A comparison of approximate methods for calculation of rectangular dielectric waveguides

Physical Problems Institute, Academy of Sciences of the USSR. Translated from Isvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 1, pp. 93–97, January, 1990.     

Attenuation coefficient of single-mode periodic waveguides

It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate coefficient α=-?ln(T)?/L. In this Letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the group velocity decreases. This result, that contradicts common beliefs and experimental practices aiming at measuring α, is supported by a theoretical study of light transport in the limit of very small imperfections, and by numerical results obtained for two waveguide geometries that offer contrasted damping behaviors.     

On the scalar modal analysis of optical waveguides using approximate methods

We have discussed the approximate methods which are used for obtaining scalar guided modes of optical waveguides. The methods include the perturbation method, the variational method including the Rayleigh-Ritz method, and the Galerkin and the collocation method. The main purpose of this paper is to discuss the inter-relationships and equivalences of these methods, and to bring out the fact that these relationships have, in fact, not been recognized in the guided wave optics literature, although in the numerical electromagnetics and applied mathematics literature some of these relationships are well known. We have also pointed out specific examples where, due to this lack of recognition of relationships, there are repetitions in the literature. In particular, we have noted that the Rayleigh-Ritz method and the Galerkin method have been used using the same set of basis functions for the same kind of waveguides without recognizing the existing literature. We have also reported for the first time an explicit relationship between the Galerkin method and the collocation method. This relationship also points out in which cases one method is more accurate and/or numerically efficient than the other. Another interesting relationship explored is that between the perturbation method and the variational method.     

Silicon-based rectangular hollow integrated waveguides

This paper describes the simulation, fabrication and characterization of silicon-based rectangular hollow waveguides. Numerical evaluation of such structures has been done using both modal propagation and ray tracing, low total losses and multimodal behavior, even for small core sizes, are predicted. Since light propagation in rectangular hollow waveguides strongly depends on the Fresnel coefficients at the facets, the technological processes have been optimized to obtain wall angles close to 89° and wall and base average roughness of 57 nm and <5 nm, respectively. Hence, roughness is negligible to the working wavelength (678 nm). Measured waveguides show total losses close to 6.0 dB for 3.0 cm length. The non-lineal response due to mode filtering in hollow waveguides has also been experimentally observed. Finally, loss simulations and measurements are in agreement, especially for the widest waveguides. For thinner structures, the reduction of the depth due to the DRIE process, together with the blundering of the vertices, causes a dramatic attenuation increase. All these effects should be taken into consideration when defining hollow structures.     

Coupling of single-mode Ti-diffused LiNbO3 waveguides to single-mode fibers

We report on measurements of the near-field intensity distribution of single-mode T-diffused LiNbO₃ waveguides and on the alignment tolerances when coupled to a single mode fiber. Coupling efficiencies of typically 77 to 87% are calculated and a value as high as 80% has been measured experimentally for a y-cut substrate and TM-like polarisation. The total insertion loss of 1 cm long single-mode Ti-diffused waveguides (c-cut) inserted between single-mode fibers was typically 10 dB.     

Selective transparency of single-mode waveguides with surface scattering

Random surface scattering in a one-mode waveguide is studied for a surface profile that has long-range correlations along the waveguide. Analytical treatment of this scattering shows that, with the proper choice of surface, one can arrange any desired combination of transparent and nontransparent frequency windows. We suggest a method for finding such profiles and demonstrate its effectiveness by making use of direct numerical simulations.     

Silver halide single-mode strip waveguides for the mid-infrared

We report the demonstration of single-mode AgCl(x)Br(1-x) strip waveguides for the mid-infrared (MIR). The waveguides were made by the deposition of AgCl(x)Br(1-x) layers on top of a Si-SiO(2) substrate, followed by photolithographic and lift-off processing. The propagation losses of 20 dB/cm were measured at λ=10.6 μm using the cut-back method. The development of these waveguides is a crucial step toward realizing AgCl(x)Br(1-x) MIR integrated optical circuits, which would be used for applications such as chemical sensing and stellar interferometry.     

Radiation field propagation in low-contrast single-mode optical waveguides

In short waveguides used in integrated optical circuits, the radiation field is often present in the guiding region of a waveguide as well as the guided modes. We show that this can be investigated efficiently by extracting the radiation part from the total input field and simulating its evolution along the waveguide by use of the beam propagation method. The results are presented for a single-mode waveguide and a waveguide junction excited by a Gaussian beam. For a noncentred excitation, a considerable fraction of the radiation power is still in the guiding region after propagation over several tens of micrometres, and can be coupled to guided modes past the junction.     

Tees on partially filled rectangular waveguides

We propose an analytical solution of the problem of determination of external parameters of T-shaped E and H tees on partially filled rectangular waveguides. The solution is tested for a particular case of E and H tees on hollow rectangular waveguides and compared with the known solution obtained by the numerical method. Calculated results show good agreement. Numeral results are given for tees on partially filled rectangular waveguides.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 7, pp. 901–909, July, 1996.     

Optical characteristics of bent dielectric rectangular waveguides

Bent rectangular waveguide characteristics are analysed using conformal transformation and four-layered waveguide approximation. Using this method the physical model is clear, the optical characteristic expressions given are uncomplicated and the computed result is in good agreement with the results of Marcatili and Marcuse.     

Turnstile coupling of rectangular and circular waveguides

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1137–1143, September, 1989.     

An accurate variational analysis of single-mode diffused channel waveguides

We present a procedure based on the variational principle to obtain the modal propagation characteristics of single-mode diffused channel waveguides with arbitrary index profiles. The only assumption in our method, in addition to the scalar approximation, is that the trial field is separable along the depth and the width directions. The method is iterative, with each cycle of iteration requiring the solution of two planar waveguide propagation problems. The convergence is usually achieved within 2–3 cycles of iteration. Comparisons with other methods show that our method gives much better accuracy.     

A new theory of rectangular optical waveguides

A new theoretical treatment of the dispersion theory for rectangular optical waveguides is presented. The theoretical basis of the effective dielectric constant method is investigated, and it shows how corrections can be calculated systematically. The result is a new set of eigenvalue equations, simple in form, and which provide very accurate values for the propagation constant.     

改进的光波导标量近似有限元分析

本文首次将波矢量的匹配条件应用于标量近似有限元法求解条形波导,从而将二维问题简化成两个一维问题.其结果除了具有标量近似有限元法的一切优点外,还为节省计算机的存储和时间提供了一条新的途径.     

Systematic design of single-mode coupled-resonator optical waveguides in photonic crystals

By establishing a direct relation between the dispersion and the field profile of a coupled-resonator optical waveguide (CROW) and those of its constituent cavities, we present a systematic method for the design of a single-mode CROW and for control of its dispersion. The procedure includes the design of a single-mode cavity and control of its frequency by engineering its structure. Then, by chaining these cavities in the proper direction and at an appropriate distance, we achieve the desired dispersion for the CROW.