Photon Structure and Wave Function from the Vector Potential Quantization

A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.

Photonic band structures of quadrangular multiconnected networks

By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks （QMNs） with a different number of connected waveguide segments （NCWSs） and various matching ratio of waveguide length （MRWL）. It is found that all photonic bands are wide bands when the MRWL is integer. If the integer attribute of MRWL is broken, narrow bands will be created from the wide band near the centre of band structure. For two-segment-connected networks and three-segment-connected networks, it obtains a series of formulae of the band number and width. On the other hand, it proposes a so-called concept of two-segment-connected quantum subsystem and uses it to discuss the complexity of the band structures of QMNs. Based on these formulae, one can dominate the number, width and position of photonic bands within designed frequencies by adjusting the NCWS and MRWL. There would be potential applications for designing optical switches, optical narrow-band filters, dense wavelength-division-multiplexing devices and other correlative waveguide network devices.

Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph

This paper presents the theoretical investigation of hierarchical sub-wavelength photonic structures with various periods and numbers of layers, which were fabricated using a high-order waveguide-mode interference field. A 442-nm laser was used to excite high-order waveguide modes in an asymmetric metal-cladding dielectric waveguide structure. The dispersion curve of the waveguide modes was theoretically analyzed, and the distribution of the interference field of high-order waveguide modes was numerically simulated using the finite-element method. The various dependences of the characteristics of hierarchical sub-wavelength photonic structures on the thickness and refractive index of the photoresist and the waveguide mode were investigated in detail. These hierarchical sub-wavelength photonic structures have various periods and numbers of layers and can be fabricated by a simple and low-cost method.

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

Au Microdisk-Size Dependence of Quantum Dot Emission from the Hybrid Metal-Distributed Bragg Reflector Structures Employed for Single Photon Sources

We investigate metallic microdisk-size dependence of quantum dot （QD） spontaneous emission rate and micro- antenna directional emission effect for the hybrid metM-distributed Bragg reflector structures based on a particular single QD emission. It is found that the measured photolumineseence （PL） intensity is very sensitive to the size of metMlic disk, showing an enhancement factor of 11 when the optimal disk diameter is 2μm and the numerical aperture of microscope objective NA=0.5. It is found that for large metal disks, the Purcell effect is dominant for enhanced PL intensity, whereas for small size disks the main contribution comes from plasmon scattering at the disk edge within the light cone collected by the microscope objective.

A New Theory of the Essence and Mass of Photon

Many properties of a single photon, such as density, rest mass, and orbital angular momentum, are still unknown. In a previous study, the photon was presented as a superfluid prolate spheroid structure, with a long-axis radius, short-axis radius, and volume, embodied with two spins—transversal and longitudinal—which are responsible for the three-dimensional helical trajectory of the electromagnetic wave. In this study, the rest mass, density, and energy of photon are mathematically derived, and the relationship between the radius of photon and its frequency is demonstrated. In addition, the difference between the Compton and de Broglie wavelengths is clarified. The calculated density, volume, and rest mass of photon agree with previous experimental results. The photon’s simultaneous longitudinal and transversal spins are moving forces of longitudinal and transversal trajectories, which are the origin of the three-dimensional helix shape of the electromagnetic field. A new mechanism for the photon movement is proposed, and the reason for the zero mass moving photon is revealed;a traveling photon in space exhibits zero mass because its boundaries demonstrate zero relative velocity with the surrounding vacuum. The orbital angular momentum of photon is described using similar macroscopic rotation concepts and applying hydrodynamics laws. A rotating photon is endowed with an angular velocity vector whose magnitude measures the speed with which the radius of the principal axis sweeps an angle, and whose direction indicates the principal axis of rotation and is given by the right-hand rule. The deviation angle is calculated using trigonometric functions, and the origin of the Lorenz factor is revealed.

Photonic Band Modulation in a Two-Dimensional Photonic Crystal with a One-Dimensional Periodic Dielectric Background

A two-dimensional photonic crystal with a one-dimensional periodic dielectric background is proposed. The photonic band modulation effects due to the periodic background are investigated based on the plane wave expansion method. We find that periodic modulation of the dielectric background greatly alters photonic band structures, especially for the E-polarization modes. The number, width and position of the photonic band gaps （PBGs） sensitively depend on the structure parameters （the layer thicknesses and dielectric constants） of the one-dimensional periodic background,

Observation of trapped light induced by Dwarf Dirac-cone in out-of-plane condition for photonic crystals

Existence of out-of-plane conical dispersion for a triangular photonic crystal lattice is reported. It is observed that conical dispersion is maintained for a number of out-of-plane wave vectors（k;）. We study a case where Dirac like linear dispersion exists but the photonic density of states is not vanishing, called Dwarf Dirac cone（DDC） which does not support localized modes. We demonstrate the trapping of such modes by introducing defects in the crystal. Interestingly, we find by k-point sampling as well as by tuning trapped frequency that such a conical dispersion has an inherent light confining property and it is governed by neither of the known wave confining mechanisms like total internal reflection, band gap guidance. Our study reveals that such a conical dispersion in a non-vanishing photonic density of states induces unexpected intense trapping of light compared with those at other points in the continuum. Such studies provoke fabrication of new devices with exciting properties and new functionalities.

