Search

It is especially important to study on the change of 4H-SiC physical properties by swift heavy ion irradiation (SHI) for the future application of SiC devices in extreme irradiation environment. Herein, 4H-SiC Schottky barrier diodes (SBDs) are irradiated by 1.9 GeV 209Bi ion beams without intentional heating. The cross-sectional Micro-Raman Spectroscopy (MRS) results clearly indicated that there are new vibration bands at low fluence. This is attributed to the formation of homonuclear bonds Si–Si and C–C within the SiC network to break down the Raman selection rules. At high fluence, there are only typical Raman data for 4H-SiC crystal and the disappearance of Si–Si and C–C bonds. In addition, it is observed that the interfacial structure is modified due to the silicon and carbon atomic migration during SHI process at the metal-semiconductor interface, and then reacting at high temperature annealing treatment. Furthermore, these results suggest that the evolution of recrystallization effect is varied with irradiation fluence by the cross-sectional MRS.

The development of novel large-scale synthesis protocols for heteroatom-doped porous carbon nanosheets is highly imperative for wastewater purification and high-performance electrode materials. In the present work, we propose a simple and feasible explosion-assisted activation strategy to fabricate a kind of N-doped porous carbon nanosheet (N-PCNS) at a large scale, in which only lactose and zinc nitrate were used as raw materials. The obtained N-PCNS possesses hierarchical micro- and mesopore nanostructures with a high specific surface area of 879 m2 g−1 while keeping a high nitrogen content of 3.73 at%. The adsorption properties of the N-PCNS were systematically evaluated through adsorption of neutral red (NR) dye. The adsorption capacity of the N-PCNS was as high as 439.6 mg g−1, meanwhile the adsorption process exhibited fine correlation with the Langmuir isotherm and pseudo-second-order kinetic models. As an electrode material for supercapacitors, the specific capacitance of the N-PCNS is up to 263 F g−1 at 1 A g−1 and 194 F g−1 at 20 A g−1, revealing superior rate performance. The capacitance retention after 10 000 cycles at 20 A g−1 is 96%, demonstrating excellent cycling stability. Our work provides an effective approach to achieve the large-scale preparation of high-performance doped carbon materials.

Organic dye pollution in the water environment is a problem of global concern. Adsorption is demonstrated as a promising technology to remove organic dyes from wastewater, in which the development of highly-efficient adsorbents is still the challenging task. Herein, we reported the facile fabrication of polyamine-based cyclophosphazene hybrid (PCP-NH2) hollow microcapsules with cross-linked structure, generated by one-step precipitation polymerization between hexachlorocyclotriphosphazene and branched polyethyleneimine, and subsequent acetone treatment. Their morphology, composition and structure were confirmed by SEM, TEM, FTIR, TGA, and XPS. The endowment of hollow PCP-NH2 microcapsules as potential adsorbents were thoroughly evaluated using eight organic dyes with different surface charges. The adsorption action of hollow PCP-NH2 microcapsules highly depends on the surfaces charges, exhibiting highly-efficient and selective adsorption behavior towards anionic dyes. Especially, The adsorption capacity of the hollow PCP-NH2 microcapsules towards anionic dyes of EY, ACBK, MO and EB reaches up to 1196.36, 1190.65, 1142.77 and 1040.92 mg/g at 25 °C, respectively. The adsorption kinetics shows a better fit to pseudo second-order kinetic model, compared to pseudo-first-order kinetic and Weber’s intraparticle diffusion models. The adsorption equilibrium data followed the Langmuir isotherm well. The adsorption thermodynamic experiments demonstrated that adsorption was a physisorption process with endothermic and spontaneous characteristic.

The development of rapid, sensitive methods for α-fetoprotein and telomerase is significant because their blood concentrations are related to hepatocellular carcinoma. Therefore, the determination of α-fetoprotein and telomerase may allow the detection of liver cancer. A novel method for the high-yield synthesis of gold-silica alloy core-shell nanoparticles is reported. Gold-silica core-shells prepared by a convenient reduction provided good stability, served as immobilization carriers for the antibodies, and facilitated electron transfer. A simple label-free, three-dimensional hierarchical plasmonic nanoarchitecture was designed for the sensitive surface-enhanced Raman scattering determination of α-fetoprotein and telomerase. The active groups of the gold-silica nanoparticles allowed 4-mercaptobenzoic acid and Nile blue to absorb antibodies and generate a signal. Gold-silica@4-mercaptobenzoic acid and gold-silica@Nile blue were employed in the surface-enhanced Raman scattering immunosensor. When ...

