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Non-Equilibrium Behavior on Pulsed Laser Evaporated Surfaces
Journal of Electron Spectroscopy and Related Phenomena, 29 (1983) 147-153 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
147
NON-EQUILIBRIUM BEHAVIOR ON PULSED LASER EVAPORATED SURFACES L. Lynds and B. A. Woody United Technologies Research Center, East Hartford, CT 06108
ABSTRACT Absorption of intense pulsed laser optical fields by metallic surfaces generates dense neutral atomic beams with high average translational energies. Mechanisms explaining this behavior are based on an equilibrium model invoking high temperatures and pressures. We have made experimental observations on yttrium and uranium atomic beams produced from laser evaporated targets which suggest an alternative mechanism involving a non-equilibrium process. INTRODUCTION Intense coherent radiation (~ 10 8 w/cm 2) interacts with metallic surfaces by an indirect process (ref. 1).
Energy is coupled into a localized plasma
which in turn radiatively heats the surface.
The plasma is continuously
nourished by particles presumably in thermal equilibrium with the surface.
In-
vestigations have centered mainly around mechanical damage effects (refs. 1-4), momentum transfer (ref. 5), and deep-core ionization processes (refs. 6, 7). At lower intensities (~ 10 8 watts/cm 2 ) the coupling mechanism changes to a direct process.
Pulsed coherent radiation of solid surfaces generates a dense
neutral atomic or molecular beam with kinetic energies up to 10 eV (refs. 8-10). Mass beam kinetic energies appear to track the photon intensity within the specified range.
An equilibrium model of the process would suggest that ex-
tremely high "surface" temperatures are achieved. The emphasis in this work was on characterizing the energetics of pulse laser generated uranium and yttrium neutral beams with regard to kinetic energy and distribution of internal energy.
Mass pulses were interrogated with
high resolution cw dye lasers and a quadrupole mass filter to obtain quantitative information on species, number densities and lifetimes.
We report some
preliminary results which suggest that the coupling of pulsed coherent radiation into metallic surfaces can lead to a non-equilibrium vaporization process. 0368·2048/83/0000-0000/$03.00 © 1983 Elsevier Scientific Publishing Company
148
EXPERIMENTAL Pulsed laser evaporization experiments with uranium and yttrium were performed in a stainless-steel chamber illustrated schematically in Fig. 1.
Fig. 1.
Beam-Gas and Crossed-Beam Apparatus
Components are located on a railing so that they can be adjusted relative to optical windows.
The metal target (M) is secured inside a cylindrical housing
which can be rotated externally to maintain the focal plane on the surface and minimize geometrical effects imposed by removal of metal.
Pulsed Nd:YAG
(1064 nm) radiation is focused onto the surface at an angle of 15° to the target normal. A flow of gas (Ar) around the target, as indicated in Fig. 1, restrains the expansion of the atomic beam and forms a column having a diameter of 1-2 cm throughout the optical interrogation region.
In addition, the gas
flow thermalizes the atoms and lengthens the mass pulse from 120
~s
to 5-10 ms.
Atomic flow velocities were measured by resonance fluorescence Doppler shifts and by time of flight techniques:
1) two beam optical absorption with accompa-
nying Ar flow, and 2) mass quadrupole filter at low background pressures ~ 10- 3 Torr. Laser parameters and atom pulse characteristics for the gas flow experiments are summarized in Table 1.
In preliminary experiments parallel
plates were placed in the chamber to measure electron and ion currents. and electrons densities were approximately 10- 5 of neutral species.
Ion
Optical pumping and probing of the atomic pulses was performed orthogonally to' the flow axis with two tunable narrowband cw dye lasers (Coherent, Inc. Model 599-21).
A schematic representation of the optical measurement scheme
is illustrated in Fig. 2.
Pump and probe beams were parallel with a variable
149
TABLE 1 Source Conditions and Results Nd:YAG Laser Pulse Width (FWHM) Rep rate Wavelength Energy
Fig. 2.
Atom Pulse Conditi ons Width (FWHM) Rep rate
120 )JS 10 s-l 1064 nm 0.4 - 1.0 J
Pressure Dens ity Temperature Velocity
5 - 10 ms 10 s~ 1 0.7 - 1.~4Torr 1013_10- cm- 3 300 ~ 400 OK 7000 ern s-l
Experimental Arrangement
separation capability up to 5 cm.
