A Modified full-vectorial finite-difference beam propagation method based on H-fields for optical waveguides with step-index profiles

A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present method.     

Analytical solution of the scalar wave equation for slightly deformed optical Bragg waveguide

Using a simple analytical method, we study the electromagnetic-wave propagation in an optical Bragg waveguide which is slightly deformed at one side. We show the results of computations in the form of dispersion curves and provide a comparison with standard circular Bragg waveguides and step-index circular waveguides. We show that the correspondence between the cutoff V values for the standard step-index fiber and the new Bragg waveguide, which is slightly flattened on one side, is quite close for the lowest mode under the weak guidance condition.     

Propagation of p-polarized waves in a linearly graded index film surrounded by negative index materials

The theory of step-index waveguides is well-established. Most practical slab waveguide structures have a graded-index profile. The basic properties of graded-index planar waveguide structures are similar to those of step-index waveguides with subtle differences. The most common types of graded-index slab waveguides are linearly and exponentially graded-index profiles. We here treat linearly graded-index slab waveguide. In this work, a three-layer waveguide structure with linearly graded-index film is considered. We assume three structures: the first structure comprises a left-handed material (LHM) cladding, the second structure contains a LHM substrate layer and the third has a LHM cladding and substrate. Closed-form expressions for electric and magnetic fields and the characteristic equation are derived. The three normalized parameters: the asymmetry coefficient (a), the normalized film thickness (V) and the normalized guide index (b) are used to study the dispersion properties of the proposed slab waveguide structure.     

Multicolor Talbot effect and control of polychromatic light patterns in modulated photonic lattices

We analyze propagation of polychromatic light patterns in modulated photonic lattices created with arrays of periodically curved coupled optical waveguides. We demonstrate that in waveguide arrays with specially designed modulation periodic recurrences of input light patterns produced by white-light and supercontinuum sources can be realized, e.g., through multicolor Talbot effect.     

Numerical Method of Determining the Cutoff Frequency and Mode Speckle Pattern of Optical Waveguides

Based on a numerical solution of the nonstationary wave equation, an algorithm for determining the eigenfunctions and eigenvalues of the LP_im modes of axially symmetric optical waveguides is suggested. The cutoff frequency of the LP₁₁ mode of different waveguides is determined using the algorithm constructed. The results obtained are compared with the well-known analytical formulas and results of numerical calculations for the equivalent step-index waveguide model. Based on the analytical results obtained, an eigenfunction and eigenvalue search algorithm is suggested for a waveguide with a two-dimensional refractive index profile (in particular, for an axially nonsymmetric waveguide).__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 11–16, January, 2005.     

A Novel Three-Dimensional Wide-Angle Beam Propagation Method Based on Split-Step Fast Fourier Transform

A novel three-dimensional wide-angle beam propagation method based on the split-step fast Fourier transform is developed. The formulation is based on the three-dimensional Helmholtz wave equation. Each propagation step is performed by utilizing both the FFT and split-step scheme. The solution of Helmholtz wave equation does not make the slowly varying envelope and one-way propagation approximations. To validate the efficiency and accuracy, numerical results for a propagation beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms.     

Analysis of electrooptically induced waveguides in strontium barium niobate and optical modulators

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.     

用基于磁场的改进型有限差分法分析光波导的全矢量本征模

提出一种改进的有限差分法,用以求解全矢量磁场波方程,分析光波导承载的全矢量本征模.离散交叉项时,采用与波导结构无关的六点差分格式,考虑磁场分量的导数在芯包分界处的不连续性,比传统四点差分格式有更高的计算精度.分析阶跃型光纤、矩形和脊形光波导的全矢量本征模问题,给出全矢量基模的磁场分布及其归一化传播常数,揭示全矢量本征模的混合特性,所得结果与解析法、高精度模横向谐振法的结果吻合,验证了方法的收敛性与计算精度.     

WKB analysis of guided and semileaky modes in graded-index anisotropic optical waveguides

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.     

Low-loss, damage-resistant optical waveguides in Zn-diffused LiNbO3 by a two-step procedure

In the present work the fabrication of high-quality LiNbO₃ waveguides, based on Zn diffusion from vapor phase using a two-step diffusion process, has been demonstrated. The optical waveguides fabricated using this method have low propagation losses (less than 0.5 dB/cm measured at 633 nm), as a consequence of the high surface quality obtained. High photorefractive damage resistance is reported, and it has been related to the Zn incorporation into the LiNbO₃ crystals. Additional advantages of this waveguide fabrication method due to the low temperature of the process (<900 °C) are to prevent Li out-diffusion and to preserve ferroelectric domain structures. Received: 2 March 2000 / Accepted: 21 June 2000 / Published online: 13 September 2000     

一种模拟倾斜折射率界面光波导的新方法

针对传统离散格式下，束传播方法(BPM)模拟倾斜折射率界面出现的问题，提出了一种简明且易于编程实现的改进方案. 在横向上，通过坐标系变换和插值处理，以新颖的7点差分格式代替传统的5点差分方式；在纵向上，以四阶显式Runge-Kutta方法(RKBPM)代替二阶Crank-Nicholson算法(CNBPM)，避免了求解不规则矩阵方程，从而使计算效率显著提高. 关键词： 束传播方法 Runge-Kutta方法 光波导 脊形波导     

A simple variational analysis of diffused channel waveguides

The variational analysis of Ti:LiNbO₃ strip waveguides is resolved into two related one-dimension problems, which provides a new iterative approach for the calculation of the mode parameters and the propagation constant. The analytical expressions of the local effective index profiles can be obtained from the variational analysis. The parameters of four trial solutions for the fundamental mode in a diffused-channel waveguide have been determined by using the present method. Comparison with results using the effective method shows that these four approximate expressions are accurate enough. It is also shown that this method converges very quickly and is suitable for both diffused channel waveguides and optical waveguides with rectangular cross-section.     

