The essence of the band gap of 1-D photonic crystal with period consisting of two elements

In order to discuss the essence of 1-D photonic crystal band gap, the reflectivity of 1-D photonic crystal consisting of two elements was analyzed, and the expression of the real part of the equivalent refractive index was derived by using the transmission characteristic matrix method. Taking the 1-D photonic crystal composed of magnesium fluoride (MgF₂) and zinc sulfide (ZnS) as an example, the analytical numerical calculations of the reflectivity and the real part of the equivalent refractive index were done and the corresponding curves were drawn. It was the conclusion that, wavelength range with reflectivity of 1.0 is the same as that with real part of equivalent refractive index of zero. For the light waves in the band gap, the real part of the equivalent refractive index of 1-D photonic crystal is equal to or close to zero, namely, 1-D photonic crystal is virtual equivalent index material in the extent of band gap. In other words, the optical essence of photonic crystal band gap is that photonic crystal becomes virtual equivalent index material. This study is helpful for the study of 1-D photonic crystal with multi periods consisting of two elements.