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Intensity dependence of the rapidity of a CO2 laser plasma shutter
Volume 31, number 1
OPTICS COMMUNICATIONS
October 1979
INTENSITY DEPENDENCE OF THE RAPIDITY OF A COz LASER PLASMA SHUTTER G. MCCLELLAND, A. MILLER, J. DEMPSEY and S.D. SMITH Physics Department, Edin burgh, UK
Heriot- Watt University,
Received 2 July 1979
A photo-conductive germanium hot-hole detector has been used to directly measure the cut-off time for transmission through a laser induced breakdown plasma. By employing a dust free atmosphere and controlled plasma initiation, the breakdown intensity was varied and its effect on the cut-off rapidity was investigated. The time taken for the transmitted signal to fall to half its initial value was found to be approximately inversely proportional to the breakdown intensity. This result is shown to be in agreement with conclusions reached by means of simple theory.
1. Introduction
Laser beam produced spark breakdown of a gas has been shown to be a feasible method for the production of short laser pulses in the subnanosecond range at 10 pm [l] .The very rapid cut-off of the transmitted beam at breakdown has been used in association with a hot CO, cell [2] and a Fabry-Perot interferometer [3] to produce pulses as short as 30 ps by free induction decay and spectral filtering respectively. Recent work has also shown that the reflection from the plasma has a correspondingly rapid switch-on [4]. The rapidity of the plasma shutter depends on the speed of formation of the plasma which should, in turn, depend on the intensity of the focussed laser radiation during breakdown {S] . In this work, we have determined an approximate relationship for the rapidity of cut-off as a function of breakdown intensity by direct measurement. This relationship thus indicates the conditions required for short pulse generation by the methods referred to above [l-4]. The measurements were performed using a single longitudinal mode hybrid TEA-CO, laser, a preioniser capable of varying the breakdown intensity in a controlled manner, and a specially developed germanium hot-hole detector with a subnanosecond response time.
Previous work has investigated the dependence of the threshold intensity for breakdown as a function of pressure, laser frequency and elapsed time from the beginning of the laser pulse [6], however, to our knowledge, no previous measurements have directly observed the rapidity of the plasma shutter as a function of intensity.
2. Formation of plasma The speed of the plasma shutter depends on the growth rate of the free electron population. It has been established that the process by which energy is absorbed from. the radiation field at 10 pm is inverse bremsstrahlung [7]. The density uf free electrons in a dust-free atmosphere is normally too low to cause initiation of this process, so that a preionisation system is required to generate free electrons, thus initiating the cascade growth of the plasma. Repeated inverse bremsstrahlung absorption then creates the plasma very quickly due to the free electrons acquiring sufficient energy by absorbing photons in the presence of the gas atoms such that electron-atom collisions can produce further ionisation. A simple relationship between the intensity at breakdown and the growth rate can be derived for the resulting plasma build up and corres85
Volume 31, number 1
OPTICS COMMUNICATIONS
pending radiation loss by equating the rate of energy expen,diture in ionisation with the rate of energy absorption from the radiation. Consider a breakdown plasma triggered by the injection of a small number of free electrons when the incident intensity is lo. The free electron population prior to triggering will be approximately zero. After triggering, the rate at which energy is expended in ionisation will be de/dt=Eidn/dt,
(1)
where Ei is the ionisation potential of the breakdown gas and n is the plasma density. The rate at which energy is absorbed by inverse bremsstrahlung is given by Wright [8] as dW}dt=n(t)Nos/2Z,
(2)
where N is the density of gas molecules, u is the electron-molecule collision cross-section and I is the intensity. Since the plasma shutter is very rapid, we can assume that the intensity is constant, lo, during the plasma formation. Equating (1) and (2) and integrating gives, Inn(T)//(O)
=NU5’2107/Ei
,
(3)
where n (0) and n(7) are the plasma densities at t = 0 and t = 7. If we let t = 0 correspond to the time at which the transmission of the plasma begins to decrease (i.e. the onset of the plasma shutter), then n (0) - 1. This gives the result that the time taken to achieve any arbitrary plasma density will be inversely proportional to the breakdown intensity, r_Ei
ln(n(r))/No5/210.
