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(color online). Pulsed measurements: normalized fringe visibility for z = 219(), 119() and 9(•) mm, as a function of the plane mirror translation ∆x. The experimental data are fitted with a Gaussian curve.
Source publication
We experimentally analyze a Bessel beam produced with a conical mirror,
paying particular attention to its superluminal and diffraction-free
properties. We spatially characterized the beam in the radial and on-axis
dimensions, and verified that the central peak does not spread over a
propagation distance of 73 cm. In addition, we measured the super...
Context in source publication
Context 1
... we acquired several pairs (∆x, ∆z) for which the interference visibility is optimized. The interference was observed by scanning the plane mirror over a distance of 1 − 1.5 wavelengths with a piezoelectric transducer. For a given position z of the camera, the in- terference visibility over a range of plane mirror positions was evaluated (Fig. 5) The linear relationship predicted by Eq. (3) is ev- idenced by Fig. 6, and is characterized by a linear regression slope ∂x/∂z = (−7.5 ± 0.3) × 10 −5 . The negativity of the slope indicates that the relative path length of the Gaussian beam had to be reduced as the overall travel distance increased (i.e. smaller z val- ues), which ...
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Citations
... An alternative mechanism to control the group velocity of light is via propagation-invariant wave packets with underlying spatiotemporal structure 15 , such as Bessel-X pulses 16 , and space-time wave packets 17,18 . Based on these phenomena, various strategies have been proposed to realize the superluminal propagation [19][20][21][22] , and arbitrarily adjustable group velocities [23][24][25][26] in free space. Such implementations are facilitated by space-time coupling, where the light pulses undergo spatiotemporal sculpting via tight correlation between spatial and temporal degrees of freedom 15,18 . ...
That the speed of light in vacuum is constant is a cornerstone of modern physics. However, recent experiments have shown that when the light field is confined in the transverse plane, the observed propagation speed of the light is reduced. This effect is a consequence of the transverse structure which reduces the component of wavevector of the light in the direction of propagation, thereby modifying both the phase and group velocity. Here, we consider the case of optical speckle, which has a random transverse distribution and is ubiquitous with scales ranging from the microscopic to the astronomical. We numerically investigate the plane-to-plane propagation speed of the optical speckle by using the method of angular spectrum analysis. For a general diffuser with Gaussian scattering over an angular range of 5°, we calculate the slowing of the propagation speed of the optical speckle to be on the order of 1% of the free-space speed, resulting in a significantly higher temporal delay compared to the Bessel and Laguerre–Gaussian beams considered previously. Our results have implications for studying optical speckle in both laboratory and astronomical settings.
... The former class of baseband STWPs is the one we have studied exclusively over the past few years [27]. On the other hand, sideband STWPs have been investigated for much longer, including focus-wave modes [69][70][71], X-waves [72][73][74][75][76][77][78], and other examples [30]. We proceed to show that synthesizing baseband STWPs in the vicinity of the non-differentiable wavelength is dramatically more robust with respect to errors occurring in the realization of the synthesized AD profile in comparison to sideband STWPs, where the non-differentiable wavelength is physically inaccessible. ...
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.
... By changing the beam's transverse spatial structure, a relative delay in their arrival time is introduced. However, the reported superluminal speeds achieved with the various approaches in free space have been to data 1.00022c [105], 1.00012c [106], 1.00015c [107] and 1.111c in plasma [108]. Reports on measured subluminal speeds have been lacking and limited to delays to several micrometers over a propagation distance of~1 meter. ...
Quantum interferences of entangled photons have engendered tremendous intriguing phenomena that lack any counterpart in classical physics. Hitherto, owing to the salient properties of quantum optics, quantum interference has been widely studied and provides useful tools that ultimately broaden the path towards ultra-sensitive quantum metrology, ranging from sub-shot-noise quantum sensing to high-resolution optical spectroscopy. In particular, quantum interferometric metrology is an essential requisite for extracting information about the structure and dynamics of photon-sensitive biological and chemical molecules. This article reviews the theoretical and experimental progress of this quantum interferometric metrology technology along with their advanced applications. The scope of this review includes Hong–Ou–Mandel interferometry with ultrahigh timing resolution, entanglement-assisted absorption spectroscopy based on a Fourier transform, and virtual-state spectroscopy using tunable energy-time entangled photons.
... The former class of baseband STWPs is the one we have studied exclusively over the past few years [26]. On the other hand, sideband STWPs have been investigated for much longer, including focus-wave modes [69][70][71], Xwaves [72][73][74][75][76][77][78], among other examples [29]. We proceed to show that synthesizing baseband STWPs in the vicinity of the non-differentiable wavelength is dramatically more robust with respect to errors occurring in the realization of the synthesized AD profile in comparison to sideband STWPs, where the non-differentiable wavelength is physically inaccessible. ...
