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Optical bistability and effect of output signal pulsations due to increasing absorption in bulk ZnSe
Volume 68, number
15 November
OPTICS COMMUNICATIONS
6
OPTICAL BISTABILITY AND EFFECT OF OUTPUT INCREASING ABSORPTION IN BULK ZnSe
SIGNAL PULSATIONS
1988
DUE TO
V.A. STADNIK Varilov State Optics Institute, USSR Received 4 January
1988
Optical bistability and the effect of output signal pulsations tion domains in bulk ZnSe are discussed.
1. Introduction In the first experiments on optical bistability (OB) in semiconducting materials (see review [ 1] and references therein) the bistable operation was achieved at a refractive index non-linearity of a medium inside a Fabry-Perot cavity. It is known [ 2 ] that in dispersive OB the output signal can pulsate if a refractive index non-linearity has two contributions of opposite signs and different time constants. Such pulsations were observed in GaAs [ 31 and InSb [4]. For increasing absorption OB no external feedback such as a Fabry-Perot cavity is needed. Therefore, the spatial and temporal coexistence of high and low absorption domains is possible in bulk semiconductor samples. In this report we shall show that OB and the effect of output signal pulsations in a system that exhibits increasing absorption can result from the formation of localized and moving high absorption domains.
that arise from the formation
of localized and moving high absorp-
nal was registered in the range of the entire cross section of the transmitted beam. To avoid cavity feedback effects the samples were mounted at a small angle to the normal incidence direction. Fig. 1 shows shows increasing absorption OB. For the better coincidence of forward and backward initial state branches of the hysteresis loops in this experiment ion-implanted ZnSe samples were used [ 5 1. The hysteresis in fig. la was observed both at sharp
P
Out
(O.UJ
2. Experimental results Experiments were performed at room temperature on ZnSe samples the thickness of which was varied from 1 to 4 mm. For measurements reported here the 488 nm line of a cw argon laser (ILA-120) was used. The laser radiation was focussed.on the samples with a 12-mm focal length lens . The output sig0 030-4018/88/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
Fig. I. Increasing absorption OB in a 2-mm-thick ZnSe sample. The laser beam was focused on the front (a) and back (b) face of the sample. The horizontal arrow shows the region of output signal pulsations.
B.V.
445
Volume 68, number 6
OPTICS COMMUNICATIONS
focusing the laser beam on the front face of a sample and when the change of the laser beam radius along the whole sample thickness was unimportant. The salient feature of OB in fig. la is a decrease of the sample transmission in the lower stable branch of the hysteresis as the input signal is increased. The similar OB at the wavelength 476.5 nm has been reported in ref. [ 61. The clockwise hysteresis loop was also observed at sharp focusing the laser beam on the back (ion-implanted) face of ZnSe samples (fig. lb). It is in this case that we can obtain the most convincing evidence of the formation of high absorption domains. For this purpose the output-input characteristics of bistable elements were studied simultaneously with the spatial distribution of the luminescence brightness inside the samples. It was found that switching from high to low transmission state was associated with the appearance of a brightly shining region within the laser beam (fig. 2a and 2b). The region disappeared on switching back to the high transmission state. Therefore, there regions shall be called high absorption domains. The change of the spatial distribution of the luminescence brightness results from the following. At thermally-induced increasing absorption OB the ZnSe band edge shifts to lower energies and the incident radiation photon energy inside the high absorption domain exceeds the ZnSe band gap. The lower branch of the hysteresis in fig. 1b has a different and more complicated dependence on the input signal than in fig. la. The investigation of the temporal behaviour of the transmitted signal showed that only some part of the lower hysteresis branch was stable (fig. 1b). The output signal was constant with time only when the input signal power slightly exceeded the critical power necessary for the maintenance of the domain localized at the back face of a sample (fig. 2b). The increase in the input power resulted in a shift of the front part of the localized domain towards the front face of a sample and caused a soft excitation of weak pulsations of the output signal (fig. 3a). Hence, the part of the lower hysteresis branch corresponding to the pulsations region is timeaveraged by the X-Y recorder. The period of these pulsations can be roughly estimated as the time of the transverse heat conduction T= C p R2/ (AK), where C is the specific heat, p is the mass density, K 446
I 5 November 1988
Fig.2. The spatial distribution of the luminescence brightness near the back face of ZnSe samples: (a) in the high transmission state, (b) the localized non-pulsating high absorption domain and (c) the trace of moving high absorption domains. The length of the marker is 0.2 mm.
