Measuring high-order optical orbital angular momentum with a hyperbolic gradually changing period pure-phase grating.

We present a method to measure the high-order orbital angular momentum (OAM) state of a light beam with a static hyperbolic gradually changing period pure-phase grating (HGCP-PPG). From the number and orientation of the fringes of the Hermite-Gaussian-like diffraction intensity pattern, the OAM state of the incident Laguerre-Gaussian beam can be measured. Experimental detection of the OAM state up to ±100-order has been achieved. This method is highly efficient and robust because the HGCP-PPG is adaptive to high-order OAM beam and tolerant of the misalignment of the incident OAM beam.