Perturbation theory of low-V optical fibres with dip in the refractive index

A simple perturbation theory has been used to study the characteristics of low-V, step-index optical fibres with a dip in the centre of the refractive index profile. Analytical expressions have been derived for the cut-off frequency and propagation constant of an arbitrary mode on such a fibre. In particular, it has been shown that even when the dip is quite large, the perturbation theory results for the propagation constant of the fundamental mode and cut-off frequency of the second mode are virtually indistinguishable from exact numerical results calculated by series expansion techniques.     

基于等效衰减矢方法的非均匀光波导色散方程

利用转换矩阵理论和等效衰减矢的概念，以此为根据分析了任意折射率分布平板波导的模式传输特性，导出了意义明确的非均匀平板波导的色散方程的严格的解析解，并指出了ＷＫＢ法的局限性，数值计算的结果表明本文所得公式的结果和严格的数值解非常接近，表明本文所得的公式是严格的。     

非等效折射近似的多量子阱波导色散关系

本文导出了任意折射分布的多量子阱波导芯子区域的转移矩阵,用非等效折射近似得到了TE和TM两种偏振的色散关系.理论的精确性经数值计算比较证明是完全可靠的.     

Performance evaluation of GRIN lenses by ray tracing method

Plastic gradient-index lenses produce clear images with negligible aberration and distortion. One of the methods for fabricating these lenses involves pulling up the core fiber vertically from a polymer solution whose refractive index has been adjusted to the desired value. Since the molecules from the solution diffuse into the inner layer, the monomer components are distributed in the radial direction. The monomer distribution is fixed in the photopolymerization process, and this forming process is repeated several times with adjusting the composition of the solution; hence, a specific refractive index distribution is obtained. We considered a numerical model of the interdiffusion process and analyzed refractive index distribution that could well reproduce the experimental results. Moreover, we employed the ray tracing method to calculate the modulation transfer function and used the transfer function to evaluate the GRIN lens performance. Simulation results showed that our evaluation method well duplicates the experimental results. We thus developed an integrated simulation method for the fabrication and performance evaluation of GRIN lenses.     

Influence of the characteristic curve of the material on the diffraction efficiency of holographic volume phase gratings

The behaviour of the diffraction efficiency of holographic gratings is discussed on the basis of the multiwave coupled-wave approach, taking into consideration the photoinduced change in the refractive index of the recording medium. The cases of Bragg and off-Bragg reconstruction in Bragg and mixed diffraction are considered. The influence of the higher harmonics of the refractive index modulation profile on the diffraction efficiency is shown.     

非线性介质中强光对弱光聚焦的控制研究

从理论和实验上分析了强光控制弱光脉冲聚焦的方法, 该方法可以灵活地控制弱光的聚焦过程和特性. 通过研究两光束共同传输, 利用强抽运光在相互作用时为弱探测光提供诱导非线性效应, 从而使弱探测光发生聚焦. 得到了在抽运光保持不变情况下探测光的解析解, 并在实验上得到验证. 进一步研究了强抽运光对弱探测光焦点位置的影响. 结果显示: 通过改变抽运光功率、束宽能够有效地控制弱探测光的聚焦过程和焦点位置. 关键词： 诱导聚焦 自聚焦 非线性折射率     

Dispersion characteristics of complex refractive-index planar slab optical waveguide by using finite element method

In this paper, finite element method (FEM) mode analyses of planar slab optical waveguide having complicated refractive index profile are presented. We try to estimate the dispersion graph, mode cut-off condition, group delay and waveguide dispersion for the case of α-power and chirped-type refractive index profile. In order to obtain the more accurate result, we have derived the higher-order polynomial, which establishes the suitable relationship between b and V for different profile of optical waveguide. On the basis of the derived polynomials, the waveguide dispersion is analyzed for different type of refractive index profile waveguide. Our study shows that the waveguide dispersion can be substantially reduced when we deployed the optical waveguide having linearly chirped-type refractive index profile. Earlier too, the arbitrary refractive index profile has been analyzed but to the best of our knowledge chirped-type refractive index profile has not been analyzed till date for the case of planar slab optical waveguide.     

