共查询到20条相似文献,搜索用时 15 毫秒
1.
Ince-Gaussian beams 总被引:1,自引:0,他引:1
We demonstrate the existence of the Ince-Gaussian beams that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation. Their transverse structure is described by the Ince polynomials and has an inherent elliptical symmetry. Ince-Gaussian beams constitute the exact and continuous transition modes between Laguerre and Hermite-Gaussian beams. The propagating characteristics are discussed as well. 相似文献
2.
Ye Heng Wang Xiang Zhang 《International Journal of Infrared and Millimeter Waves》1997,18(9):1731-1737
In weakly guiding analysis of cutoff frequencies in general optical waveguides, the proposed generalized Fourier series expansion
method in elliptical coordinates has advantages in terms of generality, accuracy, efficiency and simplicity. Numerical data
of higher mode cutoffs in elliptical and rectangular optical waveguides show the excellent agreement between the present method
and the finite element method. 相似文献
3.
Ince-Gaussian solitons in strongly nonlocal nonlinear media 总被引:1,自引:0,他引:1
We have introduced a novel class of higher-order spatial optical Ince-Gaussian solitons (IGSs) that constitute the third complete family of exact and orthogonal soliton solutions of the Snyder-Mitchell model. The transverse structure of the IGSs is characterized by the Ince polynomials and has an inherent elliptical symmetry. The IGSs form the exact and continuous transition modes between Hermite-Gaussian solitons and Laguerre-Gaussian solitons. 相似文献
4.
Y. Q. Xu G. Q. Zhou 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2012,66(3):59
An analytical propagation expression of an Ince-Gaussian beam in uniaxial crystals
orthogonal to the optical axis is derived. The uniaxial crystal considered here has the
property of the extraordinary refractive index being larger than the ordinary refractive
index. The Ince-Gaussian beam in the transversal direction along the optical axis spreads
more rapidly than that in the other transversal direction. With increasing the ratio of
the extraordinary refractive index to the ordinary refractive index, the spreading of the
Ince-Gaussian beam in the transversal direction along the optical axis increases and the
spreading of the Ince-Gaussian beam in the other transversal direction decreases. The
effective beam size in the transversal direction along the optical axis is always larger
than that in the other transversal direction. When the even and odd modes of Ince-Gaussian
beams exist simultaneously, the effective beam size in the direction along the optical
axis of the odd Ince-Gaussian beam is smaller than that of the even Ince-Gaussian beam in
the corresponding direction, and the effective beam size in the transversal direction
orthogonal to the optical axis of the odd Ince-Gaussian beam is larger than that of the
even Ince-Gaussian beam in the corresponding direction. 相似文献
5.
Bandres MA 《Optics letters》2004,29(15):1724-1726
The existence of elegant Ince-Gaussian beams that constitute a third complete family of exact and biorthogonal elegant solutions of the paraxial wave equation is demonstrated. Their transverse structure is described by Ince polynomials with a complex argument. Elegant Ince-Gaussian beams constitute exact and continuous transition modes between elegant Laguerre-Gaussian and elegant Hermite-Gaussian beams. The expansion formulas among the three elegant families are derived. 相似文献
6.
本文利用椭圆柱形坐标系,严格地分析了具有任意偏心度的椭圆截面的无限长理想导电的金属棒,放在有损耗的均匀各向同性的无限介质中,对从任意方向入射的均匀平面波的散射问题;并将散射场表示为马许函数。 相似文献
7.
D. Gogny 《Nuclear Physics A》1975,237(3):399-418
A simple method is proposed to calculate the matrix elements of two-body local interactions using a harmonic oscillator basis (HOF). Using the properties of HOF, it is shown that any local potential can be replaced by a simple series for the purpose of calculating matrix elements. This series can be reduced to a finite sum when evaluating a matrix element. Its terms are separable functions of the coordinates of the two particles; hence the advantage of the method. In the present article we treat the most important components of the two-body interaction, namely central, two-body spin-orbit, and tensor forces. As a representation we have chosen spherical harmonic oscillator functions expressed with spherical coordinates. This technique appears to be very well adapted to and efficient for Hartree-Fock calculations in any representation of the HOF. A very interesting feature of this formulation is that it can be easily extended to calculations employing generalized HOF as defined by Wong. 相似文献
8.
