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8平面波垂直入射(10-2).doc

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9. Normal Incidence to a Plane Boundary A. Normal incidence to a plane between two dissipated media The plane interface between two dissipated media is assumed to coincide with the coordinate plane . The space is divided by the interface into two regions: region 1 () in which the medium parameters are , and region 2 () in which the medium parameters are . The incident and the reflected waves in region 1 are, respectively, given by and where and are, respectively, the intrinsic impedance and the wave number of the medium in region 1, and , , In region 2, there exists the transmitted wave only, where and are, respectively, the intrinsic impedance and the wave number of the medium in region 2, and The reflection coefficient and the transmission coefficient at the plane interface () are, respectively, defined by and In region 1, the wave is the sum of the incident wave and the reflected wave, given by The electric field and the magnetic field boundary conditions at the interface plane are given by These boundary conditions are solved for the reflection coefficient as follows. then then then then finally These boundary conditions can also be solved for the transmission coefficient as follows. then then then finally It is inferred from and that The combined wave of the incident and the reflected waves in region 1 must be a standing wave, and the standing-wave ratio is defined by Since then and therefore Since the magnitude of the reflection coefficient is less than or equal to one then the standing wave ratio should be It is noted that for pure traveling wave, no reflected wave exists, and ; for pure standing wave, full reflection has made, and ; for common standing wave, and ; the smaller the standing wave ratio or the magnitude of the reflection coefficient is, the larger the traveling-wave part will be, and vice versa. Conversely, it follows from that or hence Problem 2-8 A uniform plane wave traveling in +z direction with electric f
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