AbstractThe attosecond light pulse generation method won the 2023 Nobel Prize in Physics and attracted widespread interest. The attosecond pulse is obtained by generating high-order harmonics from femtosecond pulses of the periodic order, which requires many key technologies, including femtosecond pulse compression, stable control of pulse carrier phase, and improvement of pulse intensity. This paper briefly introduces the generation method of attosecond pulse, its development trend and application.
Key words: attosecond pulse, higher harmonic, periodic order of magnitude pulse, carrier envelope phase
The 2023 Nobel Prize in Physics has been announced, and the long-awaited experimental method for the generation of attosecond pulses has finally been awarded.
Five years ago, in 2018, the Nobel Prize in Physics was awarded to Gerard Mourou and his students. The reward is femtosecond pulse chirp amplification technology. It is precisely because of the chirped pulse amplification technology that people can obtain high-energy femtosecond pulses that drive higher harmonics to produce attosecond pulsesThe Nobel Prize in Physics dating back to 2005 has shown that the pulse envelope phase control technology in the optical frequency comb technology is precisely the key to obtaining isolated attosecond pulses.
Attosecond pulse generation conditions.
The conditions for generating attosecond pulses are the same as those for femtoseconds, and there must first be a spectrum wide enough to support such short pulses. According to the time-bandwidth product (δδ1), the pulse width is inversely proportional to the spectral width, i.e., the shorter the pulse, the wider the spectral width required. To get attosecond pulses of less than 1 fs, a bandwidth greater than 10 Hz is required. At the same time, the carrier wave needs a higher frequency.
From the perspective of the period of the pulse carrier, the width of the pulse cannot be less than the oscillation period of an optical carrier. When the oscillation period of light is 1 fs, the frequency is 10 Hz, and the corresponding wavelength is 300 nm. Therefore, to break the femtosecond barrier, the wavelength needs to be shortened to the ultraviolet or X-ray band.
Conventional laser media obviously do not meet this condition. First of all, solid-state laser media operate at wavelengths from visible to infrared, and the laser spectrum generated from a single laser medium, such as titanium-sapper, can only support pulses of the order of 5 fs. Even the entire visible light spectrum can only support 3 fs pulses. For gas lasers, such as excimers, the spectral bandwidth is not wide enough to support attosecond, although in the ultraviolet band.
Since the existing laser medium cannot support attosecond pulses, the method of extracavity expansion can only be used. There are at least two ways to dramatically expand the spectral range. One is cascaded Raman and the other is higher harmonics. Both optical harmonic generation methods will have a very wide multi-level spectrum across wavelength bands. Is it possible to obtain attosecond pulses from their synthesis?
Cascade Raman is a series of spectra in hydrogen (and its isotopes) that are produced using a cascade of molecular vibrational frequencies that are equally spaced and can be extended to ultraviolet light. For example, in deuterium gas, a bandwidth of 2Multi-stage Raman spectroscopy at 3 phz. Unfortunately, there is no evidence of a fixed bit difference between these Raman components, making it difficult to synthesize a pulse. It has been claimed that pulses of 200-700 as were obtained with an interval of 94 fs. The problem is that there is no evidence that these discrete spectra have a fixed phase relationship.
Fig.1 Schematic diagram of the three-step model of the principle of higher harmonic generation: ionization;Acceleration;Compound.
The principle of generating higher harmonics, as shown in Figure 1, is generally explained by a three-step model: ionization, acceleration, and recombination. Intense light pulses ionize atoms, electrons accelerate to gain energy in the light field, and in the recombination process, electrons will release their kinetic energy in the form of shorter wavelength light pulses, and this radiation in the soft X-ray band is the higher harmonic.
It is not only femtosecond pulses that can produce higher harmonics, as long as the peak power is high enough, a series of odd harmonics at equal intervals can be generated, it is just a matter of how high or low the cut-off frequency is. Although some people claim to have synthesized and measured attosecond pulses with higher harmonics, a closer look reveals that they are only doing linear autocorrelation, i.e., measuring spectral coherence time, not pulse duration.
The attosecond pulse is in each harmonic.
Anne L'Huilier's contribution is that as early as the late 1980s, she discovered that there is no need to synthesize those harmonics to make attoseconds, but that each harmonic itself is an attosecond.
Pierre Agostini used the two-photon ionization cross-correlation method or Rabbitt (reconstruction of attosecond beating by interference of two-photon transitions) method to measure the amplitude and phase of the electric field of the higher harmonic pulses, and reconstructed the time-domain waveform of the pulse, so as to obtain an average pulse duration of 250 as and a pulse interval of 1.35 fs (Figure 2).
