Fully stabilized multi-TW optical waveform synthesizer: Toward gigawatt isolated attosecond pulses

A stable 50-mJ three-channel optical waveform synthesizer is demonstrated and used to reproducibly generate a high-order harmonic supercontinuum in the soft x-ray region. This synthesizer is composed of pump pulses from a 10-Hz repetition-rate Ti:sapphire pump laser and signal and idler pulses from an infrared two-stage optical parametric amplifier driven by this pump laser. With full active stabilization of all relative time delays, relative phases, and the carrier-envelope phase, a shot-to-shot stable intense continuum harmonic spectrum is obtained around 60 eV with pulse energy above 0.24 μJ. The peak power of the soft x-ray continuum is evaluated to be beyond 1 GW with a 170-as transform limit duration. We found a characteristic delay dependence of the multicycle waveform synthesizer and established its control scheme. Compared with the one-color case, we experimentally observe an enhancement of the cutoff spectrum intensity by one to two orders of magnitude using three-color waveform synthesis.

Polarization-state-resolved high-harmonic spectroscopy of solids

Attosecond metrology sensitive to sub-optical-cycle electronic and structural dynamics is opening up new avenues for ultrafast spectroscopy of condensed matter. Using intense lightwaves to precisely control the fast carrier dynamics in crystals holds great promise for next-generation petahertz electronics and devices. The carrier dynamics can produce high-order harmonics of the driving field extending up into the extreme-ultraviolet region. Here, we introduce polarization-state-resolved high-harmonic spectroscopy of solids, which provides deeper insights into both electronic and structural sub-cycle dynamics. Performing high-harmonic generation measurements from silicon and quartz, we demonstrate that the polarization states of the harmonics are not only determined by crystal symmetries, but can be dynamically controlled, as a consequence of the intertwined interband and intraband electronic dynamics. We exploit this symmetry-dynamics duality to efficiently generate coherent circularly polarized harmonics from elliptically polarized pulses. Our experimental results are supported by ab-initio simulations, providing evidence for the microscopic origin of the phenomenon.

High-harmonic generation in solids is related to the carrier dynamics and can be used to probe dynamic processes. Here, Klemke et al. show that the polarization states of high harmonics generated from silicon and quartz are determined by the crystal symmetries but can also be dynamically controlled.

Polarization states of high-harmonics generated in silicon from elliptical drivers

The polarization states of high-harmonics generated in silicon with elliptical excitation are studies. Circularly polarized harmonics are demonstrated with both circular and non-circular excitation, determined by crystal symmetry and the dynamical response of the system.

Method for direct observation of Bloch oscillations in semiconductors

We propose a scheme for real-time observations of Bloch oscillations in semiconductors using time-resolved band gap emission spectroscopy. By solving the time-dependent Schrödinger equation, we find one remarkable band gap emission besides the normal high harmonics generated in the interaction of a mid-infrared laser pulse and a semiconductor. It is shown that the band gap emission yield is directly connected to the population in the conduction band (CB). By adopting a pump-probe scheme, the time-dependent population in the CB, that is the dynamical Bloch oscillation, can be probed by measuring the band gap emission signal versus pump-probe delay. We also present a model based on accelerated Bloch states to explain the time-resolved measurement of dynamical Bloch oscillation.

Molecular polarizability anisotropy of liquid water revealed by terahertz-induced transient orientation

Reaction pathways of biochemical processes are influenced by the dissipative electrostatic interaction of the reagents with solvent water molecules. The simulation of these interactions requires a parametrization of the permanent and induced dipole moments. However, the underlying molecular polarizability of water and its dependence on ions are partially unknown. Here, we apply intense terahertz pulses to liquid water, whose oscillations match the timescale of orientational relaxation. Using a combination of terahertz pump / optical probe experiments, molecular dynamics simulations, and a Langevin dynamics model, we demonstrate a transient orientation of their dipole moments, not possible by optical excitation. The resulting birefringence reveals that the polarizability of water is lower along its dipole moment than the average value perpendicular to it. This anisotropy, also observed in heavy water and alcohols, increases with the concentration of sodium iodide dissolved in water. Our results enable a more accurate parametrization and a benchmarking of existing and future water models.

