- Email: [email protected]
The saturation limit to picosecond, induced absorption in dyes
OpticsCommunications North-Holland
100 (1993)
OPTICS COMMUNICATIONS
113-l 17
The saturation limit to picosecond, induced absorption in dyes S. Hughes, G. Spruce, B.S. Wherrett,
K.R. Welford ’ and A.D. Lloyd
Department of Physics. Heriot- Watt University, Edinburgh EH14 4AS. UK Received
18 February
1993
The increase in transmission coefficient at high fluences, following low-fluence reverse saturable absorption (induced absorption), is demonstrated for the tricarbocyanine dye, HITCI. This novel effect is explained in terms of a modified three-level model of the singlet states. The absorption cross-section at 532 nm of the first excited state is determined to be 4.8 x lo-l6 cm’, 29 times that of the ground state. We find the lifetime of the first excited state to be 1.5 ns and that of the second excited state to be of the order of 8 ps.
At high incident radiation fluences the build-up of population in an excited state usually leads to a reduction of the corresponding absorption coefficient (saturation or bleaching). However, the absorption cross-section of the excited species may be sufficiently larger than that of the ground-state species that the induced absorption overcomes the effect of saturation. This phenomenon is observed for example in those semiconductors for which the freecarrier absorption cross-section exceeds the interband cross-section for carrier generation [ 11; it has also been reported for certain polymers and dyes [ 24]. In the latter case the expression “reverse saturable absorption” (RSA) has been used to describe the resulting transmission reduction. The RSA response associated with electronic transitions can be extremely fast, as a consequence of which there have been proposals for its application to laser mode-locking [ 5 ] and in short-pulse optical limiting [ 6,7]. We point out here, however, that once RSA action has set in, it does not necessarily continue to all higher fluences. The detailed behaviour will depend on the cross-sections and lifetimes of a series of excited states of the material. In order to demonstrate this limitation to the use of RSAs we have studied the material 1,3,3,1’,3’,3’-hexamethylindotricarbocyanine
iodide (HITCI) which is a commonly used layer dye [ 8 1. The molecular structure of HITCI is shown in fig. 1. Pulses of wavelength 532 nm and 15 ps duration, from a frequency-doubled, passively modelocked Nd3+: YAG laser were used to investigate the transmissivity of HITCI over four decades of radiation fluence. We find that the reverse saturable absorption observed at levels of typically 0.01-o. 1 J cm-* is itself reversed to absorption recovery and eventually absorption saturation for fluences greater than 2 J cmw2. A three-manifold model proves sufficient to explain the observed results. Solutions of HITCI dissolved in high-pressure liquid chromatography-grade methanol to a concentration of 1.64(-tO.O3)x lop4 Ml-‘, were employed in the experiments. The linear spectrum is dominated in the visible by a broad band centred at 740
’
Fig. l.Molecularschematicdiagramfor 1,3,3,1’,3’,3’hexamethylindotricarbocyanine iodide (HITCI )
Defence Research UK.
0030-401 S/93/$06.00
Agency, Great Malvem,
Worcs WR14 3PS,
0 1993 Elsevier Science Publishers
B.V. All rights reserved.
113
Volume
100, number
1,2,3,4
OPTICS
COMMUNICATIONS
nm, corresponding to singlet-singlet excitation; most probably excitations involving the n-electrons extended over the polymethane chain. At 532 nm, on the high-energy side of the band the linear absorption (measured independently using a spectrophotometer and using low energy laser pulses) was 2.24(*0.04)x lo3 cm-’ per Ml-‘. This corresponds to a ground-state absorption cross-section of 1.67 ( -t 0.04) x lo-” cm2. TEMoo gaussian pulses of I5 ps duration (half width e- ’ power) were focussed to a 90 urn spot-size (hw e-’ maximum) in the centre of a 1 mm pathlength cuvette containing the solution. Figure 2 shows the transmission coefficient measured for radiation fluences from 0.1 mJ cm-’ to 2 J cm-‘. The initial reduction in transmissivity (RSA), followed by recovery and ultimately saturation of the absorption, is clearly seen. Figure 3 shows the molecular level diagram for the lower singlet levels of the dye molecule. The triplet
1
1 July 1993
N3
cs32
S,
‘23-
0
N2 L
N2
S
Nl
1
Nl
SOS
NO Ground
0.9
Fig. 3. Energy level molecular model used for the theoretical analysis, showing the singlet-manifolds and, schematically, radiative absorption and stimulated absorption processes, intramanifold and inter-manifold recombination.
