Single-shot diffractive spectrometer for photonic orbital angular momentum

Vortex beams carrying orbital angular momentum (OAM) provide an infinite degree-of-freedom and hold high potential in various applications, from high-capacity optical communication to diagnosis of materials with chirality. Quantitative spatial spectrum analysis of OAM modes is essential for these applications, yet it is still a challenge to obtain the OAM spectrum under short-wavelength systems such as extreme ultraviolet (EUV) and x-ray. Here, we introduce a simple single-shot diffractive method that can reconstruct arbitrary helical wavefront and quantitatively decompose individual OAM modes. There is no need to conduct any calibration associated with the beam to be measured; the only prior knowledge required is the transmission function of a random diffusing wavefront modulator. Experimental results show that this method can retrieve the spectrum of arbitrary OAM modes with intermodal crosstalk lower than −16.91 dB for topological charge greater than 50. The proof-of-concept visible light experiments of multiplexing and demultiplexing of OAM modes showed its potential applications in laser communication and metrology. Given the simplicity of lens-less system setup, the single-shot capability, and its suitability for arbitrary OAM modes, we envision it setting up a brand-new diffractive solution for structured wavefront analysis over a broad spectral range, from visible light to EUV, x-ray, and even electron beam.