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arXiv:2403.08050

The shadow of a laser beam

Raphael A. Abrahão, Henri P. N. Morin, Jordan T. R. Pagé, Akbar Safari, Robert W. Boyd, Jeff S. Lundeen

Published Mar 12, 2024• 1 citation
arXivHTMLPDF

Abstract

Light, being massless, casts no shadow; under ordinary circumstances, photons pass right through each other unimpeded. Here, we demonstrate a laser beam acting like an object - the beam casts a shadow upon a surface when the beam is illuminated by another light source. We observe a regular shadow in the sense it can be seen by the naked eye, it follows the contours of the surface it falls on, and it follows the position and shape of the object (the laser beam). Specifically, we use a nonlinear optical process involving four atomic levels of ruby. We are able to control the intensity of a transmitted laser beam by applying another perpendicular laser beam. We experimentally measure the dependence of the contrast of the shadow on the power of the object laser beam, finding a maximum of approximately of approximately 22 percent, similar to that of a shadow of a tree on a sunny day. We provide a theoretical model that predicts the contrast of the shadow. This work opens new possibilities for fabrication, imaging, and illumination.

DOI
10.48550/arxiv.2403.08050

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Light, being massless, casts no shadow; under ordinary circumstances, photons pass right through each other unimpeded. Here, we demonstrate a laser beam acting like an object - the beam casts a shadow upon a surface when the beam is illuminated by another light source. We observe a regular shadow in the sense it can be seen by the naked eye, it follows the contours of the surface it falls on, and it follows the position and shape of the object (the laser beam). Specifically, we use a nonlinear optical process involving four atomic levels of ruby. We are able to control the intensity of a transmitted laser beam by applying another perpendicular laser beam. We experimentally measure the dependence of the contrast of the shadow on the power of the object laser beam, finding a maximum of approximately of approximately 22 percent, similar to that of a shadow of a tree on a sunny day. We provide a theoretical model that predicts the contrast of the shadow. This work opens new possibilities for fabrication, imaging, and illumination.
Light, being massless, casts no shadow; under ordinary circumstances, photons pass right through each other unimpeded. Here, we demonstrate a laser beam acting like an object — the beam casts a shadow upon a surface when the beam is illuminated by another light source. We observe a regular shadow in the sense it can be seen by the naked eye, it follows the contours of the surface it falls on, and it follows the position and shape of the object (the laser beam). Specifically, we use a nonlinear optical process involving four atomic levels of ruby. We are able to control the intensity of a transmitted laser beam by applying another perpendicular laser beam. We experimentally measure the dependence of the contrast of the shadow on the power of the laser beam, finding a maximum of approximately 22%, similar to that of a shadow of a tree on a sunny day. We provide a theoretical model that predicts the contrast of the shadow. This work opens new possibilities for fabrication, imaging, and illumination.
The Boltzmann factor not only characterises the relationship between particle energies and their respective populations as a function of temperature, but also indicates that absorption and emission processes involving photons of different colours (i.e., frequencies) are, in general, mutually independent [29]. However, this stands in contrast to experiments in the field of nonlinear optics, such as the one by Abrahao et al. (2024) [1]. The authors of that publication show that green laser light (532 nm wavelength) enhances the absorption of blue laser light (450 nm) in a ruby crystal, and explain this phenomenon using a hierarchical orbital model.In the context of an alternative interpretation of quantum mechanics [28] (as opposed to the Copenhagen interpretation), based on the works of A. Einstein (1916) [9] and H. De Raedt et al. (2005) [5], a different possible explanation emerges, which is outlined here. Based on this model and the findings of Abrahao et al. (2024), modified interference experiments are proposed. These may help clarify whether particles—such as photons—interfere with themselves [8, 13, 14, 15], or whether quantum mechanics is merely an ensemble theory, without descriptive power concerning individual events [12].
From prehistoric times has come recognition that sunlight and firelight provide warmth, and that such illumination casts shadows. Expressed in more contemporary terms one would say that light travels in rays, and that this radiation has the potential to provide heat energy to absorbing material. From the time of Newton it has been known that light sources emit radiation comprising a distribution of colors. During the nineteenth century it was recognized that radiation had characteristics of transverse waves (with wavelength associated to color) but until the late twentieth century, when lasers became laboratory tools, it was hardly necessary to delve into the equations of electromagnetic theory to treat such experiments as were then possible; interest lay primarily with thermodynamic considerations of energy flow or with measurements of the dark or bright lines seen in the distribution of light that, after passing through a slit, was dispersed by a prism or grating into constituent colors. Although laser light sources are essential for the types of atomic excitation considered in this monograph, the legacy from thermal radiation still influences many interpretations of the interaction between radiation and matter, and it is therefore useful to summarize some of those concepts. The mathematics needed for describing laser radiation, or polarized light in general, has much in common with the mathematics of quantum theory discussed starting in Sec. 3.5 and specialized to two-level atoms in Sec. 5.6. In both cases one deals with two complex-valued functions – independent electric field amplitudes or probability amplitudes – whose absolute squares are measurable.
We studied experimentally and theoretically the evolution of open atomic systems in the constant intensity laser field. The study is performed by analyzing the line shapes of Hanle electromagnetically induced transparency (EIT) obtained in different segments of a laser beam cross section of constant intensity, i.e., a $\ensuremath{\Pi}$-shaped laser beam. Such Hanle EIT resonances were measured using a small movable aperture placed just in front of the photodetector, i.e., after the entire laser beam had passed through the vacuum Rb cell. The laser was locked to the open transition ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=1$ at the D1{D}_{1}D1​ line of 87{}^{87}87Rb with laser intensities between 0.5 and 4 mW/cm2{}^{2}2. This study shows that the profile of the laser beam determines the processes governing the development of atomic states during the interaction. The resonances obtained near the beam center are narrower than those obtained near the beam edge, but the significant changes of the linewidths occur only near the beam edge, i.e., right after the atom enters the beam. The Hanle EIT resonances obtained near the beam center exhibit two pronounced minima next to the central maximum. The theoretical model reveals that the occurrence of these transmission minima is a joint effect of the preparation of atoms into the dark state and the optical pumping into the uncoupled ground level Fg=1{F}_{g}=1Fg​=1. The appearance of the transmission minima, although similar to that observed in the wings of a Gaussian beam [A. J. Krmpot et al., Opt. Express 17, 22491 (2009)], is of an entirely different nature for the $\ensuremath{\Pi}$-shaped laser beam.
In ordinary optics one exploits the interaction of radiation with matter to manipulate beams of light. One can also turn the tables and control beams of charged or neutral material particles through their interaction with light. There are deep analogies and similarities between these two sorts of optics, even though they involve very different kinds of interactions between matter and radiation. Perhaps one can exploit every such interaction for some kind of “optics”—controlling beams of photons or massive particles. In this article we will describe recent developments in the laser optics of atomic beams—how experimenters are using the radiation pressure of laser light to manipulate neutral atoms.