0.6
levels are ignored, based on the arguments presented below. RSA action relies on the excitation of a significant level of population in the first excited state (S,) and an excited-state absorption cross section ( azl) at least as large as that for the ground-state ( alo). RSA action ceases when accumulation of population in the second excited state (S,) depletes the number of molecules contributing to the absorption processes. Efficient RSA for picosecond pulses requires that the recovery rate from the S, state be slow compared to the optical pumping rate. In a separate experiment we employed a weak probe pulse of variable time-delay with respect to the pump in order to monitor the recovery of the nonlinear transmission, in the RSA regime. From this experiment we determined the lifetime rol to be 1.5 ns. reducHaving determined so,, the transmissivity tion in the RSA regime can be analysed to give the excited-state cross-section c2’. Throughout our the-
1
0.001
0.01
0.1
1
10
Fluence (Jcme2) Fig. 2. Picosecond single-pulse transmittance measurement for HITCI. Reverse saturable absorption is seen for the lower input fluences and reduction of absorption for higher fluences. 114
OPTICS COMMUNICATIONS
Volume 100, number 1,2,3,4
oretical analysis we solve the coupled rate-equations implied by fig. 3, accounting for the temporal and radial profiles of the laser irradiance and for the pulse depletion in the sample. The intra-band vibrational relaxation times, zvl and ?v29 are not yet well established for HITCI. We have consequently considered two models. In model 1 both decay processes are taken to be fast compared to other relevant timescales (T, < 1 ps). This model then corresponds more closely to that used for RSA calculations in other organic materials [ 9 1, in which ~~ is set equal to zero but the S2 population and the stimulated emission processes incorporated here are ignored. In model 2 we set ~~= 03, in order to test the effects of an extreme situation on the estimated value of the excited-state cross-section azl and the parameters of the S2 manifold. Figure 4 shows best-fit plots, for the two models, against the data of fig. 2, for the
1
-
Model 1
I--*
Model2
0.9
t 0.6
Spot size = 90 b
0.0001
0.001
0.01
0.1
1
10
-2
Fluence (Jcm -) Fig. 4. As for fig. 2, but with the inclusion of two theoretical simulations: model 1, whose vibrational lifetime is a fast r, = 0.1 ps; and model 2, which assumes a long infinite (r,=to) intra-band relaxation time.
