Frequency mixing, principle

The principles of frequency mixing and the experimental progress towards the generation of coherent VUV radiation have been reviewed by W. Jamroz and B.P. Stoicheff, by C.R. Vidaland by R. Hilbig et al. ... 

The intensity of the generated radiation grows as the product of the incident pump intensities at low conversion efficiency. In the three-wave sum-frequency mixing interaction, one photon from each of the pump waves is annihilated for each photon created in the generated wave. Complete conversion of the total radiation in both pump waves at perfect phase matching is possible in principle if they start with an equal number of photons. Otherwise the conversion will oscillate with pump intensity or crystal length, even at exact phase matching. 

A third possibility for generating coherent radiation with tunable wavelength uses the principle of optical frequency mixing, which is discussed in Sect. 5.8. 

Its principle is illustrated in Fig. 5.126 The setup consists of two cw Ti sapphire near-infrared single-mode ring lasers with wavenumbers v and V2. The output radiation of these lasers is amplified by nanosecond pump laser pulses, resulting in amplified Fourier-limited pulses in the near IR. Tunable VUV radiation with wavenumbers vyuv = 2(v3)-hV2 was produced by resonance-enhanced sum-frequency mixing in a supersonic jet of xenon, using the two-photon resonance (5p) So (5p) 6p(l/2) (J = 0) at... 

The third possibility of generating coherent radiation with tunable wavelength uses the principle of optical frequency mixing. When the radiations from two lasers with frequencies and are superimposed in a medium with a sufficiently large nonlinear part of its susceptibility, each atom is induced to forced oscillations and generates radiation with the sum frequency... 

The nonlinear optical teclmiques of up- and down-conversion are based on mixing optical beams in a suitable crystal (BBO, LiNbO, KDP, etc) witli tire generation of new optical frequencies tire physical principle is as follows. If two beams having optical frequencies cOp CO2 and wavevectors k, are mixed in a nonlinear optical crystal at tire appropriate angle, a new optical frequency co can be coherently generated witli tire following conditions satisfied ... 

A number of 2D NMR experiments, such as NOESY, have a mixing period incorporated in their pulse sequence. In principle, precession of j magnetization also occurs during the mixing period. Why do we not need to have a third Fourier transformation to monitor the precession frequencies that occur during the mixing period ... 

Another purpose of a mixing tank is to dampen out fluctuations. A mixing tank cannot change the frequency of fluctuations but can dampen the amplitude. As a general principle, a residence time equal to the cycle time of the fluctuations will cause the amplitude to be dampened by about a factor of six. 

Fig. 16 are only rarely strictly periodic, because usually rather small fluctuations in the external parameters are sufficient to trigger abrupt changes. However, in principle, mixed-mode oscillations belong to the category of multiple-periodic limit cycles. If the behavior is governed by two incommensurate frequencies, i.e., the ratio of two periodicities is an irrational number. This situation is denoted by quasiperiodicity and has been realized experimentally with periodically forced oscillations, as will be described next. 

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