Design of omnidirectional asymmetrical high reflectors for optical telecommunication wavelengths

A design for omnidirectional asymmetrical high reflectors for optical telecommunication wavelengths is described. Asymmetry was introduced by applying a power law, so that the coordinates y of the transformed object were determined through the coordinates x of the quarter-wave stack air/H(LH)¹⁵/air in accordance with the following rule y = x ^{1 + k} . Here k is the coefficient defining the asymmetry degree. It is shown that a high-reflection band at any incident angle for both polarizations, i.e., an omnidirectional high reflection band of 0.74 m for optical telecommunication wavelengths 0.85 and 1.3 m is found for the transformed system: air/Te(SiO₂/Te)¹⁵/air corresponding to the optimized k value 0.24.Received: 20 May 2004, Published online: 14 December 2004PACS: 42.70.Qs Photonic bandgap materials - 78.20.Bh Theory, models, and numerical simulation - 77.55. + f Dielectric thin films     

Design of an omnidirectional mirror using one dimensional photonic crystal with graded geometric layers thicknesses

We propose a flexible design for one-dimensional photonic crystals (1D-PCs) with a controllable omnidirectional band gap covering the optical telecommunication wavelengths which are 0.85 μm, 1.3 μm and 1.55 μm. We used for this design the chirped grating. Chirping is applied to geometric thicknesses of layers. It takes two forms, one is linear and the other is exponential. We exploit this technique to have the suitable omnidirectional band gap covering the maximum of optical telecommunication wavelengths. With a quarter wave structure, we can have an omnidirectional band gap generating only one of these wavelengths. With graded structure, we obtain, as is reported in this paper, an omnidirectional band gap which covers the wavelengths 1.3 μm and 1.55 μm at the same time with a large bandwidth. We also achieve an omnidirectional band gap containing the wavelength 0.85 μm and which is obviously larger than that of the quarter wave stack.     

OMNIDIRECTIONAL HIGH REFLECTOR FOR INFRARED WAVELENGTH

We have purposed the design of omnidirectional high reflectors with wide bandwidth (nearly 6300A⁰) for the infrared wavelength. Using translational matrix method for numerical calculation, it is found that a complete photonic band gap high reflector covering the wavelength region 11500A⁰ to 17800A⁰ is obtained for the quarter wave stack air / (n_L n_H)⁷ / air by using the tellurium (n=4.60) and TiO₂ (n=2.35) as material of high reflective index and SiO₂(n=1.45) low refractive index. Due to high refractive index of contrast of the structure i.e. SiO₂/tellurium, a large complete photonic band gap, omnidirectional high reflector, has been observed for the infrared wavelengths. This type of omnidirectional high reflector can be used in telecommunication. Besides this, we have studied the effective refractive indices (phase and group) of the proposed structures. It is observed that the effective refractive indices (phase and group) of the high omnidirectional reflector band are largely changed near the band edges due to the high refractive index of contrast, and the reflections from the internal interfaces of the structure.     

Connection Considerations of Gravitational Field in Finsler Spaces

Some alternative connection structures of the Finslerian gravitational field are considered by modifying the independent variables (x,y) (x: point and y: vector) in various ways. For example, (x ^k ,y ⁱ ) (k,i = 1,2,3,4) are changed to (x ^k ,y ⁰) (y ⁰: scalar) or (x ⁰,y ⁱ ) (x ⁰: time axis); (x ^k ,y ⁱ ) are generalized to (x ^k ,y ⁱ ,p _i ) (p _i : covector dual to y ⁱ ) or (x ^k ,y ⁱ ,q _a ) (q _a : covector different from p _i ); (x ^k ,y ⁱ ) are further generalized to (x ^k ,y ^(a)i ) (a = 1,2,…,m), (y ^(a): (a)th vector), etc.     

Band gap and band offsets of GaNAsBi lattice matched to GaAs substrate

In this paper, we calculate the band gap and the band discontinuities of a GaN _y AsBi _x structure lattice matched to GaAs substrate using the conduction and the valence band anticrossing models at the same time. The results obtained show a good agreement with experiment. The nitrogen and the bismuth concentrations leading to a wavelength emission of 1.55 μm have been determined (x = 3.5%, y = 2%). This structure shows a good electron confinement resulting in a high characteristic temperature.     

