Microwave Amplitude Modulation

The purpose of this chapter is to review the amplitude modulation technique, address the limitations of the classic studies in the light of these reeent technological advances, and present equations that can be used to make predictions about both the EPR response in the z- and x,j-directions. 

The importance of a crossed-loop or other bimodal resonator is that they offer the opportunity to measure toe x,j-components of the spin magnetization. The incentive for the development of the toeory of modulation spectroscopy in this chapter is (a) to extend it to deeper modulation than in prior treatments, and (b) predict the signals observable with x,j-detection as well as in the z-direction. Each may have its niche in measurements of spin relaxation times. 

CALCULATION OF THE MODULATION SIGNAL BY SOLVING BLOCH S EQUATIONS IN THE PRESENCE OF AMPLITUDE MODULATION 

Definitions and the Impact of Modulation on the Experimental Arrangement for Detecting the Signal 

Qh is the filling factor n is the number of turns in the coil and My are the z and y components of the magnetization, respectively po is the permeability of the free space and R is the coil radius. By comparison, the induced continuous- 

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S. K. Misra, Microwave Amplitude Modulation Technique to Measure Spin-Lattice and Spin-Spin (T2) Relaxation Tunes , in Biological Magnetic Resonance, eds. C. J. Bender and L. J. Berliner, Springer, 2006, vol. 25, Computational and Instrumental Methods in EPR, p. 1. 

MICROWAVE AMPLITUDE MODULATION TECHNIQUE TO MEASURE SPIN-LATTICE (Ti) AND SPIN-SPIN Ti) RELAXATION TIMES... 

Misra SK. 2005. Microwave amplitude modulation technique to measure spin-lattice relaxation times solution of Bloch s equations by a matrix technique. Appl Magn Reson 28 55-67. 

Microwave Amplitude Modulation Tecbnique to Measure Spin-Lattice (Ti) and Spin-Spin T2) Relaxation Times... 

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-... 

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)...

ESEEM is a pulsed EPR technique which is complementary to both conventional EPR and ENDOR spectroscopy(74.75). In the ESEEM experiment, one selects a field (effective g value) in the EPR spectrum and through a sequence of microwave pulses generates a spin echo whose intensity is monitored as a function of the delay time between the pulses. This resulting echo envelope decay pattern is amplitude modulated due to the magnetic interaction of nuclear spins that are coupled to the electron spin. Cosine Fourier transformation of this envelope yields an ENDOR-like spectrum from which nuclear hyperfine and quadrupole splittings can be determined. 

Using amplitude or frequency modulation of a carrier at frequency tog, we can achieve exact frequency division if we make sidebands of the carrier to such low frequency that we can force the condition wg-nQ = (n+2) 2-a>g = 2 so that tog/ 2 = n+1. For example, if we examine Fig. 2, we can achieve exact frequency division by any means which locks the phase of the carrier to the phase of the amplitude modulation that is, the undulations of the carrier do not "slip" under the envelope of the amplitude modulation. A divider based on these principles would be quite useful if 2 is in the microwave region (or below) where precise frequency synthesis is possible. Since 2 and n could be freely chosen, any value of uig could be measured in a single device. 

Figure 11.13 shows the energy levels involved and the transitions studied for H2 in the N = 1 rotational level of the G 1 + state. The experiments were performed using a fixed microwave frequency, typically 9204 MHz, and the resonances detected by scanning the magnetic field amplitude modulation of the microwave power at 100 kHz and lock-in amplifier detection were employed. Polarising filters were used to detect the fluorescence, so that changes in polarisation could be observed. 

Figure 11.24. Experimental arrangement used by Ernst and Kindt [44] in their pump/probe microwave/optical double resonance study of a rotational transition (18.2 GHz) in the ground state of CaCl. The photomultiplier tubes which monitor fluorescence are situated on the axis perpendicular to both the laser beam and the molecular beam. The C region, where the molecular beam is exposed to microwave radiation, is magnetically shielded to minimise stray Zeeman effects. The microwave power was amplitude modulated at 160 Hz and the modulated fluorescence detected by photomultiplier B. 

As was pointed out in the introduction, optical detection of the Zeeman transitions of the triplet state preceded the optical detection in zf. Since these former experiments resemble those in ionic crystals, researchers in this field called this technique MODR (microwave-optical double resonance). The assignment of the zf transitions as well as the relative order of the zf levels could be concluded also from the MODR techniques as in the PMDR technique. The first reported MODR experiment was made by Sharnoff (15), in which the Am = 2 transition of the C10D8 tr Plet state in a biphenyl host, using amplitude modulation of the microwave power. A few months later Kwiram reported the optical detection of the Am = + 1 for phenanthrene in biphenyl (16). The experiments were... 

The method of phosphorescence microwave double resonance (PMDR) spectroscopy is based, like the two other methods discussed above, on c.w. excitation of the Pd(2-thpy)2 compound at low temperature. Additionally, micro-wave irradiation is applied, whereby the frequency is chosen to be in resonance with the energy separation between the two substates I and III of 2886 MHz. With this set-up, one monitors the phosphorescence intensity changes in the course of scanning the emission spectrum. Technically, the phosphorescence spectrum is recorded by keeping the amplitude-modulated microwave frequency at the constant value of 2886 MHz and by detecting the emission spectrum by use of a phase-sensitive lock-in and signal averaging procedure (e.g. see [61, 75,90]). 

Fig. 8. Illustration of microwave pulse schemes for two-pulse and three-pulse ESEEM (adapted from Kevan and Bowman ). In the two-pulse experiment, the interpulse time t is varied and the amplitude modulation of the resulting electron spin echo is recorded. In the three-pulse experiment, t is fixed and the electron spin echo amplitude is recorded as a function of the interpulse time T.

Slow-passage ODMR signals frequently are observed by the continuous wave method in which the optical effect is monitored using broadband detection. On the other hand, if the triplet state decay constants are sufficiently large, the microwave power may be amplitude modulated at an audio frequency which results in modulated phosphorescence when the microwave frequency is at resonance. The phosphorescence is then monitored with narrow-band phase-sensitive detection, for a great improvement in the signal/noise ratio. The latter detection method is frequently used to produce a magnetic resonance-induced phosphorescence spectrum by a technique referred to as phosphorescence-microwave double resonance (PMDR). The microwave frequency is fixed at resonance,... 

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