Field and Wave Electromagnetic电磁场与电磁波电磁场与电磁波2011. 05. 111. Normal Incidence at a Plane Conducting Boundary xzyanraniErEiHrHiReflected waveIncident wavePerfect conductorMedium 2 ( 2= )Medium 1 ( 1= 0)z=0Review22. Oblique Incidence at a Plane Conducting Boundary i rPerfect conductorE iE rH iH rzxMedium 1 ( 1= 0)z=0anianrReflected waveIncident wavey i rPerfect conductorE iE rH iH rzxMedium 1 ( 1= 0)z=0anianrReflected waveIncident wavey3Main topic Plane Electromagnetic Waves2. Normal Incidence at Multiple Dielectric Interfaces1. Normal Incidence at a Plane Dielectric Boundary4Consider the situation in Figure where the incident uniform plane wave travels in the +z-direction, and the boundary surface is the plane z=0. The incident electric and magnetic field intensity phasors are1. Normal Incidence at a Plane Dielectric Boundary xzyanraniErEiHrHiReflected waveIncident waveMedium 1( 1, 1)z=0 EtHtantTransmittedwaveMedium 2( 2, 2)5a) For the reflected wave ( Er , Hr ):b) For the transmitted wave ( Et , Ht ):At the dielectric interface z=0 the tangential components (the x-components) of the electric and magnetic field intensities must be continuous. We have xzyanraniErEiHrHiReflected waveIncident waveMedium 1( 1, 1)z=0 EtHtantTransmittedwaveMedium 2( 2, 2)6We obtainThe ratios Er0/Ei0 and Et0/Ei0 are called reflection coefficient反反射射系系数数 and transmission cofficient透透射射系系数数, respectively. In terms of the intrinsic impedances they areNote that the reflection coefficient can be positive or negative可可正正可可负负, depending on whether 2 is greater or less than 1. The transmission coefficient , however, is always positive正正. The definitions for and apply even when the media are dissipative有有耗耗-that is even when 1 , and/or 2 are complex复复数数. Thus and may simply themselves be complex in the general case. A complex (or ) simply means that a phase shift is introduced at the interface upon reflection (or transmission).可可以以为为复数，复数， 引入一个相位引入一个相位7Reflection and transmission coefficients are related by the following equation:If medium 2 is a perfect conductor理理想想导导体体, 2=0, equations yield =-1, and =0. consequently, Er0=-Ei0, and Et0=0. The incident wave will be totally reflected全全反反射射, and a standing wave驻驻波波 will be produced in medium 1, as discussed in Section 8-6.If medium 2 is not a perfect conductor, partial reflection部部分分反反射射 will result. The total electric field in medium 1 can be written asor 8We see that E1(z) is composed of two parts: a traveling wave行行波波 with an amplitude Ei0 and standing wave驻驻波波 with an amplitude 2 Ei0. Because of the existence of the traveling wave, E1(z) does not go to zero at fixed distances from the interface界界面面上上不不为为零零; it merely has locations of maximum and minimum values.The locations of maximum and minmum E1(z) are conveniently found by rewriting E1(z) asFor dissipationless无无损损耗耗 media, 1 and 2 are real, making both and also real实实数数. However, can be positive or negative. Consider the following two cases.1. 0 ( 2 1).92. 0 ( 2 1).The ratio of the maximum value to the minimum value of the electric field intensity of a standing wave is called the standing-wave ratio (SWR), S.驻波比驻波比An inverse relation is While the value of ranges from -1 to +1, the value of S ranges from 1 to . It is customary to express S on a logarithmic scale对对数数坐坐标标. The standing-wave ratio in decibels is 20log10S.01z10The magnetic field intensity in medium 1 is obtained by combing Hi(z) and Hr(z), respectively:In a dissipationless无无损损耗耗 medium, is real; and H1(z) will be a minimum at locations where E1(z) is a maximum, and vice versa.In medium 2, (Et , Ht) constitute the transmitted wave propagating in +z-direction. We have112. Normal Incidence at Multiple Dielectric Interfaces xzyanraniErEiHrHiReflected waveIncident waveMedium 1( 1, 1)z=0 E3H3an3TransmittedwaveMedium 2( 2, 2)Medium 3( 3, 3) ani+E2+H2+ an2-E2-H2-z=dAssuming an x-polarized incident field, the total electric field intensity in medium 1 can be always be written as the sum of the incident component axEi0e-j 1z and a reflected axEr0ej 1z component :The H1(z) in region 1 that corresponds to the E1(z) is12The electric and magnetic fields in region 2 can also be represented by combinations of forward and backward waves:In region 3, only a forward wave traveling in +z-direction exists. ThusThere are a total of four unknown amplitudes: Er0, E2+ , E2- , and E3+ . They can be determined by solving the four boundary-condition equations required by the continuity of the tangential components of the electric and magnetic fields.132.1 wave impedance of the total fieldWe define the wave impedance of the total field at any plane parallel to the plane boundary as the ratio of the total electric field intensity to the total magnetic field intensity. With a z-dependent uniform plane wave, as was shown in figure, we write, in general,For a single wave propagating in the +z-direction in an unbounded medium, the wave impedance equals the intrinsic impedance, , of the medium; for a single