Mode reconstruction of a light field by multiphoton statistics

We present a simple method to reconstruct the mode distribution of multimode classical and nonclassical optical fields using a single measurement of higher-order photon number correlation functions. Knowing the underlying number and structure of occupied modes of a light field plays a crucial role in minimizing loss and decoherence of quantum information. Typically, full characterization of the mode structure involves a series of several separate measurements in spatial, temporal, frequency, and polarization domains. We experimentally demonstrate reconstruction of up to three modes with excellent agreement and study the robustness of our method in experimentally realizable regimes.