Measuring the Orbital Angular Momentum State of Light by Coordinate Transformation

We present a method to measure the orbital angular momentum (OAM) state of light by coordinate transformation. The input OAM mode with annular shape is uniaxially compressed into a linear-shaped light, so that the upper and lower portions of OAM mode overlap to produce an interference pattern, showing easily recognizable fringes both in the near field and far field. The far-field measurement is more suitable for detecting large OAM but with the cost of additional diffractive element. The incident light can illuminate any position of the device, showing good tolerance to adjust the optical path. In a practical application, the proposed scheme can be realized only by one or two elliptical lenses, which provides a convenient and economic method for measurement of OAM state.