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FAQs

A thin film Bragg reflector consists of a multilayer-stack of alternate high- and
low-index films, all one quarter wavelength thick (see figure right).
The geometrical thicknesses of the high- und low-index films are
t_{H} = λ/(4n_{H}) and
t_{L} = λ/(4n_{L}) respectively.

n_{H} and n_{L} are the indices of refraction of the high- and
low-index films, respectively and λ is
the center wavelength of the Bragg mirror.

On every interface in the stack a part of the incident beam is reflected.
The reflected parts have a phase shift of 180° only if the incident light
goes from low-index medium in a high-index medium. The relative phase difference
of all reflected beams is zero or a multiple of 360° and therefore they interfere
constructively.

The intensity of the incident light beam decreases during his travel trough
the quarter-wave stack and at the same time the reflected light increases, if
the absorptance A of the stack is negligible.

• Reflectance

*Reflectance of a Bragg mirror*

The reflectance R of a quarter-wave stack in air or free space with high-index layers outermost on both sides is given by :

with

- Y - admittance of a quarter wave stack with (2p + 1) layers
- n
_{H}- high index of refraction - n
_{L}-low index of refraction - n
_{S}- index of the substrate - (2p + 1) - number of layers in the stack

*Approximation*

If the number (2p + 1) of films in the quarter-wave stack is large and the absorption can be neglected then the reflectance R and the transmittance T can be approximated by

*Numeric examples*

Reflectance of a Bragg mirror as a function of the number p of film pairs
with n_{H} = n_{S} = 3.5 and n_{L} = 3.0.

• Spectral width

*Spectral width of the high refletion zone*

The spectral width Δλ of the high reflectance zone increases with increasing
difference of the refractive indices n_{H} - n_{L}.

Δλ can be estimated with the design wavelength λ_{0} of the quarter-wave stack by

The relative spectral width w = Δλ/λ of the high reflectance zone
as a function of the ratio of the refractive indices n_{H}/n_{L} is shown in the figure right.

• AlAs/GaAs Bragg mirror

*AlAs/GaAs Bragg mirror*

For the wavelength 1064 nm the refractive indices
of the materials GaAs and AlAs are n(GaAs) = 3.49 and n(AlAs) = 2.95, respectively.

The figures below show the spectral reflactance of AlAs/GaAS quarter-wave stacks with the center wavelength
λ_{0} = 1064 nm and different numbers of AlAs/GaAs pairs.