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The photonic spin Hall effect (PSHE) can be realized in a photonic crystal (PC) slab, that is, the unidirectional Bloch surface wave can propagate along the surface of the PC slab under the excitation of elliptical polarized magnetic dipole. It is further proved that PSHE is caused by the interference of the component surface waves excited by the different components of the incident light, which is the so called component wave interference (CWI) theory. In addition, we also find that the spin of the surface wave oscillates periodically in space, and the oscillation period is a unit cell. In a unit cell, the average spin keeps the spin orbit locked. The results show that the spin separation can also be modulated by the position and the polarization state of the magnetic dipole.

The discovery of Photonic spin Hall effect (PSHE) on surface plasmon polaritons (SPPs) is an important progress in photonics. In this paper, a method of realizing multi-channel PSHE in two-dimensional metal-air-metal waveguide is proposed. By modulating the phase difference $$\phi$$ ϕ and polar angle $$\theta$$ θ of the dipole source, the SPP can propagate along a specific channel. We further prove that PSHE results from the component wave interference theory. We believe that our findings will rich the application of SPPs in optical devices.

The main function of the curved superlens is to magnify or minify the image of the pattern cut onto the mask in a photolithograph device. It is found theoretically, in this paper, that the magnifying or minifying function deals with two important properties: one is the magnifying (or minifying) effect and the other is the image quality. The magnifying (or minifying) effect of a specific superlens device can be expressed by a linear function and the image quality can be guaranteed by a quadratic function. The ways to obtain the two functions have been demonstrated in this paper.

The finding of Photon Hall effect (PHE) on metal surface is an important progress in photonics, but it will be more practical if PHE can be realized in line-type waveguide. In this paper, we suggested a way to realize PHE in two-dimensional photonic crystal (PC) waveguide. Numerical simulation results show that the propagating direction and strength of light in the PC waveguide can be controlled by the polarization state of incident light. Different from the PHE on metal surface, the PHE in PC waveguide can be driven not only by circularly polarized light, but also by linearly polarized light. The PHE in PC waveguide can be attributed to the interference of the two component waves excited by the incident light.

The generalized scattering coefficient (GSC) method is pedagogically derived and employed to study the scattering of plane waves in homogeneous and inhomogeneous layered structures. The numerical stabilities and accuracies of this method and other commonly used numerical methods are discussed and compared. For homogeneous layered structures, concise scattering formulas with clear physical interpretations and strong numerical stability are obtained by introducing the GSCs. For inhomogeneous layered structures, three numerical methods are employed: the staircase approximation method, the power series expansion method, and the differential equation based on the GSCs. We investigate the accuracies and convergence behaviors of these methods by comparing their predictions to the exact results. The conclusions are as follows. The staircase approximation method has a slow convergence in spite of its simple and intuitive implementation, and a fine stratification within the inhomogeneous layer is required for obtai...

A novel line-type optical one-way transmission structure is proposed, which consists of a helical subwavelength metal slit. The simulation results obtained from finite-difference time-domain method show that this structure has excellent one-way transmission properties. When a polarized light propagates forward through the structure, its polarization direction will be rotated 90 degree. The backward propagation is blocked.This helical slit can also be a one-way unit of a plane-type one-way transmission structure, in which the setting angle plays an important role in determination of the transmission properties of the one-way plane via the strong coupling effect between the waves in adjacent slits.

The continuous photon Hall effect excited in a surface plasmon polariton system is proposed and realized theoretically, in which the parallel incident light illuminates the small ball nearing the surface. The scattering direction can be continually modulated in the large range of almost 180 degree by the elliptical polarization state of the incident light. The physical reason is displayed intuitively by the component waves interference principle.

A very facile way to obtain multiple interface modes in a one-dimensional photonic crystal heterostructure is proposed in this Letter. We found that the interface modes can be generated by introducing the interfaces, and the number of interface modes equals the number of introduced interfaces. All these interface modes originating from a different geometric Zak phase can create two band branches governed by the two different interfaces. We further find that the two band branches can be renormalized into one band branch with discrete energy levels in the form of sinusoidal function. We believe that these findings can be used to provide direct guidance for practical application and can also make the estimation of practical samples more convenient.

