Almudena García-Sánchez, Ángel S. Sanz
When teaching Optics, it is common to split up the formal analysis of diffraction according to two convenient approximations, in the near and far fields. Moreover, apart from a slight mention to the relationship between the wavelength and the typical size of the aperture that light is incident on, such analysis does not often involve any explicit mention to Geometrical Optics. By means of a simple laboratory demonstration, Panuski and Mungan have shown how the gradual variation of the width of a single slit leads to a smooth transition from the far field to the near field, eventually reaching what could be regarded as the Geometrical Optics limit for large enough openings. Here a simple pedagogical analysis of this transition is presented, which combines both analytical developments and numerical simulations, and is intended to serve as a guide to introduce in a more natural way (in positions, where real experiments take place) the above mentioned splitting taking as a reference such transition and its implications. In this regard, first this transition is investigated in the case of a Gaussian beam diffraction, since its full analyticity paves the way for a better understanding of the paradigmatic case of single-slit diffraction. Then, the latter case is then tackled both analytically, by means of some insightful approximations and guesses, and numerically, which explicitly shows the influence of the various parameters involved in diffraction processes, such as the typical size of the input (diffracted) wave or its wavelength, or the distance between the input and output planes. This analysis unveils staircase structures in the Fresnel regime, which seem to characterize the trend towards the Geometrical Optics limit in this case, against the smooth behaviors observed in the Fraunhofer regime.
Comments: 15 pages, 4 figures