= Quarter-wave Bragg stack
{title2=$n_Hd_H=n_Ld_L=\lambda_0/4$}
At normal incidence, alternating layers with indices $n_H,n_L$ and optical thicknesses $n_Hd_H=n_Ld_L=\lambda_0/4$ give reinforcing reflected waves near design <wavelength> $\lambda_0$. Their periodic transfer matrix has a stop band when its Bloch <phase> is complex. A finite stack has nonzero transmission and its exterior impedances matter. Introducing a suitably phased central defect can support a transmission <resonance> within the stop band; a one-dimensional stop band is not a complete three-dimensional photonic gap.
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