Omni-resonant space-time wave packets

Propagation-Invariant Space-Time Plasmonic Pulse in Subwavelength MIM Waveguide

The metal-insulator-metal (MIM) plasmonic waveguide has been highly anticipated for confining and guiding surface plasmon polaritons (SPPs) on the subwavelength scale. However, perennial drawbacks such as a short propagation length and an unbounded transverse field have set limits on the use of the MIM waveguide in various applications. Herein, diffraction- and dispersion-free MIM modes are synthesized by using space-time wave packets (STWPs) and are therefore referred to as space-time MIM (ST-MIM) waveguide modes. Compared to a Gaussian pulse of the same duration and spectral bandwidth, the ST-MIM demonstrates enhanced propagation lengths of about 2.4 times for the symmetric mode and about 6.3 times for the antisymmetric mode. In the simulations, the ST-MIMs are confined in all transverse dimensions, thereby overriding the diffraction limits. In addition, the group velocities of the ST-MIMs can be arbitrarily designed, which makes it possible to synchronize the pulse propagation speeds of the symmetric and antisymmetric MIM modes.

Universal angular-dispersion synthesizer

We uncover a surprising gap in optics with regards to angular dispersion (AD). A systematic examination of pulsed optical field configurations classified according to their three lowest dispersion orders resulting from AD (the axial phase velocity, group velocity, and group-velocity dispersion) reveals that the majority of possible classes of fields have eluded optics thus far. This gap is due in part to the limited technical reach of the standard components that provide AD such as gratings and prisms, but due in part also to misconceptions regarding the set of physically admissible field configurations that can be accessed via AD. For example, it has long been thought that AD cannot yield normal group-velocity dispersion in free space. We introduce a "universal AD synthesizer": a pulsed-beam shaper that produces a wavelength-dependent propagation angle with arbitrary spectral profile, thereby enabling access to all physically admissible field configurations realizable via AD. This universal AD synthesizer is a versatile tool for preparing pulsed optical fields for dispersion cancellation, optical signal processing, and nonlinear optics.

Non-differentiable angular dispersion as an optical resource

Introducing angular dispersion into a pulsed field associates each frequency with a particular angle with respect to the propagation axis. A perennial yet implicit assumption is that the propagation angle is differentiable with respect to the frequency. Recent work on space-time wave packets has shown that the existence of a frequency at which the derivative of the propagation angle does not exist-which we refer to as non-differentiable angular dispersion-allows for the optical field to exhibit unique and useful characteristics that are unattainable by endowing optical fields with conventional angular dispersion. Because these novel, to the best of our knowledge, features are retained in principle even when the specific non-differentiable frequency is not part of the selected spectrum, the question arises as to the impact of the proximity of the spectrum to this frequency. We show here that operating in the vicinity of the non-differentiable frequency is imperative to reduce the deleterious impact of (1) errors in implementing the angular-dispersion profile and (2) the spectral uncertainty intrinsic to finite-energy wave packets in any realistic system. Non-differential angular dispersion can then be viewed as a resource-quantified by a Schmidt number-that is maximized in the vicinity of the non-differentiable frequency. These results will be useful in designing novel phase-matching of nonlinear interactions in dispersive media.

Spatial resolution of omni-resonant imaging

Omni-resonance refers to the broadening of the spectral transmission through a planar cavity, not by changing the cavity structure, but by preconditioning the incident optical field. As such, broadband imaging can be performed through such a cavity with all the wavelengths simultaneously resonating. We examine here the spatial resolution of omni-resonant imaging and find that the spectral linewidth of the cavity resonance determines the spatial resolution. Surprisingly, the spatial resolution improves at longer wavelengths because of the negative angular dispersion intrinsic to Fabry-Pérot resonances, in contrast to conventional diffraction-limited optical imaging systems where the spatial resolution improves at shorter wavelengths. These results are important for applications ranging from transparent solar windows to nonlinear resonant image processing.

Refraction of space-time wave packets: I. theoretical principles

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, and 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.

Temporal Talbot effect in free space

The temporal Talbot effect refers to the periodic revivals of a pulse train propagating in a dispersive medium and is a temporal analog of the spatial Talbot effect with group-velocity dispersion in time replacing diffraction in space. Because of typically large temporal Talbot lengths, this effect has been observed to date in only single-mode fibers, rather than with freely propagating fields in bulk dispersive media. Here we demonstrate for the first time, to the best of our knowledge, the temporal Talbot effect in free space by employing dispersive space-time wave packets, whose spatiotemporal structure induces group-velocity dispersion of controllable magnitude and sign in free space.

Veiled Talbot Effect

A freely propagating optical field having a periodic transverse spatial profile undergoes periodic axial revivals-a well-known phenomenon known as the Talbot effect or self-imaging. We show here that introducing tight spatiotemporal spectral correlations into an ultrafast pulsed optical field with a periodic transverse spatial profile eliminates all axial dynamics in physical space, while revealing a novel veiled Talbot effect that can be observed only when carrying out time-resolved measurements. Indeed, "time diffraction" is observed, whereupon the temporal profile of the field envelope at a fixed axial plane corresponds to a segment of the spatial propagation profile of a monochromatic field sharing the initial spatial profile and observed at the same axial plane. Time averaging, which is intrinsic to observing the intensity, altogether veils this effect.