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Electron—Hole plasma in CuCl after subpicosecond photoexcitation
Volume 42, number 4
OPTICS COMMUNICATIONS
15 July 1982
ELECTRON-HOLE PLASMA IN CuCl AFTER SUBPICOSECOND PHOTOEXCITATION D. HULIN 2, A. ANTONETTI 1, L.L. CHASE 3, j.L. MARTIN 1, A. MIGUS 1, A. MYSYROWICZ 2 1 Laboratoire d'Optique Appliqu~e, ENSTA, Ecole Polytechnique, 91120 Palaiseau, France 2 Groupe de Physique des Solides de l'Ecole Normale Supdrieure, 75005 Paris, France 3 Physics Department, Indiana University, Bloomington, IN 47405, USA Received 18 April 1982
The formation of a superdense electron-hole plasma in CuC1 is reported for injected carrier densities n > 1020 em -3. The plasma lifetime is de~ermined to be r 10 -11 s.
The optical properties of CuC1 have been extensively studied, both under weak and strong excitation con, ditions. In the weak regime, the lowest electronic excited states are excitons, which are responsible for very intense absorption lines below the forbidden gap energy [1]. Under increasing input intensity, the formation of molecular entities, called biexcitons, of lower energy per electron-hole pair has been observed in absorption and emission spectroscopy [2]. Biexcitons give rise to giant optical nonlinearities [3] and it has been reported that they undergo a BoseEinstein condensation at sufficiently low temperatures [4]. If the density of electron-hole pairs injected into the crystal is further increased, one expects eventually a transition in the excited state of the system to occur, from the insulating phase consisting of excitonie particles, to a conducting phase of an electron-hole plasma. Different critical densities n c have been calculated for the onset of this insulator-conductor Mott-like transition, with values ranging between axnle 13 = 0.25 and 0.435 at T = 0 K [5,6], where a x is the exciton Bohr radius (a x = 7 )k for CuCl). Although the formation of an electron-hole plasma has been observed in several direct gap semiconductors, most notably GaAs [7], a dynamical study of the Mott transition in these materials has proved difficult, since the effective temperature of the plasma is comparable with the exciton binding energy, In CuC1, E x = 0.2 eV so that the criterion E x / k T ~, 1 should be more easily satisfied. Unfortunately, the formation of an electron260
hole plasma in CuCI has not been reported so far, because the required input light intensifies lead to irreversiblesample damage if pulses of nanosecond or subnanosecond duration are used. By using optical pulses of subpicoseeond duration, we show in this letter that it is possible to reach situations well beyond the Mott critical density, n c ~ 1020 era -3 , and pressent a dynamical study of the plasma in CuC1. Besides its fundamental interest for the understanding of the Mott transition, the dynamical behavior of the electron-hole plasma may have practical importance, since it can limit the speed of optical bistable elernents [8]. Also, it has been recently demonstrated that superdense plasmas in direct gap semiconductors can lead to pulsed laser action of ps duration and broadband wavelength tunability [9]. To generate the carriers, a UV optical pulse is used CA= 308 nm; pulse duration = 0.3 ps, energy per pulse ~10/aJ). It is obtained by frequency doubling in a KDP crystal the amplified red output from a passively mode-locked Rh 6t3 dye laser [10]. When focused to a spot of diameter ¢ ~ 200 Jam, it creates up to a few times 1021 cm -3 particles, initially with an excess energy ~ = 622 meV with respect to the minimum of the band gap. In order to have nearly homogeneous volume excitation of the sample, the c r y s t ~ film thicknesses d were chosen to be from 0.C2 ~rn to 0.1 /am, fuifflling the conditions d ~" ~-1 where a, the linear band to band absorption coefficient at 308 nm, is estimated to be 105 to 106 cm -1 . The samples are
Volume 42, number 4
-'~-[]-->--D-
/,-
T=13 K
/""
7
\
, 1
i
i /
"
~:
I*x16t'/
,~
i
'
//
::[ /
.\
I.x8,'
/
,Y',',/.,,7 ,,".
