Photochemical electron transfer at fixed distance : a synthetic model of the photosynthetic primary process

A series of meso-phenyloctamethylporphyrins covalently bonded at the 4'phenyl position to quinones via rigid bicyclo[2.2.2]octane spacers were synthesized for the study of the dependence of electron transfer reaction rate on solvent, distance, temperature, and energy gap. A general and convergent synthesis was developed based on the condensation of ac-biladienes with masked quinonespacer-benzaldehydes. From picosecond fluorescence spectroscopy emission lifetimes were measured in seven solvents of varying polarity. Rate constants were determined to vary from 5.0x10⁹sec^-1 in N,N-dimethylformamide to 1.15x10¹⁰ Sec^-1 in benzene, and were observed to rise at most by about a factor of three with decreasing solvent polarity. Experiments at low temperature in 2-MTHF glass (77K) revealed fast, nearly temperature-independent electron transfer characterized by non-exponential fluorescence decays, in contrast to monophasic behavior in fluid solution at 298K. This example evidently represents the first photosynthetic model system not based on proteins to display nearly temperature-independent electron transfer at high temperatures (nuclear tunneling). Low temperatures appear to freeze out the rotational motion of the chromophores, and the observed nonexponential fluorescence decays may be explained as a result of electron transfer from an ensemble of rotational conformations. The nonexponentiality demonstrates the sensitivity of the electron transfer rate to the precise magnitude of the electronic matrix element, which supports the expectation that electron transfer is nonadiabatic in this system. The addition of a second bicyclooctane moiety (15 Å vs. 18 Å edge-to-edge between porphyrin and quinone) reduces the transfer rate by at least a factor of 500-1500. Porphyrinquinones with variously substituted quinones allowed an examination of the dependence of the electron transfer rate constant κ_ET on reaction driving force. The classical trend of increasing rate versus increasing exothermicity occurs from 0.7 eV≤ |ΔG^0'(R)| ≤ 1.0 eV until a maximum is reached (κ_ET = 3 x 10⁸ sec^-1 rising to 1.15 x 10¹⁰ sec^-1 in acetonitrile). The rate remains insensitive to ΔG⁰ for ~ 300 mV from 1.0 eV≤ |ΔG^0’(R)| ≤ 1.3 eV, and then slightly decreases in the most exothermic case studied (cyanoquinone, κ_ET = 5 x 10⁹ sec^-1).

Wireless optical communication-based spatial pattern

We propose a novel communication technique which utilizes a set of mutually distinguishable optical patterns instead of convergent facula to transmit information. The communication capacity is increased by exploiting the optical spatial bandwidth resources. An optimum detector for this communication is proposed based on maximum-likelihood decision. The fundamental rule of designing signal spatial pattern is formulated from analysis of the probability of error decision. Finally, we present a typical electro-optical system scheme of the proposed communication. (c) 2006 Elsevier GmbH. All rights reserved.

Far-field spot compression without energy loss in main lob in wireless laser communication

Far-field spot compression without energy loss in main lob is of great significance to wireless laser communication. In this letter, we propose two schemes to obtain far-field spot compression without energy loss in main lob. One scheme is based on the simulated annealing (SA) algorithm. Using SA algorithm, we design the phase profile of the diffractive phase element (DPE). Using the designed DPE, far-field spot compression without energy loss in main lob is achieved. The other scheme is based on YG algorithm. By means of YG algorithm, we appropriately designed the DPE in the emitting plane. Using the DPE, far-field spot compression without energy loss in main lob is obtained. (c) 2007 Elsevier GmbH. All rights reserved.

On the Cesari fixed point method in a Banach space

In a paper published in 1961, L. Cesari [1] introduces a method which extends certain earlier existence theorems of Cesari and Hale ([2] to [6]) for perturbation problems to strictly nonlinear problems. Various authors ([1], [7] to [15]) have now applied this method to nonlinear ordinary and partial differential equations. The basic idea of the method is to use the contraction principle to reduce an infinite-dimensional fixed point problem to a finite-dimensional problem which may be attacked using the methods of fixed point indexes.