Developing excellent dye adsorbent with high adsorption capability and good reusability and clarifying the interaction mechanism between adsorbent and adsorbate are highly desired for eliminating water pollution. Herein, we present a novel magnetic adsorbent Fe3O4/poly(cyclotriphosphazene-co-4,4′-sulfonyldiphenol) nanotube modified by glacial acetic acid (defined as Gl-PZSNTs-Fe3O4) to remove cationic dye methylene blue (MB) from aqueous solution. Compared with the unmodified magnetic PZSNTs-Fe3O4, the Gl-PZSNTs-Fe3O4 exhibits rapid adsorption rate and high adsorption capacity. The adsorption equilibrium data was fitted well with Langmuir model, and the adsorption kinetics obeyed the pseudo-second-order kinetics model and Elovich model. Thermodynamic analysis showed that the MB adsorption onto the Gl-PZSNTs-Fe3O4 was endothermic and spontaneous. Especially, through contrasting the adsorption behavior of Gl-PZSNTs-Fe3O4 and PZSNTs-Fe3O4 towards MB dye, we highlighted the importance of glacial acetic acid modification for enhancing the adsorption capacity of the Gl-PZSNTs-Fe3O4. Meanwhile, we also proposed the adsorption mechanism of the Gl-PZSNTs-Fe3O4 towards MB dye.

In order to complete nonlinear path following smoothly and accurately, this paper proposes a method utilizing the Serret-Frenet Line-of-Sight (LOS) guidance with adaptive compensation in the horizontal plane. All regular paths are feasible. Our method takes three steps to accomplish the path following. First, the guidance law calculates the desired yaw angle. Then an adaptive compensation is added on the desired yaw which considering uncertainty and input saturation. Last, the PID controller is extended to cope with the yaw tracking and velocity control. Simulations and outfield experiments are conducted to verify the feasibility and superiority of the novel approach.

The beam waist-to-waist transformation of Gaussian beams between input and output reference planes described by the scaled fractional Fourier transform is analyzed in this paper. We obtain the transfer matrix of ABCD optical system that corresponds to the scaled fractional Fourier transform. The results show that the beam waist-to-waist transformation of Gaussian beams can be described by the scaled fractional Fourier transform when the ABCD optical system has a suitable transfer matrix. The relationship between the input and output waist planes and some particular cases when a Gaussian beam passes through a thin lens is also discussed.

The propagation of Ince-Gaussian beams in a thermal lens medium is studied in this paper. Based on the ABCD matrix for Gaussian beams passing through a thermal lens medium, distinct expressions for the beam transverse intensity distributions and the longitudinal phase shift are deduced and discussed. Similar to Laguerre and Hermite-Gaussian beams, Ince-Gaussian beams, which constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation, can also be used in other inhomogeneous media such as lenslike media and saturated absorption media.

The effects of laser radiation on soot in a vacuum were studied by Raman spectroscopy and transmission electron microscopy. It was found that defective carbon onions could be formed simply by irradiation of focused common diode lasers with intensity much lower (103–106 W/cm2) than those used in the previous work. A modified Melton model was introduced to analyze the formation of onions. The results show a threshold value of laser intensity (5.49 × 103 W/cm2), above which sublimation and rearrangement play a dominant role in the formation of onions. Such onions can also be formed with laser intensities below the threshold since neighboring graphene layers may merge and grow by capturing interstitial carbon atoms. The deposited soot is damage resistant to the diode laser radiation in air due to the rapid formation of carbon onions.

Based on the Collins diffraction integral formula and irradiance moments, the propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian (HChG) beams passing through fractional Fourier transformation systems with spherically aberrated lenses are analyzed in detail. The closed-form expressions for the propagation equation and kurtosis parameter of HChG beams passing ideal fractional Fourier transformation systems are also obtained. By using an efficient algorithm some numerical calculations are also performed in this paper. The results show that the spherically aberrated lenses greatly influence on the intensity distribution and kurtosis parameter of HChG beams passage through fractional Fourier transformation systems. The intensity distribution and kurtosis parameter of HChG beams passage through two types of Lohmann's systems with spherically aberrated lenses, respectively, are no longer equal even in the case of the same fractional order and the same spherical aberration coefficients. The fundamental periods of the two types of Lohmann's systems with spherically aberrated lenses are different, 4 for the type I and 2 for the type II. Therefore, the two optical setups for implementing the fractional Fourier transformation are no longer equivalent in the presence of spherically aberrated lenses.