,,,
// 410
15 July 1982
OPTICS COMMUNICATIONS
.-;/
/ / 400
li* 390 nm
Fig. 1. Time-integrated emission spectra of a CuC1film (thickness = 50 nm) at T = 15 K obtained with different input intensities I0 from a UV subpicoseeond laser pulse. All curves are normalized to the same height for the blexciton emission line at 391.5 nm. The line at 391.5 grows superlinearly below Ic, and siigthly sublinearly above I c (It is the threshold intensity for plasma appearance). obtained by evaporating high purity anhydrous GaG1 or high quality single crystals onto a fused silica substrate. In fig. 1, time-integrated emission spectra, recorded at 15 K in the forward direction, are shown for different excitation intensities. The emission line at 391.5 nm has been extensively studied previously [2] and corresponds to the radiative annihilation of the excitonic molecule. At very low power excitation only the biexcitonic line appears. With increasing excitation this line first broadens, and a tail develops on the low side energy. At still higher excitation a new, distinct broad band appears at even lower energy. This broad emission shows the features expected from the radiative recombination of electron.hole pairs inside a dense metallic plasma. It appears above a well-defined excitation threshold; further, with increasing excitation its width broadens and the low energy side of the emission band shifts to longer wavelengths. Particle densities in the plasma may be extracted from the value o f the reduced gap due to the presence of excited carriers. The gap reduction, which is given by the low energy edge of the emission, is well approximated at high densities and T = 0 in terms of re-
duced parameters by a universal function of n, almost independent of the particular band structure [11 ]. Applied to CuC1, it leads to a value o f n c -~ 2 X 1020 cm - 3 near the threshold for appearance of the plasma band, taking an exciton radius a x = 7 A. This value is in good agreement with an estimate of the generated particle density from the experimental conditions. It corresponds to an average distance between particles r s ~ 2 a x , close to the value obtained in ref. [6] for the transition density from an insulating to a conducting phase. The decay of the plasma emission has been measured with fast streak cameras (Thomson-CSF, and Imacon). The duration o f the signal was found to be less than l0 ps, slightly above our highest camera resolution (see fig. 2). The emission at 391.5 nm, from the biexciton gas, was also detected, both below and above plasma appearance threshold. In the latter case, it was found to succeed the signal from the plasma with a delay ( ~ 1 0 ps) larger than the 2 ps computed effect of group velocity dispersion. In the former case, the signal duration was dependent upon input intensity, ranging between r "~ 10 ps and r "~ 45 ps at lower i n tensities.
Information concerning the dynamics of the excited system may also be obtained in transmission ex-
laser
Am*..
<7 It'"'" //
i
-20
0
20
40
60
80
100 t(ps)
Fig. 2. T i m e evolution of the total luminescence of CuC1 at 15 K, recorded in single shots by a fast streak camera (UV
pulse excitation). The zero of the time scale is arbitrarily set at the position of residual red fight from the primary laser pulse. The time delay between the red laser pulse and the luminescence is well accounted for by the dispersion of optical elements between the sample and the detector. The inset shows the signal from the plasma emission alone (same time scale). 261
Volume 42, number 4
OPTICSCOMMUNICATIONS
periments, using a weak subpicosecond continuum probe which traverses the excited region of the sample at different delays following the UV pump pulse [10,12]. In the presence of a metallic plasma one ex. pects excitonic structures to disappear~Instead, at T = 0, optical gain should occur from Eg, the renormalized gap, up to/~, the chemical potential of the plasma, followed by absorption above #. At higher T, the transition from gain to loss moves to lower energies, because of the reduction of the Fermi degeneracy of the plasma. In a dynamical regime, following injection of hot carders, concomittant exciton screening and gap renormalization, the change of transmission with time will reflect both the carrier cooling (leading to the filling of the