Kneading Theory: A Functorial Approach

We study the homology theory of ? - modal maps of the interval. We give another proof of the Milnor and Thurston results about zeta-functions and we give a functorial approach to kneading theory. Our results give explicit methods for computing the sequences of lap numbers ? (f ^k ) and the sequences of numbers of periodic points in an arbitrary interval [x,y]. Received: 25 February 1998 / Accepted: 15 January 1999     

The superconducting properties of YBa2(Cu1−xMx)3O7 for M=Zn and Ni

Transverse and zero-field μSR measurements were made on YBa₂(Cu_1−xNi_x)₃O_7−y withx=0.1 and 0.2, and YBa₂(Cu_1−x Zn _x )₃O_7−y withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained, and the low temperature values of these are σ=3.2 μs⁻¹.1.6μs⁻¹, and 1 μs⁻¹ forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs⁻¹, 0.75 μs⁻¹, 0.65 μs⁻¹, and 0.4 μs⁻¹ forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made, but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect of scattering.     

Gas source molecular beam epitaxial growth model for Ga x In1−x As y P1−y on GaAs

A gas source molecular beam epitaxial (GSMBE) growth model considering an intermediate InGaAsP state is presented. This model is very simple and needs only two fitting parameters, k _In and k _Ga, which are determined experimentally from In_1-x Ga _x As _y P_1-y on InP (0<x<0.47 and 0<y<1). At a growth temperature of 480°C, k _In and k _Ga are 28 and 3 respectively. The temperature dependencies of k _In and k _Ga are also studied: the fitted activation energies are-30 and 330 meV, respectively. Using these parameters, the model is used to predict the AsH₃ and PH₃ flow rates for growing In_1-x Ga _x As _y P_1-y on GaAs (0.51<x<1 and 0<y<1). The lattice mismatch of all the epilayers grown is within 6×10^-4. This indicates that this simple GSMBE model covers the whole compositional range of lattice-matched and coherently strained InGaAsP.     

Intersubband energies in Al1−yInyN/Ga1−xInxN heterostructures with lattice constant close to aGaN

We have studied the conduction band profile and the intersubband transition energy, E₁₂, of Al_1−yIn_yN/Ga_1−xIn_xN quantum well structures. We have considered how material parameters such as non-parabolicity and the uncertainty in the bowing parameter affect E₁₂ and the corresponding wavelength, λ₁₂. The calculations include strain and cover the transition range from telecommunication wavelengths (1.55 μm) to the mid-infrared (∼ 10 μm).     

A new approach to Ermakov systems and applications in quantum physics

Milne–Pinney equation [(x)\ddot]=-w²(t)x+ k/x³\ddot x=-\omega^2(t)x+ k/{x^3} is usually studied together with the time-dependent harmonic oscillator [(y)\ddot]+w²(t) y=0\ddot y+\omega^2(t) y=0 and the system is called Ermakov system, and actually Pinney showed in a short paper that the general solution of the first equation can be written as a superposition of two solutions of the associated harmonic oscillator. A recent generalization of the concept of Lie systems for second order differential equations and the usual techniques of Lie systems will be used to study the Ermakov system. Several applications of Ermakov systems in Quantum Mechanics as the relation between Schroedinger and Milne equations or the use of Lewis–Riesenfeld invariant will be analysed from this geometric viewpoint.     

In situ XAFS experiments using a microfluidic cell: application to initial growth of CdSe nanocrystals

The design and performance of a compact fluorescense XAFS apparatus equipped with a microfluidic cell for in situ studies of nanoparticles are described. CdSe nanoparticles were prepared by solution reaction starting from trioctylphosphine‐Se. Time‐resolved experiments were performed by precisely controlling the reactor coordinates (x,y), allowing the synchrotron X‐ray beam to travel along a reactor channel, covering nucleation and initial growth of nanoparticles. Detailed analysis of EXAFS data combined with UV–vis spectra allow reliable estimation of particle size and density in the initial growth that cannot be accessible by conventional optical techniques based on a long‐range order. The Se K‐XANES spectra are interpreted by multi‐scattering calculations providing bond formation kinetics consistent with the EXAFS data.     

