Grating-assisted phase matching in extreme nonlinear optics

Self-organized spatiotemporal quasi-phase-matching in microresonators

Quasi-phase-matching (QPM) is a widely adopted technique for mitigating stringent momentum conservation in nonlinear optical processes such as second-harmonic generation (SHG). It effectively compensates for the phase velocity mismatch between optical harmonics by introducing a periodic spatial modulation to the nonlinear optical medium. Such a mechanism has been further generalized to the spatiotemporal domain, where a non-stationary spatial QPM can induce a frequency shift of the generated light. Here we demonstrate how a spatiotemporal QPM grating, consisting in a concurrent spatial and temporal modulation of the nonlinear response, naturally emerges through all-optical poling in silicon nitride microresonators. Mediated by the coherent photogalvanic effect, a traveling space-charge grating is self-organized, affecting momentum and energy conservation, resulting in a quasi-phase-matched and Doppler-shifted second harmonic. Our observation of the photoinduced spatiotemporal QPM expands the scope of phase matching conditions in nonlinear photonics.

Applying tiling and pattern theory in the design of hollow-core photonic crystal fibers for multi-wavelength beam guidance

We apply tiling and pattern theory in the design of hollow-core photonic crystal fibers for guiding light in multiple spectral bandgaps. By combining two different glass apexes in a single [3⁶;3².4.3.4] 2-uniform tiling, transmission regions with fundamental, second and third harmonic wavelengths are supported. This cladding design may also be an excellent candidate for high power beam delivery of Er/Yb, Nd:YAG and Ti:Sapphire laser sources.

Enhancing High-Order Harmonic Generation in Light Molecules by Using Chirped Pulses

One of the current challenges in high-harmonic generation is to extend the harmonic cutoff to increasingly high energies while maintaining or even increasing the efficiency of the high-harmonic emission. Here we show that the combined effect of down-chirped pulses and nuclear dynamics in light molecules allows one to achieve this goal, provided that long enough IR pulses are used to allow the nuclei to move well outside the Franck-Condon region. We also show that, by varying the duration of the chirped pulse or by performing isotopic substitution while keeping the pulse duration constant, one can control the extension of the harmonic plateau.

Quasi-phase-matching of only even-order high harmonics

High harmonic spectrum of a quasi-monochromatic pump that interacts with isotropic media consists of only odd-order harmonics. Addition of a secondary pump, e.g. a static field or the second harmonic of the primary pump, can results with generation of both odd and even harmonics of the primary pump. We propose a method for quasi-phase matching of only the even-order harmonics of the primary pump. We formulate a theory for this process and demonstrate it numerically. We also show that it leads to attosecond pulse trains with constant carrier envelop phase and high repetition rate.

Attosecond pulses with sophisticated spatio-spectral waveforms: spatio-spectral Airy and auto-focusing beams

We propose a scheme for producing attosecond pulses with sophisticated spatio-spectral waveforms. The profile of a seed attosecond pulse is modified and its central frequency is up-converted through interaction with an infrared pump pulse. The transverse profile of the infrared beam and a spatiotemporal shift between the seed and infrared pulses are used for manipulating the spatio-spectral waveform of the generated pulse beam. We present several examples of sophisticated isolated attosecond pulse beam generation, including spatio-spectral Airy beam that exhibits prismatic self-bending effect and a beam undergoing auto-focusing to a sub-micron spot without the need of a focusing lens or nonlinearity.

Attochirp-free high-order harmonic generation

A method is proposed for arbitrarily engineering the high-order harmonic generation phase achieved by shaping a laser pulse and employing xuv light or x rays for ionization. This renders the production of bandwidth-limited attosecond pulses possible while avoiding the use of filters for chirp compensation. By adding the first 8 Fourier components to a sinusoidal field of 1016 W/cm2, the bandwidth-limited emission of 8 as is shown to be possible from a Li2+ gas. The scheme is extendable to the zs-scale.

Sawtooth grating-assisted phase-matching

We show that a sawtooth phase-modulation is the optimal profile for grating assisted phase matching (GAPM). Perfect (sharp) sawtooth modulation fully corrects the phase-mismatch, exhibiting conversion equal to conventional phase matching, while smoothened, approximate sawtooth structures are more efficient than sinusoidal or square GAPM modulations that were previously studied. As an example, we demonstrate numerically optically-induced sawtooth GAPM for high harmonic generation. Sawtooth GAPM is the most efficient method for increasing the conversion efficiency of high harmonic generation through quasi-phase-matching, with an ultimate efficiency that closely matches the ideal phase-matching case.

Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source

We demonstrate fully phase-matched high harmonic emission spanning the water window spectral region important for nano- and bioimaging and a breadth of materials and molecular dynamics studies. We also generate the broadest bright coherent bandwidth (≈300  eV) to date from any light source, small or large, that is consistent with a single subfemtosecond burst. The harmonic photon flux at 0.5 keV is 10³ higher than demonstrated previously. This work extends bright, spatially coherent, attosecond pulses into the soft x-ray region for the first time.

Autoresonant propagation of incoherent light-waves

We study, theoretically and experimentally, the evolution of optical waves with randomly-fluctuating phases in a spatially chirped nonlinear directional coupler. As the system crosses its linear resonance, we observe collective self-phase-locking (autoresonance) of all mutually-incoherent waves, each with its own pump, and simultaneous amplification until the pumps are exhausted. We show that the autoresonant transition in this system exhibits a sharp threshold, common to all mutually-incoherent waves comprising the light beam.

