- Email: [email protected]
Accumulated photon echo properties in extended LaF3:Pr3+ crystals
JOURNAL OF
LUMINESCENCE ELSEVJER
Journal of Luminescence 72-74 (1997)85 l-853
Accumulated photon echo properties in extended LaF3 : Pr3+ crystals O.Kh. Khasanov*, T.V. Smirnova, O.M. Fedotova InsMute ofSolidState and Semiconducfovs Ph_vsics. 17 Br+wkisfr., Minsk 220 072, Belarlts
Abstract The accumulated
photon
echo (APE) excitation
process by N pulse pairs sequence in optically dense LaF, : Pr3+
crystals is investigated numerically. Keywords: Accumulated
photon echo; LaF3:Pr3+
2. Theory
1. Introduction Accumulated
photon
echo (APE) is known
to
from in multilevel systems with metastable levels [l]. This effect has been attracting much attention, especially for use as a possible time-domain optical memory device [2]. For this purpose Van Vleck paramagnetics LaF, : Pr3+, YAlO, : Pr3+, Y203 : Eu3+ are prospective crystals due to nuclear hyperfine interactions of both ground and excited states [3]. The successful storage and retrieval of temporal optical data in such crystals can extend up to 13 h [4]. Because of strong non-linear properties the crystals can exert backreaction on each coherent pulse from the multipulse sequence. In the work presented here we take into account the effect of the non-linear evolution of the exciting pulses on APE generation. The self-consistent system of Master and Maxwell equations has been investigated numerically and analytically. The results of the calculation have been compared with the experimental data [5]. *Corresponding
author. Fax: (172) ifttpanb%[email protected].
324694;
The APE excitation scheme has been used as in the experimental work [S]. The sample is excited by N ultrashort pulse pairs, assumed to be degenerate in frequency and in resonance with the 3H4-3P0 transition. 3H4 state is a triplet of hyperfine levels with splitting 16.7 and 8.47 MHz [6]. Consider its influence on the APE-signal generation process in extended LaF3 : Pr3 + crystals: As a model of the above-mentioned medium let us analyze four-level system where only 16-32 and 3-4 transitions are possible. Such a system allows to identify the main peculiarities of APE excitation in Van Vleck paramagnetic crystals. A Self-consistent equation system describing the interaction between the nth pulse in sequence and the resonant media takes the simplest form daij ~ij i dt + T, = h
d,j
Ek(aji
-
bij),
i,j = 1, 2 or 2, 1,
k =
1,
3,4 or 4, 3,
k =
2,
e-mail:
0022-2313/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PI1 SOO22-23 13(97)00059-8
i, j =
(1)
852
O.Kh. Khasanoo et al. /Journal
ofLuminescence
dot, -
dt
=
QZYl
+
~
dt
=
-
+
022Yo
= -
+
+
dt
aEi -+Sat=
az
04474
21c712El
c733;13
;
(2)
0441/5
+
-
@34O43
E2
(3)
~12~2lG),
c722’j2
da44
~
+
;(dl2& - d21~12ET),
+l da,, ~ dt
033y3
+
-
04476
(4)
d43g34E;)>
72-74 (1997) NSI-853
between the pairs T = 80 ms; the pulse duration rp = 10 ns, the delay time between the pulses in the pairs T = 40 ns, dij = d = 5 X 10m2’ CGSE units; the Pr3+ ions concentration is 0.05 at%; the radiation wave length i = 477.7 nm; and the pulse sequence is assumed to consist of identical pulses with areas Hi0 = n/20, where Hi0 = 2dEiz,/q is the initial area of the ith pulse.
