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Study design Numerical techniques were used to study the vibration response of idiopathic scoliosis patients with single thoracic curve. Objective To analyze the dynamic characteristics of the idiopathic scoliotic spine under the whole-body vibration condition. The influence of the upper body mass was also studied. Summary of background data The relationship between the whole-body vibration and the spinal disorders has been investigated using finite element method. However, the dynamic response features of the scoliotic spine to the vibration were poorly understood. Methods The resonant frequencies of the scoliotic spine and the effects of the body weight were studied using a finite element model described previously. Modal and harmonic analysis was conducted. The amplitudes of 6 fundamental vertebral movements around the long, coronal and sagittal axis were quantified in the frequency range of 1 to 35 Hz. Results The vibration-induced rotation amplitudes of the apex of the thoracic deformity were higher than that of the lumbar segments. The apical vertebrae had the greatest rotation amplitudes at 2 and 8 Hz, and the largest lateral translation amplitudes at 16 Hz. Vibration could cause large lateral flexion amplitudes in the apex of the thoracic deformity. The apical vertebrae had the largest side flexion amplitudes at 6 Hz. Increasing upper body mass could not change resonant frequency of vibration-induced lateral translation and rotation around the long axis of the apical vertebrae. Conclusion The scoliotic spine is more sensitive to vibration than the normal spine. For a patient with single thoracic curve, long-term whole-body vibration may do more harm to the thoracic deformity than to the lower lumbar segments. Axial cyclic loads applied to an already deformed spine may cause further rotational and scoliotic deformity. The patients with idiopathic scoliosis are more likely to suffer from vibration-induced spinal disorders than those by normal persons.

Inthiswork,amodelforanalyzingthegaincharacteristicsofheavilyEr 3+ /Yb 3+ co-doped compactfiber amplifier is presented. Four-level rate equations andfinite-difference beam propagation method are applied to simulate the optical field evolution along the active fiber. Based on this model, the influences of ion concentration, fiber length and pump power on the gain characteristics of Er 3+ /Yb 3+ co-doped phosphate glass fiber amplifiers are the- oretically investigated. Numerical results show that for a fiber length of 3.6cm the internal gain can reach 27.2dB with NEr = 2.6 × 10 26 ions/m 3 and NYb = 1.2 × 10 27 ions/m 3 when pumped with 224mW at 980nm. The gain per centimeter is 7.56dB/cm. The results can provide useful information to optimize the gain performance of these compact fiber

Enhanced transmission through sub-wavelength hole arrays and a single sub-wavelength aperture with periodic corrugations surrounded have been investigated extensively. We report the similar phenomenon through a funnel-type aperture with a sub-wavelength outlet in a thick silver film, which was obtained numerically by using finite-difference time-domain method. Properties of the transmission spectrum can be modulated by geometric parameters of the funnel-type aperture. With periodic grooves or dielectric gratings on the output surface of the structure, beaming light emission can be obtained.

The method for measuring second-order nonlinear optical coefficients based on well-known Z-scan is presented. The influence of linear absorption coefficients on normalized transmittance is discussed. Using this method, we obtained the second-order nonlinear coefficient d31(5%MgO:LiNbO3) = 4.5 × 10−12 m/v at 1064 nm, which agrees well with theoretical calculations and previous well-known values.

A finite-difference algorithm that combines the local one-dimensional approximation and the Douglas scheme is suggested to solve the three-dimensional non-linear Schrodinger equation. The truncation error in this scheme is reduced to O(Δ x ) 4 in the transverse direction, whereas that in the conventional local one-dimensional approximation is O(Δ x ) 2 . Using this scheme, the computational accuracy and computational efficiency can be improved drastically without the introduction of additional programming works and computational time. Numerical results obtained for an elliptic Gaussian beam propagating in non-linear medium verify the advantages of this method.

