To establish a theoretical basis for providing a better design method of multielement optical systems, we have developed a third-order geometric theory of a plane-symmetric multielement optical system that consists of...To establish a theoretical basis for providing a better design method of multielement optical systems, we have developed a third-order geometric theory of a plane-symmetric multielement optical system that consists of a planar light source, an arbitrary number of ellipsoidal gratings, and an image plane. Analytic formulas of spot diagrams are derived for the system by analytically following a ray-tracing formalism. With these formulas, coma, spherical aberration, and resultant aberration are discussed. To make the theory practical, we determine the aberration coefficients numerically, rather than analytically, with the aid of ray tracing that takes into account the angular distribution of rays originating from a given light source. A merit function is defined so as to represent closely the variance of the spots formed when an infinite number of rays are traced and to take into account the dimensions of the source and the last optical element. The theory is also applicable to mirror-grating or mirror systems.展开更多
Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0...Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.展开更多
A new method for the periodic solution of strongly nonlinear systemis given. By using this method, the existance and stability of the periodic solutioncan be decided, and the approximate expression of the periodic sol...A new method for the periodic solution of strongly nonlinear systemis given. By using this method, the existance and stability of the periodic solutioncan be decided, and the approximate expression of the periodic solution can also befound.展开更多
The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration...The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration is proved.展开更多
In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case ...In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.展开更多
In the present work, we investigate threshold characteristics of a single mode 1.55 μm InGaAsP vertical cavity surface emitting laser (VCSEL) with two different optical confinement structures. The device employs InGa...In the present work, we investigate threshold characteristics of a single mode 1.55 μm InGaAsP vertical cavity surface emitting laser (VCSEL) with two different optical confinement structures. The device employs InGaAsP active region, which is sandwiched between GaAs/AlGaAs and GaAs/AlAs distributed Bragg reflectors (DBRs). The optical confinement introduced by the oxide aperture or a single defect photonic crystal design with holes etched throughout the whole structure, is compared with previous work. Photonic crystal VCSEL shows 30.86% and 57.02% lower threshold current than that of the similar oxide confined VCSEL and previous results, respectively. This paper provides key results of the threshold characteristics, including the threshold current and the threshold power. Results suggest that, the 1.55 μm InGaAsP photonic crystal VCSEL seems to be the most optimal one for light sources in high performance optical communication systems.展开更多
This paper reports a continuous-wave (CW) mid-infrared intracavity singly resonant optical parametric oscillator based on periodically poled lithium niobate (PPLN) pumped by a diode-end-pumped CW Nd:YVO 4 laser. Consi...This paper reports a continuous-wave (CW) mid-infrared intracavity singly resonant optical parametric oscillator based on periodically poled lithium niobate (PPLN) pumped by a diode-end-pumped CW Nd:YVO 4 laser. Considering the thermal lens effects, it adopted an optical ballast lens and the near-concentric cavity for better operation. At the PPLN's grating period of 28.5 μm and the temperature of 140 C, the maximum idler output power of 155 mW at 3.86 μm has been achieved when the 808 nm pump power is 8.5 W, leading to an optical-to-optical conversion efficiency of 1.82%.展开更多
In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the soluti...In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.展开更多
This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.