Heterodyne experiments indicated that the jitter-limited linewidths were ~ 5 MHz (0.0002 cm- l). Atomic uranium is optically pumped via the 5L~ (ground state) ~ 7M7 transition as shown in Fig. 3. The short-lived 7M7 state (T = 205 ~ 20 ns, ref. 11) radiative1y populates the low energy odd-level the lower electronic manifold.
5 0
5 0
50.
K L and H states Vla cascades through 6, 3 6 In this work absorption measurements were per-
formed with the long-lived 5L~ and 5H~ states as the lower levels.
Ground
state populations are obtained from 5L~ ~ 7M7 absorption measurements. The optical pumping/probing scheme for atomic yttrium is depicted in Fig. 4 and involves the resonant transition 203/2 ~ 20~/2 at 16131 cm- l which radiatively populates the 4FJ states via cascades through the lower electronic manifold.
150
J!(8)
22000 I-
f
20000
18000 E 18000
" iii
8000
4000
2000
f-l f-
(4)
598.81 nm
30000
f 20000 E " iii
17)
I-
~
ff--
Fig. 3.
597.83 nm (3)
(7)
10000
],
( 5 ) - (8)
591.154 nm
Uranium Probe Transitions
Fig. 4. Scheme
Yttrium Optical Pump-Probe
These metastable quartet states are individually probed using the upper states as terminal levels.
G3
Narrow line absorption measurements of the Doppler
broadened transitions provided a direct determination of the average number density within the probing volume.
Analysis of the lineshapes indicated that
the translational temperature for U and Y in admixture with Ar was in the range of 300-500oK. RESULTS AND DISCUSSION Under the specified flow conditions, optical pumping produced easily detectable populations of U and Y metastables. Tables II and III.
Typical results are presented in
Downstream probing indicated that the metastable states had
Table II Uranium Metastable Populations 5Lo -+ 7M 6 7 Probe Pump power (mw) (nm) 20
597.632
10
Level
%Abs
5Lo 6
5.38 4.43
2
3.19
0.1
0.35
20
598.610
3.2
5Ho 3
2
7.73 6.68
0.63 0.1
11.4
591.540
5Lo 6
2.34
atoms cm- 3 1.85 x 1010 10 1. 51 x 10 10 1.08 x 10 9 1.2 x 10 1.44 x
ic"
10 9.37 x 10 10 8.05 x 10 10 2.76 x 10 5.9 x lOll
151
TABLE III Y Metastable Populations Pump -1 transition (cm ) 2
2
0
D3/ 2 -.. D3/ 2
Probe -1 transition (cm )
Population (atoms cm- 3 ) 12 9.35 x 10
16131 4 F3/2 4 F5/ 2 4 F7/ 2 4 F9/2
4 0 -.. G5/ 2 4 0 -.. G5/ 2 4 0 -.. G7/ 2 4 0 -.. G9/ 2
10
17757
4.68 x 10
17615
1 .87
17708
3.27 x lOll
17832
ri.d.
x lOll
lifetimes greater than several milliseconds in the presence of argon as a collision partner. Experiments indicated that our sensitivity limit was approx9 imately 10 atoms/cm 3 for absorption processes and perhaps 107 atoms/cm 3 with laser induced fluorescence.
However, the latter procedure does not easily yield
quantitative measurements. In the absence of optical pumping, the atomic pulses show no sign of metastable population in response to probing along the flow axis. (~10
-3
At low pressures
Torr) focused 0.4-1.0 J pulses generated maximum ground state popula-
tions with kinetic energies of 3-5 eV for U and 10-12 eV for Y.
Energy cen-
troids generally increase with laser intensity in the "averaged" intensity 2 regime of 1-10 MW/cm and are consistent with results obtained earlier by Friichtenicht (ref. 8) and Levine (ref. 12).
Equivalent equilibrium temperatures at the surface are in the range of ~ 3.5 x 104 -.. 1.4 x 105 oK. Boltzmann
distribution at the melting, boiling and intermediate temperatures for states probed in this work are presented in Table IV. If evaporation were an equilibrium process, one would expect to find significant fractions of metastable states and ions.
