非局域介质中空间光孤子传输特性的若干研究
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摘要
空间光孤子代表在非线性介质中以空间分布不变而传输的窄光束,是尺寸决定的衍射效应和非线性导致的相位调制相平衡的产物。近年来,非局域非线性光孤子的研究引起了人们的普遍关注,这是因为介质的非局域特性普遍存在于许多物理体系中,如向列液晶等。在非局域非线性介质中研究各种不同类型的空间光孤子将大大拓展孤子科学、非线性光学的研究领域,为深入理解空间孤子的物理特性提供理论基础。
本文主要研究了多种不同类型的空间孤子在非局域非线性介质中的自陷传输,其中包括非相干空间光孤子及椭圆非相干孤子在强非局域Kerr型非线性介质中的传输,任意非局域强度非线性介质中暗孤子的解析研究及暗孤子的相互作用,此外,还研究了非局域介质中的复杂孤子-矢量多极孤子,包括矢量偶极孤子和矢量项链环孤子。
作者取得的主要研究成果如下:
(1)研究了强非局域非瞬时Kerr非线性介质中一维非相干线性孤子的传输特性。使用相干密度法得到此类非相干孤子的解析解。结果显示非相干孤子的空间束宽与非相干角功率谱? 0及入射功率有关。当孤子存在条件不满足时,非相干光束在传输过程中经历周期性振荡,具体讨论了光束强度及相干特性的演化情况。
(2)系统探讨了强非局域非瞬时各向异性Kerr非线性介质中椭圆非相干孤子的传输特性。利用互相干函数法得到了此类孤子的存在曲线,发现椭圆非相干孤子的相干特性既可以是各向异性的也可以是各向同性的。当孤子存在条件不满足时,椭圆非相干光束经历周期性振荡,由于其长短轴方向的振荡周期不同,使得椭圆光束在某些传输距离处将会演化成为圆光束。
(3)解析研究任意非局域强度非线性介质中暗孤子的传输特性。应用变分法第一次描述了适用于任意非局域强度范围的暗孤子演化行为,得到了孤子各参数间的解析关系。
(4)理论上研究了非局域非线性介质中暗孤子的相互作用,应用变分法解析得到适用于任意非局域强度非线性介质中的结论,结果显示非局域性为孤子间相互作用提供吸引力,使得暗孤子束缚态得以形成。
(5)解析及数值上研究任意非局域强度非线性介质中矢量多极孤子的自陷传输,主要包括两维矢量偶极孤子和矢量项链环孤子团簇的研究。应用变分法解析推导出此类孤子的演化方程同时使用直接数值模拟方法研究其传输稳定性问题。研究表明非局域性可以提供吸引力,起到稳定矢量孤子的作用,同时与矢量作用的相结合可以完全稳定矢量多极孤子。
Spatial optical solitons represent beams, which propagate in nonlinear media without changing their profile. Their existence is a result of an interplay between size-determined diffraction and nonlinearity-induced phase modulation. There has recently been strong interest in the so-called nonlocal nonlinearity, because of its inherent features in many physical systems such as liquid crystals. The study of various kinds of nonlocal solitons have opened up a new direction in nonlinear science and led to many novel topics, providing theoretical support for further understanding of spatial solitons.
We investigate theoretically the propagation of various kinds of solitons in material with nonlocal nonlinearity, including incoherent spatial solitons and elliptic incoherent solitons in highly nonlocal medium with noninstantaneous Kerr nonlinearity, dark solitons and the interaction of dark solitons in nonlocal materials with an arbitrary degree of nonlocality, and nonlocal complex solitons: vector dipole solitons and vector-necklace-ring soliton clusters.
The main results are as follows:
(1) We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum ? 0 as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic oscillation.
(2) The propagation of elliptic incoherent beam in strongly nonlocal media with noninstantaneous anisotropic Kerr nonlinearity is fully investigated. Using the mutual coherence function approach, we obtain the existence curve of such solitons and an interesting outcome: correlation characteristics of the elliptic incoherent solitons can be anisotropic as well as isotropic. When the existence conditions of solitons are not satisfied, the elliptic incoherent beam will undergo periodic oscillation. Nonstationary evolution behaviors of the elliptic beam are shown in detail by numerical calculation. It is also obtained that the oscillation periods of the beam in x and y direction are different and the elliptic beam will become circular at some propagation distance under special conditions.
(3) We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.
(4) We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show that nonlocality induces an attractive force in the otherwise repulsive soliton interaction.
