The production of maxima and minima by the superposition of two or more light signals provides fundamental support for the wave nature of light. This result is based on the study of wave interference phenomena which remains the only approach to explain the production of those maxima and minima. In a system that is prepared to work with only one photon at a time, any detector can signal only one or zero. In 1986, a rigorously controlled experiment was designed by Grangier, G. Roger, and A. Aspect, [Europhys Lett. 1(4), p. 173, 1986] that guaranteed a single-photon beam. The explanation of the experimental results implied the interference of the wave function of a single-photon with itself. Thus, the explanation of interference that is accepted for an ensemble of photons was assumed to be valid for a single photon. In this study, we prepare a Mach-Zehnder interferometer using the same type of beam splitters used by Grangier et al. to test the assumption mentioned above. Our results allow us to explain the results of Grangier et al. because of the interaction between light and the beam splitters. Our results also verify that their wave interpretation of the results is not valid. Here, we present the essential findings of the extensive experimental evidence that supports our ideas.
In 1986, Grangier, G. Roger, and A. Aspect, [
Here, we briefly summarize the explanation of K. P. Zetie, S. F. Adams, and R. M. Tocknell, [
(In other words, it is assumed that the transmission-reflection ratio of 50/50 that applies for many photons that moves on a macro cross section is the same ratio for a single photon that moves on a micro cross section.)
The math inserted in
We introduce three important pieces of information not present in the analysis done in [
A convex lens was introduced between the laser and the MZ interferometer
(prior to BS1) to magnify the details. In
It is possible to observe vertical interference fringes on the right side of
somewhere between 0% and 100% of the arriving energy (and correspondingly reflect the complementary quantity of energy).
It is well known that the functional principle of a beam splitter with multidielectric coatings is the interference of light inside the multilayers, i.e., beam splitter interference (BSI). Under some specific conditions (not articulated in this paper) an array of maxima and minima as shown in
λ sp = λ L / d (1)
Notice that each image in
The idea developed here might be applicable to other surprising experimental results. In experiments where photons originating from two sources with random phases hit a beam splitter, the generated visibility at the detectors is larger than the 50% predicted by the classical optics theory [
In our opinion,
The classical assumption that one image is the negative of the other in
A basic setup was prepared to produce simple patterns of interference. In this way, inconvenient spatial effects could be avoided making the wave as close as possible to the ideal plane wave. In this trial, no lens was placed between the laser and the MZ interferometer. Furthermore, two lenses per beam were positioned around 30 cm after the MZ interferometer to amplify the size of the images. The MZ interferometer should produce two symmetrical outputs, where one output is the negative image of the other, according to the classical wave theory. If these conditions can fail, it must occur when the symmetry of the system could be compromised under extreme conditions. This case occurs when the path difference between the two beams is almost zero.
A video allowed us to analyze the output of the two beams.
1) The destructive interference on the left side is not completely dark.
2) The image on the right side is not the negative image of the left (i.e., symmetry was broken).
3) The photons that cannot travel to the center of the left image because of the destructive interference, where do they go? (In [
Point 3 was studied using Wolfram Mathematica 10 at different sections of our video to corroborate the images shown here. One good example consists of frames 1289 and 1290, which are separated by one thirtieth of a second.
The frames of
The left beam (
the left beam during frame 1290 (intensity decrease of 0.44, which is half as large as that in frame 1289) is larger than the decrease of 0.19 experienced by the bottom box of the left beam. In other words, some of the photons that leave the direction pointing to the top box finished at the bottom box of the left beam. On the other hand, photons that do not end in a region of destructive interference move toward neighboring regions where the interference is not destructive and do not move in the perpendicular direction where the interference is constructive, as is typically assumed. This result makes sense because photons need not “know” in advance where they can or cannot move.
Though these observations completely disprove the conclusion of [
In our opinion, when. in [
Note that all results in this study were obtained twice by using lasers with wavelengths of 650 nm and 460 nm because they cover more than half of the visual spectrum. It is possible to think that maybe the last numerical results discussed here were created by the BS or the lasers used on the experiment. A more sophisticated MZ interferometer was made using two pellicles BS (39485, Edmund Optics). This time the two-outside lens were unnecessary. Also, the helium-neon laser used this time emits light with wavelength 632 nm that is the one used to calibrate the pellicle BS, meaning a more reliable 50/50 reflection-transmission ratio. A video was recorded to help on the after-visual comparison between the MZ outputs.
is, photons of a beam that cannot travel to the regions with destructive interference do not finish on the other output where the interference remains constructive.
The results shown here do not diminish the experimental work performed by [
In short, according to our analysis of previous experiments ( [
We would like to acknowledge the junior student Carmen Vargas at Florida International University for realizing the video and for performing the light intensity calculations on the figures introduced here. To Ivan Santiago, Photographer of the Academic Imaging Services, Division of Information Technology, Florida International University, for supervising the quality of the graphical material offered here. Special mention to the Professor Francisco Mueller for supervision of all the experimental work done and for guarantee that every concept introduced were crystal clear and precise.
Parra, J.L. (2018) Single-Photon Interaction with Beam Splitters. Optics and Photonics Journal, 8, 20-28. https://doi.org/10.4236/opj.2018.82003