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Register a new userAnomalous refraction of optical space-time wave packets
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Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an optical field is the tacit presumption of the separability of its spatial and temporal degrees-of-freedom. We show here that endowing a pulsed beam with precise spatio-temporal spectral correlations unveils remarkable refractory phenomena, such as group-velocity invariance with respect to the refractive index, group-delay cancellation, anomalous group-velocity increase in higher-index materials, and tunable group velocity by varying the angle of incidence. A law of refraction for `space-time wave packets encompassing these effects is verified experimentally in a variety of optical materials. Space-time refraction defies our expectations derived from Fermats principle and offers new opportunities for molding the flow of light and other wave phenomena.
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Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics, such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call the spectral curvature. Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, X-wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.
The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibit fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence. For example, the group velocity of the refracted ST wave packet can be tuned simply by changing the angle of incidence. In paper (III) of this sequence, we present experimental verification of the refractive phenomena exhibited by ST wave packets at oblique incidence that were predicted in paper (I). We also examine a proposal for blind synchronization whereby identical ST wave packets arrive simultaneously at different receivers without textit{a priori} knowledge of their locations except that they are all located at the same depth beyond an interface between two media. A first proof-of-principle experimental demonstration of this effect is provided.
The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In paper (I) of this sequence, we described theoretically the refraction of all families of ST wave packets at normal and oblique incidence at a planar interface between two non-dispersive, homogeneous, isotropic dielectrics. Here, in paper (II) of this sequence, we present experimental verification of the novel refractive phenomena predicted for `baseband ST wave packets upon normal incidence on a planar interface. Specifically, we observe group-velocity invariance, normal and anomalous refraction, and group-velocity inversion leading to group-delay cancellation. These phenomena are verified in a set of optical materials with refractive indices ranging from 1.38 to 1.76, including MgF$_2$, fused silica, BK7 glass, and sapphire. We also provide a geometrical representation of the physics associated with anomalous refraction in terms of the dynamics of the spectral support domain for ST wave packets on the surface of the light-cone.
An optical buffer having a large delay-bandwidth-product -- a critical component for future all-optical communications networks -- remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity in free space is continuously tunable provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of ~100 for pulses of width ~1 ps are observed, with no fundamental limit on the system bandwidth.
All known realizations of optical wave packets that accelerate along their propagation axis, such as Airy wave packets in dispersive media or wave-front-modulated X-waves, exhibit a constant acceleration; that is, the group velocity varies linearly with propagation. Here we synthesize space-time wave packets that travel in free space with arbitrary axial acceleration profiles, including group velocities that change with integer or fractional exponents of the distance. Furthermore, we realize a composite acceleration profile: the wave packet first accelerates from an initial to a terminal group velocity, decelerates back to the initial value, and then travels at a fixed group velocity. These never-before-seen optical-acceleration phenomena are all produced using the same experimental arrangement that precisely sculpts the wave packets spatio-temporal spectral structure.
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