Measuring the Orbital-Angular-Momentum Complex Spectrum of Light with the Fast Fourier Transform

Measuring the orbital-angular-momentum (OAM) complex spectrum of light is very important in OAM-based applications. In this paper, we propose and experimentally demonstrate a simple scheme to measure the OAM complex spectrum of light with the fast Fourier transform (FFT). The light with input OAM modes coaxially interferes with a Gaussian light beam that is generated locally to achieve the intensity distribution of the interference. By subtracting the intensity distribution of the input OAM light from this interference intensity distribution, the OAM complex spectrum can be extracted by employing the FFT transform on the result of the subtraction. In addition, we also present an approach to enlarge the range of detectable OAM modes (from 1 to 50) and analyze the effects of optical alignment and the number of superimposed OAM modes on the measurement results. The proposed scheme is demonstrated in a proof-of-principle experiment, where six superimposed OAM modes can be measured without error, with their average deviation of amplitude and phase being 0.07 and 0.308, respectively. The proposed scheme can exploit applications in some advanced domains, including OAM sensing, OAM imaging, optical communication decoding, and various other OAM-based systems.