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.
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]
In the simplest geometry, when the rays of the absorbing light are parallel, the intensity can be described with the Beer–Lambert law,
where is coordinate in the direction of propagation. Substitution of (1) into (2) gives the equation
With the dimensionless variables , , equation (3) can be rewritten as
The solution can be expressed in terms of the Wright omega function :
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.
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 continuous, 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]
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]
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 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-ray laser 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 ]
The Beer–Bouguer–Lambert (BBL) extinction law is an empirical relationship describing the attenuation in intensity of a radiation beam passing through a macroscopically homogenous medium with which it interacts. Formally, it states that the intensity of radiation decays exponentially in the absorbance of the medium, and that said absorbance is proportional to the length of beam passing through the medium, the concentration of interacting matter along that path, and a constant representing said matter's propensity to interact.
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
Stimulated emission is the process by which an incoming photon of a specific frequency can interact with an excited atomic electron, causing it to drop to a lower energy level. The liberated energy transfers to the electromagnetic field, creating a new photon with a frequency, polarization, and direction of travel that are all identical to the photons of the incident wave. This is in contrast to spontaneous emission, which occurs at a characteristic rate for each of the atoms/oscillators in the upper energy state regardless of the external electromagnetic field.
The active laser medium is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a higher energy state previously populated by a pump source.
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Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules, electrons, positrons, protons, antiprotons and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.
In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.
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A quantum well is a potential well with only discrete energy values.
Cavity ring-down spectroscopy (CRDS) is a highly sensitive optical spectroscopic technique that enables measurement of absolute optical extinction by samples that scatter and absorb light. It has been widely used to study gaseous samples which absorb light at specific wavelengths, and in turn to determine mole fractions down to the parts per trillion level. The technique is also known as cavity ring-down laser absorption spectroscopy (CRLAS).
Self-phase modulation (SPM) 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. This variation in refractive index will produce a phase shift in the pulse, leading to a change of the pulse's frequency spectrum.
Quantum-cascade lasers (QCLs) are semiconductor lasers that emit in the mid- to far-infrared portion of the electromagnetic spectrum and were first demonstrated by Jérôme Faist, Federico Capasso, Deborah Sivco, Carlo Sirtori, Albert Hutchinson, and Alfred Cho at Bell Laboratories in 1994.
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In atomic physics, two-photon absorption (TPA or 2PA), also called two-photon excitation or non-linear absorption, is the simultaneous absorption of two photons of identical or different frequencies in order to excite an atom or a molecule from one state (usually the ground state), via a virtual energy level, to a higher energy, most commonly an excited electronic state. Absorption of two photons with different frequencies is called non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the photon dose (D), which is proportional to the square of the light intensity (D ∝ I2); thus it is a nonlinear optical process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with absorption cross section typically several orders of magnitude smaller than one-photon absorption cross section.
In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and dispersive effects in the medium. There are two main kinds of solitons:
In physical optics or wave optics, a vector soliton is a solitary wave with multiple components coupled together that maintains its shape during propagation. Ordinary solitons maintain their shape but have effectively only one (scalar) polarization component, while vector solitons have two distinct polarization components. Among all the types of solitons, optical vector solitons draw the most attention due to their wide range of applications, particularly in generating ultrafast pulses and light control technology. Optical vector solitons can be classified into temporal vector solitons and spatial vector solitons. During the propagation of both temporal solitons and spatial solitons, despite being in a medium with birefringence, the orthogonal polarizations can copropagate as one unit without splitting due to the strong cross-phase modulation and coherent energy exchange between the two polarizations of the vector soliton which may induce intensity differences between these two polarizations. Thus vector solitons are no longer linearly polarized but rather elliptically polarized.
Stimulated Raman spectroscopy, also referred to as stimulated Raman scattering (SRS), is a form of spectroscopy employed in physics, chemistry, biology, and other fields. The basic mechanism resembles that of spontaneous Raman spectroscopy: a pump photon, of the angular frequency , which is scattered by a molecule has some small probability of inducing some vibrational transition, as opposed to inducing a simple Rayleigh transition. This makes the molecule emit a photon at a shifted frequency. However, SRS, as opposed to spontaneous Raman spectroscopy, is a third-order non-linear phenomenon involving a second photon—the Stokes photon of angular frequency —which stimulates a specific transition. When the difference in frequency between both photons resembles that of a specific vibrational transition the occurrence of this transition is resonantly enhanced. In SRS, the signal is equivalent to changes in the intensity of the pump and Stokes beams. The signals are typically rather low, of the order of a part in 10^5, thus calling for modulation-transfer techniques: one beam is modulated in amplitude, and the signal is detected on the other beam via a lock-in amplifier. Employing a pump laser beam of a constant frequency and a Stokes laser beam of a scanned frequency allows for unraveling the molecule's spectral fingerprint. This spectral fingerprint differs from those obtained by other spectroscopy methods, such as Rayleigh scattering, as the Raman transitions confer different exclusion rules than those that apply to Rayleigh transitions.
Time resolved microwave conductivity (TRMC) is an experimental technique used to evaluate the electronic properties of semiconductors. Specifically, it is used to evaluate a proxy for charge carrier mobility and a representative carrier lifetime from light-induced changes in conductance. The technique works by photo-generating electrons and holes in a semiconductor, allowing these charge carriers to move under a microwave field, and detecting the resulting changes in the electric field. TRMC systems cannot be purchased as a single unit, and are generally "home-built" from individual components. One advantage of TRMC over alternative techniques is that it does not require direct physical contact to the material.
