Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

"Magic" dispersion maps with distributed Raman amplification

We analyze pulse propagation in an optical fiber with a periodic dispersion map and distributed amplification. Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes that are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps with distributed Raman amplification to compensate for the fiber loss, we find special schemes that have optimal (chirp-free) launch point locations that are independent of the fiber dispersion. Despite the variation of dispersion with wavelength due to the fiber dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical predictions are verified by direct numerical simulations. The obtained results are applied to a practical multichannel transmission system.

Optimal dispersion maps for multichannel soliton transmission with distributed Raman amplification

Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes with distributed Raman amplification, which are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps, special schemes are found that have optimal (chirp-free) launch point locations that are independent of the fibre dispersion. Despite the variation of dispersion with wavelength due to the fibre dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical results are verified by direct numerical simulations.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.