The intermolecular dynamics of liquid water impact most biological processes. Here, the authors use intense terahertz electromagnetic pulses to generate a transient, out-of-equilibrium state of the water network to show that the molecules become oriented and probe the polarizability of this anisotropic state.

Cascaded interactions mediated by terahertz radiation

We investigate a regime of parametric amplification in which the pump and signal waves are spectrally separated by only a few hundreds of GHz frequency - therefore resulting in a sub-THz frequency idler wave. Operating in this regime we find an optical parametric amplifier (OPA) behavior which is highly dissimilar to conventional OPAs. In this regime, we observe multiple three-wave mixing processes occurring simultaneously which results in spectral cascading around the pump and signal wave. Via numerical simulations, we elucidate the processes at work and show that cascaded optical parametric amplification offers a pathway toward THz-wave generation beyond the Manly-Rowe limit and toward the generation of high-energy, sparse frequency-combs.

Near- and Extended-Edge X-Ray-Absorption Fine-Structure Spectroscopy Using Ultrafast Coherent High-Order Harmonic Supercontinua

Recent advances in high-order harmonic generation have made it possible to use a tabletop-scale setup to produce spatially and temporally coherent beams of light with bandwidth spanning 12 octaves, from the ultraviolet up to x-ray photon energies >1.6  keV. Here we demonstrate the use of this light for x-ray-absorption spectroscopy at the K- and L-absorption edges of solids at photon energies near 1 keV. We also report x-ray-absorption spectroscopy in the water window spectral region (284-543 eV) using a high flux high-order harmonic generation x-ray supercontinuum with 10^{9}  photons/s in 1% bandwidth, 3 orders of magnitude larger than has previously been possible using tabletop sources. Since this x-ray radiation emerges as a single attosecond-to-femtosecond pulse with peak brightness exceeding 10^{26}  photons/s/mrad^{2}/mm^{2}/1% bandwidth, these novel coherent x-ray sources are ideal for probing the fastest molecular and materials processes on femtosecond-to-attosecond time scales and picometer length scales.

Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics

The strong ellipticity dependence of high-harmonic generation (HHG) in gases enables numerous experimental techniques that are nowadays routinely used, for instance, to create isolated attosecond pulses. Extending such techniques to solids requires a fundamental understanding of the microscopic mechanism of HHG. Here we use first-principles simulations within a time-dependent density-functional framework and show how intraband and interband mechanisms are strongly and differently affected by the ellipticity of the driving laser field. The complex interplay between intraband and interband effects can be used to tune and improve harmonic emission in solids. In particular, we show that the high-harmonic plateau can be extended by as much as 30% using a finite ellipticity of the driving field. We furthermore demonstrate the possibility to generate, from single circularly polarized drivers, circularly polarized harmonics. Our work shows that ellipticity provides an additional knob to experimentally optimize HHG in solids.The mechanisms of high-order harmonic generation in bulk system and dilute gas are different. Here the authors use first-principle methods to explore the ellipticity dependence and control of the HHG in periodic solids by involving the interband and intraband dynamics in Si and MgO.

Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids

An accurate analytic model describing the microscopic mechanism of high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results reveal that (i) the emitted HHG spectra are highly anisotropic and laser-polarization dependent even for cubic crystals; (ii) the harmonic emission is enhanced by the inhomogeneity of the electron-nuclei potential; the yield is increased for heavier atoms; and (iii) the cutoff photon energy is driver-wavelength independent. Moreover, we show that it is possible to predict the laser polarization for optimal HHG in bulk crystals solely from the knowledge of their electronic band structure. Our results pave the way to better control and optimize HHG in solids by engineering their band structure.