3. Discussion According to the analysis of equation system Eqs. (l)-(6) performed cumulative effect in optically dense medium depends on sample sizes and has a threshold character. The threshold is determined by the total initial area of all pulse sequences
i
= -
044?01
-
h
(d43g34E2
-
d34°43E?),
c5)
020 = F 8iO i=l
?j aEi
,
-2niNoil,, Crl
s 1
X
gWmd4 z, t) d4
(6)
--5
y. = y1 + y2, yol = y4 + y5 + y6, where aij are the density matrix elements, dij the dipole moment of the i-j transition, N the active centers concentration, y the refraction index, Aij = wij - O, E the envelope of the ith pulse in the medium Ej(z, t) = Ei(Z, t)exp[i(ot - kjz)], kj the wave vector of the ith pulse, Y,, the relaxation rates. As the 13) level is metastable, yS is assumed to be much less than all relaxation parameters. Here T, = yS1 is the longitudinal relaxation time and T2 the transverse irreversible relaxation time. The equation system [l-6] has been analyzed numerically at the time intervals when the sample is exposed to a laser pulse and analytically at the intervals between the pulses when the laser field is switched off. Irreversible relaxation processes during a whole pulse sequence have been taken into account. Numerical values of the system parameters correspond to the following experimental data [S]: T, = 47 ps, T, = 430 ns; the delay time
and equals to TC. Analysis has shown that APE-amplitude dependence on the pulse pairs value coincides with the experimental curve [S] when the crystal length is equal to L = 2.5x-‘, where x is the resonance absorption coefficient. Zuikov et al. [S] have used the cumulative effect curve saturation to estimate the metastable level lifetime in optically thin sample approximation: It was 1.2 s. Our investigation on the influence of propagation effect on the abovementioned saturation function in real crystals and its interpolation on optically thin sample shows that T in Ref. [S] should be doubled at least. APE-signal is known to be formed by whole history of resonant media excitation. At the same time the initial conditions for each pulse depend on the pulse number in the sequence, time delays between the pulses in pairs and between the pairs. Therefore, the echo-holograms optimization process consists of optimization on each separate pulse in sequence. Such an approach allows to get some echo signal amplification. For example, the echo intensity increases by 20% when the crystal length L = 3.2c(-‘. The result of the optimization depends on the sample length: When the crystal size is more, the optimal value of the first pulse area is very different from the value Blopt = 7c/2 typical of
O.Kh. Khasanov et al. 1 Journal of Luminescence 72-74 (1997) 851X?53
optically thin media. The optimal value of the first pulse pair should be slightly more than the threshold value equal to r-c: 810 + e20 = x + 6,
853
tals can generate large errors in the determination of medium spectroscopic parameters.
6 6 7-C.
As for optimal conditions of ACE generation by identical pulse pair sequence, the7 are the same for both optically dense and thin media since it is connected with accumulated effects.
4. Conclusion Threshold conditions and the sample length influence the nature of cumulative effect. Neglecting the bypropagation effects in optically dense crys-
References
[II M. Mitsunaga, K. Kubodera. H. Kanbe, Opt. Lett. ll(l986) 339.
PI S. Saikan, K. Kishido, A. Imaoka, K. Uchikava, A. Furusava, H. Oosawa, Opt. Lett. 14 (1989) 841. [31 V.A. Zuikov, IS. Bikbov, S.B. Karamyshev, V.V. Samartsev, Laser Phys. 5 (1995) 1. f41 W.R. Babbit, T.M. Mossberg, Opt. Commun. 65 (1988) 185. f51 V.A. Zuikov, D.F. Gainullin, V.V. Samartsev, I.F. Stelmakh, LA. Y&n, LA. Yakshin, Sov. Journ. Quantum Electron. 18 (1991) 525. C61R.E. Erickson opt. Commun. 21 (1977) 147.
LUMINESCENCE ELSEVJER
Journal of Luminescence 72-74 (1997)85 l-853
Accumulated photon echo properties in extended LaF3 : Pr3+ crystals O.Kh. Khasanov*, T.V. Smirnova, O.M. Fedotova InsMute ofSolidState and Semiconducfovs Ph_vsics. 17 Br+wkisfr., Minsk 220 072, Belarlts
Abstract The accumulated
photon
echo (APE) excitation
process by N pulse pairs sequence in optically dense LaF, : Pr3+
crystals is investigated numerically. Keywords: Accumulated
photon echo; LaF3:Pr3+
2. Theory
1. Introduction Accumulated
photon
echo (APE) is known
to
from in multilevel systems with metastable levels [l]. This effect has been attracting much attention, especially for use as a possible time-domain optical memory device [2]. For this purpose Van Vleck paramagnetics LaF, : Pr3+, YAlO, : Pr3+, Y203 : Eu3+ are prospective crystals due to nuclear hyperfine interactions of both ground and excited states [3]. The successful storage and retrieval of temporal optical data in such crystals can extend up to 13 h [4]. Because of strong non-linear properties the crystals can exert backreaction on each coherent pulse from the multipulse sequence. In the work presented here we take into account the effect of the non-linear evolution of the exciting pulses on APE generation. The self-consistent system of Master and Maxwell equations has been investigated numerically and analytically. The results of the calculation have been compared with the experimental data [5]. *Corresponding
author. Fax: (172) ifttpanb%[email protected].
