Chirped mirror
Encyclopedia
Dielectric mirror
A dielectric mirror is a type of a mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified...
with chirped
Chirp
A chirp is a signal in which the frequency increases or decreases with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly used in sonar and radar, but has other applications, such as in spread spectrum communications...
spaces—spaces of varying depth designed to reflect varying wavelengths of lights—between the dielectric layers (stack).
Chirped mirrors are used in applications like lasers to reflect a wider range of light wavelengths than ordinary dielectric mirrors, or to compensate for the dispersion of wavelengths
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
that can be created by some optical elements.
Simple explanation
An ordinary dielectric mirror is made to reflect a single frequency of light. The dielectric mirror is made of transparent materials that are uniformly layered at a depth of 1/4 the wavelength of light the dielectric mirror is designed to reflect. The dielectric mirror is transparent to other wavelengths of light except those in a very narrow band around the wavelength it is designed to reflect.A chirped mirror is made to reflect a wider range of frequencies. This is done by creating layers with different depths. There may be 10 layers with a depth designed to reflect a certain wavelength of light, another 10 layers with slightly greater depth to reflect a slightly longer wavelength of light, and so on for the entire range of wavelengths of light the mirror is designed to reflect. The result is a mirror that can reflect a whole range of light wavelengths rather than single narrow band of wavelengths.
Because light reflected from the deeper layers of the mirror travels a longer distance than the light that reflects off the surface layers, a chirped mirror can be designed to change the relative times of wavefronts of different wavelength reflecting from it. This may be used, for example, to disperse a pulse of light of different wavelengths which arrives all at one time or to tighten a pulse of light where different wavelengths arrive dispersed in time.
This ability tighten or more tightly pack a pulse of light of different wavelengths is important, because some commonly used optical elements naturally disperse a packet of light according to wavelength, a phenomenon known as chromatic dispersion
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
. A chirped mirror can be designed to compensate for the chromatic dispersion created by other optical elements in a system.
This is a simplified explanation which omits some important but more complex technical considerations.
Technical explanation
For dielectric mirrors, materials with a refractive indexRefractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of 1.5 and 2.2 are available.
The Fresnel reflection for the amplitude is about 0.2.
So with 10 layers about 0.99 of the light amplitude that is 0.98 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
Anti-reflective coating
An antireflective or anti-reflection coating is a type of optical coating applied to the surface of lenses and other optical devices to reduce reflection. This improves the efficiency of the system since less light is lost. In complex systems such as a telescope, the reduction in reflections also...
.
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
Brewster's angle
Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly...
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 think 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.
Application
In Ti-sapphire laserTi-sapphire laser
Ti:sapphire lasers are tunable lasers which emit red and near-infrared light in the range from 650 to 1100 nanometers. These lasers are mainly used in scientific research because of their tunability and their ability to generate ultrashort pulses...
s which employ Kerr-lens modelocking
Kerr-lens modelocking
Kerr-lens modelocking is a method of modelocking lasers via a nonlinear optical process known as the optical Kerr effect. This method allows the generation of pulses of light with a duration as short as a few femtoseconds....
, 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 loss 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
Self-phase modulation
Self-phase modulation is a nonlinear optical effect of light-matter interaction.An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect...
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
Chirped pulse amplification
Chirped pulse amplification is a technique for amplifying an ultrashort laser pulse up to the petawatt level with the laser pulse being stretched out temporally and spectrally prior to amplification...
these mirrors are used to correct residual variations of group delay
after a grating compressor is inserted into the system.