Circuit-slide-20 - For a uniform plane wave with general...

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For a uniform plane wave with general orientation , the direction of propagation is identified by the propagation vector , normal to the phase planes Considering the position vector we have the scalar dot product
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Plane Waves in Arbitrary Directions ) cos( )) ) sin ( ) cos ( cos( )) sin cos ( cos( ) ' cos( sin cos ' z x t E z x t E z x t E z t E z x z z x o o o o β β ϖ θ β θ β ϖ θ θ β ϖ β ϖ θ θ - - = - - = + - = - + = z x Source is normal to z z ) cos( z t E o β ϖ - z x Source is normal to z’ z’ θ zsinθ θ z x xcos θ ) cos( z y x t E z y x o β β β ϖ - - - ) . cos( r t E o β ϖ - Arbitrary source Introduce propagation vector
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For a uniform plane wave with general orientation , the direction of propagation is identified by the propagation vector , normal to the phase planes Considering the position vector we have the scalar dot product
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The electromagnetic fields of a plane wave propagating along a general direction are on the phase plane perpendicular to the propagation vector and can be written as We have assumed propagation in a dielectric by giving the same phase to the fields . In addition
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