Ru(III), Os(VIII), Pd(II) and Pt(IV) catalysed oxidation of glycyl–glycine by sodium N‐chloro‐p‐toluenesulfonamide: comparative mechanistic aspects and kinetic modelling

The Ru(III)/Os(VIII)/Pd(II)/Pt(IV)‐catalysed kinetics of oxidation of glycyl–glycine (Gly‐Gly) by sodium N‐chloro‐p‐ toluenesulfonamide (chloramine‐T; CAT) in NaOH medium has been investigated at 308 K. The stoichiometry and oxidation products in each case were found to be the same but their kinetic patterns observed are different. Under comparable experimental conditions, the oxidation‐kinetics and mechanistic behaviour of Gly‐Gly with CAT in NaOH medium is different for each catalyst and obeys the underlying rate laws:

• Rate = k [CAT]_t [Gly‐Gly]⁰ [Ru(III)][OH^?]^x
• Rate = k [CAT]_t[Gly‐Gly]^x [Os(VIII)]^y[OH^?]^z
• Rate = k [CAT]_t[Gly‐Gly]^x [Pd(II)][OH^?]^y
• Rate = k [CAT]_t[Gly‐Gly]⁰ [Pt(IV)]^x[OH^?]^y

Here, and x, y, z < 1 in all the cases. The anion of CAT, CH₃C₆H₄SO₂NCl^?, has been postulated as the common reactive oxidising species in all the cases. Under comparable experimental conditions, the relative ability of these catalysts towards oxidation of Gly‐Gly by CAT are in the order: Os(VIII) > Ru(III) > Pt(IV) > Pd(II). This trend may be attributed to the different d‐electronic configuration of the catalysts. Further, the rates of oxidation of all the four catalysed reactions have been compared with uncatalysed reactions, under identical experimental conditions. It was found that the catalysed reaction rates are 7‐ to 24‐fold faster. Based on the observed experimental results, detailed mechanistic interpretation and the related kinetic modelling have been worked out for each catalyst. Copyright © 2008 John Wiley & Sons, Ltd.     

Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips

We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length L_x vertices and of width L_y vertices and, in the L_x→∞ limit, the exponent of the ground state entropy, W=e^S₀/k_B. The strips considered, with their boundary conditions (BC), are (a) (FBC_y, PBC_x) = cyclic for L_y=3, 4, (b) (FBC_y, TPBC_x) = Möbius, L_y=3, (c) (PBC_y, PBC_x) = toroidal, L_y=3, (d) (PBC_y, TPBC_x) = Klein bottle, L_y=3, (e) (PBC_y, FBC_x) = cylindrical, L_y=5, 6, and (f) (FBC_y, FBC_x) = free, L_y=5, where F, P, and TP denote free, periodic, and twisted periodic. Several interesting features are found, including the presence of terms in P proportional to cos(2πL_x/3) for case (c). The continuous locus of points where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros. Some results are given for strips of other lattices.     

Single-frequency operation of a laser diode side-pumped Q-switched Tm:YAG laser using seeding injection technique

A laser diode (LD) side-pumped 2 μm single-frequency Q-switched Tm:YAG laser was demonstrated. The laser was injection seeded by a CW single frequency Tm:YAG laser with a twisted-mode cavity. The maximum single-frequency pulse energy was 16.3 mJ, with a pulse width of 570 ns and a pulse repetition rate of 10 Hz. The linewidth of the 2 μm single-frequency Q-switched laser was 0.68 MHz, measured by using the optical heterodyne technique. The M ² of the laser beam was measured to be 1.09 and 1.03 for x direction and y direction, respectively.     

Si/Si1−xGex/Si-based quantum wells infrared photodetector operating at 1.55 μm

A quantum well infrared photodetector consisting of self-assembled type II SiGe/Si based quantum wells operating around 1.55 μm at room temperature has been investigated. The Si_1−yGe_y/Si/Si_1−xGe_x/Si/Si_1−yGe_y stack results in a ‘W’ like profiles of the conduction and valence bands strain-compensated in the two low absorption windows of silica fibers infrared photodetectors have been proposed. Such computations have been used for the study of the p-i-n infrared photodetectors operating, around (1.3–1.55 μm) at room temperature. The quantum transport properties of electrons and holes were approved with Schrödinger and kinetic equations resolved self-consistently with the Poisson equation. The theoretical performances of the photodetector were carried out such as the dark current mechanisms, the temperature dependence of normalized dark current and the zero-bias resistance area product (R₀A).     