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.

Under the condition of rotational symmetry fractional Fourier transforms become fractional Hankel transforms. The relationships between the fractional Hankel transform and the diffraction of a misaligned optical system are established in this paper. By settling and discussing the diffraction integral formulae of a misaligned ABCD optical system, the fractional Hankel transform of an input function can be obtained by selecting a suitable reference plane under given conditions.

The apertured fractional Fourier transform (FRFT) system is introduced and applied to treat the propagation of Hermite-cosh-Gaussian beams. Based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expressions for the output field distribution of a Hermite-cosh-Gaussian beam through apertured FRFT systems are derived and compared with those obtained from diffraction integral formulae by numerical simulations. It is shown that our method can significantly improve the numerical calculation efficiency.

Summary The propagation of flattened Gaussian beams (FGBs) passing though misaligned optical systems with aperture has been studied in detail. The corresponding approximate equation has been derived, where the rectangular aperture function is expanded into a finite sum of complex Gaussian functions. Numerical examples are given to illustrate the application of the propagation equation and the properties of flattened Gaussian beams passing through a misaligned optical system with aperture are discussed.

The phase shifts of a spherical light wave passing through an aperture are simply analysed on the basis of the integral theorem of Helmholtz and Kirchhoff in terms of Kirchhoff's boundary conditions and the physical meaning of the integral. It is shown that the phase shifts of spherical light wave passing through an aperture can be divided into two categories: the additional phase shift and the phase anomaly. The additional phase shift is related to the position of the field point, but the phase anomaly is not related to the position and is a phase jump at a certain point in the field space. The results obtained can explain some cases investigated previously.

Summary It is shown that, under some conditions, the generalized diffraction integral formula for any misaligned optical system in spatial-domain could be described by the fractional Fourier transform. On the other hand, the generalized diffraction integral formula for angular spectra through any misaligned optical system in spatial-frequency domain could also be described by the fractional Fourier transform. A practical optical system with a misaligned lens is given to illustrate its application.

It is shown that fractional Fourier transform could be viewed as a tool for analysing the diffraction of misaligned optical systems, just as the fractional Fourier transforms are adapted to the mathematical expression of Fresnel diffraction. Some special cases are also discussed.

The effect of misalignment on optical fractional Fourier transforming systems is analysed in this paper. Meanwhile, a concept of perturbed fractional Fourier transform is put forward. By using the generalized misaligned diffraction integral formulae for misaligned optical systems, it is shown that the diffraction characteristics for misaligned Lohmann's fractional Fourier transforming systems and quasi-asymmetric inhomogeneous media are able to perform the perturbed fractional Fourier transform and are essentially equivalent. And also, a relative discussion is given.

Airy pattern is formed by diffraction of a plane wave through a circular aperture in the far field with certain side lobes. It is shown that Airy pattern can be truncated at the first dark ring by a circular aperture to pick up the center spot (called Airy disc) without causing additional diffraction fringes, even in the very far field. This may be called zero field truncation technique. And is very useful in practice, for example, as a good quality optical source.

A novel model of beam formed by coherent superposition of two correlated Gaussian spherical beams with different centers is presented. This kind of beam has a transverse spreading smaller than a fundamental Gaussian beam. The beam quality factor is smaller than one.

By means of Collins' diffraction integral formula in the paraxial approximation, the analytical expressions for linearly polarized and azimuthally polarized Bessel-Gauss beams through any axisymmetric optical system that can be described by an ABCD ray transfer matrix are given. For example, the transformation characteristics of these two kinds of Bessel-Gauss beams through an optical system with a lens are compared by numerical calculation. The results are analyzed and discussed.

Summary A closed-form expression for the one-dimensional off-axial cosine-Gaussian beams passing through an apertured and misaligned paraxially ABCD optical system is derived. As special cases, the corresponding closed-forms for the off-axial or non off-axial cosine-Gaussian beams passing through apertured or unapertured and misaligned or aligned optical systems are also given. The obtained results could be straightforward to the two-dimensional case or sine-Gaussian beams.

