Coupled-mode analysis of an asymmetric nonlinear directionalcoupler

A coupled-mode analysis of an asymmetric planar nonlinear directional coupler (NLDC) is presented by using the singular perturbation technique. The NLDC consists of a nonlinear waveguide with the core of Kerr-like medium and a linear waveguide situated parallel to each other. The effects of linear coupling and nonlinear modification of refractive index are treated to as small perturbations, and the modal fields of isolated linear waveguides are employed as the basis of propagation model. The self-consistent coupled-mode equations governing the power transfer are derived in analytically closed form. The representative numerical result for the input/output characteristics demonstrates that the asymmetric NLDC is useful for constructing a band-pass power-filter or a band-reject power-filter     

The calculation of switching power of symmetric and asymmetric nonlinear directional couplers with variable coupling coefficient

It is proposed that the switching power of symmetric one-coupling-length nonlinear directional couplers (NLDC) with variable coupling coefficient (VCC) can be calculated as the weighted average of the local critical power of the coupler. Further, it is shown that the switching characteristics of a one-coupling-length VCC NLDC are determined mainly by the first half of the coupler and the switching power of an asymmetric VCC NLDC can be calculated as the weighted average of the local critical power over the first half of the coupler. Both symmetric and asymmetric examples are presented.     

Switching characteristics of variable coupling coefficient nonlinear directional coupler

This paper analyzes the characteristics of the variable coupling coefficient nonlinear directional coupler (VCC NLDC) in detail. The self-switching transmission curves of three types of NLDC with different coupler length are compared. Their phase-controlled transmission curves are compared, and these device acting as pump-controlled switches are analyzed. It is found that the VCC NLDCs show digital characteristics with the increase of the input power. As phase-controlled devices, the response of the VCC NLDC is binarylike when the input power is high. As pump-controlled devices, the transmission curves of the signal are similar to their self-switching transmission curves, except for some specific details.     

具有高阶耦合色散系数双芯非线性光纤耦合器开关的数值分析

基于耦合非线性薛定谔方程(NLSE),利用分裂步长傅里叶方法(SSFM),研究了具有高阶耦合色散系数时,双芯非线性光纤耦合器中的传输和开关特性.模型中,一阶耦合色散系数的存在类似于群速度失配,二阶耦合色散系数类似于群速度色散,并且会对另一个纤芯中的信号产生线性互调制.研究表明当一阶耦合色散系数较小时,光脉冲仍能在二纤芯之间周期性耦合传输,并且表现出良好的开关特性,当一阶耦合色散系数增大时,脉冲耦合传输的周期性和陡峭的开关特性遭到破坏,光脉冲在传输中发生分裂;二阶耦合色散系数使耦合器的耦合长度减短,开关阈值功率增加,开关特性也变得更加陡峭.     

Nonlinear optical pulse coupling dynamics

The pulse coupling dynamics in a nonlinear directional coupler (NLDC) is analyzed by using the new normalized coupled nonlinear Schro/spl uml/dinger equations. The operation of an NLDC can be divided into three regions according to L/sub D//spl kappa/: Region 1 (L/sub D//spl kappa//spl les/1), Region 2 (L/sub D//spl kappa/>50), and Region 3 (1相似文献   

Hyperbolic Secant Coupling In Overmoded Waveguide

This work presents a new solution of the coupled-mode equations for a hyperbolic secant spatial variation of the coupling between two modes. An analytic expression is given for the transmission coefficient for arbitrary complex differential propagation constant and coupling strength. The expression is particular simple in the case when the differential attenuation between the modes is negligible. Design curves are presented in terms of normalized parameters. The hyperbolic secant coupling may be truncated and still yield virtually the same transmission as for infinite couping length. The required coupling length is indicated by a comparison of the ideal expression with the results of numerical integration of the coupled-mode equations. Hyperbolic secant coupling can be particularly useful for the design of short low-loss broad-band bends, twists, and mode-selective couplers in overmoded waveguide. Results of tests on 90-degree bends in rectangular and corrugated circular waveguide are consistent with the theory.     