We report the experimental results on characteristics of co-existence of third-order and transient thermally induced optical nonlinearities using a nanosecond pulse laser and CS2 solutions of nigrosine. Results show that thermally induced optical nonlinearity is very sensitive to linear absorption, beam waist size and pulsewidth. Numerical simulations obtained by solving simultaneously acoustic and electromagnetic wave equations, agrees basically with experimental results. Meanwhile, the transition of optical nonlinearity from self-focusing pattern to self-defocusing pattern was observed when the contribution from thermally induced optical nonlinearity exceeds that from third-order optical nonlinearity.

We apply a new method consisting of a coordinate transformation and a coordinate mapping technique, to simulate numerically Z-scan measurements of a nonlinear medium. A comparison of numerical results obtained by this new method with those by conventional numerical method is made. Results show that the new scheme yields a large, orders-of-magnitude range improvement in computational speed and accuracy for the analyses of closed-aperture and open-aperture Z-scan measurements, compared with conventional numerical methods.

We report an extension of variational method to study the elliptic Gaussian beam propagation in a nonlinear medium with nonlinear refraction as well as nonlinear absorption. The results obtained by this method agree quantitatively with numerical solutions. Meanwhile, results also show that the variational method takes much less time than numerical simulations using the finite difference method for analysis of elliptic Gaussian beam propagation in a thick medium with nonlinear refraction and nonlinear absorption. The validity of the variational method is checked to be very good.

Morphology-dependent resonance (MDR) of the optical forces for a particle illuminated by Airy beams is investigated with respect to its internal field distribution. We find the ring structures arising from the resonance transform significantly with the parametric evolution of Airy evanescent wave, and the interference of the internal waves have a great impact on the Q factor and the background of the resonant peak, but it’s not proper for Airy transmitted wave. The multiple reflections of the evanescent wave between the particle and the interface are also investigated, which show significant impacts on the region where the energy concentrate in.

We have studied the electron acceleration by a tightly focused cylindrical vector Gaussian beam. Different from the Lax series field, cylindrical vector Gaussian beams are vector-beam solutions of Maxwell's equations and its focusing property can be numerically analyzed by the Richards–Wolf vectorial diffraction theory. Field differences exist between the cylindrical vector Gaussian beam and the Lax series field. The cylindrical vector Gaussian beam increases the asymmetry of the electromagnetic fields, which is more beneficial to the electron acceleration. When the beam waist falls down to the order of the wavelength, the high laser intensity zone is more proper to define the reflection, capture and transmission conditions of the electrons. The injection energy and the injected angle of the electron and the initial phase of the laser beam play important roles for the electron to enter and be trapped by the high laser intensity zone.

The characteristics of the laser pulses produced by Kerr-lens mode-locking (KLM) with a microdot mirror are analyzed in this paper by using beam propagation and self-consistency approaches. The characteristics of the pulsewidth, the intracavity power, the nonlinear reflectance change and of the gain versus size of the microdot mirror are obtained. The effect of the geometry arrangement of the microdot mirror on the mode-locking is analysed, and the optimum geometry arrangement is suggested.

Using vector potential and spectrum representation, we derive the expressions of the Airy evanescent field existed at the interface. Utilizing these expressions and the Arbitrary Beam Theory, the optical forces exerted on a Mie dielectric particle in the Airy evanescent field were theoretically investigated in detail. Numerical results show that the optical forces exhibit strong oscillations which are corresponding to the distributions of the evanescent field. With the increasing the size of particle radius, Morphology Dependent Resonance occurs for the particle with specific refractive index.

Two modified Z -scan methods, in which the far-field on-axis aperture in common Z -scan is replaced by an off-axis aperture and a circular board, are suggested for measurements of n 2 with enhanced sensitivity. The calculated results show that with the increase of the distance from the off-axis aperture to the axis or the diameter of the circular board, the peak-valley normalised transmittance difference of Z -scan will increase rapidly. Also the Z -scan characteristics with a nonlinear absorption are analyzed.

