Absolute optical transparency of quarter-wavelength triple layers

Reflection properties of repetitive quarter-wavelength dielectric triple layers are analyzed analytically by the newly developed recurrent approach. This novel recurrent approach is based on unit-by-unit calculation procedure and permits to analyze group properties of repetitive units consisting of quarter-wavelength dielectric layers. For the structure of even number of quarter-wavelength triple layer units the full transparency independently from the constituting layers indices is obtained. For any odd number of triple layer units the reflection remains the same and equals to the reflection of a single unit of triple layers. All these results are obtained also by the numerical method of single expression (MSE). This is the first time to the best of our knowledge that the absolute optical transparency for any even number of repetitive quarter-wavelength triple layers is obtained. Outside of the central wavelength in a wide optical range, periodic quarter-wavelength triple layers of certain number exhibit properties of a pass-band filter.