Determination of acousto-optical effect maxima for optically isotropic crystalline material on the example of GaP cubic crystal

Oleh Buryy; Nazariy Andrushchak; Natalia Demyanyshyn; Anatoliy Andrushchak

doi:10.1364/JOSAB.36.002023

Journal of the Optical Society of America B
Vol. 36,
Issue 8,
pp. 2023-2029
(2019)
•https://doi.org/10.1364/JOSAB.36.002023

Determination of acousto-optical effect maxima for optically isotropic crystalline material on the example of GaP cubic crystal

Oleh Buryy, Nazariy Andrushchak, Natalia Demyanyshyn, and Anatoliy Andrushchak

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Oleh Buryy, Nazariy Andrushchak, Natalia Demyanyshyn, and Anatoliy Andrushchak, "Determination of acousto-optical effect maxima for optically isotropic crystalline material on the example of GaP cubic crystal," J. Opt. Soc. Am. B 36, 2023-2029 (2019)

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Abstract

The peculiarities of the acousto-optic interaction geometry optimization in the optically isotropic crystalline material are demonstrated on the example of GaP cubic crystal. The calculation algorithm takes into account the change of the optical indicatrix form during acoustic wave propagation through the crystal. On this basis, the highest achievable value of the acousto-optic figure of merit $M_{2} = 98 \cdot 10^{- 15} s^{3} / kg$ is determined by the extreme surfaces method. This value is achieved in the case of the isotropic diffraction of the light beam on the longitudinal acoustic wave. The approach developed in this work can be used for optimization of the acousto-optic interaction in other optically isotropic crystalline materials.

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Parameter	Value	Reference
Density, $kg / m^{3}$	4300	[13]
Refractive index ( $λ = 632.8 nm$ )	3.313	[14]
Elastic modulus, GPa	$C_{11} = 141.2$ ; $C_{12} = 62.53$ ; $C_{44} = 70.47$	[14]
Elasto-optic coefficients	$p_{11} = - 0.23$ ; $p_{12} = - 0.13$ ; $p_{44} = - 0.10$	[14]
Piezoelectric constant $e_{14}$ , $C / m^{2}$	−0.10	[19]
Low-frequency dielectric permittivity	11.1^a	[13]

	Incident Light Wave		Diffracted Light Wave		Acoustic Wave
Type of Acoustic Wave	Direction ${\vec{m}}_{μ}$ , $θ_{\max}$ , $φ_{\max}$ , deg.	Polarization ${\vec{i}}_{μ}$ , $θ_{μ \max}$ , $φ_{μ \max}$ , deg.	Direction ${\vec{m}}_{ν}$ , $θ_{d \max}$ , $φ_{d \max}$ , deg.	Polarization ${\vec{i}}_{ν}$ , $θ_{ν \max}$ , $φ_{ν \max}$ , deg.	Direction $\vec{a}$ , $θ_{a}$ , $φ_{a}$ , deg.	Polarization ${\vec{f}}_{q}$ , $θ_{f}$ , $φ_{f}$ , deg.	Velocity, $V_{q}$ , m/s	$\| p_{ef} \|$	$M_{2 \max}^{extr}$ , $10^{- 15} s^{3} / kg$
Isotropic “+”
$l$ ( $q = 3$ )	42; 83	54.7; 225	41.9; 83.1	54.8; 225	54.7; 225	54.7; 225	6521	0.30	98
$f$ ( $q = 2$ )	45; 0	53.2; 221.5	45.3; −0.1	53; 221.6	47.3; 156.5	104.2; 75.2	3821	0.11	60
$s$ ( $q = 1$ )	0; 0	90; 55.3	0.29; 104.2	90.2; 55.3	90.1; 104.2	89.7; 22.7	3781	0.11	64
Isotropic “−”
$l$ ( $q = 3$ )	0; 0	90; $\sim 0$	0.2; 90	90; $\sim 0$	90.1; 90	90.2; 90	5730	0.13	28
$f$ ( $q = 2$ )	0; 0	90; 135	0.27; 270	89.8; 135	89.9; 90	89.9; 0	4048	0.10	46
$s$ ( $q = 1$ )	8; 1	84.3; 225.3	8; −0.9	84.4; 225.2	90; 90	99.1; −0.1	4048	0.10	46

Parameter	Value	Reference
Density, $kg / m^{3}$	4300	[13]
Refractive index ( $λ = 632.8 nm$ )	3.313	[14]
Elastic modulus, GPa	$C_{11} = 141.2$ ; $C_{12} = 62.53$ ; $C_{44} = 70.47$	[14]
Elasto-optic coefficients	$p_{11} = - 0.23$ ; $p_{12} = - 0.13$ ; $p_{44} = - 0.10$	[14]
Piezoelectric constant $e_{14}$ , $C / m^{2}$	−0.10	[19]
Low-frequency dielectric permittivity	11.1^a	[13]

	Incident Light Wave		Diffracted Light Wave		Acoustic Wave
Type of Acoustic Wave	Direction ${\vec{m}}_{μ}$ , $θ_{\max}$ , $φ_{\max}$ , deg.	Polarization ${\vec{i}}_{μ}$ , $θ_{μ \max}$ , $φ_{μ \max}$ , deg.	Direction ${\vec{m}}_{ν}$ , $θ_{d \max}$ , $φ_{d \max}$ , deg.	Polarization ${\vec{i}}_{ν}$ , $θ_{ν \max}$ , $φ_{ν \max}$ , deg.	Direction $\vec{a}$ , $θ_{a}$ , $φ_{a}$ , deg.	Polarization ${\vec{f}}_{q}$ , $θ_{f}$ , $φ_{f}$ , deg.	Velocity, $V_{q}$ , m/s	$\| p_{ef} \|$	$M_{2 \max}^{extr}$ , $10^{- 15} s^{3} / kg$
Isotropic “+”
$l$ ( $q = 3$ )	42; 83	54.7; 225	41.9; 83.1	54.8; 225	54.7; 225	54.7; 225	6521	0.30	98
$f$ ( $q = 2$ )	45; 0	53.2; 221.5	45.3; −0.1	53; 221.6	47.3; 156.5	104.2; 75.2	3821	0.11	60
$s$ ( $q = 1$ )	0; 0	90; 55.3	0.29; 104.2	90.2; 55.3	90.1; 104.2	89.7; 22.7	3781	0.11	64
Isotropic “−”
$l$ ( $q = 3$ )	0; 0	90; $\sim 0$	0.2; 90	90; $\sim 0$	90.1; 90	90.2; 90	5730	0.13	28
$f$ ( $q = 2$ )	0; 0	90; 135	0.27; 270	89.8; 135	89.9; 90	89.9; 0	4048	0.10	46
$s$ ( $q = 1$ )	8; 1	84.3; 225.3	8; −0.9	84.4; 225.2	90; 90	99.1; −0.1	4048	0.10	46

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Journal of the Optical Society of America B