基于模式转换及双峰谐振效应的薄包层镀膜长周期光纤光栅特性研究

基于耦合模理论,首先研究了镀膜长周期光纤光栅(LPFG)高阶包层模的模式转换,划分了高阶包层模的非模式转换区及模式转换区。分析了高阶包层模有效折射率随薄膜厚度增加的响应特性,包层模谐振波长在模式转换区的偏移量要大于非模式转换区。在此基础上,研究了不同包层半径下高阶包层模谐振波长随光栅周期的变化情况,结果表明,相同包层半径下模式转换区内双峰间距的偏移量大于非模式转换区;无论在模式转换区还是非模式转换区,包层半径的减小将增加双峰间距的偏移量。最后分析了不同包层半径下的高阶包层模双峰透射谱在模式转换区及非模式转换区内的折射率响应,进而提出了薄包层镀膜LPFG的优化设计方案,当选定敏感膜层厚度及折射率处于镀膜LPFG的模式转换区内,光栅周期靠近相位匹配转折点时,将得到灵敏度高于传统LPFG双峰传感器的镀膜LPFG折射率型双峰传感器;而减小包层半径,将进一步提高传感器的分辨本领。     

Deposition of coatings on long-period fiber gratings: tunnel effect analogy

The sensitivity of Long-period fiber gratings (LPFGs), coated with high-refractive-index thin film overlays, to the refractive index and the thickness of the overlay, and to the ambient refractive index, can be enhanced with a design based on a two-overlay coating of an LPFG. The first overlay of lower refractive index than the cladding affects the guidance of a cladding mode in the second overlay of higher refractive index than the cladding. This causes a more abrupt cladding modal redistribution than with the deposition of a unique high-refractive-index overlay. The phenomenon is analyzed with a method based on a vectorial analysis of modes and the application of coupled mode theory.     

Widely tunable long-period fiber grating with nm-thick higher refractive index film overlay

By introducing a four-layer step-index waveguide modeling, the characteristics of long-period fiber grating (LPFG) with an nm-thick film overlay, which has higher refractive index than that of fiber cladding are investigated in detail. The influence of both the overlay thickness and refractive index on the tuning ability of LPFG is analyzed. The numerical results demonstrate that spectral response of LPFG is divided into three distinct regions as the overlay deposition increases and the shift of resonant wavelength is drastic in some special thickness range. In conjunction with higher-order cladding mode coupling and fiber cladding etching, the sensitivity of LPFG to the overlay refractive index is enhanced significantly and over 120 nm resonant wavelength tunable range is achieved.     

Low optical loss nano-structured \mathrm{TiO }_{2} planar waveguides by sol–gel route for photonic crystal applications

Nano-structured $\mathrm{TiO }_{2}$ planar waveguides were prepared by sol–gel route: titanium tetraisopropoxide was dissolved in isopropanol, and then hydrolyzed by adding a water/isopropanol mixture with a controlled hydrolysis ratio. The resulting sol was deposited by “dip-coating” on a glass substrate with a controlled withdrawal speed. The obtained films were annealed for 2 h at 350 and $500\,^{\circ }\mathrm C $ , respectively. The structural and morphological properties of the synthesized films were analyzed by X-ray diffraction, scanning electron microscopy, and atomic force microscopy. Optical properties such as refractive index, thickness, number of propagating modes, and attenuation coefficient were measured at 632.8 nm by m-lines spectroscopy as a function of the elaboration parameters. The films exhibit diffraction pattern consistent with an anatase phase and the $\mathrm{TiO }_{2}$ planar waveguides are multimodes and demonstrate propagation losses as low as 0.3 dB/cm.     

镀高折射率纳米膜的长周期光纤光栅特性研究

针对镀高折射率纳米膜的长周期光栅,建立了传感理论模型,研究了长周期光栅的谐振波长与纳米膜厚度及外界折射率的关系,给出不同纳米膜厚度下长周期光栅不同包层模式重组特性.研究发现,当长周期光栅外面镀上一层沿角向均匀分布的纳米膜时,随着膜厚变化会出现包层模分布的明显调制;适当选择镀膜参数和外界介质折射率,最低次包层模式HE1,2会成为镀膜层中的导模,其他的包层模式将会发生模式转换现象;对于较低次包层模式(如HE1.6),在模式转换的时候存在两步转换,而高次的包层模只有一步转换(如HE1.14).同时给出了包层模式转换对外界折射率响应的关系:当膜层厚度增加时,长周期光栅模式转换现象移至低折射率区域.     