In this paper we report on a continuous-wave (CW) intracavity singly resonant optical parametric oscillator (ICSRO) based on periodically poled LiNbO3 (PPLN) pumped by a diode-end-pumped CW Nd:YVO4 laser. Considering ...In this paper we report on a continuous-wave (CW) intracavity singly resonant optical parametric oscillator (ICSRO) based on periodically poled LiNbO3 (PPLN) pumped by a diode-end-pumped CW Nd:YVO4 laser. Considering the thermal lens effects and diffraction loss, an optical ballast lens and a near-concentric cavity are adopted for better operation. Through varying the grating period and the temperature, the tunable signal output from 1406 nm to 1513 nm is obtained. At a PPLN grating period of 29 μm and a temperature of 413 K, a maximum signal output power of 820 mW at 1500 nm is achieved when the 808 nm pump power is 10.9 W, leading to an optical-to-optical conversion efficiency of 7.51%.展开更多
Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation,the optical trapping properties of nanoparticle placed on the gold film with periodic circular holes ar...Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation,the optical trapping properties of nanoparticle placed on the gold film with periodic circular holes are investigated numerically. Surface plasmon polaritons are excited on the metal-dielectric interface, with particular emphasis on the crucial role in tailoring the optical force acting on a nearby nanoparticle. Utilizing a first order corrected electromagnetic field components for a fundamental Gaussian beam, the incident beam is added into the calculation model of the proposed method. To obtain the detailed trapping properties of nanoparticle, the selected calculations on the effects of beam waist radius, sizes of nanoparticle and circular holes, distance between incident Gaussian beam and gold film, material of nanoparticle and polarization angles of incident wave are analyzed in detail to demonstrate that the optical-trapping force can be explained as a virtual spring which has a restoring force to perform positive and negative forces as a nanoparticle moves closer to or away from the centers of circular holes. The results of optical trapping properties of nanoparticle in the vicinity of the gold film could provide guidelines for further research on the optical system design and manipulation of arbitrary composite nanoparticles.展开更多
Based on the practical situation of nondestructive examination, the calculation model of the composite scattering is established by using a three-dimensional half-space finite difference time domain, and the Monte Car...Based on the practical situation of nondestructive examination, the calculation model of the composite scattering is established by using a three-dimensional half-space finite difference time domain, and the Monte Carlo method is used to solve the problem of the optical surface with roughness in the proposed scheme. Moreover, the defect particles are observed as periodic particles for a more complex situation. In order to obtain the scattering contribution of defects inside the optical surface, a difference radar cross section is added into the model to analyze the selected calculations on the effects of numbers, separation distances, different depths and different materials of defects. The effects of different incident angles are also discussed. The numerical results are analyzed in detail to demonstrate the best position to find the defects in the optical surface by detecting in steps of a fixed degree for the incident angle.展开更多
This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invar...This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results.展开更多
The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(...The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.展开更多
The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two resu...The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.展开更多
文摘To establish a theoretical basis for providing a better design method of multielement optical systems, we have developed a third-order geometric theory of a plane-symmetric multielement optical system that consists of a planar light source, an arbitrary number of ellipsoidal gratings, and an image plane. Analytic formulas of spot diagrams are derived for the system by analytically following a ray-tracing formalism. With these formulas, coma, spherical aberration, and resultant aberration are discussed. To make the theory practical, we determine the aberration coefficients numerically, rather than analytically, with the aid of ray tracing that takes into account the angular distribution of rays originating from a given light source. A merit function is defined so as to represent closely the variance of the spots formed when an infinite number of rays are traced and to take into account the dimensions of the source and the last optical element. The theory is also applicable to mirror-grating or mirror systems.
文摘Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.
基金The project supported by the National Natural Science Foundation of China
文摘A new method for the periodic solution of strongly nonlinear systemis given. By using this method, the existance and stability of the periodic solutioncan be decided, and the approximate expression of the periodic solution can also befound.
文摘The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration is proved.
文摘In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.
文摘In the present work, we investigate threshold characteristics of a single mode 1.55 μm InGaAsP vertical cavity surface emitting laser (VCSEL) with two different optical confinement structures. The device employs InGaAsP active region, which is sandwiched between GaAs/AlGaAs and GaAs/AlAs distributed Bragg reflectors (DBRs). The optical confinement introduced by the oxide aperture or a single defect photonic crystal design with holes etched throughout the whole structure, is compared with previous work. Photonic crystal VCSEL shows 30.86% and 57.02% lower threshold current than that of the similar oxide confined VCSEL and previous results, respectively. This paper provides key results of the threshold characteristics, including the threshold current and the threshold power. Results suggest that, the 1.55 μm InGaAsP photonic crystal VCSEL seems to be the most optimal one for light sources in high performance optical communication systems.
基金Project supported in part by the National Natural Science Foundation of China (Grant Nos 10474071, 60637010, 60671036 and60278001)Tianjin Applied Fundamental Research Project, China (07JCZDJC05900)
文摘This paper reports a continuous-wave (CW) mid-infrared intracavity singly resonant optical parametric oscillator based on periodically poled lithium niobate (PPLN) pumped by a diode-end-pumped CW Nd:YVO 4 laser. Considering the thermal lens effects, it adopted an optical ballast lens and the near-concentric cavity for better operation. At the PPLN's grating period of 28.5 μm and the temperature of 140 C, the maximum idler output power of 155 mW at 3.86 μm has been achieved when the 808 nm pump power is 8.5 W, leading to an optical-to-optical conversion efficiency of 1.82%.