band edges) and carrier density evolution. This results in a more complex behavior, with a transition from absorption to gain shifting in the frequency domain with time and input intensity. Picosecond time-resolved pump and probe experiments performed in CuC1 can be well explained along these lines. Results taken at 15 K are shown in fig. 3. The continuous curve is obtained when the probe pulse precedes the pump on the sample and is therefore representative of the unexcited sample. The two lines at X = 387 nm and 378 nm are the n = 1 terms of the excitonic series from the two upper valence bands (PT, P8) and the lowest conduction band (F6). For a time delay At = 1 ps a reduction of the exciton oscillator strength occurs, as expected in the ~resence
~~-
t
Ps
1 T - 15K ,Io
400 '
~
380
X{nm)
Fig. 3. AbsorPtion spectra of CuC1at 15 K in the exciton region, recorded with a broadband subpicosecondpulse at different delays from the intense UV pump pulse. (Sample thickness= 95 nm.) 262
15 July 1982
of the plasma phase. This effect is particularly well evident in very thin samples where a nearly complete disappearance of the exciton structures is observed. At the same time (At = 1 ps), a new absorption tail, extending below the excitonic structures is apparent with an edge shifting to lower energies under increasing excitation. The excitonic oscillator strength recovers in accordance with the plasma decay time reported above, although a broadening and high energy shift of the lines persist for a longer period of the order of 100 ps. Time-resolved transmission spectra also show some evidence of a transition from optical loss to gain in the plasma spectral region below the excitons, occuring within a few ps from At = 0. A study of the cooling rate and the evolution of the chemical potential of the plasma as a function of injected particle densities is intended for a future article. We now briefly comment on the measured plasma decay. The results of fig. 2 indicate that the Iifetime of the free carriers is limited by excitonic particle formation when their density reaches n c. The initial decrease of the carrier density down to n c may have several origins: volume expansion of the excited re. glen of the sample [13], non-radiative Auger decay involving three (or more) carriers [14], and direct annihilation of electron-hole pairs. The first process should not play a significant role here, in view of the nearly homogeneous volume excitation, large lateral dimensions and short times considered. We believe that direct electron-hole pair recombination dominates over Auger non-radiative decay in the density range of our experiments because the overall radiative efficiency from the plasma increases sharply with higher input intensities well above n c (see fig. 1). To our knowledge, there are no known values for the Auger and bimolecular decay constants in CuC1. Assuming only radiative decay, we obtain for the electron-hole (bimolecular) recombination constant B a value B "- 5-X 10 -10 cm3/s. However, neglect of Auger decay and s t i m ~ t e d emission may not be justified. In conclusion, we have reported the first experimental evidence of the electron-hole plasma in CuC1, and measured its decay time ~"~ 10 -11 s. Due to its simple band structure and large exciton binding energy, CuC1 provides a good system for the study of the Mott transition.
Volume 42, number 4
OPTICS COMMUNICATIONS
This work was supported b y the Direction des Recherches Etudes et Techniques and for L.L.C. b y N.S.F. grant DMR-81-05005. We acknowledge the help of Dr. N. Peyghambarian in preparing the sam. ples.
References [1] See for instance A. Goldmann, Phys. Stat. SoL 81 (1977) 9. [2] See for instance, E. Hanamura and H. Haug, Physics Reports 33C (1977) 209. [3] G.M. Gale and A. Mysyrowicz, Phys. Rev. Lett. 32 (1974) 727; T. Mira and N. Nagasawa, Optics Comm. 24 (1978) 345; A. Maruani, J.L. Oudar, E. Batifol and D.S. Chemla, Phys. Rev. Lett. 41 (1978) 1372. [4] L.L. Chase, G. Grynberg, N. Peyghambarian and A. Mysyrowicz, Phys. Rev. Lett. 42 (1979) 1231; N. Peyghambarian, L.L. Chase and A. Mysyrowicz, Optics Comm. 41 (1982) 178. [5] N.F. Mott, Proc. Phys. Soc. London Sec. A62 (1949) 416. [6] V.E. Bisti and A.P. Silin, Soy. Phys. Solid State 20 (1978) 1068; V.E. Bisti, Soviet Physics Solid State 23 (1981) 855.