Purpose: This study measured high-mobility group box 1 (HMGB-1) levels in serum and synovial fluid (SF) in patients with primary knee osteoarthritis (OA) and correlated these levels with radiographic disease severity. Methods: Seventy-eight OA patients and 30 controls were enrolled in this study. All OA patients were scored according to the Kellgren-Lawrence (KL) grading system. HMGB-1 levels were measured by enzyme-linked immunosorbent assay (ELISA). Results: SF HMGB-1 levels were significantly higher in knee OA patients, compared with controls (P < 0.01). Moreover, SF HMGB-1 levels were positively associated with KL scores (P < 0.01). Multinomial logistic regression demonstrated that the SF HMGB-1 level was an independent factor for radiographic severity of OA (P=0.002); however, serum HMGB-1 levels did not differ significantly between OA patients and controls and did not correlate with KL scores (P > 0.05). Conclusion: These results demonstrate that HMGB-1 levels in SF of knee OA patients are independently associated with radiographic disease severity.

The radiation forces and trajectories of Rayleigh dielectric particles induced by one-dimensional Airy beam were numerically analyzed. Results show that the Airy beam drags particles into the optical intensity peaks, and guides particles vertically along parabolic trajectories. Viscosity of surrounding medium significantly affects the trajectories. Random Brownian force affects the trajectories. Meanwhile, trapping potential depths and minimum trapping particle radii in different potential wells were also discussed. The trapping stability could be improved by increasing either the input peak intensity or the particle radius.

Using numerical simulation, we have studied in detail vacuum electron acceleration induced by an Airy beam. The phase of the field varies slowly, and the intensity of the field is independent of the decaying parameter of the beam in the asymmetric field channel [(AFC) Opt. Express 18, 7300 (2010)] formed by the Airy beam. Results show that an electron entering into the AFC may be captured and gain high energy. Meanwhile, the decaying parameter, injection energy, and injection angle of the electron play important roles in the electron energy gain.

Background context The treatment of adolescent congenital deformity (late-diagnosed congenital deformity) is still unknown. The best candidates for hemivertebra excision are young patients, typically between 4 and 6 years of age. Partial excision may be feasible for older children. Purpose The purpose of this study was to assess the effect of unilateral pedicle subtraction osteotomy of hemivertebra for correction of the adolescent congenital spinal deformity. Study design Retrospective analysis. Patient sample Twelve patients with adolescent congenital deformity who underwent posterior unilateral pedicle subtraction osteotomy and correction were evaluated. Mean age at the time of surgery was 17 years. Outcome measures The charts, standing full-length posteroanterior and lateral view radiographs, and functional measures were reviewed. Methods For evaluation of surgical effectiveness, comparative analysis of the parameters of the total main curve, the segmental curve, the compensatory cranial and caudal curves, the segmental kyphosis, and the trunk shift before and after operation and at the most recent follow-up was done. Results The mean follow-up period was 40.5 months. Mean Cobb angles of the total main curve and the segmental curve were, respectively, 47.5° and 43.8° before surgery, 23.7° and 16.5° after surgery, and 22.6° and 17° at the last follow-up. The angle of segmental kyphosis was 11.8° before surgery, 6.2° after surgery, and 7.8° (range, −30° to 26°) at the final follow-up. The mean final global lordosis was within the normal range. No neurologic deficit occurred. Solid fusion was achieved for all cases. Conclusions Unilateral pedicle subtraction osteotomy with instrumentation from a posterior-only approach is indicated in older teenagers for an adolescent congenital spinal deformity. Compared with hemivertebra excision, corrective surgery with hemivertebra osteotomy has a lower intraoperative blood loss and shorter operation time.

The possibility of enhancing the energy gain in vacuum electron acceleration by Airy beams is examined. The characteristics of transverse acceleration and non-diffraction of Airy beam can lead to the formation of a long “asymmetric field channel” along the propagation axis, where the intense asymmetric field can accelerate the injected electron to higher energy. Meanwhile, the injection energy of electron plays an important role in determining the final energy gain.

