Downconversion processes

The simplest and most often used approximation allowing for analytical solutions of the downconversion problem is the parametric approximation, in which it is assumed that the pump mode is a strong coherent field that remains undepleted during the evolution. The amplitude of this classical field is an external parameter on which the solutions for the signal field depend. Equations of motion for the downconversion process are the same as in (56)... 

It is very instructive to compare the joint phase probability distributions for the signal and pump modes produced in the downconversion process shown in... 

In quantum optics a downconversion process may be visualized as the decay of a pump photon into a pair of signal and idler photons of lower frequency. Provided the pumping remains not depleted and phase matching takes place, the energy of the spontaneously downconverted light monotonically increases and that of the pump beam monotonically decreases. From this point of view the downconversion process may be regarded as the decay process of an unstable... 

Figure 24. Downconversion process coupled to an auxiliary mode b.

A downconversion process linearly coupled to an auxiliary mode b can be modeled by the following interaction Hamiltonian... 

To summarize, the statement the downconversion process is mismatched means that the nonlinear process is out of resonance in the sense that the momentum of the decay products (signal and idler photons) differs from the... 

Figure 27. Energy scheme of a mismatched downconversion process subject to linear coupling. The bottom solid lines denote a resonant process.

Another class of QKD protocols is based on entangled quantum systems [162]. Both Alice and Bob receive one member of a pair of particles obtained from the parametric downconversion process [161]. These particles feature nonclassical properties results of suitably chosen measurements on the particles exhibit, even when spatially separated, correlations that cannot be explained by any classical theory consistent with local realism. When Alice and Bob decide to establish a key, they perform independent measurements in randomly chosen bases (from a given nonorthogonal set), and using a public channel they arrive at a secret shared key in a way similar to BB84. Later developments showed a way to improve the security of this protocol by means of the so-called entanglement purification techniques [163]. 

Silicon solar cells suffer from about 50% losses because the solar spectrum does not match well with silicon absorption. Photons with wavelengths longer than the band gap (for multicrystalline silicon, mSi, Eg - 1.1 eV) are wasted, whereas shorter wavelengths are absorbed but the excess energy is lost due to thermahzation of the electrons. The optimum wavelength for absorption is 1,100 nm. Effort has therefore been directed to tailor incident radiation upon the cell by using a front panel so that the optimum response is achieved. It therefore entails that both upconversion and downconversion processes are required to be apphed to modify the energies of incident photons. 

Let us start with the short-time approximation in which we can use the symbolic manipulation computer program described in Appendix A to find the corrections coming from the quantum fluctuations of the fields. The operator formulas (94) and (95) are valid also for the degenerate downconversion because the two processes are governed by the same Hamiltonian, but now initially the second-harmonic mode is populated while the fundamental mode is initially in the vacuum state. Assuming that the pump mode at the frequency 2oo is in a coherent state fi0) (p0 = /Ni,exp(k )h)), we have... 

Fig. 20 to the same distribution for the fields produced in the second-harmonic generation process shown in Fig. 13. The differences are clearly visible. The distribution for the downconverted held from the beginning develops a two-peak phase structure, which is a consequence of the two-fold rotational symmetry of the Q function for the signal mode. It is known [57,67] that for fc-photon downconversion the Q function has fc-fold rotational symmetry and the phase distribution has k peaks, at least at the initial stages of the evolution. From Fig. 20 it is also clear that when the intensity of the signal mode reaches its...

Because of the oscillatory behavior of the intensity of the signal mode, which switches the process from the downconversion regime to the second-harmonic... 

The process of spontaneous parametric downconversion has been studied extensively [79,80] for cw (continuous-wave) pump lasers over the last decades. A great deal of attention has been paid to the process of spontaneous parametric... 

The process of spontaneous parametric downconversion is described by the following interaction Hamiltonian [79] ... 

In a dynamical explanation of QZE the inhibition of the original evolution is not a mandatory consequence. For instance, it has been shown in [105,106] that provided the phase matching condition is not fulfilled in the process of downconversion, the observation may, on the contrary, enhance the emission for a properly chosen N (inverse Zeno effect). 

The interplay between nonlinear mismatch and linear coupling is illustrated in Fig. 26. A significant production of signal photons is a clear manifestation of IZE. In correspondence with the observations in other studies [105,106] (Section VI.C), such IZE occurs only provided a substantial phase mismatch is introduced in the process of downconversion. It is worthwhile to compare the interesting behavior seen in Fig. 26 with QZE and IZE observed in a sliced nonlinear crystal (Fig. 25). It can be seen that the coupling parameter K here plays a role similar to the number of slices N, into which the crystal is cut in the latter scheme. Moreover, the sharpness of the observation (k or N), at which a maximum output intensity occurs, is approximately a linear function of the introduced phase mismatch in both schemes. There are, however, also some points of difference. For example, the maximum output intensity obtainable for... 

The latter result (82) yields a quantum probability amplitude that, under Hermitian conjugation and time reversal, correctly equates to the corresponding amplitude for the time-inverse process of degenerate downconversion. To see this, we note that the matrix element for SHG invokes the tensor product Py (—2co co, ) p([/lC., where the brackets embracing two of the subscripts (jk) in the radiation tensor denote index symmetry, reflecting the equivalence of the two input photons. As shown previously [1], this allows the tensor product to be written without loss of generality as ( 2co co, co), entailing an index-symmetrized form of the molecular response tensor,... 

Nd " ion has a disadvantage, which is called self-quenching of emission, due to its complex electronic stmcture. Por downconversion, an excited Nd " ion in the " p3/2 level could transfer part of the excitation to an unexcited Nd " ion. At room temperature, the process is dominated by the cross-relaxation process, i.e., (%3/2, " 19/2) C Ii5/2> " Ii5/2). Iti itiost Nd-doped laser materials, the final levels of the... 

Due to the simple electronic stmcture of Yb ", Yb -doped ceramic lasers have no problem of de-excitation processes like the concentration-dependent selfquenching by downconversion or upconversion cross-relaxation. However, a reduction in emission lifetime and emission quantum efficiency has been observed. In addition, cooperative processes could occur, due to the interaction between two excited Yb " ions, when the concentrations of Yb " are too high. The parasitic deexcitation processes are usually accompanied by the generation of heat that is up to twice as much as that due to the quantum defect [202]. Therefore, it is important to have a good matching between the pump and mode volume in the laser materials. 

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