Single attosecond light pulses from multi-cycle laser sources

High harmonic generation provides a means of producing attosecond pulses of light which are the shortest, controllable probes available to science for time-resolving ultrafast dynamics. We review techniques based on high harmonic generation for generating single attosecond pulses using high-power, multi-cycle laser sources, including optical-, polarisation-, and ionisation-gating schemes as well as techniques based on field synthesis. By significantly reducing the technical demands placed on the driving laser, these techniques have the potential to greatly broaden the application base for attosecond pulses.     

Optimal control of high harmonics for the generation of double attosecond pulses by using a chirped laser pulse

An efficient scheme for the optimization of ultrashort femtosecond pulse shapes interacting with an atom to control high harmonics spectrum and double attosecond pulse generation is presented. The time-dependent Schrödinger equation of one-dimensional hydrogen atom is solved numerically to obtain electric field emission. The genetic algorithm optimization method is used to control the phase and amplitude of ultrashort excitation laser pulses to generate the desired attosecond-shaped pulses. An appropriate cost function is introduced for genetic algorithm optimization of double attosecond pulse generation. It is shown that the relative intensity of two generated pulses, their delay time and duration can be controlled in this approach. Finally, the parameters of the optimized emitted attosecond pulse are compared with those of desired pulses, and the underlying physical mechanisms are discussed in detail.     

Kilohertz femtosecond UV-pumped visible beta-barium borate and lithium triborate optical parametric generator and amplifier

We demonstrate optical parametric generation and amplification of femtosecond pulses in the entire visible range using type-I phase-matched beta-barium borate and lithium triborate crystals pumped by the frequency-doubled output of a Ti:sapphire regenerative amplifier at 395 nm. The output is tunable from 470 to 770 nm with a pulse width of ~170 fs at a repetition rate of 1 kHz and a maximum output energy of ~1.1 muJ/pulse. The visible optical parametric amplifier output was then frequency doubled and sum frequency mixed with the fundamental output of Ti:sapphire at 790 nm to produce UV pulses with a conversion efficiency of greater than 25%. The second harmonic generated UV pulses are tunable from 240 to 380 nm with a maximum pulse energy of ~260 nJ/pulse.     

Laser-parameter effects on the generation of ultrabroad harmonic and ultrashort attosecond pulse in a long-plus-short scheme

By numerically solving the time-dependent Schrödinger equation for helium gas in a special two-color laser field, which is synthesized by a long (9?fs) driving pulse and a short (6?fs) controlling pulse, we discuss the influence of the carrier-envelope phase, frequency, and the intensity of the controlling pulse on the generation of harmonic spectra and isolated attosecond pluses. In the cutoff region, two or three plateaus can be controlled by optimizing these laser parameters, and an ultrabroad supercontinuum harmonic spectrum with a bandwidth of 800?eV can be produced, which can support an ultrashort isolated 4.5 as pulse generation by Fourier transformation. Furthermore, using classical ionizing and returning energy maps, time–frequency analyses are presented to explain the underlying physical mechanisms.     

Isolated sub-50 attosecond pulse generation driven by tricolor multi-cycle pulses

We theoretically investigate the high-order harmonic generation (HHG) driven by laser pulses with tri-color carrier wave in the multi-cycle regime. Through the modulation of the carrier wave, the peak of the return kinetic energy of the electron near the pulse center extends dramatically and the other peaks are suppressed by the envelope. Thus, a very broad continuum spectrum appears in the HHG. Moreover, due to the propagation effect, the long path of the electron for the continuum spectrum is eliminated effectively. Hence, the continuum spectrum is well-phase locked, from which an isolated sub-50 attosecond pulse could be obtained even for the driver pulse with duration of 30 fs.     

