Analysis of large-signal dynamic characteristics of 10-Gb/s tunable distributed Bragg reflector lasers integrated with electroabsorption modulator and semiconductor optical amplifier based on the time-dependent transfer matrix method

We investigate large-signal dynamic characteristics of tunable distributed Bragg reflector (DBR) lasers with different structures. Because of high chirp and complex structures of tunable DBR lasers, it is difficult to accurately analyze large signal chirp and output pulse shapes with analytical models. Therefore, we apply a numerical model based on the time-dependent transfer matrix method to tunable DBR lasers integrated with electroabsorption modulator (EAM) and semiconductor optical amplifier (SOA). Using this model, we find a suitable /spl alpha/-parameter range in the Bragg grating section (/spl alpha//sub Bragg/-parameter) that produces the tolerable wavelength chirp while maintaining a proper tuning range. To employ the tunable lasers in wavelength division multiplexed networks and improve flexibility of the networks, the tunable lasers should have high output power and low wavelength chirp. According to our simulation results, the EAM section had better be located in between SOA and DBR laser sections to obtain high output power and low wavelength chirp.     

Image-adaptive watermarking using 2D chirps

Linear chirps, a special case of polynomial phase exponentials, have recently been proposed for digital watermarking. In this work, we propose a known-host-state methodology for designing image watermarks that are robust to compression. We use a two-dimensional frequency-modulated chirp as a spreading function in a block-based spatial watermarking scheme. In each block, the chirp is used to embed binary phase information. Chirp parameters allow for spectral shaping of the watermark to match host content. Since host state is known to the embedder, it is possible to tune the chirp for optimum performance, particularly against compression. In contrast to existing chirp watermarking where only a single watermark is generally embedded, the proposed block chirp watermarking allows for a much higher payload. Detection is done using chirp transform subject to key exchange for security. We show that the proposed method significantly outperforms non-adaptive watermarking across all compression factors under variety of attacks.     

蓝移啁啾和红移啁啾的相互作用关系

通过研究群速度色散（GVD）和自相位调制（SPM）的相互作用，推导出了蓝移啁啾和红移啁啾共同作用所致啁啾的解析表达式。研究结果表明，当色散长度LD和非线性长度LNL确定后啁啾随Z和T的变化特性完全确定，随着LD／LNL的不同，啁啾特性发生了明显变化，通过控制输入功率可实现无啁啾传输，保持脉冲的稳定性。     

初始啁啾和光纤损耗对皮秒脉冲孤子效应压缩的影响

运用分步傅立叶方法数值模拟了皮秒脉冲在单模光纤中的传输 ,计算和分析了初始啁啾和光纤损耗对皮秒脉冲孤子效应压缩的影响。结果表明 ,两者对具有一定峰值功率的脉冲孤子效应压缩的影响具有互补性 ,即两者对脉冲压缩的作用相反。进一步研究表明 ,对在损耗光纤中传输的皮秒脉冲 ,如果给其加适当大小的初始啁啾将得到很好的压缩效果     

Wavelength chirp and dependence of carrier temperature on currentin MQW InGaAsP-InP lasers

In this paper, we derive a relation between the wavelength chirp and carrier temperature in semiconductor lasers. The coefficient relating the change in carrier temperature and chirp is expressed in terms of the temperature derivative of the optical gain, and two parameters describing the variation of refractive index produced by the variation of optical gain due to change of carrier quasi-Fermi level separation or carrier temperature. We have measured these parameters for MQW InGaAsP lasers, Using this data, we estimated the rate of the temperature increase with current above threshold in these devices, which is 0.13 K/mA     

色散阶变光纤中啁啾演变的研究

给出了色散阶变光纤中群速度色散效应导致的啁啾表达式，采用数值方法模拟了该光纤中的啁啾演变过程。研究结果表明：色散阶变光纤中的啁啾以色散缓变光纤中啁啾为中心跳跃式变化，逐渐与色散缓变光纤中啁啾重合，且比常规光纤中的啁啾小。     

Eigenfunctions of linear canonical transform

The linear canonical transform (the LCT) is a useful tool for optical system analysis and signal processing. It is parameterized by a 2×2 matrix {a, b, c, d}. Many operations, such as the Fourier transform (FT), fractional Fourier transform (FRFT), Fresnel transform, and scaling operations are all the special cases of the LCT. We discuss the eigenfunctions of the LCT. The eigenfunctions of the FT, FRFT, Fresnel transform, and scaling operations have been known, and we derive the eigenfunctions of the LCT based on the eigenfunctions of these operations. We find, for different cases, that the eigenfunctions of the LCT also have different forms. When |a+d|<2, the eigenfunctions are the scaling, chirp multiplication of Hermite functions, but when |a+d|=2, the eigenfunctions become the chirp multiplication, chirp convolution of almost-periodic functions, or impulse trains. In addition, when |a+d|>2, the eigenfunctions become the chirp multiplication and chirp convolution of self-similar functions (fractals). Besides, since many optical systems can be represented by the LCT, we can thus use the eigenfunctions of the LCT derived in this paper to discuss the self-imaging phenomena in optics. We show that there are usually varieties of input functions that can cause the self-imaging phenomena for an optical system     