1 July
1993
complete fluence regime studied. The estimated value of uzl turns out to be insensitive to rVl. From fitting in the RSA regime we obtain a 532 nm value of azl=4.8( +2.5)x lo-l6 cm2. The ratio of the excited-state to ground-state cross-sections in these experiments is therefore R = azl/a,,, z 29; this is in good agreement with the value of 30 determined by Zhu et al. [lo]. The transition from RSA to increasing transmissivity, and the data at highest fluences, can now be modelled to give a lifetime rL2 for the Sz manifold, and a limit on the cross-section ~32 for excitation out of the Sz states. Within model 1 we obtain ~~~= 9.0 (kO.5) ps, and for model 2 r12=3.0( +0.5) ps. In either case the best fits give as2 < 1.6X 1O-l8 cm2; that is R'= aJ2/cLo < 0.1. The best fit shown is achieved for model 1 with zV2< 0.1 ps. Several assumptions have been made in the above models, even ignoring the approximate manner in which the vibrational manifolds are handled. Firstly the inter-system crossing from the S, state to the metastable lowest triplet state T1 is ignored. The branching-ratio for S1 decay favours the spin-conserving S, to So transition. The commonly quoted ratio is E 100 [ 10 1, although a value of - 12 has also been reported [ 111. In either event the corresponding lifetime must be considerably longer than the pulsl duration and so triplet population by this route is inconsequential. A ratio of 100 would imply an S 1 to TI lifetime of 150 ns, a ratio of 12 gives 18 ns. Intersystem crossing from the S2 states is a more likely route to the triplet population at the highest fluences. We find however, that we would estimate similar values to those above for both a2,, ~~32 and z,~ unless the S2 branching ratio was less than unity. In the latter (unlikely) event the fluence-dependence of the transmission proves difficult to fit unless T2 to T, decay is very rapid ( -ps) and the T1 to T2 cross-section is comparable to that quoted for the S, to S2. Finally we ignore diffusion of the excited species on the basis that the laser spot-size is large compared to the range of diffusion on a 15 ps timescale. It has been common to define the critical condition for the achievement of RSA to be R SD R,= 1. This originates from taking a steady-state model, setting 7"=0, and in effect setting T,~=O. If 7” is long then the condition becomes R,=2 because the excited-state absorption now has to compete with stim115
Volume
100, number
1,2,3,4
OPTICS
COMMUNICATIONS
ulated emission back to the ground-state as well as with the ri2 decay process. In the present models the condition is considerably more complicated: R,=l+
7i2fiw
A+ ( /l-2+
x
{
+
7vib(712032z+
O*,;$L[(% fiw
7vib(712g32z+2Aw)
where fro is the photon
(l-R’)+3-R’ 2hm)
>
-I) +/4I II + &>
(1)
7s,,b
energy,
x[2+~+3$+3-c]>
(2)
and
Thus in general the transmissivity at a cw irradiante, Z, is less than at I=0 for R greater than a critical value that is itself a function of I. Theoretical steady-state response curves have a form similar to that of fig. 2. For the data of HITCI the minimum would occur for an irradiance Z, z 4 x 0” W cmm2. In practice, because the 7,,, decay does not come into play under short-pulse conditions, the critical Z, for pulsed operation was 1.4 x lo9 W cmw2. Nevertheless we believe the analytic equation ( 1) to be useful in predicting trends between materials. In practice the steady-state response would be considerably different than the chosen model predicts, because of laser heating. We have carried out experiments with 2 ns pulses and even on that time scale an extremely slow repetition rate must be used to avoid heating. In conclusion, we have demonstrated experimentally that the reverse saturable absorption, contrary to earlier suppositions, is itself reversed for high input fluences. Even for excited-to-ground absorption cross-section ratios as high as 29, the dynamic range 116
1 July 1993
of the induced absorption may be small. The reduction in material transmission is determined by the parameters measured here and of course by choice of dye concentration and sample path length. Considerably greater contrast than that implied by fig. 2 can in principle be achieved by trading-off against the low-fluence linear transmission coefficient. For example, in the present experiments the linear transmittance is 0.85 but drops only to 0.65 for a fluence of 0.1 J cm-2. The latter transmittance could be reduced to 0.05 (maintaining the transmitted fluence at less than 1 mJ cmP2) if the concentration pathlength product were increased by a factor of 10. However, the linear transmittance would then be decreased to 0.2. The ratio of the lifetimes 7,,/7,,, and the value of higher-state cross-section (a2,) are key to the overall figure-of-merit. If crJ2is small, then the maximum achievable material absorption for a molecular concentration t“ is less than J$rc7221, compared to the low fluence value of ,,VglO. However, a large population in the first excited state demands a pumping rate well in excess of 7~’ but considerably less than 7 12’ . Hence a necessary condition for taking advantage of a large R value is rol /T12 B R. In principle these findings should apply to many molecules. Indeed, we have also conduced single-pulse transmittance measurements for several other well known RSA dyes; the saturation limit is observed in all cases. We would like to acknowledge the Defence Research Agency (DRA) Malvern for supporting this research. S. Hughes would like to acknowledge funding from the UK Science & Engineering Research Council in addition to DRA-Malvem. Mr. R. Range1 Rojo and Dr. A.K. Kar are thanked for assistance with laser expertise.
