矢量椭圆空心光束的产生及其应用研究
|
摘要
矢量椭圆空心光束不仅具有一般空心光束的优点,而且具有独特的传输特性、偏振特性和分数的轨道角动量,在原子分子物理、原子分子光学、光学测量、光信息处理、生物光子学、生物医学、纳米科技、材料科学等领域都有广阔的应用前景。随着人们对光束角动量的认识,具有角动量的光束在光学镊子、光学扳手、微机械马达、纳米科技、量子保密通信、光信息存储等领域也有重要应用。而无衍射光束由于其传输不变性,一直是人们追求的热点之一。本文致力于自聚焦矢量椭圆空心光束和无衍射矢量椭圆空心光束的产生及其应用的理论研究。
首先,我们基于麦克斯韦方程的矢量模型,采用马提厄函数对椭圆介质空心光纤中传输的部分椭圆空心模式进行了详细研究；我们的研究表明：椭圆空心光纤中可以传输一些椭圆空心模式,并且光纤中传输的单个模式的平均光子角动量为零,而双模传输可以获得随传输距离正弦变化的平均光子角动量。在此基础上,我们利用椭圆空心光纤中传输的单模衍射输出,产生了角动量为零的矢量椭圆空心光束；并利用椭圆空心光纤中的双模衍射输出,产生了具有位置依赖的分数角动量的矢量椭圆空心光束。得到的两种矢量椭圆空心光束都具有自聚焦效应,光束在穿过其自聚焦平面时,椭圆长轴和短轴将发生交换。此外,两种矢量椭圆空心光束都具有位置依赖的任意偏振态。
接着,我们提出了一种采用双模传输的椭圆空心光纤和圆锥形透镜构成的光学系统来产生矢量的准马提厄空心光束的新方案。我们成功得到了一束在长达1m的传输距离内近似无衍射的椭圆空心光束,并且证明了这种光束是一种矢量准马提厄空心光束。研究表明：产生的矢量准马提厄空心光束在1.2～2.2m的区域内具有传输不变的光强分布(即无衍射特性)和随传输距离周期性旋转的径向依赖的偏振态,并且在此区域内光束中心的椭圆环具有传输不变的分数轨道角动量。此外,我们通过数值拟合,给出了描述矢量准马提厄空心光束在自由空间的光强分布和轨道角动量分布的简单表达式。
最后,本文还对产生的矢量椭圆空心光束在原子分子光学中的应用进行了理论研究。我们首先讨论了产生的自聚焦矢量椭圆空心光束在原子透镜中的应用,计算了激光失谐量和原子束的初始速率对原子透镜像差的影响。当失谐量为70GHz,原子束的初始速率为28ms时,总的像差达到最小,为26.2nm,远低于光波的衍射极限。并且我们产生的矢量椭圆空心光束在自聚焦过程中始终保持中心光强为零,十分适合于用作高分辨的原子透镜。此外,蓝失谐的矢量准马提厄空心光束在导引冷原子或冷分子的同时,可以实现对冷原子或者冷分子的旋转操控。85Rb原子在矢量准马提厄空心光束中运动的平均旋转角频率与原子在光场中所处的初始位置和入射激光的功率大小有关。初始位置距离光束中心较近的原子其平均旋转角频率较大,入射光功率较大时,原子的平均旋转频率也较大。我们清楚地看到了光束的轨道角动量对原子运动轨迹的明显扭转。重氨分子在矢量准马提厄空心光束中的质心运动也与在光束中所处的初始位置有关,当处于特定初始位置时,分子会沿椭圆形轨道作螺旋进动。此外,在矢量准马提厄空心光束中重氨分子的平均旋转角频率很高,可达9.33kHz。
Vectorial elliptical hollow beams not only have the same advantages of common hollow beams, but also unique propagation characteristics, polarization states and fractional orbital angular momentum. They have some wide applications in atomic and molecular physics, atomic and molecular optics, optical measurement, optical information processing, bio-photonics, bio-medical, nanotechnology and materials science, etc. Light beams with angular momentum have also important applications in optical tweezers, optical spanner, micro-mechanical motors, nanotechnology, quantum cryptography and optical information storage, etc. In addition, due to the propagation invariance, diffraction-free beams have been one of the hot research topics in nowadays. This thesis is dediated to the study of production of vectorial elliptical hollow beams with self-focusing effect or diffraction-free property and their applications.
Firstly, based on the vector model of Maxwell's equations, we study some elliptic hollow modes guided in an elliptic dielectric hollow fiber by using Mathieu functions. Our study shows that there are some closed elliptic hollow modes guided in the elliptical hollow fiber, and the angular momentum of a single mode in the elliptical hollow fiber exactly equals zero, however, the synthesized dual-mode field has a fractional angular momentum, which oscillates in a sinusoidal manner along the axis of the fiber. Then, we proposed a handy scheme to generate a vectorial elliptic hollow beam without angular momentum by a single mode output from the elliptic hollow fiber, and a vectorial elliptic hollow beam with a position-dependent fractional angular momentum by a dual-mode output from the fiber. Both vectorial elliptic hollow beams have a self-focusing effect in near field, and the directions of the major and minor axes of the elliptical intensity profile will be interchanged after the self-focusing plane. Both vectorial elliptic hollow beams have a position-dependent arbitrary polarization.
Secondly, we propose a promising and practical scheme to generate a vectorial Mathieu-like hollow beam by using an axicon optical system and a dual-mode elliptic hollow fiber. The intensity and polarization distributions of the beam and its fractional orbital angular momentum are investigated. Our study shows that the generated beam is a vectorial Mathieu-like hollow beam within the propagation region of 1.2～2.2 m, owing an diffraction-free intensity-profile, periodically-rotated polarization property as well as an invariant fractional orbital angular momentum. Some simple but practical formulus to describe three-dimensional propagation characteristics of such a Mathieu-like hollow beam are obtained by fitting its intensity distribution numerically.
Finally, we study the applications of the generated vectorial elliptic hollow beam in atomic and molecular optics. By using the self-focusing effect of the elliptic hollow beam, we obtain an atomic lense with a high resolution. Moreover, a blue-detuned vectorial Mathieu-like hollow beam can be used to guide cold atoms and molecules, rotating them meanwhile. When an 85Rb atom is moving in the vectorial Mathieu-like hollow beam, its average rotation angular frequency depends on the initial position and the power of the incident laser. Closer initial position to the beam center or larger incident laser power will result in higher rotation angular frequency. Our study shows that the trajectory of the atom is obviously twisted by the orbital angular momentum of the vectorial Mathieu-like hollow beam. Similarly, the center-of-mass trajectory of a ND3 molecule in the vectorial Mathieu-like hollow beam is also determined by its initial position. And molecules of certain initial position do make spiral precession along the elliptical orbit. The average rotation angular frequency of a ND3 molecule in the vectorial Mathieu-like hollow beam can be up to 9.33kHz.