Summary Analytical expressions for the one-dimensional off-axial Hermite-cosine-Gaussian beams and one-dimensional off-axial cosine-Gaussian beams passing through an apertured paraxial ABCD optical system have been respectively derived. Our results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly.

Summary When a Cos beam is apertured, it undergoes a phase shift as well as a focal shift. The propagation of relative phase shift of apertured Cos beam through free space is analysed. Based on numerical calculation it is shown that the variation rule of relative phase shift of Cos beam with Gaussian phase term is completely different from that of Cos beam without Gaussian phase term and means that the Gaussian phase term plays the main role in the description of relative phase shift.

Based on Fourier transforms the generalized diffraction integral formula for a beam through any misaligned optical system in spatial-frequency domain is derived in this paper. It is shown that the diffraction integral formula in spatial-frequency domain is related with the ray transfer matrix elements and the misaligned parameters. And some special cases are discussed, an example is also given to illustrate its application.

The concept of Fresnel number is discussed and expressions are derived for misaligned optical systems. For the case of perfectly aligned optical elements, the usual number,N, based on a Fresnel zone concept is found to be given byN = (a 2/λ)(D 1/B 1 +A 2/B 2), whereB 1,D 1 andB 2,A 2 are the transfer matrix elements of the optical systems before and after a circular aperture of radiusa respectively. A modified definition of the Fresnel number is proposed for Gaussian beam propagation. This parameterN′ G, is related to the complex beam parameter and may be represented by the angleθ = tan−1 N′ G, found in the familiar Collins chart and its dual representation. A general relation for the transformation of this Fresnel number is found. The expressions for Gaussian beam transformation are thus simplified, since the waist-waist transform is given byN′ G1 =N′ G2 = 0. Finally, these two kinds of Fresnel numbers are written as tensors when applied to cases involving elliptical apertures, astigmatic beams and nonsymmetrical systems.

Two ABCD matrices for describing weakly aperturbed gaussian beams are discussed. Employing these matrices the mode changes of a typical resonator with an aperture are given analytically in a simple way.

By means of Collins' diffraction integral formula in the paraxial approximation, the analytical expressions for an azimuthally polarized Bessel - Gauss beam through any axisymmetric optical system that can be described by an ABCD ray transfer matrix are given in this paper. Free space propagation and the Fourier transfer system are also analysed and discussed as particular cases. En utilisant la forme integrale de la diffraction de Collins nous donnons dans cet article l'expression analytique de la propagation de faisceaux de Bessel - Gauss azimutalement polarises, a travers des systemes optiques de symetrie axiale qui peuvent etre decrits par une matrice ABCD dans l'approximation paraxiale. La propagation dans l'espace libre et a travers des systemes de Fourier sont egalement analyses et discutes comme des cas particuliers.

Based on the Collins diffraction integral formula and irradiance moment definition, the propagation characteristics of the kurtosis parameter of a Gaussian beam through fractional Fourier transformation (FRFT) systems with spherically aberrated lens are studied in detail. By using the efficient algorithm introduced in this paper, some numerical calculations are done. It is shown that the kurtosis parameter of a Gaussian beam passage through FRFT systems with spherically aberrated lens is very different from that of a Gaussian beam through ideal FRFT systems. What’s more, the effect of different kinds or values of spherical aberration coefficients on the kurtosis parameter is in great difference. The values of the kurtosis parameter of a Gaussian beam through the two types of Lohmann’s systems respectively are no longer equal even in the case of the same fractional orders and the same spherical aberration coefficients. The kurtosis parameter of a Gaussian beam passage through ideal FRFT systems keeps invariable and its value is 3 in the one-dimensional case.

Based on the nonparaxial moment theory of light beam propagation, the propagation characteristics of nonparaxial scalar Gaussian beam, nonparaxial TEM and TE vector Gaussian beams have been investigated. The results reveal that both the transversal beam widths follow a simple hyperbolic law upon propagation. The analytical expressions of the beam propagation factor, beam waist and far field divergence angle are presented, respectively. Furthermore, the formulae can be very concise for highly nonparaxial cases. TE or TM polarization will result in different propagating features in the two transversal directions. The maximum transverse divergence angles of nonparaxial scalar and vector Gaussain beams are different, which indicates that nonparaxial scalar Gaussian beam is no longer approximate at subwavelength scales. When extending to the paraxial case, the results obtained are slightly different from the formerly paraxial ones. Moreover, in this case the beam propagation factor will always be greater than unity. This research also denotes some properties of subwavelength optics.