is the thermal conductivity, A is some constant and R is the laser beam radius. The values of the pulsations period could be controlled between 10 and 300 us by varying R and the input signal power. The other mode of output signal pulsations [ 71 was observed when the length of the domain run was approximately ten times as large as the thickness of the localized non-pulsating domain (lig.2c and 3b). The pulsations period can be divided into four phases: two relatively fast switching up ( lo-20 ns) and down ( l-5 us) and two slow phases. The low transmission phase corresponds to the domain motion in the sample bulk (80-200 us), and in the high transmission phase (O-400 us) which was observed in unimplanted samples no domain exists in a sample. The mean velocity of the domain motion was varied between 1O2 and 4 x 1O2cm/s. From the phenomenological viewpoint this mode of pulsation is
Volume 68. number
6
OPTICS COMMUNICATIONS
Fig. 3. The output signal temporal behaviour conditioned by (a) pulsations of the domain localized at the back face of a sample (the period of pulsations T= 116 ps) and (b) high absorption domains moving within a sample (T=221 ps).
analogous to the well known Gunn effect [ 8 1. However, the high absorption domain disappeared in the interior of a sample rather than on its front face as might be expected by analogy with the Gunn effect. The high absorption domains either moving or localized at the back face of a sample could develop microcracks in ZnSe inside the laser beam that complicated the output signal temporal behaviour and the shape of the hysteresis. A similar complicated behaviour of pulsations was also found in polycrystalline ZnSe due to starting inhomogeneities of the material.
3. Discussion
15 November
1988
can be used for the explanation of the behaviour of the domain localized at the front sample face. For example, a decrease of the sample transmission with increasing the input signal power results from the domain enlargement. Note that in work [9] a sawtooth output signal temporal behaviour has been reported. The effect may be related to non-stationary pulsations of the high absorption domain which forms at the front sample face. However, the period of these pulsations proved to be about 2 orders of magnitude higher than that of the domain localized at the back face of the sample in the present work, although both periods are dependent on the transverse thermal conduction time. For the interpretation of the most interesting output signal pulsations mode arising from the periodical domain motion (fig. 2c and 3b) we exploit the fact that at the thermal origin of the absorption coefficient non-linearity the motion of the high absorption domain is analogous to the thermal conduction regime of the propagation of the laser induced discharge in gases [ lo]. The one-dimensional model shows [ 7,101 that in a spatially homogeneous case the stable motion of the high absorption domain is possible when the laser intensity exceeds some critical value. In the experiment a domain is moving in the opposite direction to the incident radiation. At the final stage of the domain motion the laser beam is widening. Hence, the input light intensity that keeps up the domain motion decreases and in some point inside a sample becomes less than the critical intensity that results in the domain disappearance. As a consequence of this, the laser intensity increases at the back face of the sample, where in accordance with the boundary condition a new domain forms, and the process repeats. The maximum velocity of the domain motion can be estimated by Zeldovich formula [ lo] :
of the results
The experiments described here demonstrate that increasing absorption OB in bulk ZnSe is caused by the formation of localized and moving high absorption. Some properties of the local character of increasing absorption OB were reviewed in ref. [ 11. Developed models of the partial sample switching
AftersubstitutingC=0.35 J/(g “C),p=5.03g/cm3, K= 0.19W/ (cm “C) [ 111, the ZnSe band-band absorption coefficient a= 7X lo3 cm-‘, U,=200 “C and the highest input intensity 1,=4x lo5 W/cm*, we obtain v(Z,) =9.5x lo2 cm/s. The minimum do447
Volume 68, number
6
OPTICS
COMMUNICATIONS
main velocity is calculated from the expression um,,,=$Kl(CpR) whichgivesv,,,,,=l.l~lO~cm/ s at R= 15 pm and a= 1.5. These velocity values agree well with experimental data.