We propose a Z-scan theory for one-dimensional nonlinear photonic bandgap materials. The Z-scan characteristics for this material are analyzed. Results show that the Z-scan curves for photonic bandgap materials with nonlinear refraction are similar to those of uniform materials exhibiting both nonlinear refraction and nonlinear absorption simultaneously. Effects of nonlinear absorption on reflected and transmitted Z-scan results are also discussed.

The recent proposal to use Weinger transformation field (WTF) [Opt. Express 17, 4959-4969 (2009)] for describing tightly focused laser beams is investigated here in detail. In order to validate the accuracy of WTF, we derive the numerical field (NF) from the plane wave spectrum method. WTF is compared with NF and Lax series field (LSF). Results show that LSF is accurate close to the beam axis and divergent far from the beam axis, and WTF is always accurate. Moreover, electron dynamics in a tightly focused intense laser beam are simulated by LSF, WTF and NF, respectively. The results obtained by WTF are shown to be accurate.

The transmission from a single subwavelength slit in a metal film with periodic dielectric bars on its surfaces has been analyzed numerically by the finite-difference time-domain method. Results show that the role of the periodic dielectric bars is just the same as that of the periodic grooves directly on the surfaces. With the modulations of dielectric bars on the input and output surfaces of the metal film, light transmission through the subwavelength slit is enhanced extraordinarily and confined to directional emission. The CDEW model is employed to explain the mechanism of the transmission enhancement and directional emission caused by the periodic dielectric bars.

In this paper we calculate the radiation forces and moving trajectories of Mie particles induced by 1D Airy beams using the plane wave spectrum method and arbitrary beam theory. Numerical results show that both the transverse and the longitudinal radiation forces are deeply dependent on the relative refractive index, radii and positions of the scattering particles illuminated by the Airy beam. Due to the radiation forces, Mie particles with different radii and initial positions can be dragged into the nearest main intensity lobes, and move along parabolic trajectories in the direction of the Poynting vector. At the ends of these trajectories, in the presence of Brownian force, the trapped scattering particles show irregular Brownian movement near their equilibrium positions. This characteristic property of Airy beams enables optical sorting to be used more easily in the colloidal and biological sciences.

We have investigated the effect of multiple scattering to optical forces on a particle in the evanescent field produced by an optical waveguide. Considering the multiple scattering between the sphere and the waveguide, we extend the formalism based on transition matrix and reflection matrix to calculate the optical forces on a sphere near an optical waveguide. Numerical results show that the influence that multiple scattering has on the optical forces can't be ignored, especially when the structure resonance of the particle arises. Moreover, the effect of multiple scattering to optical forces is also studied in detail on the condition that the distance between the sphere and the waveguide is within the effective operating distance.

We apply a finite-difference algorithm that combines the local one-dimensional approximation and the Crank-Nicolson algorithms to solve the three-dimensional nonlinear Schrodinger equation. This scheme is unconditionally stable and accurate to second order. Therefore it offers a simple and accurate means to study a two-dimensional Z scan for arbitrary beam shape and medium length. As an example, we analyze the characteristics of a Z scan by utilizing an elliptic Gaussian beam for a thick nonlinear medium. The effects of ellipticity and waist separation of the elliptic beam on the normalized transmittance of the closed-aperture and open-aperture Z scan are demonstrated.

Optical nonlinearities of five new organophosphorus fullerene derivatives with similar structures were determined by the Z-scan method by use of a nanosecond-pulse laser at 532 nm. The experimental results demonstrate that the five derivatives have much larger excited-state absorption and nonlinear refraction than C60. The excited-state absorption cross sections are nearly two to three times that of C60. Using a five-level model to fit the experimental data, we obtained some parameters such as excited-state absorption and refraction cross sections. A simple analysis of correlations between molecular structure and nonlinear properties is given. Optical nonlinearities of the five new organophosphorus fullerene derivatives were compared with those of some other kinds of fullerene derivatives, and the results show that the nonlinearities of the new derivatives are the larger.

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.

