Rugate filter

This effect is achieved by a periodic, continuous change of the refractive index of the dielectric coating.

[2] The word "rugate" is derived from corrugated structures found in nature, which also selectively reflect certain wavelength ranges of light,[3] for example the wings of the Morpho butterfly.

[4] In rugate filters the refractive index varies periodically and continuously as a function of the depth of the mirror coating.

The refractive index profiles of a Rugate and a Bragg mirror are shown in the graph on the right.

The theory of the Bragg mirror leads to a calculation of the wavelength at which the reflection of a rugate filter is greatest.

For an alternating sequence in the Bragg mirror, the maximum reflection at a wavelength

[5] As a sanity check for the correctness of this equation, one can solve the integral for a discrete refractive index profile and substitute the period of a Bragg mirror

The figure on the right shows the reflection spectra calculated by the transfer-matrix method for the refractive index profiles of a Bragg and Rugate filter.

It can be seen that both mirrors have their maximum reflectivity at 700 nm, whereas the rugate filter has a lower bandwidth.

This peak is not present in the spectrum of the Bragg mirror because of its discrete layer system, which causes destructive interference at this wavelength.

Rugate filters are better suited for this purpose because the sinusoidal refractive index profile has anti-reflection properties similar to those of black silicon.

To achieve this, the chemical composition of the mirror must also change continuously as a function of the layer thickness.

Here, the current density during the etching process is selected so that the resulting porosity and thus the refractive index varies sinusoidally with the layer thickness.