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 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 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.
... Subsequently,˜︁ v for an X-wave produced by a coherent pulsed laser was measured by Saari, Trebino, and co-workers [163], and was found to be˜︁ v ≈ 1.00012c. This value is in agreement with estimates from other groups using different measurement techniques [202,203]. We discuss in Sec. ...
... Previou attempts at tuning the group velocity of so-called localized waves produced only minute deviations from c. Although˜︁ v for an X-wave can, in principle, take on arbitrary superluminal values, the observed values have been 1.00022c [202], 1.00012c [163], and 1.00015c [203]. As pointed out in Ref. [91], there has been much less work done historically on subluminal propagation-invariant wave packets in comparison with their superluminal counterparts. ...
Space-time wave packets (STWPs) constitute a broad class of pulsed optical fields that are rigidly transported in linear media without diffraction or dispersion, and are therefore propagation-invariant in the absence of optical nonlinearities or waveguiding structures. Such wave packets exhibit unique characteristics, such as controllable group velocities in free space and exotic refractive phenomena. At the root of these behaviors is a fundamental feature underpinning STWPs: their spectra are not separable with respect to the spatial and temporal degrees of freedom. Indeed, the spatiotemporal structure is endowed with non-differentiable angular dispersion, in which each spatial frequency is associated with a single prescribed wavelength. Furthermore, controlled deviation from this particular spatiotemporal structure yields novel behaviors that depart from propagation-invariance in a precise manner, such as acceleration with an arbitrary axial distribution of the group velocity, tunable dispersion profiles, and Talbot effects in space–time. Although the basic concept of STWPs has been known since the 1980s, only very recently has rapid experimental development emerged. These advances are made possible by innovations in spatiotemporal Fourier synthesis, thereby opening a new frontier for structured light at the intersection of beam optics and ultrafast optics. Furthermore, a plethora of novel spatiotemporally structured optical fields (such as flying-focus wave packets, toroidal pulses, and spatiotemporal optical vortices) are now providing a swath of surprising characteristics, ranging from tunable group velocities to transverse orbital angular momentum. We review the historical development of STWPs, describe the new experimental approaches for their efficient synthesis, and enumerate the various new results and potential applications for STWPs and other spatiotemporally structured fields, before casting an eye on a future roadmap for this field.
... By exciting a spatiotemporal field structure at the waveguide entrance that corresponds to a spectrally discretized X-wave, a pulsed supermode propagates invariantly along the waveguide [9][10][11]. However, synthesizing X-waves requires ultrabroadband sources [17,18], the observed deviation in their group velocity from that of a conventional wave packet is extremely small in the paraxial regime [19][20][21], and coupling them to a waveguide poses substantial experimental difficulties. As such, X-wave supermodes in multimode waveguides have to date remained theoretical entities. ...
When an optical pulse is spatially localized in a highly multimoded waveguide, its energy is typically distributed among a multiplicity of modes, thus giving rise to a speckled transverse spatial profile that undergoes erratic changes with propagation. It has been suggested theoretically that pulsed multimode fields in which each wavelength is locked to an individual mode at a prescribed axial wavenumber will propagate invariantly along the waveguide at a tunable group velocity. In this conception, an initially localized field remains localized along the waveguide. Here, we provide proof-of-principle experimental confirmation for the existence of this class of pulsed guided fields, which we denote “space-time supermodes,” and verify their propagation invariance in a planar waveguide. By superposing up to 21 modes, each assigned to a prescribed wavelength, we construct space-time (ST) supermodes in a 170-µm-thick planar glass waveguide with group indices extending from $\approx\! 1$ ≈ 1 to $\approx\! 2$ ≈ 2 . The initial transverse width of the field is 6 µm, and the waveguide length is 9.1 mm, which is $\approx\! 257 \times$ ≈ 257 × the associated Rayleigh range. A variety of axially invariant transverse spatial profiles are produced by judicious selection of the modes contributing to the ST supermode, including single-peak and multi-peak fields, dark fields (containing a spatial dip), and even flat uniform intensity profiles.
... Moreover, by varying such a space-time correlation in this approach, wave packets with different group velocities might also be potentially achieved [21,22]. Based on this approach, there have been some experimental demonstrations of different optical wave packets including: (a) diffraction-free light sheets with one-dimensional (1D) transverse spatial profiles and controllable group velocities in free space [21,22]; (b) diffraction-free 2D non-OAM Bessel-based wave packets with superluminal or subluminal group velocities in free space or plasma [23][24][25][26][27][28][29]. ...
Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%). Moreover, the group velocity can be controlled from 0.9933c to 1.0069c (c is the speed of light in vacuum). These ST OAM wave packets might find applications in imaging, nonlinear optics, and optical communications. In addition, our approach might also provide some insights for generating other interesting ST beams.
... By exciting a spatiotemporal field structure at the waveguide entrance that corresponds to a spectrally discretized X-wave, a pulsed supermode propagates invariantly along the waveguide [9][10][11]. However, synthesizing X-waves requires ultrabroadband sources [17,18], the observed deviation in their group velocity from that of a conventional wave packet is extremely small in the paraxial regime [19][20][21], and coupling them to a waveguide poses substantial experimental difficulties. As such, X-wave supermodes in multimode waveguides have to date remained theoretical entities. ...
When an optical pulse is spatially localized in a highly multimoded waveguide, its energy is typically distributed among a multiplicity of modes, thus giving rise to a speckled transverse spatial profile that undergoes erratic changes with propagation. It has been suggested theoretically that pulsed multimode fields in which each wavelength is locked to an individual mode at a prescribed axial wave number will propagate invariantly along the waveguide at a tunable group velocity. In this conception, an initially localized field remains localized along the waveguide. Here, we provide proof-of-principle experimental confirmation for the existence of this new class of pulsed guided fields, which we denote space-time supermodes, and verify their propagation invariance in a planar waveguide. By superposing up to 21 modes, each assigned to a prescribed wavelength, we construct space-time supermodes in a 170-micron-thick planar glass waveguide with group indices extending from 1 to 2. The initial transverse width of the field is 6 microns, and the waveguide length is 9.1 mm, which is 257x the associated Rayleigh range. A variety of axially invariant transverse spatial profiles are produced by judicious selection of the modes contributing to the ST supermode, including single-peak and multi-peak fields, dark fields (containing a spatial dip), and even flat uniform intensity profiles.
... Pulsed multifrequency Bessel beams, which neither diffract nor disperse, such as X-waves [26] and focus wave modes [27,28], have also been studied extensively. So far, pulsed Bessel beams that propagate at subluminal [29,30], superluminal [31][32][33][34][35], and accelerating group velocities [36,37] have been demonstrated. Alternatively, the angular dispersion of pulsed Bessel beams can be used to compensate for the material dispersion of the propagation medium, resulting in both diffraction-free and dispersion-free propagation [38]. ...
The group velocity of an optical beam in free space is usually considered to be equal to the speed of light in vacuum. However, it has been recently realized that, by structuring the beam's angular and temporal spectra, one can achieve well pronounced and controlled subluminal and superluminal propagation. In this work, we consider multifrequency Bessel beams that are known to propagate without divergence and show a variety of possibilities to adjust the group velocity of the beam by means of designed angular dispersion. We present several examples of multifrequency Bessel beams with negative and arbitrary positive group velocities, as well as longitudinally accelerating beams and beams with periodically oscillating local group velocities. The results of these studies can be of interest to scientists working in the fields of optical beam engineering, light amplitude and intensity interferometry, ultrafast optics, and optical tweezers.
... Subsequently, for an X-wave produced by a coherent pulsed laser was measured by Saari, Trebino, and co-workers [162], and was found to be ≈ 1.00012 . This value is in agreement with estimates from other groups using different measurement techniques [194,195]. We discuss in Section 7 why a significant departure of for an X-wave from is not feasible in the paraxial regime. ...
... Although for an X-wave can -in principle -take on arbitrary superluminal values, the observed values have been 1.00022 [194], 1.00012 [162], and1.00015 [195]. As pointed out in [79], there has been much less work done historically on subluminal propagationinvariant wave packets in comparison to their superluminal counterparts. ...
"Space-time" (ST) wave packets constitute a broad class of pulsed optical fields that are rigidly transported in linear media without diffraction or dispersion, and are therefore propagation-invariant in absence of optical nonlinearities or waveguiding structures. Such wave packets exhibit unique characteristics, such as controllable group velocities in free space and exotic refractive phenomena. At the root of these behaviors is a fundamental feature underpinning ST wave packets: their spectra are not separable with respect to the spatial and temporal degrees of freedom. Indeed, the spatio-temporal structure is endowed with non-differentiable angular dispersion, in which each spatial frequency is associated with a single prescribed wavelength. Furthermore, deviation from this particular spatio-temporal structure yields novel behaviors that depart from propagation invariance in a precise manner, such as acceleration with an arbitrary axial distribution of the group velocity, tunable dispersion profiles, and Talbot effects in space-time. Although the basic concept of ST wave packets has been known since the 1980's, only very recently has rapid experimental development emerged. These advances are made possible by innovations in spatio-temporal Fourier synthesis, thereby opening a new frontier for structured light at the intersection of beam optics and ultrafast optics.
