艾里光束
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Sharply autofocused ring-Airy beams transforming
into non-linear intense light bullets
Light bullets
Airy光束
• Airy光束这一新型无衍射光束替换传统的高 斯光束，解决激光在传播过程中的衍射效 应，从而实现激光在自由空间的远距离传 播。Airy光束的提出受启发于在量子力学框 架下的Airy波包的提出，由于旁轴近似下的 麦克斯韦方程与一维自由空间中的薛定谔 方程具有相同的形式，故Airy型光束可以存 在。Airy光束在构建自会聚光束、等离子体、 微粒操控、光子弹和大气传输等方面具有 良好的应用前景
• 无衍射光束中最具代表的是沿着直线传播 的贝塞尔光束和沿着曲线传播的艾里光束。 相比于前者，艾里光束除了具备无衍射特 性，它还具备自弯曲特性和自愈的奇异特 性。因此很快引起了人们的普遍关注。艾 里光束在2007年首次由Christodoulides研 究小组实验实现。
• 一个简明的实验装置如图所示。把计算的 相位膜片输入到液晶空间光调制器中，对 通过傅里叶透镜的入射的高斯光束进行相 位调制，调制后的光束经过傅里叶透镜再 次变换到时域，即可产生艾里光束。与传 统的高斯光束相比，同尺寸主瓣的Airy光束 传播距离可以比高斯光束大六到七倍。另 外，自弯曲特性也可以得到很好的验证。
Figure 7 | Experimental setup. FT, Fourier transform. FT lens (400 mm); f 1(300 mm); Obj (microscope objective x 8, 0.2 numerical aperture).
Figure 2 | Simulation results in the non-linear propagation regime in air. (a) Peak intensity distribution of the ring-Airy beam versus propagation distance for various input powers. (b) Maximum peak intensity at the plateau region (z =40 cm) as a function of the input power for the ring-Airy (black squares), EEGB (blue triangles) and ECGB (red dots). (c) Graphic representation of accelerating ring-Airy beams in the linear and non-linear regime.
Flot of intensity distributions. Radial intensity distribution of the ring-Airy, EEGB and ECGB used in the simulations.
Figure 1 | Focus shift in the non-linear regime. Focus position as a function of the input power for the ring-Airy beam (black squares) and the two Gaussian beams with equivalent contrast (red dots) and equivalent envelope (blue triangles).
Figure 4 | Experimental and simulation results of the non-linear propagation regime in the bulk of fused silica. (a) Non-linear fluorescenceemission images in false colours (the beam propagates from left to right). (b) Experimental intensity distribution (normalized values) along the propagation axis for various input energies. The curves are shifted upwards for visualization purposes. (c) Comparative numerical simulation results of the peak intensity along the propagation.
Figure 3 | Spatiotemporal dynamics in the non-linear propagation regime. Intensity isosurfaces for an EEGB (first row), an ECGB (second row) and a ring-Airy wavepacket (third row) at various positions along z after the non-linear focus. Beam propagation direction is from left to right.
• 利用艾里光束构建自会聚光束，因此着重 关注它的自弯曲传输特性，以期望艾里光 束在自弯曲的过程中实现能量的自会聚
• The equivalent envelope Gaussian beam (EEGB) defined as the Gaussian beam with full-width at half maximum (FWHM) equal to the diameter of the ring-Airy beam and the equivalent peak contrast Gaussian beam (ECGB), which, in the linear regime, reaches the same peak intensity contrast value at the focus
into non-linear intense light bullets
Light bullets
Airy光束
• Airy光束这一新型无衍射光束替换传统的高 斯光束，解决激光在传播过程中的衍射效 应，从而实现激光在自由空间的远距离传 播。Airy光束的提出受启发于在量子力学框 架下的Airy波包的提出，由于旁轴近似下的 麦克斯韦方程与一维自由空间中的薛定谔 方程具有相同的形式，故Airy型光束可以存 在。Airy光束在构建自会聚光束、等离子体、 微粒操控、光子弹和大气传输等方面具有 良好的应用前景
• 无衍射光束中最具代表的是沿着直线传播 的贝塞尔光束和沿着曲线传播的艾里光束。 相比于前者，艾里光束除了具备无衍射特 性，它还具备自弯曲特性和自愈的奇异特 性。因此很快引起了人们的普遍关注。艾 里光束在2007年首次由Christodoulides研 究小组实验实现。
• 一个简明的实验装置如图所示。把计算的 相位膜片输入到液晶空间光调制器中，对 通过傅里叶透镜的入射的高斯光束进行相 位调制，调制后的光束经过傅里叶透镜再 次变换到时域，即可产生艾里光束。与传 统的高斯光束相比，同尺寸主瓣的Airy光束 传播距离可以比高斯光束大六到七倍。另 外，自弯曲特性也可以得到很好的验证。
Figure 7 | Experimental setup. FT, Fourier transform. FT lens (400 mm); f 1(300 mm); Obj (microscope objective x 8, 0.2 numerical aperture).
Figure 2 | Simulation results in the non-linear propagation regime in air. (a) Peak intensity distribution of the ring-Airy beam versus propagation distance for various input powers. (b) Maximum peak intensity at the plateau region (z =40 cm) as a function of the input power for the ring-Airy (black squares), EEGB (blue triangles) and ECGB (red dots). (c) Graphic representation of accelerating ring-Airy beams in the linear and non-linear regime.
Flot of intensity distributions. Radial intensity distribution of the ring-Airy, EEGB and ECGB used in the simulations.
Figure 1 | Focus shift in the non-linear regime. Focus position as a function of the input power for the ring-Airy beam (black squares) and the two Gaussian beams with equivalent contrast (red dots) and equivalent envelope (blue triangles).
Figure 4 | Experimental and simulation results of the non-linear propagation regime in the bulk of fused silica. (a) Non-linear fluorescenceemission images in false colours (the beam propagates from left to right). (b) Experimental intensity distribution (normalized values) along the propagation axis for various input energies. The curves are shifted upwards for visualization purposes. (c) Comparative numerical simulation results of the peak intensity along the propagation.
Figure 3 | Spatiotemporal dynamics in the non-linear propagation regime. Intensity isosurfaces for an EEGB (first row), an ECGB (second row) and a ring-Airy wavepacket (third row) at various positions along z after the non-linear focus. Beam propagation direction is from left to right.
• 利用艾里光束构建自会聚光束，因此着重 关注它的自弯曲传输特性，以期望艾里光 束在自弯曲的过程中实现能量的自会聚
• The equivalent envelope Gaussian beam (EEGB) defined as the Gaussian beam with full-width at half maximum (FWHM) equal to the diameter of the ring-Airy beam and the equivalent peak contrast Gaussian beam (ECGB), which, in the linear regime, reaches the same peak intensity contrast value at the focus