Radiation from a rectangular waveguide with infinite flange--Exact solution by the correlation matrix method

A rectangular waveguide is terminated by an infinite conducting flange and radiates into half-space. Modal expansions of the TE and TM waveguide fields lead to Hermitian forms for the incident and reflected waveguide power (
P_{wg} = P_{wg}^{+} - P_{wg}^{-}
) in terms of the corresponding electric field mode amplitude vectors and a diagonal field admittance matrix [
Y
]. The power radiated from the aperture is expressed in terms of correlation functions of the aperture electric fields, and yields a Hermitian form for the radiated power
P_{r}
in terms of the electric mode amplitude vectors and a matrix derived from the field correlation functions-the correlation matrix. Applying the principle of conservation of complex power (
P_{wg} = P_{r}
) leads directly to a nonvariational expression for the scattering matrix [S] for the flanged termination. From [S] the effective
TE_{10}
load admittance
Y_{L, 10}
can be deduced. Numerical results for the latter are compared graphically with previous variational results. Also given are the farfield power patterns for two aperture sizes which are then compared with the traditional patterns due to the
TE_{10}
mode only.