Calculations of spontaneous emission rates of a single-impurity molecule in uniaxial host crystals

In a uniaxial host crystal the spontaneous emission rate of the dipole transition of the zero-phonon line of a single-impurity molecule depends on the angle between the transition dipole moment and the optical axis of a crystal and as well as on the ordinary and extraordinary refractive indices. The relative spontaneous emission rate (the spontaneous emission rate divided by the spontaneous emission rate in the case when the transition dipole moment is parallel to the optical axis) is determined through a simple formula by one coefficient. Here this coefficient is calculated as a function of the extraordinary refractive index for 40 values of the ordinary refractive index on the interval from 1.25 to 3.20. For comparison, the effects caused by the nearness to the plane interface between cinnabar crystal (HgS) and air, as an example, are calculated.     

Propagation of an arbitrary incident light in a uniaxially planar slab

Similarly to the Jones calculus, a propagation formulation of an arbitrary incident light in a uniaxially planar slab with any orientation of the optic axis is derived, where both the multi-reflections and multi-refractions and the phase difference between the ordinary and extraordinary waves arising at the interface are considered. Unlike the case of propagation in the stratified isotropic media, the elements of the reflection and transmission matrices not only include the reflection and transmission coefficients, but also comprise phase differences caused by the mutual couples between ordinary (O) and extraordinary (E) waves. At this point, the propagation of an arbitrary light in a stratified uniaxially anisotropic media may be viewed as the multi-reflections and multi-refractions of a compound wave composed of one O wave and one E wave.     

Surface integral method to determine guided modes in uniaxially anisotropic embedded waveguides

A surface integral method is presented to calculate the eigenmodes of an uniaxially anisotropic embedded channel waveguide. The electromagnetic field components are expressed with electric and magnetic vector potentials which are parallel with the optic axis and for which the scalar Helmholtz-equations hold using surface integral representation and the Green's functions of the vector potentials. The single component vector potentials are expanded in Fourier-series on the internal side of the dielectric interface. The Fourier-coefficients and the corresponding eigenvalues are obtained by minimizing the quadratic difference of the longitudinal field components in the cladding and core along the dielectric interface. The convergence of the series expansion is examined numerically and the eigenvalues obtained with the surface integral method agree with those obtained by Finite Element Method up to 5 significant digits.     

Characteristics of paraxial propagation of a super Lorentz-Gauss SLG₀₁ mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss(SLG) 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Characteristics of paraxial propagation of a super Lorentz—Gauss SLG01 mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

原子在两个平行镜面间两层电介质板中的自发辐射率

利用光子的闭合轨道理论,我们研究了原子在两个平行镜面间两层电介质板（折射率分别为n1,n2）中的自发辐射率. 自发辐射率呈现出多周期的振荡结构。自发辐射率的傅立叶变换中的每一个峰和光子从原子出发到返回原子的一条闭合轨道相对应。结果表明自发辐射率和两层电介质的宽度和折射率有关。和只有一层电介质的辐射率比较,当两层电介质的折射率n1 和 n2 差别很小时, 两层电介质之间分界面的反射效应可以忽略;但是当二者的差别很大时,发射效应变得非常重要且自发辐射率中的振荡减弱。本文的结果为原子在不同电介质间的自发辐射率的研究提供了新的理解。     

单轴晶体光轴任意取向时非寻常光的折射规律

在单轴晶体光轴任意取向的情形下 ,应用惠更斯原理导出了非寻常光折射方向的普遍计算公式 ,并给出了确定非寻常光线折射面和折射角的具体解。结合几种熟知的特殊情形进行了简要讨论 ,揭示了文中所得到的折射规律较之斯涅尔定律更具有普遍性 ,从而为光学系统中各类单轴晶体光学元件的应用提供了一个理论依据     

Analogien zwischen außerordentlichen und ordentlichen Wellen nach nichtorthogonaler Koordinatentransformation und die parabolischen Näherungsgleichungen

Within the limits of Linear Optics we treat analogies between ordinary and extraordinary waves in uniaxial media which become conspicuous through a nonorthogonal transformation of coordinates. To any ordinary wave solution in unbounded uniaxial media we can construct a corresponding extraordinary wave solution by interchanging electrical and magnetical field components. Boundary conditions for instance for ideal conducting plane surfaces approximately preserve their original form, if the optical axis or the middle wave vector are normal to the surface. The parabolic approximative equations for slowly varying amplitudes are derived, the polarisation of these waves being considered as a slowly varying quantity. Further these approximative equations are expanded to include frequency dispersion. Through the specified transformation we can simplify problems with extraordinary waves.     

Homogenization of magnetodielectric photonic crystals

We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity epsilon(r) and permeability micro(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, omega-->0 and epsilon--> infinity.     

