The theory of Bloch and Wangsness for nuclear magnetic resonance signals is applied to multiple-quantum transitions. In most of the NMR experiments, the energy level schemes are only slightly different from an equally spaced Zeeman pattern, so that a simultaneous absorption of several radiation quanta with the same frequency can take place. It is found that the multiplicity, or the number of quanta absorbed in the transition, is most easily determined through the specific dependence of the multiple quantum signals on the rf field amplitude. The dependence of the signals on various relaxation parameters is developed and is found to provide information about relaxation processes which is not derivable from ordinary singlequantum transitions.A method of enhancing multiple transitions by audio-modulating the radio-frequency field is described. This is helpful in cases where the frequency deviations from an equally spaced Zeeman pattern are so large that a direct multiple transition is too weak to be observed.
Using an rf-excited strip-line CO(2) laser with large lateral dimensions (a high Fresnel number) in a hemiconfocal optical cavity configuration, we observe modes that are distinctively off axial. They can be viewed as folded Gaussian beams with trajectories in the shapes of the letters M and W. Either of these modes can be isolated by suppressing the other mode through the introduction of a suitably positioned obstacle into the cavity. Computer simulations of the radiation propagation in the cavity yielded field distributions conforming to the observed pattern.
An enhanced two-photon emission has been observed which is due to a strong laser radiation. The intensity of this process is very high when compared with a corresponding spontaneous twophoton emission. 1 Enhancement takes place even though the populations of the emitting atomic or molecular states are not inverted. The laser radiation is coherently amplified and the process provides a method for laser amplification.Spontaneous two-photon emission is generally a weak process responsible for the decay of metastable states. 1 A continuous distribution of photon pairs is emitted with the energy sum of each pair equal to the separation of the initial and final states of the emitting system (Fig. 1). The contribution of these processes to the decay rate of the emitting state can be obtained by integrating over the distribution of possible photon pairs. 2 This rate is negligibly small compared with that for a cascade of single emissions, if such a process is possible.A two-photon decay is illustrated in Fig. 1. The energy separation E z -E 1 is equal to ftu) x + fiw 2 , where o> x and oo 2 are the emitted complementary frequencies. Levels E 3 and E x have the same parity if the system has inversion symmetry, but the following discussion need not be limited to such systems. The existence of a virtual state E 2 inside the energy interval E 3 -E l is helpful for two-photon emission, but is not essential.Physical insight into the important features of the process is obtained if the intensities of the radiation fields are discussed in terms of average photon occupation numbers n 1 and n 2 of the radiation modes. For "laser" fields, the average n will account only for field modes that are within the angular spread of the beam. This means that, in such fields, the contribution of spontaneous emission to radiation modes outside the laser beam is disregarded.Let the population densities of the emitting and final states be N 3 and N l9 respectively. The two-photon decay rate for one photon within the frequency region co x and O^ + AOJ and a second photon with the complementary frequency is 3 dNJdt= -4K + 1)(^2 + l)^3~^2 Ar J ? where 167T 3 a = ^( a) i)^a , 2) a, i w 2 A^(1)
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