Extended Finite Difference Time Domain Analysis of Induced Phase Modulation and Four-Wave Mixing between Two-Color Femtosecond Laser Pulses in a Silica Fiber with Different Initial Delays

Abstract

The scattering of positronium (Ps) by lithium (Li) is investigated using the staticexchange approximation and a two-state close-coupling approximation (CCA) including exchange. The major effect of very high polarizability of Li, at least 30 times higher than hydrogen and more than four times higher than Ps, has been considered in the present CCA scheme in a dynamic way by using the Li(2p) state of the target Li atom in the basis set. Different scattering parameters, e.g. s-, p-and d-wave phase shifts below the excitation threshold, the partial wave elastic and excitation cross sections for s-, p-and d-waves, the integrated elastic and excitation cross sections, the quenching cross sections, and the ortho-para conversion ratios are presented in the incident energy range from 0.068 E 100 eV. The present study reveals that the long-range dipole correlation potential has an appreciable effect in the cases of Ps and Li scattering in the lower energy region 0.068 E 30 eV. In the incident energy region above 30 eV, both the results almost coincide with the first Born results. A sharp maximum in the elastic cross sections near 3 eV and three sharp peaks in excitation cross sections near the incident energies of 0.425, 13.0 and 19.0 eV appear in the present results, which are consistent with the minima in the conversion ratios. The p-wave singlet elastic phase shifts calculated by the CCA method are higher by a factor of nearly π/2 than the corresponding static exchange results below 0.439 eV. † Present address: 4285 4286 H Ray and electron-electron exchange (Fraser 1961, 1962, 1968, Fraser and Kraidy 1966, Hara and Fraser 1975 is essential. Inclusion of these features evidently complicates the problem.Here an attempt has been made to calculate different scattering parameters using a CCA including the effect of exchange and dipole polarizability for the Ps-Li system. An exact treatment of the exchange interaction is made in all the first Born matrix elements used as input for the CCA. It is to be noted that the mean static interaction in the case of the Ps-atom scattering vanishes due to coincidence of charge and mass centre in Ps. Again the excitation cross section vanishes for the processes in which the parity of Ps changes by an even number, unless exchange is included. There are a few studies dealing with the collision of Ps with one-and two-electron systems, e.g. Ps-H (

Comparison between Finite-Difference Time-Domain Method and Experimental Results for Femtosecond Laser Pulse Propagation

“…(Nakamura et al, 2005b) Figures 13 and 14 show the IPM-induced spectra obtained by the previous experiment (Xu et al, 1999) and the extended FDTD calculation with different initial time delays between the two pulses, these figures indicate spectra after propagation of 3 mm fiber with the initial delays T d of (a) 0, (b) -40, and (c) -80 fs, respectively. The pulse energies after fiber propagation of the two pulses are the same value, 40 nJ.…”

“…11. Spectra obtained (a) experimentally (Xu et al, 1999) and (b) numerically (Nakamura et al, 2005b) for two pulses at center wavelengths of 795 nm (solid line) and 640 nm (dashed line) before propagation in a 3 mm silica fiber. and 2382 fs 2 for the fundamental and signal pulses, respectively.…”

“…We measured the IPM-induced spectra with different initial time delays between the two pulses. (Xu et al, 1999) and (b) numerically (Nakamura et al, 2005b) obtained spectra induced by SPM in 3 mm single-mode fused-silica fiber. The thin solid line represents the spectrum induced by the SPM of the pulse at the center wavelength of 795 nm and the thin dashed line represents the spectrum induced by the SPM of the pulse at the center wavelength of 640 nm at the pulse duration of 120 fs and the energy of 20 nJ in the 3 mm fiber for each pulse.…”

“…The DFWM is robust for chirping. (Cundiff et al, 1999), (Geraghty et al, 1998) www.intechopen.com (Nakamura et al, 2005b) When the two pulses meet at the end of the fiber T d = 80 fs, the trailing edge of the signal pulse mainly interacts with the leading edge of the fundamental pulse and the chirped pulses gradually become overlapping at the places where the pulses are temporally broadened; therefore, the interaction length is long. As a result, the four-wave mixing effect is enhanced and a larger parabolic phase curve of the anti-Stokes light in the spectral phase is observed.…”

Finite-Difference Time Domain Analysis of Ultrashort Pulse Laser Light Propagation under Nonlinear Coupling

“…The next step is to obtain linear polarization P. To precisely describe Group Velocity Dispersion (GVD) we apply Sellmeier's formation to FDTD method (20) which has three linear polarizations P m (m = 1, 2, 3) of that evolution equations are written as…”