324694;
The APE excitation scheme has been used as in the experimental work [S]. The sample is excited by N ultrashort pulse pairs, assumed to be degenerate in frequency and in resonance with the 3H4-3P0 transition. 3H4 state is a triplet of hyperfine levels with splitting 16.7 and 8.47 MHz [6]. Consider its influence on the APE-signal generation process in extended LaF3 : Pr3 + crystals: As a model of the above-mentioned medium let us analyze four-level system where only 16-32 and 3-4 transitions are possible. Such a system allows to identify the main peculiarities of APE excitation in Van Vleck paramagnetic crystals. A Self-consistent equation system describing the interaction between the nth pulse in sequence and the resonant media takes the simplest form daij ~ij i dt + T, = h
d,j
Ek(aji
-
bij),
i,j = 1, 2 or 2, 1,
k =
1,
3,4 or 4, 3,
k =
2,
e-mail:
0022-2313/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PI1 SOO22-23 13(97)00059-8
i, j =
(1)
852
O.Kh. Khasanoo et al. /Journal
ofLuminescence
dot, -
dt
=
QZYl
+
~
dt
=
-
+
022Yo
= -
+
+
dt
aEi -+Sat=
az
04474
21c712El
c733;13
;
(2)
0441/5
+
-
@34O43
E2
(3)
~12~2lG),
c722’j2
da44
~
+
;(dl2& - d21~12ET),
+l da,, ~ dt
033y3
+
-
04476
(4)
d43g34E;)>
72-74 (1997) NSI-853
between the pairs T = 80 ms; the pulse duration rp = 10 ns, the delay time between the pulses in the pairs T = 40 ns, dij = d = 5 X 10m2’ CGSE units; the Pr3+ ions concentration is 0.05 at%; the radiation wave length i = 477.7 nm; and the pulse sequence is assumed to consist of identical pulses with areas Hi0 = n/20, where Hi0 = 2dEiz,/q is the initial area of the ith pulse.
3. Discussion According to the analysis of equation system Eqs. (l)-(6) performed cumulative effect in optically dense medium depends on sample sizes and has a threshold character. The threshold is determined by the total initial area of all pulse sequences
i
= -
044?01
-
h
(d43g34E2
-
d34°43E?),
c5)
020 = F 8iO i=l
?j aEi
,
-2niNoil,, Crl
s 1
X
gWmd4 z, t) d4
(6)
--5
y. = y1 + y2, yol = y4 + y5 + y6, where aij are the density matrix elements, dij the dipole moment of the i-j transition, N the active centers concentration, y the refraction index, Aij = wij - O, E the envelope of the ith pulse in the medium Ej(z, t) = Ei(Z, t)exp[i(ot - kjz)], kj the wave vector of the ith pulse, Y,, the relaxation rates. As the 13) level is metastable, yS is assumed to be much less than all relaxation parameters. Here T, = yS1 is the longitudinal relaxation time and T2 the transverse irreversible relaxation time. The equation system [l-6] has been analyzed numerically at the time intervals when the sample is exposed to a laser pulse and analytically at the intervals between the pulses when the laser field is switched off. Irreversible relaxation processes during a whole pulse sequence have been taken into account. Numerical values of the system parameters correspond to the following experimental data [S]: T, = 47 ps, T, = 430 ns; the delay time
and equals to TC. Analysis has shown that APE-amplitude dependence on the pulse pairs value coincides with the experimental curve [S] when the crystal length is equal to L = 2.5x-‘, where x is the resonance absorption coefficient. Zuikov et al. [S] have used the cumulative effect curve saturation to estimate the metastable level lifetime in optically thin sample approximation: It was 1.2 s. Our investigation on the influence of propagation effect on the abovementioned saturation function in real crystals and its interpolation on optically thin sample shows that T in Ref. [S] should be doubled at least. APE-signal is known to be formed by whole history of resonant media excitation. At the same time the initial conditions for each pulse depend on the pulse number in the sequence, time delays between the pulses in pairs and between the pairs. Therefore, the echo-holograms optimization process consists of optimization on each separate pulse in sequence. Such an approach allows to get some echo signal amplification. For example, the echo intensity increases by 20% when the crystal length L = 3.2c(-‘. The result of the optimization depends on the sample length: When the crystal size is more, the optimal value of the first pulse area is very different from the value Blopt = 7c/2 typical of
O.Kh. Khasanov et al. 1 Journal of Luminescence 72-74 (1997) 851X?53
optically thin media. The optimal value of the first pulse pair should be slightly more than the threshold value equal to r-c: 810 + e20 = x + 6,
853
tals can generate large errors in the determination of medium spectroscopic parameters.
6 6 7-C.
As for optimal conditions of ACE generation by identical pulse pair sequence, the7 are the same for both optically dense and thin media since it is connected with accumulated effects.
4. Conclusion Threshold conditions and the sample length influence the nature of cumulative effect. Neglecting the bypropagation effects in optically dense crys-
References
[II M. Mitsunaga, K. Kubodera. H. Kanbe, Opt. Lett. ll(l986) 339.
PI S. Saikan, K. Kishido, A. Imaoka, K. Uchikava, A. Furusava, H. Oosawa, Opt. Lett. 14 (1989) 841. [31 V.A. Zuikov, IS. Bikbov, S.B. Karamyshev, V.V. Samartsev, Laser Phys. 5 (1995) 1. f41 W.R. Babbit, T.M. Mossberg, Opt. Commun. 65 (1988) 185. f51 V.A. Zuikov, D.F. Gainullin, V.V. Samartsev, I.F. Stelmakh, LA. Y&n, LA. Yakshin, Sov. Journ. Quantum Electron. 18 (1991) 525. C61R.E. Erickson opt. Commun. 21 (1977) 147.