Amplitude modulators

The integral describes the spatial amplitude modulation of the excited magnetization. It represents the excitation or slice profile, g(z), of the pulse in real space. As drops to zero for t outside the pulse, the integration limits can be extended to infinity whereupon it is seen that the excitation profile is the Fourier transfonn of the pulse shape envelope ... 

Lau K T, Bar-Chaim N, Ury I and Yariv A 1983 Direct amplitude modulation of semiconductor GaAs lasers up to X-band frequencies Appi. Phys. Lett. 43 11... 

The ODMR spectrometer resembles the PA spectrometer shown in Figure 7-1, with the sample placed in a microwave cavity between the pole pieces of an electromagnet. The sample is constantly illuminated by the pump and probe beams amplitude-modulated microwaves arc coupled into the cavity through a waveguide. Changes Si in PL or ST in probe transmission are delected by lock-in am-... 

With t = 0 the present expression reduces to the result obtained in Eq. (3.28). If, e.g., t = 2, then spectral exchange takes place both within the branches of an isotropic scattering spectrum (Fig. 6.1) and between them. The latter type of exchange is conditioned by collisional reorientation of the rotational plane, whose position is determined by angle a. As a result, the intensity of adsorbed or scattered light is redistributed between branches. In other words, exchange between the branches causes amplitude modulation of the individual spectral component, which accompanies the frequency modulation due to change of rotational velocity. 

Luminescence lifetimes are measured by analyzing the rate of emission decay after pulsed excitation or by analyzing the phase shift and demodulation of emission from chromophores excited by an amplitude-modulated light source. Improvements in this type of instrumentation now allow luminescence lifetimes to be routinely measured accurately to nanosecond resolution, and there are increasing reports of picosecond resolution. In addition, several individual lifetimes can be resolved from a mixture of chromophores, allowing identification of different components that might have almost identical absorption and emission features. 

Equation (1.8) represents a plane wave exp[i(A x — mt)] with wave number k, angular frequency m, and phase velocity m/A, but with its amplitude modulated by the function 2 cos[(AA x — Amt)/2]. The real part of the wave (1.8) at some fixed time to is shown in Figure 1.2(a). The solid curve is the plane wave with wavelength X = In jk and the dashed curve shows the profile of the amplitude of the plane wave. The profile is also a harmonic wave with wavelength... 

Thus, the wave packet P(jc, 0 represents a plane wave of wave number ko and angular frequency mo with its amplitude modulated by the factor B(x, i). This modulating function B x, i) depends on x and t through the relationship [x — (dm/dA )o/]. This situation is analogous to the case of two plane waves as expressed in equations (1.7) and (1.8). The modulating function B(x, t) moves in the positive x-direction with group velocity given by... 

Figure 1.5 shows the real part of the plane wave exp[i(A ox — coot)] with its amplitude modulated by B(x, t) of equation (1.20). The plane wave moves in the positive x-direction with phase velocity Uph equal to o)o/ko. The maximum amplitude occurs at x = v t and propagates in the positive x-direction with group velocity Ug equal to (dm/dA )o. 

As before, the wave packet is a plane wave of wave number ko and angular frequency mo with its amplitude modulated by a factor that moves in the positive x-direction with group velocity given by equation (1.16). Following... 

The wave packet, then, consists of the plane wave expi[kox — u>ot with its amplitude modulated by... 

Figure 6.2. (I) Conventional phosphorescence spectrum of 2,3-dichloroquinoxa-line in durene at 1.6°K. (II) am-PMDR spectrum, obtained by amplitude modulation of microwave radiation that pumps the tv-t, (1.055 GHz) zf transition with the detection at the modulation frequency. Only bands whose intensities change upon microwave radiation (1.055 GHz) and thus originate from tv or rz appear in the am-PMDR spectrum. Transitions from r and rv appear with opposite sign (phase-shifted by 180°). (Hb, lie ) Polarization of the am-PMDR spectral transitions, relative to the crystal axes. The band at 0,0-490 cm-1 originates from both the r and t spin states its intensity does not change upon the 1.055-GHz saturation (no band in II) however, its polarization does rhanp. (bands in Hb and IIc ). (Reproduced with permission from M. A. El-Sayed.tt7W)...

