An Intriguing Interpretation of 1D and 2D Non-Diffracting Modes in Cosine Profile

Abstract

We provide a simple analysis based on ray optics and Dirac notation for 1D (one-dimensional) and 2D (two-dimensional) non-diffracting modes in the cosine profile, which are often called Cosine beams. We explore various kinds of structured modes formed by the superposition of two 1D Cosine beams. We then went on to understand the properties of the Bessel beams in terms of Cosine beams. For the first time, we report on the generation of three-dimensional tunable needle structures based on the interference of 1D Cosine beams. These size-tunable optical needles can have multiple advantages in material processing. Also, we report, for the first time, on the Talbot effect in Cosine beams. Straightforward mathematical calculations are used to derive analytical expressions for Cosine beams. The present method of demonstrating Cosine beams may be utilized to understand other structured modes. The Dirac notation-based interference explanation used here can provide new researchers with an easy way to understand the wave nature of light in a fundamental aspect of interferometric experiments as well as in advanced-level experiments such as beam engineering technology, imaging, particle manipulation, light sheet microscopy, and light–matter interaction. We also provide an in-depth analysis of similarities among Cosine, Bessel, and Hermite–Gaussian beams.