Optical harmonics generation in low-temperature laser-produced plasmas

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15 February 1997

OPTICS COMMUNICATIONS Optics Communications 135 (1997) 25 I-256

Optical harmonics generation in low-temperature laser-produced plasmas R.A. Ganeev, V.I. Redkorechev, NPO “Akadempribor”,

T. Usmanov

Tashkent 700143, Uzbekistan

Received 5 December 1995; revised version received 3 June 1996; accepted 25 September 1996

Abstract Results of odd harmonics generation (up to eleventh, A = 96 nm) of laser radiation (A = 1.054 nm, T = 3 ps) in a low-temperature atmospheric plasma and a surface plasma in vacuum are reported. Maximum efficiency was achieved for third harmonics generation (r] = 10m3). High-order harmonics generation and frequency conversion optimization depending on radiation and nonlinear media characteristics are considered.

1. Introduction Recent investigations have demonstrated that a plasma is a promising nonlinear medium for the generation of optical harmonics covering a wide spectral range. In addition to traditional nonlinear media - such as KDP, ADP and other crystals, gases, metal vapors, and dyes, as well as ion beams - a laser plasma should make it possible to widen the range of the generated coherent radiation to the VUV part of the spectrum. Nonlinear optical effects (harmonics generation, CARS, etc.) in a weakly excited laser-produced plasma have a number of distinctive features from those in a dense laser plasma produced by high-intensity (1O’6-1O’8 W/cm*) optical fields [ 1,2]. In particular optical harmonics generation (HG) in the visible and near ultraviolet (UV) ranges has been investigated in a laser plasma formed by optical breakdown in gases and on metal surfaces under the action of radiation of 1010-1012 W/cm2 intensities [3,4]. One of the mechanisms increasing significantly the efficiency of multiphoton processes (in particular, harmonics generation) under optical breakdown conditions (or other methods for the excitation of a medium) is an enhancement of high-order nonlinear susceptibilities because of filling of the excited states of atoms and ions [5,6]. A quasi-resonance is then attained between the electronic states of the excited atoms and ions, on the one hand, and the frequencies of the pump radiation, on the other hand. In such 0030-4018/97/$17.00

cases the multiple ionization of a gas by laser radiation as well as by focusing of this radiation in the form of a rare gas jet [7] generates converted radiation in the visible and near ultraviolet parts of the spectrum, and also in the vacuum ultraviolet (VW) range. Recently it was shown [8] that by using various ions very high harmonics, above 400 eV should be possible using low-frequency high-intensity lasers. From the I,,,, = Zp + 31Jpformula (where Zr is ionization energy and Up is the ponderomotive energy) one can expect that for ions with high ionization potentials, low-frequency lasers can generate harmonic radiation with shorter wavelength than in the case of the rare-gas atoms. Recent investigations of harmonics generation and frequency mixing in a plasma [4,8-131 with the aid of independent lasers have demonstrated the importance of the influence of the characteristics of the gas surrounding a target on the efficiency of the nonlinear processes near the target, and also of the possibility of generation of high order optical harmonics in a plasma. Our aim has been to investigate the generation, in a low temperature laser plasma, of harmonics lying in the short wavelength part of the spectrum (IJV and near-VUV). We shall consider the problems of generation of high-order harmonics (up to the eleventh) with the use of one laser, serving both as the heating and probe source and of optimization of the processes of frequency conversion as a function of the characteristics of the radiation and of the nonlinear medium. We

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shall show that this method is promising for the development of efficient sources of short-wavelength coherent radiation.

