Further Theoretical Investigations for Laser Relative Intensity Noise with Fiber Nonlinearities and Higher Order Dispersion

In this article, we theoretically investigate relative intensity noise (RIN) in optical communication systems with fiber nonlinearities due to optical Kerr effects and higher order dispersion. The impact of modulation frequencies, launch power, and laser bias current on RIN has been illustrated. We show that RIN increases with modulating frequencies up to the resonance frequency and launch power, and decreases in the laser bias current. We also show that higher order dispersion terms have no impact on the RIN, but with first order dispersion compensation the higher order dispersion terms have significant impact at high modulating frequencies. The RIN with and without fiber nonlinearities is further investigated. It has been shown that the RIN with fiber nonlinearity is more than the RIN without nonlinearity and the effect of nonlinearity appears at higher modulation frequencies only.     

Further Theoretical Investigations for Laser Relative Intensity Noise with Fiber Nonlinearities and Higher-Order Dispersion

In this article, we theoretically investigate relative intensity noise (RIN) in optical communication systems with fiber nonlinearities due to optical Kerr effects and higher-order dispersion. The impact of modulation frequencies, launch power, and laser bias current on RIN has been illustrated. We show that RIN increases with modulating frequencies up to the resonance frequency, launch power, and decrease in the laser bias current. We also show that higher-order dispersion terms have no impact on the RIN, but with first-order dispersion compensation the higher-order dispersion terms have significant impact at high modulating frequencies. The RIN with and without fiber nonlinearities is further investigated. It has been shown that the RIN with fiber nonlinearity is more than the RIN without nonlinearity and the effect of nonlinearity appears at higher modulation frequencies only.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Theoretical Investigations of Third-Order Dispersion Term on Relative Intensity Noise for Dispersive Optical Communication System

In this article we present improved theoretical investigations into relative intensity noise (RIN), including the impact of a third-order dispersion term for dispervive optical communication systems. It has been shown that the third-order dispersion term has no impact on RIN even at high noise frequencies as reported by other authors, but with second-order dispersion compensation, the RIN can be dramatically reduced, thereby improving overall system performance. Further, the impact of fiber length and laser linewidth has been investigated for RIN. It has been shown that, as the fiber length increases, the value of RIN increases but the improvement over RIN with second-order dispersion compensation decreases. Also, with decrease in the value of linewidth, the RIN can be reduced to a great extent.     

Relative Intensity Noise in Optical Single Side Band Systems with Multiple In-Line Amplifiers: Analysis and Validation

This article analyzes and validates through simulation the influence of fiber nonlinearity, dispersion, and loss on the Relative Noise Intensity (RIN) spectrum at fiber output in externally modulated optical single side band (OSSB) systems. The analysis includes the RIN generated by the laser source, the effect of the OSSB modulator, and noise generated by the in-line optical amplifiers. The analysis takes into account conversion between phase noise and intensity noise introduced by fiber transmission. It is shown that, depending on the operating conditions, the system performance may be predominantly affected either by the laser RIN or by the noise generated by the in-line optical amplifiers. The impact of the OSSB modulator can be relevant when the RIN of the system is dominated by the laser noise and should therefore be considered.     

Relative Intensity Noise in Optical Single Side Band Systems with Multiple In-Line Amplifiers: Analysis and Validation

Abstract

This article analyzes and validates through simulation the influence of fiber nonlinearity, dispersion, and loss on the Relative Noise Intensity (RIN) spectrum at fiber output in externally modulated optical single side band (OSSB) systems. The analysis includes the RIN generated by the laser source, the effect of the OSSB modulator, and noise generated by the in-line optical amplifiers. The analysis takes into account conversion between phase noise and intensity noise introduced by fiber transmission. It is shown that, depending on the operating conditions, the system performance may be predominantly affected either by the laser RIN or by the noise generated by the in-line optical amplifiers. The impact of the OSSB modulator can be relevant when the RIN of the system is dominated by the laser noise and should therefore be considered.     