(4)
This simple approach neglects several factors which can effect the relationship. Firstly, the laser beam does not have a uniform intensity at the focus, but at best will have a gaussian spatial profile. This can be further complicated by optical aberrations of the focussing lens, however in this work, the beam geometry and laser power were kept constant and only the breakdown intensity altered using the preioniser. This analysis’.also assumed that the eIectrons will remain in the focal volume -during-the build~up; howeverthis-loss-should be small. Creation of any electrons by multiphoton excitation at this wavelength is also negligible. Self-focussing of the laser beam by the plasma constitutes a 86
October 1979
greater problem in this type of work, making it diffcult to determine the absolute intensity,in the focal region [9]. During plasma build us, the radiation can also be lost through reflection and scattering. As much as 70% of the time averaged incident pulse has been observed in backscattering [IO], but the reflection will be small until the number of free electrons nears the critical density for plasma resonance. In spite of the inadequaties of this simple model, the observed cut-off time should still be approximately inversely proportional to the incident intensity.
3. The plasma shutter Breakdown was achieved by focussingthe outputs of a h~b~iid~~A_C:Q2’~~into_a~x~a controlled nitrogen gas content, fig. 1. The hybrid laser ensured stable output (better than 5%), free from axial mode beating, which is normally characteristic of TEA CO, lasers, and the clean nitrogen atmosphere avoided the random breakdown which is produced in air. This was extremely important here to give a reproducible breakdown at the same intensity for each pulse. The lenses used for focussing and recollimating were spherically corrected f/l germanium doublets of 2.5 cm focal length. The incident beam diameter was such that only approximately half of the focussing lens was illuminated. The maximum intensity in the focal region, neglecting possible~abetrationand selffocussing effect, was calculated to be - lo9 W cme2. Plasma triggering and control was achieved by allowing the ~rrrt slightly cfiF_ metal iris situated just beyond the focus,.Transl&on of the iris through small distances along the beam axis allowed the breakdown point to be set at a range of positions on the temporal profile of the pulse, thus giving various possible values of breakdown intensity. This-device has been describti-m~&fti-iirY~E~fG] By adjusting the lens, Lx, the transmitted signal was focussed onto the crystal face of the hot-hole detector. It proved necessary to vary the spot size at the detector as’the thre”shoId was varied since, for breakdo&~ly in the pulse, the transmitted power was low and all of-the-radla~s6fi~dt6~~~-Eone~~~d at-thedetec?orGn the other hand, for breakdown at the peak of the laser pulse, crystal damage would have resulted during a total power measurement as well as saturation of the
October 1979
OPTICS COMMUNICATIONS
Volume 31, number 1
-
::
Breakdown Cell.
Photon
Fig. 1. Schematic representation
electronic transitions responsible for the photoconductive signal. Therefore, in this situation, the laser beam was defocussed. For peak power measurements at each preioniser setting a demountable plane mirror was used to send the beam onto a calibrated photon drag detector.
4. The detection system To carry out time resolved measurements of pulses with less than 1 ns falling edges, one is severely limited in the choice of available detectors and oscilloscopes. The photon drag detector, although potentially a very fast instrument, is severely limited in its sensitivity (typically 0.3 mV/kW) and oscilloscope amplifiers are limited to 500 MHz bandwidths. We have tackled this problem in these experiments using a Tektronix 7A21N direct access unit with a Tektronix 7904 oscilloscope and a germanium hot-hole detector. The direct acces unit has no amplification and gives a 4 V/div deflection. The combination with the oscilloscope gives a 1 GHz bandwidth and a rise time of -300 ps. Thus, signals greater than 1 volt are required for observation. This value can be obtained by making use of the inter-valence band photo-conductivity in p-type germanium when infrared radiation causes electronic transitions between the light and heavy hole bands [ 11). The intrinsic response time of such a detector is determined by the relaxation time of - 2 ps but, in practice is limited by the photon transit time in the crystal. The detector was constructed using a 1 cm long crys-
Drag
of the experimental lay-out.
