Ray-pulse matrices: a rational treatment for dispersive opticalsystems

A new formalism to describe beam propagation in paraxial optical systems with dispersive elements, including both spatial and temporal variations in the propagating signal, is presented. This formalism makes use of 4×4 ray-pulse matrices which take account of dispersive effects up to quadratic phases in both spatial coordinates (as in the usual paraxial ABCD matrix approach) and in the temporal domain. How to use these matrices to write a space-time integral analogous to a generalized Huygens integral is shown, and propagation laws for Gaussian ray pulses which are space- and time-varying analogs of the conventional results for Gaussian beams are derived. The formalism should be useful for analyzing dispersive optical systems such as prism beam expanders, femtosecond pulse compression systems, and dispersive mode-locked laser cavities     

基于频域分析的光学相干显微镜中的色散补偿

提出基于频域分析的色散补偿方法,对光学相干显微镜的干涉信号进行快速傅里叶变换,得到频率幅值极大值对应的平均波数,将提取的解包裹后的相位以平均波数为中心做多项式拟合,得到二阶色散系数。实验中,通过在参考臂中插入不同厚度的色散介质来引入两个干涉臂色散介质的光程差,并求得相应的二阶色散系数。通过最小二乘线性拟合,证实了二阶色散系数和色散介质的相对厚度具有很好的线性关系。根据该线性关系,可以在参考臂中插入适当厚度的色散介质来完全补偿干涉系统的二阶色散。     

Bi-end dispersion compensation for ultralong optical communicationsystem

Bi-end dispersion compensation (DC) for ultralong nonreturn-to-zero (NRZ) optical transmission system is studied. Both the loss and dispersion of the transmission fiber are periodically compensated. Two dispersive elements are placed at the input and output ends of a compensation period, respectively, to compensate for fiber dispersion. The pulse compression owing to self-phase modulation (SPM) can be adjusted by the compensation ratios of the dispersive elements at the two ends of a compensation period. Therefore, the pulse compression can be optimized and the system performance can be improved to compare with the system with either pre- or postdispersion compensation. The rules to design the system are considered. The transmission system of 10-Gb/s bit rate, 9000-km transmission distance, and 100-km compensation period is taken as an example. The second-order fiber dispersion is assumed to be completely compensated. Wave equation is numerically solved to study the system performance which is represented by Q factor. The relations of several system parameters and Q factor are studied. The system parameters include the compensation ratios of the dispersive elements at the two ends of a compensation period, dispersion of transmission fiber, signal power, and the compensation ratios of third-order fiber dispersion. If the third-order fiber dispersion cannot be completely compensated, it is found that one can use a higher signal power to improve the system performance     

钛宝石晶体色散特性的理论研究

本文采用激光经典理论中色散与吸收(增益)的关系,结合钛宝石吸收与荧光光谱资料,计算了钛宝石晶体的色散特性,得到了钛宝石在吸收区的反常色散和增益区正常色散曲线。结果表明,在一般条件下,由吸收和增益所造成的折射率变化可以忽略,在考虑折射率与波长的关系时,仍可按正常色散处理.     

Accurate solution of the volume integral equation forhigh-permittivity scatterers

We present a formalism based on the method of moment to solve the volume integral equation using tetrahedral (3-D) and triangular (2-D) elements. We introduce a regularization scheme to handle the strong singularity of the Green's tensor. This regularization scheme is extended to neighboring elements, which dramatically improves the accuracy and the convergence of the technique. Scattering by high-permittivity scatterers, like semiconductors, can be accurately computed. Furthermore, plasmon-polariton resonances in dispersive materials can also be reproduced     

Scalar off-resonant modulation instability in rare-earth-doped fiber amplifiers

Presents an analytical model which describes the dynamics of the modulation instability in a nonlinear, dispersive, homogeneously broadened and nonsaturable fiber amplifiers. The general case of arbitrary detuning between the laser frequency and the resonance frequency and arbitrary bandwidth of the amplifying transition is treated. The model accounts both for the gain dispersion and for the gain-induced, near resonant refractive index dispersion, Simple closed form expressions for the combined gain coefficients of the Stokes and anti-Stokes frequencies are obtained.     

