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17th Congress of the International Commission for Optics: Optics for Science and New Technology

Photonic interpretation of refractive index

Hassan Kaatuzian

Published Sep 1, 1996• 2 citations
Publisher

Abstract

In this paper we'll introduce a new treatment called photonics -which is based on wave-particle nature of light- to estimate theortically the refractive index of a dense material in microscopic scales. The main result obtained from this research is the prediction of wave- particle unification! In stead of wave- particle Duality nature of light. The starting points in photonics are planck formula, Hamilton principle, Jacobi and Maupertuis' functions. We've successfully estimated microscopic delay parameter "τ", related directly to macroscopic parameter "n": The index of refraction.

DOI
10.1117/12.2299045

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arXiv:2303.10998•Mar 20, 2023•0 citations
In this paper we'll introduce a new treatment called photonics -which is based on wave-particle nature of light- to estimate theortically the refractive index of a dense material in microscopic scales. The main result obtained from this research is the prediction of wave- particle unification! In stead of wave- particle Duality nature of light. The starting points in photonics are planck formula, Hamilton principle, Jacobi and Maupertuis' functions. We've successfully estimated microscopic delay parameter "τ", related directly to macroscopic parameter "n": The index of refraction.
Neither the pure wave theory nor the pure particle theory can explain the nature of light. Light must be both a particle and a wave. It is a wave because it exhibits interference effects. At the same time, the fact that the photographs contain discrete dots is a direct demonstration that light refuses to be split into units of less than a single photon. We found a general equations that solved all the problems in the current theories for the photon and explained the nature of light by suggesting new hypotheses. According to our results, the photon is a particle which has mass and associated with a wave. The results of the research proved that the refractive index of materials varies with the natural mass of the photon.
Quantum mechanics is one of basics theories of modern physics, and it is also a theory established with some debates of assumptions. However, in the teaching process, if the assumption of wave-particle duality is directly given, it will be particularly difficult for students to understand. Therefore, based on the teaching practice and previous research, we assume that light corresponds to a kind of real particle starting from the classical electromagnetic theory, according to the description methods of wave optics and geometric optics, and the form of functional equations. Subsequently, employing Planck's quantum conditions, we discuss the connection between the wave nature and particle nature of light. And then the Planck-Einstein relation and the de Broglie relationship are derived, which reflect the wave-particle duality of light and real particle.
The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........
We are now in the beginning of quantum supremacy to build Quantum Computers (Q.C.). So, a theoretical roadmap is required. It seems experimental works in Q.C. is ahead, in comparison with theory. In this study, Nano-Refraction (N.R.), as basic concept in developing Quantum Photonic Computers (Q.P.C.), is defined and discussed. N.R., is quite different from classical macroscopic refraction. It plays major role in photon deflection, when it travels in few atomic layers from the boundary between two transparent materials. Specifically, when we’re looking for a theoretically intuitive explanation of how advanced materials work in atomic scales in atto-second regime. To explain N.R., mathematically, Quantum Electrodynamics (QED) may help. But QED, only can describe how N.R. occurs in Hilbert space and does not explain why it happens in Real space? Why attosecond optical pulses are squeezed in kilometers long optical fibers coiled in first reported development of Q.C. in 2020. Also, “Duality” has no reply in this area. For answering why?, in this paper, we’ll use Quantum Photonic (Q.P.) theoretical analysis. Q.P., is based on Bohmian mechanics with intuition physics belief and “Causality”. Bohm theory in shadow of Quantum Mechanics (Q.M.) has been mostly ignored and even boycotted during last 70 years. Q.P. corpuscular viewpoint of light, estimated both physically and mathematically with enough precision, that flight route of photons at first few molecular surfaces in boundary region is not refracted suddenly. As can be observed macroscopically in Snell’s refraction equation. But instead, N.R. is happened gradually in attosecond regime (figure 2). Finally, it asymptotes to macroscopic refraction, in large space-time scales according to “correspondence” principle. Errors in our theoretical analysis using Montecarlo time domain simulation, compared with experiments, always are much less than or at most five percent.
All known optical materials have an index of refraction of order unity. Despite the tremendous implications that an ultrahigh index could have for optical technologies, little research has been done on why the refractive index of materials is universally small, and whether this observation is fundamental. Here, we investigate the index of an ordered arrangement of atoms, as a function of atomic density. At dilute densities, this problem falls into the realm of quantum optics, where atoms do not interact with one another except via the scattering of light. On the other hand, when the lattice constant becomes comparable to the Bohr radius, the electronic orbitals begin to overlap, giving rise to quantum chemistry. We present a minimal model that allows for a unifying theory of index spanning these two regimes. A key aspect is the treatment of multiple light scattering, which can be highly non-perturbative over a large density range, and which is the reason that conventional theories of the index break down. In the quantum optics regime, we show that ideal light-matter interactions can have a single-mode nature, allowing for a purely real refractive index that grows with density as (N/V)1/3(N/V)^{1/3}(N/V)1/3. At the onset of quantum chemistry, we show how two physical mechanisms (excited electron tunneling dynamics and the buildup of electronic density-density correlations) can open up inelastic or spatial multi-mode light scattering processes, which ultimately reduce the index back to order unity while introducing absorption. Around the onset of chemistry, our theory predicts that ultrahigh index (n∼30n\sim 30n∼30), low-loss materials could in principle be allowed by the laws of nature.