In this study, an analytical solution is proposed to solve the general problems of three-wave mixing with pump depletion. The so-called quasi-phase-matching (QPM) for χ ( 2 ) nonlinearities, including sum frequency generation (SFG), second harmonic generation (SHG) and difference frequency generation (DFG), is amended when the depletion of the pumping light power is considered. The optimum domain width and the corresponding conversion efficiency are discussed. The optimum domain widths deviate from the coherence length l c = π / Δ k , but the deviation is so small that it can be ignored according to the actual situation. The applicable scope of undepleted pump approximation (UPA) is estimated by a proposed relative tolerance. Analysis indicates that the relative tolerance showing the difference of conversion efficiency between the UPA and the exact solution is solely determined by the conversion efficiency. Based on the relative tolerance curves for SFG, SHG, and DFG, two models are developed: one can be used to describe the SFG and SHG processes, whereas the other can be used for the DFG process. These findings can be used to provide direct guidance for practical application, and can also make the estimation of practical samples more convenient.

We investigate light transport in metal slits filled with a one-dimensional periodic stack of low- and high-index dielectric media. We have analytically extracted an exact independent-mode model where each transverse eigenmode is subject to its own Bragg scattering and dispersion modulation. The analytical model allows for easy analysis of the complex band structures calculated by means of the finite-difference time-domain method, where the physical origin of each band can be identified and assigned to a certain eigenmode of a metal slit. The analytical model is also very efficient and convenient to analyze the optical transmission spectra for these metal slits. The origin of all subtle spectral features can be discerned from the band diagram analysis of the relevant independent eigenmodes. A comparative study shows that the simple analytical independent-mode theory is powerful in handling the intrinsic light transport problems for periodically modulated metal slits and analyzing their complicated spectru...

The magnetic properties of ferromagnetic (FM) single-layered nanobelts are investigated if there exists a single-ion anisotropy. The magnetic quantities as functions of belt width and temperature are calculated. The spontaneous magnetization, area of the hysteresis loop. and energy level extension increase with belt width, and decrease with temperature. The Curie temperature increases with belt width. The energy spectra are calculated. When the belt width is fixed, a higher temperature leads to lower energy spectra. The spin-wave energy, as well as the energy level extension, drops with temperature rising, and becomes zero as the temperature reaches the Curie temperature. The results are compared with those of FM single-walled nanotubes. The Curie point T c of a nanobelt is always smaller than that of a nanotube, when the width of the former and the perimeter of the latter are equal, and the reason is analyzed.

We introduce a method to obtain and describe the multiple defect modes in the multiple photonic quantum-well structure [(AB)mC]n(AB)m. It is found that the relationship between structural parameters and defect modes can be obtained by analytically solving the dispersion relationship for the photonic crystal with its periodic unit [(AB)mC], and a laconic and unifying expression can be used to describe the energy levels of both the interface modes and defect modes. The internal mechanism to determine the related parameters is revealed. We believe that these findings can be used to provide direct guidance for practical application.

We investigate one-dimensional nonlinear photonic crystals consisting of ferroelectric domains with the modulated polarization directions. Significant enhancement of second harmonic generation (SHG) is observed from numerical simulations when the frequency of fundamental wave is aimed at the photonic band edge. We devise the model structure with optimal configuration of the polarization directions of the ferroelectric domains in terms of simulated annealing algorithm. The conversion efficiencies of the ‘forward’ and ‘backward’ SHGs can be engineered.

The spontaneous emission (SE) behavior of the polarized atoms in a dielectric thin slab embedded in dielectric or metallic medium is analyzed. It is found that the SE rate of the polarized atoms in the vicinity of interface between the slab and surrounding medium can be considerably varied when changing the polarized direction of atoms. A switching operation of atomic SE between the inhibition and enhancement processes of the SE can be realized. In a dielectric thin slab embedded in metallic medium, the SE rate of the atoms near the dielectric–metal interface is enhanced greatly owing to the effect of surface-plasmon polaritons. Our findings imply that the tuning of the polarized orientation of atoms in the dielectric thin slab can effectively control the atomic SE processes.