首先,我们基于麦克斯韦方程的矢量模型,采用马提厄函数对椭圆介质空心光纤中传输的部分椭圆空心模式进行了详细研究；我们的研究表明：椭圆空心光纤中可以传输一些椭圆空心模式,并且光纤中传输的单个模式的平均光子角动量为零,而双模传输可以获得随传输距离正弦变化的平均光子角动量。在此基础上,我们利用椭圆空心光纤中传输的单模衍射输出,产生了角动量为零的矢量椭圆空心光束；并利用椭圆空心光纤中的双模衍射输出,产生了具有位置依赖的分数角动量的矢量椭圆空心光束。得到的两种矢量椭圆空心光束都具有自聚焦效应,光束在穿过其自聚焦平面时,椭圆长轴和短轴将发生交换。此外,两种矢量椭圆空心光束都具有位置依赖的任意偏振态。
接着,我们提出了一种采用双模传输的椭圆空心光纤和圆锥形透镜构成的光学系统来产生矢量的准马提厄空心光束的新方案。我们成功得到了一束在长达1m的传输距离内近似无衍射的椭圆空心光束,并且证明了这种光束是一种矢量准马提厄空心光束。研究表明：产生的矢量准马提厄空心光束在1.2～2.2m的区域内具有传输不变的光强分布(即无衍射特性)和随传输距离周期性旋转的径向依赖的偏振态,并且在此区域内光束中心的椭圆环具有传输不变的分数轨道角动量。此外,我们通过数值拟合,给出了描述矢量准马提厄空心光束在自由空间的光强分布和轨道角动量分布的简单表达式。
最后,本文还对产生的矢量椭圆空心光束在原子分子光学中的应用进行了理论研究。我们首先讨论了产生的自聚焦矢量椭圆空心光束在原子透镜中的应用,计算了激光失谐量和原子束的初始速率对原子透镜像差的影响。当失谐量为70GHz,原子束的初始速率为28ms时,总的像差达到最小,为26.2nm,远低于光波的衍射极限。并且我们产生的矢量椭圆空心光束在自聚焦过程中始终保持中心光强为零,十分适合于用作高分辨的原子透镜。此外,蓝失谐的矢量准马提厄空心光束在导引冷原子或冷分子的同时,可以实现对冷原子或者冷分子的旋转操控。85Rb原子在矢量准马提厄空心光束中运动的平均旋转角频率与原子在光场中所处的初始位置和入射激光的功率大小有关。初始位置距离光束中心较近的原子其平均旋转角频率较大,入射光功率较大时,原子的平均旋转频率也较大。我们清楚地看到了光束的轨道角动量对原子运动轨迹的明显扭转。重氨分子在矢量准马提厄空心光束中的质心运动也与在光束中所处的初始位置有关,当处于特定初始位置时,分子会沿椭圆形轨道作螺旋进动。此外,在矢量准马提厄空心光束中重氨分子的平均旋转角频率很高,可达9.33kHz。
Vectorial elliptical hollow beams not only have the same advantages of common hollow beams, but also unique propagation characteristics, polarization states and fractional orbital angular momentum. They have some wide applications in atomic and molecular physics, atomic and molecular optics, optical measurement, optical information processing, bio-photonics, bio-medical, nanotechnology and materials science, etc. Light beams with angular momentum have also important applications in optical tweezers, optical spanner, micro-mechanical motors, nanotechnology, quantum cryptography and optical information storage, etc. In addition, due to the propagation invariance, diffraction-free beams have been one of the hot research topics in nowadays. This thesis is dediated to the study of production of vectorial elliptical hollow beams with self-focusing effect or diffraction-free property and their applications.
Firstly, based on the vector model of Maxwell's equations, we study some elliptic hollow modes guided in an elliptic dielectric hollow fiber by using Mathieu functions. Our study shows that there are some closed elliptic hollow modes guided in the elliptical hollow fiber, and the angular momentum of a single mode in the elliptical hollow fiber exactly equals zero, however, the synthesized dual-mode field has a fractional angular momentum, which oscillates in a sinusoidal manner along the axis of the fiber. Then, we proposed a handy scheme to generate a vectorial elliptic hollow beam without angular momentum by a single mode output from the elliptic hollow fiber, and a vectorial elliptic hollow beam with a position-dependent fractional angular momentum by a dual-mode output from the fiber. Both vectorial elliptic hollow beams have a self-focusing effect in near field, and the directions of the major and minor axes of the elliptical intensity profile will be interchanged after the self-focusing plane. Both vectorial elliptic hollow beams have a position-dependent arbitrary polarization.
Secondly, we propose a promising and practical scheme to generate a vectorial Mathieu-like hollow beam by using an axicon optical system and a dual-mode elliptic hollow fiber. The intensity and polarization distributions of the beam and its fractional orbital angular momentum are investigated. Our study shows that the generated beam is a vectorial Mathieu-like hollow beam within the propagation region of 1.2～2.2 m, owing an diffraction-free intensity-profile, periodically-rotated polarization property as well as an invariant fractional orbital angular momentum. Some simple but practical formulus to describe three-dimensional propagation characteristics of such a Mathieu-like hollow beam are obtained by fitting its intensity distribution numerically.
Finally, we study the applications of the generated vectorial elliptic hollow beam in atomic and molecular optics. By using the self-focusing effect of the elliptic hollow beam, we obtain an atomic lense with a high resolution. Moreover, a blue-detuned vectorial Mathieu-like hollow beam can be used to guide cold atoms and molecules, rotating them meanwhile. When an 85Rb atom is moving in the vectorial Mathieu-like hollow beam, its average rotation angular frequency depends on the initial position and the power of the incident laser. Closer initial position to the beam center or larger incident laser power will result in higher rotation angular frequency. Our study shows that the trajectory of the atom is obviously twisted by the orbital angular momentum of the vectorial Mathieu-like hollow beam. Similarly, the center-of-mass trajectory of a ND3 molecule in the vectorial Mathieu-like hollow beam is also determined by its initial position. And molecules of certain initial position do make spiral precession along the elliptical orbit. The average rotation angular frequency of a ND3 molecule in the vectorial Mathieu-like hollow beam can be up to 9.33kHz.
引文
1. J. Yin, W. Gao, and Y. Zhu, "Generation of dark hollow beams and their applications," in Progress in Optics, E. Wolf, ed. (Elsevier Science Bv, Amsterdam,2003), pp.119-204.
2. Z. Bouchal, "Nondiffracting optical beams:physical properties, experiments, and applications," Czech. J. Phys.53,537-578 (2003).
3. L. Allen, M. W. Beijersbergen, R. J. C.Spreeuw, and J. P. Woerdman, "Oribital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A45,8185-8189 (1992).
4. V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91,093602 (2003).
5. M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun.156, 300-306(1998).
6. M. J. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World, 35-40(1997).
7. J. E. Molloy, K. Dholakia, and M. J. Padgett, "Optical tweezers in a new light," J. Mod. Opt.50,1501-1507 (2003).
8. J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre-Gaussian and Gaussian beams," Opt. Express 16,10117-10129 (2008).
9. V. Arrizon, G. Mendez, and D. Sanchez-de-La-Llave, "Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators," Opt. Express 13,7913-7927 (2005).
10. Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, "Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator," Opt. Lett.32,1411-1413 (2007).
11. Y. Cai and L. Zhang, "Coherent and partially coherent dark hollow beams with rectangular symmetry and paraxial propagation properties," J. Opt. Soc. Am. B 23,1398-1407(2006).
12. A. Ottl, S. Ritter, M. Kohl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett.95,090404 (2005).
13. J. C. Gutierrez-Vega, "Characterization of elliptic dark hollow beams," Laser Beam Shaping IX 7062,706207 (2008).
14. G. M. Gallatin and P. L. Gould, "Laser focusing of atomic beams," J. Opt. Soc. Am. B 8,502-508(1991).
15. A. V. Nestrov and V. G. Niziev, "Laser beam with axially symmetric polarization," J. Phys. D 33,1817-1822 (2000).
16. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12,3377-3382 (2004).
17. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett.86, 5251-5254(2001).
18. G. M. Lerman, Y. Lilach, and U. Levy, "Demonstration of spatially inhomogeneous vector beams with elliptical symmetry," Opt. Lett.34, 1669-1671 (2009).
19. A. Chafiq, Z. Hricha, and A. Belafhal, "Propagation properties of vector Mathieu-Gauss beams," Opt. Commun.275,165-169 (2007).
20. R. I. Hernandez-Aranda, J. C. Gutierrez-Vega, M. Guizar-Sicairos, and M. A. Bandres, "Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems," Opt. Express 14,8974-8988 (2006).
21. S. Chavez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O'Neil, I. Mac Vicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B 4, S52-S57 (2002).
22. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun.144,210-213 (1997).
23. Y. Cai and Q. Lin, "Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems," J. Opt. Soc. Am. A 21,1058-1065(2004).