All-regions tunable high harmonic enhancement by a periodic static electric field

Simulations show that a static electric field periodically distributed in space can be used to control the production of coherent light by high-order harmonic generation in a wide spectral range covering extreme-ultraviolet and soft x-ray radiation. The radiation yield is selectively enhanced due to symmetry breaking induced by a static electric field on the interaction between the driving laser and the medium. The spectral position of the enhancement is tuned by varying the periodicity of the static electric field which matches twice the coherence length of the harmonics in the desired region. We find that the static electric field strength inducing enhancement decreases for shorter wavelengths and predict an increase of more than two orders of magnitude for harmonics in the water window spectral range with a static electric field as weak as 1.12 MV/cm.

Enhanced high harmonic generation from multiply ionized argon above 500 eV through laser pulse self-compression

By combining laser pulse self-compression and high harmonic generation within a single waveguide, we demonstrate high harmonic emission from multiply charged ions for the first time. This approach enhances the laser intensity and counteracts ionization-induced defocusing, extending the cutoff photon energy in argon above 500 eV for the first time, with higher spectral intensity and cutoff energy than He for the same input laser parameters. This Letter demonstrates a pathway for extending high harmonic emission to very high photon energies using large, multiply charged, ions with high ionization potentials.

Autoresonant dynamics of optical guided waves

We study, theoretically and experimentally, autoresonant dynamics of optical waves in a spatially chirped nonlinear directional coupler. We show that adiabatic passage through a linear resonance in a weakly coupled light-wave system yields a sharp threshold transition to nonlinear phase locking and amplification to predetermined amplitudes. This constitutes the first observation of autoresonance phenomena in optics.

Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum

We show how bright, tabletop, fully coherent hard X-ray beams can be generated through nonlinear upconversion of femtosecond laser light. By driving the high-order harmonic generation process using longer-wavelength midinfrared light, we show that, in theory, fully phase-matched frequency upconversion can extend into the hard X-ray region of the spectrum. We verify our scaling predictions experimentally by demonstrating phase matching in the soft X-ray region of the spectrum around 330 eV, using ultrafast driving laser pulses at 1.3-microm wavelength, in an extended, high-pressure, weakly ionized gas medium. We also show through calculations that scaling of the overall conversion efficiency is surprisingly favorable as the wavelength of the driving laser is increased, making tabletop, fully coherent, multi-keV X-ray sources feasible. The rapidly decreasing microscopic single-atom yield, predicted for harmonics driven by longer-wavelength lasers, is compensated macroscopically by an increased optimal pressure for phase matching and a rapidly decreasing reabsorption of the generated X-rays.

Quasi-phase-matched high harmonic generation in hollow core photonic crystal fibers

The potential of hollow core photonic crystal fiber as a nonlinear gas cell for efficient high harmonic generation is discussed. The feasibility of phase-matching this process by modulating the phase of ionization electrons using a counter-propagating laser field is shown. In this way, harmonics with energies of several hundreds of eV can be produced using fs-laser pump pulses of microJ energy.

Quasi-phase-matching and dispersion characterization of harmonic generation in the perturbative regime using counterpropagating beams

It is shown theoretically that second harmonic generation can be quasi-phase-matched by using a pump beam consisting of a forward propagating field and a counterpropagating pulse train. The counterpropagating setup can also be used for direct measurement of the coherence length of the nonlinear process which can determine the dispersion properties of the medium.

Extended phase matching of high harmonics driven by mid-infrared light

We demonstrate that phase-matched frequency upconversion of ultrafast laser light can be extended to shorter wavelengths by using longer driving laser wavelengths. Experimentally, we show that the phase-matching cutoff for harmonic generation in argon increases from 45 to 100 eV when the driving laser wavelength is increased from 0.8 to 1.3 microm. Phase matching is also obtained at higher pressures using a longer-wavelength driving laser, mitigating the unfavorable scaling of the single-atom response. Theoretical calculations suggest that phase-matched high harmonic frequency upconversion driven by mid-infrared pulses could be extended to extremely high photon energies.

Quasi-periodic and random quasi-phase matching of high harmonic generation

Quasi-phase matching schemes employing quasi-periodic or random spatial modulations, previously applied to perturbative nonlinear optics, are demonstrated theoretically for the extreme nonlinear optical process of high harmonic generation. We show that quasi-periodic quasi-phase matching of high harmonic generation can be used for simultaneous enhancement of arbitrarily chosen spectral regions. We also demonstrate enhancement of a single extremely wide bandwidth using random quasi-phase matching.

Coherent ultrafast core-hole correlation spectroscopy: x-ray analogues of multidimensional NMR

We propose two-dimensional x-ray coherent correlation spectroscopy for the study of interactions between core-electron and valence transitions. This technique may find experimental applications in the future when very high intensity x-ray sources become available. Spectra obtained by varying two delay periods between pulses show off-diagonal crosspeaks induced by coupling of core transitions of two different types. Calculations of the N1s and O1s signals of aminophenol isomers illustrate how novel information about many-body effects in electronic structure and excitations of molecules can be extracted from these spectra.

Harnessing attosecond science in the quest for coherent X-rays

Modern laser technology has revolutionized the sensitivity and precision of spectroscopy by providing coherent light in a spectrum spanning the infrared, visible, and ultraviolet wavelength regimes. However, the generation of shorter-wavelength coherent pulses in the x-ray region has proven much more challenging. The recent emergence of high harmonic generation techniques opens the door to this possibility. Here we review the new science that is enabled by an ability to manipulate and control electrons on attosecond time scales, ranging from new tabletop sources of coherent x-rays to an ability to follow complex electron dynamics in molecules and materials. We also explore the implications of these advances for the future of molecular structural characterization schemes that currently rely so heavily on scattering from incoherent x-ray sources.