Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1604.03869

Electromagnetic fields, size, and copy of a single photon

Shan-Liang Liu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Photons are almost involved in each field of science and daily life of everyone. However, there are still some fundamental and puzzling questions such as what a photon is.The expressions of electromagnetic fields of a photon are here proposed. On the basis of the present expressions, we calculate the energy, momentum, and spin angular momentum of a photon, derive the relations between the photon size and wavelength, and reveal the differences between a photon and its copy. The results show that the present expressions properly describe the particle characteristics of a photon; the length of a photon is half of the wavelength, and the radius is proportional to square root of the wavelength; a photon can ionize a hydrogen atom at the ground state only if its radius is less than the Bohr radius; a photon and its copy have the phase difference of π and constitute a phase-entangled photon pair; the phase-entangled n-photon train results from the sequential stimulated emissions and belongs to the Fock state. A laser beam is an ensemble of the n-photon trains and belongs to the coherent state. The threshold power of a laser is equal to the power of the n-photon train. These provide a bridge between the wave theory of light and quantum optics and will further advance research and application of the related fields.

Explore related subjects

physics.optics

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shan-Liang Liu. 2018-05-30. Electromagnetic fields, size, and copy of a single photon. https://arxiv.org/abs/1604.03869

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Mid-infrared reconfiguration of population flow in lanthanide nanocrystals

Converting mid-infrared (MIR) radiation to visible or near-infrared wavelengths is essential for imaging and sensing, yet achieving sensitive, low-power, and scalable detection remains challenging. Lanthanide nanocrystals provide an alternative through ratiometric luminescence but are typically constrained by Boltzmann statistics, which tie population distributions to lattice temperature and limit signal contrast. Here we show that MIR irradiation rebalances dissipative relaxation pathways, driving lanthanide emitters into a non-Boltzmann steady state that enables non-thermal control of population distributions. This allows emission behaviors inaccessible under thermal equilibrium. We exploit this regime to achieve linear MIR detection with respect to MIR power across 6.8 to 8.6 micrometers. The ratiometric response is intrinsically independent of the pump power, enabling operation at an ultralow excitation power of 10 uW, several orders of magnitude lower than conventional approaches. Using standard silicon photodetectors, we then demonstrate room-temperature MIR imaging with detection limits approaching 4 nW um-2. Our results establish lanthanide nanoparticles as an efficient platform for MIR conversion and sensing in nanophotonic systems.

physics.optics↗
arXiv2026

Metasurface-integrated VCSEL designed for polarization control in optical Ising machines

The orthogonal polarization states of vertical-cavity surface-emitting lasers (VCSELs) can be used to describe candidate solutions to the Ising Hamiltonian, which is useful for solving quadratic unconstrained binary optimization problems. However, the natural anisotropy of VCSELs tends to overly favor one polarization state, which impedes the system from working as desired. In this work, we have designed and fabricated a metasurface, which may lead to a VCSEL with reduced undesired anisotropy. By changing the geometric size of nano-structures in the metasurface, the polarization state of the output light can be altered. Based on the injection-locking theory and spin-flip model, we numerically show that VCSELs with lowered anisotropy are more easily affected by the injection locking needed in Ising systems. Additionally, we numerically study the evolution of a 3-bit VCSEL-based Ising system and verify that the computational accuracy of the photonic Ising machine can be improved to more than twice that of its counterpart with higher anisotropy.

physics.optics↗
arXiv2026

Topological Optical Frequency Combs

Optical frequency combs (OFCs) are revolutionary light sources characterized by discrete and equally spaced spectral lines, and they have found widespread applications in metrology, spectroscopy, and communications. In the early stages, OFCs were realized using mode-locked lasers. With advancements in the fabrication of high-quality factor ($Q$) microresonators and the increasing demand for miniaturized and integrable photonic chips, microresonator-based OFCs, commonly referred to as microcombs, have been developed. Although early studies of microcombs primarily focused on single microresonators or a few resonators, a significant breakthrough occurred in 2021 when it was theoretically predicted that light propagating in the topological edge channel of an array of ring resonators could generate nested frequency combs known as topological OFCs. Since then, the field of topological OFCs has progressed rapidly, with experimental observations made in 2024. This Perspective will introduce the history of OFCs, placing particular emphasis on the emergence and development of topological OFCs, as well as exploring the research challenges and opportunities associated with them.

physics.optics↗