Coupled waves on optical fibers by power conservation

Using only power conservation, the authors derive the coupling coefficients of coupled-mode theory and a new power conservation law. The derivation provides physical insight into the mechanism of wave coupling on optical fibers. It shows explicitly that the coupled-mode approximation is not generally applicable to Maxwell's equations, since the polarizability of perturbations is omitted. Examples include nonlinear fiber couplers and fiber nonuniformities, with emphasis on their polarization characteristics. An important class of unsolved problems is revealed     

A multiple-scale analysis of grating-assisted couplers

Optical directional couplers with longitudinal periodic perturbations or gratings are analyzed by a multiple-scale solution to the coupled-mode equations. The use of two length scales in the analysis becomes the key to obtaining globally valid analytic solutions, which are shown to be in excellent agreement with the exact numerical solutions. Because of the nonorthogonality of the coupled modes in the structure, two different coupling lengths, a maximum power transfer length and a zero crosstalk length, are predicted for the power exchange. The spectral properties of the coupler are also studied through a generalized multiple scale method     

Dielectric grating induced by cavity standing wave as a newexplanation of origin of nonlinear gain in semiconductor diode lasers

The nonlinear gain due to induced index and gain grating caused by the cavity standing wave is analysed using coupled-mode equations. The grating coupling coefficient is calculated using the rate equation with an ambipolar diffusion term. The self-consistent solution of the coupling coefficient and the optical field indicate the existence of a nonlinear gain term with a surprisingly large magnitude. This gain nonlinearity is shown to contribute significantly to the modulation damping factor of semiconductor diode lasers     

Three-dimensional analysis of a directional coupler exhibiting aKerr nonlinearity

The propagating beam method is used to carry out a fully three-dimensional analysis of a nonlinear optical waveguide and a directional coupler formed from a pair of nonlinear waveguides. It is shown that, for interesting levels of the index nonlinearity, a beam in a monomode waveguide can undergo mild self-focusing and self-phase modulation. The behavior or the nonlinear coupler, on the other hand, is quantitatively similar to that predicted by coupled-mode theory. On the basis of the calculated power transfer characteristics of the nonlinear coupler, three schemes for using the device as a switch have been proposed. It is found that one of these, which is based on the operation of the coupler at a power close to the critical power, permits a larger power to be switched by a very small one     

Analysis of optical fiber directional coupling based on theHE11 modes. II. The nonidentical-core case

For pt.I see ibid., vol.8, no.6, p.823-31 (1990). The analysis of the directional coupling between two single-mode optical fiber cores based on the exact HE₁₁ modes is extended to the cases involving nonidentical fibers. The coupled-mode theory in the vectorial form is used, and analytical expressions for the coupling coefficients and the butt coupling coefficient appearing in the conventional and the coupled-mode equations are presented. The accuracy of the conventional and new theories as applied to the two-core system is examined by comparing the coupled-mode predictions with the exact numerical values for different core-radius ratios, waveguiding strengths, polarization states, and core separations. It is shown that the errors in the coupled-mode theories increase as the two cores become more dissimilar. As long as the dissimilarity between the cores is kept small, the coupled-mode calculations using the HE₁₁ modes in predicting the coupling strength can be of satisfactory accuracy even when the individual guides are not weakly guiding ones. It is found that the new theory may give relatively large errors in the touching-core case with distinctly different core radii     

Compact 300-J/300-GW Frequency-Doubled Neodymium Glass Laser—Part I: Limiting Power by Self-Focusing

Small-scale self-focusing is the main cause of power limitation in nanosecond Nd:glass lasers. We report pioneer observation in experiment of laser beam noise amplification for $B$ -integral (nonlinear phase) order of unity, i.e., without destruction of nonlinear medium. Analytical dependences of noise amplification coefficient on the $B$-integral have been obtained for one nonlinear medium as well as for two nonlinear media separated by an air gap with image relay. A simple analytical dependence has been found for an optimal distance between two nonlinear media for which the maximum allowable value of $B$ -integral increases from 2.7 to 4.3. The maximum attainable energy in neodymium-phosphate glass lasers with rod amplifiers 10 cm in diameter is 400 J with a pulse duration of 1 ns.      

A unified approach for the coupled-mode analysis of nonlinearoptical couplers

A unified approach for the coupled-mode analysis of nonlinear optical couplers is proposed. This approach is basically an extension of the work of [Haus, vol. 5, p. 16, 1987] to include optical nonlinearity. After the nonlinear coupled-mode theory is established, various basis functions are used as trial fields to derive coupled-mode equations. It is found that two published coupled-mode theories can in fact be deduced from the proposed one with individual linear or nonlinear waveguide modes serving as trial fields, thus making the coupled-mode equations from variational principle and reciprocity theorem equivalent. Coupled-mode equations based on system modes are also presented. Furthermore, analytical and/or numerical methods for solving coupled-mode equations are included. More research and discussion can be conducted based on the knowledge addressed in this paper     

