Investigation on characteristics of W-type fiber with an inner cladding made of negative refractive index materials

A doubly clad optical fiber with an inner cladding made of negative refractive index material was proposed and the modes distribution, dispersion and time delay were investigated by fully vectorial numerical method. The results indicate that HE₁₂ mode can be operated as a single mode, the cut-off frequency of modes shifts to low normalized frequency with increasing thickness of inner cladding made of negative index materials, large negative dispersion and time delay can be obtained and tailored by the inner cladding. These results provide theoretical basis for designing novel fibers or optical devices.     

包层为负折射率介质的抛物型渐变光纤色散特性分析

研究了纤芯为各向同性非均匀材料,而包层为负折射率均匀介质光纤的色散特性.在纤芯满足弱渐变条件的假定下,按矢量场分析法,通过芯层与包层的介电常数比ξ和磁导率比η,讨论了导波模式色散特性对左手介质包层材料的依赖性.分析表明,ξ和 η对轴对称模色散曲线的低频段影响较大,但对非轴对称模影响不大.ξ和 η对导波模式的截止频率没有影响.由于该光纤中的HEm1模的截止频率都等于0,所以不存在理论上的单模区,但仍可近似实现无色散传输.     

Perturbation theory of low-V optical fibres with dip in the refractive index

A simple perturbation theory has been used to study the characteristics of low-V, step-index optical fibres with a dip in the centre of the refractive index profile. Analytical expressions have been derived for the cut-off frequency and propagation constant of an arbitrary mode on such a fibre. In particular, it has been shown that even when the dip is quite large, the perturbation theory results for the propagation constant of the fundamental mode and cut-off frequency of the second mode are virtually indistinguishable from exact numerical results calculated by series expansion techniques.     

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.     

Optical delay lines using coupled slab waveguides and ring resonator with a negative refractive index core

Total delay time of a structure composed of a slab waveguide coupled with a ring resonator where negative refractive index material is replaced in the core of the structure is investigated in this work. In this paper, a two-port ring resonator (TPRR) which is made of a core with negative refractive index has been used to generate a time delay for a Gaussian-shaped pulse with 1 GHz bandwidth. It is shown that the creation of the ring how causes more n_g of a straight waveguide and results are compared with positive refractive index core TPRR. We have used metamaterial to make an n < 0 media and have used two cascaded metamaterial rings to increase the bandwidth.     

Effective dielectric constant of two-dimensional photonic crystals in optical bands

By using the Fourier expansion method, we have developed an approach to calculate the effective dielectric index of a two-dimensional photonic crystal. The approach is very general: it can take into account various Bravais lattice structure as well as arbitrary spatial variation of the dielectric index. It has been found that near a nondegenerate frequency ω_n(Γ) at Γ point, the transverse magnetic (TM) mode is ordinary, as it is independent of the propagation direction, whereas in general the transverse electric (TE) mode depends on the propagation direction, it is extraordinary. Therefore, a two-dimensional photonic crystal can always be described by an effective dielectric index for TM mode near the nondegenerate frequency ω_n(Γ). However, the TE mode is much more complicated unless the lattice structure is highly symmetric. Moreover, a two-dimensional square photonic crystal has been identified as an effective birefringent crystal having two negative refractive indexes from the perspective of Snell's law.     

基于耦合介质纳米线的深亚波长局域波导

提出了一种基于耦合介质纳米线的深亚波长局域波导,通过两根紧邻的高折射率介质纳米线的耦合,该波导可以将光场有效束缚在纳米线之间的低折射率纳米缝隙中. 计算模拟的结果表明,该波导的有效模场面积达到Λ²₀/200,比单根纳米线波导小一个数量级,这种深亚波长的模场束缚能力可以与表面等离激元混合波导相比拟. 计算模拟的结果还表明,纳米线可能带有的低折射率氧化膜、低折射率衬底的存在、以及纳米线间尺寸存在的一定差异对于该波导结构的实际应用都不会产生很大 关键词： 介质波导 亚波长局域 表面等离激元波导 纳米线     

Wave refraction and backward magnon–plasmon polaritons in left-handed antiferromagnet/semiconductor superlattices

Characteristics of the bulk electromagnetic waves in teraHertz frequency region are examined in a left-handed superlattice (SL) which consists of alternating layers of nonmagnetic semiconductor and nonconducting antiferromagnetic materials. General problem on the sign of the refractive index for anisotropic media is considered. It is shown that the phase refraction index is always positive while the group refractive index can be negative when some general conditions are fulfilled. Effective permittivity and permeability tensors of the SL are derived for perpendicular and parallel orientation of the magnetic anisotropy axis with respect to the plane of the layers. Problem of anomalous refraction for transverse electric and transverse magnetic-type polarized waves is examined in such media. Analytical expressions for both the phase and group refractive indices are obtained for various propagated modes. It is shown that, in general, three different types of the refracted waves with different relative orientation of the phase and group velocity vectors are possible in left-handed media. Unusual peculiarities of the backward modes corresponding to the coupled magnon–plasmon polaritons are considered. It is shown, in particular, that the number of the backward modes depends on the free charge carrier's density in semiconductor layers, variation of which allows to create different frequency regions for the wave propagation.     

