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Main operational principle of a multilayer dispersive mirror (DM)

Example of a multilayer mirror in the EUV: 68 % maximum peak reflectivity of a MoSi multilayer at 93 eV measured at BessyII (right)

Multilayer mirrors are periodic stacks of layer materials with different refractive index in alternating arrangement. At each interface part of the incoming light is reflected, while the rest penetrates deeper into the stack and is partly reflected at other interfaces. All partly reflected coherent beams interfere with each other. If for example the optical thickness of all layers is exactly equal to a quarter of the wavelength of the incoming light (“quarter wave stack”), all the beams add up constructively. High reflectivity is achievable, in the visible up to 99.999 % by using highly transparent oxide materials.
In the XUV short wavelength range, nanometer layers of metal and semiconductor materials are used and reflectivity is limited to 70-80 % due to the high absorption coefficient of all materials in the soft X-ray range. The achievable values are highly dependent on the wavelength, the material combination and sophisticated deposition mechanisms.

Physical principal of an a-periodic mirror design. Both positive and negative dispersion can be introduced to the incoming radiation.

Broad-bandwidth dispersive multilayer mirrors are achieved by extending the idea to aperiodic multilayer stacks.
In order to control the group delay, the combination of layers with high and low refractive indices must have very carefully selected thicknesses. Such a structure provides different penetration depths for different spectral components.
This can be used for example to compensate for the intrinsic dispersion of a light pulse that passed through media and what would broaden a pulse due to the wavelength-dependent group velocity.    

The main operational principle of a DM compressor allows one to realize ultrashort pulses by using the effect of pulse broadening in a dispersive medium. The broader pulse has less peak intensity, can be amplified and is finally recompressed by the use of chirped mirrors.

The way how dispersive optics works: A generalized transform-limited short pulse, which can be calculated by inverse Fourier transform of an arbitrary input spectrum, propagates in a dispersive media or set of dispersive materials. The penetrated pulse will be extended in the dispersive media, due to dispersion of elements (in laser oscillator or compressor). By employing a DM compressor (chirped mirrors in the Figure), dispersion can be compensated, thus the pulse will be compressed. In the classical approach, the designer makes the mirror dispersion as close as possible to the dispersion of laser elements with an opposite sign.