15 July 1982
[7] S. Tanaka, H. Kobayashi, H. Saito and S. Shionoya, J. Phys. Soc. Jap. 49 (1980) 1051; E.O. Gobel, P.H. Liang and D. yon der Linde, Solid State Comm. 37 (1981) 609. [8] H.M. Gibbs, S.L. McCall, T.N.C. Venkatesan, A. Passner, A.C. Gossard and W. Wiegman, CLEA 1979, IEEE J. Quantum Electron. QE-15 (1979) 108 D. [9] T.C. Damen, M.A. Dugay, J. Shah, J. Stone, J.M. Wiesenfeld and R.A. Logan, AppL Phys. Lett. 39 (1981) 142. [10] E.P. Ippen and C.V. Shank, Subpicosecond spectrscopy, in: Picosecond Phenomena Springer Series in Chemical Physics, VoL 4, eds. C.V. Shank, E.P. Ippen and S.L. Shapiro (1978) p. 103; A. Migus, C.V. Shank, E.P. Ippen and R.L Fork, IEEE J. J. Quantum Elec. QE-18 (1982) 101; J.L. Martin, R. Astier, A. Migus and A. Antonetti, in: Springer Series in Optical Sciences, Vol. 22 (1980) 229. [11 ] C. Benoit a la Guillaume, to appear in Collective excitations in solids, (Plenum Press). [12] C.V. Shank, R.L. Fork, R.F. Leheny and J. Shah, Phys. Rev. Lett. 42 (1979) 112; D. yon der Linde and R. Lambrich, Phys. Rev. Lett. 42 (1979) 1090. [13] D.IL Auston and D.V. Shank, Phys. Rev. Lett. 32 (1974) 1120; A. Cornet, M. Pugnet, J. Collet, R. Amand and M. Brousseau, J. de Physique C7 (1981) 471. [14] D.H. Auston, C.V. Chank and P. Lefur, Phys. Rev. Lett. 35 (1977) 1022.
263
OPTICS COMMUNICATIONS
15 July 1982
ELECTRON-HOLE PLASMA IN CuCl AFTER SUBPICOSECOND PHOTOEXCITATION D. HULIN 2, A. ANTONETTI 1, L.L. CHASE 3, j.L. MARTIN 1, A. MIGUS 1, A. MYSYROWICZ 2 1 Laboratoire d'Optique Appliqu~e, ENSTA, Ecole Polytechnique, 91120 Palaiseau, France 2 Groupe de Physique des Solides de l'Ecole Normale Supdrieure, 75005 Paris, France 3 Physics Department, Indiana University, Bloomington, IN 47405, USA Received 18 April 1982
The formation of a superdense electron-hole plasma in CuC1 is reported for injected carrier densities n > 1020 em -3. The plasma lifetime is de~ermined to be r 10 -11 s.
