= Drude-Lorentz reflectivity minimum
{c}
{title2=$\omega_{\min}\simeq\omega_{pc}/\sqrt{\epsilon_b-1}$}
A doped <semiconductor> at frequencies far below its bound-electron resonances can have
$$
\epsilon_r(\omega)\simeq\epsilon_b-\frac{\omega_{pc}^2}{\omega(\omega+i\gamma_c)},\qquad
\omega_{pc}^2=\frac{n_ce^2}{\epsilon_0m_c^*}.
$$
For a weakly absorbing nonmagnetic half-space adjacent to <vacuum>, the normal-incidence <optical reflectance> is minimized near refractive-index matching, $\epsilon_r\simeq1$. When $\epsilon_b>1$ and $\gamma_c$ is small this gives $\omega_{\min}\simeq\omega_{pc}/\sqrt{\epsilon_b-1}$. The zero of the <real part> of $\epsilon_r$, near $\omega_{pc}/\sqrt{\epsilon_b}$, is a distinct frequency. Increasing the <carrier density> shifts the minimum to shorter <wavelength> if the carrier <effective mass> and background response remain fixed. With appreciable loss, the minimum must be found from the full complex <Fresnel equations>.
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