Two-photon absorption
[2] Thirty years later, the invention of the laser permitted the first experimental verification of two-photon absorption when two-photon-excited fluorescence was detected in a europium-doped crystal.
[6] To apply this theorem it is important to consider that the order in perturbation theory to calculate the probability amplitude of an all-optical
If there were an intermediate electronic state in the gap, this could happen via two separate one-photon transitions in a process described as "resonant TPA", "sequential TPA", or "1+1 absorption" where the absorption alone is a first order process and the generated fluorescence will rise as the square of the incoming intensity.
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 two-photon absorption 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.
So, many materials can be used for the Kerr effect that do not show any one- or two-photon absorption and thus have a high damage threshold.
The relationship between the selection rules for one- and two-photon absorption is analogous to those of Raman and IR spectroscopies.
Below are a series of tables outlining the electric-dipole selection rules for two-photon absorption in a bulk material.
[8][9] Light polarized in the plane of the well (i.e., TE-polarized) can excite transitions from the light-hole (LH) or the heavy-hole (HH) band.
However, light polarized normal to the plane of the QW (i.e., TM-polarized) can only excite transitions from the light-hole band.
Pulsed lasers are most often used because two-photon absorption is a third-order nonlinear optical process,[12] and therefore is most efficient at very high intensities.
Relation between the two-photon excited fluorescence and the total number of absorbed photons per unit time
The molecular two-photon absorption cross-section is usually quoted in the units of Goeppert-Mayer (GM) (after its discoverer, Physics Nobel laureate Maria Goeppert-Mayer), where Considering the reason for these units, one can see that it results from the product of two areas (one for each photon, each in cm2) and a time (within which the two photons must arrive to be able to act together).
The large scaling factor is introduced in order that 2-photon absorption cross-sections of common dyes will have convenient values.
[16] In 1992, with the use of higher laser powers (35 mW) and more sensitive resins/resists, two-photon absorption found its way into lithography.
Photopolymerization for 3D microfabrication is used in a wide variety of applications, including microoptics,[19] microfluids,[20] biomedical implants,[21] 3D scaffolds for cell cultures[22] and tissue engineering.
As a result, it is possible to use excitation in the far infrared region where the human body shows good transparency.
When particles are larger, scattering increases approximately linearly with wavelength: hence clouds are white since they contain water droplets.
So, although longer wavelengths do scatter less in biological tissues, the difference is not as dramatic as Rayleigh's law would predict.
This leads to triplet-triplet annihilation, which gives rise to singlet oxygen, which in turn attacks cancerous cells.
However, using TPA materials, the window for excitation can be extended into the infrared region, thereby making the process more viable to be used on the human body.
[24][25][26][27][28][29] It allows controlling the activity of endogenous proteins in intact tissue with pharmacological selectivity in three dimensions.
The ability of two-photon excitation to address molecules deep within a sample without affecting other areas makes it possible to store and retrieve information in the volume of a substance rather than only on a surface as is done on the DVD.
It was not until the 1990s that rational design principles for the construction of two-photon-absorbing molecules began to be developed, in response to a need from imaging and data storage technologies, and aided by the rapid increases in computer power that allowed quantum calculations to be made.
The most important features of strongly two-photon absorption molecules were found to be a long conjugation system (analogous to a large antenna) and substitution by strong donor and acceptor groups (which can be thought of as inducing nonlinearity in the system and increasing the potential for charge-transfer).
[31][32] Compounds with interesting two-photon absorption properties also include various porphyrin derivatives, conjugated polymers and even dendrimers.
In one study [33] a diradical resonance contribution for the compound depicted below was also linked to efficient two-photon absorption.
With the transition towards shorter laser pulses, from picosecond to subpicosecond durations, noticeably reduced TPA coefficient have been obtained.
[39] Two-photon emission is important for applications in astrophysics, contributing to the continuum radiation from planetary nebulae (theoretically predicted for them in [40] and observed in [41]).