干涉法测量光学材料非线性折射率的方法研究

提出了一种基于楔形平板等厚干涉原理测量光学玻璃非线性折射率变化的方法。在理论分析的基础上,建立了变形的等厚干涉条纹变化△e／e与待测玻璃平片（K9玻璃）折射率变化量△nb之间的数学模型;在选取一定的实验条件下,获得等厚干涉实验测量干涉图样,并利用MATLAB对实验所得的干涉图进行图像数据处理分析计算,恢复出非线性变化光学玻璃材料的折射率变化量△nb该方法的测量精度可达10^-6。     

电光材料调制误差对平行光束干涉投影的影响

为研究电光材料调制误差对干涉条纹质量的影响,建立了电光晶体对干涉条纹的成像模型,分析了晶体折射率、平面度与波前调制的关系及其非理想情况下的条纹成像特征。实验表明,晶体折射率的畸变会使干涉条纹变形,折射率离散化阶数直接造成投影条纹的高次谐波成分,甚至使投影条纹严重失真;在折射率线性增长的情况下,晶体平面度在0.1 μm的范围内也会引起干涉条纹畸变。     

Generation of femtosecond double pulse by adjusting the refractive index modulation of volume holographic grating

Based on the modified Kogelnik’s coupled-wave theory, expressions of diffraction field distribution of volume holographic grating (VHG) are derived when it is illuminated by an ultrashort pulse. It is found that the diffracted pulse is involved into two pulses, and the two-pulse interval is found to be proportional to the refractive index modulation of the VHG. Moreover, the emergence of double pulses is periodic. An overmodulation effect of refractive index modulation of transmitted VHG is used to explain this particular diffraction behavior of the VHG. Results of our study provide a feasible method to generate interval adjustable double pulse with a simple system.     

Angular Multiplexing Gratings Characterization in Dichromated Gelatin and Thoughts on Diffractive Optical Memory

We were mainly concerned here with multiple exposure gratings that allow interactions and coupling between gratings. We started the study of interactions and coupling with five gratings recorded in dichromated gelatin (DCG). Having determined experimentally the characteristic parameters of these five gratings, we used a method developed by Oxford University to synthesize the modulation profile. Entering these parameters of each grating into our computing programs (based on the alternative theory of diffraction in modulated media) and by varying the amplitude modulation, the latter was deduced by adjusting the numerical curve to the experimental one. We then extended the study to nine multiplexed gratings. This study allowed us to know the range of the amplitude modulation such that a certain number of angular multiplexing can be done in DCG. Several undesirable effects which we had experimentally observed appeared then during the reconstruction of any one of the multiplexed images, such as cross-talk effect. We noted the good concordance between experimental and theoretical results. We finally illustrated cross-talk effect in a diffractive memory where, if the amplitude modulation was first calculated, the number of multiplexing for an angular range could then be determined and the angular separation achieved to avoid cross-talk.     

A fully vectorial effective index method to analyse the propagation properties of microstructured fiber

Based on numerical simulation, we theoretically study the linear and nonlinear properties of microstructured fiber. Using the fully vectorial effective index method, we calculate the effective refractive index for different air hole size. We show how the linear properties such as spot size, numerical aperture, splice loss and bend loss can be controled by changing the air hole size. We also propose the same method for analysing effective area and self-phase modulation of microstructured fiber for different designing parameters. We compare all our results with other numerical methods.     

非均匀平板波导的色散方程

利用转移矩阵理论分析了任意折射率分布平板波导的传输特性，导出了非均匀平板波导的近似解析色散方程，并指出了ＷＫＢ近似的局限性，数值比较的结果表明，文中所得公式的精确度优于传统的ＷＫＢ方法和其它近似方法。     

Study on mechanism of ultrasonic fluorescence modulation in light scattering medium based on diffusion approximation with varying refractive index

In this study, we propose a model to describe the mechanism of ultrasonic fluorescence modulation based on the application of a modified diffusion approximation, which is derived from the radiative transfer equation with consideration of the varying refractive index. The model was evaluated by computation with finite element method (FEM) to simulate the physical phenomena of our previous experiments. The simulation shows that the measured power of the modulated fluorescence signal at the boundary of 40-mm-thick light scattering medium (scattering coefficient and anisotropy factor of 1.36mm^?1 and 0.67, respectively) with the fluorophore located at the center was 10^?20 of the incident laser power. The analysis based on the simulation results indicates the significant property of the modulation in which the modulated signal is combination including two processes generated from the variation of the refractive index and fluorophore concentration (the contributions of these are equivalent), whereas the contribution of the variation of the scattering coefficient is negligibly small. The profile of the fluorescence image and the characteristics of the quadratic relationship between the modulated intensity signal and the sound pressure are consistent with our previous experimental results.     