References
[ 1] E.W. Van Stryland,
H. Vanherzeele, M.A. Woodall, M.J. Soileau, A.L. Smirl, S. Guha and T.F. Bagger, Opt. Eng. 24 (1985) 613. [2] D.J. Hatter, M.L. Shand and Y.B. Band, J. Appl. Phys. 56 (1984) 865. [3] W. Blau, H. Byrne and W.M. Dennis, Optics Comm. 56 (1985) 25. [4] Y.B. Band and B. Schatf, Chem. Phys. Lett. 127 (1986) 381.
Volume
100, number
1,2,3,4
OPTICS
COMMUNICATIONS
[S] Y.B. Band and R. Bavli, Proc. Fritz Harz Int. Symp (Plenum, New York, 1985) p. 23. [6] Y.B. Band, Proc. Fritz Hat-z Int. Symp (Plenum, New York, 1985) p. 123. [7] D.R. Coulter, V.M. Miskowski and J.W. Perry, SPIE Materials for Optical Switches, Isolaters and Limiters 1105 ( 1989) 42.
1 July 1993
[ 81 F.P. Fouausser,
D.J. Lougnor and J. Faurr, Optics Comm. 18 (1976) 263. [ 9 ] G.R. Allan, D.R. Labergerie, S.J. Rychnovsky, T.F. Boggess, A.L. Smirl and L. Tutt, J. Phys. Chem. 96 (1992) 631. [lo] X.R. Zhu and J.M. Harris, Chem. Phys. 142 (1990) 301. [ 111 J. Ivra, Z. Burshtein and E. Miran. Appl. Optics 30 (1991) 2484.
117
100 (1993)
OPTICS COMMUNICATIONS
113-l 17
The saturation limit to picosecond, induced absorption in dyes S. Hughes, G. Spruce, B.S. Wherrett,
K.R. Welford ’ and A.D. Lloyd
Department of Physics. Heriot- Watt University, Edinburgh EH14 4AS. UK Received
18 February
1993
The increase in transmission coefficient at high fluences, following low-fluence reverse saturable absorption (induced absorption), is demonstrated for the tricarbocyanine dye, HITCI. This novel effect is explained in terms of a modified three-level model of the singlet states. The absorption cross-section at 532 nm of the first excited state is determined to be 4.8 x lo-l6 cm’, 29 times that of the ground state. We find the lifetime of the first excited state to be 1.5 ns and that of the second excited state to be of the order of 8 ps.
At high incident radiation fluences the build-up of population in an excited state usually leads to a reduction of the corresponding absorption coefficient (saturation or bleaching). However, the absorption cross-section of the excited species may be sufficiently larger than that of the ground-state species that the induced absorption overcomes the effect of saturation. This phenomenon is observed for example in those semiconductors for which the freecarrier absorption cross-section exceeds the interband cross-section for carrier generation [ 11; it has also been reported for certain polymers and dyes [ 24]. In the latter case the expression “reverse saturable absorption” (RSA) has been used to describe the resulting transmission reduction. The RSA response associated with electronic transitions can be extremely fast, as a consequence of which there have been proposals for its application to laser mode-locking [ 5 ] and in short-pulse optical limiting [ 6,7]. We point out here, however, that once RSA action has set in, it does not necessarily continue to all higher fluences. The detailed behaviour will depend on the cross-sections and lifetimes of a series of excited states of the material. In order to demonstrate this limitation to the use of RSAs we have studied the material 1,3,3,1’,3’,3’-hexamethylindotricarbocyanine
iodide (HITCI) which is a commonly used layer dye [ 8 1. The molecular structure of HITCI is shown in fig. 1. Pulses of wavelength 532 nm and 15 ps duration, from a frequency-doubled, passively modelocked Nd3+: YAG laser were used to investigate the transmissivity of HITCI over four decades of radiation fluence. We find that the reverse saturable absorption observed at levels of typically 0.01-o. 1 J cm-* is itself reversed to absorption recovery and eventually absorption saturation for fluences greater than 2 J cmw2. A three-manifold model proves sufficient to explain the observed results. Solutions of HITCI dissolved in high-pressure liquid chromatography-grade methanol to a concentration of 1.64(-tO.O3)x lop4 Ml-‘, were employed in the experiments. The linear spectrum is dominated in the visible by a broad band centred at 740
’
Fig. l.Molecularschematicdiagramfor 1,3,3,1’,3’,3’hexamethylindotricarbocyanine iodide (HITCI )
Defence Research UK.
