ОПТИКА И СПЕКТРОСКОПИЯ, 2015, том 118, № 4, с. 604-618
^ НЕЛИНЕЙНАЯ ^^^^^^^^^^^^
И КВАНТОВАЯ ОПТИКА
УДК 535.2
LASER HARMONIC ENHANCEMENT USING THE QUASI-PHASE-MATCHING IN LASER PLASMA
© 2015 г. R. A. Ganeev
Ophthalmology and Advanced Laser Medical Center, Saitama Medical University, Saitama 350-0495, Japan
E-mail: rashid_ganeev@mail.ru Received June 6, 2014
The recently developed quasi-phase-matching techniques for the high-order harmonics generating in the multiple plasma jets produced on the surfaces of various targets are reviewed. The achievement of 40* enhancement of the quasi-phase-matched harmonics of 804 nm radiation in the range of 35th harmonic in the cases of metal plasmas is analyzed. We demonstrate various approaches in formation of the multi-jet structures during laser ablation by applying the perforated targets and multi-slit shields.
DOI: 10.7868/S0030403415040054
1. INTRODUCTION
Creation of the coherent extreme ultraviolet (XUV) radiation sources through the harmonic generation by different means and using the gases and surfaces, as nonlinear media, is a well elaborated technique, though it shows the low efficiency of those sources. In the meantime, the relatively high efficiencies of generating harmonics obtained using several plasma formations, resonance-induced enhancement of individual harmonics, efficient harmonic generation from the plasma plumes contained the clusters of different materials, and other features have demonstrated the attractiveness of the high order harmonic generation (HHG) in the laser produced plasmas. The harmonic yield from plasmas has been markedly increased by proper optimization of the (a) intensity of the heating pulse, (b) delay between the heating pulse and driving femtosecond pulse, (c) focal position of the driving radiation in the plasma plume, (d) pulse duration of the heating radiation, (e) chirp of the driving radiation, (g) plasma characteristics, and (f) use of the nanosized targets [1].
The maj ority of plasma harmonic studies were carried out using the short length plasma plumes (<0.5 mm). In the meantime, one could expect that the application of longer plasmas would further enhance the conversion efficiency due to the quadratic dependence of the nonlinear optical response of the medium on the length of the laser-matter interaction. To create an extended ablated area on the target surface one has to carefully choose the conditions of plasma formation. The absorption of extended plasma can prevent the enhancement of harmonic yield. The presence of free electrons and excited ions in the extended plasma plumes can cause the growth of the phase mismatch between the driving and harmonic waves during prop-
agation of the laser pulse through the medium. One of the ways to overcome the latter obstacle is a division of extended plasma onto a group of small jets to create a condition for the quasi-phase-matching (QPM) between the interacting waves. The concept of the QPM for the HHG in the multi-jet media has previously been demonstrated using the gaseous media [2—4], while various peculiarities of this technique have been reported in [5—11].
The HHG of laser radiation in the extended gaseous media has long been considered as an inefficient process due to exceeding of the medium length over the coherence length (Lcoh) of HHG. Across a distance equal to the Lcoh a phase mismatch of n grows and causes destructive interference between the driving and harmonic waves. This process is one of the major limitations of the HHG conversion efficiency, especially in the case of abundant presence of the free electrons in the medium. QPM either "reversing" or cancelling the nonlinear process in the medium region where the polarization and the harmonic field are initially out of phase. In "perturbative" nonlinear optics, QPM is routinely used to correct the phase mismatch, e.g., by reversing periodically the orientation of the nonlinear crystal at intervals Lcoh. For gas harmonics in the XUV region, QPM aims at cancelling the out-of-phase emission. As it has been shown in multiple gas jet schemes, once the waves depart from the medium, their phase flips [3, 4]. The process of frequency conversion can then be efficiently continued in another bunch of medium.
