Scaling law and polarization of second harmonic emission from laser generated plasma

Volume 39, number 4

OPTICS COMMUNICATIONS

15 October 1981

SCALING LAW AND POLARIZATION OF SECOND HARMONIC EMISSION FROM LASER GENERATED PLASMA A.P. SCHWARZENBACH, P. LADRACH and J.E. BALMER Institute of Applied Physics, University of Berne, CH-3012 Bern, Switzerland Received 22 June 1981

Measurements are described of the intensity and polarization of the second harmonic emission from a plasma generated by 1.054 ~m, 35 ps laser pulses at oblique incidence. It is shown that the measured sealing cannot be explained by a simple power law and that at high intensities the degree of polarization of the second harmonic radiation does not depend on the polarization of the incident laser light.

Detailed knowledge of the processes governing the absorption of focused laser radiation by an inhomogeneous plasma is of considerable interest to the laser fusion program. At the high intensities and temperatures involved, the main contribution to the total absorption has been shown theoretically and experimentally to be due to a collective process: resonance absorption [1-3] in the case of short pulses and steep gradients. At critical density this process leads to the excitation of longitudinal plasma waves (Langmuir waves) with a frequency equal to the incident laser frequency. Coupling of one of these Langmuir waves with another Langmuir wave or with the incident electromagnetic wave can then lead to generation of the second (or higher) harmonic of the incident radiation [ 4 - 6 ] . Measurements of intensity, spectrum and polarization characteristics of the second harmonic (SH) emission can thus provide information about the nonlinear processes occurring at or near the critical density. Observations of SH emission in short pulse laser plasma experiments have been reported previously [7-10] but no account is given, for example, of the state of polarization of the SH radiation emitted. This letter describes measurements of the intensity scaling and polarization characteristics of SH emission with respect to the intensity and the polarization of the incident laser beam for a range of laser intensities from the onset of plasma formation near 2 X 1011 W/

0 030-4018/81/0000-0000]$ 02.75 © 1981 North-Holland

cm 2 (perspex target) [1] up to 1014 W/cm 2. It is found that over this range of intensities (corresponding to seven orders of magnitude of SH emission) the SH scaling cannot be explained by a single power law. By means of a simple estimate it will be shown that satisfactory agreement between theory and experiment can be obtained if the intensity dependence of the field energy dissipation mechanism and of the density scale length L = n c (dne/dx)-I at critical density is taken into account. The latter has been shown to be determined by free hydrodynamic expansion at low intensities [12,13] and by ponderomotive force effects at high laser intensities [13,14]. The experiments reported here were performed with laser pulses of 35 ps FWHM generated by an active-passive mode-locked Nd : Phosphate glass oscillator Q'o = 1.054 #m). A three-state amplifier chain including threefold Pockels cell pulse isolation yielded single pulse energies up to 0.5 Joule with any prepulse energy being discriminated to less than 10 - 6 of the main pulse energy. The pulses were focused obliquely by an t"/4 single lens corrected for 1.054/am onto plane perspex (C502H8) slab targets located in vacuum. For the whole set of measurements the angle of incidence was held fixed at 0 = 20 °, which is near the optimum angle for resonance absorption at an incident laser intensity of 2 X 1013 W/cm 2 [3]. A halfwave plate allowed the incident beam polarization to 247

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be rotated from s (E vector orthogonal to incidence plane) to p (E vector in incidence plane). Variation of the incident intensity was achieved by means of neutral density filters placed in the output beam, while the laser system was always fired at constant power. In order to exclude any effects due to laser performance, part of the laser output was upconverted to 26o 0 in a KD*P crystal and simultaneously recorded by a vacuum photodiode. The generation of SH power in the crystal was checked over five orders of magnitude to obey the well-known square law with respect to fundamental power. The light emission in the direction of specular reflection from the target surface was collimated through a lens with f number equal to that of the focusing lens. After eliminating the specularly reflected fundamental light with a Schott BG 18 filter, the second harmonic light beam was split into its two orthogonal polarizations by means of a dielectric polarizer. The s- and ppolarized fractions of SH emission from the plasma were then recorded by two separate photomultipliers as functions of incident laser intensity (I0) and polarization (s or p). The results obtained for the intensities P2 and/~ of the two orthogonal polarization of SH emission are shown in fig. 1 (a) for p-polarized and in fig. 1 (b) for s-polarized incident laser light. It is seen that in spite of the high degree of linear polarization (better than 95%) of the incident light, the SH emission contains an appreciable fraction of orthogonally polarized light, reaching nearly 80% in the case of s-polarized incidence at low intensities (fig. lb). Using the definition P_ (IP - IS)/(I p + I s) for the degrees of polarization P0 and P2 of either wavelength we may calculate the ratio II = P2/Po from fig. 1. Fig. 2 shows a plot of this ratio as a function of incident laser intensity. It is seen to remain nearly constant in the case of p-polarized incident light but to strongly depend on intensity in the case of s-polarized incidence. A similar series of measurements has been performed on perspex targets coated with ~0.5 g m of gold. Here, essentially the same characteristics of SH emission have been found, with the exception that the two curves corresponding to fig. 1 (b) only intersect at an intensity ~ 6 X 1013 W/cm 2. The main difference, however, is a tenfold increase in conversion efficiency to SH light in the case of the gold target. 248