High-dynamic-range arrival time control for flexible, accurate and precise parametric sub-cycle waveform synthesis

We introduce a simple all-inline variation of a balanced optical cross-correlator (BOC) that allows to measure the arrival time difference (ATD), over the full Nyquist bandwidth, with increased common-mode rejection and long-term stability. An FPGA-based signal processing unit allows for real-time signal normalization and enables locking to any setpoint with an unprecedented accuracy of 0.07 % within an increased ATD range of more than 400 fs, resulting in attosecond resolution locking. The setup precision is verified with an out-of-loop measurement to be less than 80 as residual jitter paving the way for highly demanding applications such as parametric waveform synthesizers.

Attosecond precision multi-kilometer laser-microwave network

Synchronous laser-microwave networks delivering attosecond timing precision are highly desirable in many advanced applications, such as geodesy, very-long-baseline interferometry, high-precision navigation and multi-telescope arrays. In particular, rapidly expanding photon-science facilities like X-ray free-electron lasers and intense laser beamlines require system-wide attosecond-level synchronization of dozens of optical and microwave signals up to kilometer distances. Once equipped with such precision, these facilities will initiate radically new science by shedding light on molecular and atomic processes happening on the attosecond timescale, such as intramolecular charge transfer, Auger processes and their impacts on X-ray imaging. Here we present for the first time a complete synchronous laser-microwave network with attosecond precision, which is achieved through new metrological devices and careful balancing of fiber nonlinearities and fundamental noise contributions. We demonstrate timing stabilization of a 4.7-km fiber network and remote optical-optical synchronization across a 3.5-km fiber link with an overall timing jitter of 580 and 680 attoseconds root-mean-square, respectively, for over 40 h. Ultimately, we realize a complete laser-microwave network with 950-attosecond timing jitter for 18 h. This work can enable next-generation attosecond photon-science facilities to revolutionize many research fields from structural biology to material science and chemistry to fundamental physics.

40-µJ passively CEP-stable seed source for ytterbium-based high-energy optical waveform synthesizers

We demonstrate experimentally for the first time a ~40-µJ two-octave-wide passively carrier-envelope phase (CEP)-stable parametric front-end for seeding an ytterbium (Yb)-pump-based, few-optical-cycle, high-energy optical parametric waveform synthesizer. The system includes a CEP-stable white-light continuum and two-channel optical parametric chirped pulse amplifiers (OPCPAs) in the near- and mid-infrared spectral regions spanning altogether a two-octave-wide spectrum driven by a regenerative amplifier. The output pulses are compressed and fully characterized to demonstrate the well-behaved spectral phase of this seed source.

Jitter analysis of timing-distribution and remote-laser synchronization systems

We present a powerful jitter analysis method for timing-distribution and remote-laser synchronization systems based on feedback flow between setup elements. We synchronize two different mode-locked lasers in a master-slave configuration locally and remotely over a timing-stabilized fiber link network. Local synchronization reveals the inherent jitter of the slave laser as 2.1 fs RMS (>20 kHz), whereas remote synchronization exhibits an out-of-loop jitter of 8.55 fs RMS integrated for 1 Hz - 1 MHz. Our comprehensive feedback model yields excellent agreement with the experimental results and identifies seven uncorrelated noise sources, out of which the slave laser's jitter dominates with 8.19 fs RMS.

Cascaded parametric amplification for highly efficient terahertz generation

A highly efficient, practical approach to high-energy multi-cycle terahertz (THz) generation based on spectrally cascaded optical parametric amplification (THz-COPA) is introduced. Feasible designs are presented that enable the THz wave, initially generated by difference frequency generation between a narrowband optical pump and optical seed (0.1-10% of pump energy), to self-start a cascaded (or repeated) energy downconversion of pump photons in a single pass through a single crystal. In cryogenically cooled, periodically poled lithium niobate, unprecedented energy conversion efficiencies >8% achievable with existing pump laser technology are predicted using realistic simulations. The calculations account for cascading effects, absorption, dispersion, and laser-induced damage. Due to the simultaneous, coupled nonlinear evolution of multiple phase-matched three-wave mixing processes, THz-COPA exhibits physics distinctly different from conventional three-wave mixing parametric amplifiers. This, in turn, governs optimal phase-matching conditions, evolution of optical spectra, and limitations of the nonlinear process. Circumventing these limitations is shown to yield conversion efficiencies ≫10%.

