Sigma-delta modulators track a signal by accumulating the error between an input signal and a feedback signal. The accumulated energy is amplitude analyzed by a comparator. The comparator output signal is fed back and subtracted from the input signal. This thesis is primarily concerned with designing accumulators for inclusion in an optical sigma-delta modulator. Fiber lattice structures with optical amplifiers are used to perform the accumulation. Two fiber lattice structures are designed, modeled, tuned, tested, and characterized. The testing results for both models are plotted and tabulated. One result is that accumulation is inversely proportional to coupling ratio. Also, the optical gain necessary to drive either fiber lattice structure to a monotonically increasing response is identical. With less than 10 (113 of optical gain, a wide range of accumulation rates are available. Initial integration of one fiber lattice structure into a first-order sigma-delta modulator is accomplished with results consistent with those from an ideal model. The design for a second-order sigma-delta modulator is developed, tested, and preliminary results shown.