An economic method for the solution of the scalar wave equation for arbitrarily shaped optical waveguides

The discrete sine method, in which the basis functions consist of sine functions defined on a set of parallel discretization lines, is discussed. The method is a combination of a scalar version of the finite difference method and sine method. The choice of the basis set leads for the eigenvalue equation to be solved, to a sparse matrix with a small bandwidth. As a consequence, the propagation constant of guided modes in optical waveguides may be calculated with short computation times and low storage needs. Results obtained with the method for three different wave guiding structures are compared with those of other method

Enhancing the Performance of Integrated Optical Sensor by Slow-light: Theoretical Study on Ring-Resonator Based Structures

In this work, the performance of three kinds of integrated optical ring-resonator based slow-light structures for sensing applications is theoretically studied using the transfer matrix method and the complex transmission coefficient approach. Enhancement of sensing performance due to the slowlight phenomenon is quantitatively formulated. The modeling results show that using realistic structure parameters, a refractive index detection limit of one order better than the state of the art Mach-Zehnder interferometer sensing structure is possible by the inclusion of such a slow-light structure. The role of ring(s) attenuation constant in limiting the usable light slowness and the achievable sensor resolution is also discussed. For a sufficiently small ring attenuation constant, the optimal sensing performance of a single resonator circuit can be better than that of multiple resonator circuits, while offering less fabrication complexities, cleaner spectra, shorter device length, and higher figure of merit

Coupled mode theory for resonant excitation of waveguiding structures

Resonant coupling of light beams via high-index media or gratings to planar waveguiding structures are of interest for both applications and from a theoretical point of view. Coupled Mode theory (CMT) can give an accurate description of the coupling process in terms of relatively simple expressions involving often a large number of coupling parameters. In this paper it is shown, using time reversal and energy conservation how these parameters are interrelated. The evaluation of the remaining independent parameters is shown to be possible using a few reflection and transmission coefficients for incoming plane waves, including in the calculations, if present, the effect of the grating. Further, it is proved that under certain condition a grating coupler may show exactly 100% reflection. Analytical expressions for the reflected and transmitted beams and the amplitude distribution of the excited mode are given for the case of incoming Gaussian beams. A few applications of the theory and considerations on its applicability are presented

A new method for the calculation of propagation constants and field profiles of guided modes of nonlinear channel waveguides based on the effective index method

In this paper, an extension of the effective index method (EIM) to waveguiding structures containing ideal or saturable third-order nonlinear materials is presented. By applying separation of variables to the dominant field component, the complete problem is subdivided into two scalar problems in the lateral and transverse direction, as in the case of the normal EIM. Making use of the strong transverse confinement, as observed in most real waveguide structures, the nonlinear index changes of the various transverse sections can be lumped into nonlinear effective indexes of the equivalent layered planar structures. By using these nonlinear effective indexes in self-consistent field calculations in the transverse direction, a complete approximate solution is obtained. In this way, the amount of computational effort required for the calculation of the effective indexes and field profiles of the waveguides can be reduced significantl

Ultra-sharp soliton switching in a directional coupler

By a numerical investigation it is shown that a directional coupler, described by two linearly coupled non-linear Schro¨dinger equations, can be used to construct a soliton switch with an extremely narrow transition region

Characterisation of slow light in a waveguide grating

A grating was defined in a silicon nitride waveguide, using a combination of both conventional lithography and laser interference lithography. The structure was optically characterized in the 1520 – 1560 nm wavelength range by combining transmission measurements with the analysis of local out-of-plane scattered light, using a high-resolution infrared camera. From the measured power enhancement of the first Bloch-mode resonance above the long-wavelength band edge we estimated a Q > 10^4 and a group velocity of < 0.1 c

Time domain beam propagation method for the simulation of temporal solitons in periodic media

A time domain beam propagation method for the simulation of optical pulses propagating through Kerr-nonlinear structures is presented. The method is verified by simulation of the known solitary wave solutions in nonlinear periodic medi