Terahertz generation in lithium niobate driven by Ti:sapphire laser pulses and its limitations

We experimentally investigate the limits of 800-nm-to-terahertz (THz) energy conversion in lithium niobate at room temperature driven by amplified Ti:sapphire laser pulses with tilted pulse front. The influence of the pump central wavelength, pulse duration, and fluence on THz generation is studied. We achieved a high peak efficiency of 0.12% using transform limited 150 fs pulses and observed saturation of the optical-to-THz conversion efficiency at a fluence of 15 mJ/cm(2) for this pulse duration. We experimentally identify two main limitations for the scaling of optical-to-THz conversion efficiencies: (i) the large spectral broadening of the optical pump spectrum in combination with large angular dispersion of the tilted pulse front and (ii) free-carrier absorption of THz radiation due to multi-photon absorption of the 800 nm radiation.

Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses

High-energy isolated attosecond pulses required for the most intriguing nonlinear attosecond experiments as well as for attosecond-pump/attosecond-probe spectroscopy are still lacking at present. Here we propose and demonstrate a robust generation method of intense isolated attosecond pulses, which enable us to perform a nonlinear attosecond optics experiment. By combining a two-colour field synthesis and an energy-scaling method of high-order harmonic generation, the maximum pulse energy of the isolated attosecond pulse reaches as high as 1.3 μJ. The generated pulse with a duration of 500 as, as characterized by a nonlinear autocorrelation measurement, is the shortest and highest-energy pulse ever with the ability to induce nonlinear phenomena. The peak power of our tabletop light source reaches 2.6 GW, which even surpasses that of an extreme-ultraviolet free-electron laser.

The short duration of attosecond pulses makes them interesting for ultrafast experiments, although it has so far been difficult to generate isolated attosecond pulses with sufficiently high power. Here the authors achieve high-intensity isolated attosecond pulses with a tabletop setup, based on a scaled-up high-order harmonic generation process.

Broadband continuum generation in mode-locked lasers with phase-matched output couplers

The concept of intracavity phase matching is proposed and demonstrated both theoretically and experimentally with a broadband phase-matched dielectric output coupler for linear-cavity few-cycle Ti:sapphire oscillators. The spectrum in the matched wavelength range is enhanced by >10  dB while maintaining good beam quality via resonantly enhanced continuum generation. The enhanced spectral components can be continuously tuned by varying the intracavity dispersion. Because dielectric coatings offer flexible design capabilities, this approach is applicable to various lasers with different gain media to obtain custom-tailored spectra, which have the potential to benefit several applications, such as shorter pulse generation, seeding of ytterbium lasers for pumping optical parametric amplifiers, and direct f-2f detection of the carrier-envelope phase.

Carrier envelope phase stabilization of a Yb:KGW laser amplifier

In this paper we report on the active stabilization of the carrier envelope phase (CEP) of a Yb:KGW chirped pulse amplifier laser system seeded by a Yb-doped solid-state Kerr-lens mode-locked oscillator. The regenerative amplifier delivers 180 fs CEP stable pulses of 30 μJ-1 mJ energy at a repetition rate tunable from 1 to 200 kHz. The bandwidth of the feedback loop was extended by a factor of 5 using a specially designed high-pass filter, which resulted in a dramatic decrease of CEP jitter below 0.45 rad after the amplifier.

Dual-chirped optical parametric amplification for generating few hundred mJ infrared pulses

An ultrafast high-power infrared pulse source employing a dual-chirped optical parametric amplification (DC-OPA) scheme based on a Ti:sapphire pump laser system is theoretically investigated. By chirping both pump and seed pulses in an optimized way, high-energy pump pulses can be utilized for a DC-OPA process without exceeding the damage threshold of BBO crystals, and broadband signal and idler pulses at 1.4 μm and 1.87 μm can be generated with a total conversion efficiency approaching 40%. Furthermore, few-cycle idler pulses with a passively stabilized carrier-envelope phase (CEP) can be generated by the difference frequency generation process in a collinear configuration. DC-OPA, a BBO-OPA scheme pumped by a Ti:sapphire laser, is efficient and scalable in output energy of the infrared pulses, which provides us with the design parameters of an ultrafast infrared laser system with an energy up to a few hundred mJ.

