Chirped mirror
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A chirped mirror is a dielectric mirror with chirped spaces between the dielectric layers (stack).
For dielectric mirrors materials with a refractive index of 1.5 and 2.2 are available. The Fresnel reflection for the amplitude is about 0.2. So with 10 layers about 0.88 of the light amplitude that is 0.99 of the light intensity is reflected. Chirped mirrors use 60 layers. So the light of a specific frequency interacts only with one sixth of the whole stack.
The surface leads to an early reflection of a pulse with an unaltered chirp. This is prevented by sparing some layers for anti-reflective coating. In a simple case this is done with a single layer of MgF2, which has a refractive index of 1.38 (in the near infrared). The bandwidth is large, but not one octave. Going from normal incidence to Brewster's angle p-polarized is less and less reflected. To eliminate residual reflections from the surface in the case of multiple mirrors, the distance between the surface and the stack is different for every mirror.
Naively one would though that the chirp starts outside the desired wavelength range, and any wavelength within the range experiences a complete resonance fade in and fade out. A detailed calculation (references in the external link ) says, that the reflectivity of the mirror must be chirped also by not allotting the λ/2 equally across high and low index of refraction material. These are called double chirped mirrors.
[edit] Application
In Ti-sapphire laser which employ Kerr-lens modelocking chirped mirrors are often used as the sole means to compensate group delay variations. Considering the above numbers a single mirror can compensate 4 µm optical path length. Considering the group velocity this is enough for the 3 m air inside the cavity, for the 3 mm of Ti:sapphire crystal three more mirrors are needed, so that a simple Z-cavity can already be compensated. On the other hand the gain of the crystal of about 1.1 which is high enough to compensate the lost of 8 mirrors, which gives more degrees of freedom in group delay compensation. More critically for short pulses is that the frequency components outside the gain range of the crystal generated indirectly by self-phase modulation are not lost through the end or folding mirrors but and are transmitted through the out-couple mirror. In a kind of decision by majority the modes of the laser decide which group delay to choose, and spectral components close to this delay are emphasized in the output. Due to the ripples in the compensation, the spectrum also has ripples. A single stack reflects between 780 nm and 800 nm. The chirped mirror with 6 times the layers can be reflective from 730 nm to 850 nm. The gain of Ti:Sa is greater than one between 600 nm and 1200 nm. To reflect this bandwidth higher losses have to be accepted.
In Chirped pulse amplification these mirrors are used to correct residual variations of group delay after a grating compressor is inserted into the system.