基金This work was supported by the Basic Program in Natural Sciences, Vietnam and Thai Research Fund Grant, Thailand
文摘In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.
基金the National Natural Science Foundation of China(1 0 1 71 0 88) and the National Natural Science Foundation of Jiangsu Educational Committee(99KJ1 1 0 0 0 5 )
文摘This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.
基金Project supported partly by the National Natural Science Foundation of China (Grant Nos 60637010 and 60671036)the National Basic Research Program of China (Grant No 2007CB310403)the Tianjin Applied Fundamental Research Project, China(Grant No 07JCZDJC05900)
文摘In this paper we report on a continuous-wave (CW) intracavity singly resonant optical parametric oscillator (ICSRO) based on periodically poled LiNbO3 (PPLN) pumped by a diode-end-pumped CW Nd:YVO4 laser. Considering the thermal lens effects and diffraction loss, an optical ballast lens and a near-concentric cavity are adopted for better operation. Through varying the grating period and the temperature, the tunable signal output from 1406 nm to 1513 nm is obtained. At a PPLN grating period of 29 μm and a temperature of 413 K, a maximum signal output power of 820 mW at 1500 nm is achieved when the 808 nm pump power is 10.9 W, leading to an optical-to-optical conversion efficiency of 7.51%.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61701382,61601355,and 61571355)the China Postdoctoral Science Foundation(Grant No.2016M602770)the Xi’an Technological University Principal Foundation Key Project,China(Grant No.XAGDXJJ18001)
文摘Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation,the optical trapping properties of nanoparticle placed on the gold film with periodic circular holes are investigated numerically. Surface plasmon polaritons are excited on the metal-dielectric interface, with particular emphasis on the crucial role in tailoring the optical force acting on a nearby nanoparticle. Utilizing a first order corrected electromagnetic field components for a fundamental Gaussian beam, the incident beam is added into the calculation model of the proposed method. To obtain the detailed trapping properties of nanoparticle, the selected calculations on the effects of beam waist radius, sizes of nanoparticle and circular holes, distance between incident Gaussian beam and gold film, material of nanoparticle and polarization angles of incident wave are analyzed in detail to demonstrate that the optical-trapping force can be explained as a virtual spring which has a restoring force to perform positive and negative forces as a nanoparticle moves closer to or away from the centers of circular holes. The results of optical trapping properties of nanoparticle in the vicinity of the gold film could provide guidelines for further research on the optical system design and manipulation of arbitrary composite nanoparticles.
基金supported by the National Natural Science Foundation of China(Grant Nos.61308071,61601355,and 61571355)the Natural Science Foundation of Shaanxi Province,China(Grant No.2016JM6011)
文摘Based on the practical situation of nondestructive examination, the calculation model of the composite scattering is established by using a three-dimensional half-space finite difference time domain, and the Monte Carlo method is used to solve the problem of the optical surface with roughness in the proposed scheme. Moreover, the defect particles are observed as periodic particles for a more complex situation. In order to obtain the scattering contribution of defects inside the optical surface, a difference radar cross section is added into the model to analyze the selected calculations on the effects of numbers, separation distances, different depths and different materials of defects. The effects of different incident angles are also discussed. The numerical results are analyzed in detail to demonstrate the best position to find the defects in the optical surface by detecting in steps of a fixed degree for the incident angle.
基金Supported by NSFC(10801056, 10971057)NSF of Guangdong Province (8451063101000730)Doctoral Program of Higher Education of China(20094407110001)
文摘This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results.
文摘The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.
基金Supported by National Natural Science Foundation of China (11371276,10901118)Elite Scholar Program in Tianjin University,P.R.China
文摘The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.
基金Supported by National High Technology Research and Development Program （863 Program） （2007AA04Z179）, National Natural Science Foundation of China （60774044）, and Professional Research Foundation forhdvaneed Talents of Jiangsu University （07JDG037）