Narrow-linewidth chirped frequency comb from a frequency-shifted feedback Ti:sapphire laser seeded by a phase-modulated single-frequency fiber laser

Frequency-shifted feedback (FSF) lasers have emerged as powerful tools for precision distance metrology. At the output of a Michelson interferometer, the detected rf spectra of the FSF laser light contain a length-dependent heterodyne beat signal whose linewidth ultimately limits the achievable accuracy of length measurements. Here, we demonstrate a narrow-linewidth chirped frequency comb from an FSF Ti:sapphire ring laser seeded by a phase-modulated, ultra-low-phase-noise, single-frequency fiber laser. We experimentally investigate the influence of the seed laser linewidth on the resulting width and shape of the length-dependent rf beat signal. An ultranarrow heterodyne beat linewidth of <20 Hz is observed.

Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse

We propose and demonstrate the generation of a continuum high-order harmonic spectrum by mixing multicycle two-color (TC) laser fields with the aim of obtaining an intense isolated attosecond pulse. By optimizing the wavelength of a supplementary infrared pulse in a TC field, a continuum harmonic spectrum was created around the cutoff region without carrier-envelope phase stabilization. The obtained harmonic spectra clearly show the possibility of generating isolated attosecond pulses from a multicycle TC laser field, which is generated by an 800 nm, 30 fs pulse mixed with a 1300 nm, 40 fs pulse. Our proposed method enables us not only to relax the requirements for the pump pulse duration but also to reduce ionization of the harmonic medium. This concept opens the door to create an intense isolated attosecond pulse using a conventional femtosecond laser system.

Self-compression of millijoule 1.5 microm pulses

We demonstrate a four-stage optical parametric chirped-pulse amplification system that delivers carrier-envelope phase-stable approximately 1.5 microm pulses with energies up to 12.5 mJ before recompression. The system is based on a fusion of femtosecond diode-pumped solid-state Yb technology and a picosecond 100 mJ Nd:YAG pump laser. Pulses with 62 nm bandwidth are recompressed to a 74.4 fs duration close to the transform limit. To show the way toward a terawatt-peak-power single-cycle IR source, we demonstrate self-compression of 2.2 mJ pulses down to 19.8 fs duration in a single filament in argon with a 1.5 mJ output energy and 66% energy throughput.

Highly stable ultrabroadband mid-IR optical parametric chirped-pulse amplifier optimized for superfluorescence suppression

We present a 9 GW peak power, three-cycle, 2.2 microm optical parametric chirped-pulse amplification source with 1.5% rms energy and 150 mrad carrier envelope phase fluctuations. These characteristics, in addition to excellent beam, wavefront, and pulse quality, make the source suitable for long-wavelength-driven high-harmonic generation. High stability is achieved by careful optimization of superfluorescence suppression, enabling energy scaling.

Scalable Yb-MOPA-driven carrier-envelope phase-stable few-cycle parametric amplifier at 1.5 microm

Carrier-envelope phase-stable 4 microJ pulses at approximately 1.5 microm are obtained from a femtosecond Yb:KGW-MOPA-pumped two-stage optical parametric amplifier. This novel technology represents a highly attractive alternative to traditional Ti:sapphire front-ends for seeding multimillijoule-level optical parametric chirped-pulse amplifiers. For this task, we demonstrate stretching of the OPA output to approximately 40 ps and recompression to 33 fs pulse duration. As a stand-alone system, our tunable two-stage OPA might find numerous applications in time-resolved spectroscopy and micromachining.

Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers

We investigate the carrier-envelope phase dynamics of octave-spanning Ti:sapphire lasers and perform a complete noise analysis of the carrier-envelope phase stabilization. We model the effect of the laser dynamics on the residual carrier-envelope phase noise by deriving a transfer function representation of the octave-spanning frequency comb. The modelled phase noise and the experimental results show excellent agreement. This greatly enhances our capability of predicting the dependence of the residual carrier-envelope phase noise on the feedback loop filter, the carrier-envelope frequency control mechanism and the pump laser used.

