Abstract-A method is described to construct modal fields for an arbitrary one-or two-dimensional refractive index structure. An arbitrary starting field is propagated along a complex axis using the slowly varying envelope approximation (SVEA). By choosing suitable values for the step-size, one mode is maximally increased in amplitude on propagating, until convergence has been obtained. For the calculation of the next mode, the mode just found is filtered out, and the procedure starts again. The method is tested for one-dimensional refractive index structures, both for nonabsorbing and for absorbing structures, and is shown to give fast convergence.

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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.