Parametric processes, nonlinear optics

The most widely used source for the polarization-entangled photons today utilizes the process of spontaneous parametric down-conversion in nonlinear optical crystals [Kwiat 1995], A typical picture of the emerging radiation is shown in Fig. 1. 

A few further general remarks are in order at this stage. One is to note the fact that the sum over intermediate molecular states, as in Eqs. (76) and (79), in principle applies not only to electronic but also to vibrational levels. Although this issue initially received most attention in connection with molecular hyperpolarizabilities [44], it applies equally to other optical response tensors. The vibrational contributions, which were previously largely overlooked, have now been extensively studied and shown to be important in many applications [45,46]. Second, the polarizabilities associated with nonlinear parametric processes may in most circumstances be regarded as properties of the ground-state molecule, since it is the molecular ground state that usually constitutes the... 

Power, E. A. and S. Zienau, 1959, Philos. Trans. Roy. Soc. London Ser. A251, 427-454. Reintjes, J. F., 1984, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, Orlando, Florida) pp. 355-357. 

Thus as well as returning the molecule to its original state, the four-wave process transfers no momentum to the molecule if the phase matching condition is met. Such a mechanism is known generally in nonlinear optics as a parametric process, and is associated with optimum conversion efficiency. 

In the parametric process (Fig. 6.42a), a pump photon Ikwp is split in a nonlinear optical crystal into a signal photon and an idler photon ha>i, such that energy and momentum are conserved ... 

In the parametric amplifier two laser beams are focused into the nonlinear optical crystal the seed laser beam with frequency co and a strong pump beam with cop. Due to the parametric process in the nonlinear crystal, a new wave is generated with a difference frequency coi = cop- cog, (Fig. 6.42b). Most of the pump photons split up into a signal and an idler photon where the signal photons superimpose the seed photons and amplify the weak seed beam. 

Fig. 6.42 Schematic diagram of a parametric process (a) collinear optical parametric amplifier, (b) parametric process in a nonlinear optical crystal, (c) noncollinear optical parametric amplifier NOPA...

The first successful experimental realization of squeezing was reported by Slusher and coworkers [1335], who used the four-wave mixing in a Na-atomic beam as nonlinear process (Fig. 9.99). The Na atoms are pumped by a dye laser at the frequency coi = co )8, which is slightly detuned from the resonance frequency coq. In order to increase the pump power, the Na beam is placed inside an optical resonator tuned to the pump frequency co]. Because of parametric processes (Vol. 1, Sect. 6.7) of the two pump waves (coi, A l) inside the resonator, new waves at u)l are generated at this four-wave mixing process (signal and idler wave). Conservation of energy and momentum demands... 

FIGURE 30 Temporal variation of (a) intensity, (b) phase, and (c) frequency produced by a medium with a positive nonlinear refractive index, (d) Spectrum of a self-phase-modulated pulse. The asymmetry results from a rise time that was 1.4 times faster than the full time. [Part (d) reproduced from Reintjes, J. (1984). Nonlinear Optical Parametric Processes in Liquids and Gases, Academic Press, Orlando, FL.]... 

Reintjes, J. (1984). Nonlinear Optical Parametric Processes in Liquids and Gases, Academic, New York. 

The Optical Parametric Oscillator (OPO) process should also be mentioned. Here a nonlinear crystal in a cavity is used to generate two new frequencies (oji and 0J2) out of a single one (a ) that is used to pump the crystal. Energy conservation requires Ui- U 2 = ct . The frequency division between the two new waves (the signal and the idler) is chosen by the phase matching condition. The parametric process can also be used in Optical Parametric Amplifiers (OPA). Parametric laser light generation was reviewed in [8.77,78]. 

Besides the various types of tunable lasers discussed in the foregoing sections, sources of tunable coherent radiation have been developed that are based on the nonlinear interaction of intense radiation with atoms or molecules in crystals or in liquid and gaseous phases. Second-harmonic generation, sum- or difference-frequency generation, parametric processes, or stimulated Raman scattering are examples of such nonlinear optical mixing techniques. These techniques cover the whole spectral range from the vacuum ultraviolet (VUV)... 

Reintjes J (1984) Nonlinear Optical Parametric Processes Simon U and Tittel FK (1997) In Experimental Methods in... 

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