Vortex beam with helical wavefront has great applications, such as optical communication, optical manipulation, quantum information processing, etc. due to its infinite topological charge. Under disturbance or misalignment, the energy on vortex beam will be cast onto neighbored vortex beams and we get the OAM spectrum, which is essential to the applications of vortex beams. To measure the OAM spectrum, the measurement and reconstruction of the optical field is usually of great importance but an additional reference light is not easy to achieve. Therefore, this paper proposes a self-interferometry scheme suitable for unknown light fields. By incorporating a diffuser into a Sagnac-like loop, we realize a selfinterferometer. Then a two dimensional parallel grating is used to project the interfered field into a Sudoku squares. Tuning the polarization of each square by waveplate and polaroid, five interference patterns are obtained. By performing calculations on the five interference patterns, we can reconstruct the complex field of the original light. Then, a canonical routine, e.g. spiral harmonic expansion, is performed to get the OAM spectrum. This work provides a new method for measuring unknown light field and its OAM spectrum without extra reference light and has potential applications in the accurate detection and analysis of emitted signals in free-space optical communications.
Fermat spiral photon sieve (FSPS) containing many circular holes arranged along several Fermat spiral lines is an interesting element to generate vortex beam because of its special chiral structure. This work models the FSPS and derive the diffraction field analytically. In addition to the familiar azimuthal periodicity at the focal plane in previous works, we find the longitudinal periodicity of the generated vortex beams which present themselves as many families and therefore the multi-foci property is also discovered. We relate the vortex families with the parameters of FSPS and shows the rules. This work is helpful for design of FSPS and generation of vortex beams.
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