Oscillation coherent electric

Figure 1. Fundamentals of ICR excitation. The applied magnetic field direction is perpendicular to the page, and a sinusoidally oscillating radiofrequency electric field is applied to two opposed plates (see upper diagrams). Ions with cyclotron frequency equal to ("resonant" with) that of the applied rf electric field will be excited spirally outward (top right), whereas "off-resonant" ions of other mass-to-charge ratio (and thus other cyclotron frequencies) are excited non-coherently and are left with almost no net displacement after many cycles (top left). After the excitation period (lower diagrams), the final ICR orbital radius is proportional to the amplitude of the rf electric field during the excitation period, to leave ions undetected (A), excited to a detectable orbital radius (B), or ejected (C).

To extend the special concept of coherent electric oscillations to further phenomena, we assume two rather general postulates ... 

The microwave detected MODR scheme closely resembles pulsed nuclear magnetic resonance (Hahn, 1950), optical coherent transients by Stark switching (Brewer and Shoemaker, 1971) and laser frequency switching (Brewer and Genack, 1976). The on-resonance microwave radiation field, ojq = ( 2 — Ei)/H, creates an oscillating bulk electric dipole polarization (off-diagonal element of the density matrix, pi2(t)). The oscillation is at u>o u>r, where ojr is the (Mj-dependent) Rabi frequency,... 

Finally, in this section, possible frequencies for the excitation of coherent vibrations should be considered. Originally special reference was made to membrane oscillations as their high polarization will then yield coherent electric oscillations (cf. Ref. 7, with earlier literature). Since the thickness of a membrane is about 10" cm and its elastic constant is equivalent to a velocity of sound of about lO cm/s, a frequency of the order of 10 Hz was expected, corresponding to electromagnetic waves in the millimeter region. When based on proteins or DNA, however, both higher and lower frequencies may be expected. 

At small diameters (d < 30 nm] the absorption/extinction spectra are dominated by the dipole resonance (/ = 1) and the incident electric field causes the conduction electrons to oscillate coherently along the Eo -polarization direction. Moreover the scattering, which is a radiative process and requires coupling between electric and magnetic fields, is negligible. Thus the extinction efficiency is very close to the absorption efficiency, as it can observed in the spectra reported in Fig. 3.1. 

Second, after an appropriate time interval to allow the gas pulse to reach an optimum position between the cavity mirrors, a 1 qs pulse of monochromatic microwave radiation is introduced into the cavity, which is itself tuned to the correct matching resonant frequency. The pulse carries with it a band of frequencies Av 1 MHz, centred at the resonant frequency v of the cavity. The cavity has a bandwidth of approximately 1 MHz, so that the microwave radiation density is high. If the molecular species under investigation has one or more resonant frequencies within this bandwidth, an appreciable macroscopic polarisation is induced, corresponding classically to a phase-coherent oscillation of the molecular electric dipole moments. The microwave pulse must arrive at the correct time interval after the gas pulse. 

Since VSFS is a coherent technique, and as Equation (25) implies, the oscillating electric field from each vibrational state involved in the generation of sum-frequency light can interfere with that from every other state and with that from the non-resonant response. This is quite different from IR spectroscopy where spectra are simple superpositions of intensity from individual vibrational modes. As such, VSFS leads to interesting line shapes that can be interpreted incorrectly if spectral intensities are compared visually without fitting the spectrum. 

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