Four-wave mixing analysis in WDM optical communication systems with higher-order dispersion

Four-wave mixing (FWM) is one of the major limiting factors in WDM optical fiber communication systems. In this paper, we analyze the individual and combined effect of second-, third-, fourth- and fifth-order dispersion parameters on FWM at different input channel powers and core effective areas, which have not been calculated earlier. FWM power versus channel power graphs for individual and combined effects of dispersion parameters have been presented, and it has been observed that FWM reduces for combined effect of dispersion parameter.     

Perturbation of higher-order solitons by fourth-order dispersion in optical fibers

We study analytically and numerically how the radiation emitted by fundamental solitons in the form of dispersive waves is affected by the third and fourth-order dispersions when a higher-order soliton undergoes the fission process inside an optical fiber. Our results show that two dispersive wave sidebands appear in the output spectrum on opposite sides of the input spectrum. The frequencies of these sidebands are set by the relative magnitudes of the third- and fourth-order dispersion parameters, but are not affected much by the Raman process. A well defined phase-matching condition accurately predicts these conjugate frequencies of dispersive wave. The relative amplitudes of these two sidebands are not equal because of the asymmetry induced by the third-order dispersion and higher-order nonlinearities. It is found that with increasing fourth-order dispersion the amplitude of both spectral components eventually saturate and the relative power level associated with one of the components can exceed 10% of the launched power under suitable conditions. This component is the one that will form even in the absence of fourth-order dispersion and its wavelength may lie on the red or the blue side of the launched wavelength depending on the sign of the dispersion slope at this wavelength. It is also observed that soliton order itself significantly influence the peak amplitude of the radiation and play a minor role in determining radiation frequencies. We believe, these results should be of relevance for applications requiring an ultrabroadband optical source and understanding the interesting facts of supercontinuum generation.     

Four-wave mixing in hollow photonic-crystal fibers

A radical enhancement of four-wave mixing in hollow-core photonic-crystal fibers is experimentally demonstrated. An enhancement ratio of about 800 relative to the regime of tight focusing is achieved for the four-wave mixing process 3ω=2ω+2ω?2ω, where ω and 2ω are the frequencies of fundamental radiation and the second harmonic of picosecond Nd:YAG laser pulses.     

Four-wave mixing of quasi-monochromatic waves and few-cycle pulses

Four-wave coherent mixing models for two quasi-monochromatic pumping fields and pulses of a two-component Stokes field with an elliptic polarization and a duration on the order of the period of oscillations have been derived for a two-level medium with a forbidden dipole transition. It is shown that, under the unidirectional wave propagation conditions and in the absence of depletion of pumping, the system of Maxwell-Bloch equations can be reduced to a new completely integrable system of equations. Nonsoliton radiation dynamics of generation of Stokes field pulses is studied in the framework of the integrable reduction of this model. The apparatus for the inverse problem algorithm corresponding to the solvable problem is developed. An approximate asymptotic expression for the leading front of the pulse packet being generated is obtained for various initial and boundary conditions. The application of these results for describing parametric processes involving various types of waves is discussed.     

Optical solitons in birefringent fibers with spatio-temporal dispersion

This paper studies the propagation of solitons through birefringent fibers in the presence of spatio-temporal dispersion. Both Kerr and parabolic laws of nonlinearity are addressed. The exact 1-soliton solutions are obtained. There are several constraint conditions that ensure soliton solutions are derived. Three types of solitons are obtained: bright, dark and singular solitons.     

Four-wave mixing with large stokes shifts in heavily Ge-doped silica fibers

Four-wave mixing (FWM) in nonlinear germanosilicate fibers with GeO2 concentrations as high as 67 mol.% in the core is studied theoretically and experimentally. Large frequency shifts of 1875-3829 cm(-1) are observed in the mixed-mode pump parametric process. The dependence of FWM phase matching on the GeO2 concentration, core diameter, and index profile is demonstrated. The 2.5% conversion efficiency of an 887 nm signal to a 1.3 microm communication band is obtained at a 2 W cw pump power inside the fiber.     

Periodic solitons in dispersion decreasing fibers with a cosine profile

Periodic solitons are studied in dispersion decreasing fibers with a cosine profile. The variable-coefficient nonlinear Schr¨odinger equation, which can be used to describe the propagation of solitons, is investigated analytically. Analytic soliton solutions for this equation are derived with the Hirota’s bilinear method. Using the soliton solutions, we obtain periodic solitons, and analyze the soliton characteristics. Influences of physical parameters on periodic solitons are discussed. The presented results can be used in optical communication systems and fiber lasers.     

Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response

We analyse modulational instability (MI) of electromagnetic waves in a large variety of optical fibers having different refractive-index profiles. For the normal-, anomalous-, and zero-dispersion regimes of the wave propagation, we show that whenever the second-order dispersion competes with higher-order dispersion (HOD), propagation of plane waves leads to a rich variety of dynamical behaviors. Most of the richness comes from the existence of critical behaviors, which include situations in which the HOD suppresses MI in the anomalous dispersion regime, and other situations in which the HOD acts in the opposite way by inducing non-conventional MI processes in the normal- and anomalous-dispersion regimes. We show that non-conventional MI sidebands are more prone to Raman-induced degradations than ordinary MI sidebands can be.     