The optical properties of CuC1 have been extensively studied, both under weak and strong excitation con, ditions. In the weak regime, the lowest electronic excited states are excitons, which are responsible for very intense absorption lines below the forbidden gap energy [1]. Under increasing input intensity, the formation of molecular entities, called biexcitons, of lower energy per electron-hole pair has been observed in absorption and emission spectroscopy [2]. Biexcitons give rise to giant optical nonlinearities [3] and it has been reported that they undergo a BoseEinstein condensation at sufficiently low temperatures [4]. If the density of electron-hole pairs injected into the crystal is further increased, one expects eventually a transition in the excited state of the system to occur, from the insulating phase consisting of excitonie particles, to a conducting phase of an electron-hole plasma. Different critical densities n c have been calculated for the onset of this insulator-conductor Mott-like transition, with values ranging between axnle 13 = 0.25 and 0.435 at T = 0 K [5,6], where a x is the exciton Bohr radius (a x = 7 )k for CuCl). Although the formation of an electron-hole plasma has been observed in several direct gap semiconductors, most notably GaAs [7], a dynamical study of the Mott transition in these materials has proved difficult, since the effective temperature of the plasma is comparable with the exciton binding energy, In CuC1, E x = 0.2 eV so that the criterion E x / k T ~, 1 should be more easily satisfied. Unfortunately, the formation of an electron260
hole plasma in CuCI has not been reported so far, because the required input light intensifies lead to irreversiblesample damage if pulses of nanosecond or subnanosecond duration are used. By using optical pulses of subpicoseeond duration, we show in this letter that it is possible to reach situations well beyond the Mott critical density, n c ~ 1020 era -3 , and pressent a dynamical study of the plasma in CuC1. Besides its fundamental interest for the understanding of the Mott transition, the dynamical behavior of the electron-hole plasma may have practical importance, since it can limit the speed of optical bistable elernents [8]. Also, it has been recently demonstrated that superdense plasmas in direct gap semiconductors can lead to pulsed laser action of ps duration and broadband wavelength tunability [9]. To generate the carriers, a UV optical pulse is used CA= 308 nm; pulse duration = 0.3 ps, energy per pulse ~10/aJ). It is obtained by frequency doubling in a KDP crystal the amplified red output from a passively mode-locked Rh 6t3 dye laser [10]. When focused to a spot of diameter ¢ ~ 200 Jam, it creates up to a few times 1021 cm -3 particles, initially with an excess energy ~ = 622 meV with respect to the minimum of the band gap. In order to have nearly homogeneous volume excitation of the sample, the c r y s t ~ film thicknesses d were chosen to be from 0.C2 ~rn to 0.1 /am, fuifflling the conditions d ~" ~-1 where a, the linear band to band absorption coefficient at 308 nm, is estimated to be 105 to 106 cm -1 . The samples are
Volume 42, number 4
-'~-[]-->--D-
/,-
T=13 K
/""
7
\
, 1
i
i /
"
~:
I*x16t'/
,~
i
'
//
::[ /
.\
I.x8,'
/
,Y',',/.,,7 ,,".
,,,
// 410
15 July 1982
OPTICS COMMUNICATIONS
.-;/
/ / 400
li* 390 nm
Fig. 1. Time-integrated emission spectra of a CuC1film (thickness = 50 nm) at T = 15 K obtained with different input intensities I0 from a UV subpicoseeond laser pulse. All curves are normalized to the same height for the blexciton emission line at 391.5 nm. The line at 391.5 grows superlinearly below Ic, and siigthly sublinearly above I c (It is the threshold intensity for plasma appearance). obtained by evaporating high purity anhydrous GaG1 or high quality single crystals onto a fused silica substrate. In fig. 1, time-integrated emission spectra, recorded at 15 K in the forward direction, are shown for different excitation intensities. The emission line at 391.5 nm has been extensively studied previously [2] and corresponds to the radiative annihilation of the excitonic molecule. At very low power excitation only the biexcitonic line appears. With increasing excitation this line first broadens, and a tail develops on the low side energy. At still higher excitation a new, distinct broad band appears at even lower energy. This broad emission shows the features expected from the radiative recombination of electron.hole pairs inside a dense metallic plasma. It appears above a well-defined excitation threshold; further, with increasing excitation its width broadens and the low energy side of the emission band shifts to longer wavelengths. Particle densities in the plasma may be extracted from the value o f the reduced gap due to the presence of excited carriers. The gap reduction, which is given by the low energy edge of the emission, is well approximated at high densities and T = 0 in terms of re-
duced parameters by a universal function of n, almost independent of the particular band structure [11 ]. Applied to CuC1, it leads to a value o f n c -~ 2 X 1020 cm - 3 near the threshold for appearance of the plasma band, taking an exciton radius a x = 7 A. This value is in good agreement with an estimate of the generated particle density from the experimental conditions. It corresponds to an average distance between particles r s ~ 2 a x , close to the value obtained in ref. [6] for the transition density from an insulating to a conducting phase. The decay of the plasma emission has been measured with fast streak cameras (Thomson-CSF, and Imacon). The duration o f the signal was found to be less than l0 ps, slightly above our highest camera resolution (see fig. 2). The emission at 391.5 nm, from the biexciton gas, was also detected, both below and above plasma appearance threshold. In the latter case, it was found to succeed the signal from the plasma with a delay ( ~ 1 0 ps) larger than the 2 ps computed effect of group velocity dispersion. In the former case, the signal duration was dependent upon input intensity, ranging between r "~ 10 ps and r "~ 45 ps at lower i n tensities.
