Fourier modal methods for modeling optical dielectric waveguides

This work contains new materials relative to the use of Fourier expansion techniques, also called plane-wave expansion techniques, for modelling normal modes of optical waveguides. Two rigorous fully vectorial methods are presented and benchmarked for a classical rib waveguide geometry well studied in the literature. The first method relies on a pole extraction and on a one-dimensional expansion scheme. A four-digit accuracy for the normalized propagation constant B is obtained for the dominant TE and TM modes of the benchmark problem and for a small number of retained Fourier harmonics. Better accuracy is anticipated for larger truncation ranks. The second method relies on a two-dimensional expansion scheme in Fourier space and provides a three-digit accuracy for the normalized propagation constant.     

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.     

Complex FEM modal solver of optical waveguides with PML boundary conditions

A full-wave modal analysis of two-dimensional, lossy and anisotropic optical waveguides using the finite element method (FEM) is presented. In order to describe the behavior of radiating fields, anisotropic perfectly matched layer boundary conditions are applied for the first time in modal solvers. The approach has been implemented using high order edge elements. The resulting sparse eigenvalue algebraic problem is solved through the Arnoldi method. Application to an antiresonant reflecting optical waveguide is reported.     

Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

AbstactAbstact This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.     

Engineering transverse Bragg resonance waveguides for large modal volume lasers

We recently analyzed a new class of laser amplifier based on transverse Bragg reflection. We show that the unique properties of Bragg confinement make it possible through modal loss discrimination to achieve single-transverse-mode operation with transverse modal size that is an order of magnitude larger than in lasers that depend on total internal reflection for transverse confinement.     

Zero-birefringence photosensitive polyimides for optical waveguides

Zero-birefringence (delta n < 1 x 10(-6)) photosensitive fluorinated polyimides are synthesized for use in polymer optical waveguides. To obtain zero birefringence, the UV exposure time and copolymer content of photosensitive polyimides are controlled. Zero birefringence combined with photoprocessing of the material has excellent potential for applications in high-performance wavelength division multiplexing components such as polarization-independent arrayed waveguide gratings and Bragg wavelength filters.     

Athermal waveguides for optical communication wavelengths

We report on the design, fabrication, and characterization of temperature insensitive strip silicon-on-insulator racetrack resonators. The influence of various parameters, such as waveguide width, waveguide height, ring radius, coupling length, ring gap, and operating wavelength, on temperature-dependent wavelength shift is examined. A resonant wavelength shift of 0.2 pm/K at a 1550 nm wavelength is measured for 335 nm × 220 nm waveguides. A significant reduction of waveguide propagation losses, improved ring Q value, and higher extinction ratio are obtained after overlaying the silicon waveguides with a polymer cladding.     

CdTe epilayers for uses in optical waveguides

CdTe epilayers have been grown by vapor phase epitaxy (VPE) on glass, MgO, sapphire, LiNbO₃ and mica substrates. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) studies show the good structural quality of the epilayers. In these epilayers, a few optical modes were excited with a 1.33-μm laser. The measured propagation losses were in the range between 5 dB/cm and less than 0.5 dB/cm. From dark-mode m-lines, the epilayer thickness was found to be in the 1–3 μm range, in good accord with that obtained by SEM measurements. The refractive index obtained from the fitting is also in good accord with that of bulk CdTe. Received: 7 October 1999 / Accepted: 13 March 2000 / Published online: 5 July 2000     

Organic crystals growth for optical channel waveguides

Optical channel waveguides of meta-nitroaniline (m-NA) crystal, which has potential applications to nonlinear optical devices, have been fabricated on glass substrates having fine grooves. The crystal growth was performed by zone-melting, scanning a CO₂ laser beam along the grooves filled with the polycrystal m-NA. Optical and X-ray observations showed that zone-melting changed the polycrystalline state to a single crystalline state with the 〈001〉 direction along the groove. The scattering loss for a 5 mm-long m-NA crystal waveguide (100 μm both in width and in depth) was found to decrease from 50 dB to 2.5 dB with this process.     

Theory of optical waveguides

This report summarizes the activities at the 3rd International Workshop on Optical Waveguide Theory, held at the Scuola Superiore Guglielmo Reiss Romoli, L'Aquila, Italy, on 9–11 September, 1978.     

Complex coupled-mode theory for tapered optical waveguides

A coupled-mode formulation based on complex local modes is developed for tapered and longitudinally varying optical waveguides. Different from the conventional coupled-mode theory that requires integration over the entire spectrum of radiation modes, the new formulation treats the radiation fields via discrete complex modes similarly to the guided modes. Accuracy, convergence, and scope of validity for the solutions of the complex coupled-mode equations are investigated in detail for a typical single-mode waveguide taper. It is demonstrated that the complex coupled-mode theory has overcome the difficulties of the conventional theory in simulation of radiation field effects while preserving the simplicity and intuitiveness of this popular method.     

Measurements on high-bandwidth optical waveguides

Frequency response measurements on six high-bandwidth optical waveguides made by the doped deposited silica process are reported. One of these had an extrapolated bandwidth in excess of 3 GHz-km. From plane wave measurements the actual or optimum waveguide profile may be determined given the other. Data taken on a germanium borosilicate waveguide is in agreement with interference measurements.     

Leaky modes in optical waveguides

Solutions of the scalar wave equation are presented giving, explicitly, the excitation and subsequent attenuation of leaky modes in optical waveguides.     

Numerical analyses of optical couplers for planar waveguides

The paper presents the results of numerical analyses of optical structures realized in the form of planar waveguides made of materials with high values of the refractive index n ??1.85. The analysed structures consist of a waveguide and input-output systems. Input-output couplers are realized in the form of prisms as well as Bragg??s grating couplers. Numerical investigations were carried out by applying the finite difference time domain (FDTD) method.     

Nonlinear planar asymmetrical optical waveguides for sensing applications

This paper provides a theoretical analysis for TE polarized waves guided by a linear film surrounded by two asymmetrical nonlinear media for sensing applications. The sensitivity of the proposed sensor is derived. The conditions required for the sensor to exhibit its maximum sensitivity are presented. This analysis covers the case when the measurand is homogeneously distributed in the covering medium. We show that nonlinear sensors have sensitivities higher than those of linear sensors. The authors believe that optical sensing can be improved by introducing nonlinear waveguides.     

Dichroic optical waveguides and lasers

The transverse structure of modes in optical waveguides and resonators filled with dichroic media is investigated. Two families of Hermite-Gaussian modes, corresponding to two orthogonal polarizations of radiation, are found for transversely one-dimensional field distributions and for approximating the characteristics of the medium by quadratic functions of the transverse coordinate. Angular selectivity is displayed by extraordinary waves and is manifested in a decrease in the increment of the mode upon an increase in the mode number. With account of the absence of deformation in the lowest mode due to selection, this implies that resonators containing dichroic media (including photon crystals) are promising for reducing the angular divergence of laser beams.