Generation of carrier-envelope phase-controlled isolated attosecond pulses using chirped femtosecond excitation lasers

ABSTRACT

We present an efficient approach for producing a carrier-envelope phase controlled isolated attosecond pulse by an optimized intense driving laser pulse. High-order harmonics are produced by numerically solving the time-dependent Schrödinger equation for the one-dimensional hydrogen atom in an ultrashort laser pulse. We define an efficient cost function to optimize the laser pulse by a genetic algorithm scheme. Our approach produces single attosecond pulses with desired properties, including the carrier-envelope phase, central frequency, and duration. Also, we analyze the time–frequency profiles of the attosecond emissions to gain a deeper insight into the underlying physical mechanism.     

Shaping polarization of attosecond pulses via laser control of electron and hole dynamics

We show how laser control over both electronic and hole dynamics in aligned molecules can be used to shape polarization of attosecond pulses produced via high harmonic generation driven by two-color, linearly polarized laser fields.     

Hyperbolic chaos generator based on coupled drift klystrons

A scheme of the generator of chaotic oscillations in the microwave band is proposed that is based on two drift klystrons coupled in a ring circuit. The first klystron doubles the frequency of the input signal and the second klystron mixes the second harmonic signal and the reference signal representing a periodic sequence of radio pulses filled with the third harmonic, followed by separation of the differential first harmonic signal. As a result, the transformation of the signal phase during the period of pulse repetition is described by a stretching map of the circle (Bernoulli map) and demonstrates chaotic behavior. Results of numerical calculations are presented that confirm the implementation of the proposed mechanism to ensure the generation of robust, structurally stable chaos in the system under consideration.     

Subharmonic emissions from microbubbles: effect of the driving pulse shape

The aims of this work are to investigate the response of the ultrasonic contrast agents (UCA) insonified by different arbitrary-shaped pulses at different acoustic pressures and concentration of the contrast agent focusing on subharmonic emission. A transmission setup was developed in order to insonify the contrast agent contained in a measurement chamber. The transmitted ultrasonic signals were generated by an arbitrary wave generator connected to a linear power amplifier able to drive a single-element transducer. The transmitted ultrasonic pulses that passed through the contrast agent-filled chamber were received by a second transducer or a hydrophone aligned with the first one. The radio frequency (RF) signals were acquired by fast echographic multiparameters multi-image novel apparatus (FEMMINA), which is an echographic platform able to acquire ultrasonic signals in a real-time modality. Three sets of ultrasonic signals were devised in order to evaluate subharmonic response of the contrast agent respect with sinusoidal burst signals used as reference pulses. A decreasing up to 30 dB in subharmonic response was detected for a Gaussian-shaped pulse; differences in subharmonic emission up to 21 dB were detected for a composite pulse (two-tone burst) for different acoustic pressures and concentrations. Results from this experimentation demonstrated that the transmitted pulse shape strongly affects subharmonic emission in spite of a second harmonic one. In particular, the smoothness of the initial portion of the shaped pulses can inhibit subharmonic generation from the contrast agents respect with a reference sinusoidal burst signal. It also was shown that subharmonic generation is influenced by the amplitude and the concentration of the contrast agent for each set of the shaped pulses. Subharmonic emissions that derive from a nonlinear mechanism involving nonlinear coupling among different oscillation modes are strongly affected by the shape of the ultrasonic driving pulse.     

Autocorrelation measurements of bursts of picosecond pulses

In a master oscillator power amplifier system a powerful train of pulses can be generated. A simple method is described to measure the duration of these pulses. The measurements have been performed both at the fundamental frequency (1053 nm) and at the second harmonic (527 nm). In accordance with theoretical expectations we have observed a narrowing of the pulse owing to frequency doubling.     

Application of high harmonic radiation in surface science

The development of compact and commercially available table-top, ultra-short pulse laser systems with pulse energies of the order of a few mJ, pulse durations of less then 30 fs and repetition rates of several kHz enables routinely the generation of high harmonic radiation with photon energies up to 100 eV. Thereby many different applications in surface science become possible that benefit from the particular characteristics of this kind of light source. In future, especially time resolved measurements that take advantage of the ultra-short pulses in the femtosecond and attosecond regime will attract considerable attention. Also the access to the whole Brillouin zone will stimulate new, time-resolved experiments. In this paper we will discuss applications of high harmonics to study surface properties using microscopy and photoelectron spectroscopy, and highlight investigations of dynamic processes in the XUV and soft X-ray regime.     

