Dispersive Mirrors

Dispersive mirrors are mirrors — usually a kind of laser mirrors — which provide some amount of chromatic dispersion. They can be used for dispersion compensation within a laser resonator or for the compression of ultrashort pulses, for example, or for other applications in femtosecond laser optics and optical signal processing.

Usually, dispersive mirrors are made in the form of dielectric mirrors, and they can be based on different operation principles:

• Some simple designs are essentially realizing a Gires–Tournois interferometer, where the chromatic dispersion results from interference effects at an off-resonant optical resonator. It is possible to obtain a large amount of chromatic dispersion (many thousands of fs²) of any sign, but only with a limited optical bandwidth. The higher the amount of chromatic dispersion, the more stringent is the limit for the optical bandwidth.
• A totally different operation principle is that of the chirped mirror, where the optical penetration depth is wavelength-dependent. According to a very simplified picture, the resulting chromatic dispersion can be explained as resulting from a wavelength-dependent path length. With proper optimization and precise growth of the dielectric structure, ultrabroadband mirrors e.g. for octave-spanning titanium–sapphire lasers can be produced.

Apart from the amount of chromatic dispersion in the bandwidth, it is often important to achieve a high precision of the whole spectral dispersion profile. For example, one may use such mirrors for compensating even higher-order chromatic dispersion in the resonator of a mode-locked laser.

Usually, dispersive mirrors are highly reflecting. If there is any significant transmission, the chromatic dispersion for the transmitted light is generally totally different from the chromatic dispersion for the reflected light.

Compared with ordinary highly reflecting laser mirrors, which are generally designed as Bragg mirrors, dispersive mirrors tend to exhibit higher parasitic losses (i.e., a somewhat lower reflectance) and a lower optical damage threshold. This results from the substantially deeper penetration depth into the dielectric structure. (See Figure 3 of the article on chirped mirrors.) The higher parasitic losses also imply a higher degree of thermal lensing on such mirrors, if they are used for high-power laser beams. With optimized high-power dispersive mirrors, however, thermal effects can be kept on a quite low level compared with those at other kinds of dispersive elements, e.g. prism pairs. Key aspects for such an optimization are the minimization of parasitic losses and the use of a mirror substrate material with a low thermal expansion coefficient and a high thermal conductivity.

If a simple reflection on a dispersive mirror does not provide sufficiently much chromatic dispersion, one may use multiple reflections, e.g. between two dispersive mirrors, where the two mirror surfaces are parallel to each other and non-normal incidence is used (see Figure 1). Note that the angle of incidence should not be too large because the chromatic dispersion depends on that angle. Obviously, the total power losses and the total strength of thermal lensing scale with the number of reflections.

Sometimes, a matched pair of two different dispersive mirrors is used, where the dispersion errors of both mirrors are partially compensated.

Designing Dispersive Mirrors

For designing dispersive mirror coatings, a flexible simulation and design software is indispensable. The RP Coating software is an ideal tool for such work, as it is particularly flexible. For example, you can define an initial chirped mirror design with a limited number of parameters and numerically optimize only those (rather than each individual layer thickness separately), which is far more efficient. Thereafter, you may still apply a local optimization of all layer thickness values.

A common performance limitation of dispersive mirrors, particularly chirped mirrors, is the occurrence of dispersion oscillations (also called ripples). These are periodic deviations of the actual group delay dispersion (GDD) from the target curve, caused by interference effects (impedance mismatch) at the interface between the mirror stack and the ambient air. Such ripples can be detrimental to pulse quality, causing the formation of pre-pulses or pedestals in the time domain.

To mitigate this, manufacturers may employ double-chirped mirror (DCM) designs which improve impedance matching. Another effective strategy is the use of matched pairs: two mirrors manufactured with slightly different layer designs such that their dispersion oscillations are out of phase. When a beam reflects off both mirrors in sequence, the oscillations partially cancel each other out, resulting in a much smoother net dispersion profile.