Acknowledgement The author thanks S.I. Anisimov, L.V. Keldysh, N.N. Rozanov and V.B. Timofeev for useful discussions.
References [I] F. Henneberger,
448
Phys. Stat. Sol. (b) 137 (1986)
371.
I5 November
I988
[ 21 S.L. McCall, Appl. Phys. Lett. 32 ( 1978) 284. [3] J.L. Jewell, H.M. Gibbs, S.S. Tamg, A.C. Gossard and W. Wiegmann, Appl. Phys. Lett. 40 ( 1982) 29 1. [4] H.A. MacKenzie, J.J.F. Reid, H.A. Al-Attar and E. Abraham, Optics Comm. 60 ( 1986) 18 1. [ 51 V.A. Stadnik and LSh. Chasanov, Zh. Tekh. Fiz. Pisma I3 (1987) 337. [6] M.R. Taghizadeh, J. Janossy and S.D. Smith, Appl. Phys. Lett. 46 (1985) 331; Kar et al., J. Opt. Sot. Am. B 3 ( 1986) 345. [ 71 V.A. Stadnik, Zh. Eksper. Teor. Fiz. Pisma 45 ( 1987) 42. [ 81 V.L. Bench-Bruevich. I.P. Zvyagin and A.T. Mironov, Domennaya electricheskaya neustoichivost’ v poluprovodnikakh, Nauka, Moscow, 1972. [ 91 H.M. Gibbs, G.R. Olbright, N. Peyghambarian, H.E. Schmidt, S.W. Koch and H. Haug, Phys. Rev. A 32 ( 1985) 692. [ IO] Yu.P. Raizer, Uspekhi Fiz. Nauk. 132 ( 1980) 549. [ 1 I ] Physico-Chimicheskie svoistva poluprovodnikovykh veshchestv, ed. A.V. Novoselova (Nauka, Moscow, I979 )
15 November
OPTICS COMMUNICATIONS
6
OPTICAL BISTABILITY AND EFFECT OF OUTPUT INCREASING ABSORPTION IN BULK ZnSe
SIGNAL PULSATIONS
1988
DUE TO
V.A. STADNIK Varilov State Optics Institute, USSR Received 4 January
1988
Optical bistability and the effect of output signal pulsations tion domains in bulk ZnSe are discussed.
1. Introduction In the first experiments on optical bistability (OB) in semiconducting materials (see review [ 1] and references therein) the bistable operation was achieved at a refractive index non-linearity of a medium inside a Fabry-Perot cavity. It is known [ 2 ] that in dispersive OB the output signal can pulsate if a refractive index non-linearity has two contributions of opposite signs and different time constants. Such pulsations were observed in GaAs [ 31 and InSb [4]. For increasing absorption OB no external feedback such as a Fabry-Perot cavity is needed. Therefore, the spatial and temporal coexistence of high and low absorption domains is possible in bulk semiconductor samples. In this report we shall show that OB and the effect of output signal pulsations in a system that exhibits increasing absorption can result from the formation of localized and moving high absorption domains.
that arise from the formation
of localized and moving high absorp-
nal was registered in the range of the entire cross section of the transmitted beam. To avoid cavity feedback effects the samples were mounted at a small angle to the normal incidence direction. Fig. 1 shows shows increasing absorption OB. For the better coincidence of forward and backward initial state branches of the hysteresis loops in this experiment ion-implanted ZnSe samples were used [ 5 1. The hysteresis in fig. la was observed both at sharp
P
Out
(O.UJ
2. Experimental results Experiments were performed at room temperature on ZnSe samples the thickness of which was varied from 1 to 4 mm. For measurements reported here the 488 nm line of a cw argon laser (ILA-120) was used. The laser radiation was focussed.on the samples with a 12-mm focal length lens . The output sig0 030-4018/88/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
Fig. I. Increasing absorption OB in a 2-mm-thick ZnSe sample. The laser beam was focused on the front (a) and back (b) face of the sample. The horizontal arrow shows the region of output signal pulsations.