Demonstration of a HeNe/CH4-based optical molecular clock

We implement a simple optical clock based on the F2(2) [P(7), v3] optical transition in methane. A single femtosecond laser's frequency comb undergoes difference frequency generation to provide an IR comb at 3.39 microm with a null carrier-envelope offset. This IR comb provides a phase-coherent link between the 88-THz optical reference and the rf repetition rate. Comparison of the repetition rate signal with a second femtosecond comb stabilized to molecular iodine shows an instability of 1.2 x 10(-13) at 1 s, limited by microwave detection of the repetition rates. The single-sideband phase noise of the microwave signal, normalized to a carrier frequency of 1 GHz, is below -93 dBc/Hz at 1-Hz offset.

Experimental implementation of optical clockwork without carrier-envelope phase control

We demonstrate optical clockwork without the need for carrier-envelope phase control by use of sum-frequency generation between a continuous-wave optical parametric oscillator at 3.39 microm and a femtosecond mode-locked Ti:sapphire laser with two strong spectral peaks at 834 and 670 nm, a spectral difference matched by the 3.39-microm radiation.

Carrier-wave Rabi flopping: role of the carrier-envelope phase

Recently, a dependence of Rabi flopping on the carrier-envelope phase of the exciting laser pulses was predicted theoretically [Phys. Rev. Lett. 89, 127401 (2002)] for excitation of a thin semiconductor film with intense few-cycle pulses. Here, we report corresponding experiments on 50-100-nm thin GaAs films excited with 5-fs pulses. We find a dependence on the carrier-envelope phase arising from the interference of sidebands from the fundamental or the third-harmonic Mollow triplet, respectively, with surface second-harmonic generation.

Light-induced gaps in semiconductor band-to-band transitions

We observe a triplet around the third harmonic of the semiconductor band gap when exciting 50-100 nm thin GaAs films with 5 fs pulses at 3 x 10(12) W/cm(2). The comparison with solutions of the semiconductor Bloch equations allows us to interpret the observed peak structure as being due to a two-band Mollow triplet. This triplet in the optical spectrum is a result of light-induced gaps in the band structure, which arise from coherent band mixing. The theory is formulated for full tight-binding bands and uses no rotating-wave approximation.

Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics

In contrast with traditional nonlinear optics, a peak at the spectral position of the second harmonic of a laser can also be generated in an inversion-symmetric medium in the regime of extreme nonlinear optics. We describe the underlying mechanism of such third-harmonic generation in disguise of second-harmonic generation and compare theory with the optical as well as the radio-frequency spectra measured in recent experiments on thin ZnO films. The peak at twice the carrier-envelope offset frequency in the radio-frequency spectra is shown to be an unambiguous signature of such a process.

Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO

We excite ZnO samples with two-cycle optical pulses directly from a mode-locked oscillator with average powers of several tens of milliwatts. The emitted light reveals peaks at the carrier-envelope offset frequency f(ø) and at 2f(ø) in the radio-frequency spectra. These peaks can still be detected in layers as thin as 350 nm-a step toward determining the carrier-envelope offset phase itself.

Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics

We study the influence of the carrier-envelope offset phase of few-cycle pulses on nonperturbative resonant extreme nonlinear optics in a semiconductor. If the Rabi frequency becomes comparable to the light frequency, the different Rabi sidebands interfere around twice the laser center frequency, giving rise to a signal which strongly depends on the carrier-envelope offset phase. This signature should be measurable in GaAs samples.

Signatures of carrier-wave Rabi flopping in GaAs

For excitation of the model semiconductor GaAs with optical pulses which are both extremely short ( 5 fs) and extremely intense ( approximately 10(12) W cm(-2)), we can meet the condition that the Rabi frequency becomes comparable to the band gap frequency-a highly unusual and previously inaccessible situation. Specifically, in this regime, we observe carrier-wave Rabi flopping, a novel effect of nonlinear optics which has been predicted theoretically and which is related to the failure of the area theorem.