24. C. Zhao, X. Lu, L. Wang, and H. Chen, "Hollow elliptical Gaussian beams generated by a triangular prism," Opt. Laser Technol.40 575-580 (2008).
25. Y. Cai and Q. Lin, "The elliptical Hermite-Gaussian beam and its propagation through paraxial systems," Opt. Commun.207,139-147 (2002).
26. Y. Cai and Q. Lin, "Decentered elliptical Hermite-Gaussian beam," J. Opt. Soc. Am A 20,1111-1119(2003).
27. C. Gao, H. Weber, and H. Laabs, "Twisting of three-dimensional Hermite-Gaussian beams," J. Mod. Opt.46,709-719 (1999).
28. Z. Mei and D. Zhao, "Decentered controllable elliptical dark-hollow beams," Opt. Commun.259,415-123 (2006).
29. V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, "Elliptic Laguerre-Gaussian beams," J. Opt. Soc. Am. A 23,43-56 (2006).
30. R. Chakraborty and A. Ghosh, "Generation of an elliptic Bessel beam," Opt. Lett.31,38-40 (2006).
31. R. Chakraborty and A. Ghosh, "Generation of an elliptic hollow beam using Mathieu and Bessel functions," J. Opt. Soc. Am. A 23,2278-2282 (2006).
32. J. C. Gutierrez-Vega, "Theory and numerical analysis of the Mathieu functions," http//homepages.mty.itesm.mx/jgutierr/Mathieu/Mathieu.pdf (2003-02-14).
33. P. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, Inc., New York, NY,1953).
34. C. A. Dartora, M. Zamboni-Racheda, K. Z. Nobrega, E. Recami, and H. E. Hernandez-Figueroa, "General formulation for the analysis of scalar diffraction-free beams using angular modulation:Mathieu and Bessel beams," Opt. Commun.222,75-80 (2003).
35. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Shaping soliton properties in Mathieu lattices," Opt. Lett.31,238-240 (2006).
36. C. Lopez-Mariscal, J. C. Gutierrez-Vega, V. Garces-Chavez, and K. Dholakia, "Observation of the angular momentum transfer in the Mie regime using Mathieu beams," Proc. SPIE 5930,59301U (2005).
37. C. Lopez-Mariscal, J. C. Gutierrez-Vega, V. Garces-Chavez, and K. Dholakia, "Orbital angular momentum transfer in helical Mathieu beams," Opt. Express 14,4182-1187(2006).
38. C. A. Dartora and H. E. Hernandez-Figueroa, "Properties of a localized Mathieu pulse," J. Opt. Soc. Am. A 21,662-667 (2004).
39. J. Davila-Rodriguez and J. C. Gutierrez-Vega, "Helical Mathieu and parabolic localized pulses," J. Opt. Soc. Am. A 24,3449-3455 (2007).
40. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Alternative formulation for invariant optical fields:Mathieu beams," Opt. Lett.25, 1493-1495 (2000).
41. S. Chavez-Cerda, J. C. Gutierrez-Vega, and G. H. C. New, "Elliptic vortices of electromagnetic wave fields," Opt. Lett.26,1803-1805 (2001).
42. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, "Experimental demonstration of optical Mathieu beams," Opt. Commun.195,35-40 (2001).
43. J. C. Gutierrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22,289-298 (2005).
44. C. Lopez-Mariscal, M. A. Bandres, and J. C. Gutierrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng.45,068001 (2006).
45. M. Guizar-Sicairos and J. C. Gutierrez-Vega, "Generalized Helmholtz-Gauss beam and its transformation by paraxial optical systems," Opt. Lett.31, 2912-2914(2006).
46. R. J. Hernandez-Hernandez, R. A. Terborg, I. Ricardez-Vargas, and K. Volke-Sepulveda, "Experimental generation of Mathieu-Gauss beams with a phase-only spatial light modulator," Appl. Opt.49,6903-6909 (2010).
47. M. A. Bandres and J. Gutierrez-Vega, "Ince-Gaussian beams," Opt. Lett.29, 144-146(2004).
48. M. A. Bandres and J. C. Gutierrez-Vega, "Ince-Gaussian modes of the paraxial wave equation and stable resonators," J. Opt. Soc. Am. A 21,873-880 (2004).
49. U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, "Observation of Ince-Gaussian modes in stable resonators," Opt. Lett.29,1870-1872 (2004).
50. T. Ohtomo, K. Kamikariya, K. Otsuka, and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15,10705-10717 (2007).
51. J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutierrez-Vega, "Generation of helical Ince-Gaussian beams with a liquid-crystal display," Opt. Lett.31,649-651 (2006).
52. T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun.203,1-5 (2002).
53. Y. Mushiake, K. Matsumura, and N. Nakajima, "Generation of radially polarized optical beam mode by laser oscillation," Proc. IEEE 60,1107-1109 (1972).
54. K. Youngworth and T. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7,77-87 (2000).
55. G. M. Lerman and U. Levy, "Effect of radial polarization and apodization on spot size under tight focusing conditions," Opt. Express 16,4567-4581 (2008).
56. B. Hao and J. Leger, "Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam," Opt. Express 15, 3550-3556 (2007).
57. D. Deng, Q. Guo, L. Wu, and X. Yang, "Propagation of radially polarized elegant light beams," J. Opt. Soc. Am. B 24,636-643 (2007).
58. D. Deng and Q. Guo, "Analytical vectorial structure of radially polarized light beams," Opt. Lett.32,2711-2713 (2007).
59. N. Passilly, R. d. S. Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, "Simple interferometric technique for generation of a radially polarized light beam," J. Opt. Soc. Am. A 22,984-991 (2005).
60. T. Hirayama, Y. Kozawa, T. Nakamura, and S. Sato, "Generation of a cylindrically symmetric, polarized laser beam with narrow linewidth and fine tunability," Opt. Express 14,12839-12845 (2006).
61. L. W. Davis and G. Patsakos, "TM and TE electromagnetic beams in free space," Opt. Lett.6,22-23 (1981).
62. Z. Bouchal and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt. 42,1555-1566(1995).
63. A. Ashkin and J. M. Dziedzic, "Optical Levitation of Liquid Drops by Radiation Pressure," Science 187,1073-1075 (1975).
64. H. Felgner, O. Muller, and M. Schliwa, "Calibration of light forces in optical tweezers," Appl Opt.34,977-982 (1995).
65. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett.11, 288-290(1986).
66. L. Allen and M. J. Padgett, "The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density," Opt. Commun.184, 67-71 (2000).
67. M. Padgett, J. Arlt, N. Simpson, and L. Allen, "An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes," Am. J. Phys 64,77-82(1996).
68. L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Progress in Optics IV 39,291-372 (1999).
69. A T O'Neil, I Mac Vicar, L Allen, and M J Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett.88, 253601 (2002).
70. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light:An optical spanner," Opt. Lett.22,52-54 (1997).
71. J. W. R.Tabosa and D. V. Petrov, "Optical Pumping of Orbital Angular Momentum of Light in Cold Cesium Atoms," Phys. Rev. Lett.83,4967-4970 (1999).
72. A. Mair, A. Vaziri, and G. Weihs, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412,313-316 (2001).
73. G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light:preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett.,88,013601 (2002).
74. R. J. Voogd, M. Singh, S. F. Pereira, A. S. v. d. Nes, and J. J. M. Braat, "The use of orbital angular momentum of light beams for super-high density optical data storage," in OSA Technical Digest Series (Optical Society of America, 2004), FTuG14.
75. L. Accatino, G. Bertin, and M. Mongiardo, "Elliptical cavity resonators for dual-mode narrowband filters," IEEE Trans. Microwave Theory Tech.45, 2393-2401 (1997).
76. S. R. Rengarajan and J. E. Lewis, "Dielectric Loaded Elliptical Wave-Guides," IEEE Trans. Microwave Theory Tech.28,1085-1089 (1980).
