field at point P radiated by an electric source into an unbounded medium， symbolizes the field at point P radiated by the electric source into a medium in the presence of an electric screen, namely, an infinite, very thin, perfect electric conductor with an opening A, denotes the field at point P radiated by the electric source into a medium in the presence of a magnetic screen, namely, a flat, very thin, perfect magnetic conductor A, A wordy statement of the Babilet’s principle is that “when the field behind a screen with an opening is added to the field of a complementary structure, the sum is equal to the field when there is no screen”. An electric screen and a magnetic screen are said to be complementary, if these two screens superimposed cover an entire plane with no overlapping. The proof of Babilet’s principle will be given step by step below. B. Love’s equivalence for electric and magnetic screens For acquiring , the actual electric screen problem can be transferred to the following equivalent problem by using tangential field components on the screen, on the electric conducting screen S, and , on the aperture A: For acquiring , the other actual problem can be transferred to the following equivalent problem by using tangential field components on the screen, , on fictitious screen S, and on the magnetically conducting screen A: Superposition of the electric screen and the magnetic screen forms a complementary screen on , producing field and at point P by sources , , on S , , on A It follows from the equivalence principle that the sources and on S and on A radiate no field in region (imagining the sources are short-circuited), and they will not be considered. As a result, on the mathematical plane , only the sources on S on A exist and radiate field in region . Namely, the actual problem will b