R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416-1427 (1992)
Strontium barium niobate (SBN) was doped with rhodium to enhance its photorefractive behavior. Crystals with six different Rh concentrations, ranging from 0.015 to 0.20 wt. %, were grown and characterized. With a higher Rh concentration the following trends were observed at a wavelength of 514.5 nm: (i) a larger linear absorption coefficient α, (ii) a larger maximum two-beam-coupling coefficient Γ, (iii) a higher net coupling coefficient (Γ − α), (iv) a longer two-beam-coupling time response, (v) a shorter fixed-level-gain time response, (vi) a constant photoionization cross section, and (vii) a smaller photorefractive sensitivity. With extraordinary polarization used to invoke the large r33 electro-optic coefficient, two-beam-coupling coefficients exceeding 60 cm−1 were measured in thin (∼1 mm) plates of the heavily Rh-doped crystals, which is consistent with the expected coupling by inference from measurements with ordinary polarization in thick (∼5 mm) crystals. Contradirectional two-beam coupling in SBN along the ĉ axis (independent of polarization, since r13 = r23) gave a coupling coefficient of almost 14 cm−1 for the 0.20-wt. % sample; the contradirectional coupling coefficient decreased approximately in proportion with the decreasing Rh-doping concentration in the other crystals. Estimated photorefractive charge densities ranged from ∼4 × 1016 to ∼8 × 1017 cm3, which constituted approximately 1% of the total Rh-doping concentration.
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Rh-Doped SBN:60 Sample Dimensions,a Absorption Coefficients,b and Doping Levelsc at Various Rh Concentrations
Rh Conc. (wt. %)
Sample Description
La (mm)
Lc (mm)
α (cm−1)
ND (×1019 cm−3)
Ratio (no. Nb/no. Rh)
0.015
∼Cube
5.50
6.02
0.54
0.46
3524
0.025
∼Cube
5.70
5.87
0.79
0.77
2115
0.035
∼Cube
5.90
5.96
0.92
1.08
1510
0.070
∼Cube
5.10
6.24
1.67
2.16
755
0.10
∼Cube
5.65
5.37
3.09
3.09
529
0.20
∼Cube
6.10
6.27
6.22
6.18
264
0.070
Thin slab
1.00
0.10
Thin slab
0.90
0.20
Thin slab
0.45
0.070
Rectangular prism
4.98
19.0
La is the interaction length along the â axis, and Lc is the interaction length along the ĉ axis.
At 514.5 nm. ND is the Rh number density and the ratio is the number of Nb atoms divided by the number of Rh atoms [see Eq. (1) and relation (2)].
Effective Electro-Optic Coefficientsa and Photorefractive Charge Densitiesb Determined from Two-Beam-Coupling Measurementsc for Various Rh-Doping Concentrations in SBN:60
Rh Conc. (wt. %)
Sample Description
r13ζ(K) (pm/V)
N13eff(×1016) (cm−3)
r33ζ(K) (pm/V)
N33eff(×1016) (cm−3)
Γ2k (cm−1)
N2keff(×1016) (cm−3)
0.015
∼Cube
36.6
4.2 ± 0.2
0.78
3.7
0.025
∼Cube
41.3
7.6 ± 0.4
1.94
9.4
0.035
∼Cube
43.8
9.8 ± 0.7
2.65
12.9
0.070
∼Cube
39.1
23.2 ± 1.5
64.0
26.8 ± 3.3
4.63
23.1
0.10
∼Cube
37.5
24.9 ± 2.9
7.97
41.4
0.20
∼Cube
32.9
94.6 ± 28.2
13.80
77.5
0.070
Thin slab
37.0
23.0 ± 2.8
251.9
25.2 ± 4.0
0.10
Thin slab
37.8
49.3 ± 6.3
160.5
72.7 ± 15.0
0.20
Thin slab
34.1
81.5 ± 17.8
147.3
231.1 ± 265.0
r13ζ(K) for ordinary polarization and r33ζ(K) for extraordinary polarization, where ζ(K) is the electron–hole competition factor (Ref. 32). N13eff and N33eff with ordinary and extraordinary polarizations, respectively, for codirectional two-beam coupling and N2keff for contradirectional two-beam coupling (errors correspond to deviations from fitted curves).
