Fiber waveguide arrays as model system for discrete optics

Optical waveguide arrays consisting of a two-dimensional arrangement of weakly coupled waveguides represent the basis of the new research field of discrete optics. For studying the nonlinear pulse dynamics, fiber waveguide arrays offer specific advantages such as a high optical damage threshold and an accessible range of anomalous dispersion. Coherent coupling of such waveguides for reasonable propagation lengths requires, however, a high structural quality of the waveguides and their superstructure, which is beyond conventional fiber technology. Design, fabrication and characterization of such a fiber waveguide array are described. The linear propagation properties in such a system are modeled and compared with experimental measurements. The high structural homogeneity and good optical quality of the arrays as well as the limits of the nearest-neighbor approximation are demonstrated.     

The freeze of intrapulse Raman scattering effect of ultrashort solitons in optical fiber

The effect of intrapulse Raman scattering (IRS) for the propagation of the femtosecond solitons in an optical fiber is investigated. To factually simulate its influence, a combination of 27 Lorentian lines to fit experimental Raman gain profile is adopted. By using nonlinear Schrödinger equation and finite-difference time domain method, the propagations of femtosecond fundamental solitons in an optical fiber are numerically calculated. When the initial power is suitably enhanced, it is found that the pulse shape is almost the same as initial pulse and the delay Raman response only makes small pulse shift. In other words, when ultrashort soliton is considered, the IRS effect is similarly frozen under the enhanced initial power.     

Solitonen in Wellenleitern mit nichtlinearer optischer Beschichtung

Solitons in a Waveguide with a Thin Nonlinear Optical Slab Starting from Maxwell's equations the influence of a thin nonlinear optical slab embed in a waveguide on the propagation of a monomode (TE) pulse is investigated. The amplitude of the pulse is described by a nonlinear Schrödinger equation (NLS) containing parameters of the waveguide with the nonlinear slab and leading to solitons in the nonlinear modified waveguide.     

Photonic crystal slow light waveguides with large delay–bandwidth product

In this paper, we propose the use of two two-dimensional photonic crystal line defect waveguides for slow light with large delay–bandwidth product (DBP). One includes air rings localized at each side of the line defect and the other modifies the radius and distance of holes at each side of the waveguide. We show that we can achieve a very flat band corresponding to nearly constant group index over a broad frequency range by adjusting the parameters of the structure. We show further that the group velocity dispersion (GVD) can reach a relatively small amount and the DBP can be more than 0.6 for the first waveguide and 0.34 for the second waveguide. Numerical simulation by the finite-difference time-domain (FDTD) method demonstrates the propagation of the broadband pulse.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

具有几个光振荡周期的飞秒激光脉冲

从麦克斯韦方程组出发 ,推导出了具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输的方程和非线性光纤的折射率。给出了描述具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输方程的解。研究了在非线性光纤中自相位调制导致具有几个光振荡周期的飞秒激光脉冲频谱展宽 (脉宽压缩 )的详细物理过程。研究了非线性光纤中飞秒光孤子产生的条件     

Three-dimensional FDTD method for optical pulse propagation analysis in microstructured optical fibers

We propose a three-dimensional (3D) finite-difference time-domain (FDTD) method to analyze the pulse propagation characteristics in microstructured optical fibers (MOFs). The computation domain size is greatly reduced by adopting the technique of moving problem space. The propagating pulse is virtually held in the buffer cell of the problem space as simulation continues. This method is capable to investigate the temporal evolution of the propagating pulse. Spectral information can be obtained by Fourier analysis. As an example, the influence of the kerr nonlinearity on the optical pulse propagation in a Lorentz dispersive MOF is demonstrated. The model is also used to simulate the nonlinear interactions between the pump spectral broadening and third harmonic generations in a highly nonlinear fused silica nanowire with good agreement with the generalized nonlinear envelop equation (GNEE) model.     

高非线性光纤产生自相似抛物线脉冲的特性研究

基于脉冲在光纤中传输所满足的非线性薛定谔方程,采用数值计算的方法对脉冲在高非线性光纤中演化成自相似抛物线脉冲的传输特性进行了研究。结果表明,脉冲在不同初始能量和啁啾参量的情况下,高非线性光纤产生自相似抛物线脉冲,且随着归一化长度的增大,脉冲的自相似指数从0.0796减小到0.0720。进一步的研究表明:啁啾高斯脉冲在光纤传输过程中,脉冲逐渐展宽,同时正啁啾越大,其自相似演化结果越差;参数N=8的正负啁啾脉冲分别演化成平顶自相似抛物线脉冲以及三角形脉冲。     

Nonlinear femtosecond pulse reshaping in waveguide arrays

We observe nonlinear pulse reshaping of femtosecond pulses in a waveguide array owing to coupling between waveguides. Amplified pulses from a mode-locked fiber laser are coupled to an AlGaAs core waveguide array structure. The observed power-dependent pulse reshaping agrees with theory, including shortening of the pulse in the central waveguide.     

快速与慢速饱和吸收体被动锁模掺铒光纤激光器的理论分析

利用半导体饱和吸收波导作为慢速饱和吸收体与非线性快速饱和吸收体相结合，建立了共同被动锁模掺铒光纤激光器的理论模型-分析了半导体饱和吸收波导、光纤自相位调制和自振幅调制对锁模脉冲宽度和脉冲啁啾的影响- 关键词：     

Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x-y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.     

