A linear-operator formalism for bianisotropic waveguides

A bianisotropic waveguide can be defined as a cylindrical waveguide filled with bianisotropic materials, and all the conventional waveguides are special cases of the bianisotropic waveguide. In this paper, guided wave propagation in bianisotropic waveguide is analyzed by the theory of linear operators, and two types of adjoint waveguides and inner products are introduced respectively. Based on the concept of adjoint waveguides, the functional expressions of the field equations can be obtained, and from which the eigenvalue problem of the bianisotropic waveguide can be solved. Also, bi-orthogonality relations of guided modes are derived. These biorthogonality relations reported here can be used to expand electromagnetic fields in terms of a complete set of modes in straight bianisotropic waveguide. As an example of application, mode matching formulae for a discontinuity problem are given.     

Spinor formalism for waveguides

The authors first prove that there exists a close relationship between the spinor fields and the electromagnetic transverse fields TE, TM.Then the spinor formalism is applied to the waveguide theory and explicit formulae are given for waveguides with rectangular or circular cross section. An interesting feature of the spinor formalism is to require only two components.     

A spectral technique for the analysis of time and space-transientsin planar dielectric waveguides

A novel method is proposed for the analysis of transients in dielectric guide, e.g., when excited by a Gaussian beam pulsed in time and modulated by a cosine waveform. This approach, utilizing the full modal spectrum of the guide, results more reliable than existing numerical techniques, while, by virtue of its analytical nature, greatly reducing the computational complexity of the problem     

The method of lines for the analysis of lossy planar waveguides

The method of lines is extended to calculate the losses of waveguide structures. Ohmic losses in metallizations (with frequency-dependent, extremely high dielectric constants) and dielectric losses are simultaneously considered. Despite the high ratios of the dielectric constants of the metallizations and the dielectrics, the analysis and numerical treatment are carried out accurately. Using nonequidistant discretizations the results are computed efficiently, and an approximate value of the propagation constant close to the exact value is found by extrapolation. The phase constant deviates less than 0.5%. The attenuation may deviate up to 2%. The advantages of the method of lines are a small computation time and, due to the analytical solutions of the fields in one direction, a very good approach to the fields inside the strip as well as to the strong fields directly adjacent at the edges. The results for a single microstrip line are shown and compared with those of other authors     

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.     

A simple numerical analysis of planar optical waveguides using waveimpedance transformation

A simple numerical approach for studying arbitrary profile planar optical waveguides based on wave impedance transformation is presented. The only mathematics involved in this approach is the wave impedance transformation formula, which has been widely used in the field of microwaves. Because of its simplicity, the method can be implemented in short but effective computer codes. The method is exact when the index profiles are of step-index shapes and is shown to be very accurate in comparison with the exact analytical solutions for graded refractive index profiles     

Coupled-mode analysis of anisotropic dielectric planar branching waveguides

We present a theoretical study of mode propagation in anisotropic planar branching waveguides consisting of isotropic and anisotropic layers. The characteristic equation of anisotropic five-layered structure is introduced to calculate the propagation constants and field patterns of the branching-waveguide modes. Coupled-mode analysis shows that the normalized parameter is effective for the evaluation of mode-coupling effects in the anisotropie branching waveguides as well as in the isotropic branching waveguides.     

Coupled mode analysis of dielectric planar branching waveguides

The mode conversion behavior of planar dielectric branching waveguides is studied as a function of branching angle, propagation direction of modes, and thickness ratio of branches. The multimode coupled equation and new step approximation method of branch taper are introduced, which give the accurate analysis of mode behavior in the branching waveguide of a large taper angle.     

Local field analysis of bent graded-index planar waveguides

A local field analysis is proposed for bent planar waveguides with arbitrary refractive index profiles. Exact vector wave equations that include the gradient index, or polarization correction, term are derived for both transverse electric and transverse magnetic modes from Maxwell's equations in a local bent coordinate system. The approximate local field and correction to the propagation constants are obtained by perturbation analysis. As an example of the method, an infinitely extended parabolic index profile is studied     

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.     

