Distributed Bragg reflector

A distributed Bragg reflector uses a periodic refractive index structure to make successive weak reflections add coherently. Near the design wavelength, constructive wave interference produces strong reflection even when a single interface reflects only a small fraction of incident radiant power.

A quarter-wave Bragg stack alternates layers with optical thickness ${\lambda }_0/4$ at normal incidence. Measuring transmission across wavelength reveals a rejected band rather than a perfectly reflecting surface at every frequency. Such mirrors provide wavelength selection in an optical resonator; their reflection band shifts with incidence angle and material dispersion.

At normal incidence, alternating layers with indices $n_H,n_L$ and optical thicknesses $n_H{d}_H=n_L{d}_L={\lambda }_0/4$ 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.