This appears to be in sharp contrast to our observations on
thermal equilibrium source ovens and to the proposed mechanisms involving the subsurface explosions of bubbles containing gaseous atoms at high pressures and temperatures (refs. 3, 4, 10). It has been demonstrated that Nd:YAG radiation at intensity levels between 8 7 10 and 6 x 10 w/cm 2 is efficiently coupled into metal targets (refs. 13, 14). Extrapolating these results to the uranium targets used in this work, we compared the number of atoms available from the laser pulse energy to the number
152
TABLE IV Bo ltzmann distribution of states No. density (atoms cm -3 ) nu n1
Upper Level
U
Term
E(cm -1 )
T ( OK)
5 Ho 3
3868.486
300 * 1405 2273 ** 4407
U
\0
7
3800.829
300 * 1405 2273 ** 4407
Y
4 F5/2
11078.61
* 1795 ** 3611
* Melting point data
nu/nl 8 1.3 x 102 LOx 102 4.7 x 101 1.5 x 10-
5 1.3 x 10 12 4.3 x 10
8.9 x 1013
8 1.4 x 102 2.4 x 101 1.0 x 101 3.3 x 10-
5 3.1 x 10 12 9.7 x 10
7 1.3 x 10 13 8.3 x 10
4 2.1 x 102 1.8 x 10-
10 1.3 x 10 17 4.1 x 10
6 x 1013 19 2.3 x 10
7 1.3 x 10
** Boiling point data
in a typical mass pulse based on absorption measurements. Assuming an irrotational fluid field the equation of continuity is expressed as: \J •
(p(t)v) = d~~t)
(1 )
where p(t) is the time evolved density of the atomic ground state and v is an average flow velocity. Assuming a simple rectangular pulse function, the pulse 16 17 17 contained 10 to 10 atoms compared to 5 x 10 atoms calculated from laser pulse energy and the solid heat of vaporization.
Conversion of energy to
neutral atoms appears to be a relatively efficient process in agreement with other observations. A crude calculation shows that there are n
=5
20 x 1018 ~ 10 photons per
pulse and that the ratio of photons to a single surface atom is approximately 2 in the range of (4 x 10- - 1) during one period of the lattice vibration. The photon dynamics suggests that adiabatic multiphoton excitation of surface vibrational modes with energy-pooling may account for the anomolous behavior of the energy distribution in pulse evaporated atomic beams.
Of course, this mechanism
is higly speculative particularly in view of the work of Yen, et al. (ref. 15) which reports that the electron-phonon energy relaxation is less than 1 ps in metallic zirconium.
153
In summary, the distribution of population in the metastable states carries a partial history of dynamical processes occurring on the surfaces during dissociation in the presence of large optical fields.
In dramatic contrast
to thermal oven atomic sources, the laser vaporized atoms appear in their ground electronic states with high densities and high kinetic energies.
Within
the sensitivity of absorption measurements and LIF detection, long-lived metastable states were not observed.
We determined that the metastable states
resulting from optical pumping could survive in the environment and over the distances of the measurements. radiate below 800 nm.
In addition, dimers were observed but did not
These observations provide an alternative view for the
coupling of coherent pulsed radiation into surfaces.
REFERENCES 1.
J. F. Ready, 3, 11 (1963); Effects of High-Power Laser Radiation
(Academic, New York, London, 1971). C. DeMichelis, IEEE J. Quantum Electron, QE-6, 630 (1970). F. W. Dabby and U. C. Park, IEEE J. Quantum Electron, QE-8, 106 (1972). F. P. Gagliano and U. C. Park, Appl. Opt. 13, 274 (197~ S. A. Metz, Appl. Phys. l.et t . , g, 211 (1973). A. Caruso, B. Bertotti and P. Guipponi, Nuovo Cimento 45B, 176 (1966). A. Caruso and F. Gratton, Plasma Physics 10, 867 (1968--).-J. F. Friichtenicht, Rev. Sci. Instrum. 45, 51 (1974). S. P. Tang, N. G. Utterback and J. F. Friichtenicht, J. Chem. Phys. §!, 3833 (1976). 10. N. G. Utterback, S. P. Tang and J. F. Friichtenicht, Phys. Fluids ~' 900 (1976). 11. E. Miron, R. David, G. Erez, S. Lavi and L. A. Levin, J. Opt. Soc. Am. 69, 256 (1979). 12. L. P. Levine, J. F. Ready, and E. Bernal, IEEE, J. Quantum Electron. QE-4, 18 (1968). 13. M. von Allmen, J. Appl. Phys., 1L, 5460 (1976). 14. M. von Allmen, P. Blaser, K. Affolter and E. Sturmer, IEEE J. Quant. Electron, ~' 85 (1978).. 15. R. Yen, J. M. Liu, N. Bloembergen, J. K. Yee, J. G. Fuzimoto and M. ~1. Salour, Appl. Phys. Lett., 40, 185 (1982).
