Finite-difference method without spurious solutions for thehybrid-mode analysis of diffused channel waveguides

Diffused dielectric channel waveguides with an arbitrarily varying refractive index profile in the cross-sectional plane are analyzed with a rigorous finite-difference method. The method is formulated in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. The analysis includes the complete set of hybrid modes, takes mode-conversion effects and complex waves into account, and allows the immediate inclusion of large index difference levels as well as the two-dimensional continuously varying index profile function without the usual staircase approximation. As an example, dispersion characteristics are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as channel waveguides with refractive index variations having stepped, linear, Gaussian, and exponential function profiles. The theory is verified by comparison with results available from other rigorous methods     

Analysis of optically controlled planar dielectric waveguidesoperating in the millimeter-wave band using FDTD

The finite-difference time-domain (FDTD) technique is applied to the analysis of planar dielectric waveguides controlled by means of an optical beam. This beam, with an appropriate energy, induces a nonuniform plasma in a semiconductor layer deposited on the waveguide core. The resulting effects are analyzed through the phase dispersion characteristics. Due to the complexity of the problem, the FDTD formulation does not allow the calculation of the attenuation characteristic, particularly when the plasma presents an intermediate density, which causes a strong interaction with the guided mode. The simulations shown here suggest that the light beam may have an effective control of the phase response of a single waveguide and of the coupling between two parallel coupled waveguides     

Dispersion characteristics of asymmetric coupled anisotropic dielectric waveguides using FDFD

The formulation is developed in the frequency domain and the finite difference method is used for the numerical solution of the scalar wave equation, written in terms of the transverse components of the magnetic field. As a result a conventional eigenvalue problem is obtained without the presence of spurious modes due to the implicit inclusion of the divergence of the magnetic field equal to zero. The formulation is developed to include biaxial anisotropic dielectrics with an index profile varying arbitrarily in the cross section of the waveguide under analysis. This formulation is then applied to the analysis of the influence on the dispersion characteristics of the dimensions of asymmetric coupled rectangular uniaxial anisotropic dielectric waveguides. As expected, the reduction of the height or the width of one of the rectangular dielectric waveguides causes the dispersion curves to move towards higher frequencies.     

Coupled mode formulation for directional couplers with longitudinalperturbation

A grating-assisted directional coupler is investigated using an improved coupled-mode formulation for multi-waveguide systems with longitudinal perturbation. This approach is capable of handling three-dimensional structures as well as a complex index of refraction and nonisotropic media. The case of two coupled channel waveguides is closely examined, and a numerical analysis is carried out for several cases of slab structures     

Coupled mode theory of parallel waveguides

A new coupled mode formulation for parallel dielectric waveguides is described. The results apply to any guided modes (TE, TM, or hybrid) in waveguides of arbitrary cross-section, dissimilar index, and nonidentical shape. Additional index perturbations not included within the waveguides are encompassed by the theory. Propagation constants and mode patterns for the coupled modes computed according to this theory are shown to agree very well with numerical solutions for the system modes when the latter can be determined. Moreover, the new results are more accurate than those obtained from prior coupled mode formulations. It is shown that even for Iossless guides the coupling coefficients from waveguide"b"to"a"and from"a"to"b,"described by kaband kbarespectively, are not related by their complex conjugates if the guides are not identical.     

A variational finite-difference method for analyzing channel waveguides with arbitrary index profiles

A variational, finite-difference method for computing the normalized propagation constants and the normalized field profiles of channel waveguides with arbitrary index profiles as well as aspect ratios is presented. Mode dispersion curves and the field profiles of the fundamental mode of channel waveguides having profiles of practical interest are included.     

The use of FDTD for the analysis of magnetoplasma channelwaveguides

The finite-difference time-domain (FDTD) method is used for the analysis of magnetoplasma rectangular channel waveguides. Single and parallel-coupled waveguides are considered. The effect of varying the amplitude and the orientation of the bias magnetic field B₀ on the dispersion characteristics of the first modes is examined. However, the FDTD formulation, does not excite evanescent modes for a sufficiently long time interval, particularly when in the presence of the propagating or dynamic modes. As a result, the nonreciprocal properties of these structures, primarily associated with the evanescent modes, could not be investigated     

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.     