2. Experimental

135 (1997) 251-256

I PM10

A,

A,

schemes

Several conditions have to be satisfied in the studies of nonlinear optical processes that occur when laser radiation interacts with a plasma. First, since the growth time of a laser plasma ranges from several tens to hundreds of nanoseconds, it is necessary to synchronize the moment of passage of fundamental pulses and the moment of readiness of “optimal” plasma. This term means the conditions of the laser plasma characterized by certain parameters (such as degree of ionization and excitation of atoms and ions, plasma reflection coefficients at the frequencies of the probe and generated radiation, etc.) which satisfy efficient development of nonlinear optical processes. The main parameter in the case of HG of a probe radiation in an atmospheric plasma and in a surface plasma in vacuum is the degree of excitation of the nitrogen and oxygen molecules and of the target atoms. This parameter affects the high-order nonlinear susceptibilities responsible for the efficiency of HG in these media. Second, the location of the focusing volume of the probe radiation with respect to different zones of the plasma is of considerable importance [ 11,131. An optimization of the frequency conversion is accomplished by adjusting the distance between the target surface and “plasma-radiation” interaction zone. Third, depending on the experimental geometry, it is possible to create a point-like plasma as well as an extended one. This also depends on the selection of the optimal conditions of the frequency conversion in a lowtemperature laser plasma. In view of this situation and with the aim of identifying the conditions for efficient generation of harmonics of laser radiation, we carried out two series of experiments on a laser-produced atmospheric plasma and on a surface plasma in vacuum, which differed with respect to the nature and geometry of the action of the heating radiation. 2.1. Harmonic generation in a surface atmospheric plasma A neodymium phosphate glass laser with passive mode locking (solution of soviet dye 3274-u in ethanol) generated a train of pulses (A = 1.054 nm) of 8 ps duration. The separation between the pulses was 10 ns, the train duration was 230 ns, and the energy of a train was 20 mJ. Two-stage amplification was followed by focusing of the radiation (by a lens with f = 20‘cm) on the aluminum target (Fig. la) located in the focusing zone. Since the first pulses in a train knocked out excited and ionized particles from the target, these particles then ionized (“ignited”) atmo-

OA

1 PC

NFO 1

6 1. Experimental setup. (a) Scheme 1: PMLO - passive mode-locked oscillator; A,, A, - amplifiers; L - focusing lens; T _ aluminum target; F - filter; S - spectrograph, P - photographic film, PM - photomultiplier; PV - pulse voltmeter; SL - spherical tens. (b) Scheme 2: NFO - passive mode-locked oscillator with negative feedback, PC - Pockels cell; M - mirrors; GP - glass plate; OA - Q-switched oscillator-amplifier; BS - beam splitter; CL - cylindrical lens; T - target; VM - vacuum monochromator; PM - photomultiplier; PV - pulse voltmeter.

Fig.

spheric gases near the focusing zone. The subsequent maintenance (“heating”) of the plasma plume was ensured by the later pulses in the laser radiation train. The focused radiation had the following characteristics. The energy of a pulse train was 250 mJ, the duration of a pulse was 8 ps, the number of pulses in a train was 23-25, and the power density of a single pulse at the focus was up to 6 X lOI3 W/cmm2. The harmonics of the probe laser radiation generated in the plasma were directed to a spectrograph (ISP-30 model). The converted radiation could be photographed and it was also possible to record the harmonic radiation with a photomultiplier and to send the resultant signals to pulse voltmeters. In this case the laser radiation played a dual role. It acted as a “seed” and the source of heat for an atmospheric laser plasma, but some of this radiation passed through the plasma plume and was used as a probe. This experimental geometry had the advantages of its simplicity, but it suffered from several shortcomings. It was difficult to study the influence of the characteristics of a

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plasma growing in a direction perpendicular to the laser radiation on the conversion. process. This was due to the fact that when a “seed” target was moved along a given direction, it was not possible to determine uniquely the ratio of the heating and probe radiations. However, the simplicity of such experiments and the feasibility of investigating the whole spectrum of the output radiation provided a certain amount of information which made it possible to estimate the nonlinear optical characteristics of a plasma. 2.2. Generation