Isolated attosecond pulse generation with the chirped two-color laser field

We propose a scheme to generate isolated attosecond pulse using a linearly chirped two-color laser field, which includes a fundamental laser field and a weak infrared control laser field in the multicycle regime. The fundamental laser field consists of one linearly up-chirped and one linearly down-chirped pulses. The control pulse is chirped free. We compare the attosecond pulse generated in the chirped two-color field and the chirp-free field. It is found that an IAP can be generated even without carrier envelop phase stabilization in the chirped two-color laser field with a duration of 40 fs. We also discuss the influence of the relative intensity, relative phase, time delay, and chirping parameters on the generation of IAPs.     

Distortion cancellation of frequency converted pulses with simple linear signal processing and application to frequency modulation to amplitude modulation conversion in high power lasers

It is known that a linear filter may be easily compensated with its inverse transfer function. However, it was shown that this approach could also be valid even for such a complex nonlinear system as frequency conversion. As a matter of fact, it is possible to at least partly precompensate for distortions occurring within, or even downstream from, frequency conversion crystals with a simple linear optical filter set upstream. In this paper, we give the theoretical background and derive the optimum precompensation filter from simple analytical formulas even in the case of saturation. We first show the relevance of our approach for Gaussian pulses: the pulse may be short or not and chirped or not, and the same linear precompensation filter may be used as long as saturation is not reached. We then study the case of phase-modulated pulses, as can be found on high power lasers such as lasers for fusion. We show that previous experimental results are in perfect agreement with these calculations. Finally, justified by our simple analytical formulas, we present a rigorous parametrical study giving the distortion reduction for any second and third harmonic generation system in the case of phase-modulated pulses.     

A second-order autocorrelator for single-shot measurement of femtosecond laser pulse durations

A second-order autocorrelator for single-shot measurement of ultrashort laser pulse durations has been set up. It is based on recording the spatial profile of non-collinear phase-matched second harmonic generation in a KDP crystal using a CCD camera-framegrabber combination. Performance of the system is described from measurement of 250 femtosecond transform-limited laser pulses from a passively mode-locked, diode pumped Nd:glass laser. It can also be used for measurement of picosecond laser pulses in the multi-shot scanning mode.     

Nonlinear propagation of ultrasound through microbubble contrast agents and implications for imaging

Microbubble contrast agents produce nonlinear echoes under ultrasound insonation, and current imaging techniques detect these nonlinear echoes to generate contrast agent images accordingly. For these techniques, there is a potential problem in that bubbles along the ultrasound transmission path between transducer and target can alter the ultrasound transmission nonlinearly and contribute to the nonlinear echoes. This can lead to imaging artefacts, especially in regions at depth. In this paper we provide insight, through both simulation and experimental measurement, into the nonlinear propagation caused by microbubbles and the implications for current imaging techniques. A series of investigations at frequencies below, at, and above the resonance frequency of microbubbles were performed. Three specific effects on the pulse propagation (i.e., amplitude attenuation, phase changes, and harmonic generation) were studied. It was found that all these effects are dependent on the initial pulse amplitude, and their dependence on the initial phase of the pulse is shown to be insignificant. Two types of imaging errors are shown to result from this nonlinear propagation: first, that tissue can be misclassified as microbubbles; second, the concentration of microbubbles in the image can be misrepresented. It is found that these imaging errors are significant for all three pulse frequencies when the pulses transmit through a microbubble suspension of 6 cm in path length. It also is found that the first type of error is larger at the bubble resonance frequency.     

