Frequency matching, absorption conditions

The term non-linear resonance describes the resonant absorption of potential energy from higher-order trapping fields. Such absorption occurs when combinations of an ion s secular frequencies match harmonic sidebands of the RF drive frequency. Conditions for non-linear resonance exist in all QITs but the effect on ion motion is dependent upon the order, sign (+ or -) and strength of the superimposed non-linear fields. Due in large part to the work of Franzen and co-workers [87-92], the phenomenon of non-linear fields and their contribution to non-linear resonance effects in ion traps is now well understood. In addition to the quadrupolar resonance, there are a series of resonance conditions desaibed by Equations 9.11 and 9.12 where V is an integer 0 and n is the order of the multipole. The overall order of the resonance (AO is described by Equation 9.13. 

According to (8.12), the Raman scattering cross section increases considerably if the laser frequency matches a transition frequency coij of the molecule (resonance Raman effect) [8.20,8.21]. With tunable dye lasers and optical frequency doubling this resonance condition can often be realized. The enhanced sensitivity of resonant Raman scattering can be utilized for measurements of micro-samples or of very small concentrations of molecules in solutions, where the absorption of the pump wave is small in spite of resonance with a molecular transition. 

The first requirement for IR absorption is that a frequency in the impinging source of IR radiation must correspond to the frequency of the vibration as expressed in Eq. (2.3). Frequency matching is a necessary condition for absorption but not the only one. An additional requirement is some mode of interaction between the impinging IR radiation and the molecule (there must be something to catch the radiation). Even if the IR radiation has the same frequency as the normal vibration of the molecule, it will be absorbed only under certain conditions. The rules determining optical absorption are known as selection rules. 

Atomic and Molecular Energy Levels. Absorption and emission of electromagnetic radiation can occur by any of several mechanisms. Those important in spectroscopy are resonant interactions in which the photon energy matches the energy difference between discrete stationary energy states (eigenstates) of an atomic or molecular system = hv. This is known as the Bohr frequency condition. Transitions between... 

In c.w.-n.m.r. spectroscopy, a relatively weak, but rapidly oscillating, magnetic field is produced on the x axis by the application of a continuous, low-powered radiofrequency (r.f.) to the transmitter coil(s). As this radiofrequency approaches the resonance frequency, the magnetization vector is very slightly tipped out of the z axis, and precesses about this axis. When this frequency of precession is matched by the r.f. applied (the resonance condition), some of the individual, nuclear moments undergo transitions to the less-stable energy-level represented by precession about the — z direction, accompanied by absorption of energy from the transmitter coil. 

Typically the source is tuned with the sample in place and then locked to match the cavity resonance frequency so as to achieve maximum energy storage and minimum reflected power. This reflected power is directed through a one-way coupler called a circulator to a crystal diode detector to convey information about sample absorption in the cavity. An iris opening to the cavity is adjusted to match the impedance of the cavity to that of the source so as to produce minimum reflection of radiation from the cavity. This condition gives maximum sensitivity for the impedance mismatch produced when sample absorption occurs in the cavity. 

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