Thermal strain analysis in optical planar waveguides

For the first time, we derive an analytical form of the thermal-induced strain equation for the waveguide core layer in an optical planar waveguide, which is based on elastic interaction theory in multilayered isotropic structures off the edges by thin-film approximation. This derived equation addresses how material and structural characteristics affect the magnitude and the distribution of the strain. By this equation, the strain-induced birefringence can be reduced or eliminated by proper waveguide design.     

Low-loss bends in planar optical ridge waveguides

Bending losses lower than 0.7 dB for 90° bend sections with radii of curvature as small as 75 μm were measured on silicon-based Al₂O₃ ridge waveguides with SiO₂ cladding layers at a wavelength of 632.8 nm. These values, which are close to the calculated values, are the lowest thus far reported     

Multichannel optical splitters based on planar multimode silica-glass waveguides

The calculated optical characteristics and the technology for the structure formation of multichannel optical splitters are presented. The splitters are based on planar optical waveguides made of silica glass obtained via microwave plasma chemical deposition. Multimode splitters of the 16 × 16 type for the fiber optic data-transmission systems are produced with the use of the planar waveguides.     

Properties of four-layer planar optical waveguides near cutoff

Mode properties of four-layer planar optical waveguides near cutoff are considered. The four-layer structures considered are applicable to waveguiding layers formed on cladding layers above either silicon or gallium arsenide substrates. Perturbation approaches are shown to be accurate except near mode cutoff where a numerical solution of the four-layer equations is required. Numerical calculations of waveguide attenuation due to substrate coupling for thermally nitrided silicon dioxide and for gallium aluminum arsenide waveguides are presented for a variety of layer thicknesses, layer material compositions, and wavelengths. Comparison to some experimental data is included.     

Prism-coupling of light into narrow planar optical waveguides

The efficiency and selectivity of the prism-coupler for exciting single modes in narrow planar optical waveguides is investigated both theoretically and experimentally. A previously published calculation of the coupling efficiency between a plane input wave with finite cross section and a number of waveguide modes, as a function of both the incidence angle and the skew angle, is extended to include the effects of diffraction, which are shown to play a dominant role for small focal widths of the input beam. The theoretical predictions are compared with experimental results obtained at 633 nm on an embedded ridge-type waveguide structure. A number of mechanisms reducing coupling selectivity and stability are discussed, and some practical rules are given for obtaining good stability and selectivity     

Numerical solution of silicon-clad diffused planar optical waveguides

Computer modelling studies indicate that silicon-clad diffused planar optical waveguides exhibit a damped periodic oscillation in their attenuation and phase constant curves and that the attenuation is reduced significantly by reducing the maximum index change.     

Numerical analysis of planar optical waveguides using matrix approach

We present here a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices. We show the applicability of the method for obtaining leakage losses and absorption losses, as well as for calculating beat length in directional couplers. The method involves straightforward 2 × 2 matrix multiplications, and does not require the solutions of any transcendental or differential equations.     

Modal characteristics of bent dual mode planar optical waveguides

Modal characteristics of bent dual-mode planar optical waveguides are obtained. The bending-induced changes in the modal power distribution is found to be quite different for the two modes. Surprisingly, unlike the fundamental mode, bending causes the fractional modal power for the second mode to increase in the inner core-half and to decrease in the outer core-half of the waveguide. Interestingly, this leads to a decrease in effective index of the second mode due to bending at sufficiently high V-values     

Simplified numerical analysis of optical fibres and planar waveguides

A convenient and efficient numerical technique is presented for determining modal properties of an optical fibre or planar waveguide. A simple recurrence relation, suitable for programming on only a pocket calculator, leads to parameters such as group velocity and cutoff wavelengths. The method is particularly useful for analysing single mode fibres, and an example of current interest is given.     

Finite-element solution of planar arbitrarily anisotropic diffused optical waveguides

The finite-element method for propagation in planar anisotropic diffused optical waveguides with arbitrary permittivity tensor is presented. A Galerkin procedure has been introduced to the finite-element formulation, to study both the nonleaky and leaky surface waves. The complex propagation constants are determined as a function of frequency for possible modes of propagation. The accuracy of the method has been checked by calculating the nonleaky and leaky surface waves of Ti-diffused LiNbO3waveguides with Gaussian index profiles. The numerical results of Ti-diffused LiNbO3waveguides with dielectric overlays are also presented and the effects of dielectric overlays on the propagation characteristics for the nonleaky and leaky surface waves are examined.     