77. S. Choi and K. Oh, "A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber," Opt. Commun.221,307-312 (2003).
78. J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, "Generation of a dark hollow beam by a small hollow fiber," Opt. Commun.138,287-292 (1997).
79. M. J. Renn, D. Montgomery,O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, "Laser-Guided Atoms in Hollow-Core Optical Fibers," Phys. Rev. Lett.75,3253-3256(1995).
80. M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and D. Z. Anderson, "Evanescent-wave guiding of atoms in hollow optical fibers," Phys. Rev. A 53, R648-R651(1996).
81. Y. Ni, N. C. Liu, and J. P. Yin, "Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel," J. Opt. B 5,300-308 (2003).
82. C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys.33,3235-3243 (1962).
83. L. J. Chu, "Electromagnetic waves in elliptic hollow pipes of metal," J. Appl. Phys.9,583-591(1938).
84. G. R. Valenzuela, "Impedances of an elliptic waveguide (for the eH1 mode)," IRE Trans. Microwave Theory Tech.8,431-435 (1960).
85. J. G. Kretzsch, "Wave Propagation in Hollow Conducting Elliptical Waveguides," IEEE Trans. Microwave Theory Tech. MT18,547-554 (1970).
86. J. G. Kretzsch, "Attenuation Characteristics of Hollow Conducting Elliptical Waveguides," IEEE Trans. Microwave Theory Tech. MT20,280-284 (1972).
87. G. Falciasecca, C. G. Someda, and F. Valdoni, "Comments on 'Attenuation characteristics of hollow conducting elliptical waveguides'," IEEE Trans. Microwave Theory Tech. MTT-21,154-154 (1973).
88. S. R. Rengarajan and J. E. Lewis, "Surface Impedance of Elliptical Hollow Conducting Wave-Guides," Electron. Lett.15,637-639 (1979).
89. D. A. Goldberg, L. J. Laslett, and R. A. Rimmer, "Modes of Elliptic Wave-Guides-a Correction," IEEE Trans. Microwave Theory Tech.38, 1603-1608(1990).
90. S. R. Rengarajan and J. E. Lewis, "Single-Mode Propagation in Multilayer Elliptical Fiber Wave-Guides," Radio Sci.16,541-547 (1981).
91. C. Shu, "Analysis of elliptical waveguides by differential quadrature method," IEEE Trans. Microwave Theory Tech.48,319-322 (2000).
92. S. J. Zhang and Y. C. Shen, "Eigenmode sequence for an elliptical waveguide with arbitrary ellipticity," IEEE Trans. Microwave Theory Tech.43,227-230 (1995).
93. M. Schneider and J. Marquardt, "Fast computation of modified Mathieu functions applied to elliptical waveguide problems," IEEE Trans. Microwave Theory Tech.47,513-516 (1999).
94. D. L. Young, S. P. Hu, C. W. Chen, C. M. Fan, and K. Murugesan, "Analysis of elliptical waveguides by the method of fundamental solutions," Microwave Opt. Tech. Lett.44,552-558 (2005).
95. T. Xiong and R. Yang, "Propagating Characteristics of Confocal Elliptical Waveguide Filled with Multilayered Dielectrics," J. Southwest Jiaotong Univ. 12,130-135(2004).
96. K. Halterman, S. Feng, and P. L. Overfelt, "Guided modes of elliptical metamaterial waveguides," Phys. Rev. A 76,013834 (2007).
97. I. Gomez-Castellanos and R. M. Rodrfguez-Dagnino, "Intensity distributions and cutoff frequencies of linearly polarized modes for a step-index elliptical optical fiber," Opt. Eng.46,45003 (2007).
98. V. M. Nair, S. Sarkar, and S. K. Khijwania, "Scalar variational analysis of fundamental mode in single-mode elliptical core fiber using super-Gaussian approximation," IEEE Photonics Tech. Lett.20,1381-1383 (2008).
99. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York,1964), pp. p721-750.
100. F. A. Alhargan, "Algorithms for the computation of all Mathieu functions of integer orders," ACM Trans. Math. Softw.26,390-407 (2000).
101. H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, "Optical-Potential for Atom Guidance in a Cylindrical-Core Hollow-Fiber," Opt. Commun.115, 57-64(1995).
102. J. Yin, Y. Zhu, and Y. Wang, "Evanescent light-wave atomic funnel:A tandem hollow-fiber, hollow-beam approach," Phys. Rev. A 57,1957-1966 (1998).
103. H. Ito, K. Sakaki, T. Nakata, W. H. Jhe, and M. Ohtsu, "Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: Theoretical approach," Ultramicroscopy 61,91-97 (1995).
104. S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent Atomic Wave-Guides from Hollow Optical Fibers-Quantized Atomic Motion," Phys. Rev. A 50,2680-2690 (1994).
105. K. T. Gahagan and G. A. Swartzlander, "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," J. Opt. Soc. Am. B 16,533-537 (1999).
106. Y. I. Shin, K. Kim, J. A. Kim, H. R. Noh, W. Jhe, K. Oh, and U. C. Paek, "Diffraction-limited dark laser spot produced by a hollow optical fiber," Opt. Lett.26,119-121 (2001).
107. H. Li and J. Yin, "Propagation properties of electromagnetic fields in elliptic dielectric hollow fibres and their applications," Chin. Phys. B 19,083204 (2010).
108. D. G. Glen and G. Shekhar, "Modeling and propagation of near-field diffraction patterns:A more complete approach," Am. J. Phys 72,1195-1201 (2004).
109. Z. Wang, Q. Lin, and Y. Wang, "Control of atomic rotation by elliptical hollow beam carrying zero angular momentum," Opt. Commun.240,357-362 (2004).
110. J. Yin, K. Kim, W. Shim, Y. Zhu, and W. Jhe, "Observation and discrimination of the mode patterns in a micron-sized hollow optical fiber and its synthetic measurements:far-field micro-imaging technique," Opt. Eng.37,2277-2283 (1998).
111. R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, Calif.,1964).
112. M. V. Berry, "Index formulae for singular lines of polarization," J. Opt. A: Pure Appl. Opt.6,675-678 (2004).
113. W. Gao and O. Korotkova, "Changes in the state of polarization of a random electromagnetic beam propagating through tissue," Opt. Commun.270, 474-478 (2007).
114. V. Westphal and S. W. Hell, "Nanoscale Resolution in the Focal Plane of an Optical Microscope," Phys. Rev. Lett.94,143903 (2005).
115. M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized rotation of atoms from photons with orbital angular momentum," Phys. Rev. Lett.97,170406 (2006).
116. H. Li and J. Yin, "Generation of a vectorial elliptic hollow beam by an elliptic hollow fiber," Opt. Lett.36,457-459 (2011).
117. A. R. Sidorov, Y. Zhang, A. N. Grigorenko, and M. R. Dickinson, "Nanometric optical tweezers based on nanostructured substrates," Opt. Commun.278, 439-444 (2007).
118. J. Wu, H. Li, and Y. Li, "Encoding information as orbital angular momentum states of light for wireless optical communications," Opt. Eng.46,019701 (2007).
119. M. B. Alvarez-Elizondo, R. Rodrlguez-Masegosa, and J. C. Gutierrez-Vega, "Generation of Mathieu-Gauss modes with an axicon-based laser resonator," Opt. Express 16,18770-18775 (2008).
120. J. H. McLeod, "The axicon:a new type of optical element," J. Opt. Soc. Am. 44,592-597(1954).
121. R. M. Herman and T. A. Wiggins, "Production and uses of diffractionless beams," J. Opt. Soc. Am. A 8,932-942 (1991).
122. J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun.177,297-301 (2000).
123. J. S. A. Collins, "Lens-System Diffraction Integral Written in Terms of Matrix Optics," J. Opt. Soc. Am.60,1168-1177 (1970).