Determined by Eqs. (3)–(5) and relation (6) from data presented in Figs. 5, 6, and 8.
Table 4
Photorefractive Parametersa Based on the Measurements of Two-Beam-Coupling Response Times for Various Rh-Doping Concentrations in SBN:60
Rh Conc. (wt. %)
[μτR](×10−10) (cm2/V)
σd(×10−12) (Ω cm)−1
σph/σd
τ2bc (s)
τfg (s)
0.015
2.8
0.064
9.9
1.11
7.7 × 10−2
0.025
0.88
0.0038
75.8
2.65
1.3 × 10−2
0.035
0.39
0.010
14.2
4.89
7.4 × 10−3
0.070
0.11
0.012
5.9
9.18
1.3 × 10−3
0.10
0.0094
0.0029
4.2
54.4
5.3 × 10−4
0.20
0.0015
<0.008
195.6
1.0 × 10−4
Including the mobility–recombination-time product μτR, the dark conductivity σd, the photoconductivity-to-dark-conductivity ratio σph/σd at 1 W/cm2, the steady-state two-beam-coupling response time τ2bc at an incident intensity of 1 W/cm2, and the fixed-gain time response τfg [see the data presented in Fig. 10 along with relation (7) and Eq. (9); note that estimates of τfg used values of
from Table 5].
Table 5
Optimized Codirectional Two-Beam-Coupling Parametersa Predicted from Contradirectional Two-Beam-Coupline Measurement for the Series of Rh-Doned SBN:60 Samples
Rh Conc. (wt. %)
(deg)
(cm−1)
(deg)
(cm−1)
Spr (cm3/J)
s(×10−19) (cm2)
0.015
24.5
24.6
25.9
4.1
1.7 × 10−4
1.17
0.025
37.1
37.7
42.4
6.6
7.4 × 10−5
1.04
0.035
42.4
43.4
50.8
7.8
4.0 × 10−5
0.86
0.070
53.1
55.3
122.2
10.6
1.5 × 10−5
0.78
0.10
64.9
68.7
72.8
14.7
1.7 × 10−6
1.01
0.20
77.8
83.4
180.0
20.9
2.8 × 10−7
1.02
From the contradirectional effective photorefractive charge density N2keff, estimates are given for the optimal external beam-crossing angles
and
along with the maximum two-beam-coupling coefficients
and
for extraordinary and ordinary polarizations, respectively (see Subsection 4.2), the photorefractive sensitivity Spr [see relation (8) in Subsection 4.C], and the photoionization cross section s [see Subsection 4.E].
Tables (5)
Table 1
Rh-Doped SBN:60 Sample Dimensions,a Absorption Coefficients,b and Doping Levelsc at Various Rh Concentrations
Rh Conc. (wt. %)
Sample Description
La (mm)
Lc (mm)
α (cm−1)
ND (×1019 cm−3)
Ratio (no. Nb/no. Rh)
0.015
∼Cube
5.50
6.02
0.54
0.46
3524
0.025
∼Cube
5.70
5.87
0.79
0.77
2115
0.035
∼Cube
5.90
5.96
0.92
1.08
1510
0.070
∼Cube
5.10
6.24
1.67
2.16
755
0.10
∼Cube
5.65
5.37
3.09
3.09
529
0.20
∼Cube
6.10
6.27
6.22
6.18
264
0.070
Thin slab
1.00
0.10
Thin slab
0.90
0.20
Thin slab
0.45
0.070
Rectangular prism
4.98
19.0
La is the interaction length along the â axis, and Lc is the interaction length along the ĉ axis.
At 514.5 nm. ND is the Rh number density and the ratio is the number of Nb atoms divided by the number of Rh atoms [see Eq. (1) and relation (2)].
