Optical realization of Newton-cotes-based integrators for dark soliton generation

An optical integrator is an analog optical signal processor that performs the time integral of an input optical signal. This paper presents a theory of Newton-Cotes optical integrators for high-speed optical signal processing. The Newton-Cotes optical integrators are designed using the cascade of a finite impulse response (FIR) optical waveguide filter with an infinite impulse response (IIR) optical waveguide filter. To demonstrate the effectiveness of the proposed optical integrators, the authors show, by means of computer simulations, that a trapezoidal optical integrator can generate a fundamental dark-soliton pulse that can propagate stably over a large distance of single-mode optical fiber. Although the analysis is directed at optical integrators implemented using waveguide technology, the theory, design method, and results are applicable to other physical systems such as optical systems based on free-space optics, fiber optics, and fiber gratings.