124. B. P. S. Ahluwalia, W. C. Cheong, X. C. Yuan, L. S. Zhang, S. H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett.31, 987-989 (2006).
125. M. d. Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, "Axially symmetric hollow beams using refractive conical lenses," Opt. Laser Eng.39 283-291 (2003).
126. B. M. Rodriguez-Lara and R. Jauregui, "Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry," Phys. Rev. A 78, 033813 (2008).
127. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12,5448-5456 (2004).
128. J. J. McClelland and M. R. Scheinfein, "Laser focusing of atoms:a particle-optics approach," J. Opt. Soc. Am. B 8,1974-1986 (1991).
129. V. I. Balykin and V. S. Letokhov, "The possibility of deep laser focusing of an atomic beam into the A-region," Opt. Commun.64,151-156 (1987).
130. R. J. Celotta, R. Gupta, R. E. Scholten, and J. J. McClelland, "Nanostructure fabrication via laser-focused atomic deposition," J. Appl. Phys.79,6079-6083 (1996).
131. 印建平,”原子分子光学,”研究生讲义(2004).
132. P. Desbiolles, M. Arndt, P. Szriftgiser, and J. Dalibard, "Elementary Sisyphus process close to a dielectric surface," Phys. Rev. A 54,4292 (1996).
133. J. Yin, Y. Zhu, W. Jhe, and Z. Wang, "Atom guiding and cooling in a dark hollow laser beam," Phys. Rev. A 58,509 (1998).
134. W. L. Power, L. Allen, M. Babiker, and V. E. Lembessis, "Atomic motion in light beams possessing orbital angular momentum," Phys. Rev. A 52,479 (1995).
135. R. Fulton, A. I. Bishop, and P. F. Barker, "Optical stark decelerator for molecules," Phys. Rev. Lett.93,243004 (2004).
136. J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, "Measurement of the Electron Electric Dipole Moment Using YbF Molecules," Phys. Rev. Lett.89, 023003 (2002).
137. E. R. Hudson, H. J. Lewandowski, B. C. Sawyer, and J. Ye, "Cold Molecule Spectroscopy for Constraining the Evolution of the Fine Structure Constant," Phys. Rev. Lett.96,143004 (2006).
138. D. DeMille, F. Bay, S. Bickman, D. Kawall, D. Krause, S. E. Maxwell, and L R. Hunter, "Investigation of PbO as a system for measuring the electric dipole moment of the electron," Phys. Rev. A 61,052507 (2000).
139. M. S. Elioff, J. J. Valentini, and D. W. Chandler, "Subkelvin cooling NO molecules via 'Billiard-like' collisions with Argon," Science 302,1940-1943 (2003).
140. P. Soldan, M. T. Cvitas, J. M. Hutson, P. Honvault, and J. M. Launay, "Quantum dynamics of ultracold Na+ Na2 collisions," Phys. Rev. Lett.89, 153201 (2002).
141. N. Balakrishnan, R. C. Forrey, and A. Dalgarno, "Quenching of H2 vibrations in ultracold 3He and 4He collisions," Phys. Rev. Lett.80,3224 (1998).
142. D. DeMille, "Quantum computation with trapped polar molecules," Phys. Rev. Lett.88,067901 (2002).
143. E. R. Hudson, C. Ticknor, B. C. Sawyer, C. A. Taatjes, H. J. Lewandowski, J. R. Bochinski, J. L. Bohn, and J. Ye, "Production of cold formaldehyde molecules for study and control of chemical reaction dynamics with hydroxyl radicals," Phys. Rev. A 73,063404 (2006).
144. W. Schollkopf and J. P. Toennies, "Nondestructive mass selection of small van der Waals clusters," Science 266,1345-1348 (1994).
145. M. Arndt, O. Nairz, J. Voss-Andreae, C. Keller, G. V. d. Zouw, and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401,680-682 (1999).
146. A. P. Mosk, M. W. Reynolds, T. W. Hijmans, and J. T. M. Walraven, "Photoassociation of Spin-Polarized Hydrogen," Phys. Rev, Lett.82,307 (1999).
147. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, "Observation of Bose-Einstein condensation of molecules," Phys. Rev. Lett.91,250401 (2003).
148. J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, "Magnetic trapping of calcium monohydride molecules at milliKelvin temperatures," Nature 395,148-150 (1998).
149. T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, "Two-dimensional trapping of dipolar molecules in time-varying electric fields," Phys. Rev. Lett.92,223001 (2004).
150. N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, and F. Merkt, "Multistage Zeeman deceleration of hydrogen atoms," Phys. Rev. A 75,031402 (2007).
151. T. Seideman, "Time-resolved photoelectron angular distributions as a probe of coupled polyatomic dynamics," Phys. Rev. A 64,042504 (2001).
152. M. F. Gelin, C. Riehn, V. V. Matylitsky, and B. Brutschy, "Rotational recurrences in thermal ensembles of nonrigid molecules," Chem. Phys.290, 307-318(2003).
153. R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, "High-Order Harmonic Generation in Aligned Molecules," Phys. Rev. Lett.87, 183901 (2001).
154. S. Ramakrishna and T. Seideman, "Intense Laser Alignment in Dissipative Media as a Route to Solvent Dynamics," Phys. Rev. Lett.95,113001 (2005).
155. K. F. Lee, D. M. Villeneuve, P. B. Corkum, and E. A. Shapiro, "Phase control of rotational wave packets and quantum information," Phys. Rev. Lett.93, 233601 (2004).
156. H. Stapelfeldt and T. Seideman, "Colloquium:Aligning Molecules with Strong Laser Pulses," Rev. Mod. Phys.75,543-557 (2003).
157. J. J. Larsen, H. Sakai, C. P. Safvan, I. Wendt-Larsen, and H. Stapelfeldt, "Aligning molecules with intense nonresonant laser fields," J. Chem. Phys. 111,7774-7781 (1999).
158. M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Davila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett.89,143601 (2002).
159. L. Santos, G. V. Shlyapnikov, P. Zoller, and M. Lewenstein, "Bose-Einstein condensation in trapped dipolar gases," Phys. Rev. Lett.85,1791 (2000).
160. J. J. Larsen, I. Wendt-Larsen, and H. Stapelfeldt, "Controlling the Branching Ratio of Photodissociation Using Aligned Molecules," Phys. Rev. Lett.83, 1123(1999).
161. J. Aldegunde, H. Ran, and J. M. Hutson, "Manipulating ultracold polar molecules with microwave radiation:The influence of hyperfine structure," Phys. Rev. A 80,043410 (2009).
2. Z. Bouchal, "Nondiffracting optical beams:physical properties, experiments, and applications," Czech. J. Phys.53,537-578 (2003).
3. L. Allen, M. W. Beijersbergen, R. J. C.Spreeuw, and J. P. Woerdman, "Oribital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A45,8185-8189 (1992).
4. V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91,093602 (2003).
5. M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun.156, 300-306(1998).
6. M. J. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World, 35-40(1997).
7. J. E. Molloy, K. Dholakia, and M. J. Padgett, "Optical tweezers in a new light," J. Mod. Opt.50,1501-1507 (2003).
8. J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer, and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre-Gaussian and Gaussian beams," Opt. Express 16,10117-10129 (2008).
9. V. Arrizon, G. Mendez, and D. Sanchez-de-La-Llave, "Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators," Opt. Express 13,7913-7927 (2005).
10. Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, "Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator," Opt. Lett.32,1411-1413 (2007).
11. Y. Cai and L. Zhang, "Coherent and partially coherent dark hollow beams with rectangular symmetry and paraxial propagation properties," J. Opt. Soc. Am. B 23,1398-1407(2006).
