Automated spatiotemporal diffraction of ultrashort laser pulses

Space-time wave packets localized in all dimensions

Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to nonlinear and quantum optics. However, synthesizing such wave packets requires introducing non-differentiable angular dispersion with high spectral precision in two transverse dimensions, a capability that has eluded optics to date. Here, we describe an experimental strategy capable of sculpting the spatio-temporal spectrum of a generic pulsed beam by introducing arbitrary radial chirp via two-dimensional conformal coordinate transformations of the spectrally resolved field. This procedure yields propagation-invariant ‘space-time’ wave packets localized in all dimensions, with tunable group velocity in the range from 0.7c to 1.8c in free space, and endowed with prescribed orbital angular momentum. By providing unprecedented flexibility in sculpting the three-dimensional structure of pulsed optical fields, our experimental strategy promises to be a versatile platform for the emerging enterprise of space-time optics.

Propagation-invariant wave packets confined in space and time can be useful for optical sensing, imaging, and nonlinear and quantum optics. Here the authors demonstrate control over the angular dispersion of optical wave packets in two-transverse dimensions to synthesize space-time wave packets localized in all dimensions.

Diffraction-free pulsed optical beams via space-time correlations

Diffraction places a fundamental limitation on the distance an optical beam propagates before its size increases and spatial details blur. We show here that imposing a judicious correlation between spatial and spectral degrees of freedom of a pulsed beam can render its transverse spatial profile independent of location along the propagation axis, thereby arresting the spread of the time-averaged beam. Such correlation introduced into a beam with arbitrary spatial profile enables spatio-temporal dispersion to compensate for purely spatial dispersion that underlies diffraction. As a result, the spatio-temporal profile in the local time-frame of the pulsed beam remains invariant at all positions along the propagation axis. One-dimensional diffraction-free space-time beams are described - including non-accelerating Airy beams, despite the well-known fact that cosine waves and accelerating Airy beams are the only one-dimensional diffraction-free solutions to the monochromatic Helmholtz equation.

An optical FPGA: reconfigurable simultaneous multi-output spectral pulse-shaping for linear optical processing

We demonstrate a pulse-shaping technique that allows for spectrally resolved splitting of an input signal to multiple output ports. This ability enables reconfigurable creation of splitters with complex wavelength-dependent splitting ratios, giving similar flexibility to a Field Programmable Gate Array (FPGA) in electronics. Our technique can be used to create reprogrammable optical (interferometric) circuits, by emulating their multi-port spectral transfer functions instead of the traditional method of creating an interferometer by splitting and recombining the light with an added delay. We demonstrate the capabilities of this technique by creating a Mach-Zehnder interferometer, an all-optical discrete Fourier transform filter, two nested Mach-Zehnder interferometers and a complex splitter with a triangular-shaped response.

Coherently Controlled Ultrafast Four-Wave Mixing Spectroscopy

A novel approach to coherent nonlinear optical spectroscopy based on two-dimensional femtosecond pulse shaping is introduced. Multiple phase-stable output beams are created and overlapped at the sample in a phase-matched boxcars geometry via two-dimensional femtosecond pulse shaping. The pulse timing, shape, phase, and spectral content within all beams may be specified, yielding an unprecedented level of control over the interacting fields in nonlinear spectroscopic experiments. Heterodyne detection and phase cycling of the nonlinear signal are easily implemented due to the excellent phase stability among all output beams. This approach combines the waveform generation capabilities of magnetic resonance spectroscopy with the wavevector specification and phase matching of nonlinear optical spectroscopy, yielding the control capabilities and signal selectivity of both. Results on four prototype systems are used to illustrate some of the novel possibilities of this method.

Complete characterization of a spatiotemporal pulse shaper with two-dimensional Fourier transform spectral interferometry

Spatiotemporal pulse shaping is characterized with two-dimensional Fourier transform spectral interferometry. A deformable-mirror-based bidimensional pulse shaper is used to create simple spatiotemporal structures on a femtosecond pulse, structures that are directly calculated from the measured spatiospectral phases and intensities.

Diffraction-based femtosecond pulse shaping with a two-dimensional spatial light modulator

A new diffraction-based method is proposed and demonstrated for simultaneous shaping of both the phase and amplitude of femtosecond laser pulses by use of a phase-only two-dimensional spatial light modulator. The method suppresses certain types of temporal replica features ordinarily observed in femtosecond pulse shaping owing to imperfections in modulator devices and allows for multiplexed outputs suitable for use in various applications.

Femtosecond shaping of transverse and longitudinal light polarization

Femtosecond laser pulse shaping techniques have been restricted to propagating transverse electromagnetic waves. We present a scheme for pulse shaping of optical near fields based on the excitation of longitudinal electromagnetic fields with polarization-shaped light pulses. By solving Maxwell's equations for a model nanostructure, i.e., a scanning tunneling microscope tip, with help from the boundary-element method, we demonstrate that the electric field vector oscillates in a complex yet controllable fashion in three dimensions. Many applications are envisioned because literally another dimension in the optimal control of light-matter interaction is accessible.

Degenerate four-wave mixing spectroscopy based on two-dimensional femtosecond pulse shaping

We report noncollinear, degenerate four-wave mixing experiments that employ a new device based on two-dimensional femtosecond pulse shaping that delays and modulates all incident fields. Heterodyne detection is easily implemented due to the full phase stability of the device.