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 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.     

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.     

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.     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

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.     

基于高阶色散管理和相位共轭技术的色散补偿

相位共轭技术能够同时且高效地补偿二阶色散及非线性效应，且该技术同信号比特率、调制方式无关，是最有前景的色散补偿技术之一。理论分析了在高阶色散作用下，超短高斯脉冲信号在中距相位共轭通信系统中的传输演化特性，数值模拟了在二阶、三阶和四阶色散作用下，飞秒高斯脉冲信号在基于中距相位共轭技术的光纤色散管理链中的动态传输过程。结果表明，相位共轭技术和高阶色散管理相结合，不仅可以补偿和复原包括奇数阶和偶数阶色散在内的全部色散和非线性所引入的信号失真和畸变，而且能够减弱时分复用系统中脉冲之间的相互作用，使得信号在传输一个周期后恢复波形，从而提高了相位共轭系统对失真信号的补偿性能。     

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.     

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.     

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.     

微结构光纤近红外色散波产生的研究

采用有限元法对实验室自制的非线性微结构光纤进行理论分析, 表明该光纤具有良好的非线性和色散波产生的相位匹配特性. 为实现微结构光纤非线性的全光纤化, 本实验采用中心波长为1032 nm的光纤飞秒激光器作为抽运源, 获得了753–789 nm 的近红外色散波. 实验中发现色散波中心波长和带宽随着抽运功率的改变会产生明显变化, 并且在不同光纤长度时, 色散波的频移量不同, 脉冲展宽及频谱也会有明显的变化. 实验结果与理论分析一致. 这些结果对实现微结构光纤非线性的全光纤化具有良好的借鉴作用, 为生物医疗应用特别是非线性光学显微成像术的近红外光源研究打下基础.     

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.     

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.     

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.     

High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser

High-power supercontinua are demonstrated in highly nonlinear, dispersion-shifted fibers with a continuous-wave Raman fiber laser. Supercontinuum growth is experimentally studied under different combinations of fiber length and launch power to show output powers as high as 3.2 W and bandwidths greater than 544 nm. Modulation instability (MI) is observed to seed spectral broadening at low launch powers, and the interplay between MI and stimulated Raman scattering plays an important role in the growth of the continuum at high launch powers. The effect on continuum generation of parametric four-wave mixing coupled with the higher-order dispersion properties of the fiber is investigated.     

Compton散射对五阶非线性下零色散附近调制不稳定性的影响

应用多光子非线性Compton散射模型和非线性薛定谔方程,研究了Compton散射对五阶非线性零色散附近调制不稳定性的影响.将入射光和Compton散射光作为产生调制不稳定性的机制,分析了光纤损耗、四阶色散和五阶非线性对增益谱的影响.结果表明:散射下的正或负五阶非线性分别使零色散附近的增益谱宽和峰值比散射前增大得更大或...