A scalar variational conformal mapping technique for weakly guiding dielectric waveguides

A novel approach of combining the finite-element method with the conformal mapping technique is proposed for solving the scalar variational formulas for weakly guiding dielectric waveguides. This approach avoids spurious modes and gives satisfactory results even for modes near cutoff, requiring less computer memory and time. Various specific dielectric structures, such as the rectangular guide, channel guide, and rib guide, are considered to estimate the error associated with the scalar formulation relative to the vectorial formulation. The efficiency of this approach is demonstrated with an analysis of a directional coupler whose coupling properties are described by means of numerical results such as propagation constants, field distributions, etc.     

Coupling between photonic crystal waveguides

A calculation procedure for evaluation of the coupling length of two parallel coupled channel waveguides in a planar photonic crystal is proposed. The first step of the calculation is evaluation of the band structure of a photonic crystal containing two coupled linear defects. The eigenvalue corresponding to eigenstates localized in the linear defect (the waveguide) is split due to the coupling. This splitting is treated within the coupled-mode theory that yields a simple relation between the splitting and the coupling length. The MIT photonic bands code is used to evaluate the coupling between channel waveguides in silicon./sup 1/ These calculations show that in contrast to the finite-difference time-domain approach, the method is effective for three-dimensional light propagation.     

A vectorial boundary element method analysis of integrated optical waveguides

In this paper, a new vectorial boundary element method is introduced and applied to the modal analysis of dielectric waveguides with piecewise homogeneous refractive indexes. The procedure, which is free of spurious modes, determines the full field distribution from the longitudinal fields at the refractive index boundaries. Singular kernels are evaluated through series solutions while the electric field discontinuity at corners is accommodated through either a grid refinement technique or a semianalytic approach. Our formalism generates propagation constants and modal field distributions for several representative refractive index profiles with far higher accuracy than standard finite-difference or finite-element procedures.     

Impedance boundary method of moments for accurate and efficientanalysis of planar graded-index optical waveguides

An impedance boundary method of moments (IBMOM) is proposed to accurately and efficiently compute the propagation characteristics including the number of guided modes of general graded-index dielectric slab waveguide structures. The method is based on Galerkin's procedure in the method of moments and employs the exact impedance boundary condition at the interfaces between the graded-index region and constant-index cladding. Legendre polynomials are utilized in the field expansion. Computational results are shown for waveguides with various inhomogeneous refractive index profiles. The results indicate that typically five Legendre polynomials are sufficient for accurate solutions of the dominant TE and TM modes in optical waveguides having a finite region of inhomogeneous refractive index. Diffused optical waveguides with untruncated index profiles as well as coupled dielectric waveguides can be accurately analyzed using ten Legendre polynomials     

Characterization of Silver/Polystyrene (PS)-Coated Hollow Glass Waveguides at THz Frequency

Finite-element analysis based on the full-vectorial H-field formulation has been established as one of the most powerful and accurate modal solution approaches for optical guided-wave devices. Among the available optical waveguides, those incorporating thin metal layers supporting the surface plasmon modes (SPMs) and coupling of these modes to dielectric modes have recently been proven to be attractive for many applications. In this paper, the H-field approach incorporating the perturbation technique is used in calculating the complex propagation characteristics of silver/polystyrene (PS)-coated hollow glass waveguides for terahertz frequency radiation. The propagation and attenuation characteristics of the SPMs at the metal/dielectric interfaces are presented. The formation of the coupled supermodes and the effect of the PS coating thickness on the attenuation characteristics of these waveguides are also investigated and shown to be critical to their design optimization.     

