Focusing phase-shift functions

Phase contrast transfer function. The phase shifts due to the combination of spherical aberration and defect of focus can be combined into a single phase factor x given by... 

Since the phase delay experienced by the propagating optical signal is proportional to the refractive index, the OKE causes a nonlinear intensity-dependent delay in addition to the linear contribution. The intensity of a pulse varies across both its temporal and its spatial profile. Therefore, different parts of the profile will experience a different refractive index. As a result, the OKE provides a modulation function that follows the pulse profile and continues to strongly shape the pulses on each cavity round trip until the pulse is compressed to its final steady-state value. This mechanism leads to self-mode-locking caused by the effects of self-phase-modulation (SPM) [194, 195] and self-focusing. Both phenomena are a consequence of different parts of an optical signal experiencing different refractive indices and thus different nonlinear phase shifts. 

The earliest applications of the replica integral equation approach date back to the beginning of the 1990s. They focused on quite simple QA systems such as hard-sphere (HS) and LJ (12,6) fluids in HS matrices (see, for example. Refs. 4, 286, 290, 298, 303, 312, and 313 for reviews). Fiom a technical point of view, these studies have shown that the replica integral equations yield accurate correlation functions compared with parallel computer simulation results [292, 303, 314, 315]. Moreover, concerning phase behavior, it turned out that the simple LJ (12,6) fluid in HS matrices already displays features also observed in experiments of fluids confined to aerogels [131, 132]. These features concern shifts of the vapor liquid critical temperature toward values... 

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The multiple interaction effects beyond dimer model are of interest. These effects in the liquid phase as well as structures are not so clear, although the network structure has been discussed for NMA. We focus on the system which shows relatively large shift in the liquid phase, namely, FA and NMF. The trimer to pentamer structures were examined by TD-DFT. The structures of 3FA-5FA are shown in Fig. 3.15. The interaction energies and the vertical excitation energies including the energy shifts are summarized in Table 3.6. The calculations were performed with cc-pVTZ with s and p diffuse functions on C, N, and O. 

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