Chapter8 Plane Electromagnetic WavesPlane waves in perfect dielectricPlane waves in conducting mediaPolarizations of plane wavesNormal incidence on a planar surfacePlane waves in arbitrary directionsOblique incidence at boundaryPlane waves in anisotropic mediaV
Chapter 8 Plane Electromagnetic Waves Plane waves in perfect dielectric Plane waves in conducting media Polarizations of plane waves Normal incidence on a planar surface Plane waves in arbitrary directions Oblique incidence at boundary Plane waves in anisotropic media
1.WaveEguations2.PlaneWavesinPerfectDielectric3.Plane Waves in Conducting Media4.Polarizationsof PlaneWaves5.Normal Incidence on A Planar Surface6.Normal Incidence at Multiple Boundaries7. Plane Waves in Arbitrary Directions8.ObligueIncidenceatBoundarybetweenPerfectDielectrics9.Null and Total Reflections1o.Obliguelncidenceat ConductingBoundary11.ObliqueIncidenceat Perfect ConductingBoundary12. Plane Waves in Plasma13. Plane Waves in FerriteV
1. Wave Equations 2. Plane Waves in Perfect Dielectric 3. Plane Waves in Conducting Media 4. Polarizations of Plane Waves 5. Normal Incidence on A Planar Surface 6. Normal Incidence at Multiple Boundaries 7. Plane Waves in Arbitrary Directions 8. Oblique Incidence at Boundary between Perfect Dielectrics 9. Null and Total Reflections 10. Oblique Incidence at Conducting Boundary 11. Oblique Incidence at Perfect Conducting Boundary 12. Plane Waves in Plasma 13. Plane Waves in Ferrite
1.Wave EquationsIn infinite, linear homogeneous,isotropic media, a time-varyingelectromagneticfield satisfiesthefollowing equations:o"E(r,t)aJ(r,t)?E(r,t)-μeVp(r,t)uat?ato"H(r,t)V?H(r,t)-μs-VxJ(r,t)at?which are called inhomogeneous wave equations,andJ(r,t)= J'(r,t)+oE(r,t)whereJ'(ristheimpressedsource.u√
1. Wave Equations In infinite, linear, homogeneous, isotropic media, a time-varying electromagnetic field satisfies the following equations: = − − + = − ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) 1 ( , ) 2 2 2 2 2 2 t t t t t t t t t t J r H r H r r E r J r E r which are called inhomogeneous wave equations,and J(r,t) = J(r,t) +E(r,t) where J (r, is the impressed source. t)
The relationship between the charge density p(r, t) and the conductioncurrentoE(r,t)isapV- (cE) =atIn a region without impressed source, J = O. If the medium is aperfect dielectric, then, = O . In this case, the conduction current iszero, and p= O. The aboveeguation becomeso’E(r,t)VE(r,t)-u8=0at?o"H(r,t)v?H(r,t)- μe=0at?Whichare called homogeneous wave equations.To investigate the propagation of plane waves, we first solve thehomogeneouswave equations.u7
t = − (E) In a region without impressed source, J ' = 0. If the medium is a perfect dielectric, then, = 0 . In this case, the conduction current is zero, and = 0. The above equation becomes = − = − 0 ( , ) ( , ) 0 ( , ) ( , ) 2 2 2 2 2 2 t t t t t t H r H r E r E r Which are called homogeneous wave equations. To investigate the propagation of plane waves, we first solve the homogeneous wave equations. The relationship between the charge density (r, t) and the conduction current is E(r,t)
For a sinusoidal electromagnetic field, the above equation becomes?E(r)+k?E(r) = 0V?H(r)+k’H(r) = 0which are called homogeneous vectorHelmholtzeguations,and herek=ovucInrectangularcoordinatesystem,wehave?H.(r)+k?H.(r) = 0V?E,(r)+k?E(r)=0V?E,(r)+k'E,(r) =0?H,(r)+k"H,(r)= 0?E.(r)+k?E.()= 0V?H.(r)+k"H.(r)= 0whicharecalledhomogeneous scalarHelmholtzeguationsAll ofthese equations have the same form, and the solutions aresimilar.u
For a sinusoidal electromagnetic field,the above equation becomes + = + = ( ) ( ) 0 ( ) ( ) 0 2 2 2 2 H r H r E r E r k k which are called homogeneous vectorHelmholtz equations, and here k = In rectangular coordinate system, we have + = + = + = ( ) ( ) 0 ( ) ( ) 0 ( ) ( ) 0 2 2 2 2 2 2 r r r r r r z z y y x x E k E E k E E k E + = + = + = ( ) ( ) 0 ( ) ( ) 0 ( ) ( ) 0 2 2 2 2 2 2 r r r r r r z z y y x x H k H H k H H k H which are called homogeneous scalarHelmholtz equations. All of these equations have the same form, and the solutions are similar