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1.
Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, analytical expressions for the transversal and axial field distribution of plane waves propagating through a thin lens followed by a small circular aperture are derived and used to study the focusing and diffraction properties of plane waves. Some special cases of our general result are discussed, and illustrative numerical calculation results are given. It is found that the vectorial nonparaxial approach should be applied if the aperture dimension is comparable with the wavelength or the focusing is strong. 相似文献
2.
Starting from the vectorial Rayleigh diffraction integral formula and without using the far-field approximation, a solution of the wave equation beyond the paraxial approximation is found, which represents vectorial non-paraxial elliptical Gaussian beams in free space. The far-field expressions for non-paraxial Gaussian beams and elliptical Gaussian beams can be regarded as special cases treated in this paper. Some basic propagation properties of vectorial non-paraxial elliptical Gaussian beams, including the irradiance distribution, phase term, beam widths and divergence angles are studied. Numerical results are given and illustrated. 相似文献
3.
Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field. 相似文献
4.
Q. Cui 《Theoretical chemistry accounts》2006,116(1-3):51-59
Efficient vectorial processes such as the transduction of bioenergy and signals are characteristics that strikingly distinguish living systems from inanimate materials. Recent developments in biophysical and biochemical techniques have provided new information about the structure, dynamics and interaction of biomolecules involved in vectorial life processes at multiple length and temporal scales. This wealth of data makes it possible to carry out theoretical and computational studied of key mechanistic questions associated with complex life processes at an unprecedented level. Using two “vectorial biomolecular machines”, myosin and cytochrome c oxidase, as examples, we discuss the identification of interesting and biologically relevant questions that require thorough theoretical analysis. Technical challenges and recent progress related to these theoretical investigations are briefly summarized 相似文献
5.
Junji Yamauchi Takashi Ando Yasuhiro Akimoto Hisamatsu Nakano 《Fiber and Integrated Optics》1996,15(4):353-363
A wavelength filter consisting of single-mode and few-mode fibers is investigated numerically. A simple finite-difference beam-propagation method, in which a transparent boundary condition can be imposed, is developed for circularly symmetric waveguides. After confirming the validity of the numerical method by the mode-mismatch loss, we calculate the propagating field in the fiber wavelength filter, in which interference between LP01, and LP02 modes occurs. To improve the filtering operation, a depressed-index fiber is employed for the few-mode fiber. The effects of the radius and refractive index of the depressed section on the transmission power are revealed and discussed. Power is suppressed to less than 0.1% at 1.3 μm, while maintaining power transmission of more than 85% at 1.55 μm. It is also found that the filtering operation shifts to higher wavelengths as the input power is increased when we choose a self-focusing nonlinear material in the depressed section. 相似文献
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7.
Based on the vectorial Rayleigh–Sommerfeld integrals, the analytical propagation expression of a vectorial Laguerre–Gaussian beam beyond paraxial approximation is presented. The far field expression and the scalar paraxial result are obtained as special cases of the general formulae. According to the analytical representation, the light intensity distribution of the vectorial Laguerre–Gaussian beam is depicted in the reference plane. The light intensity distribution of a vectorial Laguerre–Gaussian beam with cos m is also compared with that of a vectorial Laguerre–Gaussian beam with sin m. 相似文献
8.
We describe a wave-front displacement system using a novel configuration of a pair of wedge prisms. The wave-front propagation, through the displacement system, is analyzed using the exact ray trace. The main advantage, of this configuration, is that the shearing (direction and magnitude) is constant from the displacement system to the image plane. The direction of the shearing depends on the relative orientation of the prisms. The magnitude of the shearing is proportional to the distance between prisms. The proportionality constant depends on the wedge angle and the material of fabrication of the prisms, and it gives the sensitivity to the displacement of the system. The deviation of the shearing due to the difference between the wedge angles is larger than that the produced by the oblique incidence of the wave-front. The experimental results confirm the theoretical data. 相似文献
9.
A complete closed form vectorial solution to the Kepler problem 总被引:2,自引:0,他引:2
The paper gives an exact vectorial solution to the Kepler problem. A vectorial regularization that linearizes the Kepler problem
is given using a Sundman transformation. Closed form expressions describing the Keplerian motion are deduced. A unified approach
to the classic Kepler problem is offered, by studying both rectilinear and non-rectilinear Keplerian motions with the same
instrument. The approach is an elementary one and only simple vectorial computations are involved. 相似文献
10.
The degree of asphericity is estimated by determining the average radius of curvature in different sections, at various points on the surface of a sphere, and the deviation from it. We employ the vectorial shearing interferometer (VSI) as the instrument to determine the radius of curvature from two subapertures of the transparent glass sphere. We incorporate the sphere as a thick lens into the interferometric setup, illuminating it with an expanded beam. The spherical aberration, introduced by the sphere in the wave front, depends on the local sphere radius, on the refraction index of the glass, and on the cone angle of the source. The wave front aberrated by the sphere impinges on the VSI. Here, the wave front is divided in two in amplitude, it is sheared vectorially, and it is superimposed with itself. The fringe pattern is formed in the intersection of the wave fronts. The shape of the resulting fringe pattern is directly related to spherical aberration. We estimate qualitatively the degree of asphericity, comparing the phase gradients in different sections of the sphere. Here, we report on the experimental setup to test the asphericity, the results with different vectorial shearing (magnitude and direction). Finally, we perform a comparison with the theoretical predictions. 相似文献