Electron acceleration in vacuum driven by a tightly focused radially polarized Gaussian beam has been studied in detail. Weniger transformation method is used to eliminate the divergence of the radially polarized electromagnetic field derived from the Lax series approach. And, electron dynamics in an intense radially polarized Gaussian beam is analyzed by using the Weniger transformation field. The roles of the initial phase of the electromagnetic field and the injection angle, position and energy of electron in energy gain of electron have been studied in detail.

A triple-layer guided-mode resonance Brewster filter consisting of a homogeneous layer and two identical gratings with their refractive indices equal to that of the homogeneous layer is presented. The spectral properties of this filter are analyzed based on the coupling modulation of two identical binary gratings at Brewster angle for a TM-polarized wave. The grating layer between substrate and homogeneous layers can significantly change the linewidth and resonant mode position, which are due to the asymmetric field distribution inside the grating layers. The tunability of the resonance can be altered on different resonant channels and a practical filter can be obtained in TM2 waveguide mode. Variation of filling factor can alter the field localization in the grating structure and significantly adjust the linewidth of the filter.

Using numerical simulation, we have studied in detail vacuum electron acceleration driven by two crossed Airy beams with identical characteristics except for opposite accelerating directions. An electron injected along the longitudinal central axis is only affected by the combined longitudinal electric field. In addition, a suitable crossed Airy beams scheme is more beneficial to the energy gain of an electron than the single Airy beam acceleration scheme [Opt. Lett.35, 3258 (2010)OPLEDP0146-959210.1364/OL.35.003258]. Meanwhile, the cross angle, the injection energy of the electron, and the initial phase of the Airy beams play significant roles in the energy gain of the electron.

A composite optical limiting configuration is proposed, which consists of a one-dimensional photonic bandgap structure and a thick bulk material. Using the backward split-step scheme, we studied the transmission and optical limiting properties of the composite structure. Results show that the performance of the optical limiting of the composite structure is better than that of the single bulk material and the optical limiting ability is improved by almost two orders of magnitude. The effects of the number of periods and the thickness of the bulk material on the nonlinear transmittance of this structure are studied. The contribution of nonlinear refraction and absorption to the composite optical limiting is also analyzed.

The normal elliptically polarized light Z-scan method is modified by adding a quarter-wave plate and an analyzer before the detector. The normalized transmittance formulas of modified elliptically polarized light Z-scan are obtained for media with negligible nonlinear absorption. Compared with normal linearly and elliptically polarized light Z-scan methods, an increase of sensitivity by a factor of larger than 4 is achieved for the real part of third-order susceptibility component's measurements using this modified elliptically polarized light Z-scan method. The analytical results are verified by studying the real part of independent susceptibility components of CS(2) liquid. Moreover, the potential application for cross-polarized wave generation is discussed.

Electron acceleration in vacuum induced by a tightly focused chirped laser pulse has been studied. For a fixed laser output power, the tightly focused chirped laser pulse can accelerate electrons to much higher energies. Focusing laser down to the order of wavelength requires inclusion of terms of third order at least in the diffraction angle e in the description of the associated field. Retained electron energy depends strongly on frequency chirp parameter and initial position of the electron. Besides, retained energy increases with laser intensity, pulse duration, and initial velocity of electron, and varies periodically with laser constant phase.

For an electron accelerated by a tightly focused Gaussian laser beam, its dynamics are usually simulated through the field obtained by Lax approach [Phys. Rev. A 11, 1365 (1975)]. However, as Lax series field (LSF) is not always convergent, the obtained results are usually inaccurate and even illogical. Here we report that the divergence of LSF can be eliminated by using Weniger transformation, and the electron dynamics simulated by this new field are logical and accurate.

Nonlinear absorption of carbon disulfide (CS2) was studied in the wavelength region of 420-530nm by using Z-scan method with nanosecond pulses. Large nonlinear absorption was found in the short-wavelength region (420-460nm). The optical limiting properties of CS2 were also studied, and results showed that CS2 has good optical limiting capability in the 420-460nm region. The mechanism of the nonlinear absorption was analyzed by the temporal profile of pulses going through CS2. The large nonlinear absorption is believed to arise from a combination of two-photon absorption and the excited-state absorption induced by two-photon absorption.