B.V.
445
Volume 68, number 6
OPTICS COMMUNICATIONS
focusing the laser beam on the front face of a sample and when the change of the laser beam radius along the whole sample thickness was unimportant. The salient feature of OB in fig. la is a decrease of the sample transmission in the lower stable branch of the hysteresis as the input signal is increased. The similar OB at the wavelength 476.5 nm has been reported in ref. [ 61. The clockwise hysteresis loop was also observed at sharp focusing the laser beam on the back (ion-implanted) face of ZnSe samples (fig. lb). It is in this case that we can obtain the most convincing evidence of the formation of high absorption domains. For this purpose the output-input characteristics of bistable elements were studied simultaneously with the spatial distribution of the luminescence brightness inside the samples. It was found that switching from high to low transmission state was associated with the appearance of a brightly shining region within the laser beam (fig. 2a and 2b). The region disappeared on switching back to the high transmission state. Therefore, there regions shall be called high absorption domains. The change of the spatial distribution of the luminescence brightness results from the following. At thermally-induced increasing absorption OB the ZnSe band edge shifts to lower energies and the incident radiation photon energy inside the high absorption domain exceeds the ZnSe band gap. The lower branch of the hysteresis in fig. 1b has a different and more complicated dependence on the input signal than in fig. la. The investigation of the temporal behaviour of the transmitted signal showed that only some part of the lower hysteresis branch was stable (fig. 1b). The output signal was constant with time only when the input signal power slightly exceeded the critical power necessary for the maintenance of the domain localized at the back face of a sample (fig. 2b). The increase in the input power resulted in a shift of the front part of the localized domain towards the front face of a sample and caused a soft excitation of weak pulsations of the output signal (fig. 3a). Hence, the part of the lower hysteresis branch corresponding to the pulsations region is timeaveraged by the X-Y recorder. The period of these pulsations can be roughly estimated as the time of the transverse heat conduction T= C p R2/ (AK), where C is the specific heat, p is the mass density, K 446
I 5 November 1988
Fig.2. The spatial distribution of the luminescence brightness near the back face of ZnSe samples: (a) in the high transmission state, (b) the localized non-pulsating high absorption domain and (c) the trace of moving high absorption domains. The length of the marker is 0.2 mm.
is the thermal conductivity, A is some constant and R is the laser beam radius. The values of the pulsations period could be controlled between 10 and 300 us by varying R and the input signal power. The other mode of output signal pulsations [ 71 was observed when the length of the domain run was approximately ten times as large as the thickness of the localized non-pulsating domain (lig.2c and 3b). The pulsations period can be divided into four phases: two relatively fast switching up ( lo-20 ns) and down ( l-5 us) and two slow phases. The low transmission phase corresponds to the domain motion in the sample bulk (80-200 us), and in the high transmission phase (O-400 us) which was observed in unimplanted samples no domain exists in a sample. The mean velocity of the domain motion was varied between 1O2 and 4 x 1O2cm/s. From the phenomenological viewpoint this mode of pulsation is
Volume 68. number
6
OPTICS COMMUNICATIONS
Fig. 3. The output signal temporal behaviour conditioned by (a) pulsations of the domain localized at the back face of a sample (the period of pulsations T= 116 ps) and (b) high absorption domains moving within a sample (T=221 ps).
analogous to the well known Gunn effect [ 8 1. However, the high absorption domain disappeared in the interior of a sample rather than on its front face as might be expected by analogy with the Gunn effect. The high absorption domains either moving or localized at the back face of a sample could develop microcracks in ZnSe inside the laser beam that complicated the output signal temporal behaviour and the shape of the hysteresis. A similar complicated behaviour of pulsations was also found in polycrystalline ZnSe due to starting inhomogeneities of the material.
