Three-level model

Figure 28. (a) Schematic level structure of a three-level model, (b) Floquet diagram of the three-... 

Figure 29. Complete excitation from 11 > to 2 > by one period of frequency chirping in the case of the three-level model. Upper part-time variation of the population. Middle part-time variation of laser frequency. Bottom part-envelope of the laser pulse. Taken from Ref. [42].

Dirk CW, Cheng L, Kuzyk MG (1992) A simplified three-level model describing the molecular third-order nonlinear optical susceptibility. Int J Quantum Chem 43 27-36... 

Using a simple, three level model we can develop a feeling for the microwave powers required to observe radiatively assisted collisional energy transfer between Rydberg atoms.3 Consider the dipole-dipole atomic system shown in Fig. 15.1(a). In the Na ns + ns— np + (n - l)p resonant collisions described in the previous chapter the ns state corresponds to both s and s of Fig. 15.1(a) and the n — 1 and np states correspond to p and p of Fig. 15.1(a), respectively. The collisions occurs via the interaction... 

In general, the optimization of organic molecules for third order nonlinear optical applications has enjoyed much less success than for second order optical nonlinearities. The major reason for this has been the questionable validity of the two-level model for y, and the difficult assessment of the contribution of two-photon states for the more acceptable three-level model. 

Figure 9.2. Temperature dependence of the relaxation time of OH in different host lattices obtained from optical (open symbols) and caloric (filled symbols) measurements. The latter have been corrected by the factor 2/3 derived from the three level model. (From Kapphan [1974].)...

If the molecule has full centrosymmetry also the dipolar term Dx vanishes. The discussion of the molecules discussed in this work will rely to a large extent on the above equations of the three level model. 

The symmetry dependence of the second-order hyperpolarizabilities of PTAs was first assessed on monomers and dimers with different substitution patterns (Table 2). The difference of asymmetric and symmetric geometries can be seen in the three level model Eq.(80). The dipolar term D = /Eqi only occurs... 

In conclusion, in short PTAs, Afi in the dipolar term of the three level model optimizes the value of the second-order hyperpolarizability. 

The second-order hyperpolarizability of the tetrasubstituted TEEs are analyzed with the three-level model of the sum-over-states expression. The rotational average of the second-order hyperpolarizability y (Eq.(49)) in the case of THG of a two-dimensional, planar molecule is... 

For TEE molecules the dipolar terms in the three level model are of special interest as they contain the difference dipole moment Ap which vanish perpendicular to a mirror plane. The dipolar contribution yD to the overall nonlinearity... 

Computer network infrastructure should be qualified in support of validated applications. Bristol Meyer Squibb have adopted a three-level model to assist the quahfication of their computer network infrastrucmre. This approach is summarized in Table 14.3. Layer 1 comprises computers that provide shared resources such as servers, hosts, mainframes, and mini computers. Layer 2 is the network infrastrucmre (e g., hubs, routers, and switches). Layer 3 comprises the user desktop environment (i.e., workstations, personal computers, and laptops). 

Consider a three-level model Hamiltonian with e enstates 1 ), 2)> 1 3) and eigenvalues 3, 3, 3 ... 

THG. The subscript 3 represents the laboratory axis 3. Nrlti) is the number density oi trans molecules oriented in the direction Q, which also can be denoted as (Figure 12.2). In the three-level model, the dynamics of the rans-population is described by equation... 

Three-Level Model A three-level model appropriately describes two-photon absorption of centrosymmetric chromophores in which a higher excited state is directly populated by TP excitation (Figure 3.2a). Thus, the TP excited state is a higher excited state, which is populated under resonant conditions as long as Eq. (27)10 fulfills the necessary conditions. 

Figure 3.29. Theoretical three-level model for description of TPA in monomeric (n — 1) and dimeric (n — 2) forms. (From Ref. [296] with permission of Elsevier.)...

However, the two values become approximately identical when the SHG response is extrapolated at m = 0. The essentially octupolar nature of 2 and 15 requires at least a three-level model. In general, due to the predominance of the Q band in the absorption spectrum, it appears reasonable to consider the ground and the two lowest degenerate excited states. Assuming a molecular symmetry, the nonzero with... 

In the SOS procedure, the theoretical description of hyperpolarizability tensors /3ijk and requires a three-level model. Within this formalism, the more general expression for is given by ... 

In this case, the second-order hyperpolarizability y can be considered as a unidimensional parameter defined along the axis x of the molecule following the single component Yxxxx- Equation 3 can be simpUfied into the relationship Eq. 5, when applying the three-level model in which the lowest excited state 11) and the two-photon excited state 2) are considered to be the most significant... 

Fig. 2 Schematic representation of the TPA process, (a) In the case of the three-level model for symmetric systems (b) in the case of the two-level model for noncentrosym-metric systems...

Nimzi et al. [53] showed the two-level model was well adapted for the 4-(N-(2-hydroxyethyl-J -ethyl)-amino-4 -nitrobenzene (DRl) dye, while a three-level model had to be considered for the 4-dibutylamino-4 -nitrobenzene (DEANS) system, due to electron-vibration interactions values of /zoi. and A/zoi could be deduced for both molecules. 

The structure of quadrupolar molecules is generally noted as D-n-D or A-7t-A (see Fig. 1). For these molecules, the term Ayxoi of the relationship Eq. 5 cancels and this equation can be rewritten as Eq. 7, and molecules fulfill the three-level model represented in Fig. 2a. 

Typical CNDO/S linear and two-photon absorption spectra of polyphenyls are displayed in Fig. 33 [157]. The low energy optical response of all compounds is accurately described by a three-level model with parameters that are summarized in Table 6. Transition energies are red-shifted, and transition dipole moments increase with the monomer munber n. 

Table Power dependenq a of parameters describing the two-photon absorption of polyphenyls in the three-level model...

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