of probe-radiation

harmonics

in a plasma

In light of the above comments, we modified the experimental setup (Fig. lb), so as to avoid the abovementioned shortcomings. We used a generator of picosecond pulses with a negative feedback loop, formed by the fast photomultiplier (14 ELU FK model) and low-voltage modulator (ML-102A model) in conjunction with a polarizer. Part of the radiation was deflected to the photomultiplier controlling the modulator, the Q factor of the cavity decreased, and the linear stage of the growth of lasing spread out in time. Passive mode locking was ensured by circulating a solution of dye 3274-u in ethanol through a mirror cell. An extended train of picosecond pulses (A = 1.054 nm) was generated; its total duration was 3 ps and the duration of single pulses was 1.4 ps. Separation of a short sequence of pulses from the whole train was carried out by a Pockels cell. This short sequence was directed to a Q-switched oscillator-amplifier in which the whole accumulated inversion was utilized in the generation of a giant pulse [ 141. A train of picosecond pulses amplified in this way was split into two beams by a mirror. Qne beam (representing the “heating” pulse train) was focused by a cylindrical lens (f= 10 cm) on a target located in front of the entry slit of a vacuum monochromator (VMR-2 model). A plasma plume of 3 mm X 0.15 mm dimensions formed above the target surface. The second beam (“probe” radiation) propagated perpendicular to the direction of plasma growth and was focused inside the plasma by a spherical lens with f= 12 cm in such a way that the whole volume of the waist of the focused radiation was in the atmospheric plasma zone created by the heating pulse train. The intensity of the probe radiation in the plasma interaction zone was varied from 3 X 10” to 5 X 1013 W/cm* (7 = 3 ps). The probe radiation and the harmonics generated at the plasma were directed to the monochromator and then detected by a photomultiplier. The target was made of various materials (Al, W, Ta). A three-coordinate manipulator made it possible to move the target along the z-axis and thus control the zone of the interaction of the probe radiation with the plasma relative to the target plane. In the experiment on the surface plasma in vacuum the target was inside a vacuum chamber placed flush against the entry slit of the vacuum monochromator. This avoided the influence of atmospheric gases on the growth of the

surface plasma. It was thus possible to observe generation of higher harmonics with wavelengths less than 200 nm. These experiments were carried out at a pressure of 10m5 Torr in the chamber. There is a difference between the technical arrangements adopted in Refs. [3,4,11,13] and by us in order to optimize the delay between the heating and probe beams. In the cited investigations the delay was ensured by the use of independent nanosecond lasers, synchronized relative to one another to a high degree of precision, whereas in our case a train of probe picosecond pulses always included a pulse for which the plasma was “optimal” (from the point of view of the nonlinear optical processes) when the generation of a specific harmonic was most efficient. In this way, the delay between the heating and generated trains was selected almost automatically.

3. Results and discussion of experiments 3.1. Generation of higher harmonics an atmospheric plasma

of laser radiation

in

Our experiments demonstrated that an atmospheric plasma is a medium suitable for efficient conversion of coherent infrared radiation to the visible and UV ranges, limited by the atmospheric transmission edge (200 nm). We shall now give the results of an investigation of the temporal, spectral, and energy characteristics of the generated radiation and of the plasma. Analysis of oscillograms of the train of the probe (A = 1.054 pm) and output (h = 35 1 nm) radiation pulses showed that efficient third harmonic generation began after some delay. The delay time between two trains was due to the process of growth of the laser plasma. Each subsequent probe radiation pulse arrived at the target simultaneously with the heating train of pulses. For the first pulses of a probing radiation optimal conditions of frequency conversion in laser-produced plasma are not attained (a “nonlinear” medium has not yet been created). However, every later heating pulse improved successively the conditions for the conversion of the probe radiation into harmonics because of the absorption in the plasma and its excitation. We observed changes in the delay time between the starting pulses of a train of heating pulses and a train of harmonics pulses. The average delay time for third harmonics generation was 100 + 25 ns. The instability of the delay time was evidently due to an instability of the energy of the train of the heating radiation pulses, which in our case was 10%. Efficient harmonic generation began after a certain time interval during which between six and twelve heating radiation pulses reached the target. This delay could increase for each higher order of the harmonics. In addition to the energy characteristic of the heating and probe pulse trains, the efficiency of harmonic generation was affected significantly by the ratio of the energies