Effective Electro-Optic Coefficientsa and Photorefractive Charge Densitiesb Determined from Two-Beam-Coupling Measurementsc for Various Rh-Doping Concentrations in SBN:60
Rh Conc. (wt. %)
Sample Description
r13ζ(K) (pm/V)
N13eff(×1016) (cm−3)
r33ζ(K) (pm/V)
N33eff(×1016) (cm−3)
Γ2k (cm−1)
N2keff(×1016) (cm−3)
0.015
∼Cube
36.6
4.2 ± 0.2
0.78
3.7
0.025
∼Cube
41.3
7.6 ± 0.4
1.94
9.4
0.035
∼Cube
43.8
9.8 ± 0.7
2.65
12.9
0.070
∼Cube
39.1
23.2 ± 1.5
64.0
26.8 ± 3.3
4.63
23.1
0.10
∼Cube
37.5
24.9 ± 2.9
7.97
41.4
0.20
∼Cube
32.9
94.6 ± 28.2
13.80
77.5
0.070
Thin slab
37.0
23.0 ± 2.8
251.9
25.2 ± 4.0
0.10
Thin slab
37.8
49.3 ± 6.3
160.5
72.7 ± 15.0
0.20
Thin slab
34.1
81.5 ± 17.8
147.3
231.1 ± 265.0
r13ζ(K) for ordinary polarization and r33ζ(K) for extraordinary polarization, where ζ(K) is the electron–hole competition factor (Ref. 32). N13eff and N33eff with ordinary and extraordinary polarizations, respectively, for codirectional two-beam coupling and N2keff for contradirectional two-beam coupling (errors correspond to deviations from fitted curves).
Determined by Eqs. (3)–(5) and relation (6) from data presented in Figs. 5, 6, and 8.
Table 4
Photorefractive Parametersa Based on the Measurements of Two-Beam-Coupling Response Times for Various Rh-Doping Concentrations in SBN:60
Rh Conc. (wt. %)
[μτR](×10−10) (cm2/V)
σd(×10−12) (Ω cm)−1
σph/σd
τ2bc (s)
τfg (s)
0.015
2.8
0.064
9.9
1.11
7.7 × 10−2
0.025
0.88
0.0038
75.8
2.65
1.3 × 10−2
0.035
0.39
0.010
14.2
4.89
7.4 × 10−3
0.070
0.11
0.012
5.9
9.18
1.3 × 10−3
0.10
0.0094
0.0029
4.2
54.4
5.3 × 10−4
0.20
0.0015
<0.008
195.6
1.0 × 10−4
Including the mobility–recombination-time product μτR, the dark conductivity σd, the photoconductivity-to-dark-conductivity ratio σph/σd at 1 W/cm2, the steady-state two-beam-coupling response time τ2bc at an incident intensity of 1 W/cm2, and the fixed-gain time response τfg [see the data presented in Fig. 10 along with relation (7) and Eq. (9); note that estimates of τfg used values of
from Table 5].
Table 5
Optimized Codirectional Two-Beam-Coupling Parametersa Predicted from Contradirectional Two-Beam-Coupline Measurement for the Series of Rh-Doned SBN:60 Samples
Rh Conc. (wt. %)
(deg)
(cm−1)
(deg)
(cm−1)
Spr (cm3/J)
s(×10−19) (cm2)
0.015
24.5
24.6
25.9
4.1
1.7 × 10−4
1.17
0.025
37.1
37.7
42.4
6.6
7.4 × 10−5
1.04
0.035
42.4
43.4
50.8
7.8
4.0 × 10−5
0.86
0.070
53.1
55.3
122.2
10.6
1.5 × 10−5
0.78
0.10
64.9
68.7
72.8
14.7
1.7 × 10−6
1.01
0.20
77.8
83.4
180.0
20.9
2.8 × 10−7
1.02
From the contradirectional effective photorefractive charge density N2keff, estimates are given for the optimal external beam-crossing angles
and
along with the maximum two-beam-coupling coefficients
and
for extraordinary and ordinary polarizations, respectively (see Subsection 4.2), the photorefractive sensitivity Spr [see relation (8) in Subsection 4.C], and the photoionization cross section s [see Subsection 4.E].