基于高非线性微结构光纤的全光再生研究

提出了利用高非线性微结构光纤自相位调制效应进行全光再生的研究方案。分析了一组微结构光纤的色散和非线性特性。结果显示光纤的非线性系数与光纤结构有密切关系。通过减小有效模面积,可以提高光纤的非线性系数。采用一种高空气填充比的高非线性微结构光纤作为非线性介质,进行了基于自相位调制效应的全光再生研究。结果表明,由于微结构光纤的高非线性,采用较短的光纤长度就可以实现较好的再生效果。同时,输入微结构光纤的峰值功率、滤波器的参量选择对光再生的效果有重要的影响,它们必需满足一定要求,才能实现光再生。此外,对再生器的传输特性进行了研究。通过调整输入峰值功率和滤波器的参量,可以对不同宽度的光脉冲信号进行全光再生。     

基于数字相干叠加的相干光正交频分复用系统中光纤非线性容忍性研究

光正交频分复用系统中的光纤非线性效应制约着系统进一步的扩容. 针对此问题, 提出一种数字相干叠加的方法, 用于提高相干光正交频分复用系统对光纤非线性的容忍性. 仿真中, 5通道的波分复用下偏振复用相干光正交频分复用系统的每个通道传输四进制正交振幅调制映射的71.53 Gbit/s信号在光纤中传输400 km. 首先, 通道间隔为25 GHz, 与传统相干光正交频分复用系统相比, 色散补偿前后, 使用数字相干叠加的相干光正交频分复用系统的信噪比分别提升了6.02 dB和9.05 dB, 最佳入纤光功率均增大了2 dB; 其次, 通道间隔为50 GHz, 色散补偿前后, 信噪比分别提升了4.9 dB和8.75 dB. 通过理论推导及仿真, 验证了所提方法能有效消除相干光正交频分复用系统的一阶非线性失真, 进而提高系统对光纤非线性的容忍性.     

Transmission performance of 20 × 10 Gb/s WDM signals using cascaded optimized SOAs with OOK and DPSK modulation formats

We investigated 20 channels at 10 Gb/s wavelength division multiplexing (WDM) transmission over 1190 km single mode fiber and dispersion compensating fiber using cascaded inline semiconductor optical amplifier at a span of 70 km for RZ-DPSK (return zero differential phase-shift keying) modulation format by using same channel spacing, i.e. 100 GHz. We show for RZ-OOK (return zero on-off keying) format a transmission distance of up to 1050 km with Q factor more than 15 dB, without any power drops. We developed the SOA model for inline amplifier having minimum cross-talks and ASE (amplified spontaneous emission) noise power with sufficient gain. At optimal bias current of 400 mA, a high constant gain of 36.5 dB is obtained up to a saturation power of 21.36 mW. So reduction of cross-talk and distortion is possible by decreasing the bias current at appropriate amplification factor.The DPSK modulation format has less cross-talk as compared to OOK format for nonlinearities and saturation case. The impact of optical power received and Q factor at different distance for both RZ-OOK and RZ-DPSK modulation format has been illustrated. We have shown the optical spectrum and clear Eye diagram at the transmission distance of 1190 km in RZ-DPSK system and 1050 km in RZ-OOK systems.The bit error rate (BER) for all channels observed is less than 10⁻¹⁰ up to gain saturation for both DPSK and OOK systems. Finally, we investigated that the transmission distance decreases with a decrease in channel spacing of up to 20 GHz.     