We present a method that combines the Z-scan technique with nonlinear ellipse rotation (NER) to measure third-order nonlinear susceptibility components. The experimental details are demonstrated, and a comprehensive theoretical analysis is given. The validity of this method is verified by the measurements of the nonlinear susceptibility tensor of a well-characterized liquid, CS2.

Transmission through a single subwavelength slit surrounded by nonperiodic or approximately periodic grooves in perfect conductive film has been analyzed numerically by the finite-difference time-domain method. Results show that the periodicity of the grooves is not the necessary condition to enhance the transmission, but is sufficient to obtain high enhancement. A spectrum with low enhancement and multiple peaks is obtained through a slit with nonperiodic grooves that is due to the resonances at different wavelengths caused by nonperiodicity. The spectrum of a slit with approximately periodic grooves is almost similar to that of a slit with absolutely periodic grooves regardless of whether the grooves are symmetric with respect to the slit, especially when the deflection of the grooves is very small compared to the grooves' period.

Using the Gaussian decomposition (GD) method, we studied the characteristics of a Z scan for a thin nonlinear medium with a large nonlinear phase shift induced by a pulsed laser. It has been verified that the GD method is still valid for analyses of Z-scan measurements with a large nonlinear phase shift and is better than some others, i.e., Fresnel-Kirchhoff diffraction and the aberration-free approximation model. By comparing the peak-to-valley configuration of Z-scan curves for a large nonlinear phase shift induced by a pulsed laser with that by a cw laser, we found that some peak-to-valley features of Z-scan curves appear as the aperture size or the light intensity increases in the case of a large nonlinear phase shift. Meanwhile, we carried out the Z-scan experiments of pure CS2 by a picosecond pulsed laser to verify the theoretical calculations in the case of a large nonlinear phase shift. The experimental results agree well with the theoretical calculations.

The type of donor used is found to influence greatly the optical nonlinearities of iodine charge-transfer (CT) complexes in solutions for several solvents. The magnitude and sign changes of nonlinear absorption of iodine CT complexes for different solvents as donors are observed, which implies the transition from saturable absorption to reverse saturable absorption. Compared with C60 in toluene, iodine CT complexes with toluene and benzene demonstrate larger reverse saturable absorption. Meanwhile, flexible alteration of optical nonlinearities is easily obtained by adjusting the mixture ratio of different solvents, yielding a prospective means of constructing a nonlinear medium with a large nonlinear coefficient.

We present a theoretical model of optical beam propagation in a nonlinear medium for determining the nonlinear refraction and nonlinear absorption accurately and simultaneously by a single Z-scan method. The model is based on the Gaussian decomposition method and symmetric analysis. In principle, accurate nonlinear refraction and nonlinear absorption can be obtained simultaneously by exact experimental data, no matter how much they are. The treatment procedure of Z-scan experimental data is demonstrated.

Using a Gaussian decomposition method and a distributed lens model, we have analyzed the Z-scan measurements of thick optical nonlinear media with nonlinear refraction and nonlinear absorption. With the introduction of correction functions that include saturation of nonlinear refraction and coupling between nonlinear refraction and nonlinear absorption, analytic solutions to closed-aperture and open-aperture Z-scan characteristics were obtained. Detailed comparisons of the analytic solutions with numerical solutions were made, and the two kinds of solution coincided well, no matter how much nonlinear refraction or nonlinear absorption there was.

We present a theoretical analysis of beam propagation in thick nonlinear media by using the Gaussian decomposition method and considering a thick medium as a stack of thin media. Simple analytic solutions of Z-scan characteristics and optical limiting with thick nonlinear media are obtained. Comparisons of these results with those obtained by use of a distributed-lens model and Gaussian-Laguerre mode decomposition are made. Good agreement is obtained with a distributed-lens model.