Refractive index change and absorption coefficient of T shaped quantum wires: comparing with experimental results

In this work, we have studied the optical properties of a GaAs/Al $_{x}$ Ga $_{1-x}$ As T-shaped quantum wire. In this regard, we have obtained the refractive index change and absorption coefficient. We have also studied the temperature effect on absorption coefficient. The results show that the refractive index change and absorption coefficient decrease and shift towards higher energies when temperature increases. Finally, to check our results, we have compared the absorption coefficient obtained from this work with experimental data at 5 K. Our theoretical prediction has some deviations with experimental data.     

Optical properties of nano-multi-layered quantum dot: oscillator strength, absorption coefficient and refractive index

In this paper, the exact solution of Schrödinger equation for multi-layered quantum dot (MLQD) within the effective mass approximation and dielectric continuum model is obtained with finite and infinite confining potential (CP). The MLQD is a nano-structured semiconductor system that consists of a spherical core (GaAs) and a coated spherical shell (Ga $_{1-x}$ Al $_{x}$ As) as the whole dot is embedded inside a bulk material (Ga $_{1-y}$ Al $_{y}$ As). Using the obtained energies, wave functions and taking advantage of numeric calculations, the oscillator strength, refractive index and absorbtion coefficient change associated with intersubband electronic transition from the ground state to the first allowed excited state are investigated for different CPs (both finite and infinite) and shell thicknesses. The results show that all values of ground state energy for large core dot radius approach the same value (the energy of bulk material) independent of CPs and shell thicknesses. Also it is shown that the optical properties are strongly affected by the changes in CPs and shell thicknesses.     

Late-time tails of fields around Schwarzschild black hole surrounded by quintessence

The evolution of scalar, electromagnetic and gravitational fields around spherically symmetric black hole surrounded by quintessence are studied with special interest on the late-time behavior. In the ring down stage of evolution, we find in the evolution picture that the fields decay more slowly due to the presence of quintessence. As the quintessence parameter $\epsilon $ decreases, the decay of $\ell =0$ mode of scalar field gives up the power-law form of decay and relaxes to a constant residual field at asymptotically late times. The $\ell >0$ modes of scalar, electromagnetic and gravitational fields show a power-law decay for large values of $\epsilon $ , but for smaller values of $\epsilon $ they give way to an exponential decay.     

Skyrme-QRPA calculations for low-lying excitation modes in deformed neutron-rich nuclei

Low-frequency modes of excitation in deformed neutron-rich nuclei are studied by means of the quasiparticle random-phase approximation on the Skyrme-Hartree-Fock-Bogoliubov mean field. We investigate the microscopic structure of the soft $\ensuremath K^{\pi} = 0^{+}$ modes systematically in neutron-rich magnesium isotopes with N = 22, 24, 26 and 28 close to the drip line, and it is found that the strong collectivity in ³⁴Mg and ⁴⁰Mg is acquired due to the coherent coupling between the $ \beta$ vibration and the pairing vibration of neutrons. Microscopic structure of the $\ensuremath K^{\pi} = 2^{+}$ modes changes gradually associated with the location of the Fermi level of neutrons, and it is found that the proton particle-hole excitation generating the $ \gamma$ -vibrational mode in ²⁴Mg continues to play a key role in the near-drip-line nucleus ⁴⁰Mg . The low-frequency octupole excitations are also investigated and the microscopic mechanism for the enhancement of transition strengths is discussed.     

Enhancement of sensitivity in long-period fiber gratings with deposition of low-refractive-index materials

It was proved [Opt. Lett. 30, 720 (2005)] that the deposition of an overlay of higher refractive index than that of the cladding on a long-period fiber grating (LPFG) causes large shifts in the attenuation bands induced by the grating. The result is an enhancement of the sensitivity of the LPFG to variations in the ambient and overlay refractive indices or the overlay thickness. The limitation of the previous design to materials with higher refractive indices than that of the cladding of the LPFG is overcome with a five-layer model. To this purpose, a first overlay of higher refractive index than that of the cladding of the LPFG will enhance the sensitivity of the device to variations in the refractive index of a second overlay of lower refractive index than that of the cladding of the LPFG. Moreover, it is proved that, if the second overlay is thick enough, its behavior resembles that of an infinite layer.     