250步混沌强度解析混沌特征及其在心率研究中的应用

应用250步混沌强度分析Lorenz系统，分别对3维和x分量进行了计算表明，250步混沌强度与Lorenz系统的参数有明显关系.计算了正常人的窦性心率的250步混沌强度，得到了它与年龄的关系：y=6.4623-0.0496x，相关系数为-0.669，这一结果支持了Goldberger的观点，如果人的250步混沌强度照此规律衰减，将在130岁降到0.     

Instability Zones of a Periodic 1D Dirac Operator and Smoothness of its Potential

Let L be the differential operatorwhere P(x),Q(x) are 1-periodic functions such that The operator L, considered on [0,1] with periodic (y(0)=y(1)), or antiperiodic (y(0)=−y(1)) boundary conditions, is self-adjoint, and moreover, for large |n| it has, close to nπ, a pair of periodic (if n is even), or antiperiodic (if n is odd) eigenvalues λ⁺_n , λ^-_n. We study the relationship between the decay rate of the instability zone sequence γ_n = λ_n⁺ - λ_n^-, n → ± ∞, and the smoothness of the potential function P(x).The first author acknowledges the hospitality of The Mathematics Department of The Ohio State University during academic year 2003/2004. His research is partially supported by Grant MM–1401/04 of the Bulgarian Ministry of Education and Science.     

A simple model for optimization design of high performance In1−x−y Ga y Al x As strained MQW DFB lasers

It is well known that complex rate equations and the couple wave equation have to be solved by the method of iteration in the simulation of multi-quantum well (MQW) distributed feedback Bragg (DFB) lasers, and a long CPU time is needed. In this paper, from the oscillation condition of lasers, we propose a simple and fast model for optimization of In_1–x–y Ga _y Al _x As strained MQW DFB lasers. The well number and the cavity length of 1.55 m wavelength In_1–x–y Ga _y Al _x As MQW DFB lasers are optimized using the model. As a result, the simple model gives almost the same results as the complex one, but 90% CPU time can be saved. In addition, a low threshold, high maximum operating temperature of 550–560 K, and high relaxation oscillation frequency of over 30 GHz MQW DFB laser is presented.     

Properties of Hg implanted Hg1? x Cd x Te infrared detectors

Experimental performance parameters of Hg implanted Hg_1−x Cd _x Te photovoltaic detectors are analyzed. At 77K, for 8–14 μm band, a comparison is made between performances and theoretical ultimate diffusion limits in low frequency direct detection. Experimental features are well-explained by a model based on the Auger band-to-band process for carrier recombination. Peak detectivities exceeding 10¹¹ cm Hz^1/2W⁻¹, external quantum efficiencies as high as 90%, and zero-bias resistance-area products better than 1 Ω·cm² have been achieved in devices with 12 μm cutoff wavelengths. In the 3–5 μm band performances are far from the diffusion limit. Notwithstanding, at 77K zero-bias resistance-area products are better than 10⁴Ω·cm² and detectivities of the order of 10¹² cm Hz^1/2W⁻¹ were observed at 5 μm. Predominant generation-recombination contribution are present at room temperature in 1–1.3 μm photodiodes whose detectivities, primarily limited by the Johnson noise, at 1.3 μm are higher than 10¹¹ cm Hz^1/2W⁻¹ at 300 K. The high frequency response of the photodiodes is also discussed. Response times as low as 0.5 ns are reached despite some limitations arising from the implanted layer sheet resistance. Work supported by CNR-CISE contract No. 73.01435.     

The anisotropic 3D Ising model

An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order--disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J_x and J_y ) are small compared to the third exchange energy (J_z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J_z /k _B T _c)sinh(2(J_x ?+?J_y )/k _B T _c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k _B T _c/J_z ?=?2[ln(J_z /(J_x ?+?J_y ))?ln(ln(J_z /(J_x ?+?J_y ))?+?O(1)]^?1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ～0.84 at ((H_x ?+?H_y )/H_z )?=?10^?2 to ～0.76 at ((H_x ?+?H_y )/H_z )?=?10^?20.