Fast and effective analysis methods for fiber Raman amplifiers

A series of new single-step methods and their corresponding algorithms with automatic step size adjustment for model equations of fiber Raman amplifiers are proposed and compared in this paper. On the basis of the Newton-Raphson method, multiple shooting algorithms for the two-point boundary value problems involved in solving Raman amplifier propagation equations are constructed. A verified example shows that, compared with the traditional Runge-Kutta methods, the proposed methods can increase the accuracy by more than two orders of magnitude under the same conditions. The simulations for Raman amplifier propagation equations demonstrate that our methods can increase the computing speed by more than 5 times, extend the step size significantly, and improve the stability in comparison with the Dormand-Prince method. The numerical results show that the combination of the multiple shooting algorithms and the proposed methods has the capacity to rapidly and effectively solve the model equations of multipump Raman amplifiers under various conditions such as co-, counter- and bi-directionally pumped schemes, as well as dual-order pumped schemes.

RAMAN PHONONS OF SILICON WIRES

Using the Keating model and the Raman polarizability of Alben et al., the phonon Raman spectra of silicon wires are calculated. With the calculation results, the Raman spectra of porous silicon of some published papers are analyzed. Until now different authors have had different views on the luminescence mechanism of porous silicon, which may mainly result from the fact that they had different samples.

NEAR-RESONANT RAMAN-SCATTERING FROM GAAS/ALAS SUPERLATTICES

This article presents the results of near-resonant Raman scattering measurements on GaAs/AlAs superlattices at room temperature. A strong enhancement of GaAs LO phonon-even modes resulted owing to a dipole-allowed Frohlich interaction in superlattices. Similar to the previous results, the LO phonon-even modes in a polarized configuration are observed. In contrast to previous work, however, what we observed in depolarized configurations is the LO phonon-odd modes instead of even modes. It is confirmed that the selection rules for near-resonant Raman scattering from LO phonons in this kind of superlattices are the same as those for off-resonant scattering. From the second-order Raman scattering, it is confirmed that polarized second-order Raman scattering spectra consist of overtones and combinations of two even modes, and depolarized second-order Raman scattering spectra consist of combinations of an even mode and an odd mode. Our experimental results coincide with the predictions using the recently developed Huang-Zhu model. A brief discussion on interface modes and their combination with confined modes is also presented.

STUDY OF RAMAN-SPECTRA OF ZNSE-ZNTE STRAINED LAYER SUPERLATTICES

The Raman spectra of the II-VI wide band-gap compound ZnSe-ZnTe semiconductor strained-layer superlattices have been studied. The relations between the Raman shifts of the longitudinal optical phonon modes and the superlattice-structure parameters have been determined. When the layer thickness exceeds 40 angstrom, the change of the LO phonon-mode frequency shifts with the layer thickness is minimal, whereas when the layer thickness is smaller than 40 angstrom, great shifts have been observed. We estimate that the critical thickness of ZnSe-ZnTe SLS is about 40 angstrom. We have also found that the shifts induced by strain are much larger than the red shifts due to confinement.

NEAR-RESONANCE RAMAN-SCATTERING OF LONGITUDINAL OPTICAL PHONON MODES AND INTERFACE MODES IN GAAS/ALAS SUPERLATTICES

The near-resonance Raman scattering of GaAs/AlAs superlattices is investigated at room temperature. Owing to the resonance enhancement of Frohlich interaction, the scattering intensity of even LO confined modes with A1 symmetry becomes much stronger than that of odd modes with B2 symmetry. The even modes were observed in the polarized spectra, while the odd modes appear in the depolarized spectra as in the off-resonance case. The second-order Raman spectra show that the polarized spectra are composed of the overtone and combinations of even modes, while the depolarized spectra are composed of the combinations of one odd mode and one even mode. The results agree well with the selection rules predicted by the microscopic theory of Raman scattering in superlattices, developed recently by Huang and co-workers. In addition, the interface modes and the combinations of interface modes and confined modes are also observed in the two configurations.

RAMAN-SCATTERING BY LO PHONONS IN (GAAS)N1/(ALAS)N2 ULTRATHIN-LAYER SUPERLATTICES

Raman spectra of (GaAs)n1/(AlAs)n2 ultrathin-layer superlattices were measured at room temperature and under off-resonance conditions. The experimental results show that there are two effects in ultrathin-layer superlattices: the confinement effect of LO phonons and the alloy effect. It is found that the relative intensity of the disorder-activated TO mode can give a measure of the alloy effect. The Raman spectra of one-monolayer superlattices measured in various scattering configurations are very similar to those of the Al0.5Ga0.5As alloy, and thus the alloy effect is prominent. However, in the case of monolayer number n greater-than-or-equal-to 4, the confined effect is prominent, while the alloy effect is only shown as an interface effect.