负折射率介质光纤的导模异常特性分析

对芯层为负折射率介质,敷层为普通介质的光纤的导模进行了研究,并对芯层与敷层介电常数比值（ξ）和磁导率比值（η）变化对导模色散特征的影响进行分析.分析表明负折射率光纤具有许多不同于常规光纤的反常特征,如存在表面波模,存在TM00模和TE00模以及存在多个单模传输模式和单模传输区间等.同时对负折射率介质光纤的单模传输条件进行了分析,发现单模传输模式和传输区间随ξ和η的不同而改变.     

Ordinary and extraordinary cyclotron waves in metals

Dispersion equations for the ordinary and extraordinary cyclotron waves propagating perpendicular to the magnetic field in metals in the critical region where the wavelength is comparable to the electron Larmor radius are derived as an infinite but rapidly converging power series expansion in δ( = Ω/Ω-M). Numerical studies for the cyclotron wave propagation near the first seven resonances are carried out. The non-local behaviour of those waves in the critical region 01 ⩽ kR ⩽ 3-0 is studied. For the ordinary waves the first few resonances show significant dispersion than those near higher resonances which are dispersion-free. Only one extraordinary wave propagates near the fundamental cyclotron frequency. For the higher resonances, two modes propagate near each of the resonant frequencies, of which one mode remains constant for all values ofkR whereas the second mode shows significant dispersion. But beyond the fifth resonance both the modes are dispersion free.     

Fused silica as a composite nanostructured material

A method for calculating the refractive index of optical fused silica by applying the model of effective permittivity of composite homogeneous media is proposed and realized. The calculation was performed using the tabular data of the refractive index of crystalline α quartz and the ratio of the quartz glass and α quartz densities. It was suggested that fused silica contains nanosized pores with a glass filling number q immersed in a matrix with a density differing from the α quartz density by a factor of κ, where κ is slightly less than unity. It was established that the Maxwell-Garnett model makes it possible to calculate the refractive index of quartz glass and its dispersion in the transparency range (404 nm ≤ λ ≤ 671 nm) with a deviation less than 0.0002 from the tabular values. The calculated and experimental values coincide at q = 0.155 and κ = 0.986.     

Interpretation of photo-polarimetric observations of comet 17P/Holmes

We present multispectral photo-polarimetric observations of comet 17P/Holmes taken at three different dates. These observations show the evolution of the negative polarization branch (NPB) as a function of time and wavelength. We perform discrete-dipole approximation (DDA) simulations on agglomerated debris particles of various sizes and refractive indices. Our simulations show that the observations are consistent with the cloud being composed of agglomerated debris particles having refractive indices of approximately m=1.5-1.6+0.1i. Our results are also consistent with the particles obeying a power-law size distribution r^-a and having a lower particle-radius cut-off of approximately 0.6 μm, where the index a∼3.5 for the early observations and shrinks to a∼1.5 for the later observations. This is consistent with the smaller, more accelerated particles in the distribution being propelled out of the field of view.     

负媒质模型的时域有限差分法分析

 负折射率媒质是一种人造媒质,在某一微波波段内其介电常数和磁导率同时为负值。对TE模电磁场满足的麦克斯韦方程组进行数值处理,解决了直接利用时域有限差分方法在Yee’s网格下计算负折射率媒质内部场分布时的数值发散问题。通过数值算例,验证了方法的可行性,模拟了负折射率媒质内部及周围的电磁场分布。     

Defect modes properties in periodic lossy multilayer containing negative index materials with symmetric and asymmetric geometric structures

In this paper, the characteristic matrix method is used to study the propagation of electromagnetic waves through one-dimensional lossy photonic crystals composed of negative and positive refractive index material layers with symmetric and asymmetric geometric structures with a defect layer at the center of the structure. First, the positive index material defect layer is considered, and the effects of the polarization and the angle of incidence on the defect mode in the transmission spectra of the both structures are investigated. The results show that the number of the defect modes in the transmission spectra depends on the geometry (symmetric or asymmetric) of the structure. In addition, it is shown that the defect mode frequency increases as the angle of incidence increases. This property is independent of the geometry of the structure. Then, for normal incidence, the negative index material defect layer is considered, and the properties of defect modes for both structures are investigated. The results can lead to designing new types of transmission narrow filters.     