Perfect-lens-material condition from adjacent absorptive and gain resonances

We suggest, based on the principle of causality and for a material exhibiting adjacent absorptive and gain resonances, that there can be an intervening frequency where perfect imaging is in theory possible. At this frequency, both the dielectric constant and the permeability are negative, leading to a negative refractive index, and there is no loss. In such a material exhibiting a double resonance, the gain must be at the higher frequency. Through appropriate tuning of the refractive index, all propagating and evanescent fields from the object could then in principle be reconstructed at the image plane, subject to practical implementation limits.     

Investigation of thermal influence on the bandgap properties of liquid-crystal photonic crystal fibers

We have analyzed the thermal influence on the bandgap properties of liquid-crystal photonic crystal fibers. The bandgap parameters which affect the transmission conditions have been investigated. It is observed that the photonic bandgap can be thermally tuned, i.e. the red or blue shift of the bandgap results from the temperature dependence of the refractive index of the liquid crystal. For the planar alignment of liquid-crystal filled cladding, the ordinary refractive index plays a major role in determining the bandgap properties; the extraordinary refractive index comes into influence while the ordinary refractive index is relatively constant of temperature. The analyses agree well with the experiments results.     

Propagation of Ince-Gaussian beams in uniaxial crystals orthogonal to the optical axis

An analytical propagation expression of an Ince-Gaussian beam in uniaxial crystals orthogonal to the optical axis is derived. The uniaxial crystal considered here has the property of the extraordinary refractive index being larger than the ordinary refractive index. The Ince-Gaussian beam in the transversal direction along the optical axis spreads more rapidly than that in the other transversal direction. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the spreading of the Ince-Gaussian beam in the transversal direction along the optical axis increases and the spreading of the Ince-Gaussian beam in the other transversal direction decreases. The effective beam size in the transversal direction along the optical axis is always larger than that in the other transversal direction. When the even and odd modes of Ince-Gaussian beams exist simultaneously, the effective beam size in the direction along the optical axis of the odd Ince-Gaussian beam is smaller than that of the even Ince-Gaussian beam in the corresponding direction, and the effective beam size in the transversal direction orthogonal to the optical axis of the odd Ince-Gaussian beam is larger than that of the even Ince-Gaussian beam in the corresponding direction.     

Plasmon modes of a superlattice — Classical vs quantum limits

The collective plasmon excitations of a superlattice are investigated in both the classical and quantum limits. Using a model that is applicable to superlattices whose constituent layers are either semiconductor- semiconductor, semiconductor-metal, or metal-metal, we show that the surface plasmon interface modes of each layer (slab) couple via the long range Coulomb interaction into two bands of plasmons with dispersion along the superlattice axis. Results for plasmon dispersion are presented for the classical limit (de Broglie wavelength less than the layer width) where the response is treated via a solution of Maxwell's equations using the bulk 3-D dielectric constant to describe each intervening layer. These results are compared to the plasmon dispersion in the quantum regime where the wave-vector frequency dependent dielectric constant of the superlattice is calculated taking into account quantization effects (subband structure). The relationship between the modes in both limits is derived.     

光轴方向任意的晶体连续双折射双反射

根据惠更斯定理,研究了单轴晶体光轴任意方向的双折射与全内双反射,给出了光线方向和光波法线方向的普遍公式.讨论了在晶体内沿多个面的连续双折射双反射,分析了前一界面输出量和后一界面输入量之间的联系,得到多次双折射双反射后的光线方向和光波法线方向.在此基础上,适当地选取晶体的界面参数,相当于选取光轴方向,可以使o光和e光的分离角Δoe更大.光轴方向任意的晶体连续双折射双反射对晶体器件的最优化设计非常有帮助.最后给出了改变斜入射2×2电光开关的出射面参数使Δoe优化的实例.     

单轴晶体的光程差和Lyot型滤光器的视场

 建立了以光线入射方向和晶体光轴方向为基准的入射坐标系，利用波法线反曲面方程和电磁场在晶体折射界面处切向分量连续性的边界条件，得到了晶体中波法线方向、射线方向、波法线折射率和射线折射率的表达式。从非常光的射线方向和射线折射率出发，得到了在任意的晶体光轴方向和入射角条件下，光通过单轴晶体后寻常光、非常光的光程差表达式。对Lyot型滤光单元的透射率和视场进行了计算分析后发现，滤光单元的透射率随光线入射角的变化呈现一定的周期性，视场随光轴倾角的增大而减小。得出了透射率和视场随光轴倾角(光轴与晶体表面的夹角)和光线入射角(光线在晶体表面的入射角)的变化规律。讨论了通过改变晶体倾角实现滤光器调谐和补偿晶体厚度加工误差等技术问题。     