A long-range hybrid THz plasmonic waveguide with low attenuation loss

Numerical solutions are obtained for the proposed novel hybrid terahertz plasmonic waveguide structure, namely the silicon metal silicon (SMS) waveguide. It is shown that the SMS waveguide can overcome the diffraction limit while still maintaining a sizeable propagation length. The geometric dependence of the mode characteristics of this structure is analyzed in detail, showing strong confinement and low loss with propagation lengths exceeding 14 mm at normalized mode areas of 1.72 × 10⁻². By using the FEM method (Comsol), the guiding properties of the hybrid terahertz surface plasmon polariton (HTSPP) waveguide are numerically analyzed at the THz frequency, and a combination of double-structured comparisons of the best features of the terahertz plasmonic waveguide is made. Depending on the height used and how the mode confinement is measured, various modal designs, such as double microwire structures, are developed. The structures indicate that we verified the possibility of low attenuation loss of hybrid THz plasmonics propagation. The effective mode area A_eff, energy distribution, and propagation length L_p versus height for waveguides with Si microwire and SiO₂ are shown. The numerical calculation results reveal a potential for use in applications such as optical force in trapping and transporting biomolecules, and in high-density integrated circuits.     

Dispersion parameters and nonlinear optical properties of silicon nitride rib waveguides

Silicon nitride rib waveguides are numerically studied by use of a full-vectorial mode solver program based on finite difference method. Dispersion parameters, up to the third-order, are computed for waveguides of heights 0.8 μm, 0.9 μm, and 1 μm. Like silicon-on-insulator waveguides, silicon nitride rib waveguides allow us to tailor dispersion parameters at telecom wavelengths. Deeply-etched silicon nitride rib waveguides of height up to 1.5 μm are investigated for correct geometries to achieve polarization independence. The computations lead to a minimum etch depth which can be written as linear function of the waveguide height. Etch-depth and waveguide height dependencies of the nonlinear refractive index coefficient of the silicon nitride are studied. It is shown that third-order optical nonlinearities in silicon nitride rib waveguides can be enhanced by suitable choices of waveguide parameters.     

Enhancing surface plasmon polariton propagation by two-layer dielectric-loaded waveguides on silver surface

We report a study of a two-layer dielectric-loaded surface plasmon polariton waveguide (TDLSPPW) which consisted of two dielectric layers (high-index/low-index) on a silver film. The discontinuity of the electric field at the interfaces resulted in a concentrated field in the low-index region. It efficiently reduced the propagation loss of the surface plasmon polariton mode. The mode fields and corresponding complex propagation constants were calculated by a vector finite-difference method. The propagation properties were measured by a modified near-field optical microscope. It is confirmed that the propagation length of the proposed TDLSPPW was about 1.6 times longer than conventional single-layer SPP waveguides. In addition, a 90^° waveguide turn with 3 μm radius showed that the bending loss was smaller than 2 dB.     

Optical pulse propagation in an irregular waveguide with spatially distributed Kerr-like nonlinearity

A nonstationary two-dimensional problem of propagation of a femtosecond pulse in a planar waveguide comprised of linear and nonlinear sections connected in series is solved using the finite-difference method. The accuracy of the finite-difference techniques is analyzed as applied to solution of stationary and nonstationary two-dimensional quasi-linear equations of light propagation in step-index waveguides. The effects of wave instability on the dynamics of the spatiotemporal pulse distribution in a nonlinear waveguide are studied. It is shown that, due to the retarded nonlinear response of the medium and the dependence of the group velocity of the pulse on its intensity, radiation continuously leaks from the fiber core to the cladding as the pulse propagates along the fiber.     

Loss calculations in bent multimode optical waveguides

We present a straightforward geometric optics method to calculate the power attenuation induced by a circular bend in the axis of a multimode optical waveguide. The method involves tracing of rays and use of generalized power transmission coefficients. Both slab and fibre waveguides (with either step-index or parabolic core profiles) have been considered; the source has been assumed to be Lambertian.     

掩埋型离子交换玻璃光波导的变分分析

用变分法对离子交换法制备的掺铒光波导的传播特性进行了分析,推导出了适用于掩埋型离子交换玻璃沟道光波导中场分布传播常量的变分表达式,构建了场分布的厄米-高斯型试探解,在两种不同实验条件下,采用变分法确定了试探解中的待定参量,获得光波导中的场分布,利用传播常量的变分公式和已确定的场分布计算得到了传播常量和有效折射率。计算数据表明:导波区域的有效折射率稍稍地大于限制层的折射率,说明离子交换法制备的波导器件是弱波导;高的辅助退火电场强度和适当的退火时间下,所制备的光波导可以支持更多光模式的传输。该方法计算过程简洁、快速,计算结果与实验结果吻合。     

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].     

Synthesis of a fluorinated photoresist for optical waveguide devices

A linear fluorinated bis-phenol-A novolac resin (LFAR) for optical waveguide was synthesized based on 4,4′-(hexafluoro-isopropylidene)diphenol, epoxy chloropropane and formaldehyde. Negative fluorinated photoresist (FP) was made by composing the LFAR, diphenyl iodonium salt and solvent. The film, which was made by spin-coating FP, had good UV light lithograph sensitivity, large hardness and high glass transition temperature (T _g >170°C, after crosslinking). Low-loss optical waveguides with very smooth top surface were fabricated from the resulting FP by direct UV exposure and chemical development. For waveguides without upper cladding, the propagation loss of the channel waveguides was measured to be 0.21 dB/cm at 1550 nm.