Design of an extreme-ultraviolet monochromator free from temporal stretching

High-order harmonic generation in gases by use of femtosecond lasers is a source of ultrashort pulses in the extreme-ultraviolet (XUV). For many applications it is necessary to select radiation of only one specific harmonic order without affecting the duration of the ultrashort pulse. A three-grating monochromator that meets this demand has been designed and modeled by ray tracing as well as by wave-optical simulations. The only remaining temporal stretching of an XUV pulse is due to distortion of the pulse front on the gratings and is predicted to be approximately 1 fs. The design has been successfully tested in the near infrared. Finally, the monochromator is also capable of eliminating any existing linear chirp in the harmonic pulses, thus compressing them to shorter durations.     

Generation of Fourier-transform-limited 35-ns pulses with a ramp-hold-fire seeding technique in a Ti:sapphire laser

We report on an injection-seeded Ti:sapphire laser pumped by the second harmonic of a Nd:YAG laser. The resonance between the low-power seed laser and the slave cavity is achieved by a ramp-hold-fire technique. Because of the triangular cavity design, the spatial beam profile is excellent; and combined with the narrow-linewidth pulses, the conversion efficiencies for nonlinear frequency generation are excellent.     

Passive harmonic mode-locking of a fiber laser at controllable repetition rates from fundamental to eighth-order harmonic operation

We have experimentally reported a passively harmonic mode-locked fiber laser at controllable repetition rates. The pulse train is continuously tunable and controllable from the fundamental cavity frequency to the eighth-order harmonic frequency. The pulses in the proposed laser disappear one by one when the pump power is decreased and, at the same time, the remaining pulses self-organize into a new, stable, uniform distribution in the cavity at each state. The experimental results indicate a supermode suppression of more than 40 dB. By appropriately increasing the coupler output ratio and lengthening the laser cavity, the enhanced mutual influence of the global and local soliton interactions induced by the CW components and the dispersive waves plays the key role in separating pulses stably and uniformly in the cavity. Our laser has the potential to generate chirp-free pulses at even higher rates and shorter pulses for use in future time-division multiplexing systems.     

Contrast imaging by non-overlapping dual frequency band transmit pulse complexes

SURF contrast imaging, as described previously in the literature, is a contrast agent detection technique achieved by processing of the received signals from transmitted dual frequency band pulse complexes with overlapping high-frequency (HF) and low-frequency (LF) pulses. The transmitted HF pulses are used for image reconstruction, whereas the transmitted LF pulses are used to manipulate the scattering properties of the contrast agent. As with harmonic contrast agent detection techniques, nonlinear wave propagation will, in most situations, also limit the specificity with the SURF contrast technique when transmitting overlapping HF and LF pulses. The present paper proposes an alternative SURF contrast imaging technique using transmit dual frequency band pulse complexes with non-overlapping HF and LF pulses. If the frequency of the LF manipulation pulse is close to the bubble resonance frequency, numerical simulations indicate a significant ring-down effect of the LF bubble radius response. Utilizing this bubble ring-down effect and transmitting the HF pulse just after the LF pulse, a contrast agent specificity approaching infinity accompanied by a contrast agent sensitivity only for contrast bubbles having resonance frequencies within a narrow frequency range may be obtained.     

Generation of isolated attosecond pulses using unipolar and laser fields

A new scheme to generate isolated attosecond pulses is presented that involves the use of a laser field and of a unipolar field. The laser field has a pulse of intensity I = 1.5×10¹⁴ W cm^?2 and wavelength λ = 820 nm. The unipolar pulse is an asymmetric pulse consisting of a sharp peak, lasting approximately half a laser period, i.e. nearly 1.4 fs, followed by a long and shallow tail. We show that on combining these two fields, it is possible to generate isolated attosecond pulses as short as 1/10 of a laser period, i.e. approximately 270 as. Moreover, it is argued that this scheme is robust either against small variations of the laser envelope, or against small changes in the delay between the laser pump and the unipolar pulse.