2. 3. 4. 5. 6. 7. 8. 9.
147
NON-EQUILIBRIUM BEHAVIOR ON PULSED LASER EVAPORATED SURFACES L. Lynds and B. A. Woody United Technologies Research Center, East Hartford, CT 06108
ABSTRACT Absorption of intense pulsed laser optical fields by metallic surfaces generates dense neutral atomic beams with high average translational energies. Mechanisms explaining this behavior are based on an equilibrium model invoking high temperatures and pressures. We have made experimental observations on yttrium and uranium atomic beams produced from laser evaporated targets which suggest an alternative mechanism involving a non-equilibrium process. INTRODUCTION Intense coherent radiation (~ 10 8 w/cm 2) interacts with metallic surfaces by an indirect process (ref. 1).
Energy is coupled into a localized plasma
which in turn radiatively heats the surface.
The plasma is continuously
nourished by particles presumably in thermal equilibrium with the surface.
In-
vestigations have centered mainly around mechanical damage effects (refs. 1-4), momentum transfer (ref. 5), and deep-core ionization processes (refs. 6, 7). At lower intensities (~ 10 8 watts/cm 2 ) the coupling mechanism changes to a direct process.
Pulsed coherent radiation of solid surfaces generates a dense
neutral atomic or molecular beam with kinetic energies up to 10 eV (refs. 8-10). Mass beam kinetic energies appear to track the photon intensity within the specified range.
An equilibrium model of the process would suggest that ex-
tremely high "surface" temperatures are achieved. The emphasis in this work was on characterizing the energetics of pulse laser generated uranium and yttrium neutral beams with regard to kinetic energy and distribution of internal energy.
Mass pulses were interrogated with
high resolution cw dye lasers and a quadrupole mass filter to obtain quantitative information on species, number densities and lifetimes.
We report some
preliminary results which suggest that the coupling of pulsed coherent radiation into metallic surfaces can lead to a non-equilibrium vaporization process. 0368·2048/83/0000-0000/$03.00 © 1983 Elsevier Scientific Publishing Company
148
EXPERIMENTAL Pulsed laser evaporization experiments with uranium and yttrium were performed in a stainless-steel chamber illustrated schematically in Fig. 1.
Fig. 1.
Beam-Gas and Crossed-Beam Apparatus
Components are located on a railing so that they can be adjusted relative to optical windows.
The metal target (M) is secured inside a cylindrical housing
which can be rotated externally to maintain the focal plane on the surface and minimize geometrical effects imposed by removal of metal.
Pulsed Nd:YAG
(1064 nm) radiation is focused onto the surface at an angle of 15° to the target normal. A flow of gas (Ar) around the target, as indicated in Fig. 1, restrains the expansion of the atomic beam and forms a column having a diameter of 1-2 cm throughout the optical interrogation region.
In addition, the gas
flow thermalizes the atoms and lengthens the mass pulse from 120
~s
to 5-10 ms.
Atomic flow velocities were measured by resonance fluorescence Doppler shifts and by time of flight techniques:
1) two beam optical absorption with accompa-
nying Ar flow, and 2) mass quadrupole filter at low background pressures ~ 10- 3 Torr. Laser parameters and atom pulse characteristics for the gas flow experiments are summarized in Table 1.
In preliminary experiments parallel
plates were placed in the chamber to measure electron and ion currents. and electrons densities were approximately 10- 5 of neutral species.
Ion
Optical pumping and probing of the atomic pulses was performed orthogonally to' the flow axis with two tunable narrowband cw dye lasers (Coherent, Inc. Model 599-21).
A schematic representation of the optical measurement scheme
is illustrated in Fig. 2.
Pump and probe beams were parallel with a variable
149
TABLE 1 Source Conditions and Results Nd:YAG Laser Pulse Width (FWHM) Rep rate Wavelength Energy
Fig. 2.
Atom Pulse Conditi ons Width (FWHM) Rep rate
120 )JS 10 s-l 1064 nm 0.4 - 1.0 J
Pressure Dens ity Temperature Velocity
5 - 10 ms 10 s~ 1 0.7 - 1.~4Torr 1013_10- cm- 3 300 ~ 400 OK 7000 ern s-l
Experimental Arrangement
separation capability up to 5 cm.