Investigation of the properties of extraordinary mode in three-dimensional magnetized plasma photonic crystals with diamond lattices as Voigt effects are considered

In this paper, the properties of extraordinary mode for two types of three-dimensional magnetized plasma photonic crystals (3D MPPCs) composed of homogeneous dielectric and magnetized plasma with diamond lattices are theoretically investigated for electromagnetic (EM) wave based on a modified plane wave expansion (PWE) method, as Voigt effects are considered. As EM wave propagates in such 3D MPPCs, the EM wave can be divided in two modes due to the influence of Lorentz force. One is named extraordinary mode and another is ordinary mode. The equations for calculating the dispersive relationships for extraordinary mode as propagating through two types of structures (dielectric spheres immersed in magnetized plasma background or vice versa), are theoretically deduced. The influences of dielectric constant of dielectric, plasma collision frequency, filling factor, the external magnetic field and plasma frequency on the properties of extraordinary mode for both types of MPPCs are investigated in detail, respectively, and some corresponding physical explanations are also given. From the numerical results, it has been shown that not only the locations but also bandwidths and relative bandwidths of the photonic band gaps obtained by extraordinary mode for both types of 3D MPPCs can be manipulated by plasma frequency, filling factor, the external magnetic field and the relative dielectric constant of dielectric, respectively. However, the plasma collision frequency has no effect on the frequency ranges and relative bandwidths of PBGs for two types of 3D MPPCs. The locations of flatbands regions cannot be tuned by any parameters except for plasma frequency and the external magnetic field.     

Characteristics analysis of hybrid plasmonic waveguide for low-loss lightwave guiding

It has been experimentally demonstrated that a low-loss guided hybrid mode is supported if a metal strip is embedded in a low index polymer layer surrounded by two high index slabs. In this paper, further numerical analyses on the guided hybrid modes are reported to fully elucidate the characteristics of the hybrid plasmonic waveguide. For a one-dimensional slab structure with a metal film of infinite width, simulation results exhibit that low-loss guided hybrid modes are associated with surface plasmon modes and dual dielectric slab modes. The optical properties of the guided modes are improved by increasing the field intensity which is confined into lossless dielectric layers by decreasing the metal film thickness and increasing the refractive index and thickness of the high-index slabs. The finite element method is used to investigate the lateral mode confinement of the optical guided modes by the corresponding metal strip. By reducing the metal film width, the guided modes are confined in the plane transverse to the direction of propagation and the characteristics are significantly improved. The hybrid plasmonic waveguide can be exploited for long-range propagation-based application such as optical interconnection.     

On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy

The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time-domain, a finite-difference algorithm to compute the frequency-domain reflectance from reflection data for a pulsed plane wave that is normally incident on a dielectric half-space and (ii) in the frequency-domain, the deflection of an obliquely incident Gaussian beam on transmission through a dielectric slab. The dielectric medium was found to be an active medium with a negative real part for its refractive index. Thereby, a recent controversy in the scientific literature was resolved.     

Refractive index dependent local electric field enhancement in cylindrical gold nanohole

We report on the local electric field characters in a long cylindrical gold nanohole. Theoretical calculation results based on quasi-static model show that the local environmental dielectric constant dependent electric field intensity and field distribution in the gold nanohole show quite unique properties, different from those in the thin gold nanotube. Because of the thick gold wall, no plasmon hybridization exists. So there is only one resonance frequency taking place, and the intense local field has been focused into the gold nanohole. Our main finding is that, the local field in the nanohole is largely dependent on the inner hole refractive index and outer environmental refractive index. The competition between inner hole and outer polarization leads to a non-monotonic change of the local field intensity with increasing the dielectric constant of the nanohole. This refractive index controlled local field enhancement in cylindrical gold nanohole presents a potential for tunable surface-enhanced fluorescence and novel nano-optical biosensing applications.     

Penetration of an ordinary wave into a weakly inhomogeneous magnetoplasma at oblique incidence

A theory is given describing the propagation of high-frequency electromagnetic waves in a plane-stratified weakly inhomogeneous plasma. The density gradient is supposed to be perpendicular to the external magnetic field and the wave vector is expected not to be generally parallel to the plane given by both the preceding vectors. The analysis points out that the ordinary wave can penetrate through the plasma resonance region if the direction of vacuum wave vector is chosen appropriately. Analytical expressions for the reflecion and transmission coefficients are obtained and their dependence on the direction cosines of the wave vector of the incident is studied. The paper further shows in outline that, after transmission through the plasma resonance, the ordinary wave is transformed into an extraordinary wave and the latter is reflected back to the region of the hybrid resonance. In this region the extraordinary wave is fully transformed into the Bernstein modes.