Numerical Simulation Of Nonlinear Propagation Research Articles

Numerical Simulation of the Nonlinear Propagation of Ultrashort Pulses in Fiber Amplifiers Using Time-Frequency Representations

To predict the behavior of high power pulsed lasers, fine numerical simulations of nonlinear propagation of short chirped pulses in fiber amplifiers are needed. In particular, the gain used in the nonlinear Schrödinger equation (NLSE) should take into account the simultaneous dependence of the gain with frequency (i.e. gain dispersion) and time (i.e. gain saturation). We propose here a method using a time-frequency representation (TFR) of the pulse to compute the gain that can be used in the NLSE. Basic TFRs can be computed by estimating the group delay or the instantaneous frequency of the pulse but the low numerical complexity of these methods introduce some limitations in term of cases that can be properly simulated. We show that the more time-consuming computation of the reassigned spectrogram (RS) of the pulse allows to obtain a gain more suitable for general cases than can be encountered in high energy ultrafast lasers.

Supercontinuum generation in photonic crystal fibers infiltrated with nitrobenzene

A photonic crystal fiber made of fused silica glass and infiltrated with nitrobenzene (C6H5NO2) was proposed as a new nonlinear medium for supercontinuum generation (SG). The guiding properties of the fiber structure were studied numerically, including estimation of the effective refractive index, attenuation, and dispersion of the fundamental mode. Based on the obtained results, three optimized structures were selected and tested numerically for SG. With numerical simulations of nonlinear propagation, we demonstrated the feasibility of spectrally broad and coherent SG in the proposed structures. For the first we obtained a supercontinuum (SC) in the range of 0.8–1.8 µm, for the second in the range of 0.8–2.1 µm, and for the third 1.3–2.3 µm. The pulse energy was in the range of 0.06–0.5 nJ while the pulse duration was 90 fs or 120 fs. For all structures an SC was formed in the first centimeter of the light propagation and conveniently allowed to assume short segments of the fibers. The proposed fibers are good candidates for all-fiber SC sources constituting an attractive alternative to glass-core fibers, since the nonlinearity of nitrobenzene is significantly higher than that of silica. The proposed solution may lead to new low-cost all-fiber optical systems for SG.

Fast accurate optical measurement of medical ultrasonic field in combination with numerical simulation of nonlinear propagation

Fast and accurate measurement of ultrasonic field is necessary to ensure the safety and efficacy of therapeutic as well as diagnostic applications of medical ultrasound. The most common method for the purpose is hydrophone scanning. However, it requires a long scanning time and potentially disturbs the field, which is limiting the efficiency of developing such applications. This study proposes an optical phase contrast method in combination of a CT algorithm. Ultrasonic pressure field modulates the phase of the light passing through the field. A phase plate was employed to shift the phase of the non-diffracted component of the light typically by 90 degrees. The phase modulation of the diffracted component was converted to amplitude modulation through interference with the phase-shifted non-diffracted component and then measured by camera. From the measured projected 2D data, the 3D pressure field was reconstructed by a CT algorithm. An upstream field, in which the optical phase does not wrap and the effect of nonlinear propagation can be ignored, was thereby quantified. Nonlinear ultrasonic propagation was simulated based on a pseudo spectral method using the upstream pressure field as the input. Both pressure waveform and absolute pressure from the proposed method agreed well with those directly from hydrophone scanning.

Nonlinear effects in optical signal transmission using a multimode fibre with weak coupling

We present the results of numerical simulation of nonlinear propagation of an optical signal in multimode gradient- and step-index fibres with weak coupling. It is found that when signals propagate in different modes, the system quality factor (Q-factor) for a gradient-index fibre increases with the number of the modes involved. The quality degradation of the transmitted data with increasing the number of the involved modes is demonstrated for the case when the signals in different modes travel at the same velocity. It is shown that the use of a step-index fibre may significantly deteriorate the signal quality due to the presence of a mode with a small dispersion parameter.

A numerical simulation of nonlinear propagation of gravity wave packet in three-dimension compressible atmosphere

By using FICE scheme, a numerical simulation of nonlinear propagation of gravity wave packet in three-dimension compressible atmosphere is presented. The whole nonlinear propagation process of the gravity wave packet is shown; the basic characteristics of nonlinear propagation and the influence of the ambient winds on the propagation are analyzed. The results show that FICE scheme can be extended in three-dimension by which the calculation is steady and kept for a long time; the increase of wave amplitude is faster than the exponential increase according to the linear gravity theory; nonlinear propagation makes the horizontal perturbation velocity increase greatly which can lead to enhancement of the local ambient winds; the propagation path and the propagation velocity of energy are different from the results expected by the linear gravity waves theory, the nonlinearity causes the change in propagation characteristics of gravity wave; the ambient winds alter the propagation path and group velocity of gravity wave.

The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)