Effective-index method with built-in perturbation correction forintegrated optical waveguides

It is well known that the conventional effective-index method for the analysis of rectangular-core waveguides can in general produce accurate results only when the modes of the waveguides are operated in the far-from-cutoff region. In this paper, an improved effective-index method, called the effective-index method with built-in perturbation correction, is described. This method is as efficient as the conventional method pet produces much more accurate results. Numerical examples for single waveguides and directional couplers are presented to demonstrate the accuracy of the method with results obtained from an improved Fourier decomposition method as the references     

Stress analysis method for elastically anisotropic material basedoptical waveguides and its application to strain-induced opticalwaveguides

A numerical approach for the stress analysis of elastically anisotropic material-based optical waveguides is newly formulated with the finite element method (FEM). The stress analysis method developed here is linked to the guided mode analysis method to produce a two-step analysis of acoustooptic modulation of optical waveguides. Numerical examples are shown for strain-induced optical waveguides on LiNbO₃ substrates     

Analysis of the guided modes in slab-coupled waveguides using a variational method

The waveguiding properties of the slab-coupled waveguides (i.e., the optical stripline and the rib waveguide) are investigated by the vector variational method. The slab-coupled waveguides are low-loss optical waveguides which are easy to fabricate and design. In this paper, the propagation constants and the field intensity distributions of the slab-coupled waveguides are presented, and the effects on the wave-guiding properties caused by changing their geometrical parameters are discussed. The results obtained by employing the variational method are compared with those obtained by using other methods.     

A new method for the calculation of the dispersion of nonperiodic photonic crystal waveguides

We present a new method for the calculation of the dispersion diagrams of general nonuniform waveguides. The method is based on the spatial Fourier transform (SFT) of the electromagnetic field distribution along the guiding direction. We demonstrate the validity and robustness of the SFT technique using several test cases. As an application, we apply the method to analyze the dispersion of biperiodic photonic crystal waveguides and show that the guiding bandwidths of these waveguides can be significantly enhanced by a proper choice of the two distinctive spatial periods of the biperiodic waveguides.     

Mode dispersion of trapezoidal cross-section dielectric optical waveguides by the effective-index method

The mode dispersion of dielectric optical waveguides is calculated by the effective-index method and is compared with previously reported experimental and theoretical finite-element results for trapezoidal cross-section waveguides. Agreement between experimental and predicted results is very good. This is significant because it means that stripe waveguides can be designed with specific modal propagation properties using the much simpler effective-index method even though the waveguide cross-section is not rectangular.     

Improved full-vectorial beam propagation method with high accuracy for arbitrary optical waveguides

An improved finite-difference (FD) full-vectorial beam propagation method is introduced for arbitrary optical waveguides with a dramatic improvement in accuracy. This method is developed based on the generalized Douglas scheme and a novel FD formula for the cross-coupling terms which, expressed in explicit form, is independent of specific types of waveguides. The present method is demonstrated for a strongly guiding rib waveguide.     

Analysis of lossy dielectric guides by transverse magnetic fieldfinite elements method

Recently a transverse magnetic field formulation of the finite element method for solving lightwave propagation in lossless optical waveguides was demonstrated using only two components of the magnetic field. We extend this formulation to include loss in the waveguides, and compare the results from this formulation with those of other formulations for three different types of waveguides. Our results from the new approach show good agreement with those from previously published data. No perturbation technique is needed to arrive at these results     

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     

Semivectorial beam-propagation method for analyzing polarized modesof rib waveguides

The authors report a semivectorial beam-propagation method which can determine the form birefringence in rib or channel waveguides. In this approach, a finite-difference equation is solved by using the alternating-implicit method to simulate the propagation of the optical beam. Since boundary conditions are incorporated into the finite-difference equation, polarized modes can be simulated. Numerical results on three well-known rib waveguides are presented with comparisons to published data     

Radiation method for the measurement of mode-conversion levels

A novel method for the determination of mode-conversion levels in overmoded waveguides is described. It relies on a swept-frequency measurement of the perturbation of the dominant-mode radiation pattern of the open-ended waveguide, owing to the presence of higher-order modes. Results are reported for mode-conversion effects in corrugated waveguides at frequencies near 9 GHz. Excellent agreement with the trapped-resonance method is demonstrated, although the present technique has advantages over this method when the mode excitation level is high or the waveguide length is imprecisely known.     

Iterative simplex-finite difference method for the characterizationof optical waveguides

A new method is presented for reconstructing smooth refractive index profiles of optical waveguides from measured effective indexes. It is based on the semivectorial finite difference method to solve the polarized wave equation for a given refractive index profile. An iterative simplex algorithm is used to find the best refractive index parameters that give, as a solution, effective indexes close to the measured ones. The method is applied successfully to Ag⁺-Na ⁺ ion-exchanged glass slab waveguides and to diffused Mg/Ti:LiNbO₃ slab waveguides. Dopant concentration profiles are obtained by using secondary ion mass spectrometry. The relationship between the refractive index change and the dopant concentration is determined for both cases. The iterative simplex algorithm-finite difference method (ISA-FDM) is compared to other index profile reconstruction methods, and the advantages with respect to WKB-based methods are pointed out     

A bidirectional beam propagation method for periodic waveguides

For waveguiding structures with multiple longitudinal reflecting interfaces, a bidirectional beam propagation method has been developed using a scattering operator formulation and rational approximations to the square root and the propagation operators. For periodic waveguides, it is possible to significantly speed up the method when scattering operators for a waveguide with s₁+s₂ periods are obtained directly from those operators associated with waveguides having s₁ and s₂ periods. The required computing time is then proportional to the logarithm of the total number of periods     

