Modulation frequency, second-harmonic

The curve is elevated relative to zero by a constant amount (0.125) and has a contribution of 2o), double the modulation frequency (+, second harmonic). Both these contributions are not included in the experimental reversing heat flow which contains only the contribution to the first harmonic ( , see Sect. 4.4.3). Accepting the present analysis, it is possible to determine y and x from the reversing heat capacity by matching the last term of the equation in Figs. 6.118 and 4.131, and then use the paramters describing the match to compute (A), the actual response of the TMDSC to the quasi-isothermal temperature modulation. 

Once quantum chemistry has provided all the information required, that is, rotational and centrifugal distortion constants and, if the case, hyperfine parameters as well as line intensities, a graphical simulation of the rotational spectrum can be performed. The latter requires the knowledge of the experimental technique involved. For example, if the frequency modulation with second harmonic detection is performed, then the second derivative of the natural spectrum is obtained (as seen in Figure 6.2). The graphical representation of the computed spectrum can then be... 

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

Raman excitation. and I2s are the high-frequency and low-frequency components of the pump light pulse. A probe pulse of frequency 12 interacts with the coherence to present the optical response of the fundamental frequency 12 + C0fsl2. (c) Fourth-order coherent Raman scattering, the optical response of the second harmonic frequency 212 + co 2I2 is modulated by the vibrational coherence. 

In addition to the fourth-order response field Tfourth, the probe light generates two SH fields of the same frequency 211, the pump-free SH field Eq(2 Q), and the pump-induced non-modulated SH field non(td> 211). The ground-state population is reduced by the pump irradiation and the SH field is thereby weakened. The latter term non(td, 211) is a virtual electric field to represent the weakened SH field. Time-resolved second harmonic generation (TRSHG) has been applied to observe E on (td, 211) with a picosecond time resolution [20-25]. The fourth-order field interferes with the two SH fields to be detected in a heterodyned form. 

The frequency of modulation il is now the main parameter, and we are able to switch the system of SHG between different dynamics by changing the value of il. To find the regions of where a chaotic motion occurs, we calculate a Lyapunov spectrum versus the knob parameter il. The first Lyapunov exponent A,j from the spectrum is of the greatest importance its sign determines the chaos occurrence. The maximal Lyapunov exponent Xj as a function of is presented for GCL in Fig. 6a and for BCL in Fig. 6b. We see that for some frequencies il the system behaves chaotically (A-i > 0) but orderly Ck < 0) for others. The system in the second case is much more damped than in the first case and consequently much more stable. By way of example, for = 0.9 the system of SHG becomes chaotic as illustrated in Fig. 7a, showing the evolution of second-harmonic and fundamental mode intensities. The phase point of the fundamental mode draws a chaotic attractor as seen in the phase portrait (Fig. 7b). However, the phase point loses its chaotic features and settles into a symmetric limit cycle if we change the frequency to = 1.1 as shown in Fig. 8b, while Fig. 8a shows a seven-period oscillation in intensities. To avoid transient effects, the evolution is plotted for 450 < < 500. 

The MIIPS of compensated pulses is shown in Fig. lb. To corroborate phase information retrieved from MIIPS, phase characterization was also done using second harmonic generation frequency resolved optical gating (SHG-FROG) [7], SHG-FROG traces of the pulses before and after compensation are shown in Fig. lc and Id. The final pulse-shaping step involved the controlled phase modulation of transform-limited pulses. 

The dHvA measurements were carried out using a field modulation technique at liquid helium temperatures and in magnetic fields up to 6 T. Second harmonic frequency signals of the pick-up coil were detected and analyzed by fast-Fourier analysis. 

Equations (16) and (17) describe second-harmonic generation (SHG) and third-harmonic generation (THG) of one laser beam with a single polarization. Self-phase modulation (SPM) of a single laser beam is described in Eq.(18) as e.g. employed in z-scan experiments [6]. Equation (19) is the cross-phase modulation (XPM) process between two laser beams and Eq.(20) describes the four wave mixing with degenerate frequencies (DFWM). 

For second harmonic generation (SHG), the tensor is y(2)(—2co co, co) (useful for frequency doubling and parametric down-conversion) while for the linear electrooptic or Pockels71 effect the tensor is y(2)(— co co, 0) (useful for Q-switching of lasers, for phase or amplitude modulators, and for beam deflectors) for optical rectification the tensor is y 2>(0 00, —co) for frequency mixing the tensor is y(2)(— co3 oolr co2) (useful for frequency up-converters, optical parametric oscillators, and spectroscopy). 

PVA, 88 mg) was mixed with 0.2 ml of HEPES buffer solution (1 x 10-2 mol dm 3 HEPES, 10 ml total) at pH 7.0 containing BCECF (5 mg) and stirred for several minutes at room temperature. The mixture was then cast on an ITO-coated quartz substrate by a spin-coating method, and water was removed by evaporation. A semitransparent aluminum (Al) film was deposited on the dried polymer film by a vacuum vapor deposition method. The ITO and Al films were used as electrodes. A sinusoidal ac voltage with a modulation frequency of 40 H z was applied to a sample polymer, and the field-induced change in fluorescence intensity was detected with a lock-in amplifier at the second harmonic of the modulation frequency. A dc component of the fluorescence intensity was simultaneously observed. 

A prerequisite for the development indicated above to occur, is a parallel development in instrumentation to facilitate both physical and chemical characterization. TEM and SPM based methods will continue to play a central role in this development, since they possess the required nanometer (and subnanometer) spatial resolution. Optical spectroscopy using reflection adsorption infrared spectroscopy (RAIRS), polarization modulation infrared adsorption reflection spectroscopy (PM-IRRAS), second harmonic generation (SFIG), sum frequency generation (SFG), various in situ X-ray absorption (XAFS) and X-ray diffraction spectroscopies (XRD), and maybe also surface enhanced Raman scattering (SERS), etc., will play an important role when characterizing adsorbates on catalyst surfaces under reaction conditions. Few other methods fulfill the requirements of being able to operate over a wide pressure gap (to several atmospheres) and to be nondestructive. 

Numerical simulations of this model were carried out to test expectations. The results are shown in Figs. 8 and 9. The figure 8 shows the amplitude of the detected signal at the third harmonic of the modulation frequency when the operating point corresponds to the second node, i.e., n = 2, and the Bo is selected for the detection of radiation in the vicinity of 400 GHz, which lies near the lower edge of the Terahertz band, where the device sensitivity to such radiation has been confirmed by our experiments, see Fig. 3, for example. As confirmed by the simulations, the 3 harmonic sensing concept yields indeed a narrow band detector, with sensitivity between roughly 200 and 800 GHz, as... 

In recent years there has been a growing interest in the search for materials with large macroscopic second-order nonlinearities [20-22] because of their practical utility as frequency doublers, frequency converters and electro-optic modulators [23] by means of second-harmonic generation, parametric frequency conversion (or mixing) and the electro-optic (EO) effect. They are described by X (2w w, u)), 0, w), respectively. In order to optimize... 

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