15 October 1981

108 a)

I 2 [a.u.]

b) c~Io2"9

107

eoio4'I 106

lo 5

1¢ 103 102

1 d/oo

//,,

10

; ................

1

1011

d2

Io 3

lo1 101

I 0 [Wlcm 2 ]

.......... 1012 lo 3. I0 [ Wlcm21

Fig. 1. Measured scaling of SH emission from the plasma versus incident laser intensity. Points marked o (+) represent p-(s-) polarized fractions of SH. a) p-polarized incident light, b) s-polarized incident light. Solid lines are power fits to the experimental points.

In order to interpret these results we consider the laser light electric field which is known to be resonantly enhanced in the region of the critical density n c [15,16] : =

IE(x)l

Eo¢(r) t (2nkoL)I/2(x2 + A2)1/2'

(1)

where E 0 and k 0 are the vacuum values of the laser electric field and wavenumber, respectively, ~- = (koL) 1/3 sin 8 and (I)(z) is the well-known resonance function first derived by Denisov [15]. The width A of the resonance is determined by the dissipation mechanism of the field energy, i.e. A = LVei/Co0 for collisions and A = (X2L)l/3 for plasma wave convection. Here Vei = 3.4 Zne e4 In A(meTe3) - 1/2 is the electron-ion collision frequency and ~kD = (kZe/ 47rnce2)l/2 the Debye length. For T e ~ 200 eV the former of the two is the dominant'process in our case. Since the amplitude of the SH radiation is propor-

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,

,

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OPTICS COMMUNICATIONS

,,,,,i

'

,

,.,

,

,,,,I

,

,

,,,,,

++

T[ ~+

o

o

o 3

(3

% o oo

-I

i

t

,ll,|l

1011

,

,

,

,,,lll

1012 Io[ W/cm 2]

i

'

'

' ' ' '

1013

I01&

Fig. 2. H = P2/Poof the degrees of polarization of SH emission versus incident laser intensity. Points marked (+) for P0 = 1 (p-polarized incident light) and (o) forP0 = - 1 (spolarized incident light).

15 October 1981

in reasonable agreement with the experimental data up to an intensity of"-1013 W/cm2. The scaling of SH intensity in the remaining high intensity regine is explained by the onset of density profile modification, which will occur at a substantially lower value of laser intensity than in the nonresonant case, since the enhanced electric field at critical density causes an enhanced ponderomotive pressure in this region [17]. The intensity at which the laser pressure tends to dominate the plasma pressure can be expressed as Vo/Ue -~ 1, with v0 = eEo/m e w 0 and v e = ( T e / m e ) 1/2 is "1015W/cm 2 for an electron field Emax is used to calculate o0, the intensity required for the onset of the steepening is "1013 W / cm 2, in good agreement with the experiment. Using this and the formula for L derived from numerical simulations by Estabrook and Kruer [14] in our eq. (2), we obtain : 12 ocI03"1 for/0 > 3 X 1013 W/cm 2 ,

tional to the square of the amplitude of the fundamental and the intensities of either radiation field are given by I = (c/81r)eE2, where e is the dielectric constant of the medium, it is obvious that 12to = IE~(x)l 4 and with Emax = E ( x = 0) in eq. (1) we easily fred:

1 2 ~ i02~4(~)L2/a4,

(2)

where I 0 - (c/8zr)E 0 is the vacuum value of the incident laser intensity. Note that our simple estimate fully agrees with the scaling obtained from the exact theoretical calculation [6]. The dependence of ~(r) on r is approximated by the parabola ~(r) = -3.1 r 2 + 4.0 ~-- 0.13 in the neighbourhood of the resonance maximum rmax ~ 0.65. Inserting this and the value for A, determined by collisions in this intensity regime, into (2) we fred : 12 ~ I2L2/3v~i 4 .