tal of 2.5 Cl cm p-type germanium with a (100) face. The crystal was inserted into one arm of a four resistor bridge and a 400 V bias pulse applied across the bridge. This pulse (10 PS long) was produced by a thermistor high voltage pulse circuit [ 121 to give a square pulse with minimum droop, and kept short to avoid resistance heating of the germanium. By earthing the centre of one arm of the bridge, a signal could be observed with only minimal voltage offset once the bias pulse was synchronised with the laser discharge. The sensitivity of the detector measured against a calibrated joule meter was 18.5 mV/kW at 10.6 E.crnin this arrangement. For a 1 cm crystal, the transit time of the radiation is 120 ps, however, the device was circuit response limited at about 400 ps, measured by time domain reflectometry. This was fast enough for the laser intensities available in this work.
5. Results and conclusions The oscilloscope trace showing the plasma cut-off was recorded for a series of different breakdown. Enlargements (fig. 2) of the original photographs were made, and in each case, the time (T) required for the transmitted power to fall to half its breakdown value was measured. Several results were obtained for each breakdown intensity and the average values of r were calculated. Fig. 3 shows the reciprocal of r plotted as a function of laser power at breakdown. Despite the difficulty of obtaining accurate measurements the general 87
Volume 31, number 1
OPTICS COMMUNICATIONS
October 1979
Fig. 2. Enlargement of a typical hot-hole detector signal (negative going).
trend is quite clear with the results falling on a linear curve within experimental error. Thus, for the limited range of values examined, the relationship between r and breakdown intensity differs little from the inverse proportionality predicted by the simple theory, assuming that intensity is proportional to laser power. The most rapid cut-off measured here produced a value of 7 - 800 ps and corresponded to breakdown at the peak of the pulse (i.e. a power of 500 kW or an intensity of - 109 W cmP2). We may conclude, therefore, that a plasma shutter produced by a laser power of this order of magnitude will give a subnanosecond cut-off. The relationship shown in fig. 3 shows that the cutoff speed tends to rise at a slightly higher rate at the highest intensities. This may be a result of self-focussing and would therefore produce a more pronounced effect in experiments employing higher powers than those available here. The loss of transmitted radiation resulting from increased scattering at high intensities might also cause the cut-off speed to be greater than predicted although this loss should be small during the initial stages of plasma growth. Further investigation of the relationship between laser power and cut-off speed would be useful and should lead to a better understanding of the processes involved in the formation of the plasma. The limit of the hot-hole detector speed has not yet been reached since a more powerful laser is required to obtain shorter cut-off times.
88
Fig. 3. Experimental relationship between l/r and laser power.
[l] E. Yablonovitch, Phys. Rev. 10, (1974) 1888. [2] E. Yablonovitch and J. Goldhar, Appl. Phys. Lett. 25 (1974) 580. [3] R.A. Fisher and B.J. Feldman, Optics Lett. 1 (1977) 161. [4] G. McClelland and S.D. Smith, Optics Comm. 27 (1978) 101. [5] C. Crey-Morgan, Rep. Prog. Phys. 38 (1975) 621. [6] R.C. Tomlinson, Phys. Rev. Lett. 14 (1965) 489. [7] Y.B. Zeldovich and Yu. P. Raizer, J. Exp. Theor. Phys. 47 (1964) 1150. [S] J.K. Wright, Proc. Phys. Sot. 84 (1964) 41. [ 91 A.J. Alcock, Laser interactions and related plasma phenomena, Vol. 2, ed. H.J. Sulartz and H. Kora (Plenum, New York 1972). [lo] R.P. Godwin, C.G.M. Van Kessel, J.N. Olsen, P. Sachsenmaier, R. Sigel and K. Eidmann, 2. Naturforsch 32a (1977) 1100. [ll] A.F. Gibson and P.N.D. Maggs, J. Phys. D: Appl. Phys. 7 (1974) 292. [12] B. Griffmg, Rev. Sci. Instrum 45 (1974) 964.