However, the time interval between these harmonic attosecond pulses is very close, and no high-speed optical switch has been found that can separate one of the attosecond pulses.
Fig.2 The amplitude and phase of the electric field measured by Agostini et al. using the rabbitt method for five harmonics from the 11th to the 19th, and then reconstructed pulse time-domain waveforms. The half-height width of each peak is 250 as, and the interval is 135 fs。The cosine function waveform (dashed line) represents the IR probe electric field at zero delay.
A supercontinuum near the cut-off frequency.
As early as 1996, Margret Murnane et al. found that the spectral width of higher harmonics increases as the pulses that excite higher harmonics are continuously shortened. When the pulse is shortened to the order of the period, the higher harmonics near the cut-off frequency are unexpectedly joined together to form a small supercontinuum. As shown in Figure 3, when the pulse is shortened from 30 fs to 7 fs (relative to 2. at a wavelength of 800 nm).6 optical periods), the waveforms of the higher harmonics are connected.
Fig.3 Higher harmonics generated by the incident of laser light with different pulse widths into neon gas.
Ferenc Krausz's group further demonstrated that the spectra near the cut-off frequency are only connected when the carrier envelope of a periodic order of magnitude pulse is equal to 0 (Figure 4). The advantage of being near the cut-off frequency is that the small supercontinuum after the cut-off frequency can be separated by spectral filtering. This is known as an "isolated" attosecond pulse.
Fig.4 In the numerical simulation of the high-order harmonic soft X-ray spectra excited by periodic pulses, the shaded curve at the bottom of (a-d) is the variation of the higher-order harmonic radiation spectrum with the carrier envelope phase in the cut-off frequency range. In (a), when the carrier envelope phase () is 0, the higher harmonics in the cut-off frequency region are connected, and the other curve is the continuum filtered out by the Gaussian filter.
Shortening the pulse to a single cycle was not too difficult at the time. When the prism compression pulse reached its limit, Krausz of the Technical University of Vienna and his compatriot Robert Szipocs, who works at the Hungarian Institute of Physics, proposed to compensate for the dispersion in the laser cavity with a so-called chirped mirror, in which the Szipocs were responsible for the coating. Using this chirp mirror, Krausz ended up with a pulse of about 5 fs, or quasi-single-cycle. The use of chirp mirror technology to compensate for dispersion in the laser cavity, or even outside the laser cavity, is an important step towards single-cycle pulses. The chirp mirror is still a very important dispersion compensation element to this day.
Although the pulses coming out of the laser oscillator reach the order of periods, the pulse energy is only about 1 nj. Such low pulse energies are not sufficient to excite higher harmonics. Fortunately, chirped pulse amplification technology is already a conventional technology, which can amplify the pulse to the order of millijoules. However, due to gain narrowing and residual dispersion, the amplified pulses can only be compressed to 30 fs.
Nisoli et al. from the Polytechnic University of Milan have found that ionization of noble gases can break through the limitation of the gain medium on the pulse spectrum. They proposed to use an air-core fiber with a diameter of about 100 m filled with inert gas to expand the spectrum. The hollow core fiber with a length of tens of centimeters can not only maintain a single transverse mode spot, but also has a small dispersion, and can be compressed with a chirp mirror. They end up with a pulse energy of a few hundred microjoules, and it's a quasi-single-cycle pulse.
But how do you control the carrier envelope phase of the pulse to zero?
Carrier envelope phase control and optical frequency combing.
When the pulse is shortened to the order of the cycle, that is, under the envelope of the pulse, there is only one carrier period, whether the peak of the carrier and the envelope corresponds is very important. Because in such a short pulse, it is the electric field of the pulse, not the envelope, that is at work. The strength of the pulse depends on whether the two peaks coincide. Only when these two peaks coincide can the strongest electric field be obtained.
In the schematic diagram of the carrier envelope phase (Fig. 5(a)), there is the carrier-envelope phase phase, which depends on the difference in group velocity and phase velocity due to dispersion in the laser cavity. With such a small bit difference, it is difficult to make time-domain measurements within one period of the carrier.
The method of measurement was proposed by Ursula Keller of the Swiss Federal University of Technology. The group she led used the Fourier transform to derive the relationship to the initial frequency, and named it. In the MHz range, it can be easily measured in the frequency domain, and the fundamental frequency-octave-beat frequency method (-to-2) was invented to measure it. This method also provides a key technology for the formation of optical frequency comb.
Fig. 5 (a) Schematic diagram of carrier envelope phase difference(b) The initial frequency of the frequency domain and a fundamental frequency and its multiplication.