Effective-index method with built-in perturbation correction forthe vector modes of rectangular-core optical waveguides

The effective-index method (EIM) with built-in perturbation correction is developed for the analysis of the vector modes of general rectangular-core optical waveguides. This method maintains the simplicity and the high efficiency of the conventional EIM, yet produces significantly more accurate results. Numerical examples for a wide range of waveguides are presented to demonstrate the accuracy of the method for the calculation of the propagation constants and the modal birefringence     

Finite element method using port truncation by perfectly matchedlayer boundary conditions for optical waveguide discontinuity problems

A powerful algorithm based on a finite element method (FEM) is newly formulated for the analysis of waveguide discontinuities. In an earlier approach, FEM was applied to the finite region with discontinuities, and a mode expansion technique was applied to the uniform waveguides that are connected to the input and output ports of finite region. Although, in the present approach, the uniform waveguides are replaced by perfectly matched layer (PML) boundary conditions, it is possible to treat periodically varying waveguide structures such as photonic crystal (PC) waveguides. A combined method of beam propagation method (BPM) and FEM is also shown in such a form that a mode expansion technique is not required. To show the validity and usefulness of the present approach, numerical examples for optical gratings, circuit components based on PC waveguides and optical directional couplers are presented     

Guided-wave characteristics of optical graded-index planarwaveguides with metal cladding: a simple analysis method

The guided mode characteristics of metal-clad graded-index waveguides are generally determined by complex eigenvalue equations or perturbative methods. However, these methods either require several iterations in the complex plane or are only suited to the class of waveguides whose guided field can be described analytically. We describe a method of calculating complex propagation constants for metal-clad graded-index waveguides under very general but weakly guiding conditions. The method, based on Galerkin's formalism using trigonometric basis functions, allows arbitrary inhomogeneous and complex refractive index profiles. Applications to three generally used waveguide models show our approach to be in good agreement with other analytical or numerical methods     

An assessment of finite difference beam propagation method

A finite-difference beam propagation method (FD-BPM) is outlined and assessed in comparison with a conventional beam propagation method (FFT-BPM) which uses fast Fourier transformation. In the comparative study three straight waveguides with different index profiles that are frequently encountered in integrated optics are utilized. Using both methods normalized effective index values of the eigenmodes of these waveguides are calculated and compared with the exact values obtained from analytical expressions. As a further accuracy criterion, the power loss due to numerical errors when an eigenmode of a waveguide is excited is evaluated. Based on this comparison the accuracy, computational efficiency, and stability of the FD-BPM are assessed     

Investigation of 3D semivectorial finite-difference beampropagation method for bent waveguides

A three dimensions of semivectorial finite difference beam propagation method (FD-BPM) in cylindrical coordinates is investigated in order to analyze the optical wave propagation in the bent waveguides with the strong lateral confinement which will keep low radiation loss. The three dimensional (3D) semivectorial wave propagation equation is programmed in the quick and unconditionally stable procedure by using the alternating direction implicit method. This version of FD-BPM could well express the polarization characteristics of modal field near the dielectric interfaces and accurately simulate the wave propagation in bent waveguides even at a very small radius (<100 μm). Moreover, it is pointed out that the numerical precision of the algorithm is intensively affected by the propagation loss of bent waveguides along with the propagation step length of beam propagation method     

Numerical modeling of second harmonic generation in opticalwaveguides using the finite element method

A numerical study of second harmonic generation (SHG) in optical waveguides is presented using the finite element method (FEM) and the Crank-Nicholson split-step procedure. Results are given for a Cherenkov radiation scheme in both planar and channel waveguides. Also presented are results obtained on frequency doubling for guided modes in both planar and channel waveguides, using the quasi-phase-matching scheme     

Generalized moment method analysis of planar reactively loadedrectangular waveguide arrays

A combined modal expansion and moment method is applied for analyzing finite planar arrays of rectangular waveguides in an infinite ground plane including reactively loaded waveguide elements. The analysis, which is based on the moment method for solving the aperture problem, in combination with the modal analysis for the reactively loaded waveguide cavities or feeding waveguides, extends the network formulation of single apertures to multiple waveguide arrays including reactively loaded elements. Two orthogonally polarized sets of basic functions are utilized to model the expansion into the complete set of eigenmodes is used to formulate the waveguide cavity problem. The theory is applied to a finite planar array of arbitrarily spaced rectangular waveguides, where reactive loads are realized by placing sliding electrical conductors at specified distances in each of the unfed waveguides. Numerical design examples show that beamforming, beamsteering, and the improvement of the crosspolarization behavior is possible by a suitable choice of the geometrical parameters. The theory is verified by results available from the literature as well as newly performed experimental measurements     

A modified ray-optic method for arbitrary dielectric waveguides

A modified ray-optic method (MRO) is proposed for evaluating the propagation characteristics of dielectric waveguides with arbitrary refractive index profile. The authors correct the error caused by assuming a constant phase shift for any mode at the turning point on the substrate side. Very simple formulas are given for calculating the dispersion characteristics including those for planar optical waveguides and single-mode fibers. The results are more accurate than those of the ordinary ray-optic method, especially in the near cutoff regions, and agree well with those of the exact numerical methods. A comparison with other analytical and the exact numerical methods shows that the proposed method is simpler than other methods. This method can be extended to other more complicated cases