(3+1)-dimensional localized self-accelerating Airy elegant Ince-Gaussian wave packets and their radiation forces in free space 下载免费PDF全文
We construct analytically linear self-accelerating Airy elegant Ince–Gaussian wave packet solutions from(3+1)-dimensional potential-free Schr odinger equation. These wave packets have elliptical geometry and show different characteristics when the parameters(p, m) and ellipticity ε are adjusted. We investigate these characteristics both analytically and numerically and give the 3-dimensional intensity and phase distribution of these wave packets. Lastly, we analyze the radiation forces on a Rayleigh dielectric particle. In addition, we also find an interesting phenomenon that if the energy distribution between every part of wave packets is uneven at the input plane, the energy will be transferred between every part in the process of transmission. 相似文献
9.
We analyze the concept of a nondegenerate superintegrable system in n-dimensional Euclidean space. Attached to this idea is the notion that every such system affords a separation of variables
in one of the various types of generic elliptical coordinates that are possible in complex Euclidean space. An analysis of
how these coordinates are arrived at in terms of their expression in terms of Cartesian coordinates is presented in detail.
The use of well-defined limiting processes illustrates just how all these systems can be obtained from the most general nondegenerate
superintegrable system in n-dimensional Euclidean space. Two examples help with the understanding of how the general results are obtained.
The text was submitted by the authors in English. 相似文献
10.
利用强非局域非线性介质中傍轴光束传输的线性模型(Snyder-Mitchell模型)讨论了椭圆坐标系下光束传输过程,通过设立Ince多项式对Gauss函数的调制解得到了强非局域非线性介质中光束稳定传输的Ince-Gauss解.当Ince-Gauss光束的入射功率为临界功率时,光束保持孤子形式传输,否则传输光束的束宽呈现周期性波动,即为呼吸子形式.同时还数值模拟了呼吸子的传输过程.Ince-Gauss光在一定条件下可以连续转换为Hermite-Gauss光或Laguerre-Gauss光,图示展现了几个低阶Ince型光孤子及其转换情况.
关键词:
强非局域非线性介质
Ince-Gauss光
Laguerre-Gauss光
Hermite-Gauss光 相似文献
11.
12.
光纤中光的偏振态的几种表示方法 总被引:6,自引:0,他引:6
阐述了光纤中影响光的偏振态的几个因素。用椭圆表示法和邦加(Poincare)球图形表示法对光的任意偏振态进行了描述,并用平面的史密斯圆图来等效邦加球。编制了QUICK BASIC计算机程序,绘制了史密斯圆图的等α线、等δ线和等β线,程序能快速显示任意偏振态的椭圆表示和史密斯圆图表示,讨论了史密斯圆图的特性和应用。 相似文献
13.
We report what is to our knowledge the first observation of Ince-Gaussian modes directly generated in a stable resonator. By slightly breaking the symmetry of the cavity of a diode-pumped Nd:YVO4 laser and its pump beam configuration we were able to generate single high-order Ince-Gaussian modes of high quality. The observed transverse modes have an inherent elliptic structure and exhibit remarkable agreement with theoretical predictions. 相似文献
14.
To describe a 5-particle system, ‘principal-axis hyperspherical’ coordinates (made up of one hyperradius and eight angles as internal coordinates) and three Euler angles as external (rotational) coordinates are used. A mathematical procedure to derive, in a systematic manner, the exact quantum mechanical Hamiltonian of the system in terms of these coordinates is presented. A generalized angular momentum vector operator, which allows the generation of a profitable standard representation for the angular part of the problem, is introduced. 相似文献
15.
