Transformation of Laguerre-Gaussian beams into 1D array of Hermite-Gaussian modes under the Talbot effect

Diffraction efficiency management by complex binary gratings

The diffraction efficiencies of a complex binary diffraction grating with a rectangular profile are controlled through the steps' phases, amplitudes, and duty cycle, based on analytical expressions. It is demonstrated that the zeroth-diffraction order can be canceled for any arbitrary value of the duty cycle, provided that a π-phase difference is imposed, along with a specific ratio of the steps' amplitudes. This feature is not feasible for separated amplitude-only and phase-only rectangular binary gratings in the context of one-dimensional gratings. In this framework, a key analytic relationship between the duty cycle and the steps' amplitude ratio is derived, allowing the design of such gratings with this desired feature across a wide range of conditions, not limited to a duty cycle of 0.5. Concerning the higher diffraction orders, it is proved that their intensities cancel or maximize for fixed duty cycle no matter the amplitude and phase values of the steps. The intensity of the m-th diffraction order possesses m maxima and m - 1 zeros on the full range of the duty cycle. All these features were corroborated experimentally. The broad insight of such a grating allows the design of gratings with diffraction efficiencies tailored for specific applications.

Fourier reciprocity between generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian beams carrying orbital angular momenta

We explore two distinct families of orbital angular momentum carrying light beams, which we refer to as generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian vortex beams, respectively. We show that the fields of the two vortex families are related via a Fourier transform. Hence, one family can be viewed as a source of the far-field intensity distribution of the other and vice versa. We also examine the orbital angular momentum evolution of both beam families on their free space propagation and establish a relationship between the orbital angular momentum, TC, and beam ellipticity factors. Our results may find applications to optical communications and imaging with structured light.