A new structure of negative-refractive-index material is proposed, which is composed of ferromagnetic wires setting in two-dimensional Bravais lattice (FWL) with the application of external magnetic field. The refractive index of the FWL consisting of ferrum wires arranged in square lattice is calculated. The refractive index exhibits negative value in the GHz region. A notable characteristic of the FWL is that the negative refractive index is tunable by the applied external field.

We have studied second-harmonic generation (SHG) from quasi-one-dimensional aperiodic optical superlattices (AOSs) of finite lateral width by inverting poled ferroelectric domains. The search for optimal AOS structures corresponds with solving a difficult inverse source problem. We describe the design principle in real-space representation and undertake model designs. The numerical simulations show that the constructed AOSs can implement multiple-wavelength SHG with identical effective nonlinear coefficients at the pre-assigned wavelengths of the incident light. We investigate the effects of mode–mode coupling and the lateral width of the superlattice on the SHG for two cases: incident light beams of plane-wave and Gaussian profiles. When the number of modes increases, the effective nonlinear coefficient decreases in an oscillatory fashion at the beginning and then tends to a constant. For an incident plane-wave beam, the dependence of the effective nonlinear coefficient on the width of the sample is quite weak, while for an incident Gaussian beam this dependence exhibits a rapid decrease at the beginning and then tends to a constant. We display the variation in the effective nonlinear coefficients with the distance of propagation of the optical wave from where the incident light beam impinges on the sample surface and find that this variation exhibits monotonically increasing behaviour. This clearly infers that the contribution of every block to the optical SHG process takes the form of constructive addition. It is expected that this new design method may provide an effective and useful technique for constructing nonlinear optical material to match various practical applications.

Ultra-thin optical coating comprising nanometer-thick silicon absorbing films on iron substrates can display strong optical interference effects. A resonance peak of longitudinal Kerr rotation with the silicon thickness of was found at the wavelength of 660 nm. The optical properties of silicon thin films were well controlled by the sputtering power. Non-iridescence color exhibition and Kerr rotation enhancement can be manipulated and encoded individually.

Second harmonic generation (SHG) in a two-dimensional (2D) nonlinear photonic crystal (NPC) with finite width along [Formula: see text]-direction that is embedded in air is investigated, without adopting the traditional approximations such as a plane-wave approximation (PWA) and slowly varying amplitude approximation (SVAA). The so-called quasi-phase-matching (QPM) and the corresponding SHG conversion efficiency can be modulated significantly by the field of fundamental wave (FW). It is assumed that the incident light, along [Formula: see text]-direction, is normally launched upon the surface of the sample, and QPM for different directions is investigated. It is found that the QPM shows significant differences, compared with the traditional QPM along the two different directions: in the direction of finite width of the sample, the peak value of SHG conversion efficiency is deviated from the traditional case and it gets to its peak values when the transmittance resonance occurs. However, in the other direction, the deviation from the traditional QPM arises from the field modulation of the second harmonic wave (SHW) and in this direction, it is investigated that the full width at half maximum of QPM is much wider than that in the direction of finite width of the sample. These results can be used to provide a theoretical guidance for achieving QPM SHG.

Second harmonic generation (SHG) from the aperiodic optical superlattice (AOS) in considering the pump depletion is investigated. It is found the domain configuration designed in undepleted pump approximation (UPA) can also be used to achieve multiple wavelength SHGs with high enough conversion efficiency for an exact solution. The applicable scope of UPA was estimated by a relative tolerance based on the related SHG conversion efficiency calculated in UPA and an exact solution. Results reveal that the relative tolerance is solely determined by the conversion efficiency, and unrelated to the sample configuration, pump intensity, incidental wavelength and nonlinear media. A model to evaluate an exact solution is proposed, and it is suggested that the SHG conversion efficiency can be easily assessed by the developed model. These results can be used to provide direct guidance for practical application, and can also make the estimation of practical samples more convenient.