12. A. Ottl, S. Ritter, M. Kohl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett.95,090404 (2005).
13. J. C. Gutierrez-Vega, "Characterization of elliptic dark hollow beams," Laser Beam Shaping IX 7062,706207 (2008).
14. G. M. Gallatin and P. L. Gould, "Laser focusing of atomic beams," J. Opt. Soc. Am. B 8,502-508(1991).
15. A. V. Nestrov and V. G. Niziev, "Laser beam with axially symmetric polarization," J. Phys. D 33,1817-1822 (2000).
16. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12,3377-3382 (2004).
17. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett.86, 5251-5254(2001).
18. G. M. Lerman, Y. Lilach, and U. Levy, "Demonstration of spatially inhomogeneous vector beams with elliptical symmetry," Opt. Lett.34, 1669-1671 (2009).
19. A. Chafiq, Z. Hricha, and A. Belafhal, "Propagation properties of vector Mathieu-Gauss beams," Opt. Commun.275,165-169 (2007).
20. R. I. Hernandez-Aranda, J. C. Gutierrez-Vega, M. Guizar-Sicairos, and M. A. Bandres, "Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems," Opt. Express 14,8974-8988 (2006).
21. S. Chavez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O'Neil, I. Mac Vicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B 4, S52-S57 (2002).
22. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun.144,210-213 (1997).
23. Y. Cai and Q. Lin, "Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems," J. Opt. Soc. Am. A 21,1058-1065(2004).
24. C. Zhao, X. Lu, L. Wang, and H. Chen, "Hollow elliptical Gaussian beams generated by a triangular prism," Opt. Laser Technol.40 575-580 (2008).
25. Y. Cai and Q. Lin, "The elliptical Hermite-Gaussian beam and its propagation through paraxial systems," Opt. Commun.207,139-147 (2002).
26. Y. Cai and Q. Lin, "Decentered elliptical Hermite-Gaussian beam," J. Opt. Soc. Am A 20,1111-1119(2003).
27. C. Gao, H. Weber, and H. Laabs, "Twisting of three-dimensional Hermite-Gaussian beams," J. Mod. Opt.46,709-719 (1999).
28. Z. Mei and D. Zhao, "Decentered controllable elliptical dark-hollow beams," Opt. Commun.259,415-123 (2006).
29. V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, "Elliptic Laguerre-Gaussian beams," J. Opt. Soc. Am. A 23,43-56 (2006).
30. R. Chakraborty and A. Ghosh, "Generation of an elliptic Bessel beam," Opt. Lett.31,38-40 (2006).
31. R. Chakraborty and A. Ghosh, "Generation of an elliptic hollow beam using Mathieu and Bessel functions," J. Opt. Soc. Am. A 23,2278-2282 (2006).
32. J. C. Gutierrez-Vega, "Theory and numerical analysis of the Mathieu functions," http//homepages.mty.itesm.mx/jgutierr/Mathieu/Mathieu.pdf (2003-02-14).
33. P. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, Inc., New York, NY,1953).
34. C. A. Dartora, M. Zamboni-Racheda, K. Z. Nobrega, E. Recami, and H. E. Hernandez-Figueroa, "General formulation for the analysis of scalar diffraction-free beams using angular modulation:Mathieu and Bessel beams," Opt. Commun.222,75-80 (2003).
35. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Shaping soliton properties in Mathieu lattices," Opt. Lett.31,238-240 (2006).
36. C. Lopez-Mariscal, J. C. Gutierrez-Vega, V. Garces-Chavez, and K. Dholakia, "Observation of the angular momentum transfer in the Mie regime using Mathieu beams," Proc. SPIE 5930,59301U (2005).
37. C. Lopez-Mariscal, J. C. Gutierrez-Vega, V. Garces-Chavez, and K. Dholakia, "Orbital angular momentum transfer in helical Mathieu beams," Opt. Express 14,4182-1187(2006).
38. C. A. Dartora and H. E. Hernandez-Figueroa, "Properties of a localized Mathieu pulse," J. Opt. Soc. Am. A 21,662-667 (2004).
39. J. Davila-Rodriguez and J. C. Gutierrez-Vega, "Helical Mathieu and parabolic localized pulses," J. Opt. Soc. Am. A 24,3449-3455 (2007).
40. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Alternative formulation for invariant optical fields:Mathieu beams," Opt. Lett.25, 1493-1495 (2000).
41. S. Chavez-Cerda, J. C. Gutierrez-Vega, and G. H. C. New, "Elliptic vortices of electromagnetic wave fields," Opt. Lett.26,1803-1805 (2001).
42. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, "Experimental demonstration of optical Mathieu beams," Opt. Commun.195,35-40 (2001).
43. J. C. Gutierrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22,289-298 (2005).
44. C. Lopez-Mariscal, M. A. Bandres, and J. C. Gutierrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng.45,068001 (2006).
45. M. Guizar-Sicairos and J. C. Gutierrez-Vega, "Generalized Helmholtz-Gauss beam and its transformation by paraxial optical systems," Opt. Lett.31, 2912-2914(2006).
46. R. J. Hernandez-Hernandez, R. A. Terborg, I. Ricardez-Vargas, and K. Volke-Sepulveda, "Experimental generation of Mathieu-Gauss beams with a phase-only spatial light modulator," Appl. Opt.49,6903-6909 (2010).
47. M. A. Bandres and J. Gutierrez-Vega, "Ince-Gaussian beams," Opt. Lett.29, 144-146(2004).
48. M. A. Bandres and J. C. Gutierrez-Vega, "Ince-Gaussian modes of the paraxial wave equation and stable resonators," J. Opt. Soc. Am. A 21,873-880 (2004).
49. U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, "Observation of Ince-Gaussian modes in stable resonators," Opt. Lett.29,1870-1872 (2004).
50. T. Ohtomo, K. Kamikariya, K. Otsuka, and S.-C. Chu, "Single-frequency Ince-Gaussian mode operations of laser-diode-pumped microchip solid-state lasers," Opt. Express 15,10705-10717 (2007).
51. J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutierrez-Vega, "Generation of helical Ince-Gaussian beams with a liquid-crystal display," Opt. Lett.31,649-651 (2006).
52. T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun.203,1-5 (2002).
53. Y. Mushiake, K. Matsumura, and N. Nakajima, "Generation of radially polarized optical beam mode by laser oscillation," Proc. IEEE 60,1107-1109 (1972).
54. K. Youngworth and T. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7,77-87 (2000).
55. G. M. Lerman and U. Levy, "Effect of radial polarization and apodization on spot size under tight focusing conditions," Opt. Express 16,4567-4581 (2008).
56. B. Hao and J. Leger, "Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam," Opt. Express 15, 3550-3556 (2007).
57. D. Deng, Q. Guo, L. Wu, and X. Yang, "Propagation of radially polarized elegant light beams," J. Opt. Soc. Am. B 24,636-643 (2007).
58. D. Deng and Q. Guo, "Analytical vectorial structure of radially polarized light beams," Opt. Lett.32,2711-2713 (2007).
59. N. Passilly, R. d. S. Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, "Simple interferometric technique for generation of a radially polarized light beam," J. Opt. Soc. Am. A 22,984-991 (2005).
60. T. Hirayama, Y. Kozawa, T. Nakamura, and S. Sato, "Generation of a cylindrically symmetric, polarized laser beam with narrow linewidth and fine tunability," Opt. Express 14,12839-12845 (2006).
61. L. W. Davis and G. Patsakos, "TM and TE electromagnetic beams in free space," Opt. Lett.6,22-23 (1981).
62. Z. Bouchal and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt. 42,1555-1566(1995).
63. A. Ashkin and J. M. Dziedzic, "Optical Levitation of Liquid Drops by Radiation Pressure," Science 187,1073-1075 (1975).
64. H. Felgner, O. Muller, and M. Schliwa, "Calibration of light forces in optical tweezers," Appl Opt.34,977-982 (1995).
65. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett.11, 288-290(1986).
66. L. Allen and M. J. Padgett, "The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density," Opt. Commun.184, 67-71 (2000).