(5) We study properties of the vector multipole solitons in nonlocal media with an arbitrary degree of nonlocality, such as two-dimensional vector dipole solitons and vector-necklace-ring solitons. We apply the variational approach to find the exact solution of such solitons and investigate their stability by using directly numerical simulations. We show that the nonlocality induces an attractive force, in combination with vector property can completely stabilize the vector mulitpole solitons.
本文主要研究了多种不同类型的空间孤子在非局域非线性介质中的自陷传输,其中包括非相干空间光孤子及椭圆非相干孤子在强非局域Kerr型非线性介质中的传输,任意非局域强度非线性介质中暗孤子的解析研究及暗孤子的相互作用,此外,还研究了非局域介质中的复杂孤子-矢量多极孤子,包括矢量偶极孤子和矢量项链环孤子。
作者取得的主要研究成果如下:
(1)研究了强非局域非瞬时Kerr非线性介质中一维非相干线性孤子的传输特性。使用相干密度法得到此类非相干孤子的解析解。结果显示非相干孤子的空间束宽与非相干角功率谱? 0及入射功率有关。当孤子存在条件不满足时,非相干光束在传输过程中经历周期性振荡,具体讨论了光束强度及相干特性的演化情况。
(2)系统探讨了强非局域非瞬时各向异性Kerr非线性介质中椭圆非相干孤子的传输特性。利用互相干函数法得到了此类孤子的存在曲线,发现椭圆非相干孤子的相干特性既可以是各向异性的也可以是各向同性的。当孤子存在条件不满足时,椭圆非相干光束经历周期性振荡,由于其长短轴方向的振荡周期不同,使得椭圆光束在某些传输距离处将会演化成为圆光束。
(3)解析研究任意非局域强度非线性介质中暗孤子的传输特性。应用变分法第一次描述了适用于任意非局域强度范围的暗孤子演化行为,得到了孤子各参数间的解析关系。
(4)理论上研究了非局域非线性介质中暗孤子的相互作用,应用变分法解析得到适用于任意非局域强度非线性介质中的结论,结果显示非局域性为孤子间相互作用提供吸引力,使得暗孤子束缚态得以形成。
(5)解析及数值上研究任意非局域强度非线性介质中矢量多极孤子的自陷传输,主要包括两维矢量偶极孤子和矢量项链环孤子团簇的研究。应用变分法解析推导出此类孤子的演化方程同时使用直接数值模拟方法研究其传输稳定性问题。研究表明非局域性可以提供吸引力,起到稳定矢量孤子的作用,同时与矢量作用的相结合可以完全稳定矢量多极孤子。
Spatial optical solitons represent beams, which propagate in nonlinear media without changing their profile. Their existence is a result of an interplay between size-determined diffraction and nonlinearity-induced phase modulation. There has recently been strong interest in the so-called nonlocal nonlinearity, because of its inherent features in many physical systems such as liquid crystals. The study of various kinds of nonlocal solitons have opened up a new direction in nonlinear science and led to many novel topics, providing theoretical support for further understanding of spatial solitons.
We investigate theoretically the propagation of various kinds of solitons in material with nonlocal nonlinearity, including incoherent spatial solitons and elliptic incoherent solitons in highly nonlocal medium with noninstantaneous Kerr nonlinearity, dark solitons and the interaction of dark solitons in nonlocal materials with an arbitrary degree of nonlocality, and nonlocal complex solitons: vector dipole solitons and vector-necklace-ring soliton clusters.
The main results are as follows:
(1) We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum ? 0 as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic oscillation.
(2) The propagation of elliptic incoherent beam in strongly nonlocal media with noninstantaneous anisotropic Kerr nonlinearity is fully investigated. Using the mutual coherence function approach, we obtain the existence curve of such solitons and an interesting outcome: correlation characteristics of the elliptic incoherent solitons can be anisotropic as well as isotropic. When the existence conditions of solitons are not satisfied, the elliptic incoherent beam will undergo periodic oscillation. Nonstationary evolution behaviors of the elliptic beam are shown in detail by numerical calculation. It is also obtained that the oscillation periods of the beam in x and y direction are different and the elliptic beam will become circular at some propagation distance under special conditions.
(3) We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.
(4) We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show that nonlocality induces an attractive force in the otherwise repulsive soliton interaction.
(5) We study properties of the vector multipole solitons in nonlocal media with an arbitrary degree of nonlocality, such as two-dimensional vector dipole solitons and vector-necklace-ring solitons. We apply the variational approach to find the exact solution of such solitons and investigate their stability by using directly numerical simulations. We show that the nonlocality induces an attractive force, in combination with vector property can completely stabilize the vector mulitpole solitons.
引文
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