Heterodyne experiments indicated that the jitter-limited linewidths were ~ 5 MHz (0.0002 cm- l). Atomic uranium is optically pumped via the 5L~ (ground state) ~ 7M7 transition as shown in Fig. 3. The short-lived 7M7 state (T = 205 ~ 20 ns, ref. 11) radiative1y populates the low energy odd-level the lower electronic manifold.
5 0
5 0
50.
K L and H states Vla cascades through 6, 3 6 In this work absorption measurements were per-
formed with the long-lived 5L~ and 5H~ states as the lower levels.
Ground
state populations are obtained from 5L~ ~ 7M7 absorption measurements. The optical pumping/probing scheme for atomic yttrium is depicted in Fig. 4 and involves the resonant transition 203/2 ~ 20~/2 at 16131 cm- l which radiatively populates the 4FJ states via cascades through the lower electronic manifold.
150
J!(8)
22000 I-
f
20000
18000 E 18000
" iii
8000
4000
2000
f-l f-
(4)
598.81 nm
30000
f 20000 E " iii
17)
I-
~
ff--
Fig. 3.
597.83 nm (3)
(7)
10000
],
( 5 ) - (8)
591.154 nm
Uranium Probe Transitions
Fig. 4. Scheme
Yttrium Optical Pump-Probe
These metastable quartet states are individually probed using the upper states as terminal levels.
G3
Narrow line absorption measurements of the Doppler
broadened transitions provided a direct determination of the average number density within the probing volume.
Analysis of the lineshapes indicated that
the translational temperature for U and Y in admixture with Ar was in the range of 300-500oK. RESULTS AND DISCUSSION Under the specified flow conditions, optical pumping produced easily detectable populations of U and Y metastables. Tables II and III.
Typical results are presented in
Downstream probing indicated that the metastable states had
Table II Uranium Metastable Populations 5Lo -+ 7M 6 7 Probe Pump power (mw) (nm) 20
597.632
10
Level
%Abs
5Lo 6
5.38 4.43
2
3.19
0.1
0.35
20
598.610
3.2
5Ho 3
2
7.73 6.68
0.63 0.1
11.4
591.540
5Lo 6
2.34
ic"
10 9.37 x 10 10 8.05 x 10 10 2.76 x 10 5.9 x lOll
151
TABLE III Y Metastable Populations Pump -1 transition (cm ) 2
2
0
D3/ 2 -.. D3/ 2
Probe -1 transition (cm )
Population (atoms cm- 3 ) 12 9.35 x 10
16131 4 F3/2 4 F5/ 2 4 F7/ 2 4 F9/2
4 0 -.. G5/ 2 4 0 -.. G5/ 2 4 0 -.. G7/ 2 4 0 -.. G9/ 2
10
17757
4.68 x 10
17615
1 .87
17708
3.27 x lOll
17832
ri.d.
x lOll
lifetimes greater than several milliseconds in the presence of argon as a collision partner. Experiments indicated that our sensitivity limit was approx9 imately 10 atoms/cm 3 for absorption processes and perhaps 107 atoms/cm 3 with laser induced fluorescence.
However, the latter procedure does not easily yield
quantitative measurements. In the absence of optical pumping, the atomic pulses show no sign of metastable population in response to probing along the flow axis. (~10
-3
At low pressures
Torr) focused 0.4-1.0 J pulses generated maximum ground state popula-
tions with kinetic energies of 3-5 eV for U and 10-12 eV for Y.
Energy cen-
troids generally increase with laser intensity in the "averaged" intensity 2 regime of 1-10 MW/cm and are consistent with results obtained earlier by Friichtenicht (ref. 8) and Levine (ref. 12).
Equivalent equilibrium temperatures at the surface are in the range of ~ 3.5 x 104 -.. 1.4 x 105 oK. Boltzmann
distribution at the melting, boiling and intermediate temperatures for states probed in this work are presented in Table IV. If evaporation were an equilibrium process, one would expect to find significant fractions of metastable states and ions.