Calculation of effective index for different dielectric waveguides structures made of PVCi/PMATRIFE polymers at telecom-wavelength \lambda =1.55\,\upmu m

In this paper, a number of polymeric waveguide structures have been analyzed by using two distinct techniques which are: effective index method (EIM) and numerical simulation based on finite difference method (FDM). The main aim of this investigation is the calculation of effective indexes (EI) of the following structures: rib, ridge and buried channel waveguides at telecom wavelength $\lambda =1.55\,\upmu \hbox {m}$ for different dimensions of waveguide cores varying from 1.5–4  $\upmu \hbox {m}$ . Moreover, other optical propagation characteristics such as: confinement factor, normalized and propagation constant have been studied in TE polarisation. Otherwise the effect of the structure parameters and dimensions on the dispersion characteristics has been investigated. On the other hand, the optical field distribution has been computed using commercial software named OlympIOs. The polymers applied in the design of waveguide structures are the PVCi (n = 1,562 $\lambda = {1.55}\,\upmu $ m) used as core layer and the PMATRIFE (n = 1,409 $\lambda = 1.55\,\upmu $ m) used as substrate or cladding layer. The results obtained using EIM and simulation based on FDM show that effective index and field confinement factor of TE fundamental mode increase monotonously with the increasing dimension of core. The obtained results are in good agreement with published data based on other numerical methods.     

Characterization of a large core photonic crystal fiber made of lead–bismuth–gallium oxide glass for broadband infrared transmission

We report on characterization of a large solid core, photonic crystal fiber dedicated to broadband transmission range from visible to mid-infrared. We have fabricated a multi-mode photonic crystal fiber, made of a heavy metal-oxide glass based on the $\hbox {PbO}{-}\hbox {Bi}_{2}\hbox {O}_{3}{-}\hbox {Ga}_{2}\hbox {O}_{3}$ system, modified with $\hbox {SiO}_{2}$ and CdO, synthesized in-house, which shows good transmission up to $4.5\,\upmu \hbox {m}$ , as well as good rheological properties that permit multiple thermal processing steps without crystallization. The core of the fiber is created by replacement of central 60 tubes with solid rods. The photonic cladding is composed of 8 rings of air holes with a filling factor of 0.42. Simulation results shows that the fiber can be used for broadband transmission in the range of 430–3,000 nm. Calculated effective mode area of the fiber is $295\,\upmu \hbox {m}^{2}$ . We have measured attenuation of the fiber in the range 800–1,700 nm and its sensitivity to bending losses. Attenuation ranges from 1 to 4 dB/m in the considered range and bending losses are below 0.7 dB.     

Possible anomalies in Higgs decay: charm-suppression and flavour-violation

It is suggested that the Higgs boson may have a branching ratio into the $c\bar{c}$ mode suppressed by several orders of magnitude compared with conventional predictions and in addition some small but detectable flavour-violating modes such as $b\bar{s}$ and $\tau \bar{\mu}$ . The suggestion is based on a scheme proposed and tested earlier for explaining the mixing pattern and mass hierarchy of fermions in terms of a rotating mass matrix. If confirmed, the effects would cast new light on the geometric origin of fermion generations and of the Higgs field itself.     

\mathcal{PT}-symmetric nonlinear metamaterials and zero-dimensional systems

A one dimensional, parity-time ( $\mathcal{PT}$ )-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken $\mathcal{PT}$ -phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern ( $\mathcal{PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the interelement coupling. In the presence of nonlinearity, the $\mathcal{PT}$ dimer chain configuration with balanced gain and loss supports nonlinear localized modes in the form of a novel type of discrete breathers below the lower branch of the linear spectrum. These breathers that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance between gain and loss is also considered. Fundamental gain-driven breathers occupy both sites of a dimer, while their energy is almost equally partitioned between the two split-rings, the one with gain and the other with loss. We also introduce a model equation for the investigation of classical $\mathcal{PT}$ symmetry in zero dimensions, realized by a simple harmonic oscillator with matched time-dependent gain and loss that exhibits a transition from oscillatory to diverging motion. This behavior is similar to a transition from the exact to the broken $\mathcal{PT}$ phase in higher-dimensional $\mathcal{PT}$ -symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of a piece-wise constant gain/loss function that allows the construction of a phase diagram with alternating stable and unstable regions.     

On the {{\mathcal{N}}=2} Superconformal Index and Eigenfunctions of the Elliptic RS Model

We define an infinite sequence of superconformal indices, ${{\mathcal{I}}_n}$ , generalizing the Schur index for ${{\mathcal{N}}=2}$ theories. For theories of class ${{\mathcal{S}}}$ we then suggest a recursive technique to completely determine ${{\mathcal{I}}_n}$ . The information encoded in the sequence of indices is equivalent to the ${{\mathcal{N}}=2}$ superconformal index depending on a maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars–Schneider model.     

