329lect24 - 24 Wave reflections, standing waves, radiation...

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Unformatted text preview: 24 Wave reflections, standing waves, radiation pressure In this lecture we will examine the phenomenon of plane-wave reflections at an interface separating two homogeneous regions where Maxwells equations allow for traveling TEM wave solutions. The solutions will also need to n ( D +- D- ) = s n ( B +- B- ) = 0 n ( E +- E- ) = 0 n ( H +- H- ) = J s satisfy the boundary condition equations repeated in the margin. We will consider a propagation scenario in which (see margin): Region 1 Region 2 H i x y z E i E t H t H r E r 1. Region 1 where z < is occupied by a perfect dielectric with medium parameters 1 , 1 , and 1 = 0 , 2. Region 2 where z > is homogeneous with medium parameters 2 , 2 , and 2 , 3. Interface z = 0 contains no surface charge or current except possibly in 2 limit which will be considered separately at the end. In Region 1 we envision an incident plane-wave with linear-polarized field phasors E i = xE o e- j 1 z and H i = y E o 1 e- j 1 z , where E o is the wave amplitude due to far away source located in z - region, 1 = 1 1 and 1 = 1 1 . 1 Fields above satisfy Maxwells equations in Region 1, but if there were no other fields in Regions 1 and 2 boundary condition equations requiring continuous tangential E and H at the z = 0 interface would be violated. In order to comply with the boundary condition equations we postulate a set of reflected and transmitted wave fields in Regions 1 and 2 as follows: Incident: E i = xE o e- j 1 z , H i = y E o 1 e- j 1 z , Reflected: E r = x E o e j 1 z , H r =- y E o 1 e j 1 z , Transmitted: E t = xE o e- 2 z , H t = y E o 2 e- 2 z . In Region 1 we postulate a reflected plane-wave with linear-polarized field phasors E r = x E o e j 1 z and H r =- y E o 1 e j 1 z including an unknown that we will refer to as reflection coefficient . Note that the reflected wave propagates in- z direction (direction of H r and the exponential terms have been adjusted accordingly). In Region 2 we postulate a transmitted plane-wave with linear-polarized field phasors E t = xE o e- 2 z and H t = y E o 2 e- 2 z including an unknown that we will refer to as reflection coefficient . Note that the transmitted wave propagates in z direction, and since Region 2 is conducting we have 2 = j 2 2 + j 2 and 2 = ( j 2 )( 2 + j 2 ) = 2 + j 2 . 2 To determine the unknowns and we enforce the following boundary conditions at z = 0 where the fields simplify as shown in the margin: Incident at z = 0 : E i = xE o , H i = y E o 1 , Reflected at z = 0 : E r = x E o , H r =- y E o 1 Transmitted at z = 0 : E t = xE o , H t = y E...
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329lect24 - 24 Wave reflections, standing waves, radiation...

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