Nonlinear dynamics of a laser diode with optical feedback systemssubject to modulation

The nonlinear dynamic behavior of a direct frequency-modulated diode laser with strong optical feedback is examined and compared to a laser diode subject to electro-optically modulated, strong optical feedback. Direct modulation is achieved by sinusoidal modulation of the diode laser injection current. Electro-optic modulation is achieved by applying a sinusoidal voltage to an intracavity phase modulating element. The output state (characterized by the output power versus time, the intensity noise spectrum and the optical frequency spectrum) for both types of modulation is dependent on the ratio of the modulation frequency to the external cavity resonant frequency, and the modulation power. A number of distinct states are observed: conventional amplitude modulation (with FM spectra); multimode, low-noise amplitude modulation; multimode, high-noise amplitude modulation; periodic limit-cycle operation; quasi-periodicity; chaos; low-frequency fluctuations; and mode-locking. There are significant differences between the direct and electro-optic frequency-modulation cases. The onset of the dynamic instability is characterized as a noisy period-one oscillation for direct modulation and a low-frequency fluctuation for intracavity electro-optic modulation. Phase portraits produced experimentally with the use of a digital phosphor oscilloscope are shown to agree well with those constructed from output power versus time data. This represents an experimental method for examining the dynamics phase portraits in real-time     

Statistical amplitude and phase variations in mode-locked lasers

The influence of statistical amplitude or phase variations in the modes of a mode-locked laser on the time-dependent output intensity and on the relative efficiency of nonlinear optical processes is investigated. The ensemble-averaged intensity, the time-dependent distribution of the resulting complex amplitude, and the second-order moment of the intensity distribution are calculated and discussed for both types of variations. As long as no systematic amplitude or phase changes are introduced, the pulse shape is maintained, but superimposed on a fluctuating background, and the efficiency for nonlinear optical processes is reduced. For random phase fluctuations over 2π the pulse behavior disappears completely and the output becomes Gaussian or chaotic light.     

Impact of Optical Transmission on Multiband OFDM Ultra-Wideband Wireless System With Fiber Distribution

Multiband (MB) orthogonal frequency-division multiplexing (OFDM) ultra-wideband (UWB) wireless, which provides high data rate access, is required to be distributed by using optical fiber. The performance of MB-OFDM UWB over fiber transmission system is investigated considering optical modulation and demodulation impact. Theoretical analysis of the effect of fiber dispersion, optical transmitter, and optical receiver response on system performance is carried out considering amplitude and phase distortion. Experiments are conducted and verified by our theoretical analysis and good agreement is obtained. It is found that RF modulation index of $sim {hbox {4}}%$ is optimum for optical transmitter with Mach–Zehnder modulator, and optical receiver with Chebyshev-II response is the best for MB-OFDM UWB over fiber. Compared to back-to-back UWB over fiber, optical transmission is mainly limited by laser phase noise converted relative intensity noise and phase distortion induced by fiber dispersion when optimum modulation index is used. Higher modulation index is limited by amplitude and phase distortion to OFDM signal induced by optical transmitter and receiver response nonlinearities and fiber dispersion and the spectral mask. It is also found that highly received optical power is required for transmission of MB-OFDM UWB signal over fiber.      

不同的外部光反馈强度下外腔半导体激光器大信号调制特性

基于等效腔理论,计及光线在外腔中多次反馈的情况后,从理论上研究了不同的反馈强度下,外腔半导体激光器(ECSL)的大信号调制特性。数值模拟的结果表明:当外部光反馈非常强或非常弱时,调制深度在一个较大的变化范围之内,ECSL的光子数呈现单周期变化规律,且峰值光子数随调制深度呈现单调上升的趋势;当外部光反馈处于中度反馈时,当调制深度取不同值时,ECSL的光子数呈现单周期、多周期甚至混沌现象。     

Analytical Models for Phase-Modulation-Based Microwave Photonic Systems With Phase Modulation to Intensity Modulation Conversion Using a Dispersive Device

