Group velocity of modes and pulse distortion in dielectric optical waveguides

After a brief summary of the main factors causing pulse distortion in optical fibres, expressions are derived for phase velocity, group velocity and dispersion, that is velocity variation with frequency, of each mode. The analysis is carried out by making extensive use of the functiony(x) (y andx being the arguments of the first and second kind Bessel functions that appear in the solutions of Maxwell equations), that we call characteristic function. By using this function we obtain particularly simple and compact formulas that make easier the analysis of the behaviour of velocity and dispersion near and far from cut-off. It will also be seen that the ratio between the power propagating in the core,W ₁, and the power in the cladding,W ₂, for each mode takes a very simple form if expressed by means of the characteristic function: this fact permits a direct relation to be found between group velocity and power flow in an optical fibre. The study of the ratioW ₁/W ₂ will show that, contrary to expectation, for some modes, a substantial fraction of energy travels inside the core, even near cut-off. Expressions are given forW ₁/W ₂ at cut-off, and far from cut-off. Plots of velocity and dispersion are shown. On the grounds of the obtained results pulse distortion in optical fibres is discussed.     

Tunnelling leaky modes on optical waveguides

The lossless dielectric waveguide of circular cross section with an index of refraction greater than its surround supports trapped modes in addition to two subclasses of leaky modes: refracting and tunnelling modes. Refracting modes leak because their fields are formed by waves that undergo refraction at the core-cladding interface. Tunnelling modes leak because their fields are formed by waves that undergo a form of electromagnetic tunnelling at the core-cladding interface due to the curvature of its cross section. Tunnelling modes have a very slow leakage compared to refracting modes and are therefore important for the understanding of propagation in multimode, optical waveguides of circular cross section.     

Coupled surface polariton with guided wave polariton modes in asymmetric metal clad dielectric waveguides

It is emphasized that in metal-dielectric layered systems with a thin metallic layer, surface plasmon-polaritons (SP) can couple with guided wave polaritons (GWP) and form new hybrid modes with properties of both SP and GWP. This is illustrated by analyzing the properties of electromagnetic modes in an asymmetric metal-clad-dielectric-slab waveguide and their dependence on the thickness of metal cladding.     

电压调控多种金属膜波导特性研究

采用自由空间耦合的方法,激发双面金属包覆波导中的超高阶导模,通过在双面金属包覆介质波导的两个金属膜上加不同的电压,改变导波层铌酸锂的厚度和折射率,得到不同参数下的衰减全反射谱,从而验证超高阶导模的偏振不灵敏性及对导波层厚度和折射率十分灵敏的特殊性质,实验结果与理论相吻合。比较相同条件下反射率的变化,得到铝包覆波导的灵敏度要高于金包覆波导。所得结果对集成光电子器件的研制有一定的参考价值。     

Experimental analysis of metal coated dielectric waveguides

This paper concerns the experimental characteristics of metal coated dielectric waveguides with a rectangular surface corrugation. Waveguide are designed to operate at a second Bragg frequency of 90 GHz. The period, height and the duty cycle of a rectangular grating were calculated using the chosen frequency. A metallic layer of aluminum is sputtered on one side of the slab waveguide. The purpose of the metallic layer is to simulate a layer of high density plasma on the surface of the waveguide similar to that obtained by optical excitation of semiconductor structures. Experiments were performed to examine the far field radiation pattern, attenuation constant and the dispersion relation. Due to the presence of the plasma layer there will be an angular shift in the far field radiation pattern. We have observed angular shifts of about 20 in the radiation pattern of the waveguide before and after coating. Measurements are made in the frequency range of 88–95 GHz. This waveguide structure can be used to design an electronically steerable antenna and an electronic phase shifter operating in the millimeter-wave frequency band.Supported in part by the Army Research Office.     

