Nonlinear transmission method

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]. 

In a separate study, the cross section of diphenylbutadiene in chloroform has been measured at 532 nm by two different methods and reported to be 40 8GM by degenerate four-wave mixing, and 34 12GM by nonlinear transmission [66]. It should be pointed out that both results were obtained using ns excitation pulses, but that the cross sections obtained by the two methods are comparable one to the other and on the same order of the cross sections listed earher (although those were obtained in a different wavelength range). 

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. 

Because of this wide range of applications, much effort was dedicated to the design and synthesis of new molecules with optimized TPA efficiency in this context, the characteristics of the designed molecules (linear absorption, solubility, substituents...) will depend on the targeted application. The TPA response of moleciUes can be imderstood in the context of its TPA cross-section ajpA. which can be measmed using different techniques, such as nonlinear transmission, two-photon induced fluorescence and the Z-scan method although in a pure TPA process ajpA does not depend on the laser pulse duration, the nonlinear absorption can be more efficient in the nanosecond regime than in the femtosecond one, due to excited state reabsorption phenomena [34]. 

TPA can be measured by the transmission method or by the Z-scan technique. Moreover, two-photon fluorescence can serve to measure TPA absorption cross-sections, provided that a fluorescent excited state is reached by TPA. In nonlinear... 

The evaluation of TPA activity of the materials can be made by various techniques such as up-converted fluorescence emission, nonlinear transmission, transient absorption, Z-scan, and four-wave mixing [122]. Among them, the up-converted fluorescence emission method is a simpler technique and the setup is shown in Fig. 49.10. In this method, the TPA cross-section value, 0-2 can be estimated according to the following equation [123] ... 

Before going into the details of various materials and their third-order NLO properties, it would serve well to have an idea of the characterization techniques used for their study. To study the effect of the real part of third-order susceptibility, Z-scan measurements, degenerate four-wave mixing (DFWM), optical heterodyne detection of optical Kerr effect (OHD-OKE), and differential optical Kerr effect (DOKE) detection are employed. For the study of TPA, techniques such as nonlinear transmission (NLT) method, two-photon excited fluorescence (TPEF) method, and Z-scan measurements are used. The observables from the above-mentioned techniques vary depending on the inherent limitations of the technique. The nature of the light source employed like the central wavelength of the laser. 

Method indicates the experimental technique which is used to measure the TPA cross section (NLT, nonlinear transmission WLC, white light continuum). 

An interferometric method was first used by Porter and Topp [1, 92] to perfonn a time-resolved absorption experiment with a -switched ruby laser in the 1960s. The nonlinear crystal in the autocorrelation apparatus shown in figure B2.T2 is replaced by an absorbing sample, and then tlie transmission of the variably delayed pulse of light is measured as a fiinction of the delay This approach is known today as a pump-probe experiment the first pulse to arrive at the sample transfers (pumps) molecules to an excited energy level and the delayed pulse probes the population (and, possibly, the coherence) so prepared as a fiinction of time. 

Many interesting phenomena can arise in nonlinear periodic structures that possess the Kerr nonlinearity. For analytic description of such effects, the slowly varying amplitude (or envelope) approximation is usually applied. Alternatively, in order to avoid any approximation, we can use various numerical methods that solve Maxwell s equations or the wave equation directly. Examples of these rigorous methods that were applied to the modelling of nonlinear periodical structures are the finite-difference time-domain method, transmission-line modelling and the finite-element frequency-domain method." ... 

As described in the section on nonlinear absorption, the transmission of a pulse which is short compared to the various molecular relaxation times is determined by its energy content. A measurement of the energy transmission ratio will then give the peak intensity of the pulse when its pulse shape is known 44>. In fact, the temporal and spatial pulse shape is of relatively little importance. Fig. 11 gives the energy transmission as a function of the peak intensity I [W/cm2] for the saturable dye Kodak 9860 with the pulse halfwidth as a parameter. It is seen that this method is useful in the intensity region between 10 and 1010 MW/cm2 for pulses with halfwidths greater than 5 to 10 psec. Since one can easily manipulate the cross-section and hence the intensity of a laser beam with a telescope, this method is almost universally applicable. 

Information about nonlinear absorptive properties of a sample can be derived simply by measuring the sample transmission as a function of the incident light intensity. We note that Eq. (5) can therefore be inverted to read T-1 = 1 + fi2LI a linear dependence of the inverse transmission on the incident intensity can be used to determine the j82 value. Because of the ease of determining the value of fi2 with open-aperture Z-scan, Z-scan is often the preferred method for quickly determining the nonlinear absorption coefficient. Point-by-point transmission measurements can be undertaken to verify the applicability of Eq. (5). 

Figure 6 shows an experimental setup to measure nonlinear transmittance by the pump-probe method. The pump is used to excite the sample and the transmission of the probe is measured. The probe beam may be delayed relative to the pump beam in order to perform time delay experiments. A continuum of frequencies may be used as the probe, thereby allowing... 

Most transducers converting chemical concentration into an electrical signal have a nonlinear response for example, electrode potential and optical transmission are not directly proportional to concentration. In general, this nonlinearity is easily and simply corrected in equilibrium analytical measurements. However, it is considerably more difficult to instrumentally correct the response-versus-concentration function in reaction-rate methods, and often the correction itself can introduce significant errors in the analytical results. For example, the simple nonlinear feedback elements employed in log-response operational-amplifier circuits are not sufficiently accurate in transforming transmittance into absorbance to be used for many analytical purposes. 

A difficulty arises because the photonic crystal structures for the visible region are not easy to fabricate. However, in this chapter we describe a facile extrusion method for fabricating polymers with a ID structure like that shown in Figure 2. The nanolayered polymeric structures can consist of many thousands of layers and have a modulation in the nonlinear refractive index in the direction normal to the surface of the layers. Such materials are the nonlinear analogue of polymeric multilayer interference mirrors. (10,11,12) They are also the ID analogue of the 2D photonic crystals studied by Lin et. al. (13) The latter workers demonstrated that photonic crystals do indeed provide an effective method for converting an intensity dependent refractive index into an intensity dependent transmission. 

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