Characterization of Zak Space Support of a Discrete Chirp

General conditions are derived for an (N=KL²)-point discrete chirp with chirp rate a and carrier frequency b to have minimal support on the LtimesKL Zak transform lattice. Earlier, it has been shown that when the normalized chirp parameters amacr= aK, amacr= aK ², and 2bmacr = 2bK are integers, the last two of the same parity, then the discrete chirp is supported at KL points. Here, this condition is relaxed, by allowing amacr to be a rational number, i.e., amacr = n/d, n, disin Z, (n,d)=1, and requiring only that amacr and bmacrL be integers of arbitrary parity. It is shown that the support of the Zak space chirp satisfying the new condition then increases to dKL points. The results provide foundations for future constructions of sophisticated radar and communications signal processing algorithms. Examples of direct applications of the Zak space conditions in chirp parameter estimation, chirp detection, and chirp de-noising are included     

Analysis of chirp power penalty in 1.55-µm DFB-LD high-speed optical fiber transmission systems

In a 1.55-μm high-speed transmission system using a DFB-LD, the chirp effect in the LD is a factor limiting transmission span length. In order to evaluate the chirp effect, we derive expressions for the chirp power penalty for two cases: the cases of the chirp occurring in both edges of the pulse and in the whole time of the pulse. The calculations based on the results of the LD chirp measurement predict that the chirp effect will be significant above 2 Gbit/s even if the zero dispersion wavelength of fiber is shifted to the 1.55-μm band. Transmission experiments performed at 1.2 Gbit/s and 2.4 Gbit/s verify this prediction.     

Proposal and Analysis of Distributed Reflector‐Laser Diode Integrated with an Electroabsorption Modulator

A novel integrated laser, that is, a distributed reflector laser diode integrated with an electroabsorption modulator, is proposed to improve the output efficiency, single‐mode stability, and chirp. The proposed laser can be realized using the selective metalorganic vapor phase epitaxy technique (that is, control of the width of the insulating mask), and its fabrication process is almost the same as the conventional electroabsorption modulated laser (EML) process except for the asymmetric coupling coefficient structure along the cavity. For our analysis, an accurate time‐domain transfer‐matrix‐based laser model is developed. Based on this model, we perform steady‐state and large‐signal analyses. The performances of the proposed laser, such as the output power, extinction ratio, and chirp, are compared with those of the EML. Under 10‐Gbps NRZ modulation, we can obtain a 30% higher output power and about 50% lower chirp than the conventional EML. In particular, the simulation results show that the chirp provided by the proposed laser can appear to have a longer wavelength side at the leading edge of the pulse and a shorter wavelength side at the falling edge.     

光孤子传输中的啁啾及F－P腔消啁啾技术

对啁啾的产生、啁啾对孤子传输的影响进行了研究，并对孤子消啁啾技术进行实验研究     

Low chirp observed in directly modulated quantum dot lasers

We have examined the dynamic properties of high-aspect-ratio InAs-quantum-dot (QD) lasers at room temperature. A novel characteristic of low chirp in the lasing wavelength under 1-GHz current modulation was found in the quantum dot lasers. This is more than one order of magnitude less than the typical chirp (0.2-nm) found in a conventional quantum well laser that we used as a reference. Low chirp was obtained not only in the ground state lasing but in the second level lasing of quantum dots as well.     

Chirp characteristics of dual-drive. Mach-Zehnder modulator with afinite DC extinction ratio

In this letter, we present theoretical and experimental studies on the chirp of the dual-drive Mach-Zehnder (MZ) modulator with a finite DC extinction ratio. The chirp of the modulator was measured using the fiber response peak method and compared with the theoretically calculated values. The results show that the residual chirp of the MZ modulator could be substantially reduced by driving the modulator in a push-pull mode with unequal amplitude signals     

DFB半导体激光器的频移和色散脉冲崎变

根据分布反馈（ＤＦＢ）半导体激光器的耦合波理论和电吸收调制器模型，推导出了描述ＤＦＢ／ＥＡ集成器件中调制器的端面反射造成的激光器的静态频移和动态频移的解析表达式，动态频移（“反射啁啾”）正比于调制器的有效端面反射率。利用动态频移模型对光脉冲经过反常色散光纤传输后的波形进行了计算机仿真，取得了与实验一致的结果。结果表明：无论脉冲的初始啁啾的正负如何，“反射啁啾”总是使得传输后的脉冲变窄，当反射啁啾为正时，脉冲的上升沿出现“过冲”，而下降沿变缓；当反射啁啾为负时，情况与之相反。     

