A method for the calculation of the propagation of a light beam through an inhomogeneous medium is presented. A theoretical analysis of this beam-propagation method is given, and a set of conditions necessary for the accurate application of the method is derived. The method is illustrated by the study of a number of integrated-optic structures, such as thin-film waveguides and gratings.

Beam-propagation method: analysis and assessment

The solution of the scalar wave equation in the parabolic approximation is considered through the finite-difference and the Fourier-transform (i.e., beam propagation method) techniques. Examples are taken from the field of integrated optics and include propagation in straight, tapered, Y-branched, and coupled waveguides. A comparison of numerical results obtained by the two methods is presented, and a comparison with other analytical or numerical methods is also given. In the numerous cases studied it is shown that the finite-difference method yields a large, order-of-magnitude range improvement in accuracy or computational speed when compared with the Fourier-transform method.

Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications

We summarize field propagation techniques for fibre and integrated optics with emphasis on fast Fourier transform, finite-difference, finite-element and Lanczos methods for both paraxial and wide-angle calculations.

A guide to electric field propagation techniques for guided-wave optics

Diffused channel-waveguide couplers were fabricated on z-cut y-propagating LiNbO3 crystals by the indiffusion of titanium. Both mode spot sizes and coupling lengths were measured. The fields and coupling lengths were computed for both TM and TE polarizations from fabrication conditions. Good agreement was obtained between the measured and computed mode spot sizes and coupling lengths. It is concluded that the calculation method could aid in the design of such couplers.

Comparison of calculated and measured performance of diffused channel-waveguide couplers

We experimentally demonstrate spin waves coupling in two laterally adjacent magnetic stripes. By the means of Brillouin light scattering spectroscopy, we show that the coupling efficiency depends both on the magnonic waveguides' geometry and the characteristics of spin-wave modes. In particular, the lateral confinement of coupled yttrium-iron-garnet stripes enables the possibility of control over the spin-wave propagation characteristics. Numerical simulations (in time domain and frequency domain) reveal the nature of intermodal coupling between two magnonic stripes. The proposed topology of multimode magnonic coupler can be utilized as a building block for fabrication of integrated parallel functional and logic devices such as the frequency selective directional coupler or tunable splitter, enabling a number of potential applications for planar magnonics.

Directional multimode coupler for planar magnonics: Side-coupled magnetic stripes

A numerical technique to obtain the wave behavior in tightly coupled multimode fibers with inhomogeneous indices is introduced in this paper. The specific problem of the coupling characteristics of two parallel multimode fibers whose index profile is parabolic is treated in detail. It was found that in spite of the fact that rather complicated coupling behavior is observed when multimodes exist, total guide power still exchanges among the fibers in a periodic manner, and the coupling length still increases monotonically as a function of the separation distance between the fibers. It has also been demonstrated that by simply specifying the index profiles of the coupling structure (provided that the profiles are slowly varying), the coupling characteristics can be generated with our technique.

R. Szejn

Papers

Multimode inhomogeneous fiber couplers.