Phase-shifting by melatonin is attributed to its action at MT2 receptors present in the SCN (Liu et al. 1997). The chronobiological effect of melatonin is due to its direct influence on the electrical and metabolic activity of the SCN, a finding that has been confirmed both in vivo and in vitro. The application of melatonin directly to the SCN significantly increases the amplitude of the melatonin peak, thereby suggesting that in addition to its phase-shifting effect melatonin directly acts on the amplitude of the oscillations (Pevet et al. 2002). However, this amplitude modulation seems to be unrelated to clock gene expression in the SCN (Poirel et al. 2003). 

The signals S+ and S are now amplitude-modulated as a function of tp, therefore, a double hypercomplex Fourier transformation of these data, following for instance the States-Haberkom-Ruben procedure, yields a pure-absorption 2D spectrum with sign discrimination in the 12 j dimension [169]. 

Hellstrand You have shown the coding of the response to PE in terms of frequency of oscillations, but not amplitude modulation. Have you come across any example where the modulation of amplitude also changes the force of contraction, or do you think the amplitude is constant in this system ... 

Hellstrand That is what I am getting at. There are a lot of phase shifts in this system. One observation we have made is that under hypoxia we see a decrease in amplitude but an increase in frequency of the waves. We are trying to model a case where this would account for reduction of force simply on the basis of non-linearity of the [Ca2+] versus myosin phosphorylation versus force reactions. It seems intuitively that this could explain why there can be a reduction in force although there is no reduction in the overall level of global Ca2+. Is amplitude modulation something that people have seen ... 

Fig. 10.12. Pulse sequence for amplitude modulated 2D J-resolved spectroscopy. The experiment is effectively a spin echo, with the 13C signal amplitude modulated by the heteronuclear coupling constant(s) during the second half of the evolution period when the decoupler is gated off. Fourier transformation of the 2D-data matrix displays 13C chemical shift information along the F2 axis of the processed data and heteronuclear coupling constant information, scaled by J/2, in the F1 dimension.

Fig. 10.13. 2D J-resolved NMR spectrum of santonin (4). The data were acquired using the pulse sequence shown in Fig. 10.12. Chemical shifts are sorted along the F2 axis with heteronuclear coupling constant information displayed orthogonally in F . Coupling constants are scaled as J/2, since they evolve only during the second half of the evolution period, t /2. 13C signals are amplitude modulated during the evolution period as opposed to being phase modulated as in other 13C-detected heteronuclear shift correlation experiments.

Similar to the PIP, the Hamiltonian [Eq. (52a)] of a periodic pulse shows an infinite number of effective RF fields with both x and y components of the scaling factors X a and the phases 0na. The periodic pulse, however, acquires a different symmetry as that of the PIP. From Eq. (52c) and = ana, it follows that the scaling factor Xm, is symmetric in respect to the sideband number n, while the phase 6na is anti-symmetric according to Eq. (51c). These symmetries seem to be a coincidence arising from the mathematical derivations. As a matter of fact, they are the intrinsic natures of the periodic pulse. Considering the term f x i)Ix for instance, any Iy component created by the rotating field denoted by a> must be compensated at any time t by its counter-component oj n in order to reserve the amplitude modulated RF field. 

Assume a 180° PIP is applied at the centre of the 13CO in the middle of the 13C evolution time for homonuclear decoupling and at the same time a compensating PIP is applied on the other side of the l3C (Fig. 11) to minimize the disturbance to the 13C that may have a transverse or longitudinal magnetization. The two simultaneous PIPs become an amplitude modulated pulse described by 2/i cos (27iAft)Ix, where f is the pulse strength of each 180°... 

To reduce spurious signals due to drifts of the EPR line setting arising from mechanical and thermal instabilities, double coding of the ENDOR information is often employed23). Normally a low-frequency Zeeman modulation (30-300 Hz) is applied while the rf field is frequency or amplitude modulated at frequencies of about 1-30 kHz. This modulation scheme, however, has two major disadvantages ... 

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