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of these pulses. We compared the efficiencies of conversion to the fifth harmonic of a train of probe pulses with the parameter (Y= EI/E2 (E, is the energy of the train of probe pulses and E, is the energy of the train of heating pulses). The ratio of the energies of these two pulse trains was altered by inserting a suitable splitting mirror (Fig. lb). It was found (Fig. 2a) that there was an optimal value of the parameter (Y which was governed by a number of factors. An increase in the conversion efficiency (71) with increase of the parameter LYwas related to an increase in the probe pulse energy. On the other hand, the proportion of the radiation used to heat the plasma decreased and this reduced the fraction of the excited atoms and ions in the interaction zone and lowered n correspondingly. We could assume that in the case of other harmonic orders the optimal values of the parameter (Y should be different. The energy of the heating radiation pulses was selected so that the influence of the atmospheric plasma on the characteristics of the target surface (reflection coefficient, crater formation) was negligible. We investigated the influence of the distance A between the target and the focusing zone of the probe beam on the conversion efficiency. This distance was varied in the course of an experiment by a manipulator which controlled the position of the target relative to the waist of the probe radiation. The dependence q(A), plotted in Fig. 3, demonstrated a considerable influence of this parameter on the nonlinear conversion to the third harmonic, which was associated with optimization of the plasma characteristics (plasma density and degree of excitation of higher states of the atmospheric molecules) in the interaction zone. The parameter A can be optimal when the four-photon process is phase-matched. A calculation of an integral which takes account of the phase mismatch between the third-harmonic and pump radiations [15] involves, in particular determination of the electron density in the waist zone. An estimate of the conversion efficiency was difficult, in view of indetermination of the contribution of each of the pulses in the heating train to the process, resulting in

7.a.u. I

-

0.5 -

I

i

. 2

3

4

5

Fig. 2. Fifth harmonic conversion efficiency versus parameter (a) atmospheric plasma; (b) target plasma in vacuum.

d a,

135 (1997) 251-256

I

I Fig. 3. Third harmonic

conversion

2 efficiency

A,l?ltll

versus parameter

A.

an increase in the plasma density, and also because of a time delay between the maxima of the envelopes of the output and plasma-generating radiation trains. According to Ref. [4], the latter factor could also be associated with the attainment of phase matching. It is well-known fact that the focusing geometry is the main factor for the phase-matching conditions and harmonic efficiency. An anomalous behavior of the harmonic generation in the tight focusing limit in ions was discussed in recent publications [ 11,13,16,17]. In our experiments the appearance of the lines of excited gases in the spectrograms coincided with a significant increase in the efficiency of conversion to the third, fifth, and even second harmonics. In an atmospheric plasma, regarded as an isotropic medium (which is true for the microscopic volume occupied by the waist of the probe radiation) it is possible to generate only the odd laser radiation harmonics 11,151. It is important to stress that under our conditions the second harmonic is of much lower (by two or three orders of magnitude) intensity compared with the third harmonic. Second harmonic generation is evidently due to a gradient mechanism (resulting from inhomogeneities of the optical characteristics of the plasma), as pointed out on a number of occasions (see, for example, Ref. [2]). The maximum efficiency (10m3) has been achieved in the conversion of infrared radiation to the third harmonic. The reported conversion efficiencies of similar processes (3 X low2 [5]) have been achieved, as pointed out above, by the use of nanosecond laser radiation pulses as the plasma-generating radiation, which is locked firmly on the time scale and delayed relative to the picosecond probe radiation pulses. In our case, however, the delay between the probe and heating radiations is ensured automatically. In addition to simplification of the experimental setup, this also reduces the efficiency of the nonlinear processes because it is not possible to convert the first pulses of the probe radiation.

25s

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tally. The efficiency maximum shifted towards a higher fraction of the heating radiation (Fig. 2b). Obviously, in the absence of atmospheric gases it was necessary to use a considerable proportion of the heating radiation in the overall balance of the probe and heating radiations. The harmonic orders and their efficiencies are presented in Table 1. Odd harmonics were investigated up to the eleventh (A = 96 nm). Two points should be noted. First, the degree of excitation of the surface plasma affected significantly the nonlinear optical processes occurring in the plasma, which was particularly marked in the case of higher harmonics (ninth and eleventh). The intensity of the eleventh harmonic was comparable with the intensity of the plasma radiation emitted in a nearby range. The line spectrum of the target material and the plasma continuum extending over a wide range were observed. Second, a significant role in the experiments was played by modification of the target surface caused by the high-intensity heating radiation. This factor was eliminated (it gave rise to microcraters and altered the reflection coefficient of the target) by manipulating the position of the target relative to the heating radiation. The dependence q(r), where I is the probe radiation intensity obeyed a power law for the generation of the eleventh harmonic and the power exponent ranged from 7 to 10 as the distance to the target was varied. When the target surface was approached during harmonic generation in the plasma, the Kerr effect and the shift of the populations, as well as the Raman scattering and absorption of the generated radiation all began to play a role. The influence of the Raman scattering in these experiments should be considered separately and will not be discussed here. However, the influence of the Kerr effect and different stages of the growth of a plasma affected the attainment of phase matching and resulted in a mismatch. This circumstance should be taken into account in the search for the optimal conditions for the generation of harmonics and sum frequencies in a plasma. A change in the experimental conditions (focusing into parts of the plasma with the lower density, experiments in the atmosphere or in lowdensity gases) could reverse the sign of the dispersion of the medium. Earlier estimates [18] have indicated that the influence of the Kerr effect can increase the power exponent in the dependence v(Z) for both lower and higher

