3(a), then it will only be detected by the TM-mode of microwave radiation with n = 1 and the contributions from all the other modes (n = 0 and n > 1) will be small compared to the leading [TM.sub.m,1]-mode.
Furthermore, we would like to add that this paper provides a proof that the wave-shaped deformations (to the first-order approximation) can be reduced to the simple displacements reported in [5, 6] with the suitable choice of the TM-modes, being an important new result showing that essentially the same mathematical tools can be used to cover the broad range of deformations.
Identifying two T[E.sub.mn] or T[M.sub.mn] with the azimuthal mode number m for ([absolute value of m] = 1, ..., [L/2 - 1])) differing by a sign, the variation of the TE- and TM-mode field components with respect to the angle variable [theta] can occur only in [L/2] + 1 essentially distinct ways.
We conclude with the remark that the analysis of the TE- and the TM-modes of a vane-loaded circular cylindrical waveguide presented in this paper parallels the analysis of the solenoidal and the irrotational modes of a cylindrical magnetron cavity presented in .
Knowing the fields at the aperture of the antenna, the TE and TM-mode
coefficients can be calculated from the formulations provided in this section.
The impedances [Z.sub.n], which correspond to the n-th harmonic TM-mode in the z-direction, can be represented by the equivalent transmission-line circuit of Figure 5.
[Z.sup.air.sub.n] represents the wave impedance of the n-th TM-mode in air (region 1), and [Z.sup.d.sub.n] is the equivalent impedance of the n-th TM-mode in the grounded dielectric of height h (region 2).
The TM-mode Maxwell's equations for a lossless dispersive medium under current investigation are simplified as
This set of TM-mode equations applicable to the three investigated dispersive media, which are characterized by their constitutive equations for the relative electrical permittivities [[epsilon].sub.r], contains the ideal Maxwell's equations and the terms due to the polarization current [[J.bar].sub.d] summarized in Equations (4)-(6), and the absorbing terms defined only in the attached convolution perfect matching layer.
Akinbiyi, "The use of asymptotes to estimate TE- and TM-mode
losses in long conductors," IEEE Transactions on Magnetics, Vol.
To measure the divergence of the scattered reflection-beam from Si or Si nano-pillar surface, a CW Nd:YAG laser (532 nm) with output power of 10 mW and a linear polarizer with extinction ratio up to 10000 : 1 are used to produce the TE and TM-mode
Next, this interaction results in the excitation of the WM slab by the high-order TM-modes
generated at the waveguide termination.