Vector modes of rectangular-core dielectric waveguides: An improved perturbation approach

We present an improved analysis to obtain vector modes of a rectangular-core waveguide (RCW) structure whose dielectric constant profile is separable in x and y coordinates. Using this analysis, a perturbation method is then developed to obtain vector modes of a practical RCW. The propagation constants so obtained for a fully-buried and a ridge RCW structure using the present analysis are found to be in better agreement with reported numerical values than the ones obtained with an earlier reported perturbation approach [Kumar et al., Opt. Lett. 8 (1983) 63].     

Numerical analysis of the three co-directional guided modes in optical period dielectric waveguides using inverse Gaussian apodization

We describe and analyze the inverse Gaussian apodization among the three co-directional guided modes using the supermodes theory and the transfer matrix method. The propagation condition is related to the two phase matching distribution induced by two long period co-spatial gratings. It is seen that one input mode can be converted into another two modes with each mode having two peaks at its transmission spectrum. Through adopting the inverse Gaussian apodization, the input mode A turns to having two peaks while the converted mode B has six peaks and mode C has three peaks around the central frequency in the transmission spectrum. Of particular interest is when adjusting the maximum coupling apodization strength from 100 to 1500, the frequency space in mode A changes nearly linearly from 340 GHz to 5100 GHz which is twice of the mode B at each coupling strength, while the mode C can be turned nearly linearly from 350 GHz to 5200 GHz. Additionally, the power at the central frequency of input mode A will almost totally move to the converted mode C. This kind of design can form the basis for a new generation of multi-wavelength-tunable bandpass optical filtering mode converting, add/drop multiplexing and optical switching.     

"Ideal" optical delay lines based on tailored-coupling and reflecting, coupled-resonator optical waveguides

We present a design of "ideal" optical delay lines (i.e., constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs. We present a simple formalism for deriving the time-domain coupling coefficients and convert these coefficients to field coupling coefficients of ring resonators. The reflecting CROWs possess a delay-bandwidth product of 0.5 per resonator, larger than that of any kind of transmitting CROW. In the presence of uniform gain, the gain enhanced by slow light propagation and the constant group delay result in efficient and dispersion-free amplifiers.     

Exact transcendental equation for scalar modes of rectangular dielectric waveguides

Conclusion A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.     

Ultrasmall optical logic gates based on silicon periodic dielectric waveguides

An ultrasmall silicon periodic dielectric waveguides-based multimode interference all-optical logic gate has been proposed. The device consists of three 205 nm wide single-mode input waveguides, a 1.1 μm wide and 5.5 μm long multimode interference waveguide, and three 205 nm wide single-mode output waveguides. The total length and width of the device are 13.7 μm and 3.2 μm, respectively. By changing the states of the input optical signals and/or control signals launched into the device, multifunctional logic functions including OR, NAND, NOR, and NOT gates are performed, and each logic function can be realized at a specific output waveguide in accordance with the launched control signals. The ultrasmall multifunctional logic device has potential applications in high density photonic integrated circuits.     

On the accuracy of the WKB approximation in optical dielectric waveguides

Eigenvalues and field distributions for optical waveguides obtained from the WKB approximation have been compared with those found from geometrical optics and from more rigorous weakly-guiding LP mode theories in the cases of the step-index and parabolic-index profiles. In all cases it is found that the zero-order WKB approximation yields very accurate eigenvalues provided care is taken in the choice of phase factors in the eigenvalue equation. Expressions are deduced for the required phase factors for guides of arbitrary index profile in both two- and three-dimensions, and physical interpretations are given in terms of ray optics. The first-order WKB field distributions are found to give good agreement with the mode fields everywhere except in the vicinity of the caustics.     

任意截面介质波导导模的叠代矩量法分析

本文提出用以计算任意截面介质波导色散关系的叠代矩量法,并给出用叠代矩量法计算椭圆介质波导、三角形波导、平切圆波导、蛋形截面波导等的传播特性的实例.计算结果与有限元法、点匹配法等精确数值计算结果符合很好.本方法简便易行,计算工作量较小.     

Geometrical theory of coupling errors in dielectric optical waveguides

The power losses due to coupling errors between source and fibre or two fibres are evaluated by means of a geometrical analysis of the coupling between an emitting and a detecting surfac. The theory is apllied to actual cases of separation, displacement and misalignment between a uniformly emitting lambertian source and fibre, and between two fibres. Good agreement is obtained with experimental results found in the literature.     