Information concerning the dynamics of the excited system may also be obtained in transmission ex-
laser
Am*..
<7 It'"'" //
i
-20
0
20
40
60
80
100 t(ps)
Fig. 2. T i m e evolution of the total luminescence of CuC1 at 15 K, recorded in single shots by a fast streak camera (UV
pulse excitation). The zero of the time scale is arbitrarily set at the position of residual red fight from the primary laser pulse. The time delay between the red laser pulse and the luminescence is well accounted for by the dispersion of optical elements between the sample and the detector. The inset shows the signal from the plasma emission alone (same time scale). 261
Volume 42, number 4
OPTICSCOMMUNICATIONS
periments, using a weak subpicosecond continuum probe which traverses the excited region of the sample at different delays following the UV pump pulse [10,12]. In the presence of a metallic plasma one ex. pects excitonic structures to disappear~Instead, at T = 0, optical gain should occur from Eg, the renormalized gap, up to/~, the chemical potential of the plasma, followed by absorption above #. At higher T, the transition from gain to loss moves to lower energies, because of the reduction of the Fermi degeneracy of the plasma. In a dynamical regime, following injection of hot carders, concomittant exciton screening and gap renormalization, the change of transmission with time will reflect both the carrier cooling (leading to the filling of the band edges) and carrier density evolution. This results in a more complex behavior, with a transition from absorption to gain shifting in the frequency domain with time and input intensity. Picosecond time-resolved pump and probe experiments performed in CuC1 can be well explained along these lines. Results taken at 15 K are shown in fig. 3. The continuous curve is obtained when the probe pulse precedes the pump on the sample and is therefore representative of the unexcited sample. The two lines at X = 387 nm and 378 nm are the n = 1 terms of the excitonic series from the two upper valence bands (PT, P8) and the lowest conduction band (F6). For a time delay At = 1 ps a reduction of the exciton oscillator strength occurs, as expected in the ~resence
~~-
t
Ps
1 T - 15K ,Io
400 '
~
380
X{nm)
Fig. 3. AbsorPtion spectra of CuC1at 15 K in the exciton region, recorded with a broadband subpicosecondpulse at different delays from the intense UV pump pulse. (Sample thickness= 95 nm.) 262
15 July 1982
of the plasma phase. This effect is particularly well evident in very thin samples where a nearly complete disappearance of the exciton structures is observed. At the same time (At = 1 ps), a new absorption tail, extending below the excitonic structures is apparent with an edge shifting to lower energies under increasing excitation. The excitonic oscillator strength recovers in accordance with the plasma decay time reported above, although a broadening and high energy shift of the lines persist for a longer period of the order of 100 ps. Time-resolved transmission spectra also show some evidence of a transition from optical loss to gain in the plasma spectral region below the excitons, occuring within a few ps from At = 0. A study of the cooling rate and the evolution of the chemical potential of the plasma as a function of injected particle densities is intended for a future article. We now briefly comment on the measured plasma decay. The results of fig. 2 indicate that the Iifetime of the free carriers is limited by excitonic particle formation when their density reaches n c. The initial decrease of the carrier density down to n c may have several origins: volume expansion of the excited re. glen of the sample [13], non-radiative Auger decay involving three (or more) carriers [14], and direct annihilation of electron-hole pairs. The first process should not play a significant role here, in view of the nearly homogeneous volume excitation, large lateral dimensions and short times considered. We believe that direct electron-hole pair recombination dominates over Auger non-radiative decay in the density range of our experiments because the overall radiative efficiency from the plasma increases sharply with higher input intensities well above n c (see fig. 1). To our knowledge, there are no known values for the Auger and bimolecular decay constants in CuC1. Assuming only radiative decay, we obtain for the electron-hole (bimolecular) recombination constant B a value B "- 5-X 10 -10 cm3/s. However, neglect of Auger decay and s t i m ~ t e d emission may not be justified. In conclusion, we have reported the first experimental evidence of the electron-hole plasma in CuC1, and measured its decay time ~"~ 10 -11 s. Due to its simple band structure and large exciton binding energy, CuC1 provides a good system for the study of the Mott transition.
