Nonlinear TPA

In the case of SHG in waveguide nonlinear crystals, we describe a theoretical model which accounts for the temporal behavior of the interacting pulses and the possible z-dependence of the phasematching condition. The model also describes the observed saturation and subsequent decrease in SHG conversion efficiency in the waveguide samples, as a result of two-photon absorption (TPA) of the second harmonic (SH) wave. The results of this model are later compared with experimental data from SHG experiments using femtosecond pulses in the waveguide nonlinear crystals of periodically-poled potassium titanyl phosphate (ppKTP) and appKTP. This model is presented in section 2.3. 

Among the mechanisms of nonlinear absorption, TPA is the most important and widely used for 3D laser lithography in resists and resins. TPA requires smaller incident powers than higher-order processes, for example multipho-... 

It is noteworthy that nonlinearity of the absorption, required for 3D microfabrication can be provided via thermal mechanisms [53,54]. In the case of tightly focused laser pulses, linear absorption is most efficient at the focus, where local heating can create the conditions required for polymerization. Usually the absorption increases with temperature and thermal polymerization may become dominant at the focus. It is usually difficult to confirm the TPA mechanism from the direct transmission measurements due to the nar-... 

The most widely employed material characterization techniques in third-order nonlinear optics are third-harmonic generation (THG) [21], degenerate four wave-mixing (DFWM) [22], Z-scan [6], and optical limiting by direct two-photon absorption (TPA) and fluorescence spectroscopy induced by TPA [23]. All of them will be discussed in the following. Further measurement techniques such as electric-field induced second-harmonic generation (EFISH) [24], optical Kerr... 

If intrinsic two-photon absorption cross-sections are the subject of investigation short pulses (ps or fs) should be used and two-photon fluorescence (see below) should be measured to verify the Independence of the TPA process. Most often, two-photon absorption is measured either with the Z-scan technique (see above) or with the nonlinear transmission method [38]. 

The TPA cross section (7>) is proportional to the second-order nonlinear polarizability y. This is derived by consideration of interactions of light with matter causing a change in the dipole moment that is the induced dipole moment /iirld. Induced polarization Pind is proportional to /(ind and the field strength E of the incident light, Eq. (7) [50, 73] ... 

Under conditions in which the material is isotropic only, the odd nonlinear susceptibilities contribute to TPA. The even terms vanish because orientation is required. Therefore, the lowest nonlinear absorption is described by the imaginary part of y° corresponding to Stokes-Raman, anti-Stokes-Raman scattering, and TPA [16, 22, 23, 35, 45, 50, 53, 70, 73, 280, 281],... 

Vibrational Contributions Contribution of vibrational modes has been described for TPA [5-9, 11-17, 19, 22, 23, 31, 37, 61, 235, 309, 343-345] and for other nonlinear optical processes [346]. One classical example is the 1A j -1 B2u TP transition of benzene, the so-called green band. This electronic transition is allowed due to a vibronic coupling mechanism [346]. Semiempirical [60, 61] as well as ab initio response theory calculations using the Herzberg-Teller expansion [344] demonstrate the role of vibronic coupling. Such contributions can either enhance an allowed transition or intensify a symmetry-forbidden transition. 

Experimental Techniques in Nonlinear Absorption Measurements of TPA yield nonlinear absorption coefficient/TPA cross section (compare Ref. [54] for further details). The nonlinear absorption coefficient [j is related to 8 as [i = 8NAcch x 10 3 (fi in cm/GW, /VA Avogadro s number with 6.02 x 1023 moP1, cch = chromophore concentration in mol/L).11 In general, the following techniques have been applied to quantify the TPA cross section[53, 54], which are complementary methods for determination of either [j or 8. 

Two-photon excited fluorescence (TPEF) is one of the most useful ways to quantify TPA in optical materials competing with nonlinear absorption. While nonlinear transmission yields absolute quantities describing TPA, TPEF requires knowledge of the collection efficiency if absolute data must be acquired. Thus, the use of standards is the method of choice to determine 5 in case of TPEF. 

Many TPA data taken with ns lasers and fs lasers are available in the literature. According to the problems arising with ns lasers applying nonlinear absorption, the fs laser should be the light source of choice to quantify TPA data. However,... 

Polymers 19-32 [27, 33, 296, 381-394] represent some examples used in nonlinear absorption studies. Investigations show that large 8 can be obtained if the unsaturated chain is stiff. This keeps distortion of the re-system as small as possible, and becomes more clear by comparing the data of the stiff ladder-type polymer 20 with the more flexible PPV 22. In other words, the more planar the entire re-system, the larger the amplitude of the TPA (Table 3.4). 

TPA chromophore 107 represents, in analogy to its dipolar analog 52, a typical quadrupolar chromophore with both increased linear and nonlinear absorption properties [428]. Thus, the extinction coefficient and 8 are about 1.3 and 1.4 times larger (about /2) in comparison with that of 52. This again shows that incorporation of the electron-deficient triazine results in an increase of 8 for quadrupolar compounds considering both OP and TP quantities. 

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