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1.
S. Sujecki 《Opto-Electronics Review》2011,19(2):145-150
A rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise
refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that
expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring
node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference
approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of
the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size. 相似文献
2.
We present an efficient algorithm for determining mode eigenvalues as well as field distributions of optical waveguides with two-dimensional transverse refractive index profile. The algorithm is devised with the analytical perturbation correction method combined with the finite difference approximation of Helmoltz's equation. The technique is simple and does not involve solving any eigenvalue equation or matrix formalism. The algorithm reduces abruptly the computation time required for the field convergence to mode, and can calculate any higher-order modes without the need of any pre-conditioning the field w.r.t. waveguide geometry, or calculation of previous order modes and/orthogonalization. The analysis can yield precisely both scalar and polarized modes. By applying it to waveguide problems whose solutions are otherwise known, the efficacy of the method has been established. 相似文献
3.
Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm 总被引:1,自引:0,他引:1
we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of
any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz’s
equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and
can be applied straightforwardly to calculate the guided as well as quasi- or leaky modes of any arbitrary planar structure
without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application,
the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure
and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical
problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy. 相似文献
4.
An electrooptically induced optical waveguide can be formed by applying a DC voltage between electrodes fabricated on the surface of a crystal with strong electrooptic coefficients (for example, strontium barium niobate). Calculations of the refractive index profile and the optical mode size for such waveguides are presented. Approximate solutions for the fundamental mode are used to analyse the power coupling between a single-mode step-profile fibre and these waveguides. The power transmission losses in the straight and S-shaped waveguides are estimated by using a finite-difference beam propagation method (FD-BPM). The calculations predict that a new kind of modulator/switch can be realized with the induced waveguides. The important characteristics of these devices are discussed and compared with LiNbO3 optical waveguide modulators. 相似文献
5.
《Optics Communications》1987,61(1):11-15
A method for the formation of gradient index tapered optical waveguides with predicted shape is proposed and described analytically. The method is applicable for structures fabricated by electric-field assisted ion-exchange in glass. The technique is based on the control of the taper shape by applying a non-uniform electrical field during the waveguide formation process. For experimental verification optical waveguides with tapers were formed by electrically induced migration of K+ ions. An optical coupler based on such a tapered waveguide has demonstrated 1.2° outcoupled beam divergence. The method proposed can be used to form different integrated optical elements, e.g. mode filters, horn structures etc. 相似文献
6.
Fibre mode expansion for 2-D waveguide calculations 总被引:1,自引:0,他引:1
A numerical method is introduced which is devised to calculate the lower-order modes of optical waveguides with two-dimensional
transverse index profiles embedded in a homogeneous cladding medium. We propose a method based on a series expansion using
guided modes of an optical fibre. To test the method, it is applied to a three-layer optical-fibre and the results are compared
with the exact analytical solutions. The error in the calculation of the modal effective indices is found to be less than
10−6. This method allows the modelling of symmetric 2 × 2 completely fused fibre couplers. Effective indices and polarization
corrections are compared with results obtained by the field correction method. The adiabaticity criterion is calculated for
these couplers.
This revised version was published online in November 2006 with corrections to the Cover Date. 相似文献
7.
Sourabh Roy 《Optics Communications》2011,284(13):3280-3287
In this article, we describe a useful technique for calculating modes of practical optical waveguides having two-dimensional arbitrary transverse refractive index profile. The method uses a finite difference platform for evaluating Helmholtz's equation in scalar and semivectorial forms through a field evolution algorithm. The method is straightforward, easy to handle and does not involve any complex analysis or matrix formulation. We tested the accuracy of our analysis approach by applying it on a large number of realistic waveguide problems having known results or results available in the literature. The formulation has facilitated us to study the modal properties, viz., field distribution, birefringence, dispersion and mode effective area, of a variety of practical two-dimensional structures namely, planar structure, coupler, semiconductor optical waveguides, optical fibers and arbitrary profile microstructured fibers which are uniquely important in photonics and guided-wave devices. The algorithm will therefore be very useful in designing and studying any arbitrary-structure waveguides, and to explore new geometry and properties. 相似文献
8.
Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation
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Based on the polynomial interpolation, a new finite difference (FD)
method in solving the full-vectorial guided-modes for step-index optical
waveguides is
proposed. The discontinuities of the normal components of the electric
field across abrupt dielectric interfaces are considered in the absence of
the limitations of scalar and semivectorial approximation, and the present
FD scheme can be applied to both uniform and non-uniform mesh grids. The
modal propagation constants and field distributions for buried rectangular
waveguides and optical rib waveguides are presented. The hybrid nature of
the vectorial modes is demonstrated and the singular behaviours of the minor
field components in the corners are observed. Moreover, solutions are in good
agreement with those published early, which tests the validity of the
present approach. 相似文献
9.
10.
Ya Li Zhang Ning Hua Zhu Ji Min Wen E. Y. B. Pun P. S. Chung 《Optical and Quantum Electronics》2007,39(15):1289-1296
The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+–Na+ ion-exchanged Er3+–Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite–Gaussian functions as the trial field distribution are
determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with
those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions
of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization
of Er3+–Yb3+ ions co-doped waveguides. 相似文献
11.
WKB analysis of graded-index anisotropic optical waveguides is briefly presented. The angular dependencies of the propagation characteristics of both guided and semileaky modes are calculated numerically for the out-diffused and in-diffused LiNbO3 waveguides with parabolic index profile. The results for the out-diffused waveguide are compared with those obtained from the rigorous theory and the applicability of the WKG method is discussed for semileaky mode loss calculations. The angular dependence of the propagation constants of a TiO2-diffused LiNbO3 waveguide is demonstrated experimentally, too. 相似文献
12.
