Abstract

A transversal filter is the most basic optical signal processing device that can be built from a fiber optic tapped delay line. If x(t) represents the lightwave signal in the fiber, the output of the transversal filter is given by where {h_n} = tap weights determined by a spatial light modulator and d_n = time delay for the (n + 1)th tap. Selecting values of the impulse response terms {h_n} and the tap delays we can design low-pass, high-pass, bandpass, and bandstop filters, arithmetic Fourier transform calculators, equalizers, etc. The characteristics of analog fiber optic processors are affected by the optical error sources: spatial errors in tap weights, attenuation and position errors in taps, detector noise, and dispersion in fiber. The total effect of these error sources produces a new transfer function, H′(ω) = H(ω) + D(ω) − jωT[H(ω) ∗ S(ω)] + E(ω), where D(ω), S(ω), and E(ω) are Fourier transforms of the spatial errors, the time delay errors, and the detector noise, T = sampling time and ∗ represents a convolution. From this theory upper bounds on the deviations in the performance measures of a transversal filter have been determined. We found that low-pass transversal filters are robust with respect to optical roundoff errors. We observed that the use of Hamming and Hann windows can make fiber optic transversal filters more robust.

© 1989 Optical Society of America