0030-401 S/93/$06.00
Agency, Great Malvem,
Worcs WR14 3PS,
0 1993 Elsevier Science Publishers
B.V. All rights reserved.
113
Volume
100, number
1,2,3,4
OPTICS
COMMUNICATIONS
nm, corresponding to singlet-singlet excitation; most probably excitations involving the n-electrons extended over the polymethane chain. At 532 nm, on the high-energy side of the band the linear absorption (measured independently using a spectrophotometer and using low energy laser pulses) was 2.24(*0.04)x lo3 cm-’ per Ml-‘. This corresponds to a ground-state absorption cross-section of 1.67 ( -t 0.04) x lo-” cm2. TEMoo gaussian pulses of I5 ps duration (half width e- ’ power) were focussed to a 90 urn spot-size (hw e-’ maximum) in the centre of a 1 mm pathlength cuvette containing the solution. Figure 2 shows the transmission coefficient measured for radiation fluences from 0.1 mJ cm-’ to 2 J cm-‘. The initial reduction in transmissivity (RSA), followed by recovery and ultimately saturation of the absorption, is clearly seen. Figure 3 shows the molecular level diagram for the lower singlet levels of the dye molecule. The triplet
1
1 July 1993
N3
cs32
S,
‘23-
0
N2 L
N2
S
Nl
1
Nl
SOS
NO Ground
0.9
Fig. 3. Energy level molecular model used for the theoretical analysis, showing the singlet-manifolds and, schematically, radiative absorption and stimulated absorption processes, intramanifold and inter-manifold recombination.
0.6
levels are ignored, based on the arguments presented below. RSA action relies on the excitation of a significant level of population in the first excited state (S,) and an excited-state absorption cross section ( azl) at least as large as that for the ground-state ( alo). RSA action ceases when accumulation of population in the second excited state (S,) depletes the number of molecules contributing to the absorption processes. Efficient RSA for picosecond pulses requires that the recovery rate from the S, state be slow compared to the optical pumping rate. In a separate experiment we employed a weak probe pulse of variable time-delay with respect to the pump in order to monitor the recovery of the nonlinear transmission, in the RSA regime. From this experiment we determined the lifetime rol to be 1.5 ns. reducHaving determined so,, the transmissivity tion in the RSA regime can be analysed to give the excited-state cross-section c2’. Throughout our the-
1
0.001
0.01
0.1
1
10
Fluence (Jcme2) Fig. 2. Picosecond single-pulse transmittance measurement for HITCI. Reverse saturable absorption is seen for the lower input fluences and reduction of absorption for higher fluences. 114
OPTICS COMMUNICATIONS
Volume 100, number 1,2,3,4
oretical analysis we solve the coupled rate-equations implied by fig. 3, accounting for the temporal and radial profiles of the laser irradiance and for the pulse depletion in the sample. The intra-band vibrational relaxation times, zvl and ?v29 are not yet well established for HITCI. We have consequently considered two models. In model 1 both decay processes are taken to be fast compared to other relevant timescales (T, < 1 ps). This model then corresponds more closely to that used for RSA calculations in other organic materials [ 9 1, in which ~~ is set equal to zero but the S2 population and the stimulated emission processes incorporated here are ignored. In model 2 we set ~~= 03, in order to test the effects of an extreme situation on the estimated value of the excited-state cross-section azl and the parameters of the S2 manifold. Figure 4 shows best-fit plots, for the two models, against the data of fig. 2, for the
1
-
Model 1
I--*
Model2
0.9
t 0.6
Spot size = 90 b
0.0001
0.001
0.01
0.1
1
10
-2
Fluence (Jcm -) Fig. 4. As for fig. 2, but with the inclusion of two theoretical simulations: model 1, whose vibrational lifetime is a fast r, = 0.1 ps; and model 2, which assumes a long infinite (r,=to) intra-band relaxation time.