Recently, optical phase modulation has been widely used in microwave photonics (MWP) systems, such as radio over fiber systems, photonic microwave filters, optical microwave and millimeter-wave signal generators, and optical subcarrier frequency up-converters. An optical phase-modulated signal can be converted to an intensity-modulated signal in a dispersive optical fiber. Due to the intrinsic nonlinearity of optical phase modulation, for linear applications such as microwave signal distribution and filtering, the modulation index should be kept small to minimize the unwanted modulation nonlinearity. However, for nonlinear applications such as microwave frequency multiplication and subcarrier frequency upconversion, the modulation index should be large to maximize the frequency multiplication and upconversion efficiency. In this paper, for the first time to our knowledge, we develop a thorough theoretical framework for the characterization of phase-modulation-based MWP systems, in which the phase modulation to intensity modulation conversion is realized using a dispersive fiber. Analytical models for the distributions of single-tone and two-tone microwave signals and for microwave frequency multiplication and subcarrier frequency upconversion are developed, which are verified by numerical simulations. The analytical models for single-tone and two-tone transmissions are further confirmed by experiments. The developed analytical models provide an accurate mathematical tool in designing phase-modulation-based MWP systems.     

Nonharmonic large amplitude modulation of a semiconductor laser ina self-homodyne interferometric optical system

A self-homodyne interferometric optical system fed by a modulated semiconductor laser is analyzed theoretically and experimentally. Both the intensity and frequency modulation of the laser diode with large modulation index are considered. For nonharmonic modulation, the effect of the AM-FM transfer function of the laser diode is taken into account. Theoretical and experimental results obtained show good agreement. Applications of the system for the characterization of wideband optical detectors and the measurements of the FM response of the laser diode are discussed. By using triangular modulation, novel characterization techniques are proposed. Results obtained by these techniques are in good agreement with those obtained by other measurement techniques     

Frequency domain analysis of an optical FM discriminator

Measurement of optical phase and frequency deviations using a frequency-domain network analysis approach is described. The frequency domain transfer functions are given which relate the conversion of optical phase, frequency, and intensity modulation into photodetector current after passing through a quadrature biased Mach-Zehnder interferometer. It is shown that the error term in the phase and frequency transfer functions depends only to second order on any accompanying intensity modulation. Experimental data are given illustrating the analytical results     

Significant performance advantage of electroabsorption modulatorintegrated distributed feedback laser (EML) transmitter in transportingmulticarrier QAM signals

Data are presented that show that, for transporting quadrature amplitude modulated (QAM) radiofrequency (RF) subcarriers in suboctave frequency range, electroabsorption modulator integrated distributed feedback lasers (EMLs) can he modulated with significantly higher (2.5 times) modulation index without any in-band signal distortion as compared to the directly or externally modulated (using LiNbO₃ MZ modulator) distributed feedback (DFB) laser transmitters in the 1.55-μm band. This occurs when the selection of frequency range and biasing the modulator section of an EML is such that the third-order intermodulation distortion is suppressed and the second-order distortion is outside the in-band frequency range. We have used an equivalent of 64- and 256-QAM 40 carriers in 550-800 MHz with the test carrier modulated with 5.063 M symbols per second. For a given bit error rate (BER), the receiver sensitivity was as much as 4 dB (optical) higher with an EML-based transmitter compared to all other transmitters. The results are presented for QAM signals but they are equally applicable for other formats of digital modulation of RF carriers, such as quadrature phase shift keying (QPSK) in suboctave frequency range     

Microwave photonic notch filter with complex coefficient based on four wave mixing

A microwave photonic notch filter with a complex coefficient is proposed and demonstrated based on four wave mixing (FWM). FWM effect of two single-frequency laser beams occurs in a highly nonlinear fiber (HNLF), and multi-wavelength optical signals are generated and used to generate the multi-tap of microwave photonic filter (MPF). The complex coefficient is generated by using a Fourier-domain optical processor (FD-OP) to control the amplitude and phase of the optical carrier and phase modulation sidebands. The results show that this filter can be changed from bandpass filter to notch filter by controlling the FD-OP. The center frequency of the notch filter can be continuously tuned from 5.853 GHz to 29.311 GHz with free spectral range (FSR) of 11.729 GHz. The shape of the frequency response keeps unchanged when the phase is tuned.     