Slow Light Transmission in Chalcogenide Photonic Crystal Waveguide

The slow light propagation in a line defect waveguide in chalcogenide photonic crystal of As2S3 rods in air medium has been investigated. It is found that the filling factor of the chaleogenide photonic crystal and the size of defect rods decide the propagation of the guided mode. An increase in the filling factor results in a sharp decrease of the group velocity in the photonic crystal waveguide. It has been demonstrated that, by tuning the filling factor and size of defect rods, the group velocity will be reduced up to about 0.22c.

Tunability of One-Dimensional Plasma Photonic Crystals with an External Magnetic Field

We investigated in detail how photonic band structures （PBSs） of one dimensional plasma photonic crystals （PPCs） are tuned after being exposed to an external magnetic field. We showed that the properties of PBSs of PPCs are tuned correspondingly because the dielectric constant of the micro plasma layer is modified differently in different frequency ranges due to magneto-optical effects. Two numerical cases are calculated and discussed to study the magneto-optical effects on the properties of PBSs, including the Faraday and Voigt effects.

Supersymmetry of In-group and “Out-group” Particles and Some Strange Phenomena

The symmetry of the in-group particles, which are of three-generation fermions, and the “out-group” ones, which are not admitted by three-generation fermions, is discussed. It was found that the “out-group” antiparticles of Bose type, which came into being because of CP （ charge Conjugation-Parity conservation） violation in the early universe and became heavier due to the phase transformation from low temperature to high temperature, are the supersymmetric companions of the in-group particles of Fermi type. The ratio of the number density of photons to that of protons calculated with Planck distribution method is about 0.61× 10^10, which is close to the observed value （ about 10^10） available in literature. A theoretical analysis of the structure of a photon suggests that the photon has a quark-gluon structure, which is consistent with the experimental result reported in literature. As the lightest particle in the supersymmetric companions, the calculated mass of a neutralino is 320 GeV. The so-called “vast area of desert” in mass scale appears to be the supersymmetry area of the three-generation particles, and “neutralinos” are the source of the moving of galaxies and the dark matter of non-baryons.

Biomimetic Photonic Structures with Tunable Structural Colours： From Natural to Biomimetic to Applications

Natural photonic structure with tunable structural colours is one of the most miraculous structures which always catches our eyes. However, the application of artificial photonic structures is limited. Moreover, because of the ability of tunable colours, photonic structure is the excellent candidate for many fields, such as sensor, bioassay, anti-counterfeiting, optical components, photocatalytic, fibers and fabrics. Considering the superior tunable optical property and other excellent performance such as robust mechanical strength, wettability, there are new domains and novel routes for this material that deserve us to explore. In this review, some natural photonic structures are discussed. Some novel fabrication methods and applications will be mentioned in this article. Furthermore, this review provides an insight and outlook for the photonic material with tunable eolours focusing on fabrication, design and applications.

Recent progress in terahertz modulation using photonic structures based on two-dimensional materials

Terahertz(THz)technology has attracted great attention in the past few decades for its unique applications in various fields,including spectroscopy,noninvasive detection,wireless communications,and imaging.In parallel to this,the practical,fast,and broadband modulation of THz waves is becoming indispensable.Two-dimensional(2D)materials exhibit unusual optical and electrical properties,which has prompted tremendous interest and significant advances in THz modulation.This review provides the recent progress in 2D materials-based THz modulators,outlining the operating principles,including all-optical,electro-optic,magneto-optic,and other exotic mechanisms.We focus on the recent advances in THz modulation by the designed photonic structures,such as heterostructure,metamaterial,capacitor,optical cavity,and waveguide integration.Lastly,we discussed the challenges and opportunities for 2D materials-based THz modulators and presented our prospects for the future development.

