New Approaches in Frequency Conversion of Laser Radiation in Plasma Plumes

Rashid A. Ganeev

Institute of Ion-Plasma and Laser Technologies, Tashkent, Uzbekistan.

DOI: 10.4236/opj.2013.34041                

Abstract

Recent studies of plasma harmonic generation are reviewed. We show the advances of this technique for generation of coherent ultrashort pulses in the extreme ultraviolet range. Among the achievements highlighted in this review are the comparative experimental and theoretical studies of high-order harmonic generation in silver plasma, isolated subfemtosecond pulse generation in Mn plasma ablation, stable generation of high-order harmonics of femtosecond laser radiation from laser produced plasma plumes at 1 kHz pulse repetition rate, and high-order harmonic generation in fullerenes using few- and multi-cycle pulses of different wavelengths. We show that new developments of plasma harmonic studies can lead to the creation of an attractive field of laser ablation induced high-order harmonic generation spectroscopy.

Keywords

High-Order Harmonic Generation; Laser Plasma; Ultrashort Laser Pulses

1. Introduction

Coherent short wavelength radiation is of increasing importance for a broad variety of basic and applied research in various fields of physical, chemical, and life sciences. Among them, femtosecond time-resolved coherent diffractive imaging and photo-induced processes at surfaces and nanoparticles, as well as lithography, plasma diagnostics, and materials processing and diagnostics are of foremost interest. The high-order harmonic generation (HHG) from femtosecond laser pulses allows producing coherent radiation in the extreme ultraviolet (XUV) spectral range. Table-top lasers render these processes possible with the prospect of wide-spread scientific applications. Presently, predominantly few gases are employed as target media for HHG. Other efforts rely on the creation of harmonics at solid surfaces, either by a coherent wake field excitation or, for petawatt class lasers, on a relativistically moving electron gas acting as a plasma mirror. So far, however, only low conversion efficiencies have been obtained, despite the enormous efforts. Other methods include XUV free-electron lasers and X-ray lasers.

To promote the use of XUV radiation it seems therefore appropriate to advance laboratory scale sources to a higher application level. Many interesting experiments can be performed by HHG based on laboratory scale femtosecond lasers. These sources may cover the spectral range between 10 and 100 eV photon energy of harmonics, and with few-cycles laser systems even up to several 100 eV. For practical applications of high-order harmonic sources higher conversion efficiency and thus an increase in the photon flux and also of the maximum photon energy of the harmonic radiation would be beneficial. HHG itself can be used as a spectroscopic tool for analysis of the optical, nonlinear optical and structural properties of the emitters of harmonic generation presently comprising on a few noble gases. The generation of high-order harmonics in laser-produced plasmas from various solid-state targets, being for this purpose a relatively new and largely unexplored medium, promises to yield these advances.

Most interestingly, recent studies have shown that enhanced high-order harmonics can be generated also from the ablated nanoparticles, which opens the prospects for applications of local field enhancement, broad plasmonic resonances and a more efficient recombination processes for plasma HHG. As a highly interesting perspective an increase of the harmonic output by quasi phase matching in specially prepared plasmas may be considered. For the plasma a different and more flexible technique than used in neutral gases can be applied. The plasma may be spatially modified using a long pulse co-propagating with the fundamental driving pulse, and conditions might be found where quasi phase matching is possible over a long distance in the plasma, while the constructive and destructive interference of harmonic waves in such plasmas containing different emitters can provide a new knowledge about the phase-related characteristics of this process. Thus the above approach can be useful for producing an efficient source of short-wavelength ultra-short pulses for various applications and studies of the properties of harmonic emitters. The laser ablation induced high-order harmonic generation spectroscopy is a new method for the studies of material science and can be considered as one of the most important applications of HHG.

In this review, we discuss the realization of new ideas emerged during last few years, which further improved the HHG efficiency through harmonic generation in specially prepared plasmas and allowed the spectral and structural studies of matter through the plasma harmonic spectroscopy. We also present the current status of plasma HHG studies, and show new trends and perspectives in the developments of this filed.

The structure of the review is as follows. In Section 2, the comparative experimental and theoretical studies of high-order harmonic generation in silver plasma are discussed. Isolated sub-femtosecond pulse generation in the XUV range using Mn plasma ablation is analyzed in Section 3. Section 4 is devoted to the methods of stable generation of the high-order harmonics of femtosecond laser radiation from laser produced plasma plumes at 1 kHz pulse repetition rate. HHG in fullerenes using fewand multi-cycle pulses of different wavelengths is discussed in Section 5. Short summary remarks presented in Section 6 give some clues on future developments and perspectives of this interesting field of optics.

2. Studies of HHG Cut-Off in Silver Irradiated by Femtosecond Pulses

In this Section, we present the results of theoretical and experimental study of HHG in the ensemble of silver particles irradiated by intense femtosecond pulses of Ti:sapphire laser. It is shown that the photoemission spectra exhibit unusual behavior when the laser field strength approaches near-atomic values. In subatomic field strength the cut-off frequency increases linearly with laser pulse intensity. However, when the field strength approaches near-atomic region firstly cut-off frequency slows down and then saturates. To give new interpretation of such kind of photoemission spectrum behavior the light-atom interaction theory based on the use of eigenfunctions of boundary value problem for “the atom in an external field” instead of the traditional basis of the “free atom” eigenfunctions has been proposed.