The method of lines for the analysis of planar waveguides withfinite metallization thickness

The method of lines is extended to calculate waveguide structures with finite metallization thickness. The normally used range of metallization thickness is not a limit for the method. Particularly when calculating small or moderate thicknesses, it is possible to derive the dispersion constant with only one computed result. When using the optimal edge parameter, P_opt, for that computation, the deviation from the exact dispersion constant is less than 0.5%. The advantage of the method of lines is that only small line numbers are necessary. Hence, the computing time is very small     

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.     

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.     

Rugorous analysis of planar waveguides with two-dimensionally periodic layer

Rigorous analysis of planar waveguides with two-dimensionally periodic (2DP) layer is presented. Characteristic solutions in periodic layer are exactly represented by a double Fourier series known as the Floquet solutions. The vector amplitudes of space harmonics are proved to be governed by five-term recurrence relation in the operator-vector form for sinusoidal modulation. A general transmission-line network representation of two-dimensionally periodic medium and multiport network representation of uniform-periodic-medium interface are introduced. Any layered structures cascading with periodic ones can be analyzed. Numerical results based on the established theory are also presented to illustrate characteristics of 2DP medium and structure.     

Graded-index planar dielectric waveguides

Properties of planar dielectric waveguides having a diffusion-induced index of refraction distribution are investigated. It is found that the spatial distribution of modes, group velocity, and mode spectrum of these guides differed qualitatively from the corresponding properties found in a slab waveguide. These results were experimentally verified by measuring the mode spectrum of a dielectric waveguide having an assumed complimentary error-function distribution of refractive index.     

A Planar transversal junction of two planar waveguides

A rigorous analytic method is used to solve the wave-propagation problem for a planar transversal junction of two planar waveguides. The problem is reduced to an iteratively solved system of integral equations of the second kind. Dependences of the transmission and reflection coefficients of guided waves, radiation patterns, and the power of the radiation field on the ratios of the waveguide thicknesses and the waveguide permittivities are obtained.     

WKB analysis of planar surface waveguides with truncated index profiles

We present a WKB analysis of planar surface waveguides with truncated arbitrary refractive index profiles. It is shown that the phase change at the turning point on the substrate side approaches zero near the cutoff. The validity of the conventional assumption of constant phase change ofpi/2at the turning point is investigated, and the consequent errors near the mode cutoffs are analyzed for index profiles of practical interest.     

A numerical technique for the determination of the propagationcharacteristics of nonlinear planar optical waveguides

A numerical method is proposed and implemented into computer code for the analysis of propagation characteristics of nonlinear optical waveguides. This technique follows the concept of the shooting method, and the fourth-order Runge-Kutta method is adapted to integrate the differential wave equation from one side to the other. An error function is defined to estimate the discrepancy between the computed and expected boundary values. A secant method is then used to evaluate the sign and magnitude of the correction term for the initial guesses of effective index. This procedure is performed in an iterative manner until the error reduces to a specified range. Experiments show that very accurate results can be obtained through this method, and only six to seven iterations are needed for solutions to converge. With this method we analyze nonlinear waveguides with varying guide parameters for realization of their behavior. All the findings and results can be used in further investigations of optical devices composed of waveguide structures     

A transverse displacement at the junction of two planar dielectric waveguides

The guided-wave transmission and reflection coefficients, the pattern, and the energy of the radiated field are calculated as functions of the value of the displacement at the junction of two single-mode waveguides for various values of the permittivity of waveguiding layers. It is shown that the correction to the wave transmission coefficient calculated at the first and second iteration steps increases while the permittivity grows, and the way this correction increases is demonstrated.     

Solid immersion lenses in planar waveguides

In this paper, solid immersion lenses (SILs) in silicon-based planar waveguides are designed and fabricated. The lenses are designed by the ray-tracing method to optimize the lens profiles. Experimental results show that a minimum spot size of 0.77 /spl mu/m can be obtained as the calculation prediction. Hence, the SILs combined with other optical components in planar waveguides can alleviate the alignment, tilt, and packaging problems in free-space optical systems.