OPTICS COMMUNICATIONS
October 1979
INTENSITY DEPENDENCE OF THE RAPIDITY OF A COz LASER PLASMA SHUTTER G. MCCLELLAND, A. MILLER, J. DEMPSEY and S.D. SMITH Physics Department, Edin burgh, UK
Heriot- Watt University,
Received 2 July 1979
A photo-conductive germanium hot-hole detector has been used to directly measure the cut-off time for transmission through a laser induced breakdown plasma. By employing a dust free atmosphere and controlled plasma initiation, the breakdown intensity was varied and its effect on the cut-off rapidity was investigated. The time taken for the transmitted signal to fall to half its initial value was found to be approximately inversely proportional to the breakdown intensity. This result is shown to be in agreement with conclusions reached by means of simple theory.
1. Introduction
Laser beam produced spark breakdown of a gas has been shown to be a feasible method for the production of short laser pulses in the subnanosecond range at 10 pm [l] .The very rapid cut-off of the transmitted beam at breakdown has been used in association with a hot CO, cell [2] and a Fabry-Perot interferometer [3] to produce pulses as short as 30 ps by free induction decay and spectral filtering respectively. Recent work has also shown that the reflection from the plasma has a correspondingly rapid switch-on [4]. The rapidity of the plasma shutter depends on the speed of formation of the plasma which should, in turn, depend on the intensity of the focussed laser radiation during breakdown {S] . In this work, we have determined an approximate relationship for the rapidity of cut-off as a function of breakdown intensity by direct measurement. This relationship thus indicates the conditions required for short pulse generation by the methods referred to above [l-4]. The measurements were performed using a single longitudinal mode hybrid TEA-CO, laser, a preioniser capable of varying the breakdown intensity in a controlled manner, and a specially developed germanium hot-hole detector with a subnanosecond response time.
Previous work has investigated the dependence of the threshold intensity for breakdown as a function of pressure, laser frequency and elapsed time from the beginning of the laser pulse [6], however, to our knowledge, no previous measurements have directly observed the rapidity of the plasma shutter as a function of intensity.
2. Formation of plasma The speed of the plasma shutter depends on the growth rate of the free electron population. It has been established that the process by which energy is absorbed from. the radiation field at 10 pm is inverse bremsstrahlung [7]. The density uf free electrons in a dust-free atmosphere is normally too low to cause initiation of this process, so that a preionisation system is required to generate free electrons, thus initiating the cascade growth of the plasma. Repeated inverse bremsstrahlung absorption then creates the plasma very quickly due to the free electrons acquiring sufficient energy by absorbing photons in the presence of the gas atoms such that electron-atom collisions can produce further ionisation. A simple relationship between the intensity at breakdown and the growth rate can be derived for the resulting plasma build up and corres85
Volume 31, number 1
OPTICS COMMUNICATIONS
pending radiation loss by equating the rate of energy expen,diture in ionisation with the rate of energy absorption from the radiation. Consider a breakdown plasma triggered by the injection of a small number of free electrons when the incident intensity is lo. The free electron population prior to triggering will be approximately zero. After triggering, the rate at which energy is expended in ionisation will be de/dt=Eidn/dt,
(1)
where Ei is the ionisation potential of the breakdown gas and n is the plasma density. The rate at which energy is absorbed by inverse bremsstrahlung is given by Wright [8] as dW}dt=n(t)Nos/2Z,
(2)
where N is the density of gas molecules, u is the electron-molecule collision cross-section and I is the intensity. Since the plasma shutter is very rapid, we can assume that the intensity is constant, lo, during the plasma formation. Equating (1) and (2) and integrating gives, Inn(T)//(O)
=NU5’2107/Ei
,
(3)
where n (0) and n(7) are the plasma densities at t = 0 and t = 7. If we let t = 0 correspond to the time at which the transmission of the plasma begins to decrease (i.e. the onset of the plasma shutter), then n (0) - 1. This gives the result that the time taken to achieve any arbitrary plasma density will be inversely proportional to the breakdown intensity, r_Ei
ln(n(r))/No5/210.