(3)

In the short pulse regime, the density scale length L = Cstp, where c s = (Z. Te/Mi) 112 is the ion-acoustic

velocity, Z and Mi the average ion charge and mass, respectively, tp the laser pulse length and T e o~I20/5 [12]. The functional dependence of Z on Te, obtained from solving the time-dependent ionization rate equations, can be crudely approximated by 2 =Tle/4 This finally leads to : 12 ccI4"2

for/0 < 1013 W/era 2 ,

(4)

in excellent agreement with the experiment. Herel A = (X2L) 1/3 has to be used, since Te ~ 200 eV at these intensities [ 12]. Generation of SH harmonic radiation by the resonance process is thought to preserve the polarization of the pump, so that the orthogonally polarized components of the SH should not appear at all. In the case of p-polarized laser radiation the observation of ~15% of s-polarized SH can be attributed to depolarization of the incident beam by the plasma in agreement with a measured depolarization of 10% to 30% in the reflected light at the fundamental frequency found in [ 18] under similar experimental conditions. In conclusion the data presented support the existing theories of SH generation accompanying reso. nance absorption in the case of p-polarized incident light if hydrodynamic effects such as plasma expansion and ponderomotive pressure and the concomittant dependence of the plasma density scale length on incident laser intensity are taken into account. In addition, the data imply that the laser/plasma interaction for short pulses changes from coUisional at intensities ~1013 W/era 2 to collective at intensities ~3 X 1013 W/cm 2. The authors would like to thank Prof. H.P. Weber for stimulating discussions. This work was supported by the Swiss National Science Foundation. 249

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References [ 1] D.W. Forsiund, J.M. Kindel, K. Lee, E.L. Lindmann and R.L. Morse, Phys. Rev. A l l (1975) 679. [2] K.R. Manes, V.C. Rupert, J.M. Auerbach, P. Lee and J.E. Swain, Phys. Rev. Lett. 39 (1977) 281. [3] J.E. Balmer and T.P. Donaldson, Phys. Rev. Lett. 39 (1977) 1084. [4] N.W. Erokhin, V.E. Zakharov and S.S. Moiseev, Zh. Eksp. Teor. Fiz. 56 (1969) 1,179 [Sov. Phys.- JETP 29 (1969) 101. [5] A.V. Vinogradov and V.V. Pustovalov, Zh. Eksp. Teor. Fiz. 63 (1972) 940 [Soy. Phys.- JETP 36 (1973) 492]. [6] N.G. Basov, V.Yu. Bychenkov, O.N. Krokhin, M.V. Osipov, A.A. Rupasov, V.P. Silin, G.V. Sklizkov, A.N. Starodub, V.T. Tikhonchik and A.S. Shikanov, Zh. Eksp. Teor. Fiz. 76 (1979) 2093 [Soy. Phys.- JETP 49 (1979) 1059]. [7] A. Caruso, A. De Angelis, G. Gatti, R. Gratton and S. MarteUiccu, Phys. Lett. 33A (1970) 29.

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[8] L.M. Goldman, J. Soures and M.J. Lubin, Phys. Rev. Lett. 31 (1973) 1184. [9] E.A. McLean, J.A. Stamper, B.H. Ripha, H.R. Griem, J.M. McMahon and S.E. Bodner, Appt. Phys. Lett. 31 (1977) 825. [10] A.G.M. Maaswinkel, Optics Comm. 35 (1980) 236. [ 11 ] J.E. Balmer, T.P. Donaldson, W. Seka and J.A. Zimmermann, Optics Comm. 24 (1978) 109. [12] T.P. Donaldson, J.E. Balmer and J.A. Zimmermann, J. Phys. D13 (1980) 122. [ 13] B. Luther-Davies, Optics Comm. 34 (1980) 421. [14] K. Estabrook and W.L. Kruer, Phys. Rev. Lett. 40 (1978) 42. [15] N.G. Denisov, Zh. Eksp. Teor. Fiz. 31 (1956) 609 [Soy. Phys.- JETP 4 (1957) 544]. [16] J.T.M. Boyd and W.T. Hewitt, J. Phys. D10 (1977) 249. [17] K. Baumggrtel and K. Sauer, Phys. Lett. 70A (1979) t07. [18] J. Soures, L.M. Goldman and M. Lubin, Nuct. Fusion 13 (1973) 829.