Measuring the complex orbital angular momentum spectrum of light with a mode-matching method.

The relative phase shift among different components in the superposition of orbital angular momentum (OAM) states contains significant information. However, with existing methods of measuring the OAM spectrum, the phase term of the spectrum coefficient is hard to obtain. In this Letter, a mode-matching method is proposed to identify the complex OAM spectrum with a Mach-Zehnder interferometer and a charge-coupled device camera. It has the potential to extend the applications of OAM in scenarios sensitive to the phase factor, for instance, in imaging and quantum manipulation. The method is experimentally demonstrated with the superposition of two or three OAM states, while the maximum deviation of the energy ratio and the relative phase shift is 8.4% and 5.5% of 2π, respectively.