67. M. Padgett, J. Arlt, N. Simpson, and L. Allen, "An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes," Am. J. Phys 64,77-82(1996).
68. L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Progress in Optics IV 39,291-372 (1999).
69. A T O'Neil, I Mac Vicar, L Allen, and M J Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett.88, 253601 (2002).
70. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light:An optical spanner," Opt. Lett.22,52-54 (1997).
71. J. W. R.Tabosa and D. V. Petrov, "Optical Pumping of Orbital Angular Momentum of Light in Cold Cesium Atoms," Phys. Rev. Lett.83,4967-4970 (1999).
72. A. Mair, A. Vaziri, and G. Weihs, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412,313-316 (2001).
73. G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light:preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett.,88,013601 (2002).
74. R. J. Voogd, M. Singh, S. F. Pereira, A. S. v. d. Nes, and J. J. M. Braat, "The use of orbital angular momentum of light beams for super-high density optical data storage," in OSA Technical Digest Series (Optical Society of America, 2004), FTuG14.
75. L. Accatino, G. Bertin, and M. Mongiardo, "Elliptical cavity resonators for dual-mode narrowband filters," IEEE Trans. Microwave Theory Tech.45, 2393-2401 (1997).
76. S. R. Rengarajan and J. E. Lewis, "Dielectric Loaded Elliptical Wave-Guides," IEEE Trans. Microwave Theory Tech.28,1085-1089 (1980).
77. S. Choi and K. Oh, "A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber," Opt. Commun.221,307-312 (2003).
78. J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, "Generation of a dark hollow beam by a small hollow fiber," Opt. Commun.138,287-292 (1997).
79. M. J. Renn, D. Montgomery,O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, "Laser-Guided Atoms in Hollow-Core Optical Fibers," Phys. Rev. Lett.75,3253-3256(1995).
80. M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and D. Z. Anderson, "Evanescent-wave guiding of atoms in hollow optical fibers," Phys. Rev. A 53, R648-R651(1996).
81. Y. Ni, N. C. Liu, and J. P. Yin, "Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel," J. Opt. B 5,300-308 (2003).
82. C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys.33,3235-3243 (1962).
83. L. J. Chu, "Electromagnetic waves in elliptic hollow pipes of metal," J. Appl. Phys.9,583-591(1938).
84. G. R. Valenzuela, "Impedances of an elliptic waveguide (for the eH1 mode)," IRE Trans. Microwave Theory Tech.8,431-435 (1960).
85. J. G. Kretzsch, "Wave Propagation in Hollow Conducting Elliptical Waveguides," IEEE Trans. Microwave Theory Tech. MT18,547-554 (1970).
86. J. G. Kretzsch, "Attenuation Characteristics of Hollow Conducting Elliptical Waveguides," IEEE Trans. Microwave Theory Tech. MT20,280-284 (1972).
87. G. Falciasecca, C. G. Someda, and F. Valdoni, "Comments on 'Attenuation characteristics of hollow conducting elliptical waveguides'," IEEE Trans. Microwave Theory Tech. MTT-21,154-154 (1973).
88. S. R. Rengarajan and J. E. Lewis, "Surface Impedance of Elliptical Hollow Conducting Wave-Guides," Electron. Lett.15,637-639 (1979).
89. D. A. Goldberg, L. J. Laslett, and R. A. Rimmer, "Modes of Elliptic Wave-Guides-a Correction," IEEE Trans. Microwave Theory Tech.38, 1603-1608(1990).
90. S. R. Rengarajan and J. E. Lewis, "Single-Mode Propagation in Multilayer Elliptical Fiber Wave-Guides," Radio Sci.16,541-547 (1981).
91. C. Shu, "Analysis of elliptical waveguides by differential quadrature method," IEEE Trans. Microwave Theory Tech.48,319-322 (2000).
92. S. J. Zhang and Y. C. Shen, "Eigenmode sequence for an elliptical waveguide with arbitrary ellipticity," IEEE Trans. Microwave Theory Tech.43,227-230 (1995).
93. M. Schneider and J. Marquardt, "Fast computation of modified Mathieu functions applied to elliptical waveguide problems," IEEE Trans. Microwave Theory Tech.47,513-516 (1999).
94. D. L. Young, S. P. Hu, C. W. Chen, C. M. Fan, and K. Murugesan, "Analysis of elliptical waveguides by the method of fundamental solutions," Microwave Opt. Tech. Lett.44,552-558 (2005).
95. T. Xiong and R. Yang, "Propagating Characteristics of Confocal Elliptical Waveguide Filled with Multilayered Dielectrics," J. Southwest Jiaotong Univ. 12,130-135(2004).
96. K. Halterman, S. Feng, and P. L. Overfelt, "Guided modes of elliptical metamaterial waveguides," Phys. Rev. A 76,013834 (2007).
97. I. Gomez-Castellanos and R. M. Rodrfguez-Dagnino, "Intensity distributions and cutoff frequencies of linearly polarized modes for a step-index elliptical optical fiber," Opt. Eng.46,45003 (2007).
98. V. M. Nair, S. Sarkar, and S. K. Khijwania, "Scalar variational analysis of fundamental mode in single-mode elliptical core fiber using super-Gaussian approximation," IEEE Photonics Tech. Lett.20,1381-1383 (2008).
99. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York,1964), pp. p721-750.
100. F. A. Alhargan, "Algorithms for the computation of all Mathieu functions of integer orders," ACM Trans. Math. Softw.26,390-407 (2000).
101. H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, "Optical-Potential for Atom Guidance in a Cylindrical-Core Hollow-Fiber," Opt. Commun.115, 57-64(1995).
102. J. Yin, Y. Zhu, and Y. Wang, "Evanescent light-wave atomic funnel:A tandem hollow-fiber, hollow-beam approach," Phys. Rev. A 57,1957-1966 (1998).
103. H. Ito, K. Sakaki, T. Nakata, W. H. Jhe, and M. Ohtsu, "Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: Theoretical approach," Ultramicroscopy 61,91-97 (1995).
104. S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent Atomic Wave-Guides from Hollow Optical Fibers-Quantized Atomic Motion," Phys. Rev. A 50,2680-2690 (1994).
105. K. T. Gahagan and G. A. Swartzlander, "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," J. Opt. Soc. Am. B 16,533-537 (1999).
106. Y. I. Shin, K. Kim, J. A. Kim, H. R. Noh, W. Jhe, K. Oh, and U. C. Paek, "Diffraction-limited dark laser spot produced by a hollow optical fiber," Opt. Lett.26,119-121 (2001).
107. H. Li and J. Yin, "Propagation properties of electromagnetic fields in elliptic dielectric hollow fibres and their applications," Chin. Phys. B 19,083204 (2010).
108. D. G. Glen and G. Shekhar, "Modeling and propagation of near-field diffraction patterns:A more complete approach," Am. J. Phys 72,1195-1201 (2004).
109. Z. Wang, Q. Lin, and Y. Wang, "Control of atomic rotation by elliptical hollow beam carrying zero angular momentum," Opt. Commun.240,357-362 (2004).
110. J. Yin, K. Kim, W. Shim, Y. Zhu, and W. Jhe, "Observation and discrimination of the mode patterns in a micron-sized hollow optical fiber and its synthetic measurements:far-field micro-imaging technique," Opt. Eng.37,2277-2283 (1998).
111. R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, Calif.,1964).
112. M. V. Berry, "Index formulae for singular lines of polarization," J. Opt. A: Pure Appl. Opt.6,675-678 (2004).
113. W. Gao and O. Korotkova, "Changes in the state of polarization of a random electromagnetic beam propagating through tissue," Opt. Commun.270, 474-478 (2007).
114. V. Westphal and S. W. Hell, "Nanoscale Resolution in the Focal Plane of an Optical Microscope," Phys. Rev. Lett.94,143903 (2005).
