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 r_{33} 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 r_{13} = r_{23}) 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 × 10^{16} to ∼8 × 10^{17} cm^{3}, which constituted approximately 1% of the total Rh-doping concentration.

Gary L. Wood and R. R. Neurgaonkar J. Opt. Soc. Am. B 11(7) 1211-1220 (1994)

References

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Rh-Doped SBN:60 Sample Dimensions,^{a} Absorption Coefficients,^{b} and Doping Levels^{c} at Various Rh Concentrations

Rh Conc.(wt. %)

Sample Description

L_{a}(mm)

L_{c}(mm)

α(cm^{−1})

N_{D}(×10^{19} 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

L_{a} is the interaction length along the â axis, and L_{c} is the interaction length along the ĉ axis.
At 514.5 nm. N_{D} 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 Coefficients^{a} and Photorefractive Charge Densities^{b} Determined from Two-Beam-Coupling Measurements^{c} for Various Rh-Doping Concentrations in SBN:60

Rh Conc.(wt. %)

Sample Description

r_{13}ζ(K)(pm/V)

N_{13}^{eff}(×10^{16})(cm^{−3})

r_{33}ζ(K)(pm/V)

N_{33}^{eff}(×10^{16})(cm^{−3})

Γ_{2}_{k}(cm^{−1})

N_{2}_{k}^{eff}(×10^{16})(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

r_{13}ζ(K) for ordinary polarization and r_{33}ζ(K) for extraordinary polarization, where ζ(K) is the electron–hole competition factor (Ref. 32). N_{13}^{eff} and N_{33}^{eff} with ordinary and extraordinary polarizations, respectively, for codirectional two-beam coupling and N_{2}_{k}^{eff} 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 Parameters^{a} Based on the Measurements of Two-Beam-Coupling Response Times for Various Rh-Doping Concentrations in SBN:60

Rh Conc.(wt. %)

[μτ_{R}](×10^{−10})(cm^{2}/V)

σ_{d}(×10^{−12})(Ω cm)^{−1}

σ_{ph}/σ_{d}

τ_{2bc}(s)

τ_{fg}(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 μτ_{R}, the dark conductivity σ_{d}, the photoconductivity-to-dark-conductivity ratio σ_{ph}/σ_{d} at 1 W/cm^{2}, the steady-state two-beam-coupling response time τ_{2bc} at an incident intensity of 1 W/cm^{2}, and the fixed-gain time response τ_{fg} [see the data presented in Fig. 10 along with relation (7) and Eq. (9); note that estimates of τ_{fg} used values of
${\mathrm{\Gamma}}_{max}^{(\text{e})}$ from Table 5].

Table 5

Optimized Codirectional Two-Beam-Coupling Parameters^{a} Predicted from Contradirectional Two-Beam-Coupline Measurement for the Series of Rh-Doned SBN:60 Samples

Rh Conc.(wt. %)

$2{\theta}_{max}^{(e)}$(deg)

${\mathrm{\Gamma}}_{max}^{(e)}$(cm^{−1})

$2{\theta}_{max}^{(o)}$(deg)

${\mathrm{\Gamma}}_{max}^{(o)}$(cm^{−1})

S_{pr}(cm^{3}/J)

s(×10^{−19})(cm^{2})

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 N_{2}_{k}^{eff}, estimates are given for the optimal external beam-crossing angles
$2{\theta}_{max}^{(e)}$ and
$2{\theta}_{max}^{(o)}$ along with the maximum two-beam-coupling coefficients
${\mathrm{\Gamma}}_{max}^{(e)}$ and
${\mathrm{\Gamma}}_{max}^{(o)}$ for extraordinary and ordinary polarizations, respectively (see Subsection 4.2), the photorefractive sensitivity S_{pr} [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 Levels^{c} at Various Rh Concentrations

Rh Conc.(wt. %)

Sample Description

L_{a}(mm)

L_{c}(mm)

α(cm^{−1})

N_{D}(×10^{19} 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

L_{a} is the interaction length along the â axis, and L_{c} is the interaction length along the ĉ axis.
At 514.5 nm. N_{D} 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 Coefficients^{a} and Photorefractive Charge Densities^{b} Determined from Two-Beam-Coupling Measurements^{c} for Various Rh-Doping Concentrations in SBN:60

Rh Conc.(wt. %)

Sample Description

r_{13}ζ(K)(pm/V)

N_{13}^{eff}(×10^{16})(cm^{−3})

r_{33}ζ(K)(pm/V)

N_{33}^{eff}(×10^{16})(cm^{−3})

Γ_{2}_{k}(cm^{−1})

N_{2}_{k}^{eff}(×10^{16})(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

r_{13}ζ(K) for ordinary polarization and r_{33}ζ(K) for extraordinary polarization, where ζ(K) is the electron–hole competition factor (Ref. 32). N_{13}^{eff} and N_{33}^{eff} with ordinary and extraordinary polarizations, respectively, for codirectional two-beam coupling and N_{2}_{k}^{eff} 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 Parameters^{a} Based on the Measurements of Two-Beam-Coupling Response Times for Various Rh-Doping Concentrations in SBN:60

Rh Conc.(wt. %)

[μτ_{R}](×10^{−10})(cm^{2}/V)

σ_{d}(×10^{−12})(Ω cm)^{−1}

σ_{ph}/σ_{d}

τ_{2bc}(s)

τ_{fg}(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 μτ_{R}, the dark conductivity σ_{d}, the photoconductivity-to-dark-conductivity ratio σ_{ph}/σ_{d} at 1 W/cm^{2}, the steady-state two-beam-coupling response time τ_{2bc} at an incident intensity of 1 W/cm^{2}, and the fixed-gain time response τ_{fg} [see the data presented in Fig. 10 along with relation (7) and Eq. (9); note that estimates of τ_{fg} used values of
${\mathrm{\Gamma}}_{max}^{(\text{e})}$ from Table 5].

Table 5

Optimized Codirectional Two-Beam-Coupling Parameters^{a} Predicted from Contradirectional Two-Beam-Coupline Measurement for the Series of Rh-Doned SBN:60 Samples

Rh Conc.(wt. %)

$2{\theta}_{max}^{(e)}$(deg)

${\mathrm{\Gamma}}_{max}^{(e)}$(cm^{−1})

$2{\theta}_{max}^{(o)}$(deg)

${\mathrm{\Gamma}}_{max}^{(o)}$(cm^{−1})

S_{pr}(cm^{3}/J)

s(×10^{−19})(cm^{2})

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 N_{2}_{k}^{eff}, estimates are given for the optimal external beam-crossing angles
$2{\theta}_{max}^{(e)}$ and
$2{\theta}_{max}^{(o)}$ along with the maximum two-beam-coupling coefficients
${\mathrm{\Gamma}}_{max}^{(e)}$ and
${\mathrm{\Gamma}}_{max}^{(o)}$ for extraordinary and ordinary polarizations, respectively (see Subsection 4.2), the photorefractive sensitivity S_{pr} [see relation (8) in Subsection 4.C], and the photoionization cross section s [see Subsection 4.E].