空间激光通信高速多制式光调制技术

空间激光通信调制技术以幅度调制和相位调制为主,单一通信终端只能适应特定的调制格式,灵活性较差,存在星间链路组网应用的局限性。文章基于数字处理的光调制技术,采用LiNbO₃晶体正交相位调制器,结合闭环偏压控制算法,实现了光调制格式、调制速率可变的星载光调制器,并针对空间应用对幅度调制和相位调制方式进行了优化,最大化光纤放大器效率。该技术硬件实现了625Mb/s~5Gb/s通信速率分档可调,OOK,BPSK和QPSK调制格式可变,发射EVM优于9%,实际引入灵敏度损耗小于1dB。该调制器已经完成所有空间环境试验,可广泛适用于各种体制的激光通信终端,进行星地、星间激光通信建链。同时,该调制器具备模拟调制的功能,可实现星间微波光子信号的透明转发。     

Dependence of optical receiver sensitivity, in a 147-Mbit/sheterodyne DPSK system, as a function of optical and electricalparameter variations

Measurements of the changes in optical receiver sensitivity are described. They are caused by (a) the effect of bandpass and low-pass filtering, (b) the dependence on integer and noninteger values of the intermediate-frequency-to-bit-rate ratio, (c) the influence of the local oscillator power, and (d) the impact of deviation from ideal π phase-shift modulation. The studies were conducted at λ=1.523 μm and at a bit rate of 147.75 Mb/s, using external-cavity lasers with negligible phase noise. The results demonstrate the conditions for optimum DPSK system performance in the absence of laser phase noise. The receiver degradation observed for deviations from optimal electrical and optical conditions have been measured and found to be in good agreement with earlier theoretical calculations of microwave phase modulated schemes     

基于半导体激光器窄线宽光子微波信号获取

为了研究光注入半导体激光器(SL)产生的光子微波信号的性能, 基于SL的速率方程和光纤布喇格光栅(FBG)滤波理论, 采用数值仿真的方法进行了理论分析, 得到了各种注入参量下的光谱、功率谱和线宽, 并讨论了反馈参量对微波线宽的影响, 考虑到光注入下产生的微波线宽较宽, 进一步引入FBG光反馈窄化了微波信号的线宽。结果表明, 当SL仅在光注入作用下时, 通过改变注入参量, 可实现微波频率连续可调谐和微波强度最大化; 微波线宽随着反馈强度的增加逐渐变窄, 通过适当调节反馈参量可将微波线宽压缩到10kHz以下。该研究结果可为半导体激光器在光生微波中的应用提供一定的理论参考。     

Message Encryption by Phase Modulation of a Chaotic Optical Carrier

We present a numerical and experimental evaluation of message encryption by phase modulation, using a chaotic optical carrier generated by a laser subject to delayed optical feedback. This method offers better security than the conventional amplitude masking, where the signal is simply added to the chaotic waveform     

基于相位调制等效展宽激光线宽的极低相噪光电振荡器

光电振荡器是一种采用光电结合方式的新型微波频率源,其利用光学长时储能,可以实现极低相位噪声的信号输出。文章研究了光纤中散射噪声对光电振荡器相位噪声的影响,重点介绍了基于相位调制等效展宽激光线宽,抑制布里渊散射噪声架构,通过理论公式推导以及实验验证,表明了上述架构可极大改善光电振荡器的相位噪声。实验中采用调制频率为50 MHz、调制幅度为3.1的相位调制信号对激光线宽进行等效展宽,得到在10 GHz频率下为-157.3 dBc/Hz@10 kHz的极低相位噪声信号输出。     

激光强回馈系统的动态调制稳频技术

激光强回馈系统与弱回馈系统相比,在无任何电子细分条件下就可获得纳米级的分辨率。但是,由于其回馈水平高,容易发生模式转换或偏振跳变,稳频十分困难。提出了一种激光强回馈系统的动态调制稳频方法,研究了动态调制稳频中的零点定位、清零补偿等关键技术及算法。实验结果表明,通过采用动态调制稳频技术,消除了激光强回馈系统中的模式转移及偏振跳变现象,获得了调制均匀、幅值相等的回馈条纹,有效地解决了激光强回馈系统的稳频问题,大大提高了系统的抗干扰能力,对进一步研究高精度强回馈测量系统具有重要意义。     

A variable coefficient microwave photonic filter based on multi-wavelength fiber laser and Mach-Zehnder interferometer

A microwave photonic filter（MPF） with variable coefficient is proposed and demonstrated, which is constructed by a multi-wavelength fiber laser and Mach-Zehnder interferometer（MZI）. Through changing the slope characteristics of Mach-Zehnder interference spectrum adjusted by optical variable delay line（OVDL）, the conversion from phase modulation（PM） to intensity modulation（IM） is realized. The multi-wavelength fiber laser with Lyot-Sagnac optical filter has variable wavelength spacing. So the designed filter has a variable number of taps and tap weights. As a result, the tunable range of passband center frequency is 2.6 GHz. The reconfigurability of MPF can be also realized by adjusting the output of fiber laser.     

