introduced nonconforming UPML theory into DG calculations in the case of TM wave
and compared the local relative error between PML and first-order SM-ABC .
From (9) and (25), the TM wave
equation in the beam region can be obtained as
Smol'kin, "Method of cauchy problem to solve a nonlinear transmission eigenvalue problem for tm wave
propagating in a circle double-layer dielectric waveguide with kerr nonlinearity," Izvestiya Vysshikh Uchebnykh Zavedenij.
The above formulations can be applied to TM wave
by simple replacements of [p.sub.i], [p.sub.0], and [p.sub.s] as follows:
Since biaxial anisotropic medium is a reciprocal medium, if total transmission occurs at the boundary when a TM wave
is incident from isotropic medium into biaxial anisotropic medium, total transmission will also occur when this TM wave
is incident from biaxial anisotropic medium into the same isotropic medium.
Analogous derivations for TM wave
result in a similar formula with [E.sub.[phi]] replaced with [H.sub.[phi]] and [H.sub.[phi]] replaced with [-E.sub.[phi]] which is the consequence of the natural symmetry of Maxwell equations.
where coefficients [q.sub.i,s] = [n.sub.i,s]cos[[theta].sub.j,s] for the TE wave and coefficients [q.sub.i,s] = cos[[theta].sub.j,s] / [n.sub.i,s] for the TM wave
, where the subscripts i, j and s correspond to the quantities in the incident medium, periodic medium of photonic crystal and substrate respectively.
For two-dimensional electromagnetic scattering problems, rectangular components of the electromagnetic field may be classified as independent groups, namely, TM wave
and TE wave.
Similarly, for the induced current of the TM wave
, we get
The above calculations can be used for TM wave
by substituting [p.sub.l] = cos [[theta].sub.l]/[n.sub.l] where l = 0, 1, 2 and 3.
Consider a TM wave
incident from air (z < 0) to the metamaterial slab (z > 0), such that the total, incident, and reflected magnetic fields at z < 0 are given by
Simulated absorption values at the resonances for TE and TM waves
. Angle TE Wave TM Wave
(degrees) First Second First Second 0[degrees] 98.46% 99.91% 98.46% 99.89% 15[degrees] 98.49% 99.81% 98.58% 99.88% 30[degrees] 98.56% 99.93% 98.52% 99.65% 45[degrees] 98.51% 99.96% 98.50% 99.93% 60[degrees] 98.45% 99.97% 98.53% 99.94% 75[degrees] 98.47% 99.72% 98.56% 99.90% 90[degrees] 98.37% 99.91% 98.41% 99.94%