Adielectric mirror, also known as a Bragg mirror, is a type of mirror composed of multiple thin layersofdielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified reflectivity at different wavelengthsoflight. Dielectric mirrors are also used to produce ultra-high reflectivity mirrors: values of 99.999% or better over a narrow range of wavelengths can be produced using special techniques. Alternatively, they can be made to reflect a broad spectrum of light, such as the entire visible range or the spectrum of the Ti-sapphire laser.
Diagram of a dielectric mirror. Thin layers with a high refractive index n1 are interleaved with thicker layers with a lower refractive index n2. The path lengths lA and lB differ by exactly one wavelength, which leads to constructive interference.
The reflectivity of a dielectric mirror is based on the interference of light reflected from the different layers of a dielectric stack. This is the same principle used in multi-layer anti-reflection coatings, which are dielectric stacks which have been designed to minimize rather than maximize reflectivity. Simple dielectric mirrors function like one-dimensional photonic crystals, consisting of a stack of layers with a high refractive index interleaved with layers of a low refractive index (see diagram). The thicknesses of the layers are chosen such that the path-length differences for reflections from different high-index layers are integer multiples of the wavelength for which the mirror is designed. The reflections from the low-index layers have exactly half a wavelength in path length difference, but there is a 180-degree difference in phase shift at a low-to-high index boundary, compared to a high-to-low index boundary, which means that these reflections are also in phase. In the case of a mirror at normal incidence, the layers have a thickness of a quarter wavelength.
The color transmitted by the dielectric filters shifts when the angle of incident light changes.
Dielectric mirrors exhibit retardance as a function of angle of incidence and mirror design.[2]
As shown in the GIF, the transmitted color shifts towards the blue with increasing angle of incidence. Regarding interference in the high reflective index medium this blueshift is given by the formula
,
where is any multiple of the transmitted wavelength and is the angle of incidence in the second medium.
See thin-film interference for a derivation. However, there is also interference in the low refractive index medium. The best reflectivity will be at
[3]
,
where is the transmitted wavelength under perpendicular angle of incidence and
Anelectron microscope image of an approximately 13 micrometre piece of dielectric mirror being cut from a larger substrate. Alternating layers of Ta2O5 and SiO2 are visible on the bottom edge.
Polymeric dielectric mirrors are fabricated industrially via co-extrusion of melt polymers,[5] and by spin-coating[6]ordip-coating[7] on smaller scale.