Unlike some other functional dependences of PRM–NRM transitions studied so far, for instance $tan\u2009h(x)$ model,^{24} the sinusoidal model provides only for relatively slow transitions and it is not equally obvious where we are “far away from the transition region.” In continuous models, the freedom of choice of parameters e.g., the permittivity $\epsilon IR(\omega )$ and $\epsilon IL(\omega )$ as well as permeability $\mu IR(\omega )$ and $\mu IL(\omega )$ in PRM and NRM media, respectively, is an asymptotic statement. For example, $tan\u2009h(\u221e)\u21921$ is only an asymptotic constant. The fact is that in a continuous model there is everywhere a spatial dependency and interdependency of material parameters. But at some asymptotic points, we calibrate the spatially constant and frequency-dependent material parameters to correspond to the actual PRM and NRM media far away from the transition region which we desire that they have. For instance, Eqs. (2) and (3) at the maxima of the cosine function (in the middle of PRM), where $\pi x/a=2n\pi $ or $x=2na$ ($n=0,1,2,3,\u2026$), give Display Formula
$\mu (\omega )=\mu 0\mu R(\omega )\u2212i\mu 0[\mu IR+\mu IL2+\mu IR\u2212\mu IL2]=\mu 0[\mu R(\omega )\u2212i\mu IR(\omega )],\epsilon (\omega )=\epsilon 0\epsilon R(\omega )\u2212i\epsilon 0[\epsilon IR+\epsilon IL2+\epsilon IR\u2212\epsilon IL2]=\epsilon 0[\epsilon R(\omega )\u2212i\epsilon IR(\omega )],$
while at the minima of the cosine function (in the middle of NRM), where $\pi x/a=(2n+1)\pi $ or $x=(2n+1)a$ ($n=0,1,2,3,\u2026$), give Display Formula$\mu (\omega )=\u2212\mu 0\mu R(\omega )\u2212i\mu 0[\mu IR+\mu IL2+\mu IR\u2212\mu IL2]=\mu 0[\mu R(\omega )\u2212i\mu IL(\omega )],\epsilon (\omega )=\u2212\epsilon 0\epsilon R(\omega )\u2212i\epsilon 0[\epsilon IR+\epsilon IL2+\epsilon IR\u2212\epsilon IL2]=\epsilon 0[\epsilon R(\omega )\u2212i\epsilon IL(\omega )].$