Functional photonic structures for external interaction with flexible/ wearable devices

In addition to vital functions,more subsidiary functions are being expected from wearable devices.The wearable technology thus far has achieved the ability to maintain homeostasis by continuously monitoring physiological signals.The quality of life improves if,through further developments of wearable devices to detect,announce,and even control unperceptive or noxious signals from the environment.Soft materials based on photonic engineering can fulfil the abovementioned functions.Due to the flexibility and zero-power operation of such materials,they can be applied to conventional wearables without affecting existing functions.The achievements to freely tailoring a broad range of electromagnetic waves have encouraged the development of wearable systems for independent recognition/manipulation of light,pollution,chemicals,viruses and heat.Herein,the role that photonic engineering on a flexible platform plays in detecting or reacting to environmental changes is reviewed in terms of material selection,structural design,and regulation mechanisms from the ultraviolet to infrared spectral regions.Moreover,issues emerging with the evolution of the wearable technology,such as Joule heating,battery durability,and user privacy,and the potential solution strategies are discussed.This article provides a systematic review of current progress in wearable devices based on photonic structures as well as an overview of possible ubiquitous advances and their applications,providing diachronic perspectives and future outlook on the rapidly growing research field of wearable technology.

High efficiency filtering using two-dimensional photonic crystal coupled cavity structures

Transmission spectra of coupled cavity structures （CCSs） in two-dimensional （2D） photonic crystals （PCs） are investigated using a coupled mode theory, and an optical filter based on CCS is proposed. The performance of the filter is investigated using finite-difference time-domain （FDTD） method, and the results show that within a very short coupling distance of about 3λ, where ）, is the wavelength of signal in vacuum, the incident signals with different frequencies are separated into different channels with a contrast ratio of 20 dB. The advantages of this kind of filter are small size and easily tunable operation frequencies.

Nonlinear optical and optical limiting properties of new structures of organic nonlinear optical materials for photonic applications

The nonlinear optical （NLO） and optical limiting （OL） properties of three new structures of organic NLO guest host Poly（N-vinylcarbozole）/disperse orange 3 （PVK/DO3）, PVK/disperse orange 13 （PVK/DO13）. and PVK/disperse orange 25 （PVK/DO25） as a solution at different concentrations and as a thin-film sample are studied using continuous wave z-scan system at 532 nm. The open-aperture z-scan data of the NLO materials in the solution and thin-film samples displayed two-photon and saturable absorptions, respectively. The PVK/DO13 exhibites the largest and best values of the nonlinearities, such as n2, β, X（3） compared with those of PVK/DO3 and PVK/DO25. This nonlinearity increases as the concentration increases. Tile results indicate that these NLO materials are good candidates for optical switching and OL devices.

Complex band structures of 1D anisotropic graphene photonic crystal

The complex band structures of a 1D anisotropic graphene photonic crystal are investigated, and the dispersion relations are confirmed using the transfer matrix method and simulation of commercial software. It is found that the result of using effective medium theory can fit the derived dispersion curves in the low wave vector.Transmission, absorption, and reflection at oblique incident angles are studied for the structure, respectively.Omni-gaps exist for angles as high as 80° for two polarizations. Physical mechanisms of the tunable dispersion and transmission are explained by the permittivity of graphene and the effective permittivity of the multilayerstructure.

Photonic bandgap structure and long-range periodicity of a cumulative Fibonacci lattice

In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector(DBR)structures with the same numbers of layers. Photonic bandgaps are found at two characteristic frequencies, symmetrically separated from the central bandgap in the DBR counterpart. Field amplitude and phase distribution in the Fibonacci lattice indicates an interferential origin of the bandgaps. Fourier transform on the refractive index profile is carried out, and the result confirms a determinate long-range periodicity that agrees well with the photonic band structure.

Facile and Convenient Fabrication of Color-controlled Colloidal Magnetically Assembled Photonic Crystals

A facile, convenient and flexible method to tune the structural color of the colloidal magnetically assembled photonic crystals（CMA-PCs） was proposed. The mechanism to tune structural color could be attributed to the significant influence of the surfactant sodium dodecyl sulfate（SDS） concentration on the particle size, especially on the magnetite content of the superparamagnetic composite nanoparticles（MCNPs）. By adjusting SDS concentra- tion in miniemulsion polymerization of MCNPs, CMA-PCs with desired diffraction colors could be obtained.

An efficient dose-compensation method for proximity effect correction

A novel simple dose-compensation method is developed for proximity effect correction in electron-beam lithography.The sizes of exposed patterns depend on dose factors while other exposure parameters（including accelerate voltage,resist thickness,exposing step size,substrate material,and so on） remain constant.This method is based on two reasonable assumptions in the evaluation of the compensated dose factor：one is that the relation between dose factors and circle-diameters is linear in the range under consideration;the other is that the compensated dose factor is only affected by the nearest neighbors for simplicity.Four-layer-hexagon photonic crystal structures were fabricated as test patterns to demonstrate this method.Compared to the uncorrected structures,the homogeneity of the corrected hole-size in photonic crystal structures was clearly improved.