负折射介质中非线性色散效应对调制不稳定性的影响

研究了负折射介质中非线性色散效应对调制不稳定性的影响,揭示了若干新的不稳定性现象。得到了有任意高阶线性与非线性色散效应情形下调制不稳定性增益谱的表达式,结果表明:所有偶次非线性色散不但会影响原来的不稳定性,而且可能会导致新的不稳定性区域;而所有的奇次非线性色散将始终抑制调制不稳定性,且与其符号的正负无关。进一步研究了由色散磁导率所诱导的二阶非线性色散效应对调制不稳定性的影响。研究发现它不但能使在常规介质中不可能出现的调制不稳定性现象也能出现,而且可能会导致在无限带宽的调制频率范围内发生新的不稳定性现象,且其增益值将随调制频率的增大而单调增大。     

Delay lines with tailored high-dispersion orders for periodic optical pulses

We derive an expression for the temporal fractional Talbot effect in delay lines with arbitrary orders of dispersion. We then demonstrate, experimentally and by numerical simulations, that a simple device consisting of a number of uniform fiber Bragg gratings or of waveguides can serve for such a tailored dispersive delay line for periodic optical pulses. The device produces temporally delayed and phase-shifted replicas of the original pulses, similarly to what happens in dispersive delay lines in the fractional Talbot effect. Such devices can be useful for compensation for the nonquadratic spectral phase of diode lasers, of dispersive elements in systems used for temporal imaging, real-time spectral analysis, and periodic pulse generation.     

White light dispersion measurements by one- and two-dimensionalspectral interference

White light dispersion measurements by and two-dimensional spectral interference are shown. One-dimensional white light spectral interference measurements allow accurate characterization of dispersion using weak optical fields. Two-dimensional spectral interference allows for real-time measurements since no post-processing is needed, and therefore can be used in situations where the optical properties of the elements under test vary in time. We demonstrate the applicability of the two methods for characterizing dispersive elements such as optical glasses and dielectric coatings     

失谐对开放的无反转激光系统时间演化的影响

研究了探测场或驱动场失谐情况下开放的∧型无粒子数反转激光系统中原子响应的时间演化规律,并与探测场与驱动场都共振时的演化规律进行了比较。我们发现失谐对时间演化规律有显著的影响;当驱动场或探测场失谐时,原子对探测场和驱动扬色散的响应不再为零,双光子相干不再是纯实量;探测场失谐的变化将使粒子布居和驱动场增益（吸收）的时间演化规律明显改变;随着失谐的增大,探测场增益（吸收）、色散和双光子相干随时间的演经行为逐渐偏离标准阻尼振子的演化规律; 驱动场色散驱动场失谐量的增加而振荡时间变长,振和稳定值变大。     

Dispersion of microwave-modulated optical signals

Experimental and analytical evaluation of dispersion effects that control intersymbol interference in gigabit, single-mode-fiber, digital systems is described. Both direct modulation of distributed-feedback (DFB) lasers and external modulation by Mach-Zehnder modulators are studied. The experiment uses sinusoidal modulation of the light at a microwave frequency, e.g. 5 GHz, and the subsequent measurement of signal gain or loss in a dispersive fiber. For DFB lasers, the transmission measurements are used to derive the transient and adiabatic components of chirp. It is shown that, for external modulation at 5 GHz, the 1.55- mu m optical signals suffer relatively little dispersion loss for transmission distances up to 60 km. Analytical solutions for waveform distortion are given for external modulation and show good agreement with measurements.<>     

Time-domain ABCD matrix formalism for laser mode-locking andoptical pulse transmission

ABCD matrix formalism in the time domain has been newly developed on the basis of laser beam and resonator analyses which were developed under a Gaussian paraxial approximation. We derive matrix elements for amplitude and frequency modulations, group velocity dispersion, optical bandpass filter dispersion, and lumped self-phase modulation under a parabolic approximation. Applications to AM, FM, and stretched-pulse laser mode-locking are described by using these time-domain matrices. An application to pulse transmission in a dispersion-allocated system is also described     

Finite-temperature effects in free-electron lasers

The effect of energy spread on the gain of a dense-beam free-electron laser amplifier is analyzed. The formalism includes collective effects and allows for the use of an arbitrary distribution function. The dispersion relation is solved numerically. Besides broadening of the spectrum and decrease in gain, lowering of the central emission frequency with energy spread is observed. An initial-value problem is formulated and numerically solved, with power computed as a function of distance. The relative contributions of the different modes when temperature changes are analyzed. In particular, the competing effects of a decrease in coupling loss with temperature together with Landau damping are investigated.     

On the dispersive properties of the conical spiral antenna and its use for pulsed radiation

Conical spiral antennas can have an input impedance and gain that are nearly frequency independent over a wide bandwidth. However, these antennas normally have dispersive properties that produce significant distortion when they are used to radiate a pulse. We examine this dispersion in detail and the possibility of compensating for the dispersion so that the antenna can be used for pulse radiation. First, a simple, qualitative model for this antenna is described. This model provides physical insight into the causes for the dispersion. Next, the antenna is examined using an accurate, full electromagnetic analysis done with the finite-difference time-domain method. Results from this analysis support the conclusions reached with the simple model and provide additional insight into the dispersion. Finally, an approach for compensating for the dispersion in the antenna is described, and the interesting features of the pulse radiated from this antenna, after compensation, are discussed.     

