Generation and characterization of structured vector and partially coherent beams via digital holography and interferometric techniques

Structured light has become a central topic in modern optics, offering new possibilities in beam shaping, optical communications, imaging, and quantum technologies. In this thesis, we present a comprehensive study on the generation, characterization, and coherence control of scalar and vector structured beams. The theoretical foundation is developed from solutions of the Helmholtz and paraxial wave equations, with particular focus on Gaussian-type families such as Hermite–Gaussian, Laguerre–Gaussian, Ince–Gaussian, and non-diffracting Helmholtz– Gauss beams including Bessel–Gauss and Mathieu–Gauss modes. Experimentally, we demonstrate a compact digital holography platform based on a single binary hologram encoded on a digital micromirror device (DMD). This setup allows for simultaneous phase and polarization control using two orthogonally polarized beams with conjugate amplitudes. With this method, we report the experimental generation of some vector beams, including vector Laguerre–Gauss, vector Bessel–Gauss, and, for the first time, vector athieu–Gauss beams. These beams are fully characterized through intensity measurements, Stokes polarimetry, and concurrence analysis, showing excellent agreement with theoretical predictions. Then, we explore structured beams in the partially coherent regime and introduce a digital scheme to engineer tunable coherence using random tilted wavevectors on a Digital Micromirror Device, enabling programmable control of coherence length in Gaussian-type beams. In parallel, we present a theoretical and experimental study of partially coherent Mathieu–Gauss beams, where both the coherence and ellipticity parameters are independently controlled using a rotating diffuser and spatial light modulator. The cross-correlation function and cross-spectral density reveal that these beams preserve structural features even as coherence is reduced, with nearly invariant spectral properties during propagation. Together, these results provide a unified framework for understanding and controlling both the polarization and coherence degrees of freedom of structured beams.

https://orcid.org/0000-0002-0600-8551