The following is my formulation of the Cesari fixed point method:

Let B be a Banach space and let S be a finite-dimensional linear subspace of B. Let P be a projection of B onto S and suppose Г≤B such that pГ is compact and such that for every x in PГ, P^-1x∩Г is closed. Let W be a continuous mapping from Г into B. The Cesari method gives sufficient conditions for the existence of a fixed point of W in Г.

Let I denote the identity mapping in B. Clearly y = Wy for some y in Г if and only if both of the following conditions hold:

(i) Py = PWy.

(ii) y = (P + (I - P)W)y.

Definition. The Cesari fixed paint method applies to (Г, W, P) if and only if the following three conditions are satisfied:

(1) For each x in PГ, P + (I - P)W is a contraction from P^-1x∩Г into itself. Let y(x) be that element (uniqueness follows from the contraction principle) of P^-1x∩Г which satisfies the equation y(x) = Py(x) + (I-P)Wy(x).

(2) The function y just defined is continuous from PГ into B.

(3) There are no fixed points of PWy on the boundary of PГ, so that the (finite- dimensional) fixed point index i(PWy, int PГ) is defined.

Definition. If the Cesari fixed point method applies to (Г, W, P) then define i(Г, W, P) to be the index i(PWy, int PГ).

The three theorems of this thesis can now be easily stated.

Theorem 1 (Cesari). If i(Г, W, P) is defined and i(Г, W, P) ≠0, then there is a fixed point of W in Г.

Theorem 2. Let the Cesari fixed point method apply to both (Г, W, P₁) and (Г, W, P₂). Assume that P₂P₁=P₁P₂=P₁ and assume that either of the following two conditions holds:

(1) For every b in B and every z in the range of P₂, we have that ‖b=P₂b‖ ≤ ‖b-z‖

(2)P₂Г is convex.

Then i(Г, W, P₁) = i(Г, W, P₂).

Theorem 3. If Ω is a bounded open set and W is a compact operator defined on Ω so that the (infinite-dimensional) Leray-Schauder index i_LS(W, Ω) is defined, and if the Cesari fixed point method applies to (Ω, W, P), then i(Ω, W, P) = i_LS(W, Ω).

Theorems 2 and 3 are proved using mainly a homotopy theorem and a reduction theorem for the finite-dimensional and the Leray-Schauder indexes. These and other properties of indexes will be listed before the theorem in which they are used.

Transverse intensity distributions of a broadband laser modulated by a hard-edged aperture

By means of the Huygens-Fresnel diffraction integral, the field representation of a laser beam modulated by a hard-edged aperture is derived. The near-field and far-field transverse intensity distributions of the beams with different bandwidths are analyzed by using the representation. The numerical calculation results indicate that the amplitudes and numbers of the intensity spikes decrease with increasing bandwidth, and beam smoothing is achieved when the bandwidth takes a certain value in the near field. In the far field, the radius of the transverse intensity distribution decreases as the bandwidth increases, and the physical explanation of this fact is also given. (c) 2005 Optical Society of America.

Smoothing effect in the broadband laser through a dispersive wedge

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens-Fresnel diffraction integral, Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigated in detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns of different frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patterns in the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved. (c) 2006 Elsevier B.V. All rights reserved.

Smoothing the side lobes of a focused pattern by spectral dispersion in the broadband laser

Starting from the Huygens-Fresnel diffraction integral, the propagation equations of a broadband laser passing through a dispersive lens and a dispersive wedge are derived. Smoothing effect on the side lobes of the focused pattern is achieved as the broadband laser passes through the lens because of the spectral dispersion of the lens. By inserting a dispersive wedge behind the lens, better smoothing effect is realized because a relative position shift between focused patterns of different frequency components is generated due to the spectral dispersion of the wedge. Smoothing effect on the side lobe is obtained even with small bandwidth of the broadband laser as the wedge is used. (c) 2006 Elsevier GmbH. All rights reserved.

