Optical convolution with a rectangular frequency comb for almost ideal sampling

摘要

According to the sampling theorem, bandwidth limited signals can be seen as superposition of time shifted sinc pulses weighted with the sampling values. Since sine pulses are orthogonal to each other, bandlimited signals can be perfectly sampled by an integration over the product between them and a sinc pulse with the correct time shift and bandwidth. Because sinc pulses have an infinite time length, they cannot be realized experimentally. Instead, generating a periodical sinc pulse sequence is straightforward. For a low duty cycle the pulses in such a sequence come close to single sinc pulses and thus the sampling might come closer to ideal sampling. In the frequency domain, this nearly ideal sampling is represented by a convolution between the signal spectrum and a rectangular frequency comb with many lines. The bandwidth of the comb corresponds to the sampling rate, while a bigger number of comb lines reduces the duty cycle and might enhance the sampling quality. We present the generation of a flat frequency comb with up to 33 lines in the optical domain as well as how to convolve it with an optical input spectrum for optical sampling. Already with one Mach-Zehnder modulator driven with m equidistant radio frequencies, the sampling with a comb consisting of 2m+1 lines can be realized. Additionally, with a second Mach-Zehnder modulator driven with n equidistant radio frequencies, the comb line number can be enhanced to (2m+1)(2n+1).