115. M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized rotation of atoms from photons with orbital angular momentum," Phys. Rev. Lett.97,170406 (2006).
116. H. Li and J. Yin, "Generation of a vectorial elliptic hollow beam by an elliptic hollow fiber," Opt. Lett.36,457-459 (2011).
117. A. R. Sidorov, Y. Zhang, A. N. Grigorenko, and M. R. Dickinson, "Nanometric optical tweezers based on nanostructured substrates," Opt. Commun.278, 439-444 (2007).
118. J. Wu, H. Li, and Y. Li, "Encoding information as orbital angular momentum states of light for wireless optical communications," Opt. Eng.46,019701 (2007).
119. M. B. Alvarez-Elizondo, R. Rodrlguez-Masegosa, and J. C. Gutierrez-Vega, "Generation of Mathieu-Gauss modes with an axicon-based laser resonator," Opt. Express 16,18770-18775 (2008).
120. J. H. McLeod, "The axicon:a new type of optical element," J. Opt. Soc. Am. 44,592-597(1954).
121. R. M. Herman and T. A. Wiggins, "Production and uses of diffractionless beams," J. Opt. Soc. Am. A 8,932-942 (1991).
122. J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun.177,297-301 (2000).
123. J. S. A. Collins, "Lens-System Diffraction Integral Written in Terms of Matrix Optics," J. Opt. Soc. Am.60,1168-1177 (1970).
124. B. P. S. Ahluwalia, W. C. Cheong, X. C. Yuan, L. S. Zhang, S. H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett.31, 987-989 (2006).
125. M. d. Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, "Axially symmetric hollow beams using refractive conical lenses," Opt. Laser Eng.39 283-291 (2003).
126. B. M. Rodriguez-Lara and R. Jauregui, "Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry," Phys. Rev. A 78, 033813 (2008).
127. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12,5448-5456 (2004).
128. J. J. McClelland and M. R. Scheinfein, "Laser focusing of atoms:a particle-optics approach," J. Opt. Soc. Am. B 8,1974-1986 (1991).
129. V. I. Balykin and V. S. Letokhov, "The possibility of deep laser focusing of an atomic beam into the A-region," Opt. Commun.64,151-156 (1987).
130. R. J. Celotta, R. Gupta, R. E. Scholten, and J. J. McClelland, "Nanostructure fabrication via laser-focused atomic deposition," J. Appl. Phys.79,6079-6083 (1996).
131. 印建平,”原子分子光学,”研究生讲义(2004).
132. P. Desbiolles, M. Arndt, P. Szriftgiser, and J. Dalibard, "Elementary Sisyphus process close to a dielectric surface," Phys. Rev. A 54,4292 (1996).
133. J. Yin, Y. Zhu, W. Jhe, and Z. Wang, "Atom guiding and cooling in a dark hollow laser beam," Phys. Rev. A 58,509 (1998).
134. W. L. Power, L. Allen, M. Babiker, and V. E. Lembessis, "Atomic motion in light beams possessing orbital angular momentum," Phys. Rev. A 52,479 (1995).
135. R. Fulton, A. I. Bishop, and P. F. Barker, "Optical stark decelerator for molecules," Phys. Rev. Lett.93,243004 (2004).
136. J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, "Measurement of the Electron Electric Dipole Moment Using YbF Molecules," Phys. Rev. Lett.89, 023003 (2002).
137. E. R. Hudson, H. J. Lewandowski, B. C. Sawyer, and J. Ye, "Cold Molecule Spectroscopy for Constraining the Evolution of the Fine Structure Constant," Phys. Rev. Lett.96,143004 (2006).
138. D. DeMille, F. Bay, S. Bickman, D. Kawall, D. Krause, S. E. Maxwell, and L R. Hunter, "Investigation of PbO as a system for measuring the electric dipole moment of the electron," Phys. Rev. A 61,052507 (2000).
139. M. S. Elioff, J. J. Valentini, and D. W. Chandler, "Subkelvin cooling NO molecules via 'Billiard-like' collisions with Argon," Science 302,1940-1943 (2003).
140. P. Soldan, M. T. Cvitas, J. M. Hutson, P. Honvault, and J. M. Launay, "Quantum dynamics of ultracold Na+ Na2 collisions," Phys. Rev. Lett.89, 153201 (2002).
141. N. Balakrishnan, R. C. Forrey, and A. Dalgarno, "Quenching of H2 vibrations in ultracold 3He and 4He collisions," Phys. Rev. Lett.80,3224 (1998).
142. D. DeMille, "Quantum computation with trapped polar molecules," Phys. Rev. Lett.88,067901 (2002).
143. E. R. Hudson, C. Ticknor, B. C. Sawyer, C. A. Taatjes, H. J. Lewandowski, J. R. Bochinski, J. L. Bohn, and J. Ye, "Production of cold formaldehyde molecules for study and control of chemical reaction dynamics with hydroxyl radicals," Phys. Rev. A 73,063404 (2006).
144. W. Schollkopf and J. P. Toennies, "Nondestructive mass selection of small van der Waals clusters," Science 266,1345-1348 (1994).
145. M. Arndt, O. Nairz, J. Voss-Andreae, C. Keller, G. V. d. Zouw, and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401,680-682 (1999).
146. A. P. Mosk, M. W. Reynolds, T. W. Hijmans, and J. T. M. Walraven, "Photoassociation of Spin-Polarized Hydrogen," Phys. Rev, Lett.82,307 (1999).
147. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, "Observation of Bose-Einstein condensation of molecules," Phys. Rev. Lett.91,250401 (2003).
148. J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, "Magnetic trapping of calcium monohydride molecules at milliKelvin temperatures," Nature 395,148-150 (1998).
149. T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, "Two-dimensional trapping of dipolar molecules in time-varying electric fields," Phys. Rev. Lett.92,223001 (2004).
150. N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, and F. Merkt, "Multistage Zeeman deceleration of hydrogen atoms," Phys. Rev. A 75,031402 (2007).
151. T. Seideman, "Time-resolved photoelectron angular distributions as a probe of coupled polyatomic dynamics," Phys. Rev. A 64,042504 (2001).
152. M. F. Gelin, C. Riehn, V. V. Matylitsky, and B. Brutschy, "Rotational recurrences in thermal ensembles of nonrigid molecules," Chem. Phys.290, 307-318(2003).
153. R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, "High-Order Harmonic Generation in Aligned Molecules," Phys. Rev. Lett.87, 183901 (2001).
154. S. Ramakrishna and T. Seideman, "Intense Laser Alignment in Dissipative Media as a Route to Solvent Dynamics," Phys. Rev. Lett.95,113001 (2005).
155. K. F. Lee, D. M. Villeneuve, P. B. Corkum, and E. A. Shapiro, "Phase control of rotational wave packets and quantum information," Phys. Rev. Lett.93, 233601 (2004).
156. H. Stapelfeldt and T. Seideman, "Colloquium:Aligning Molecules with Strong Laser Pulses," Rev. Mod. Phys.75,543-557 (2003).
157. J. J. Larsen, H. Sakai, C. P. Safvan, I. Wendt-Larsen, and H. Stapelfeldt, "Aligning molecules with intense nonresonant laser fields," J. Chem. Phys. 111,7774-7781 (1999).
158. M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Davila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett.89,143601 (2002).
159. L. Santos, G. V. Shlyapnikov, P. Zoller, and M. Lewenstein, "Bose-Einstein condensation in trapped dipolar gases," Phys. Rev. Lett.85,1791 (2000).
160. J. J. Larsen, I. Wendt-Larsen, and H. Stapelfeldt, "Controlling the Branching Ratio of Photodissociation Using Aligned Molecules," Phys. Rev. Lett.83, 1123(1999).
161. J. Aldegunde, H. Ran, and J. M. Hutson, "Manipulating ultracold polar molecules with microwave radiation:The influence of hyperfine structure," Phys. Rev. A 80,043410 (2009).