受控非线性自聚焦

在高功率密度激光作用下，某些线性介质中会产生非线性自聚焦现象。非线性自聚焦的产生过程具有丰富的内涵。在一定条件下它是可控的．受控成模后在线性介质中传播保持其模不变。     

Analysis of optical fiber directional coupling based on theHE11 modes. I. The identical-core case

For pt.II see ibid., vol.8, no.6, p.832-7 (1990). The directional coupling between two identical single-mode optical fiber cores is analyzed by using the coupled-mode theory in the vectorial form based on the exact HE₁₁ modes. Analytical expressions for the coupling coefficients and the butt coupling coefficient appearing in the conventional and the recently formulated new coupled-mode equations are presented. The effect of the different polarizations on the coupling is considered. The accuracy of the conventional and new theories as applied to the two-core system is examined by comparing the coupling coefficients with exact numerical values. It is shown that as long as the exact HE₁₁ modes are used, the coupled-mode calculations behave well in predicting the coupling strength beyond the weakly guiding regime, and that the simpler conventional theory can provide satisfactory results when applied in the vectorial form     

Nonorthogonal coupled-mode theory of grating-assisted codirectionalcouplers

Grating-assisted codirectional couplers are analyzed by a nonorthogonal coupled-mode theory. The coupled-mode equations are solved exactly, and the effects of all the space harmonics generated by the periodic gratings are included in the analysis. More rigorous relations among the grating period, the grating height, and the coupling length are established. The power exchange between the guides is investigated as a function of the propagation distance and the wavelength. A comparison with previous approximate solutions is made and discussed     

基于三平行光子晶体波导的多功能功分器研究

采用时域有限差分法研究三平行光子晶体直波导的传输特性及模场分布,结合耦合模理论计算光子晶体波导的耦合系数.计算结果表明,在高频段(0.33～0.42)(ωa/27πc)的范围内两耦合波导与主波导表现出相互的能量交换,实现光耦合,耦合系数随入射波频率增加而减小;而在低频段(0.31～0.33)(ωa/2πc)的范围内,两耦合波导与主波导的传输谱图同步变化,耦合波导的传输光强均约为入射光强的四分之一.最后,提出一种采用固定波导耦合长度同时实现超微结构光均分器及1/4功分器的方案,当耦合长度取L_c=(2n+1)π/2 K时,两耦合波导可将高频段相应入射波实现均分,同时将低频段中的任意入射波实现1/4功分.

Abstract：

The propagating characteristics and mode profiles of three parallel photonic crystal waveguides are studied by using finite-difference time-domain method, and the coupling coefficient between the parallel photonic crystal waveguides is obtained with coupled-mode theory. Numerical results demonstrate that for a high frequency range of (0.33～0.42)(ωa/ 2πc), they exchange energy with each other and the optical coupling is realized, the coupling coefficient decreased with the increase of input frequency; while at a low frequency range of (0.31 ～0.33) (ωa/2πc), the mode profiles of the coupling waveguides and main waveguide are changed synchronously, and the coupling waveguides propagating intensity occupies a quarter of the incident intensity. Finally, a solution realizing the ultracompact optical power equalizer and 1/4 optical beam splitter is proposed using a certain coupling length, when the coupling length is L_c= (2n+1)π/2 K, the corresponding incident wave with high frequency can be equalized, meanwhile the wave power with arbitrary frequency at low frequency can be quartered within the two coupling waveguides.     

Coupled-mode equations for pulse switching in parallel waveguides

The coupled-mode equations that describe the switching dynamics of optical pulses in two parallel waveguides are derived. These equations differ from the conventional ones in having extra coupling terms that arise from the dispersion properties of the coupling coefficient. It is shown that the coupling-coefficient dispersion can cause pulse distortion or even pulse breakup and in general produces much more significant effects than the group-velocity dispersion     

Nonlinear property analysis of long-period fiber gratings usingdiscretized coupled-mode theory

We present generalized mathematical expressions for coupled-mode equations for nonlinear pulse propagation in fiber gratings using discretized coupled-mode theory and quantitatively analyze the nonlinear properties of long-period fiber gratings, considering multimode coupling between the core mode and several cladding modes. The calculations yield nonlinear responses for the case of long-period fiber gratings, including pulse shaping and all-optical switching in the self- and cross-phase modulation regimes. In addition, we briefly discuss the group delay properties of long-period fiber gratings and present several numerical examples of nonlinear pulse compression, which is related to strong dispersion and soliton-like behavior in fiber gratings