A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Preface 1. Wave Theory of Optical Waveguides 2. Planar Optical Waveguides 3. Optical Fibers 4. Couple Mode Theory 5. Nonlinear Optical Effects in Optical Fibers 6. Finite Element Method 7. Beam Propagation Method 8. Staircase Concatention Method 9. Planar Lightwave Circuits 10. Theorems and Formulas Appendix

Fundamentals of optical waveguides

Guiding of relativistically intense laser pulses with peak power of 0.85 PW over 15 diffraction lengths was demonstrated by increasing the focusing strength of a capillary discharge waveguide using laser inverse bremsstrahlung heating. This allowed for the production of electron beams with quasimonoenergetic peaks up to 7.8 GeV, double the energy that was previously demonstrated. Charge was 5 pC at 7.8 GeV and up to 62 pC in 6 GeV peaks, and typical beam divergence was 0.2 mrad.

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Petawatt laser guiding and electron beam acceleration to 8 GeV in laser-heated capillary discharge waveguides

Today, it is well known that light possesses a linear momentum which is along the propagation direction. Besides, scientists also discovered that light can possess an angular momentum (AM), a spin angular momentum (SAM) associated with circular polarization and an orbital angular momentum (OAM) owing to the azimuthally dependent phase. Even though such angular momenta are longitudinal in general, a SAM transverse to the propagation has opened up a variety of key applications [1]. In contrast, investigations of the transverse OAM are quite rare due to its complex nature. Here we demonstrate a simple method to generate a three dimensional (3D) optical wave packet with a controllable purely transverse OAM. Such a wave packet is a spatiotemporal (ST) vortex, which resembles an advancing cyclone, with optical energy flowing in the spatial and temporal dimension. Contrary to the transverse SAM, the magnitude of the transverse OAM carried by the photonic cyclone is scalable to a larger value by simple adjustments. Since the ST vortex carries a controllable OAM in the unique transverse dimension, it has a strong potential for novel applications that may not be possible otherwise. The scheme reported here can be readily adapted for the other spectra regime and different wave fields, opening tremendous opportunities for the study and applications of ST vortex in much broader scopes.

Photonic Cyclone: spatiotemporal optical vortex with controllable transverse orbital angular momentum.

Today, it is well known that light possesses a linear momentum that is along the propagation direction. Besides, scientists also discovered that light can possess an angular momentum, a spin angular momentum (SAM) associated with circular polarization and an orbital angular momentum (OAM) owing to the azimuthally dependent phase. Even though such angular momenta are longitudinal in general, an SAM transverse to the propagation direction has opened up a variety of key applications1. In contrast, investigations of the transverse OAM are rare due to its complex nature. Here, we demonstrate a three-dimensional wave packet that is a spatiotemporal (ST) optical vortex with a controllable purely transverse OAM. Contrary to the transverse SAM, the magnitude of the transverse OAM carried by the ST vortex is scalable to a larger value by simple adjustments. Since the ST vortex carries a controllable OAM uniquely in the transverse dimension, it has strong potential for novel applications that may not be possible otherwise. The scheme reported here can be readily adapted for other spectral regimes and different wave fields, opening opportunities for the study and applications of ST vortices in a wide range of areas. By applying a spiral phase in a pulse shaper, a three-dimensional wave packet, which is a spatiotemporal optical vortex with a controllable purely transverse orbital angular momentum, is demonstrated.

Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum

Spatio-temporal optical vortices (STOVs) are a new type of optical orbital angular momentum (OAM) with optical phase circulation in space-time. In prior work [N. Jhajj et al., Phys. Rev X 6, 031037 (2016)], we demonstrated that a STOV is a universal structure emerging from the arrest of self-focusing collapse leading to nonlinear self-guiding in material media. Here, we demonstrate linear generation and propagation in free space of STOV-carrying pulses. Our measurements and simulations demonstrate STOV mediation of space-time energy flow within the pulse and conservation of OAM in space-time. Single-shot amplitude and phase images of STOVs are taken using a new diagnostic, transient grating single-shot supercontinuum spectral interferometry (TG-SSSI).

Free-space propagation of spatio-temporal optical vortices (STOVs)

Spatiotemporal optical vortices (STOVs) are a new type of optical orbital angular momentum (OAM) with optical phase circulation in space–time. In prior work [Phys. Rev. X.6, 031037 (2016)PRXHAE2160-330810.1103/PhysRevX.6.031037], we demonstrated that a STOV is a universal structure emerging from the arrest of self-focusing collapse leading to nonlinear self-guiding in material media. Here, we demonstrate linear generation and propagation in free space of STOV-carrying pulses. Our measurements and simulations demonstrate STOV mediation of space–time energy flow within the pulse and conservation of OAM in space–time. Single-shot amplitude and phase images of STOVs are taken using a new diagnostic, transient grating single-shot supercontinuum spectral interferometry.

Free-space propagation of spatiotemporal optical vortices

We demonstrate a new highly tunable technique for generating meter-scale low density plasma waveguides. Such guides can enable laser-driven electron acceleration to tens of GeV in a single stage. Plasma waveguides are imprinted in hydrogen gas by optical field ionization induced by two time-separated Bessel beam pulses: The first pulse, a J_{0} beam, generates the core of the waveguide, while the delayed second pulse, here a J_{8} or J_{16} beam, generates the waveguide cladding, enabling wide control of the guide's density, depth, and mode confinement. We demonstrate guiding of intense laser pulses over hundreds of Rayleigh lengths with on-axis plasma densities as low as N_{e0}∼5×10^{16}  cm^{-3}.

Optical Guiding in Meter-Scale Plasma Waveguides.

We demonstrate that an ultrashort high intensity laser pulse can propagate for hundreds of Rayleigh ranges in a prepared neutral hydrogen channel by generating its own plasma waveguide as it propagates; the front of the pulse generates a waveguide that confines the rest of the pulse. A wide range of suitable initial index structures and gas densities will support this “self-waveguiding” process; the necessary feature is that the gas density on axis is a minimum. Here, we demonstrate self-waveguiding of pulses of at least 1.5 × 1017 W/cm2 (normalized vector potential a0 ∼ 0.3) over 10 cm, or ∼100 Rayleigh ranges, limited only by our laser energy and length of our gas jet. We predict and observe characteristic oscillations corresponding to mode-beating during self-waveguiding. The self-waveguiding pulse leaves in its wake a fully ionized low-density plasma waveguide which can guide another pulse injected immediately following; we demonstrate optical guiding of such a follow-on probe pulse. The method is well suited to laser wakefield acceleration and other applications requiring a long laser-matter interaction length.

Self-waveguiding of relativistic laser pulses in neutral gas channels

Nonlinear self-guided propagation of intense long-wave infrared (LWIR) laser pulses is of significant recent interest, as it promises high power transmission without beam breakup and multifilamentation. Central to self-guiding is the mechanism for the arrest of self-focusing collapse. Here, we show that discrete avalanche sites centered on submicron aerosols can arrest self-focusing, providing a new mechanism for self-guided propagation of moderate intensity LWIR pulses in outdoor environments. Our conclusions are supported by simulations of LWIR pulse propagation using an effective index approach that incorporates the time-resolved plasma dynamics of discrete avalanche breakdown sites.

A. Goffin

Papers

Free-space propagation of spatio-temporal optical vortices (STOVs)

Free-space propagation of spatiotemporal optical vortices

Optical Guiding in Meter-Scale Plasma Waveguides.

Self-waveguiding of relativistic laser pulses in neutral gas channels

Self-Guiding of Long-Wave Infrared Laser Pulses Mediated by Avalanche Ionization.