Vector coupled-mode theory of dielectric waveguides

A consistent derivation of a system of vector coupled-mode (VCM) equations for parallel dielectric waveguides is presented and compared with earlier versions of the improved coupled-mode theory (ICMT). As a validity test, it is shown that the effectively scalar transverse electric and transverse magnetic (TM) coupled-mode (CM) equations are direct limits of our full VCM formulation. In particular, our formulation does not lead to the fundamental error found with earlier coupled-mode theories (CMTs) in a case of TM fields. Functional equations of our VCMT are consistent with Maxwell's equations and lead to higher precision. They can be applied to complicated arrays of strongly coupled parallel dielectric waveguides with true vectorial behavior.     

An improved finite-difference vector beam propagation formulationfor graded-index waveguides

An improved finite-difference vector beam propagation formulation for graded-index waveguides is presented. The modification over the existing version involves a more accurate representation of the Fresnel operator in finite-difference form that accounts for the gradient of the refractive index in the vector Hehmholtz equation. The modified scheme is assessed by calculating the TM mode propagation constants of single-mode planar guides that yield better agreement to the exact values over the existing scheme. Furthermore, the calculated coupling lengths of a vertical directional coupler show improved comparison to experimental data     

Vectorial beam-propagation method for integrated optics

A finite-difference beam-propagation method is derived directly from the vectorial Maxwell equations. The new approach allows the analysis of coupling between various components of the electric-field vector for optical beams propagating in dielectric waveguides as well as corresponding changes in the beam-polarisation state.<>     

Analysis of the scattering by dielectric bodies using the SIEformulation

A surface integral equation (SIE) formulation is derived in order to analyze the scattering by a homogeneous dielectric body inside a cavity to which cylindrical waveguides are coupled. Cavity and dielectric body may be arbitrarily shaped; the waveguides may be of arbitrary cross section. Completely closed dielectric-loaded cavities and structures containing metal inserts or magnetic conductors are considered as well. It is shown that the SIE formulation reduces a field problem by one dimension leading to highly efficient algorithms. From numerical results, the influence of surface current expansions is studied. The accuracy of the method is demonstrated by field plots and by the comparison of numerical results to those of other methods     

Integral equation solution to the guidance and leakage propertiesof coupled dielectric strip waveguides

The guidance and leakage properties of single and coupled dielectric strip waveguides are analyzed using the dyadic Green's function and integral equation formulation. Galerkin's method is used to solve the integral equation for the dispersion relation. The effects of the geometrical and the electrical parameters on the dispersion relation are investigated. A method for predicting the occurrence of leakage is proposed. The properties of the even and the odd leaky modes are also investigated. Results are compared with previous analysis and are shown to be in good agreement     

A joint finite-difference and FFT full vectorial beam propagationscheme

A full vectorial beam propagation scheme is developed and it is applied on 3-dimensional waveguide structures. The formulation is based on the coupled wave equations for the transverse electric field. Each propagation step is performed by utilizing both the FFT and a finite-difference implementation. Under this perspective the offered advantages of FFT and finite-differences are exploited within a single propagation step resulting in a joint propagation scheme. The scheme is applied on a step-index circular fiber where analytical solutions are readily available for cross-checking. Moreover, the dependence of the phase constant on the reference refractive index is discussed. The polarized modes and the effective mode indices are derived in the case of rib waveguides by performing propagation along imaginary distance. Further, the rib waveguide coupler is examined and the energy transfer is simulated     

Vectorial wave analysis of dielectric waveguides for optical-integrated circuits using equivalent network approach

A vectorial wave analysis of the propagation characteristics of open dielectric waveguides for optical-integrated circuits using an equivalent network approach is presented. In this approach, all of the contributions from the discrete and continuous parts of the spectrum and from the TE-TM coupling, which are neglected in the earlier equivalent network approach, are taken into account. To show the validity and usefulness of this formulation, examples are computed for optical strip waveguides, rib waveguides, rectangular dielectric waveguides, embossed waveguides, and embedded waveguides.