Returning back to plasma formation, the assumption on the enhancement of harmonic yield using extended media is correct for the moderate excitations of target surfaces, while, at high fluences of heating ablation pulse, the abundance of the free electrons appear-
ing in plasma may cancel the advantages of this extended nonlinear optical medium. A growth of plasma concentration using the increase of the fluence of heating pulse may decrease the harmonic yield because the phase mismatch causes a destructive interference of the harmonic photons generated in the first half and the second half of the extended source. The onset of destructive interference can be shifted to higher plasma densities, and hence enhanced harmonic yields, by subdividing the overall interaction length of plasma d into M sections of thickness d/M and moving them apart such that diffraction induced changes in the laser phase and amplitude between two adjacent sections can shift the phase of the atomic dipole oscillations by n (at the input of the next section with respect to the exit of the previous one) for the qth harmonic. This approach embodies the basic concept of QPM.
As in the case of gas medium, separation of the extended plasma plume into a few small sized plasma jets may restore the proper phase relationship between the driving and harmonic waves and give way for further enhancement of the yield in different XUV spectral ranges. To create QPM conditions, one has to maintain a modulation of the coupling between the driving and harmonic waves, which is periodic along the generation path. At these conditions, the enhancement of harmonics will occur only when the interference between propagating signal and newly generated signal becomes constructive.
The attractiveness of the application of the QPM for the amendment of plasma HHG is related with the adjustment of the electron concentration (Ne) in the periodically modulated plasma plume by the "optimal excitation" of the ablating target. The variation of Ne allows the manipulation of the coherence length of harmonics in different spectral ranges. The adjustment of Ne could be easily accomplished during harmonic generation in the plasma medium through the proper variation of the fluence of ablating beam on the target surface to achieve a required concentration of the free electrons in the plasma jets.
Among the approaches for plasma harmonic QPM one can consider the following techniques: (a) use of the microlithografic targets, analogously to those suggested in [12], (b) interference of the two heating beams on the target surface with variable distance between the maximums of interference pattern, (c) use of the perforated targets allowing a separation in time for the plasma jets to reach the axis of propagation of the driving beam, (d) use of the multiple strips with different distance between them as the shields installed in front of the ablating targets, which allows achieving the adjustable separation between the multiple plasma jets. Until recent time, all these approaches for plasma harmonic QPM have yet been analyzed experimentally, whilst their application would allow the optimization of the active areas of plasmas to match with the
coherence lengths of different groups of harmonics. In this review, we will discuss the findings reported using the (c) and (d) approaches.
The optimization of multi-jet formation for HHG requires the manipulation of the relative phases of driving and harmonic waves. One of the ways, which can change a dephasing between these waves, is an application of additional driving field. The use of two-color pump schemes is a well known approach for the broadening of the spectrum of generated XUV radiation and the enhancement of the harmonic yield [13— 15]. This peculiarity has been demonstrated long time ago [16] and currently it is a well elaborated technique.
The two-color pump using fundamental and second harmonic fields has become a practical way of harmonic enhancement in the gas media [13—19]. It can generate odd harmonics, which are stronger than those with the fundamental field alone. Moreover, it simultaneously generates the even harmonics. As underlined in [15], a strong harmonic generation in the case of a two-color field is possible due to the formation of a quasi-linear field, the selection of a short quantum path component, which has a denser electron wave packet, and the high ionization rate. With suitable control of the relative phase between the fundamental and second harmonic waves, this combined field significantly enhances the short path contribution while diminishing other electron paths, resulting in a clean high-harmonic spectrum. This approach has also been applied for plasma harmonic generation as well. In [20], the first observation of the growth of harmonic conversion efficiency from the plasma plumes irradiated by an intense two-color femtosecond laser beam, wherein the fundamental field and its weak second harmonic (at the energy ratio of 50 : 1) were linearly polarized orthogonal to each other, was reported. One can assume the importance of the correlation between the phases of two pumps and harmonics at the conditions of QPM in multi-jet plasma.
There is another reason for investigation of the plasma QPM using two driving pulses. In the case of plasma plumes, the two-color pump scheme offers the opportunity in observation of the resonance induced enhancement at the additional wavelengths coinciding with the even harmonics, as has been demonstrated using the narrow plasma plumes [21]. This effect could be both emphasized, or diminished in the extended plasmas. The propagation effects can start to play a decisive role
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.