Solutions for New Terrestrial Broadcasting Systems Offering Simultaneously Stationary and Mobile Services

221 p.

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Thermal stability and spectroscopic properties of Er3+-doped niobium tellurite glasses for broadband amplifiers

Three Er3+-doped tellurite glasses with compositions of 70TeO(2)-30ZnO, 70TeO(2)-20ZnO-10Nb(2)O(5) and 70TeO(2)-20ZnO-5BaO-5Nb(2)O(5) have been investigated for developing fiber and planar broadband amplifiers and lasers. The optical spectroscopic properties and thermal stability of Er3+-doped tellurite glasses have been discussed. The results show that the incorporation of Nb2O5 increases the thermal stability of Er3+-doped tellurite glasses significantly, Er3+-doped niobium tellurite glasses 70TeO(2)-20ZnO-10Nb(2)O(5) and 70TeO(2)-20ZnO-5BaO-5Nb(2)O(5) exhibit the good thermal stability (DeltaT > 150degreesC), the large emission cross-section (>10 x 10(-21) cm(2)) and broad full width at half maximum (similar to65 nm), will be preferable for broadband Er3+-doped fiber amplifiers. (C) 2004 Elsevier B.V. All rights reserved.

Near infrared broadband emission from bismuth-dysprosium codoped chalcohalide glasses

We investigate the broadband infrared emission of bismuth doped and bismuth/dysprosium codoped chalcohalide glasses. It is found that the bismuth/dysprosium codoping can drastically enhance the fluorescence as compared with either bismuth or dysprosium doped glasses. Meanwhile, the full width at half maximum of bismuth/dysprosium codoped glasses is over 170 nm, which is the largest value among all the reported rare-earth doped chalcohalide glasses. An ideal way for energy consumption between bismuth and dysprosium ions is supposed. Such improved gain spectra of both bismuth and dysprosium ions may have potential applications in developing broadband fibre amplifiers.

Effects of melting temperature on the broadband infrared luminescence of bi-doped and Bi/Dy co-doped chalcohalide glasses

Bismuth (Bi)-doped and Bi/Dy co-doped chalcohalide glasses are investigated as promising materials for amplifiers in optical communication. The samples synthesized at lower melting temperatures (MTs) are characterized by more intensified infrared emissions. With respect to the redox process of a liquid mixture at different MTs, we attribute an emission at 1230 nm to low-valent Bi ions. The lower MT favors the formation of LVB ions, i.e. Bi+ or Bi2+, while the higher MT promotes the production of higher-valent Bi ions Bi3+. An enhanced broadband infrared luminescence with the full-width at half-maximum over 200 nm is achieved from the present Bi/Dy co-doped chalcohalide glasses.

Broadband near-infrared emission from transparent Ni2+-doped silicate glass ceramics

Transparent Ni2+-doped MgO-Al2O3-TiO2-SiO2 glass ceramics were prepared, and the optical properties of Ni2+-doped glass ceramics were investigated. Broadband emission centered at 1320 nm was observed by 980 nm excitation. The longer wavelength luminescence compared with Ni2+-doped Li2O-Ga2O3-SiO2 glass ceramics is ascribed to the low crystal field hold by Ni2+ in MgO-Al2O3-TiO2-SiO2 glass ceramics. The change in optical signals at the telecommunication bands with or without 980 nm excitation was also measured when the seed beam passes through the bulk gain host.(C) 2007 American Institute of Physics.

Broadband optical amplification near 1300 nm in bismuth-doped germanate glass

In this paper, we present the broadband optical amplification in bismuth-doped germanate glass, at the second telecommunication window when excited with 808 nm and 980 nm laser diodes, respectively. The amplification range is from 1272 nm to 1348 nm wavelength, which is within the O-band of silica fiber communication. This bismuth-doped glass can be used as ultra broadband amplification material for wavelength-division-multiplexing (WDM) at the second telecommunication window.