We present a general solution of second harmonic generation (SHG) without adopting the slowly varying amplitude approximation when light is incident obliquely upon one-dimensional(1D) inhomogeneous systems. The one-dimensional nonlinear photonic crystals consisting of ferroelectric domains with the modulated polarization direction are investigated. We find that the wavelength which is located at the photonic band edge shifts to the short-wavelength with the increasing angle of incidence. The SHG is enhanced significantly when the frequencies of fundamental wave aim at the photonic band edges and the special arrangement of the polarization directions of the ferroelectric domains is satisfied.

A simple optical structure, termed a pillar-slit structure, is proposed to enhance the contrast ratio of the weak optical signal. The structure consists of a metal slit surrounded by two metal pillars and can be directly incorporated onto optical sensors. The waves excited on the incident surface are modulated by the pillars and then scattered by the slit entrance so as to generate the in-slit surface plasmon polaritons passing through the slit. The transmission power is modified by the surface wave intensity. This structure is capable of suppressing background and enhancing signal light simultaneously. A calculated illustration by the numerical simulation method shows that an increase of the contrast ratio can be exceeded 900 times.

We propose a dressed subwavelength metal slit structure, which is formed by adding a thin metallic grating near the slit entrance with a distance. The simulation computation by means of the finite-difference time-domain method shows that the transmissivity can be substantially enhanced by 30 times compared with the conventional metal slit structure. The transmission spectrum exhibits two characters of the Fabry-Perot resonance and a left-shift. The introduced grating has two effects: (1) more energy is collected from the incident plane, and (2) the effective dielectric region in the slit is extended to the region out of the entrance.

We propose a combination structure which consists of a subwavelength metal slit filled periodically with two different dielectrics to modulate slit plasmon polaritons (slit-PPs). The transmission spectra are simulated by the finite-difference time-domain method and the photonic band gaps are observed. The theoretical formula to calculate the band-gap structures is deduced and the calculation results agree satisfactorily with simulated results. This structure can be termed as slit-PP crystal.

In the past few years, new applications of terahertz wave have given rise to the development of intense terahertz wave source and modulation of terahertz wave [1–4]. However, rigorous experimental conditions or few theoretical explanations were in these works. In this paper, a method to enhance and control the THz pulse generation in air plasma by external electric field is proposed. Two theoretical models, the optics Four-Wave-Mix-Frequency and the electrodynamics electromagnetic radiation are given to explain the results of the proposed method respectively.

The spontaneous emission rate of an atom in dielectric slabs is shown to exhibit multiperiodic oscillations when the system scale is varied. These oscillations are calculated using quantum electrodynamics and analyzed using ideas from closed-orbit theory. The extracted frequencies in the emission rates by Fourier transform agree well with actions of short photon closed orbits. The oscillations in the spontaneous emission rates are interpreted as interferences of emitted photon propagating on closed orbits leaving and returning to the emitting atom. This study provides a new understanding of the spontaneous emission process for atoms in the presence of environments.

The electronic structures of the molecule ${\mathrm{C}}_{50}{\mathrm{Cl}}_{10}$ are studied in the framework of density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE) functional. The static polarizability $\ensuremath{\alpha}$ and second-order hyperpolarizability $\ensuremath{\gamma}$ are calculated by the use of a finite field approach. Both the average static polarizability $(⟨\ensuremath{\alpha}⟩=92.9\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{3})$ and the second hyperpolarizability $(⟨\ensuremath{\gamma}⟩=83.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}36}\phantom{\rule{0.3em}{0ex}}\mathrm{esu})$ are larger than those of ${\mathrm{C}}_{60}$. At the same time, the diagonal components of $\ensuremath{\alpha}$, especially the $\ensuremath{\gamma}$ in the $xy$ plane, which contains the Cl atoms, are much larger than those in the $z$ direction. The reason is mainly from the distribution of $\ensuremath{\pi}$ electrons of the HOMO in the planes perpendicular to the $z$ axis. We predict that ${\mathrm{C}}_{50}{\mathrm{Cl}}_{10}$ and its derivatives should be promising nonlinear optical materials.