Figure 5(b) shows this approach. In a spectrum beyond the octave, each frequency is an integer multiple of a frequency interval plus an initial frequency. When a certain optical frequency is doubled by a nonlinear crystal, there are two, while there is only one frequency in the spectrum that is 2 times the frequency near this fundamental frequency. The beat frequency of these two frequencies, that is.
In 2001, Krausz et al. made a 650 AS isolated attosecond pulse under various techniques. At present, the shortest pulses are in the range of 43-53 as.
The attosecond pulse drives the evolution of the light source.
Around 2010, the study of attosecond pulses changed a lot. Prior to 2010, titanium-sapphire lasers were standard and well-established attosecond pulse-driven light sources. The pulse energy is in the tens of millijoules and the repetition rate is within 1 kHz. Because of the short wavelength, the cut-off frequency is limited to around 100 ev. At the same time, the repetition rate is relatively low, limiting the average power it can produce attosecond pulses.
Since 2010, the mid-infrared parametric chirped pulse amplifier (OPCPA), which is conducive to increasing the cut-off frequency and repetition rate, has been used as the main research direction to drive the light source. However, it causes the driving wavelength to lengthen, the electron beam to diverge, and the higher harmonic order to increase, resulting in a sharp decrease in the efficiency of generating attosecond pulses.
To compensate for the loss in efficiency, the main focus has been on increasing the intensity and repetition rate of the driving light source. Mature femtosecond fiber or disk lasers with a repetition rate of 100 kHz and an average power of more than 1 kW, together with multi-cavity expansion and pulse compression, become the driving light source of the new attosecond pulses, which greatly increases the repetition rate and average power of attosecond pulses. On the other hand, the optical field synthesis technology, which autonomously controls and drives the pulsed light field waveform, can also improve the efficiency of attosecond laser generation.
Attosecond science has a bright future.
Due to the long wavelength of the driving light source, the photon energy of the attosecond pulse expands to more than 1 kev, and the pulse width also develops to 24 as per atomic unit time. This has changed the application of attosecond pulses a lot.
1) With the increase of the number of attosecond pulsed photons, small changes in the nanoscale of nanomaterials can be observed in a single pulse, making ultra-high-speed imaging with subfemtosecond resolution possible.
2) With the increase of attosecond pulse intensity, it is possible to expand to the soft X-ray band with multi-dimensional imaging techniques with nonlinear optical effects such as surface frequency doubling and four-wave mixing of ultrashort pulses. This is very important for understanding the chemical reactions and catalytic mechanisms of surfaces and interfaces.
3) With the expansion of the cut-off wavelength, if the X-ray absorption microstructure near the absorption end and the broadband X-ray absorption microstructure can be measured simultaneously, the electron dynamics and structural changes can be continuously measured with a single attosecond light source. Light-induced phase transitions, structural changes, and other long-standing topics in solid-state physics will have new research methods.
4) With the expansion of cut-off wavelengths, attosecond pulses can be used to study larger molecules in the fields of photochemistry and life sciences. In particular, with the increase in the number of photons at the wavelength of the water window, changes in DNA and protein biomolecules can be captured in the near-natural state of the aqueous environment, which will help to understand the light-induced reaction kinetics and develop control methods.
At the same time, attosecond pulses of circularly polarized light and vortex light with orbital angular momentum are also being carried out, which may play an important role in the study of chiral molecules and magnetic materials. In particular, if circular polarization of sub-KEV energy can be made, the research and development of magnetic materials, especially ultra-high-speed magnetic devices, can be accelerated.
At present, the ELI-ALPS (Extreme Light Infrastructure Attosecond Light Pulse Source), an advanced attosecond light source in Europe, has started operation. In 2013, the Institute of Physics of the Chinese Academy of Sciences realized a 160 as isolated attosecond pulse measurement experiment. The Xi'an Institute of Optics and Fine Mechanics of the Chinese Academy of Sciences independently developed a high-energy resolution attosecond fringe camera, which generated and measured an isolated attosecond pulse of 159 as, and the National University of Defense Technology reported an isolated attosecond pulse of 88 as in 2020. Huazhong University of Science and Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Institute of Modern Physics, Chinese Academy of Sciences, China Academy of Engineering Physics, Beijing Institute of Applied Physics and Computational Mathematics and other research units have also carried out a large number of experimental and theoretical studies on attosecond physics, and some have built attosecond research bases or platforms. These bases, or platforms, can not only generate attosecond pulses, but also provide services for a wider range of applications.
Author: Zhang Zhigang.
School of Electronics, Peking University).
This article is selected from Physics, Issue 12, 2023.
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