High-frequency asymptotic behavior of T-odd optical effects

It is shown that the contribution of low-frequency excitations with characteristic energy ℏω _l to T-odd (nonreciprocal) optical effects, including spatial dispersion effects, at optical frequencies ω≫ω _l can be calculated in the zeroth-order approximation with respect to the parameter ω _l/ω. This greatly simplifies their analysis. Some of these effects are found to be frequency independent in the spectral regions where the refractive index n(ω)≈ const. It is shown that frequency-independent Faraday rotation can be observed in media with zero magnetization, including in media with zero microscopic magnetic moment density. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 510–513 (10 April 1999)     

On the supraluminal group velocity and the transmission of information

The calculations are reported indicating that the transmission of information through a medium with the frequency dispersion of the refractive index n(ω), where the group velocity is higher than the speed of light in vacuum, always occurs exactly with the speed of light in vacuum. This result is valid for any functional dependence n(ω).     

Spectral measurements of dielectric characteristics of petroleum and petroleum oils in the millimeter wave range

We obtain experimental data on the complex refractive index N = n+ik of petroleum, five petroleum oils, and water-petroleum emulsion in the frequency range f = 75–120 GHz. Measurements were performed in a quasioptical equipment with a backward-wave oscillator generating the radiation and an OAP-7 optical-acoustic receivers for a temperature of 27°C of studied liquids. The refractive indices n of petroleum and oil have a weak negative dispersion (dn/df < 0) and close values. At a frequency of 100 GHz, they lie in the range n = 1.477–1.495. The absorption indices k have different frequency dependences such that k increases for four oils, while it decreases for petroleum and SM-4.5 oil with increasing f. At the frequency f = 100 GHz, the values of k vary in a wide range from 2.4 · 10⁻⁴ to 1.7 · 10⁻³. The measurement results for petroleum and oils are compared with experimental results obtained by other authors. The frequency dependences of n and k of water-petroleum emulsion for water concentrations 0.11% and 0.58% are compared with the data calculated using various analytical models of dielectric mixtures. The dependences n(f) and k(f) calculated by the Kubo-Nakamura formula are the closest to the experimental data. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 485–495, June 2007.     

Nonlinear refractive index of RECOB (RE = Gd and La) crystals

The Z-scan technique is employed to obtain the nonlinear refractive index (n ₂) of the Ca₄REO(BO₃)₃ (RECOB, where RE = Gd and La) single crystals using 30 fs laser pulses centered at 780 nm for the two orthogonal orientations determined by the optical axes (X and Z) relative to the direction of propagation of the laser beam (k//Y// crystallographic b-axis). The large values of n ₂ indicate that both GdCOB and LaCOB are potential hosts for Yb:RECOB lasers operating in the Kerr-lens mode locking (KLM) regime.     

Plasma-filled rippled wall rectangular backward wave oscillator driven by sheet electron beam

Performance of the backward wave oscillator (BWO) is greatly enhanced with the introduction of plasma. Linear theory of the dispersion relation and the growth rate have been derived and analysed numerically for plasma-filled rippled wall rectangular waveguide driven by sheet electron beam. To see the effect of plasma on the TM₀₁ cold wave structure mode and on the generated frequency, the parameters used are: relativistic factor γ = 1.5 (i.e. v/c = 0.741), average waveguide height y ₀ = 1.445 cm, axial corrugation period z ₀ = 1.67 cm, and corrugation amplitude ε = 0.225 cm. The plasma density is varied from zero to 2 ×10¹² cm^− 3. The presence of plasma tends to raise the TM₀₁ mode cut-off frequency (14 GHz at 2 ×10¹² cm^− 3 plasma density) relative to the vacuum cut-off frequency (5 GHz) which also causes a decrease in the group velocity everywhere, resulting in a flattening of the dispersion relation. With the introduction of plasma, an enhancement in absolute instability was observed.     

Spectra of high-frequency waves in hot magnetized plasmas

On the basis of numerical solution of the dispersion equation, we obtain the spectra of weakly damped high-frequency waves in a hot magnetized plasma for the case where the electron cyclotron frequency ω_He is below the plasma frequency ω_pe. It is shown that the longitudinal wave propagating at an angle to the magnetic field evolves into the slow extraordinary wave for the refractive index n ≤ 1. For n ≫ 1, the longitudinal-wave frequency increases with the refractive index, and the wave evolves into the wave with anomalous dispersion if the angle θ between the wave vector and the magnetic field is close to 90°. In the same range of θ angles, Bernstein modes appear in the spectrum of plasma eigenmode oscillations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 258–266, March 2006.