《Nuclear Physics B》1995,442(3):494-532
We derive an explicit formula for the evaluation of the classical closed string action for any off-shell string field, and for the calculation of arbitrary off-shell amplitudes. The formulae require a parametrization, in terms of some moduli space coordinates, of the family of local coordinates needed to insert the off-shell states on Riemann surfaces. We discuss in detail the evaluation of the tachyon potential as a power series in the tachyon field. The expansion coefficients in this series are shown to be geometrical invariants of Strebel quadratic differentials whose variational properties imply that closed string polyhedra, among all possible choices of string vertices, yield a tachyon potential which is as small as possible order by order in the string coupling constant. Our discussion emphasizes the geometrical meaning of off-shell amplitudes. 相似文献
16.
Thermal effects are very much influential in high power beam generators. Their impacts on special types of beams such as Helmholtz-Gauss beams have attracted special attentions. This work reports thermal effects on the generation and propagation of Ince-Gaussian beams. The results show considerable beam spot size variations for near fields under various induced heat loads. As Ince-Gaussian beams are directly related to cavity symmetry breaking, the results can greatly help system designers for circumventing these types of symmetry breaks usually encountered in high power lasers. 相似文献
17.
Eugene P. Gross 《Journal of statistical physics》1984,36(1-2):189-217
We consider the density matrices that arise in the statistical mechanics of the electron-phonon systems. In the path integral representation the phonon coordinates can be eliminated. This leads to an action that depends on pairs of points on a path, that depends explicitly on time differences, and that contains the phonon occupation numbers. The integral is reduced to a standard form by scaling to the thermal length. We use the technique of integration by parts and add specially chosen generating functionals to the action. We set down functional derivative equations for the source-dependent density matrix and for the mass operator. This allows us to develop a series of approximations for the operator in terms of exact propagators. The crudest approximation is a coherent potential approximation applicable at a general temperature. 相似文献
18.
V. I. Krivenkov 《Moscow University Physics Bulletin》2009,64(4):362-364
An invariant expression in the form of a contour integral for guided mode power flow via an arbitrary area of the cross section
of an optical fiber with constant permittivity is presented in polar and elliptical coordinates. Expressions for guided mode
power flows via the cross sections of circular and elliptical multilayer optical fibers are obtained. 相似文献
19.
Livia Corsi Guido Gentile Michela Procesi 《Communications in Mathematical Physics》2011,302(2):359-402
The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt
series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by
following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations
between contributions of the same perturbation order. In turn, this is due to symmetries in the problem. Such symmetries are
easily visualised in action-angle coordinates, where the KAM theorem is usually formulated by exploiting the analogy between
Lindstedt series and perturbation expansions in quantum field theory and, in particular, the possibility of expressing the
solutions in terms of tree graphs, which are the analogue of Feynman diagrams. If the unperturbed system is isochronous, Moser’s
modifying terms theorem ensures that an analytic quasi-periodic solution with the same Diophantine frequency vector as the
unperturbed Hamiltonian exists for the system obtained by adding a suitable constant (counterterm) to the vector field. Also
in this case, one can follow the alternative approach of studying the perturbation expansion for both the solution and the
counterterm, and again convergence of the two series is obtained as a consequence of deep cancellations between contributions
of the same order. In this paper, we revisit Moser’s theorem, by studying the perturbation expansion one obtains by working
in Cartesian coordinates. We investigate the symmetries giving rise to the cancellations which makes possible the convergence
of the series. We find that the cancellation mechanism works in a completely different way in Cartesian coordinates, and the
interpretation of the underlying symmetries in terms of tree graphs is much more subtle than in the case of action-angle coordinates. 相似文献
20.
The paper presents an analytical investigation of the electromagnetic wave propagation in a tapered core dielectric elliptical step-index fiber. Implementing Maxwell's equations in elliptical coordinates, field components are deduced that essentially incorporate Mathieu and the modified Mathieu functions. Finally, the characteristic dispersion equations are developed for even and odd modes supported by the fiber. 相似文献