Hall Layton A, Abouraddy Ayman F
Opt Express. 2022 Feb 14;30(4):4817-4832. doi: 10.1364/OE.442950.
Conventional diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields, thus producing so-called 'tilted pulse fronts'. Naturally, it is always assumed that the functional form of the wavelength-dependent propagation angle[s] associated with AD is differentiable with respect to wavelength. Recent developments in the study of space-time wave packets - pulsed beams in which the spatial and temporal degrees of freedom are inextricably intertwined - have pointed to the existence of non-differentiable AD: field configurations in which the propagation angle does not possess a derivative at some wavelength. Here we investigate the consequences of introducing non-differentiable AD into a pulsed field and show that it is the crucial ingredient required to realize group velocities that deviate from c (the speed of light in vacuum) along the propagation axis in free space. In contrast, the on-axis group velocity for conventional pulsed fields in free space is always equal to c. Furthermore, we show that non-differentiable AD is needed for realizing anomalous or normal group-velocity dispersion along the propagation axis, while simultaneously suppressing all higher-order dispersion terms. We experimentally verify these and several other consequences of non-differentiable AD using a pulsed-beam shaper capable of introducing AD with arbitrary spectral profile. Non-differentiable AD is not an exotic phenomenon, but is rather an accessible, robust, and versatile resource for sculpting pulsed optical fields.
传统的衍射和色散器件会将角色散（AD）引入脉冲光场，从而产生所谓的“倾斜脉冲前沿”。自然而然地，人们总是假定与角色散相关的波长依赖传播角的函数形式相对于波长是可微的。时空波包（其中空间和时间自由度紧密交织的脉冲光束）研究的最新进展表明存在不可微的角色散：即场配置中传播角在某些波长处没有导数。在这里，我们研究将不可微角色散引入脉冲场的后果，并表明这是在自由空间中实现沿传播轴偏离c（真空中的光速）的群速度所需的关键要素。相比之下，自由空间中传统脉冲场的轴上群速度始终等于c。此外，我们表明，要在沿传播轴实现反常或正常群速度色散，同时抑制所有高阶色散项，需要不可微角色散。我们使用能够引入具有任意光谱轮廓的角色散的脉冲光束整形器，通过实验验证了不可微角色散的这些以及其他几个后果。不可微角色散并非奇特现象，而是用于塑造脉冲光场的一种易于获取、稳健且通用的资源。
