Frequency modulation

One advantage of the photon counting teclmique over the phase-shift method is that any non-exponential decay is readily seen and studied. It is possible to detect non-exponential decay in the phase-shift method too by making measurements as a fiinction of tlie modulation frequency, but it is more cumbersome. 

Materials are also classified according to a particular phenomenon being considered. AppHcations exploiting off-resonance optical nonlinearities include electrooptic modulation, frequency generation, optical parametric oscillation, and optical self-focusing. AppHcations exploiting resonant optical nonlinearities include sensor protection and optical limiting, optical memory appHcations, etc. Because different appHcations have different transparency requirements, distinction between resonant and off-resonance phenomena are thus appHcation specific and somewhat arbitrary. 

Frequency-Modulation Spectroscopy. Frequency-modulation spectroscopy (tins) is a high sensitivity null-background infrared technique for measuring absorbances down to 10 with fast acquisition speeds. Fms involves frequency-modulating a laser source at COq to produce a carrier frequency having sidebands at cJq where is an integral multiple of the modulation frequency. Dye lasers and many other single-line sources can... 

Transfonii primary data based on sampling and modulation frequency... 

Coupling can have an additive effect on the modulation frequencies, as well as being reflected as a differential or... 

The dependence of the in-phase and quadrature lock-in detected signals on the modulation frequency is considerably more complicated than for the case of monomolecular recombination. The steady state solution to this equation is straightforward, dN/dt = 0 Nss — fG/R, but there is not a general solution N(l) to the inhomogeneous differential equation. Furthermore, the generation rate will vary throughout the sample due to the Gaussian distribution of the pump intensity and absorption by the sample... 

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

For lock-in amplification the pump is modulated at a reference frequency w (see Fig. 7-1), which means that AT is not constant over time. Rather, its magnitude (and its phase) depends on the modulation frequency [8. In order to find the frequency-dependent A7 (cu), let us assume that the recombination dynamics are monomolecular with a single lifetime r. Then we can write for the number density of excitations N at time / ... 

While it is possible to simulate the modulation frequency dependence, this must be done on a case by case basis. 

Figure 7-29. PA spectra of P3BT lilm, measured with a modulation frequency of (a) 20 Hz and (b) 20 kHz.

Jablonski (48-49) developed a theory in 1935 in which he presented the now standard Jablonski diagram" of singlet and triplet state energy levels that is used to explain excitation and emission processes in luminescence. He also related the fluorescence lifetimes of the perpendicular and parallel polarization components of emission to the fluorophore emission lifetime and rate of rotation. In the same year, Szymanowski (50) measured apparent lifetimes for the perpendicular and parallel polarization components of fluorescein in viscous solutions with a phase fluorometer. It was shown later by Spencer and Weber (51) that phase shift methods do not give correct values for polarized lifetimes because the theory does not include the dependence on modulation frequency. 

CO = 2icv excitation modulation frequency, v = modulation frequency of the oscillator,... 

The value of tan A depends upon the modulation frequency, the excited state lifetime, and the rate of rotation. The value decreases to zero when the rotation period is either longer or shorter than the excited state lifetime and is a maximum when the two times are comparable in magnitude. Tan A also increases as the modulation frequency increases. For spherical rotators, the measured value of tan A for a given modulation frequency and excited state lifetime allows the rotational rate to be calculated from... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

By measuring 0 and m at several modulation frequencies, a set of simultaneous equations can be generated that allow a determination of the best values for fluorophore lifetime and fractional contributions. The fi values from these calculations are the quantities that are used in Equations 7 and 8 to obtain weighted values ofx and Po. 

Fig. 1. EPR spectrum of the dithionite-reduced Fepr protein fromD. vulgaris [from (7)]. The protein was 272 ftmol dm" in 25 mmol dm Hepes buffer, pH 7.5, and was reduced under argon with 10 mmol dm sodium dithionite for 3 min at ambient temperature. EPR conditions microwave frequency, 9331 3 MHz modulation frequency, 100 kHz modulation amplitude, 0.63 mT microwave power, 200 mW temperature (relative gain) 16 K (6.3X).

Note <3>, equivalence ratio modulation frequency SPL, sound pressure level A, mean flame surface area fluctuation of flame area v, mean velocity at the burner outlet and v, imposed velocity... 

The "M"-flame case shows a different kind of flame interaction illustrated in Figure 5.2.4 (MF). The "M"-shape comprises two reactive sheets separated by fresh reactants. This gives rise to flame-flame interactions between neighboring branches of the "M"-shape [41]. The case presented corresponds to an equivalence ratio O = 1.13, a mixture flow velocity v/v = 1.13 m/s, a modulation level fixed to v = 0.50m/s, and a modulation frequency/= 150 Hz. The description of the flame motion over a cycle of excitation starts as in the flame-plate interaction. A velocity perturbation is generated at... 

Both methods obtain the necessary sensitivity by modulating the electrode potential between two values which define two distinct states of the electrode surface thus the chemistry to be observed is directly modulated and may be detected with great sensitivity by an appropriate form of synchronous detection. In the case of EMIRS, the modulation frequency is made sufficiently high compared to the wavelength scanning rate to enable a phase sensitive detection system to be used whereas, for SNIFTIRS, the electrode potential is held for a sufficient period at each potential to accumulate data from several interferometric scans and, after an adequate number, the two sets of data are ratioed. 

In the early work of Bewick and Robinson (1975), a simple monochromator system was used. This is called a dispersive spectrometer. In the experiment the electrode potential was modulated between two potentials, one where the adsorbed species was present and the other where it was absent. Because of the thin electrolyte layer, the modulation frequency is limited to a few hertz. This technique is referred to as electrochemically modulated infrared reflectance spectroscopy (EMIRS). The main problem with this technique is that data acquisition time is long. So it is possible for changes to occur on the electrode surface. 

At the start of each modulation pulse, a sharp peak in optical emission is seen. Similar SiH emission peaks in pulsed plasmas have been found by Scarsbrook et al. [516] and Howling et al. [321]. The sharp peak was claimed to be caused by a pulse of high-energy electrons. Overzet and Verdeyen [517] measured electron densities at a 2.9-MHz excitation frequency and modulation frequencies up to 20 kHz. The optical emission of a SQWM argon plasma was measured by Booth et al. [518], who also performed particle-in-cell modeling. 

Here, results are shown from experiments performed in ASTER, reported by Biebericher et al. [512. 519], A SiH4-H2 (50 50 flow ratio, total flow 60 seem) plasma was generated at an RF excitation frequency of 50 MHz. The substrate temperature was 250°C. The RF signal was ampitude modulated (AM) by a square wave. The modulation frequency has been varied in a range of 1-400 kHz. The modulation depth was always 90%. The duty cycle was fixed at 50%. The pressure amounted to 0.2 mbar, and the average power was kept at 10 W. With a duty cycle of 50%, this leads to a power of 20 W during the plasma-on period. 

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