By introducing a method that a hard-edged aperture function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of Wigner distribution function for a Gaussian beam passing through a cylindrical symmetric and paraxial ABCD optical system with a hard-edged aperture is obtained. Numerical calculations show that the effect of an aperture on the Wigner distribution function is prominent. The analytical results are also compared with the integral calculation results and they show that this method of expanding a hard aperture into Gaussian functions with finite numbers is proper and ascendant. This method could also be extended to studying the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with a hard-edged aperture.

We present a directed Markov random field (MRF) model that combines n-gram models, probabilistic context free grammars (PCFGs) and probabilistic latent semantic analysis (PLSA) for the purpose of statistical language modeling. Even though the composite directed MRF model potentially has an exponential number of loops and becomes a context sensitive grammar, we are nevertheless able to estimate its parameters in cubic time using an efficient modified EM method, the generalized inside-outside algorithm, which extends the inside-outside algorithm to incorporate the effects of the n-gram and PLSA language models. We generalize various smoothing techniques to alleviate the sparseness of n-gram counts in cases where there are hidden variables. We also derive an analogous algorithm to calculate the probability of initial subsequence of a sentence, generated by the composite language model. Our experimental results on the Wall Street Journal corpus show that we obtain significant reductions in perplexity compared to the state-of-the-art baseline trigram model with Good-Turing and Kneser-Ney smoothings.

Based on the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical expressions of standard and elegant Laguerre-Gaussian beams passing through a paraxial ABCD optical system with a hard-edged aperture are derived. On the basis of the truncated second-order moments method in the cylindrical coordinate system and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, an approximate method for calculating the generalized beam propagation factor is proposed. Closed-form expressions for the generalized beam propagation factor of a truncated standard and elegant Laguerre-Gaussian beam are derived that depend on the orders of Laguerre polynomial and the beam truncation parameter. Some typical numerical examples are given and compared. It is shown that the results obtained by using the obtained analytical method accord with those by using the numerical integration method.

Some developments on fractional Fourier optics are reported in this paper. First, a thick lens can be regarded as a fractional Fourier transformer. Second, relations between the Collins formulae and the fractional Fourier transform or fractional Hankel transform are bridged, we show that the Collins formulae in spatial domain or in spatial-frequency domain can be described by the fractional Fourier transform or fractional Hankel transform. Third, connections between the multi-element resonators and the scaled fractional Fourier transforms are established, it is shown that there exists twice scaled fractional Fourier transform for beams in completing one round trip, the beam oscillation in resonator can be viewed as a process of consecutive implementing scaled fractional Fourier transform. Finally, some extensions of the fractional Fourier transforms to misaligned optical systems are simply reviewed.

The variations of group velocities for Gaussian beams under different hypotheses were studied, and the rationality of the results were discussed and analysed. Then we show that the beam waist radius should be proportional to the square root ofwavelength. Under this condition, the group velocities are all equal to c on the beam axis and smaller than c off the axis.

An expression for the complex radius of curvature tensor describing every kind of gaussian beam is proposed. This expression can be used in the tensor ABCD law. The circular, orthogonal astigmatic and non orthogonal astigmatic beams are expressed by means of this tensor.

The authors report on experimental demonstrations of the diffraction and dispersion phenomena of part Fresnel phase zone plates (FPZPs) by employing a He–Ne laser beam and a white point source. The experimental results have shown that a part square FPZP can behave like a complete circular FPZP, and a part circular FPZP has a focus at 1∕3 f and f with a shift. Some numerical simulations are performed. The simulations and the experiments have shown that the diffraction and dispersion properties of part FPZPs can be well explained by the different diffraction orders.

The concept of the Fresnel number is generalized to make it possible to describe the regular polygon and slit illuminated by a homogeneous plane wave. The generalization is based on nonlinear regression of the axial intensity distribution curve. A useful analytical expression for the Fresnel number is presented. A simple experiment to show the different Fresnel numbers in one observation plane is illustrated.

When a Gaussian beam is weakly diffracted by a circular aperture it can be approximated by another Gaussian beam with slightly different properties in the far field. In this Technical Note, using the relationship between these two Gaussian beams, before and after the aperture, an ABCD matrix is defined for cascaded laser systems.