1 July
1993
complete fluence regime studied. The estimated value of uzl turns out to be insensitive to rVl. From fitting in the RSA regime we obtain a 532 nm value of azl=4.8( +2.5)x lo-l6 cm2. The ratio of the excited-state to ground-state cross-sections in these experiments is therefore R = azl/a,,, z 29; this is in good agreement with the value of 30 determined by Zhu et al. [lo]. The transition from RSA to increasing transmissivity, and the data at highest fluences, can now be modelled to give a lifetime rL2 for the Sz manifold, and a limit on the cross-section ~32 for excitation out of the Sz states. Within model 1 we obtain ~~~= 9.0 (kO.5) ps, and for model 2 r12=3.0( +0.5) ps. In either case the best fits give as2 < 1.6X 1O-l8 cm2; that is R'= aJ2/cLo < 0.1. The best fit shown is achieved for model 1 with zV2< 0.1 ps. Several assumptions have been made in the above models, even ignoring the approximate manner in which the vibrational manifolds are handled. Firstly the inter-system crossing from the S, state to the metastable lowest triplet state T1 is ignored. The branching-ratio for S1 decay favours the spin-conserving S, to So transition. The commonly quoted ratio is E 100 [ 10 1, although a value of - 12 has also been reported [ 111. In either event the corresponding lifetime must be considerably longer than the pulsl duration and so triplet population by this route is inconsequential. A ratio of 100 would imply an S 1 to TI lifetime of 150 ns, a ratio of 12 gives 18 ns. Intersystem crossing from the S2 states is a more likely route to the triplet population at the highest fluences. We find however, that we would estimate similar values to those above for both a2,, ~~32 and z,~ unless the S2 branching ratio was less than unity. In the latter (unlikely) event the fluence-dependence of the transmission proves difficult to fit unless T2 to T, decay is very rapid ( -ps) and the T1 to T2 cross-section is comparable to that quoted for the S, to S2. Finally we ignore diffusion of the excited species on the basis that the laser spot-size is large compared to the range of diffusion on a 15 ps timescale. It has been common to define the critical condition for the achievement of RSA to be R SD R,= 1. This originates from taking a steady-state model, setting 7"=0, and in effect setting T,~=O. If 7” is long then the condition becomes R,=2 because the excited-state absorption now has to compete with stim115
Volume
100, number
1,2,3,4
OPTICS
COMMUNICATIONS
ulated emission back to the ground-state as well as with the ri2 decay process. In the present models the condition is considerably more complicated: R,=l+
7i2fiw
A+ ( /l-2+
x
{
+
7vib(712032z+
O*,;$L[(% fiw
7vib(712g32z+2Aw)
where fro is the photon
(l-R’)+3-R’ 2hm)
>
-I) +/4I II + &>
(1)
7s,,b
energy,
x[2+~+3$+3-c]>
(2)
and
Thus in general the transmissivity at a cw irradiante, Z, is less than at I=0 for R greater than a critical value that is itself a function of I. Theoretical steady-state response curves have a form similar to that of fig. 2. For the data of HITCI the minimum would occur for an irradiance Z, z 4 x 0” W cmm2. In practice, because the 7,,, decay does not come into play under short-pulse conditions, the critical Z, for pulsed operation was 1.4 x lo9 W cmw2. Nevertheless we believe the analytic equation ( 1) to be useful in predicting