In spite of the twenty-year history, the effect of the HHG is still under a great interest of both experimentalists and theoreticians. The origin of this interest is manifold. From a practical point of view, the HHG is one of the effective mechanisms for producing a coherent emission in a broad range of electromagnetic wave spectrum. The presence of plateau region in the harmonic amplitude distribution in XUV region affords grounds for development of sub-femtosecond pulse formation methods. As a result, the new frontiers are opened up in science by extending the nonlinear optics and time-resolved spectroscopy to the XUV range [1] and pushing ultrafast science to the attosecond domain, enabling the XUV spectroscopy and imaging of molecular orbitals [2], surface dynamics [3], and electron motion. The HHG is the reliable route to produce attosecond light pulses [4,5] and is therefore fundamental to attosecond science [6].

At present days, the efficiency of conversion to highorder harmonics is really too small to consider this emission as a real coherent XUV source for biology, plasma diagnostics, medicine, microscopy, photolithography, etc. Hence, the search for ways of increasing the cut-off frequency and the HHG efficiency in the XUV spectral range is still among the most topical problems of nonlinear optics.

The plasma HHG was observed with the large number of periodic table elements having usually small and middle atomic numbers [7-12]. As a rule, the interaction medium is a laser plasma that is prepared by irradiation of metal surface by picosecond pulses. The maximum harmonic order, or the cut-off frequency (CF), obtained in plasma media to date varies from the sixties to seventies harmonics of fundamental frequency [12] of Ti:sapphire laser. The highest-order harmonics (the 101^st harmonic, λ = 7.9 nm) have been obtained in manganese plasmas [9]. The efficiency of conversion in the plateau region amounts to ~10⁻⁵ [10]. This value depends on both atomic energy level diagram and laser pulse parameters (intensity, energy and duration, carrier-envelope phase). The CF movement into the sub-nanometer region promises new possibilities in creating XUV coherent sources. Hence, the study of the CF dependence on the irradiated media properties and external laser pulse parameters is the problem of significant scientific and technical interest. Recently, the CF values corresponding to sixties and above harmonics have been obtained in experiments with silver plasma [10,11] and this stimulated to choose this medium for numerical simulations and compare the obtained results with the experimental data.

The traditional interpretation of the harmonic generation is usually based on the model of three-stage process that comprises the ionization of an atom, the electron acceleration in the electromagnetic field, and its subsequent collision with ion. This process is periodically repeated every half cycle of the electromagnetic wave. The evolution of the ionized electron is usually described with the help of Volkov wave functions or classical mechanics equations. It should be noted, that the use of the Volkov wave functions is due to the temporal evolution of the continuous spectrum electron wave functions in the presence of the laser field. At the same time, the spatial profile of the discrete spectrum wave functions is also changed in the presence of the external electromagnetic field. However, in the limit of zero strength fields the Volkov wave functions are transformed to the free electron wave functions, while the discrete spectrum wave functions became the atomic eigenfunctions. Hence in the weak or zero fields the eigenfunctions of discrete and continuous spectra are not mutually orthogonal and they do not compose the complete basis of the orthogonal functions. This is the most principle inconsistence of the above methods.

In those studies, the analysis was focused on the single silver atom photoemission spectra [13]. The most unusual feature of the single atom photoemission spectra is the CF saturation effect. The CF saturation means that the maximum observed harmonic order ceases to be intensity dependent at. For the first time, the effect of the CF saturation in silver plasma was experimentally observed in [10]. The maximal order of experimentally observed harmonic is equal to 71. On the other hand, the results of computer simulations performed for the single silver atom [14] have shown that the CF is saturated in the region of over atomic field strength, but at near atomic field strength the maximal order of generated harmonics is much higher than that observed experimentally. The main purpose of the presented study is to explain the difference between the experimental and theoretical results and to provide the interpretation of the main mechanisms lying in the origin of the CF saturation effect.

To study the high-order nonlinearities through the HHG, the silver target was placed inside the vacuum chamber to ignite the plume by laser ablation of this sample. Silver has previously proven to be most efficient medium for production of the plasma plumes where the highest HHG efficiency (8 × 10⁻⁶) in the XUV range was observed [15].

The pump source was a commercial, chirped pulse amplification laser system, whose output was further amplified using a homemade three-pass amplifier operated at a 10 Hz pulse repetition rate. A heating pulse was split from the amplified laser beam by a beam splitter before a pulse compressor (Figure 1). The heating pulse duration was 210 ps. A spherical lens focused the heating pulse on the target placed in the vacuum chamber. The area of ablation was equal to 0.5 mm². The heating picosecond pulse intensity at the target surface was varied in the range of I_pp = (0.5 – 5) × 10¹⁰ W∙cm⁻² by changing the energy of heating pulse. A driving femtosecond pulse at a centre wavelength of 792 nm had the energy of 12 mJ and pulse duration of 150 fs after propagation of the compressor stage. After the proper delay with regard to the heating pulse irradiation (20 - 80 ns), the driving pulse was focused by a spherical lens (f/10) on the ablation plume from the orthogonal direction. The maximum intensity of the driving pulse at the focal spot could reach 6 × 10¹⁶ W∙cm⁻². The position of laser focus was adjusted to be either before or after the laser plume to exclude the influence of considerable ionization of the silver neutrals and ions in laser plume and to maximize the harmonic yield. The intensity of the driving femtosecond pulse (I_fp) at the plasma area was adjusted between 1×10¹⁴ and 1×10¹⁵ W∙cm⁻². The distance between the HHG interaction area and target surface was varied in the range of 100 - 200 mm. The spectrum of generated highorder harmonics was analyzed by a grazing incidence XUV spectrometer with a gold-coated flat-field grating. The XUV spectrum was detected using a microchannel plate (MCP), and the optical output from the phosphor screen was recorded using a charge-coupled device (CCD) camera.

Figure 2(a) shows the image of harmonic spectrum from Ag plasma at the conditions when the femtosecond pulse was focused after the plasma plume. The harmonics up to the 55^th order were routinely observed at these

Conflicts of Interest

The authors declare no conflicts of interest.

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