Coupling coefficients of synchronous modes on two arbitrarily-shaped weakly-guiding optical waveguides

Usually, coupling coefficients of parallel weakly-guiding waveguides of arbitrary crosssectional shape with uniform infinite cladding are calculated via two-dimensional overlap integrals of the refractive-index distribution of the concerned waveguide core and the field distributions of the two coupling isolated-core modes. In this paper it is shown that, in the case of synchronous coupled modes, the calculation can be reduced to the evaluation of a line integral involving only the field functions. Convenient formulations are obtained for typical forms of the field representation.     

Control of birefringence using polymer as cladding layer in optical planar waveguides

We demonstrate theoretically that a polymer layer, when used as cladding layer for silica-based planar optical waveguides on a silicon substrate, can substantially reduce birefringence. Multilayer planar optical waveguides usually exhibit stresses that are caused by thermal-induced strains that originate from the bonding of the layers, in addition to intrinsic strains. Effect of various intrinsic properties on thermal stress as a function of thickness of the guiding layer is studied. It is shown that it is possible to achieve the thermal stress free and, hence, the stress-induced birefringence free waveguide devices by proper waveguide designs.     

Frequency response of metal clad planar optical waveguides

The propagation characteristics of metal clad planar optical waveguide as a function of wavelength are investigated theoretically for Al, Ag, and Au. The results obtained show that attenuation of the propagation modes in these guides is highly dependent on wavelength, which can be used to design an efficient integrated optical waveguide polarizer with high extinction ratios, or to select the wavelength for the surface plasmon based metal clad optical waveguide sensors. It is observed that Al is the only metal that still supports the surface plasmons in the UV region.     

A perturbation analysis of modes in diffused optical waveguides with Gaussian index profile

Inclusion of a quartic term with adjustable coefficient in the Taylor expansion approximation to gaussian index profiles of diffused optical waveguides is shown to provide an improved approximation to the true gaussian curve to beyond the e-folding depth. A first-order perturbation to the square-law “harmonic oscillator” solutions is applied to improve the calculations of mode indexes and to illustrate the manner in which the corrected wave functions are extended deeper into the substrate.     

涂覆石墨烯的椭圆形电介质纳米线光波导的模式特性分析

设计了一种涂覆石墨烯的椭圆形电介质纳米线光波导.采用分离变量法,在椭圆柱坐标系中,借助Mathieu函数,得到了色散方程.通过数值求解色散方程,可以得到模式的有效折射率和场分布,从而得到模式的传播长度.研究了工作波长、结构参数以及石墨烯的费米能对模式特性的影响,并给出了前五个模式的品质因数.计算表明,当波长从4.3μm增加到8.8μm,这5个模式的有效折射率的实部减小,基模和一阶模的传播长度增大,二阶模的传播长度先增大后减小.当改变纳米线结构参数半长轴和半短轴时,对基模和一阶模的模式特性影响较小,对二阶模的模式特性影响较大.当石墨烯的费米能从0.45 eV增加到0.72 eV时,有效折射率的实部减小,传播长度可以达到2μm左右.分离变量法得到的结果与有限元方法得到的结果完全一致.本文工作可以为基于涂覆石墨烯的电介质纳米线的光波导的设计、制作和应用提供理论基础.     

Coupled edge plasmon modes of metal/dielectric multi-wedges

We present a metallic/dielectric multi-wedge model to investigate the coupled edge plasmon modes （CEPMs）, where all wedges have a common edge and the wave propagates along the edge direction. A general theoretical method valid to many practical structures is presented. The analytical dispersion relations of CEPMs in these structures are obtained and the CEPM properties are discussed with numerical results and the dispersion relations. For all structures mentioned in this paper, we find that the structures containing an even number of metallic wedges have four CEPMs and those with an odd-number of metallic wedges have two CEPMs. Further, the periodic structures containing any odd number of periods and any even number of periods possess their common CEPMs, respectively.