3. Discussion
15 November
1988
can be used for the explanation of the behaviour of the domain localized at the front sample face. For example, a decrease of the sample transmission with increasing the input signal power results from the domain enlargement. Note that in work [9] a sawtooth output signal temporal behaviour has been reported. The effect may be related to non-stationary pulsations of the high absorption domain which forms at the front sample face. However, the period of these pulsations proved to be about 2 orders of magnitude higher than that of the domain localized at the back face of the sample in the present work, although both periods are dependent on the transverse thermal conduction time. For the interpretation of the most interesting output signal pulsations mode arising from the periodical domain motion (fig. 2c and 3b) we exploit the fact that at the thermal origin of the absorption coefficient non-linearity the motion of the high absorption domain is analogous to the thermal conduction regime of the propagation of the laser induced discharge in gases [ lo]. The one-dimensional model shows [ 7,101 that in a spatially homogeneous case the stable motion of the high absorption domain is possible when the laser intensity exceeds some critical value. In the experiment a domain is moving in the opposite direction to the incident radiation. At the final stage of the domain motion the laser beam is widening. Hence, the input light intensity that keeps up the domain motion decreases and in some point inside a sample becomes less than the critical intensity that results in the domain disappearance. As a consequence of this, the laser intensity increases at the back face of the sample, where in accordance with the boundary condition a new domain forms, and the process repeats. The maximum velocity of the domain motion can be estimated by Zeldovich formula [ lo] :
of the results
The experiments described here demonstrate that increasing absorption OB in bulk ZnSe is caused by the formation of localized and moving high absorption. Some properties of the local character of increasing absorption OB were reviewed in ref. [ 11. Developed models of the partial sample switching
AftersubstitutingC=0.35 J/(g “C),p=5.03g/cm3, K= 0.19W/ (cm “C) [ 111, the ZnSe band-band absorption coefficient a= 7X lo3 cm-‘, U,=200 “C and the highest input intensity 1,=4x lo5 W/cm*, we obtain v(Z,) =9.5x lo2 cm/s. The minimum do447
Volume 68, number
6
OPTICS
COMMUNICATIONS
main velocity is calculated from the expression um,,,=$Kl(CpR) whichgivesv,,,,,=l.l~lO~cm/ s at R= 15 pm and a= 1.5. These velocity values agree well with experimental data.
Acknowledgement The author thanks S.I. Anisimov, L.V. Keldysh, N.N. Rozanov and V.B. Timofeev for useful discussions.
References [I] F. Henneberger,
448
Phys. Stat. Sol. (b) 137 (1986)
371.
I5 November
I988
[ 21 S.L. McCall, Appl. Phys. Lett. 32 ( 1978) 284. [3] J.L. Jewell, H.M. Gibbs, S.S. Tamg, A.C. Gossard and W. Wiegmann, Appl. Phys. Lett. 40 ( 1982) 29 1. [4] H.A. MacKenzie, J.J.F. Reid, H.A. Al-Attar and E. Abraham, Optics Comm. 60 ( 1986) 18 1. [ 51 V.A. Stadnik and LSh. Chasanov, Zh. Tekh. Fiz. Pisma I3 (1987) 337. [6] M.R. Taghizadeh, J. Janossy and S.D. Smith, Appl. Phys. Lett. 46 (1985) 331; Kar et al., J. Opt. Sot. Am. B 3 ( 1986) 345. [ 71 V.A. Stadnik, Zh. Eksper. Teor. Fiz. Pisma 45 ( 1987) 42. [ 81 V.L. Bench-Bruevich. I.P. Zvyagin and A.T. Mironov, Domennaya electricheskaya neustoichivost’ v poluprovodnikakh, Nauka, Moscow, 1972. [ 91 H.M. Gibbs, G.R. Olbright, N. Peyghambarian, H.E. Schmidt, S.W. Koch and H. Haug, Phys. Rev. A 32 ( 1985) 692. [ IO] Yu.P. Raizer, Uspekhi Fiz. Nauk. 132 ( 1980) 549. [ 1 I ] Physico-Chimicheskie svoistva poluprovodnikovykh veshchestv, ed. A.V. Novoselova (Nauka, Moscow, I979 )