Spontaneous decay behavior from an assembly of atoms (or molecules) in a dielectric slab sandwiched by two dielectric semi-infinite spaces with arbitrary refractive indices is investigated. We introduce a lifetime distribution function to describe decay kinetics. The zero-point fluctuations of the electromagnetic field are calculated as a function of the position of atom in the slab. They display a symmetric profile with respect to the central plane of the slab in symmetric structure sample and the contributions of the guided modes and the radiation modes components both exhibit cosinelike variation with a base but with a phase difference of \ensuremath{\pi}. With the increase of the thickness of the slab, the oscillations become dense. In contrast, for the asymmetric structure case, the related curves are asymmetric with respect to the middle plane of slab and exhibit considerably distorted cosinelike oscillations. The dependence of the spontaneous emission rate of atoms on the thickness of the slab and the refractive indices of substrate also is surveyed. Our calculations show that quite wide or narrow lifetime distribution can occur for different thicknesses of the slab. The coexistence of both accelerated and inhibited decay processes appears. The calculated results are in good agreement with experimental results.

A micro metal slit/magnetic scatterer structure is proposed to generate electromagnetic Fano resonance. The magnetic scatterer is formed by infinite long split cylinder resonator array. The analytical transmissivity formulas are deduced from Maxwell electromagnetic theory and the Fano resonance transmission is achieved by the theoretical calculations. The enhancement of environment refractive index leads to an ultrasensitive and linear red shift of resonance peak in the THz range.

We have studied multiple wavelength second harmonic generation (SHG) in one-dimensional multiple photonic quantum-wells (PQWs) structure made of linear and nonlinear material. The numerical simulations show that the devised sample can achieve simultaneously multiple wavelength SHG with nearly identical conversion efficiency by the modulation of both the linear and nonlinear optical coefficient. The fundamental wave frequencies are aimed at the defect states by modulating the linear optical coefficient. The optimal arrangement of the polarization directions of the ferroelectric domains in multiple PQWs are determined by simulated annealing method. By tuning the polarization directions of the domains, the conversion efficiencies of "forward" and "backward" for multiple wavelength SHG can be flexibly modulated.

One of the keys to understanding the extraordinary optical transmission in a subwavelength metal slit is in what field mode is excited. We find that, compared to the usual surface plasmon polariton (SPP), the wavelength of the excited mode is squeezed and will become smaller as the slit width does. This mode is called an in-slit SPP. We show how the wavelength of this mode can be solved by a formula and clearly analyze the physical reason for the wavelength squeeze. Furthermore, the similarities and differences of the wavelength squeeze between normal incidence and oblique incidence are pointed out.

We present a type of confined one-dimensional photonic crystal (1D PC) that is composed of a 1D PC confined by perfect conductor boundaries in the lateral directions of the 1D PC. The dispersion relations are derived using the classical electromagnetic approach, and the photonic density of states and local photonic density of states are calculated numerically. It is found that the combined action of the periodic modulation and the quantization of wave vectors in the lateral directions may give rise to photonic bandgaps and sharp peaks in the photonic density of states, which provides us with an effective way to control the spontaneous emission (SE). Based on this, the SE is investigated by the lifetime distribution function. The numerical results show that there is a wide lifetime distribution with the coexistence of accelerated and inhibited decay processes of the SE.

A theoretical model has been proposed to describe the dependence of the THz wave generated in a laser-induced air plasma on the external electric field. Using this model we predict the following, (i) previously observed results show that the THz pulse enhances linearly with the increase of the external field; (ii) the THz pulse varies as a cosine function with the angle between the direction of the external electric field and the polarization of the incident exciting beam; (iii) and the amplitude is proportional to the square of the intensity of the incident pulse in a low energy region. These predictions are validated by our experiment.

In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of transmission and reflection coefficients depending on structural parameters are analyzed. Then a multi-mode multi-reflection model based on ray theory is proposed to illustrate the transmission in the step-modulated slit explicitly. The key parts of this model are the multi-mode excitation and the superposition procedure of the scatterings from all possible modes, which represent the interference and energy transfer happened at interfaces. The method we use is an improved modal expansion method (MEM), which is a more practical and efficient version compared with the previous one [Opt. Express 19, 10073 (2011)]. In addition, some commonly used methods, FDTD, scattering matrix method, and improved characteristic impedance method, are compared with MEM to highlight the preciseness of these methods., 25 pages, 9 figures