Two-quantum absorption

The factor of 2 takes into account the fact that two photons disappear in each act of absorption. Integration over the length L of the cell gives the absorption law for the two-quantum absorption ... 

Figure 6 The coefficient of the two-quantum absorption as a function of standing-wave frequency...

We begin this section by considering a two-quantum absorption detector initially in the ground state. The detector response at the space-time point X. = t, may be written in terms of the second-order correlation function [7.19, 34, 36, 41], and is given by... 

Plakhotnik T, Walser D, Pirotta M, Renn A and Wild U P 1996 Nonlinear spectroscopy on a single quantum system two-photon absorption of a single molecule Science 271 1703-5... 

The discussion in this chapter is limited to cyanine-like NIR conjugated molecules, and further, is limited to discussing their two-photon absorption spectra with little emphasis on their excited state absorption properties. In principle, if the quantum mechanical states are known, the ultrafast nonlinear refraction may also be determined, but that is outside the scope of this chapter. The extent to which the results discussed here can be transferred to describe the nonlinear optical properties of other classes of molecules is debatable, but there are certain results that are clear. Designing molecules with large transition dipole moments that take advantage of intermediate state resonance and double resonance enhancements are definitely important approaches to obtain large two-photon absorption cross sections. 

Stabo-Eeg F, Lindgren M, Nilsson KPR, Inganas O, Hammarstrdm P (2007) Quantum efficiency and two-photon absorption cross-section of conjugated polyelectrolytes used for protein conformation measurements with applications on amyloid structures. Chem Phys 336 121-126... 

Two-photon absorption occurs when the energy of a molecular transition matches the combined energy of two photons. Quantum mechanically, the absorption probability is proportional to the two-photon transition moment from the ground state, g, to the excited state, n, via intermediate state, m, and can be expressed as follows (Boyd 1992 Abe 2001) ... 

Ando, T., Urakami, T., Itoh, H., and Tsuchiya, Y. 2002. Optimization of resonant two-photon absorption with adaptive quantum control. Appl. Phys. Lett. 80 4265-67. 

In conclusion, it should be noted that fluorene derivatives 16 and 22, with large two-photon absorption cross sections, high fluorescence quantum yields and high photochemical stabihty imder one- and two-photon excitation are outstanding candidates for various linear and nonhnear optical apphcations, especially 3D fluorescence bioimaging. 

Table 6 Two-photon absorption cross sections, 32PA> and quantum yields of singlet oxygen generation, under single and two-photon excitation of 57-60 at 775 nm in ACN...

To use the two-photon fluorescence (TPF), i. e., the fluorescence excited by two-photon absorption, for the measurement of the halfwidth of ultrashort pulses from mode-locked lasers, the laser beam containing the train of pulses is split into two beams by a beam splitter (Fig. 12) which are then redirected by two mirrors Mi and M2 so that they are collinear and completely overlap in the dye cell DC which is situated in the center between the two mirrors. In the selection of the dye, it need only be remembered that it should, as far as possible, be free from absorption at the laser wavelength, have a strong absorption band at half the wavelength, and have the highest possible fluorescence quantum yield 97. Thus a... 

A typical application is the use of the (2 + 1) REMPI scheme for measuring the (v,./) distribution of H2 produced in associative desorption from a surface. When the laser is tuned to a spectroscopic transition between individual quantum states in the X -> E electronic band, resonant two-photon absorption populates the E state and this is subsequently ionized by absorption of another photon. The ion current is proportional to the number in the specific (v,./) quantum state in the ground electronic state that is involved in the spectroscopic transition. Tuning the laser to another spectroscopic feature probes another (v, J) state. Therefore, recording the ion current as the laser is scanned over the electronic band maps out the population distribution of H2(v, J) produced in the associative desorption. Ef of the (v, J) state can also often be simultaneously measured using field - free ion TOF or laser pump - probe TOF detection techniques. The (2 +1) REMPI scheme for detecting H2 is almost independent of the rotational alignment and orientation f(M) of molecules so that only relative populations of the internal states... 

Figure 1. Linewidlhs of different rotational transitions in the 14q1q vibronic band of benzene measured with Doppler-free two-photon absorption. The observed strong dependence on the quantum number J of the rotational angular momentum is evidence for a rotationally dependent intramolecular coupling process. (Taken from Ref. 3.)...

On the contrary, the semiclassical approach in the problem of the optical absorption is restricted to a great extent and the adequate description of the phonon-assisted optical bands with a complicated structure caused by the dynamic JTE cannot be done in the framework of this approach [13]. An expressive example is represented by the two-humped absorption band of A —> E <8> e transition. The dip of absorption curve for A —> E <8> e transition to zero has no physical meaning because of the invalidity of the semiclassical approximation for this spectral range due to essentially quantum nature of the density of the vibronic states in the conical intersection of the adiabatic surface. This result is peculiar for the resonance (optical) phenomena in JT systems full discussion of the condition of the applicability of the adiabatic approximation is given in Ref. [13]. 

Fig. 1.9. Absorption cross section (arbitrary units) of H20 initially prepared in the 04-0) state as a function of the photolysis wavelength A2. The first two quantum numbers specify the excitation of the two stretching modes (using a local mode assignment, see Chapter 13), the minus sign indicates the symmetry with respect to the interchange of the two H atoms, and the third quantum number denotes the bending state. Adapted from Vander Wal, Scott, and Crim (1991) calculations by Weide, Hennig, and Schinke (1989).

In view of Figure 7.11 (and similar plots for all other resonances) the peaks in the absorption spectrum can be assigned to a set of two quantum numbers (m, n ), where m is the quantum number for excitation along the dissociation bond R and n is the quantum number for excitation of the N-0 vibrational bond r. The asterisk indicates that these quantum numbers designate resonance, i.e., quasi-bound, states rather than true bound states. Asymptotically, n becomes the vibrational quantum number of the free NO molecule while m has no counterpart in the product channel. The main progression is built upon m = 0 and the second, much weaker progression corresponds to m = 1. 

In TPA induced fluorescence spectroscopy the excited state population for fluorescence is created by the simultaneous absorption of two photons instead of the one-photon absorption in standard fluorescence experiments. The principles of this technique are described in Ref. [23]. It allows an experimental determination of two-photon absorption cross-sections provided the material is fluorescent and that its two-photon fluorescence quantum efficiency is known (which is usually assumed to be equal to the one-photon fluorescence quantum efficiency if the same excited state is reached). In this case the method generally provides high sensitivity. 

Nuclear magnetic resonance (NMR) spectroscopy is routinely applied to small carbohydrate molecules. NMR spectroscopy is based on the principle that radiofrequencies are absorbed by hydrogen and carbon atoms ( H and 13C) spinning in one of two directions (spin quantum number +1 /2) in a magnetic field. In liquids, absorption is recorded as sharp peaks. The frequency displacement (chemical shift) is a function of the H and 1SC surroundings. +A is proportional to the number of photons absorbed between these two quantum states, correlating well with anomeric and... 

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