I came across this question the solution given was to use the formulae for reflection coefficient with characteristic impedance of wave guide replacing the ones in boundless medium.

What I am confused is that while deriving that formulae it was assumed that the waves are uniform plane waves but waves in rectangular wave guides are not uniform plane waves, So how can same formulae be applied here.

A more appropriate approach can be as the non uniform plane waves in wave guides can be considered as sum of two uniform plane waves at an oblique direction of propagation and then use formulae for oblique incidence reflection.Although I am not sure how snell's law can be satisfied along with second materials its own cutoff frequency but at least it is more appropriate then solution given.

  • $\begingroup$ hint: assume a single mode $TE_{10}$ propagation both in the empty and in the filled guide and match the fields at the interface: $E_x,E_y,H_z$ should be continuous at the discontinuity. $\endgroup$ – hyportnex Aug 18 at 12:41
  • $\begingroup$ @hyportnex Igf I simply match the waves according to boundary conditions for dielectric then there will not be any reflected wave isn't it because reflected wave exist because equation wise both property has to be satisfied boundary value and intrinsic impedance for a Uniform plane wave. Correct me If I am wrong.Thanks $\endgroup$ – SUNITA GUPTA Aug 18 at 12:52
  • $\begingroup$ you will not be able to match unless there is also a reflected wave $\endgroup$ – hyportnex Aug 18 at 14:17

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