Optically Injection‐Locked Mid‐IR Quantum‐Cascade Lasers: The Output‐Power–Modulation‐Bandwidth–Noise Trilogy

A comprehensive study on the output power, the modulation response, and the relative intensity noise (RIN) behavior of an optically injection‐locked mid‐infrared quantum‐cascade laser reveals that the modulation bandwidth and the output power are enhanced in the stable locking range, while the RIN of the slave laser is a superposition of the master and slave noise sources. Since the RIN level of the master laser can even take the lead, a design procedure is introduced to improve the main characteristics of a free‐running laser, including the RIN, the photon lifetime, the modulation bandwidth, and the bias current, using facet reflectivity tailoring. A figure of merit is defined and the RIN reduction of about 20 dB Hz^?1 is obtained for very low injection powers compared with the injection‐locked system before the design of master laser.     

Analysis of the impact of laser line width over RIN, power penalty and bit rate including higher-order dispersion in WDM systems

This paper investigated the effect of laser line width over relative intensity noise (RIN), power penalty and bit rate at optical distances in the range of 100-10,000 km both analytically and graphically. It is also proposed and analyzed that by reducing the laser line width to the range of KHz, we can minimize the impact of RIN and power penalty under the individual and combined impact of higher-order dispersion parameters.     

Optical phase conjugation and pseudolinear transmission

We describe the use of optical phase conjugation (OPC) to suppress intrachannel nonlinearities that limit pseudolinear transmission. We show that OPC combined with appropriate dispersion mapping is effective in suppressing intrachannel nonlinearities, even in the absence of signal-power evolution symmetry that is generally required by OPC to compensate fiber nonlinearity. An increase in signal power by 5.5 dB is observed when a single OPC is used for 40-Gbit/s pseudolinear transmission over 32 x 100 km of passive-fiber spans.     

三角形光脉冲在正色散光纤中产生的实验研究

利用一种无源非线性脉冲整形方法, 实现了在普通正色散(ND)光纤中产生三角形光脉冲, 此方法依赖于脉冲预啁啾和脉冲在ND光纤中传输时群速度色散与自相位调制的相互作用. 实验研究表明, 在较宽的脉冲预啁啾值范围内, 通过优化脉冲输入功率和脉冲传输的ND光纤长度, 均可得到典型的三角形光脉冲: 脉冲时域形状前后沿的变化率接近恒定、整个脉冲具有线性频率啁啾. 另外, 在不同的脉冲预啁啾下, 要得到高质量的三角形光脉冲, 均需要较高的脉冲输入功率; 并且脉冲预啁啾较大时, 三角形脉冲的形成对ND光纤长度和脉冲输入功率有较大的容差, 易获得三角形光脉冲.     

直接调制光反馈半导体激光器产生超宽带信号

利用直接电流调制光反馈半导体激光器产生了符合美国联邦通信委员会关于室内无线通信频谱限定的超宽带(UWB)微波信号.基于光反馈半导体激光器速率方程组, 数值分析了偏置电流、反馈强度对混沌UWB脉冲信号的影响.研究表明, 混沌UWB脉冲频谱的-10 dB带宽分别随着偏置电流的增大和反馈强度的增强而逐渐增加; 中心频率分别随着偏置电流的增大和反馈强度的增强而逐渐增大.实验中, 产生了中心频率为6.6 GHz, -10 dB带宽为9.6 GHz的混沌UWB信号. 进一步, 通过调节偏置电流和反馈强度, 可实现混沌UWB信号的中心频率和-10 dB带宽的可调谐输出, 实验结果和数值分析相符合.此外, 实验产生的混沌UWB信号经过34.08 km的光纤传输后, 其频谱形状几乎没有发生变化, 表明该方法所产生的混沌UWB信号对光纤色散有较大的容忍度. 关键词： 超宽带 混沌激光 光反馈 直接调制     

交叉相位调制提高半导体激光器混沌载波发射机带宽方法

提出半导体激光器混沌交叉相位调制(XPM)光反馈提高混沌载波发射机带宽方法,建立了有外腔光纤传输反馈XPM控制下的激光动力学物理模型.理论导出XPM作用下激光双反馈频率失谐公式,指出XPM产生的非线性相移影响了激光器增益和线宽增强因子,其光纤二阶非线性效应使激光振幅和相位变化更加丰富,而非线性相移的出现进一步增加了新的频率分量并使频谱展宽.数值结果表明,XPM使激光器混沌带宽增加到4倍以上,使激光混沌张弛振荡频率增加到2.85倍,其光纤长度、入纤光功率、面镜反射系数、光纤二阶非线性系数等都能影响激光混沌带宽.     