基于相位和强度调制的微波测频技术研究

为了更好地对微波信号进行频率测量，采用了一种基于相位调制和强度调制相结合的瞬时测频方法。一束连续波光源通过耦合器被分成两路，未知微波信号分别同时经过相位调制器和强度调制器从而对载波进行调制，之后进入两段长距离的单模光纤中。在光纤中由于色散引起的微波功率损耗的特点，可以获得单调变化的频率-幅度的映射关系，继而通过光电探测的微波信号输出功率比得到幅度比较函数；另外还分析与实现了测频范围与测频精确度的优化。结果表明，该方案结构简易，能够快速精准地测量出未知信号的频率，测量范围可以达到0.5GHz~53GHz，测量误差小于±200MHz。该方法可以有效地测量微波信号频率，可靠性强，适用范围广。     

Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback

Vertical-cavity surface-emitting lasers (VCSELs) with optical feedback are known to exhibit different transverse-mode regimes depending on the injection current. Close to threshold a VCSEL operates on the fundamental transverse mode, while for larger injection the dynamics is often multimode, with the optical feedback inducing either in-phase or anti-phase transverse mode oscillations. In this paper, we study numerically the influence of current modulation on these different feedback-induced transverse-mode regimes. The modulation amplitude and period are taken as control parameters. We find that the in-phase and anti-phase regimes are robust under weak modulation. As the modulation amplitude increases, there is a transition to a dynamics governed by the current modulation, where the total output power follows the injection current and there is either single-mode or in-phase multimode behavior. However, the effect of the current modulation depends on the modulation period. Under fast modulation, the laser cannot follow the modulation and the optical-feedback-induced effects are dominant. On the contrary, under slow modulation there is a superposition of modulation and feedback effects, with the total output following the modulated current and an underlying transverse-mode behavior mainly determined by the optical feedback. A resonant behavior was observed for modulation periods close to the internal oscillation period. In this case, current modulation induces pulsing output intensity with single-mode or in-phase multimode behavior.     

Measurement and Characterization of Microwave Interaction between Integrated Distributed Feedback Laser Diode and Electro-Absorption Modulator

Integrated electro-absorption-modulated distributed feedback laser diodes (EMLs) are attracting much interest in optical communications for the advantages of a compact structure, low power consumption, and high-speed modulation. In integrated EML, the microwave interaction between the distributed feedback laser diode (DFB-LD) and the electro-absorption modulator (EAM) has a nonnegligible influence on the modulation performance, especially at the high-frequency region. In this paper, integrated EML was investigated as a three-port network with two electrical inputs and a single optical output, where the scattering matrix of the integrated device was theoretically deduced and experimentally measured. Based on the theoretical model and the measured data, the microwave equivalent circuit model of the integrated device was established, from which the microwave interaction between DFB-LD and EAM was successfully extracted. The results reveal that the microwave interaction within integrated EML contains both the electrical isolation and optical coupling. The electrical isolation is bidirectional while the optical coupling is directional, which aggravates the microwave interaction in the direction from DFB-LD to EAM.     

Computer simulation of FSK laser spectra and of FSK-to-ASKconversion

The performance of binary frequency shift keyed (FSK) modulated two-segment semiconductor injection lasers is simulated by generating a 64-b pseudorandom step-function bit pattern. This signal, superimposed on a DC bias, is used to drive a two-segment distributed feedback (DFB) laser. To obtain the optical laser spectrum, the input signal is passed through the laser's small-signal transfer function. The resulting spectrum is passed through a Fabry-Perot filter that rejects one of the two principal peaks of the wide-deviation optical spectrum and converts the FSK modulation to amplitude shift keying (ASK) modulation. This simulation determines how different system parameters influence the performance of a laser system used for signal transmission by means of FSK-to-ASK conversion