A MATRIX METHOD FOR SOLVING PLANAR DIELECTRIC OPTICAL WAVEGUIDES

A matrix method used in multilayer stack of dielectric films is applied-to planar dielectric optical waveguides. A simple and applicable method for obtaining characteristic equation is presented.     

负胶-玻璃复合平面光波导传播特性的研究

本文报导了负胶-玻璃复合平面光波导传播特性的实验研究。测量并归纳了负胶介质薄层对银离子交换玻璃平面波导传播特性影响的实验趋势。介绍了弯曲条载波导的实验研究。     

Superimposed phase gratings in planar optical waveguides forwavelength demultiplexing applications

A theoretical analysis of superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications is developed. Using coupled-mode theory, it is shown that the coupling between the gratings affects diffraction characteristics for output beams of close angular or wavelength separation. Nevertheless, taking into account the coupling effects and adjusting critical parameters, high-performance devices are found to be achievable in carefully designed structures. The authors predict that wavelength demultiplexers having efficiencies larger than 95%, angular and wavelength separation smaller than 0.2° and 20 Å, respectively, and crosstalk attenuation lower than -40 dB are possible     

Fabrication of planar dielectric waveguides with high optical damage threshold

We realized with a simple inexpensive process planar dielectric waveguides for the visible with the following improved properties: The waveguiding layers are mixed oxide films (∼40 percent TiO2in SiO2). They are hard and durable against mechanical and chemical attack. The losses are low and comparable to other planar waveguide materials. The films withstand high energy densities and intensities for pulsed and CW Laser irradiation, respectively.     

Hybrid optical circulator using garnet-quartz composite embedded in planar waveguides

A novel hybrid configuration of optical circulator is presented. A Garnet-Quartz composite (GQC), which is comprised of four quarter-wave plates and Faraday rotator, is embedded into a groove formed across the branching waveguides pair of Mach-Zehnder interferometer. Optical path difference of the pair is 0 rad for forward path, whereas /spl pi/ for backward path with the GQC, realizing nonreciprocal operation. The forward-to-reverse isolation of 16.2-29.8 dB and the insertion loss of 8.8-9.4 dB are obtained.     

Analysis of titanium diffused planar optical waveguides in lithium niobate

Characteristics of titanium indiffused waveguides in lithium niobate have been investigated. The effects of diffusion time, temperature, and ambient atmosphere on mode structure, surface refractive index, and profile, waveguide depth, surface morphology, and composition are described. Similarities and discrepancies between these and any previously published results are discussed and mechanisms for new features proposed. The necessity for fabrication in an oxygen atmosphere at elevated temperatures is demonstrated, and directions for further investigation indicated.     

Properties of single-mode optical planar waveguides with Gaussian index profile

The properties of the fundamental guided mode in planar waveguides having a Gaussian index profile are derived by using an analytical fit to the numerical results obtained from exact solutions. The developed expression for each property has the form of a simple power series which affords improved accuracy when compared to the results obtained from approximate analytical solutions reported to date. The technique proposed here is relatively simple and can be readily extended to apply to the analysis of waveguides having other index profiles.     

General eigenvalue equations for optical planar waveguides witharbitrarily graded-index profiles

Accurate eigenvalue equations for planar waveguides with arbitrarily graded-index profile are derived and expressed in closed forms. A combination of the modified Airy functions and the Wenzel-Kramers-Brillouin (WKB) solutions are employed as field solutions, which turn out to represent almost exact field profiles. The use of new trial solutions enables us to calculate phase shifts at turning points very precisely, allowing us almost exact eigenvalues. It is demonstrated that the results obtained by the proposed method are in excellent agreement with those by the finite element method, achieving significant improvement over the conventional WKB method     

Noise limits in reconstruction of optical parameters ofsilica-based double-layer planar waveguides on silicon

The paper presents a study on the reliability and limits of the downhill simplex algorithm used to reconstruct optical parameters of double-layer silica waveguides from the measured effective indexes. It provides a number of surface plots of the merit function and explains the behavior of the algorithm in practical situations where the measured effective index data are affected by noise     

求解渐变折射率分布平面光波导模式的数值方法

本文用多种数值方法（积分插值法、有限元法及幂法）对具有渐变折射率分布的平面光波导率征方程进行了理论计算。这些方法不仅适用于任意的折射率分布，而且能够达到较高的计算精度。作为一个例子，作者对高斯分布波导进行了具体计算。计算结果表明，Arun Kumar等人用的微扰法是较好的方法。此外，本文作者通过迭代求出了更精确边界条件下的本征模。