Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermit-Lagucrre-Gaussian （HLG） beams beyond the paraxial approximation are derived. The far-field expre...Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermit-Lagucrre-Gaussian （HLG） beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.展开更多
Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the...Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.展开更多
Based on the vectorial Ftayleigh-Sommerfeld integral formula and the complex Gaussian expansion of the hardedge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam...Based on the vectorial Ftayleigh-Sommerfeld integral formula and the complex Gaussian expansion of the hardedge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.展开更多
This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards-Wolf vectorial diffraction integral, the expressions for the electric field, the velocity o...This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards-Wolf vectorial diffraction integral, the expressions for the electric field, the velocity of the femtosecond light pulse and the total angular momentum of focused pluses are derived. The numerical calculations are also given to illustrate the intensity distribution, phase contour, the group velocity variation and the total angular momentum near the focus. It finds that near the focus the femtosecond elliptically polarised vortex light pulse can travel at various group speeds, that is, slower or faster than light speed in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, it also studies the influence of the numerical aperture of the focusing objective and the time duration of the elliptically polarised vortex light pulse on the total angular momentum distribution in the focused field.展开更多
Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite struc...Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.展开更多
Based on the vectorial Rayleigh-Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss （SLG） SLGo1 mode beam in free space. The far field expression...Based on the vectorial Rayleigh-Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss （SLG） SLGo1 mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG01 mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG01 mode beam within the framework of the nonparaxial regime.展开更多
A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling ...A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10574097）.
文摘Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermit-Lagucrre-Gaussian （HLG） beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.
文摘Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.
基金supported by the Scientific Research Fund of Zhejiang Provincial Education Department,China(Grant No 20060677)
文摘Based on the vectorial Ftayleigh-Sommerfeld integral formula and the complex Gaussian expansion of the hardedge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.
基金Project supported by the National Natural Science Foundation of China(Grant No.60977068)the Natural Science Foundation of Fujian Province,China(Grant No.A0810012)the Open Research Fund of State Key Laboratory of Transient Optics and Photonics,Chinese Academy of Sciences(Grant No.SKLST200912)
文摘This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards-Wolf vectorial diffraction integral, the expressions for the electric field, the velocity of the femtosecond light pulse and the total angular momentum of focused pluses are derived. The numerical calculations are also given to illustrate the intensity distribution, phase contour, the group velocity variation and the total angular momentum near the focus. It finds that near the focus the femtosecond elliptically polarised vortex light pulse can travel at various group speeds, that is, slower or faster than light speed in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, it also studies the influence of the numerical aperture of the focusing objective and the time duration of the elliptically polarised vortex light pulse on the total angular momentum distribution in the focused field.
基金This work was supported by National Natural Science Foundation of China under Grant 11672266.
文摘Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.
基金Project supported by the National Natural Science Foundation of China (Grant No.10974179)the Natural Science Foundation of Zhejiang Province of China (Grant No.Y1090073)
文摘Based on the vectorial Rayleigh-Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss （SLG） SLGo1 mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG01 mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG01 mode beam within the framework of the nonparaxial regime.
文摘A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.
