This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half...This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Caussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.展开更多
Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the...Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.展开更多
A computer-aided heterodyne interferometer which can achieve high precision measurement for the shape of micrograph is introduced. Laser common-path heterodyne interferometer and precise phase measuring techniques are...A computer-aided heterodyne interferometer which can achieve high precision measurement for the shape of micrograph is introduced. Laser common-path heterodyne interferometer and precise phase measuring techniques are used-Besides, in lateral positioning, the mathematical expression of interference signal at the edge of the micrograph is derived on considering that the laser beam has certain radius and its distribution conforms to Gaussian distribution. Because the method of least squares is used, the system can measure with high precision not only the height but also the width. The precision of height measurement is of the order of nm.The precision of width measurement is better than 0.1μm.展开更多
Based on the angular spectrum decomposition and partial-wave series expansion methods, we investigate the radiation force functions of two Airy-Gaussian （AiG） beams on a cylindrical particle and the motion trajector...Based on the angular spectrum decomposition and partial-wave series expansion methods, we investigate the radiation force functions of two Airy-Gaussian （AiG） beams on a cylindrical particle and the motion trajectory of lhe particle. The simulations show that the particle can be pulled or propelled into either the positive or negative transverse direction by turning the phase difference between the two AiG beams appropriately; and the larger the beam widths of the two AiG beams are, the bigger the radiation force can be obtained to control the particle. In addition, the direction of the accelerated particle can be controlled while the dimensionless frequency bandwidth changes. The results indicate that the phase plays an important role in controlling the direction of the particle, which may provide a theoretical basis for the design of acoustical tweezers and the development of drug delivery.展开更多
It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For t...It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent com- bination, Zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.展开更多
基金Project supported by Natural Science Foundation of the Department of Science & Technology of Fujian Province of China (GrantNo 2007F5040)
文摘This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Caussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.
基金partially supported by National Nature Science Foundation of China(61372187)Sichuan Key Technology Research and Development Program(2012GZ0019,2013GXZ0155)the Fund of Lab of Security Insurance of Cyberspace,Sichuan Province(szjj2014-079)
文摘Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.
文摘A computer-aided heterodyne interferometer which can achieve high precision measurement for the shape of micrograph is introduced. Laser common-path heterodyne interferometer and precise phase measuring techniques are used-Besides, in lateral positioning, the mathematical expression of interference signal at the edge of the micrograph is derived on considering that the laser beam has certain radius and its distribution conforms to Gaussian distribution. Because the method of least squares is used, the system can measure with high precision not only the height but also the width. The precision of height measurement is of the order of nm.The precision of width measurement is better than 0.1μm.
基金Project supported by the National Key R&D Program,China(Grant No.2016YFF0203000)the National Natural Science Foundation of China(Grant Nos.11774167 and 61571222)+2 种基金Fundamental Research Funds for the Central Universities,China(Grant No.020414380001)State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant No.SKLA201609)AQSIQ Technology R&D Program,China(Grant No.2017QK125)
文摘Based on the angular spectrum decomposition and partial-wave series expansion methods, we investigate the radiation force functions of two Airy-Gaussian （AiG） beams on a cylindrical particle and the motion trajectory of lhe particle. The simulations show that the particle can be pulled or propelled into either the positive or negative transverse direction by turning the phase difference between the two AiG beams appropriately; and the larger the beam widths of the two AiG beams are, the bigger the radiation force can be obtained to control the particle. In addition, the direction of the accelerated particle can be controlled while the dimensionless frequency bandwidth changes. The results indicate that the phase plays an important role in controlling the direction of the particle, which may provide a theoretical basis for the design of acoustical tweezers and the development of drug delivery.
基金supported by the National Natural Science Foundation of China(Grant No.61178070)the Construction Plan for Scientific Research Innovation Teams of Universities in Sichuan Province,China(Grant No.12TD008)
文摘It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent com- bination, Zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.
