The "nonlinear" in the description of this process means that the strength of the interaction increases faster than linearly with the electric field of the light. In fact, under ideal conditions the rate of TPA is proportional to the square of the field intensity. This dependence can be derived quantum mechanically, but is intuitively obvious when one considers that it requires two photons to coincide in time and space. This requirement for high light intensity means that lasers are required to study TPA phenomena. Further, in order to understand the TPA spectrum, monochromatic light is also desired in order to measure the TPA cross section at different wavelengths. Hence, tunable pulsed lasers (such as frequency-doubled Nd:YAG-pumped OPOs and OPAs) are the choice of excitation.
laser and nonlinear optics by bb.laud PDF
Two-photon absorption can be measured by several techniques. Some of them are two-photon excited fluorescence (TPEF),[7] z-scan, self-diffraction[8] or nonlinear transmission (NLT). Pulsed lasers are most often used because TPA is a third-order nonlinear optical process,[9] and therefore is most efficient at very high intensities.
for TPA with light intensity as a function of path length or cross section x \displaystyle x as a function of concentration c \displaystyle c and the initial light intensity I 0 \displaystyle I_0 . The absorption coefficient α \displaystyle \alpha now becomes the TPA coefficient β \displaystyle \beta . (Note that there is some confusion over the term β \displaystyle \beta in nonlinear optics, since it is sometimes used to describe the second-order polarizability, and occasionally for the molecular two-photon cross-section. More often however, it is used to describe the bulk 2-photon optical density of a sample. The letter δ \displaystyle \delta or σ \displaystyle \sigma is more often used to denote the molecular two-photon cross-section.)
Another area of research is optical power limiting. In a material with a strong nonlinear effect, the absorption of light increases with intensity such that beyond a certain input intensity the output intensity approaches a constant value. Such a material can be used to limit the amount of optical power entering a system. This can be used to protect expensive or sensitive equipment such as sensors, can be used in protective goggles, or can be used to control noise in laser beams.
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