This appears to be in sharp contrast to our observations on
thermal equilibrium source ovens and to the proposed mechanisms involving the subsurface explosions of bubbles containing gaseous atoms at high pressures and temperatures (refs. 3, 4, 10). It has been demonstrated that Nd:YAG radiation at intensity levels between 8 7 10 and 6 x 10 w/cm 2 is efficiently coupled into metal targets (refs. 13, 14). Extrapolating these results to the uranium targets used in this work, we compared the number of atoms available from the laser pulse energy to the number
152
TABLE IV Bo ltzmann distribution of states No. density (atoms cm -3 ) nu n1
Upper Level
U
Term
E(cm -1 )
T ( OK)
5 Ho 3
3868.486
300 * 1405 2273 ** 4407
U
\0
7
3800.829
300 * 1405 2273 ** 4407
Y
4 F5/2
11078.61
* 1795 ** 3611
* Melting point data
nu/nl 8 1.3 x 102 LOx 102 4.7 x 101 1.5 x 10-
5 1.3 x 10 12 4.3 x 10
8.9 x 1013
8 1.4 x 102 2.4 x 101 1.0 x 101 3.3 x 10-
5 3.1 x 10 12 9.7 x 10
7 1.3 x 10 13 8.3 x 10
4 2.1 x 102 1.8 x 10-
10 1.3 x 10 17 4.1 x 10
6 x 1013 19 2.3 x 10
7 1.3 x 10
** Boiling point data
in a typical mass pulse based on absorption measurements. Assuming an irrotational fluid field the equation of continuity is expressed as: \J •
(p(t)v) = d~~t)
(1 )
where p(t) is the time evolved density of the atomic ground state and v is an average flow velocity. Assuming a simple rectangular pulse function, the pulse 16 17 17 contained 10 to 10 atoms compared to 5 x 10 atoms calculated from laser pulse energy and the solid heat of vaporization.
Conversion of energy to
neutral atoms appears to be a relatively efficient process in agreement with other observations. A crude calculation shows that there are n
=5
20 x 1018 ~ 10 photons per
pulse and that the ratio of photons to a single surface atom is approximately 2 in the range of (4 x 10- - 1) during one period of the lattice vibration. The photon dynamics suggests that adiabatic multiphoton excitation of surface vibrational modes with energy-pooling may account for the anomolous behavior of the energy distribution in pulse evaporated atomic beams.
Of course, this mechanism
is higly speculative particularly in view of the work of Yen, et al. (ref. 15) which reports that the electron-phonon energy relaxation is less than 1 ps in metallic zirconium.
153
In summary, the distribution of population in the metastable states carries a partial history of dynamical processes occurring on the surfaces during dissociation in the presence of large optical fields.
In dramatic contrast
to thermal oven atomic sources, the laser vaporized atoms appear in their ground electronic states with high densities and high kinetic energies.
Within
the sensitivity of absorption measurements and LIF detection, long-lived metastable states were not observed.
We determined that the metastable states
resulting from optical pumping could survive in the environment and over the distances of the measurements. radiate below 800 nm.
In addition, dimers were observed but did not
These observations provide an alternative view for the
coupling of coherent pulsed radiation into surfaces.
REFERENCES 1.
J. F. Ready, 3, 11 (1963); Effects of High-Power Laser Radiation
(Academic, New York, London, 1971). C. DeMichelis, IEEE J. Quantum Electron, QE-6, 630 (1970). F. W. Dabby and U. C. Park, IEEE J. Quantum Electron, QE-8, 106 (1972). F. P. Gagliano and U. C. Park, Appl. Opt. 13, 274 (197~ S. A. Metz, Appl. Phys. l.et t . , g, 211 (1973). A. Caruso, B. Bertotti and P. Guipponi, Nuovo Cimento 45B, 176 (1966). A. Caruso and F. Gratton, Plasma Physics 10, 867 (1968--).-J. F. Friichtenicht, Rev. Sci. Instrum. 45, 51 (1974). S. P. Tang, N. G. Utterback and J. F. Friichtenicht, J. Chem. Phys. §!, 3833 (1976). 10. N. G. Utterback, S. P. Tang and J. F. Friichtenicht, Phys. Fluids ~' 900 (1976). 11. E. Miron, R. David, G. Erez, S. Lavi and L. A. Levin, J. Opt. Soc. Am. 69, 256 (1979). 12. L. P. Levine, J. F. Ready, and E. Bernal, IEEE, J. Quantum Electron. QE-4, 18 (1968). 13. M. von Allmen, J. Appl. Phys., 1L, 5460 (1976). 14. M. von Allmen, P. Blaser, K. Affolter and E. Sturmer, IEEE J. Quant. Electron, ~' 85 (1978).. 15. R. Yen, J. M. Liu, N. Bloembergen, J. K. Yee, J. G. Fuzimoto and M. ~1. Salour, Appl. Phys. Lett., 40, 185 (1982).
2. 3. 4. 5. 6. 7. 8. 9.