Volume 42, number 4
OPTICS COMMUNICATIONS
This work was supported b y the Direction des Recherches Etudes et Techniques and for L.L.C. b y N.S.F. grant DMR-81-05005. We acknowledge the help of Dr. N. Peyghambarian in preparing the sam. ples.
References [1] See for instance A. Goldmann, Phys. Stat. SoL 81 (1977) 9. [2] See for instance, E. Hanamura and H. Haug, Physics Reports 33C (1977) 209. [3] G.M. Gale and A. Mysyrowicz, Phys. Rev. Lett. 32 (1974) 727; T. Mira and N. Nagasawa, Optics Comm. 24 (1978) 345; A. Maruani, J.L. Oudar, E. Batifol and D.S. Chemla, Phys. Rev. Lett. 41 (1978) 1372. [4] L.L. Chase, G. Grynberg, N. Peyghambarian and A. Mysyrowicz, Phys. Rev. Lett. 42 (1979) 1231; N. Peyghambarian, L.L. Chase and A. Mysyrowicz, Optics Comm. 41 (1982) 178. [5] N.F. Mott, Proc. Phys. Soc. London Sec. A62 (1949) 416. [6] V.E. Bisti and A.P. Silin, Soy. Phys. Solid State 20 (1978) 1068; V.E. Bisti, Soviet Physics Solid State 23 (1981) 855.
15 July 1982
[7] S. Tanaka, H. Kobayashi, H. Saito and S. Shionoya, J. Phys. Soc. Jap. 49 (1980) 1051; E.O. Gobel, P.H. Liang and D. yon der Linde, Solid State Comm. 37 (1981) 609. [8] H.M. Gibbs, S.L. McCall, T.N.C. Venkatesan, A. Passner, A.C. Gossard and W. Wiegman, CLEA 1979, IEEE J. Quantum Electron. QE-15 (1979) 108 D. [9] T.C. Damen, M.A. Dugay, J. Shah, J. Stone, J.M. Wiesenfeld and R.A. Logan, AppL Phys. Lett. 39 (1981) 142. [10] E.P. Ippen and C.V. Shank, Subpicosecond spectrscopy, in: Picosecond Phenomena Springer Series in Chemical Physics, VoL 4, eds. C.V. Shank, E.P. Ippen and S.L. Shapiro (1978) p. 103; A. Migus, C.V. Shank, E.P. Ippen and R.L Fork, IEEE J. J. Quantum Elec. QE-18 (1982) 101; J.L. Martin, R. Astier, A. Migus and A. Antonetti, in: Springer Series in Optical Sciences, Vol. 22 (1980) 229. [11 ] C. Benoit a la Guillaume, to appear in Collective excitations in solids, (Plenum Press). [12] C.V. Shank, R.L. Fork, R.F. Leheny and J. Shah, Phys. Rev. Lett. 42 (1979) 112; D. yon der Linde and R. Lambrich, Phys. Rev. Lett. 42 (1979) 1090. [13] D.IL Auston and D.V. Shank, Phys. Rev. Lett. 32 (1974) 1120; A. Cornet, M. Pugnet, J. Collet, R. Amand and M. Brousseau, J. de Physique C7 (1981) 471. [14] D.H. Auston, C.V. Chank and P. Lefur, Phys. Rev. Lett. 35 (1977) 1022.
263