Circular Fourier analysis of modes in optical waveguides under critical and supercritical conditions
An extension of the circular Fourier analysis of the mode field is presented that makes it possible to obtain a successively correctable solution to the scalar waveguide problem posed for 3D optical waveguides. The critical frequencies of rectangular and elliptic waveguides, as well as the characteristics of leaky modes in microstructural optical fibers formed by elliptical air channels, are studied. 相似文献
13.
基于变量变换伽辽金法(VTGM),建立了半矢量分析光波导本征值问题的数理模型;获得了矩形光波导、脊形光波导的本征模的模场分布及归一化传播常数,计算结果和已发表的结果非常接近.半矢量VTGM采用平面映射边界条件,避免了边界截断,又能反映模场的偏振特性,是一种较为理想的光子器件分析方法. 相似文献
14.
《Superlattices and Microstructures》1996,19(1):39-45
An extremely large electro-optic coefficient in asymmetric quantum well systems has been inferred from optical rectification measurements. To date, however, a direct measurement of the electro-optic coefficient in these materials has not been performed. We present a method to directly measure the electro-optic coefficient in an asymmetric quantum well systemconsisting of 30 Å GaAs wells, 65 Å Al(0.20)Ga(0.80)As step barriers, and 500 Å Al(0.40)Ga(0.60)As barriers. The devices consist of short waveguides with asymmetric quantum well cores. The waveguide endfaces are polished to form Fabry–Perot cavities. Electrodes are deposited running parallel to the waveguides to apply electric fields. The waveguides are analyzed using a Fourier transform infrared spectrometer. Interference fringes are observed in the reflected spectra at room temperature. The fringe spacing yields the refractive index of the material, while plots of the refractive index versus applied electric field yield the electro-optic coefficient. Absorption measurements through these waveguides showed the characteristic polarization dependent intersubband absorption. Because the electrodes appeared to be Schottky like, a large voltage was applied across the device and the voltage across the quantum wells was estimated from the device leakage current and the current-voltage characteristics of a similar device structure after scaling for length, area, and doping. There may be some uncertainty in this approximation. The maximum applied electric field is estimated to be 2.3 kV cm−1. No anomalous effects were observed in the Fabry–Perot fringe pattern in the presence of this electric field, indicating the electro-optic coefficient in these waveguides is most likely less than 0.9 nm V−1over a wide wavelength range. Clearly, however, measurements need to be performed at higher electric fields to accurately measure the electro-optic coefficient. 相似文献
15.
16.
采用离子交换法制备了Rb:KTP晶体光波导,在不同波长的耦合光下测量了TE和TM偏振波导模式的有效折射率,拟合了波导层折射率的余误差函数分布,证明了波导折射率增量的各向异性,给出了其色散关系;最后计算并讨论了Rb:KTP波导的扩散特性。 相似文献
17.
对Bragg光纤中包层制造误差对导模特性的影响进行了深入的分析和研究,给出了一般N层波导中模式场标量波动方程求解的传输矩阵方法,并将其应用在Bragg光纤模式场的分析当中。分别研究了Bragg包层存在折射率误差和厚度误差时对光纤基模模式场的有效折射率、模场半径和芯区功率占比的影响,并利用统计的方法分析了不同制作误差时导模特性的相对变化。折射率误差在1‰的水平时,基模有效折射率、模场半径和芯区功率占比的方差水平为1.55×10~(-4)、1.04×10~(-1)和1.79×10~(-2);厚度误差在2%的水平时模式场参量的方差水平分别为3.61×10~(-5)、1.84×10~(-2)和2.35×10~(-3)。 相似文献
18.
I. Savatinova E. Nadjakov L. Mashev 《Applied Physics A: Materials Science & Processing》1977,12(3):293-296
An improved method for the reconstruction of diffused waveguide index profiles from experimental mode spectra is proposed.
The method uses a parabolic approximation between successive points. It is tested on the example of an exponential profile,
and applied to the reconstruction of index profiles in Ag+ ion-exchanged waveguides from measured mode spectra. This method appears to work well also in the cases of very few mode
wave-guides. 相似文献
19.
Kambiz Abedi Vahid Ahmadi Mohammad Kazem Moravvej-Farshi 《Optical and Quantum Electronics》2009,41(10):719-733
The finite difference method is exploited for a full-vectorial analysis of mushroom-type waveguides for traveling wave electroabsorption
modulators (TWEAM) based on asymmetric intra-step-barrier coupled double strained quantum wells (AICD-SQW). In this analysis,
the discontinuities of the normal components of the electric field across abrupt dielectric interfaces which are known as
the limitations of scalar and semivectorial approximation methods are considered. The optical field distributions in mushroom-type
TWEAM based on AICD-SQW and conventional ridge-type TWEAM of the same active region for 1.55 μm operation are presented. The
important parameters in the high-frequency TWEAM design such as optical effective index which defines optical velocity and
transverse mode confinement factor are calculated. Then, the transmission line microwave properties (microwave index, microwave
loss, and characteristic impedance) of TWEAMs are obtained. The modulation response of mushroom-type TWEAM is calculated using
circuit model by considering interaction between microwave and optical fields in waveguide and compared with conventional
ridge-type TWEAM. It is found that increasing the width of p-cladding layer with the same i-layer to reduce the resistance
in p-i-n mushroom-type waveguide of TWEAM based on AICD-SQW can improve the microwave propagation loss and thus the high-speed
electro-optical response. 相似文献
20.
In this paper, the fabrication and characterization of polyethylene terephatate (PET) thin film integrated optical waveguide is presented. Dip-coating technique has been used to fabricate the optical waveguide using PET. Various waveguide properties, such as mode effective refractive index, optical loss, dispersion and waveguide thickness as a function of temperature of waveguides have been reported. The optical loss are found to be <1 dB cm–1. 相似文献