非均匀关联径向偏振部分相干光的产生

从理论和实验两方面对非均匀关联径向偏振部分相干光的产生进行了研究.理论上,基于相位关联与相干度的联系,推导出了非均匀关联径向偏振部分相干光的2×2阶交叉谱密度矩阵及相干度分布.实验上,利用一个相位型液晶空间光调制器的不同区域,对入射的完全相干的径向偏振光的两个正交偏振分量分别加载随机相位调制,并实验测量了这种光束的相干度分布及其对光强分布的影响.实验结果验证了光束相干度的非均匀关联结构,并且通过改变随机相位的高斯调制半宽可以改变光束的相干性分布.研究表明,随着随机相位的高斯调制半宽的增加,光束中两点间的相干度逐渐减小,其光强分布由圆环状逐渐变化为类平顶的光强分布.这种非均匀关联的径向偏振部分相干光在激光微操纵和材料加工等领域具有一定的潜在应用价值.     

Determination of the refractive index profile of polymer optical fiber preform by the transverse ray tracing method

In graded-index polymer optical fiber (GI-POF), the refractive index profile is an important parameter in defining its bandwidth. However, direct determination of the refractive index profile of GI-POF is difficult due to its extreme thinness. In this study, the refractive index distribution of the GI-POF is indirectly determined by measuring the refractive index distribution of the GI-POF perform by applying the transverse ray tracing method to a simplified measurement system that we developed.In this system, a parallel tabular ray is irradiated transversely to a GI-POF preform. The transverse ray from the preform is then projected on a screen, and its digital image is processed to calculate the refractive index distribution. The calculation is based on a transverse ray simulation, a computer program that we developed in which the refractive index distribution of the preform is determined by comparing the displacement of the transverse ray projected on the screen with the actual measurement.The accuracy of this new measurement method is validated by comparing the refractive index distribution of a GI-POF preform with the refractive index distribution measured by the conventional method using an interferometer. We find that the refractive index distribution measured by this novel method agrees well with that measured by the conventional method.     

Study on measuring refractive index modulation of volume phase holographic gratings

In this paper, we present an approach to measure the refractive index modulation of volume phase holographic gratings (VPHG) by use of its angular selectivity, with the advantage of avoiding the diffraction efficiency errors induced by noise. Based on Kogelnik's coupled wave theory for volume holographic gratings, the wave vectors matching relationship for reflective VPHG at different readout wavelengths is deduced and the diffraction efficiency as a function of readout angle is also obtained. Then an all-fiber experimental system is designed to measure corresponding diffraction efficiency with different readout angles for VPHG recorded in dichromate gelatin. By seeking the Bragg angle where diffraction efficiency is maximum and the blank angle where diffraction efficiency drops to the minimum value, the refractive index modulation can be calculated. The experiment results proves the feasibility of the method.     

Influence of bottom topography on the propagation of linear shallow water waves: an exact approach based on the invariant imbedding method

The wave equation for linear shallow water waves propagating over a varying bottom topography has the same form as that for p-polarized electromagnetic waves in inhomogeneous dielectric media. The role played by the dielectric permittivity in the case of electromagnetic waves is played by the inverse water depth. We apply the invariant imbedding theory of wave propagation, which has been developed mainly to study the electromagnetic wave propagation, to linear shallow water waves in the special case where the depth depends on only one coordinate. By comparing the numerical result obtained using our method, when the depth profile is linear, with an exact analytical formula, we demonstrate that our method is numerically reliable. The invariant imbedding method can be used in studying the influence of complicated bottom topography on the propagation of shallow water waves, in a numerically exact manner. We illustrate this by considering the case where a periodic modulation is added to a linear depth profile. Bragg scattering due to the periodic component competes with the tsunami effect due to the linear depth variation. This competition is seen to generate interesting physical effects. We also consider a ridge-type bottom topography and examine the resonant transmission phenomenon associated with the Fabry–Perot effect.     

Study on the instantaneous characteristics of diffracted and transmitted light of static photorefractive grating illuminated by ultra-short pulse laser

Based on Kogelnik's coupled wave theory, the time-domain diffraction and transmission of static PR gratings are theoretically studied when they are illuminated by ultra-short pulse laser. Study shows that the waveforms of the diffracted and transmitted pulses depend on the readout pulse duration, grating spacing, crystal thickness and refractive index modulation. By changing the values of these parameters, the diffracted and transmitted waveforms can be controlled. Also we find there is a displacement of diffracted and transmitted pulse along the time-axis when compared to readout pulse. Conclusions of our study could be used in many areas, such as pulse shaping and signal processing.