Raman-resonance-enhanced composite nonlinearity of air-guided modes in hollow photonic-crystal fibers

Coherent anti-Stokes Raman scattering (CARS) is used to measure relations between the resonant (Raman) and nonresonant (Kerr-type) optical nonlinearities of air-guided modes in a hollow-core photonic-crystal fiber (PCF). We demonstrate that, due to its interference nature, CARS provides a convenient tool for measuring the contribution of the fiber cladding to the total nonlinearity sensed by air-guided modes in hollow PCFs. On a Raman resonance with molecular vibrations in the gas that fills the fiber core, a two-color laser field is shown to induce optical nonlinearities that are several orders of magnitude higher than the nonresonant Kerr-type nonlinearities typical of air-guided PCF modes.     

Detailed theoretical investigation on relative intensity noise reduction enhancement based on reflective SOAs

The enhanced performance for relative intensity noise (RIN) reduction based on reflective semiconductor optical amplifiers (R-SOA) has been investigated theoretically by comparison with conventional transmission SOA. The results show that, by selecting appropriate input optical power, as large as >20 dB RIN suppression improvement can be achieved for R-SOA, without sacrificing the noise rejection bandwidth. With increased injection current, the optimized input signal power is decreased and the operation region is extended for the best RIN reduction. For RIN suppression in WDM spectrum slicing, the bandwidth optimization of receiver filter should be performed to avoid the spectral broadening induced by self-phase modulation (SPM) and four wave mixing (FWM). Our derived result is helpful for designing and optimizing the R-SOA in application of noise suppression enhancement.     

数值模拟高阶色散和非线性对光孤子传输的影响

光孤子传输中的高阶色散以及高次非线性效应是光纤通讯发展的重要制约因素。从光孤子在光纤中的一般传输方程出发, 在较大的入纤功率的前提下, 综合考虑了高阶色散、五次非线性和损耗因素, 得到其具体传输方程, 并据此从理论上分析了高阶色散和非线性对光孤子传输性能的影响。本文采用分步傅里叶方法, 以MATLAB为实现工具, 实现高阶色散和非线性对光孤子传输影响的模拟计算, 并深入分析了高阶色散和非线性导致的孤子脉冲频移现象。计算结果表明: 在入射功率较大的时候, 高阶色散效应不可忽略。当五次非线性γ2>0时,孤子脉冲主峰发生微小频移; 而当五次非线性γ2<0时, 孤子脉冲主峰基座产生微小频移; 当高阶色散β3>0时频率出现红移, 而当β3<0时, 频率出现蓝移。     

Wideband modulation instability at combination frequencies in wave beams

We study theoretically wideband modulation instability at combination frequencies in media having cubic nonlinearity of self-focusing type along with the higher-order defocusing nonlinearity. It is assumed that in a medium with a purely cubic nonlinearity, the medium dispersion does not permit modulation instability. In this case, a collapse of the wave field exists if the beam power is higher than the critical power of self-focusing. The higher-order nonlinearity limits the field at the nonlinear focus, and the instability at combination frequencies becomes possible. It turns out that the field at the nonlinear focus increases with increasing excess of the beam power over the critical power of self-focusing. The obtained values of the nonlinear dielectric permittivity are used for determination of the growth rates of instability at combination frequencies. These growth rates ensure an increase in the combination fields from noise levels up to values comparable with the field of the high-power beam. Such an increase takes place if the beam power is severalfold higher than the critical one. The developed theory can be used for explanation of spectrum superbroadening during self-focusing of sufficiently short laser pulses and high-harmonic generation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 522–532, June 2007.