Optimal and sub-optimal Loop Filter Responses for Continuous-Time ΔΣ Modulators

This paper describes a comprehensive analysis of the stability of continuous-time low-pass or band-pass ΔΣ modulators. This analysis is based on a fully S-domain approach which considers the modulator as a feedback control system with gain and phase margins. Theoretical responses for both the optimal filter and a sub-optimal one are derived using a mathematical formalism close to well-known boundary elements methods. A very accurate empirical model has also been developed and, for each case (optimal and sub-optimal), normalized sets of curves allowing to extract the maximum achievable loop gain for a given loop configuration. High achievable gains were found even in the case of ΔΣ modulators involving large delays (several clock times).     

材料色散对1维光子晶体缺陷模影响的研究

为了分析材料色散对缺陷模的影响,对色散材料采用洛伦兹振子模型,利用传输矩阵法计算了含缺陷1维光子晶体的透射谱,分析了各层的色散对该结构1维光子晶体缺陷模的影响。结果表明,无论是高、低折射率介质还是缺陷层的色散都可以引起缺陷模的频移或分裂;缺陷模的频移方向与考虑色散后光学厚度的变化有关,如果光学厚度增大,则发生红移,反之则发生蓝移;低折射率介质的色散使缺陷模频移的效果最显著。这一结果对光子晶体的设计和研究有一定的参考价值。     

Pulse compression acoustic microscopy at 750 MHz

A pulse compression acoustic microscope working at a centre frequency of 750 MHz is reported. The pulse expansion and compression is achieved by SAW dispersive delay lines. The transmitted chirp has a bandwidth of 150 MHz and a dispersion of 1 MHz/ns. A processing gain in excess of 10 dB has been achieved.     

The compound cavity optical parametric oscillator: theory andexperiment

We present the time dynamics of a compound-cavity optical parametric oscillator (OPO) using a mathematical model for the modes under the gain profile of the oscillator which accounts for pump depletion and the cavity-Q factors. The computational results show that this type of cavity is superior in that its threshold is lower than that of a simple narrow-band cavity with dispersive elements and its efficiency is increased, while its narrow linewidth remains nearly the same across the tunable range of the nonlinear crystals used. A diagram illustrating the operation state of a compound-cavity OPO is presented, which is applicable to the simple narrow-band cavity, simple broad-band cavity, compound cavity, and traveling-wave amplification. The theoretical results are compared to the experimental data from a compound-cavity OPO using a grazing-incidence prism and grating as dispersive elements     

Analysis of tunable photonic crystal devices comprising liquid crystal materials as defects

The tuning properties of two-dimensional dielectric and metallic photonic crystals, which contain nematic liquid crystal materials as defect elements or layers, are thoroughly analyzed using appropriate formulations of the finite difference time domain (FDTD) method. Our methodology correctly incorporates the anisotropy introduced by the liquid crystal materials together with the dispersive properties of the metallic elements; it is used for calculating both the dispersion diagrams of the defect-free photonic crystal as well as the device response in the presence of the defect elements. Numerical simulations reveal that defect states originating from the liquid crystal impurities can be effectively tuned by the application of a local static electric field. Indeed, tuning ranges up to almost 100 nm can be achieved requiring operating voltages lower than 4 V. It is also concluded that the placement of a defect mode relative to the bandgap edges greatly influences both its linewidth as well as its tuning range.     

Design of a transversal equalizer for electronic dispersion compensation in optical communication links

A programmable transversal equalizer for electronic dispersion compensation(EDC) in optical fiber communication systems is developed.Based on the SiGe technology with a cut-off frequency of 80 GHz,the equalizer consists of 6 seriesparallel amplifiers as delay units and 7 Gilbert variable gain amplifiers as taps,which ensure that the equalizer can work at the bit rate of 10 Gb/s.With different tap gains,the forward voltage gain of the transversal equalizer varies,which demonstrates that the equalizer has various filtering characteristics such as low pass filtering,band pass filtering,band reject filtering,and notch filtering,so it can effectively simulate the inverse transfer function of dispersive channels in optical communications,and can be used for compensating the inter-symbol interference and other nonlinear problems caused by dispersion.The equalizer(including pads) occupies an area of 0.40 mm × 1.08 mm,and its total power dissipation is 400 mW with 3.3 V power supply.