(4)
This simple approach neglects several factors which can effect the relationship. Firstly, the laser beam does not have a uniform intensity at the focus, but at best will have a gaussian spatial profile. This can be further complicated by optical aberrations of the focussing lens, however in this work, the beam geometry and laser power were kept constant and only the breakdown intensity altered using the preioniser. This analysis’.also assumed that the eIectrons will remain in the focal volume -during-the build~up; howeverthis-loss-should be small. Creation of any electrons by multiphoton excitation at this wavelength is also negligible. Self-focussing of the laser beam by the plasma constitutes a 86
October 1979
greater problem in this type of work, making it diffcult to determine the absolute intensity,in the focal region [9]. During plasma build us, the radiation can also be lost through reflection and scattering. As much as 70% of the time averaged incident pulse has been observed in backscattering [IO], but the reflection will be small until the number of free electrons nears the critical density for plasma resonance. In spite of the inadequaties of this simple model, the observed cut-off time should still be approximately inversely proportional to the incident intensity.
3. The plasma shutter Breakdown was achieved by focussingthe outputs of a h~b~iid~~A_C:Q2’~~into_a~x~a controlled nitrogen gas content, fig. 1. The hybrid laser ensured stable output (better than 5%), free from axial mode beating, which is normally characteristic of TEA CO, lasers, and the clean nitrogen atmosphere avoided the random breakdown which is produced in air. This was extremely important here to give a reproducible breakdown at the same intensity for each pulse. The lenses used for focussing and recollimating were spherically corrected f/l germanium doublets of 2.5 cm focal length. The incident beam diameter was such that only approximately half of the focussing lens was illuminated. The maximum intensity in the focal region, neglecting possible~abetrationand selffocussing effect, was calculated to be - lo9 W cme2. Plasma triggering and control was achieved by allowing the ~rrrt slightly cfiF_ metal iris situated just beyond the focus,.Transl&on of the iris through small distances along the beam axis allowed the breakdown point to be set at a range of positions on the temporal profile of the pulse, thus giving various possible values of breakdown intensity. This-device has been describti-m~&fti-iirY~E~fG] By adjusting the lens, Lx, the transmitted signal was focussed onto the crystal face of the hot-hole detector. It proved necessary to vary the spot size at the detector as’the thre”shoId was varied since, for breakdo&~ly in the pulse, the transmitted power was low and all of-the-radla~s6fi~dt6~~~-Eone~~~d at-thedetec?orGn the other hand, for breakdown at the peak of the laser pulse, crystal damage would have resulted during a total power measurement as well as saturation of the
October 1979
OPTICS COMMUNICATIONS
Volume 31, number 1
-
::
Breakdown Cell.
Photon
Fig. 1. Schematic representation
electronic transitions responsible for the photoconductive signal. Therefore, in this situation, the laser beam was defocussed. For peak power measurements at each preioniser setting a demountable plane mirror was used to send the beam onto a calibrated photon drag detector.
4. The detection system To carry out time resolved measurements of pulses with less than 1 ns falling edges, one is severely limited in the choice of available detectors and oscilloscopes. The photon drag detector, although potentially a very fast instrument, is severely limited in its sensitivity (typically 0.3 mV/kW) and oscilloscope amplifiers are limited to 500 MHz bandwidths. We have tackled this problem in these experiments using a Tektronix 7A21N direct access unit with a Tektronix 7904 oscilloscope and a germanium hot-hole detector. The direct acces unit has no amplification and gives a 4 V/div deflection. The combination with the oscilloscope gives a 1 GHz bandwidth and a rise time of -300 ps. Thus, signals greater than 1 volt are required for observation. This value can be obtained by making use of the inter-valence band photo-conductivity in p-type germanium when infrared radiation causes electronic transitions between the light and heavy hole bands [ 11). The intrinsic response time of such a detector is determined by the relaxation time of - 2 ps but, in practice is limited by the photon transit time in the crystal. The detector was constructed using a 1 cm long crys-
Drag
of the experimental lay-out.
