Abstract The well-known interference pattern of bright and dark fringes was first observed for light beams back in 1801 by Thomas Young. The maximum visibility fringes occur when the irradiance of the two beams is equal, and as the ratio of the beam intensities deviates from unity, fringe visibility decreases. An interesting outcome that might not be entirely intuitive, however, is that the wavefront of such unequal amplitude beams’ superposition will exhibit a wavy behavior. In this work, we experimentally observe the backflow phenomenon within this wavy wavefront. Backflow appears in both optics (retro- propagating light) and in quantum mechanics (QM), where a local phase gradient is not present within the spectrum of the system. It has become an interesting subject for applications as it is closely related to superoscillations whose features are used in super resolution imaging and in a particle’s path manipulations. The first successful attempt to observe backflow was made only recently in an assembly of optical fields, by synthesizing their wavefront in a complex manner. Yet, backflow is perceived as hard to detect. Here, by utilizing interference in its most basic form, we reveal that backflow in optical fields is robust and surprisingly common, more than it was previously thought to be.
Abstract The well-known interference pattern of bright and dark fringes was first observed for light beams back in 1801 by Thomas Young. The maximum visibility fringes occur when the irradiance of the two beams is equal, and as the ratio of the beam intensities deviates from unity, fringe visibility decreases. An interesting outcome that might not be entirely intuitive, however, is that the wavefront of such unequal amplitude beams’ superposition will exhibit a wavy behavior. In this work, we experimentally observe the backflow phenomenon within this wavy wavefront. Backflow appears in both optics (retro- propagating light) and in quantum mechanics (QM), where a local phase gradient is not present within the spectrum of the system. It has become an interesting subject for applications as it is closely related to superoscillations whose features are used in super resolution imaging and in a particle’s path manipulations. The first successful attempt to observe backflow was made only recently in an assembly of optical fields, by synthesizing their wavefront in a complex manner. Yet, backflow is perceived as hard to detect. Here, by utilizing interference in its most basic form, we reveal that backflow in optical fields is robust and surprisingly common, more than it was previously thought to be.
The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.
Quantum backflow is a counterintuitive phenomenon in which a forward-propagating quantum particle propagates locally backwards. The actual counter-propagation property associated with this delicate interference phenomenon has not been observed to date in any field of physics, to the best of our knowledge. Here, we report the observation of an analog optical effect, namely, transverse optical backflow where a beam of light propagating to a specific transverse direction is measured locally to propagate in the opposite direction. This observation is relevant to any physical system supporting coherent waves.
In 1801, Thomas Young devised what is now known as the Classical Double Slit Experiment. In this experiment, light waves emanating from two separate sources, interfere to form a pattern of alternating bright and dark fringes on a distant screen. By measuring the position of individual fringe centers, the fringe widths and the variation of average light intensity on the screen, it is possible to compute the wavelength of light itself. The original theoretical analysis of the experiment employs a set of geometric assumptions which are collectively referred to here as the Parallel Ray Approximation. Accordingly, any two rays of light arising from either source and convergent on an arbitrary point on the screen, are considered very nearly parallel to each other in the vicinity of the sources. This approximation holds true only when the screen to source distance is very large and the inter-source distance is much larger than the wavelength of light. The predictions that naturally follow are valid only for fringes located near the center of the screen (e.g. the equal spacing of fringes). But for those fringes located further away from the screen center, the precision of these predictions rapidly wanes. Also when the screen to source distance is comparable to the inter-source separation or when the inter-source distance is comparable to the wavelength of light, the original analysis is no longer applicable. In this paper, the theoretical foundations of Young’s experiment are re-formulated using a newly derived analytical equation of a hyperbola, which forms the locus of the points of intersections of two expanding circular wavefronts (with sources located at the respective centers of expansion). The ensuing predictions of the new analysis are compared with those of the old. And finally, it is shown that the latter approach is just a special instance of the former, when the Parallel Ray Approximation can be said to hold true.
Quantum backflow (QB), a counterintuitive interference phenomenon where particles with positive momentum can propagate backward, is important in applications involving light-matter interactions. To date, experimental demonstrations of backflow have been restricted to classical optical systems using techniques such as slit scanning or Shack-Hartmann wavefront sensing, which suffer from low spatial resolution due to the inherent limitations in slit width and lenslet array density. Here, we report an observation of azimuthal backflow (AB) both theoretically and experimentally by employing the weak measurement technique, which enables the precise extraction of photon momentum at each pixel. Our results show that a heralded single photon, prepared in specific superposition states with solely negative orbital angular momentum (OAM), can exhibit positive OAM. The effects of mode ratio, propagation distance, and OAM index on the azimuthal backflow are systematically investigated. This work provides new techniques for observing and manipulating backflow in quantum systems.
3.1 Interference of a Single Photon The kinds of study originally conducted by Thomas Young - in particular, the celebrated "double slit" experiment that we briefly examined in Chapter 1 (see Fig. 1) - provide a capacity to reveal far more than the wave nature of light, important as that is. True enough, the observed characteristic fringe pattern, when monochromatic light passes through two closely spaced slits onto a screen, appears to be simply explicable on the basis of waves from each slit undergoing constructive and destructive interference at different positions on the screen. Yet, astonishingly, these patterns of interference are still exhibited when individual photons of a low-intensity input beam reach the screen one at a time, showing that it cannot in fact be a matter of different photons having to interfere with each other. Indeed, Dirac enunciated the general principle that photons can never directly interact with each other. The double slit and other such experiments indicate that each photon interacts in a delocalized, wave-like manner with both slits at the same time. Successive experiments build interference patterns that conform to an exact mathematical distribution formula, but the position at which an individual photon is detected in any particular instance cannot be predicted; this is a quintessential illustration of quantum uncertainty. Using the path integral approach of quantum theory, the phenomenon is more accurately represented by introducing a summation over all possible routes between the source and the screen on which the pattern appears, signifying an entire "lifetime" for each photon involved in the experiment. This relates to the fact that the actual trajectory is unknown without an observation, and thus we only obtain the probabilities of the photon striking the screen at different positions and times; all trajectories (potentialities) must be considered in a superposition. Each route is considered equally probable, and the variation in phase produces quantum interference. The differences in phase of each trajectory, at varying positions on the screen, generates the fringe pattern. An intriguing variation on this experiment involves "marking" the photons so that the actual route of each photon to the screen is known. Remarkably, in such a case, the fringe patterns do not appear because quantum interference cannot occur. A consequence of the observation of the photon route is an effect that, in other quantum mechanical connections, is known as a collapse of the wavefunction. However, it is possible for the fringe patterns to reappear when information on the route of the photons is lost; this is known as a quantum eraser.
Interference is a classic property of waves. It can be seen most clearly when a coherent wave is split into two partial waves that are then recombined to produce periodic variations in the measured intensity. These variations can be observed directly as a pattern of bright and dark interference fringes on a screen. The classic interferometer set-up is the Young's double-slit experiment: a small light source emitting in a narrow frequency band is placed on one side of the slits, and an interference pattern is observed at the screen on the other side (figure a). The fringes are bright where the partial waves interfere constructively, and dark where the interference is destructive.