Optical interconnections can be beneficially employed at the chip-to-chip or backplane level of high-performance computing systems. One method of providing high speed and density interconnections among a large number of integrated circuit chips is with a passive integrated optics circuit. We have developed a method of breaking down arbitrarily complex rectilinear circuits into elementary blocks whose loss and coupling properties are known. Thus, the overall loss and noise for each connection can be calculated. A high-speed algorithm based on this method has been implemented. The high speed of our analysis system makes it suitable for incorporation in an iterative design system, which determines the minimum spacings between the guides and results in acceptable crosstalk and noise levels.