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.

Ultrafast sum-frequency polarization beats in twin Markovian stochastic correlation

An analytic closed form for the second- order or fourth- order Markovian stochastic correlation of attosecond sum- frequency polarization beat ( ASPB) can be obtained in the extremely Doppler- broadened limit. The homodyne detected ASPB signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light. fields with arbitrary bandwidth. The physical explanation for this is that the Gaussian- amplitude. field undergoes stronger intensity. fluctuations than a chaotic. field. On the other hand, the intensity ( amplitude). fluctuations of the Gaussian- amplitude. field or the chaotic. field are always much larger than the pure phase. fluctuations of the phase-diffusion field. The field correlation has weakly influence on the ASPB signal when the laser has narrow bandwidth. In contrast, when the laser has broadband linewidth, the ASPB signal shows resonant- nonresonant cross correlation, and the sensitivities of ASPB signal to three Markovian stochastic models increase as time delay is increased. A Doppler- free precision in the measurement of the energy- level sum can be achieved with an arbitrary bandwidth. The advantage of ASPB is that the ultrafast modulation period 900as can still be improved, because the energy- level interval between ground state and excited state can be widely separated.

Twin Markovian field correlation on four-level attosecond polarization beats

Based on the phase-conjugate polarization interference between two two-photon processes, we obtained an analytic closed form for the second-order or fourth-order Markovian stochastic correlation of the four-level attosecond sum-frequency polarization beat (FASPB) in the extremely Doppler-broadened limit. The homodyne-detected FASPB signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. The different roles of the amplitude fluctuations and the phase fluctuations can be understood physically in the time-domain picture. The field correlation has a weak influence on the FASPB signal when the laser has narrow bandwidth. In contrast, when the laser has broadband linewidth, the FASPB signal shows resonant-nonresonant cross-correlation, and drastic difference for three Markovian stochastic fields. The maxima of the two two-photon signals are shifted from zero time delay to the opposite direction, and the signal exhibits damping oscillation when the laser frequency is off-resonant from the two-photon transition. A Doppler-free precision in the measurement of the energy-level sum can be achieved with an arbitrary bandwidth. As an attosecond ultrafast modulation process, it can be extended intrinsically to any sum frequency of energy levels.

Two-photon asymmetric color-locking second-order stochastic correlation of attosecond polarization beats

Based on the phase-conjugation polarization interference between two two-photon processes, we theoretically investigated the attosecond scale asymmetry sum-frequency polarization beat in four-level system (FASPB). The field correlation has weak influence on the FASPB signal when the laser has narrow bandwidth. Conversely, when the laser has broadband linewidth, the FASPB signal shows resonance-nonresonance cross correlation. The two-photon signal exhibits hybrid radiation-matter detuning terahertz; damping oscillation, i.e., when the laser frequency is off resonance from the two-photon transition, the signal exhibits damping oscillation and the profile of the two-photon self-correlation signal also exhibits zero time-delay asymmetry of the maxima. We have also investigated the asymmetry of attosecond polarization beat caused by the shift of the two-photon self-correlation zero time-delay phenomenon, in which the maxima of the two two-photon signals are shifted from zero time-delay point to opposite directions. As an attosecond ultrafast modulation process, FASPB can be intrinsically extended to any level-summation systems of two dipolar forbidden excited states.

Fast calculation technique for scattering in T-matrix method

In scattering calculations using the T-matrix method, the calculation of the T-matrix involves multiplication and inversion of matrices. These two types of matrix operations are time-consuming, especially for the matrices with large size. Petrov et al. [D. Petrov, Y. Shkuratov, G. Videen, Opt. Lett. 32 (2007) 1168] proposed an optimized matrix inversion technique, which suggests the inversion of two matrices, each of which contains half the number of rows. This technique reduces time-consumption significantly. On the basis of this approach, we propose another fast calculation technique for scattering in the T-matrix method, which obtains the scattered fields through carrying out only the operations between matrices and the incident field coefficient. Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al. (c) 2008 Elsevier B.V. All rights reserved.

Correlation of electrical and optical properties in dually Cd+ and N+ ion-implanted GaAs

Cd in GaAs is an acceptor atom and has the largest atomic diameter among the four commonly-used group-II shallow acceptor impurities (Be, Mg, Zn and Cd). The activation energy of Cd (34.7 meV) is also the largest one in the above four impurities, When Cd is doped by ion implantation, the effects of lattice distortion are expected to be apparently different from those samples ion-implanted by acceptor impurities with smaller atomic diameter. In order to compensate the lattice expansion and simultaneously to adjust the crystal stoichiometry, dual incorporation of Cd and nitrogen (N) was carried out into GaAs, Ion implantation of Cd was made at room temperature, using three energies (400 keV, 210 keV, 110 keV) to establish a flat distribution, The spatial profile of N atoms was adjusted so as to match that of Cd ones, The concentration of Cd and N atoms, [Cd] and [N] varied between 1 x 10(16) cm(-3) and 1 x 10(20) cm(-3). Two type of samples, i.e., solely Cd+ ion-implanted and dually (Cd+ + N+) ion-implanted with [Cd] = [N] were prepared, For characterization, Hall effects and photoluminescence (PL) measurements were performed at room temperature and 2 K, respectively. Hall effects measurements revealed that for dually ion-implanted samples, the highest activation efficiency was similar to 40% for [Cd] (= [N])= 1 x 10(18) cm(-3). PL measurements indicated that [g-g] and [g-g](i) (i = 2, 3, alpha, beta,...), the emissions due to the multiple energy levels of acceptor-acceptor pairs are significantly suppressed by the incorporation of N atoms, For [Cd] = [N] greater than or equal to 1 x 10(19) cm(-3), a moderately deep emission denoted by (Cd, N) is formed at around 1.45-1.41 eV. PL measurements using a Ge detector indicated that (Cd, N) is increasingly red-shifted in energy and its intensity is enhanced with increasing [Cd] = [N], (Cd, N) becomes a dominant emission for [Cd] = [N] = 1 x 10(20) cm(-3). The steep reduction of net hole carrier concentration observed for [Cd]/[N] less than or equal to 1 was ascribed to the formation of (Cd, N) which is presumed to be a novel radiative complex center between acceptor and isoelectronic atoms in GaAs.

A fast-settling frequency-presetting PLL frequency synthesizer with process variation compensation and spur reduction

This paper proposes a fast-settling frequency-presetting PLL frequency synthesizer. A mixed-signal VCO and a digital processor are developed to accurately preset the frequency of VCO and greatly reduce the settling time. An auxiliary tuning loop is introduced in order to reduce reference spur caused by leakage current. The digital processor can automatically compensate presetting frequency variation with process and temperature, and control the operation of the auxiliary tuning loop. A 1.2 GHz integer-N synthesizer with 1 MHz reference input Was implemented in a 0.18μm process. The measured results demonstrate that the typical settling time of the synthesizer is less than 3μs,and the phase noise is -108 dBc/Hz@1MHz.The reference spur is -52 dBc.