Four-wave mixing in microstructure fiber

We report what we believe to be the first experimental demonstration of nondegenerate four-wave mixing in a microstructure fiber. The effect of the chi((3)) nonlinearity is enhanced in such a fiber because of the small core area, and we achieve phase matching by operating near the zero-dispersion wavelength (?750 nm) . We have observed parametric gains of more than 13 dB in 6.1-m-long fiber with a pump peak power of only 6 W. We compare our experimental gain results with those predicted by theory and explore the effects of Raman shift and (or) amplification and cascaded nonlinear mixing.     

Acoustic waves in media with hysteretic nonlinearity and linear dispersion

A hysteresis equation of state is proposed for polycrystalline solids with saturation of nonlinear losses. Effects of amplitude-dependent internal friction and higher harmonic generation that result from propagation of harmonic acoustic waves in rods made of such materials are theoretically and numerically studied.     

砷化镓晶体中的四波混频

本文报道了以1.06μm调QNd:YAG激光脉冲,采用简并四波混频的方法,在未掺杂的GaAs单晶中产生红外位相共轭短脉冲。研究了该光脉冲的主要特性。用实验的方法探讨了影响共轭光强弱的主要因素。     

Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers

We report on an experimental study of supercontinuum generation in photonic crystal fibers with low-intensity femtosecond pulses, which provides evidence for a novel spectral broadening mechanism. The observed results agree with our theoretical calculations carried out without making the slowly varying envelope approximation. Peculiarities of the measured spectra and their theoretical explanation demonstrate that the reason for the white-light generation in photonic crystal fibers is fission of higher-order solitons into redshifted fundamental solitons and blueshifted nonsolitonic radiation.     

Four-wave mixing based 10-Gb/s tunable wavelength conversion in dispersion-flattened microstructure fibers

All-optical wavelength conversion of 10-Gb/s signal based on four-wave mixing is experimentally demonstrated in a 30-m-long dispersion-flattened microstructure fiber with small positive dispersion. For an average pump power of 26 dBm, the conversion efficiency was around -19.5 dB with the fluctuation less than ±1.4 dB, covering a conversion bandwidth of 20 nm. The eye diagram of the converted signal shows good eye opening.     

双折射光子晶体光纤中基于孤子分裂的超连续光谱产生

利用亚纳焦量级、脉冲宽度为100 fs的激光脉冲在双折射光子晶体光纤中获得了450—1050 nm 的超连续光谱,且超连续光谱具有明显的分立峰状结构.分析了光谱中分立峰状结构产生的物理机制,抽运光波长处于接近零色散波长的反常色散区,形成高阶光孤子,由于高阶非线性和高阶色散的影响,高阶孤子分裂成多个基孤子,使初始光谱上演化出红移的光孤子成分和蓝移的色散波成分.理论模拟了飞秒激光脉冲在光纤中的色散特性和传输特性,较好地解释了实验结果. 关键词： 光子晶体光纤 超连续光谱产生 孤子分裂 脉冲俘获     

Stability of solitons described by KdV-type equations with higher-order dispersion and nonlinearity (analytical results)

Soliton stability described by KdV-type equations with higher-order dispersion and nonlinearity is studied analytically. Criterions of linear and nonlinear soliton stability and adjoining formulas are derived in a form that will guide a future study of soliton stability by means of numerical simulations.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Modification of the discrete spectral parameters of optical solitons in fibers with variable dispersion

The spectral parameters of solitons result from the nonlinear Fourier transform for a pulse propagating in a fiber. A new approach for controlling the discrete component of spectral parameters is proposed. In the presence of a resonance between field oscillations and fiber dispersion, the real part of spectral parameters change, which leads to multisoliton pulse separation into fundamental solitons. It is proposed to use this effect for signal decoding in communication lines operating based on the nonlinear Fourier transform.     

Four-wave mixing of picosecond pulses in hollow fibers: expanding the possibilities of gas-phase analysis

Third-harmonic, difference-frequency, and sum-frequency generation processes in hollow fibers are experimentally studied with 30-ps pulses having an energy of several millijoules. The experimental dependence of the difference-frequency signal on the pressure of the gas filling the fiber agrees well with the results of calculations when the contribution of higher order waveguide modes is taken into consideration, thus indicating the importance of nonlinear-optical processes involving higher order waveguide modes of a hollow fiber. Hollow fibers are also shown to expand the possibilities of nonlinear-optical analysis of gases by allowing the generation of third-harmonic and sum-frequency signals, which vanish in the regime of tight focusing in a medium with normal dispersion. Received: 26 September 2000 / Revised version: 15 January 2001 / Published online: 30 March 2001     

飞秒啁啾孤子在线性色散平坦光纤中的相互作用

采用分步傅里叶方法数值研究了在线性色散平坦光纤反常色散区等幅同相孤子脉冲相互作用受高阶色散、拉曼效应、光纤损耗和啁啾参量C等的影响规律。多孤子脉冲在线性和凸形色散平坦光纤中传输100个孤子周期后仍具有孤子特性。在线性色散平坦光纤,多孤子脉冲相互作用受三阶色散影响较严重,三阶色散使各脉冲产生较大的色散波和线性时延;更高阶色散的影响可以忽略;拉曼效应使脉冲产生较大的非线性时延;啁啾加强了脉冲间相互作用;光纤损耗减弱了脉冲间相互作用。