A comparative investigation of harmonic generation in an atmospheric plasma, when the converted radiation acts as the heating and probe radiation (scheme 1) and when the functions of heating and probe radiation are performed by two different beams (scheme 2). demonstrates a considerable difference between the efficiencies of nonlinear processes in these two cases. The efficiencies of harmonic generation in scheme 2 are one or two orders of magnitude higher than in the case of scheme 1. This difference is understandable if we bear in mind the difference between the plasma excitation regimes (the excitation is stronger in scheme 2), as well as the differences with respect to the interaction zone (which occupies almost the whole of the waist in scheme Z), and the feasibility of optimization of the parameters a and A. 3.2. Generation of laser radiation harmonics in a surface plasma of the target located in a vacuum chamber When the wavelength of the converted radiation is shifted to the VUV range, it is necessary to change the experimental setup because the generated radiation then lies in the region where atmospheric gases absorb very strongly. Therefore, the general relationships governing the experiments described above are still obeyed. For example, the dependence of the efficiency of conversion of the probe radiation to the ninth harmonic (A = 117 nm) on the parameter A (which is the distance between the focusing zone and the target plane) is of the same nature as in the atmosphere plasma case. We controlled plasma conditions by observing the VUV radiation by means of a VUV spectrograph without the probe radiation. For the intensities of a heating radiation above 5 X IO’* W/cm2 a plasma emission in the range of 30 to 100 nm is observable. This fact indicates that in this case a plasma is formed with charged particles in contrast with the case when for lower intensities no plasma emission is detected. The fact that the dependence q,(A) did not change significantly between generation of harmonics in a plasma involving atmospheric gases and in a target plasma demonstrated that the influence of the Kerr effect on the nonlinear processes in a plasma with a relatively high density was slight. However, the dependence q( (Y)changed drastiTable 1 Efficiencies of harmonics generation in atmospheric and target plasma Wavelength of harmonics, 527 353 211 151 117 96

nm

Number of harmonics

Efficiencies

harmonic

atmospheric

plasma

2 3 5 7 9 II

2 x 10-s 6 x 1O-4 6 X 1O-5 _ _ _

generation target plasma

2 8 2 8

x x x X

10-7 10-S 1o-5 lo+ 10-6 IO-’

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harmonics, but in the latter case this dependence may be nonmonotonic.

4. Conciusion In conclusion, we have shown the possibility of optimization of high harmonics generation in a laser plasma when only one laser is used as a heating and probe source. An analysis of two different schemes of plasma excitation both in the atmosphere and in a vacuum chamber shows that the double-beam scheme has some advantages because of possibility of optimization of the delay conditions and excitation level. We have demonstrated that the train of picosecond pulses can serve as a promising source of production of the plasma for frequency conversion. Picosecond-laser-produced plasma serves as an effective medium with the same nonlinear parameters as one excited by nanosecond pulses used in previous investigations of harmonics generation in the plasma. The duration of the pulse train of the picosecond Nd:glass laser allows to obtain automatically a corresponding delay between the heating and probe pulses when an optimal conversion to the short-wavelength radiation is realized. In our experiments odd harmonics generation (up to eleventh, A = 96 nm) of IR laser radiation in a low-temperature atmospheric plasma and a plasma produced at the targets placed in a vacuum chamber are observed. Maximum efficiency (17= 10m3) was obtained for low-order (3~) nonlinear processes, at the same time the efficiency of eleventh harmonic was N 1O-8. It would be interesting to determine the role of the target material, to obtain spectrographic data on the relationship between the generated harmonics, continuum, and line spectrum of the plasma, and to create a profiled plasma to be used as nonlinear media. This is the subject of our further investigations.

Acknowledgements This work has been supported in part by the International Scientific Foundation (Grant 7000 RU) and by the Uzbek Foundation of Fundamental Investigations.

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