掺铒光纤放大器中孤子脉冲获得线性啁啾的研究

为了研究孤子脉冲经掺铒光纤放大器演变后的啁啾特性,采用了对称分步傅立叶的数值方法,对孤子脉冲在不同增益条件下的演变和线性啁啾特性进行了数值仿真。数值计算的结果表明：当满足增益系数μ远大于1时,基孤子脉冲在放大器中传输能够获得很好的线性啁啾,且发现脉冲的啁啾特性受选取的放大器长度参量的影响;啁啾越明显的脉冲,线性啁啾所占的区域越窄。进一步研究还发现初始啁啾系数和孤子阶数对脉冲获得的线性啁啾均有很大影响,初始正啁啾系数和高孤子阶数均能增强输出脉冲的线性啁啾特性。因此,利用孤子脉冲在掺铒光纤放大器中传输的非线性效应能够获得良好的线性啁啾,这对实现高质量的脉冲压缩是很有帮助的。     

40-gb/s EA modulators with wide temperature operation and negative chirp

Broad bandwidth external modulators are widely used in optical fiber networks to avoid the chirp associated with the direct modulation of laser diode sources. For transmission application beyond 10 Gb/s, electroabsorption modulators (EAMs) offer many advantages such as low drive voltage, low chirp characteristics, small size, and added functionality through integration with a distributed feedback laser. In this letter, we present static and dynamic characterization of an EAM demonstrating the possibility to have with the same device uncooled operation at 40 Gb/s and negative chirp at low negative bias. These features are attractive for cost reduction in short link applications and for long-haul transmission. All the measurements are performed at 40 Gb/s from room temperature up to 60/spl deg/C demonstrating a negative chirp behavior for the stand-alone modulator over the entire temperature range.     

初始啁啾对色散渐减光纤中皮秒脉冲孤子效应压缩的影响

在色散沿光纤传输方向线性减小的光纤中,用分步傅里叶方法数值模拟皮秒脉冲的传输,计算和分析了初始啁啾对色散渐减光纤中皮秒脉冲的孤子效应压缩的影响.通过分析脉冲压缩比,最佳光纤长度,压缩后的脉冲峰值功率和脉冲压缩质量的变化,发现加入初始啁啾,可以使皮秒脉冲得到更好的压缩.     

初始啁啾参数对偏振模耦合产生啁啾的影响

研究了两正交偏振模耦合所致啁啾。利用耦合非线性薛定谔方程推导出带初始啁啾入射脉冲经偏振模耦合产生的啁啾表达式,分析了各因素对啁啾的影响。研究结果得出,入纤偏振角导致在两偏振方向上产生啁啾的差异;较弱的偏振走离效应对啁啾有一定影响,较强的偏振走离效应对啁啾几乎没有影响;初始啁啾则起了决定性的作用。     

Residual chirp in integrated-optic modulators

The authors have analyzed and measured the dispersion effects of residual chirp arising from asymmetry in field overlap in Mach-Zehnder structures. A clear influence of chirp was seen at 7 Gb/s and a propagation length of 75-km nondispersion shifted fiber at λ=1.55 μm. It is shown that a MZ-modulator with field overlap in one arm only and operated in the blue-shift mode is the best choice for single coplanar stripline (CPS) electrode MZ-modulators in this case. Calculations have shown good agreement with measured results. This indicates that a simple model for fiber mode propagation have shown good agreement with measured results. This can be used together with a FFT-algorithm for calculating the effect of residual chirp from external modulators in multigigabit dispersive fiber-optic systems     

Real-time restoration of images degraded by uniform motion blur infoveal active vision systems

Foveated, log-polar, or space-variant image architectures provide a high resolution and wide field workspace, while providing a small pixel computation load. These characteristics are ideal for mobile robotic and active vision applications, but have been little used due to the general lack of image processing tools that are applicable to the log-polar coordinate system. Recently, we have described a generalization of the Fourier transform (the fast exponential chirp transform), which allows frame-rate computation of full-field two-dimensional (2-D) frequency transforms directly in log-polar coordinates. In the present work, we show that is possible to achieve full-frame image de-blur at frame rate on a standard "PC" platform, using these methods, we illustrate this idea with a Wiener filter based restoration technique. The main contribution of this note is the implementation of (space-variant) image de-blur directly in log-polar coordinates, using the exponential chirp transform. The results show reasonable quality of de-blur, and suggest that these methods are relevant to applications in mobile image processing platforms in which real-time motion deblur is important, and for which it is not desirable to use extensive or custom fabricated hardware.