Electromagnetic scattering from a stack of two one-dimensional rough surfaces separating homogeneous media is modeled with a rigorous integral formulation solved by the method of moments. We present an efficient numerical method for computing the field scattered by such rough layers, in reflection as well as in transmission. We call this method propagation-inside-layer expansion (PILE) due to its straightforward physical interpretation. To our knowledge, it is the first method able to handle problems for this configuration with a huge number of unknowns. We study the convergence of this method versus a coupling condition and validate it by comparison with results from the literature.

We propose the use of binary slanted surface-relief gratings with parallel-groove walls as input and output couplers in a planar optical interconnect. Parametric optimization of cascaded output couplers is employed to design an interconnect consisting of N output couplers producing a uniform intensity distribution with a high efficiency that may be realized in one lithographic etching step. The sensitivity of a N = 4 interconnect to various fabrication errors is analyzed. We demonstrate the operation of a slanted surface-relief grating manufactured with electron-beam lithography and reactive-ion etching for an operating wavelength of lambda = 0.633 mum.

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