Saturable absorption is a property of materials where the
absorption of light decreases with increasing light
intensity. Most materials show some saturable absorption, but often only at very high optical intensities (close to the optical damage). At sufficiently high incident light intensity, the ground state of a saturable absorber material is excited into an upper energy state at such a rate that there is insufficient time for it to decay back to the ground state before the ground state becomes depleted, causing the absorption to saturate. The key parameters for a saturable absorber are its
wavelength range (where in the electromagnetic spectrum it absorbs), its dynamic response (how fast it recovers), and its saturation intensity and fluence (at what intensity or pulse energy it saturates).
Saturable absorber materials are useful in
laser cavities. For instance, they are commonly used for passive
Q-switching.
Phenomenology
Within the simple model of saturated absorption, the relaxation rate of excitations does not depend on the intensity.
Then, for the
continuous-wave (cw) operation, the absorption rate (or simply absorption) is determined by intensity :
where is linear absorption, and
is saturation intensity.
These parameters are related with the
concentration of the active centers in the medium,
the
effective cross-sections and the lifetime of the excitations.[1]
The solution can be expressed also through the related
Lambert W function.
Let . Then
With new independent variable ,
Equation (6) leads to the equation
The formal solution can be written
where is constant, but the equation may correspond to the non-physical value of intensity
(intensity zero) or to the unusual branch of the Lambert W function.
Saturation fluence
For pulsed operation, in the limiting case of short pulses, absorption can be expressed through the fluence
where time should be small compared to the relaxation time of the medium; it is assumed that the intensity is zero at .
Then, the saturable absorption can be written as follows:
where saturation fluence is constant.
In the intermediate case (neither cw, nor short pulse operation), the rate equations for
excitation and
relaxation in the
optical medium must be considered together.
Saturation fluence is one of the factors that determine
threshold in the gain media and limits the storage of energy in a pulsed
disk laser.[2]
Mechanisms and examples
Absorption saturation, which results in decreased absorption at high incident light intensity, competes with other mechanisms (for example, increase in temperature, formation of
color centers, etc.), which result in increased absorption.[3][4]
In particular, saturable absorption is only one of several mechanisms that produce
self-pulsation in lasers, especially in
semiconductor lasers.[5]
One atom thick layer of carbon,
graphene, can be seen with the naked eye because it absorbs approximately 2.3% of white light, which is π times
fine-structure constant.[6] The saturable absorption response of graphene is wavelength independent from UV to IR, mid-IR and even to THz frequencies.[7][8][9] In rolled-up graphene sheets (
carbon nanotubes), saturable absorption is dependent on diameter and chirality.[10][11]
Microwave and terahertz saturable absorption
Saturable absorption can even take place at the microwave and terahertz band (corresponding to a wavelength from 30 μm to 300 μm). Some materials, for example
graphene, with very weak energy band gap (several meV), could absorb photons at Microwave and Terahertz band due to its interband absorption. In one report, microwave absorbance of graphene always decreases with increasing the power and reaches at a constant level for power larger than a threshold value. The microwave saturable absorption in graphene is almost independent of the incident frequency, which demonstrates that graphene may have important applications in graphene microwave photonics devices such as: microwave saturable absorber, modulator, polarizer, microwave signal processing, broad-band wireless access networks, sensor networks, radar, satellite communications, and so on.[12][non-primary source needed]
Saturable X-ray absorption
Saturable absorption has been demonstrated for X-rays. In one study, a thin 50 nanometres (2.0×10−6 in) foil of
aluminium was irradiated with soft
X-raylaser radiation (
wavelength 13.5 nm). The short laser pulse knocked out core
L-shell electrons without breaking the
crystalline structure of the metal, making it transparent to soft X-rays of the same wavelength for about 40
femtoseconds.[13][14][non-primary source needed]
^T. Hasan; Z. Sun; F. Wang; F. Bonaccorso; P. H. Tan; A. G. Rozhin; A. C. Ferrari (2009). "Nanotube–Polymer Composites for Ultrafast Photonics". Advanced Materials. 21 (38–39): 3874–3899.
doi:
10.1002/adma.200901122.
S2CID36587931.