trends between materials. In practice the steady-state response would be considerably different than the chosen model predicts, because of laser heating. We have carried out experiments with 2 ns pulses and even on that time scale an extremely slow repetition rate must be used to avoid heating. In conclusion, we have demonstrated experimentally that the reverse saturable absorption, contrary to earlier suppositions, is itself reversed for high input fluences. Even for excited-to-ground absorption cross-section ratios as high as 29, the dynamic range 116
1 July 1993
of the induced absorption may be small. The reduction in material transmission is determined by the parameters measured here and of course by choice of dye concentration and sample path length. Considerably greater contrast than that implied by fig. 2 can in principle be achieved by trading-off against the low-fluence linear transmission coefficient. For example, in the present experiments the linear transmittance is 0.85 but drops only to 0.65 for a fluence of 0.1 J cm-2. The latter transmittance could be reduced to 0.05 (maintaining the transmitted fluence at less than 1 mJ cmP2) if the concentration pathlength product were increased by a factor of 10. However, the linear transmittance would then be decreased to 0.2. The ratio of the lifetimes 7,,/7,,, and the value of higher-state cross-section (a2,) are key to the overall figure-of-merit. If crJ2is small, then the maximum achievable material absorption for a molecular concentration t“ is less than J$rc7221, compared to the low fluence value of ,,VglO. However, a large population in the first excited state demands a pumping rate well in excess of 7~’ but considerably less than 7 12’ . Hence a necessary condition for taking advantage of a large R value is rol /T12 B R. In principle these findings should apply to many molecules. Indeed, we have also conduced single-pulse transmittance measurements for several other well known RSA dyes; the saturation limit is observed in all cases. We would like to acknowledge the Defence Research Agency (DRA) Malvern for supporting this research. S. Hughes would like to acknowledge funding from the UK Science & Engineering Research Council in addition to DRA-Malvem. Mr. R. Range1 Rojo and Dr. A.K. Kar are thanked for assistance with laser expertise.
References
[ 1] E.W. Van Stryland,
H. Vanherzeele, M.A. Woodall, M.J. Soileau, A.L. Smirl, S. Guha and T.F. Bagger, Opt. Eng. 24 (1985) 613. [2] D.J. Hatter, M.L. Shand and Y.B. Band, J. Appl. Phys. 56 (1984) 865. [3] W. Blau, H. Byrne and W.M. Dennis, Optics Comm. 56 (1985) 25. [4] Y.B. Band and B. Schatf, Chem. Phys. Lett. 127 (1986) 381.
Volume
100, number
1,2,3,4
OPTICS
COMMUNICATIONS
[S] Y.B. Band and R. Bavli, Proc. Fritz Harz Int. Symp (Plenum, New York, 1985) p. 23. [6] Y.B. Band, Proc. Fritz Hat-z Int. Symp (Plenum, New York, 1985) p. 123. [7] D.R. Coulter, V.M. Miskowski and J.W. Perry, SPIE Materials for Optical Switches, Isolaters and Limiters 1105 ( 1989) 42.
1 July 1993
[ 81 F.P. Fouausser,
D.J. Lougnor and J. Faurr, Optics Comm. 18 (1976) 263. [ 9 ] G.R. Allan, D.R. Labergerie, S.J. Rychnovsky, T.F. Boggess, A.L. Smirl and L. Tutt, J. Phys. Chem. 96 (1992) 631. [lo] X.R. Zhu and J.M. Harris, Chem. Phys. 142 (1990) 301. [ 111 J. Ivra, Z. Burshtein and E. Miran. Appl. Optics 30 (1991) 2484.
117