Design of segmented cladding fiber for femtosecond laser pulse delivery at 1550 and 1064 nm wavelengths

Segmented cladding fiber (SCF) is capable of single mode operation over an extended range of wavelengths while maintaining large mode area. In this paper we report the design of an SCF with mode area as large as 1,825  $\upmu \hbox {m}^{2}$ , suitable for delivery of high peak power femtosecond laser pulses at 1550 and 1064 nm wavelengths. An SCF with such a large-mode area is a few-moded fiber and its design requires careful choice of design parameters to have robustness against mode-coupling effects and bend loss. In this paper we address these issues and report a design of an SCF showing near distortion-free propagation of 100-fs, 53-kW peak power pulses at 1550-nm wavelength with 1,825- $\upmu \hbox {m}^{2}$ mode area through fundamental mode. The same fiber can also deliver 250-fs, 15-kW peak power pulses at 1064-nm wavelength with 1,793- $\upmu \hbox {m}^{2}$ mode area. The fiber has been analyzed by using the radial effective-index method in conjunction with transfer matrix method and the pulse propagation has been studied by solving the nonlinear Schroedinger equation by split-step Fourier method. Such a fiber would find applications in multiphoton microscopy and in biomedical engineering.     

Phase sensitivity of light dynamics in PT-symmetric couplers

We study the sensitivity of light dynamics to the internal phase of propagating pulses in the two types of $\mathcal {PT}$ -symmetric models. The first is a waveguide array with an embedded pair of waveguides with gain and loss, called $\mathcal {PT}$ -coupler, and the second is a planar coupler which models a chain of $\mathcal {PT}$ -symmetric couplers. For the first model we investigate the soliton scattering on the mode localized on the coupler, while for second model we study the collision of two breathers. For both models we find that the light dynamics is sensitive to the internal phases of the interacting pulses. Particularly, the $\mathcal {PT}$ -symmetry breaking can take place or not, depending on the internal phases of two signals having identical other parameters.     

An Averaging Theorem for FPU in the Thermodynamic Limit

Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\beta ^{-1}$ . Given a fixed $K$ , we construct $K$ packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order $\beta ^{1-a}$ , $a>0$ ) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $\beta $ . The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\rightarrow \infty $ , $\beta >0$ .     

Absolute E3 and M2 transition probabilities for the electromagnetic decay of the \mathrm{\ensuremath I^{\pi}=K^{\pi}=8^{-}} isomeric state in 132Ce

The decay of the $\ensuremath I^{\pi}=K^{\pi}=8^{-}$ isomeric state at 2340keV in ¹³²Ce has been investigated in the ¹²⁰Sn(¹⁶O, 4n)¹³²Ce reaction. The measurements were carried out in e - $ \gamma$ and $ \gamma$ - $ \gamma$ coincidence modes using an electron spectrometer coupled to the OSIRIS II gamma-ray array at the Heavy Ion Laboratory of the University of Warsaw. Experimentally obtained internal conversion coefficients for the $\ensuremath 8^{-} \rightarrow 6^{+}$ and $\ensuremath 8^{-} \rightarrow 5^{+}$ transitions allowed the multipolarities, mixing ratios, reduced transition probabilities and hindrance factors to be determined.     

Identification of \mathrm{\ensuremath J^{\pi} = 19/2^+} and \mathrm{\ensuremath 23/2^+} isomeric states in 127Sb

The nucleus $\ensuremath {\rm ^{127}Sb}$ , which is on the neutron-rich periphery of the $\ensuremath \beta$ -stability region, has been populated in complex nuclear reactions involving deep-inelastic and fusion-fission processes with $\ensuremath {\rm {}^{136}Xe}$ beams incident on thick targets. The previously known isomer at 2325 keV in $\ensuremath {\rm {}^{127}Sb}$ has been assigned spin and parity $\ensuremath 23/2^+$ , based on the measured $\ensuremath \gamma$ - $\ensuremath \gamma$ angular correlations and total internal conversion coefficients. The half-life has been determined to be 234(12) ns, somewhat longer than the value reported previously. The 2194 keV state has been assigned $\ensuremath J^{\pi} = 19/2^+$ and identified as an isomer with $\ensuremath T_{1/2} = 14(1) {\rm ns}$ , decaying by two $\ensuremath E2$ branches. The observed level energies and transition strengths are compared with the predictions of a shell model calculation. Two $\ensuremath 15/2^+$ states have been identified close in energy, and their properties are discussed in terms of mixing between vibrational and three-quasiparticle configurations.