tal of 2.5 Cl cm p-type germanium with a (100) face. The crystal was inserted into one arm of a four resistor bridge and a 400 V bias pulse applied across the bridge. This pulse (10 PS long) was produced by a thermistor high voltage pulse circuit [ 121 to give a square pulse with minimum droop, and kept short to avoid resistance heating of the germanium. By earthing the centre of one arm of the bridge, a signal could be observed with only minimal voltage offset once the bias pulse was synchronised with the laser discharge. The sensitivity of the detector measured against a calibrated joule meter was 18.5 mV/kW at 10.6 E.crnin this arrangement. For a 1 cm crystal, the transit time of the radiation is 120 ps, however, the device was circuit response limited at about 400 ps, measured by time domain reflectometry. This was fast enough for the laser intensities available in this work.
5. Results and conclusions The oscilloscope trace showing the plasma cut-off was recorded for a series of different breakdown. Enlargements (fig. 2) of the original photographs were made, and in each case, the time (T) required for the transmitted power to fall to half its breakdown value was measured. Several results were obtained for each breakdown intensity and the average values of r were calculated. Fig. 3 shows the reciprocal of r plotted as a function of laser power at breakdown. Despite the difficulty of obtaining accurate measurements the general 87
Volume 31, number 1
OPTICS COMMUNICATIONS
October 1979
Fig. 2. Enlargement of a typical hot-hole detector signal (negative going).
trend is quite clear with the results falling on a linear curve within experimental error. Thus, for the limited range of values examined, the relationship between r and breakdown intensity differs little from the inverse proportionality predicted by the simple theory, assuming that intensity is proportional to laser power. The most rapid cut-off measured here produced a value of 7 - 800 ps and corresponded to breakdown at the peak of the pulse (i.e. a power of 500 kW or an intensity of - 109 W cmP2). We may conclude, therefore, that a plasma shutter produced by a laser power of this order of magnitude will give a subnanosecond cut-off. The relationship shown in fig. 3 shows that the cutoff speed tends to rise at a slightly higher rate at the highest intensities. This may be a result of self-focussing and would therefore produce a more pronounced effect in experiments employing higher powers than those available here. The loss of transmitted radiation resulting from increased scattering at high intensities might also cause the cut-off speed to be greater than predicted although this loss should be small during the initial stages of plasma growth. Further investigation of the relationship between laser power and cut-off speed would be useful and should lead to a better understanding of the processes involved in the formation of the plasma. The limit of the hot-hole detector speed has not yet been reached since a more powerful laser is required to obtain shorter cut-off times.
88
Fig. 3. Experimental relationship between l/r and laser power.
[l] E. Yablonovitch, Phys. Rev. 10, (1974) 1888. [2] E. Yablonovitch and J. Goldhar, Appl. Phys. Lett. 25 (1974) 580. [3] R.A. Fisher and B.J. Feldman, Optics Lett. 1 (1977) 161. [4] G. McClelland and S.D. Smith, Optics Comm. 27 (1978) 101. [5] C. Crey-Morgan, Rep. Prog. Phys. 38 (1975) 621. [6] R.C. Tomlinson, Phys. Rev. Lett. 14 (1965) 489. [7] Y.B. Zeldovich and Yu. P. Raizer, J. Exp. Theor. Phys. 47 (1964) 1150. [S] J.K. Wright, Proc. Phys. Sot. 84 (1964) 41. [ 91 A.J. Alcock, Laser interactions and related plasma phenomena, Vol. 2, ed. H.J. Sulartz and H. Kora (Plenum, New York 1972). [lo] R.P. Godwin, C.G.M. Van Kessel, J.N. Olsen, P. Sachsenmaier, R. Sigel and K. Eidmann, 2. Naturforsch 32a (1977) 1100. [ll] A.F. Gibson and P.N.D. Maggs, J. Phys. D: Appl. Phys. 7 (1974) 292. [12] B. Griffmg, Rev. Sci. Instrum 45 (1974) 964.