All-optical power limiting in waveguides with periodically distributed Kerr-like non-linearity

A slab waveguide with an embedded non-linear grating is considered as an all-optical power-limiting device. The limiting action is based on the power losses at boundaries between grating sections, where a mode-mismatch results from the self-focusing of the fundamental mode in each non-linear section. Time-harmonic and optical pulse propagation are both modelled numerically by finite-difference techniques to demonstrate the behaviour of the device. Received: 17 May 2001 / Revised version: 7 August 2001 / Published online: 23 October 2001     

Slow light pulse propagation in dispersive media

We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse. To cite this article: T.R. Nielsen et al., C. R. Physique 10 (2009).     

Spectral broadening of a few-cycle laser pulse propagating in fused quartz

Results of theoretical study of nonlinear propagation of a few-cycle laser pulse in a fused quartz are presented. With use of the finite-difference technique we have integrated numerically the system of the nonlinear Maxwell equations describing the propagation of a linearly polarized pulse at the central wavelength in the range of zero dispersion (λ₀ = 1.27 μm) and duration 20 fs. The evolution of the laser pulse spectrum is calculated and the dependences of the shift of the spectral peak on both the strength of electric field and medium length are obtained.     

Coherent transmission and reflection spectra of ordered structures from spherical alumina particles

In this paper, two novel types of semi-slow light photonic crystal waveguide with large transmission bandwidth obtained by shifting the boundaries of a W1 waveguide in the direction of light propagation are presented. One includes air rings localized at only one side of the line defect and the other replaces the holes at each side of the waveguide by the uniform air rings which are constructed by the homocentric square dielectric rod inserted into the air holes. The structure produces unusual “n-type” transmission spectrum depending on the different parameters such as inner radius of air ring, dielectric constant of square dielectric rod, etc. It is shown that the transmission spectra of the two structures are completely different from each other. A versatile control of light propagation with large normalized bandwidth and slow light phenomena can be obtained using a unique geometrical parameter. Numerical simulation by the finite-difference time-domain (FDTD) method demonstrates the propagation of the broadband pulse.     

Temporal Soliton Propagation in Nonlinear Fiber Gratings

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The wave equation with viscoelastic attenuation and its application in problems of shallow-sea acoustics

A suitable tool for the simulation of low frequency acoustic pulse signals propagating in a shallow sea is the numerical integration of the nonstationary wave equation. The main feature of such simulation problems is that in this case the sound waves propagate in the geoacoustic waveguide formed by the upper layers of the bottom and the water column. By this reason, the correct dependence of the attenuation of sound waves in the bottom on their frequency must be taken into account. In this paper we obtain an integro-differential equation for the sound waves in the viscoelastic fluid, which allows to simulate the arbitrary dependence of acoustic wave attenuation on frequency in the time domain computations. The procedure of numerical solution of this equation based on its approximation by a system of differential equations is then considered and the methods of artificial limitation of computational domain are described. We also construct a simple finite-difference scheme for the proposed equation suitable for the numerical solution of nonstationary problems arising in the shallow-sea acoustics.     

Parametrically shaped femtosecond pulses in the nonlinear regime obtained by reverse propagation in an optical fiber

We present the experimental realization of a method to generate predetermined, arbitrary pulse shapes after transmission through an optical fiber in the nonlinear regime. The method is based on simulating the reverse propagation of the desired pulse shape in the fiber. First, linear and nonlinear parameters of a single-mode step-index fiber required for the simulation are determined. The calculated pulse shapes are then generated in a pulse shaper.     

Nonlinear compression of picosecond chirped pulse from thin-disk amplifier system through a gas-filled hollow-core fiber

We theoretically study the nonlinear compression of a 20-m J, 1030-nm picosecond chirped pulse from the thin-disk amplifier in a krypton gas-filled hollow-core fiber. The chirp from the thin-disk amplifier system has little influence on the initial pulse, however, it shows an effect on the nonlinear compression in hollow-core fiber. We use a large diameter hollow waveguide to restrict undesirable nonlinear effects such as ionization; on the other hand, we employ suitable gas pressure and fiber length to promise enough spectral broadening; with 600-μm, 6-bar(1 bar = 105Pa), 1.8-m hollow fiber,we obtain 31.5-fs pulse. Moreover, we calculate and discuss the optimal fiber lengths and gas pressures with different initial durations induced by different grating compression angles for reaching a given bandwidth. These results are meaningful for a compression scheme from picoseconds to femtoseconds.     

一种高品质中空金属光波导

讨论了高品质中空金属光波导的工作原理及其制作工艺，制备了以金和银作为波导材料的中空波导管，并对空芯以及充入不同透明液体的液芯波导的透光特性进行了测试，结果表明：与中空介质波导相比，中空金属波导具有光传输损耗低，透过率对波导弯曲与失调不甚敏感等优点；而液芯金属波导的透光效率与透明材料的折射系数无关。文中描述了在特定波段内“中空光纤”的原理，并报道了Ｈｅ－Ｎｅ和ＣＯ２激光在中空金壁波导传输的实验结果。