Determination of relative signs of electro-optic and piezoelectric coefficients by measuring optical phase shifts caused by an applied electric field

Kuniharu Takizawa; Masakatsu Okada

doi:10.1364/JOSAB.2.000289

Determination of relative signs of electro-optic and piezoelectric coefficients by measuring optical phase shifts caused by an applied electric field

Kuniharu Takizawa and Masakatsu Okada

Journal of the Optical Society of America B
Vol. 2,
Issue 2,
pp. 289-293
(1985)
•https://doi.org/10.1364/JOSAB.2.000289

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Kuniharu Takizawa and Masakatsu Okada, "Determination of relative signs of electro-optic and piezoelectric coefficients by measuring optical phase shifts caused by an applied electric field," J. Opt. Soc. Am. B 2, 289-293 (1985)

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About this Article
History
- Original Manuscript: April 25, 1984
- Manuscript Accepted: August 31, 1984
- Published: February 1, 1985

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Abstract

A simple method for measuring the relative signs of electro-optic (EO) and piezoelectric (PE) coefficients in crystals is investigated theoretically and experimentally. The method allows us to determine the relative sign of the unclamped EO coefficient r_ij and the PE coefficient d_jk by detecting independently optical phase shifts caused by both EO and PE effects and by a PE effect only. It is shown that the sign of r₆₃/d₃₆ of KDP and ADP crystals is measured by this method to be negative.

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Applied Electric Fields	Rectangular Coordinate Axes	Refractive Indices	Induced Phase Shifts

E₁ = E	$x_{1}^{'} = x_{1}$	$n_{1}^{'} = n_{o}$	$θ_{x 1}^{'} = \frac{π}{λ} n_{o} d_{14} l E$
E₂ = E₃	$x_{2}^{'} = \frac{x_{2} + x_{3}}{\sqrt{2}}$
= 0	$x_{3}^{'} = \frac{- x_{2} + x_{3}}{\sqrt{2}}$	$n_{3}^{'} = n_{o e} + ½ n_{o e}^{3} r_{41} E$	$θ_{x 3}^{'} = \frac{π}{λ} n_{o e}^{3} l E (r_{14} + \frac{d_{14}}{n_{o e}^{2}})$

E₁ = E₂	$x_{1}^{'} = \frac{x_{1} - x_{2}}{\sqrt{2}}$	$n_{1}^{'} = n_{o} + ½ n_{o}^{3} r_{63} E$	$θ_{x 1}^{'} = \frac{π}{λ} n_{o}^{3} l E (r_{63} + \frac{d_{36}}{n_{o}^{2}})$
= 0	$x_{2}^{'} = \frac{x_{1} + x_{2}}{\sqrt{2}}$	$n_{2}^{'} = n_{o} - ½ n_{o}^{3} r_{63} E$
E₃ = E	$x_{3}^{'} = x_{3}$	$n_{3}^{'} = n_{e}$	$θ_{x 3}^{'} = \frac{π}{λ} n_{e} d_{36} l E$

Applied Electric Fields	Rectangular Coordinate Axes	Refractive Indices	Induced Phase Shifts

E₁ = E	$x_{1}^{'} = \frac{x_{1} + x_{2}}{\sqrt{2}}$	$n_{2}^{'} = n_{o} - ½ n_{o}^{3} r_{22} E$	$θ_{x 2}^{'} = - \frac{π}{λ} n_{o}^{3} l E (r_{22} + \frac{2}{n_{o}^{2}} d_{22})$
E₂ = E₃	$x_{2}^{'} = \frac{- x_{1} + x_{2}}{\sqrt{2}}$

= 0	$x_{3}^{'} = x_{3}$	$n_{3}^{'} = n_{e}$	$θ_{x 3}^{'} = - \frac{2}{λ} π n_{e} d_{22} l E$
	$x_{1}^{'} = \frac{x_{1} + x_{3}}{\sqrt{2}}$	$n_{2}^{'} = n_{o}$	$θ_{x 2}^{'} = \frac{π}{λ} n_{o} d_{15} l E$
	$x_{2}^{'} = x_{2}$
	$x_{3}^{'} = \frac{- x_{1} + x_{3}}{\sqrt{2}}$	$n_{3}^{'} = n_{o e} + ½ n_{o e}^{3} r_{51} E$	$θ_{x 3}^{'} = \frac{π}{λ} n_{o e}^{3} l E (r_{51} + \frac{d_{15}}{n_{o e}^{2}})$

			$θ_{x 2} = - \frac{π}{λ} n_{o}^{3} l E (r_{22} + \frac{2}{n_{o}^{2}} d_{22})$
E₂ = E	$x_{1}^{'} = x_{1}$	$n_{1}^{'} = n_{o} + ½ n_{o}^{3} r_{22} E$	$θ_{x 3} = - \frac{2}{λ} π n_{e} d_{22} l E$

E₁ = E₃	$x_{2}^{'} = x_{2}$	$n_{2}^{'} = n_{o} - ½ n_{o}^{3} r_{22} E$	$θ_{x 1} = \frac{π}{λ} n_{o}^{3} l E (r_{22} + \frac{2}{n_{o}^{2}} d_{22})$
= 0	$x_{3}^{'} = x_{3}$	$n_{3}^{'} = n_{e}$	$θ_{x 3} = \frac{2}{λ} π n_{e} d_{22} l E$

E₃ = E		$n_{1}^{'} = n_{2}^{'}$	$θ_{x 1} = - \frac{π}{λ} n_{o}^{3} l E (r_{13} - \frac{2}{n_{o}^{2}} d_{31})$
E₁ = E₂		$= n_{o} - ½ n_{o}^{3} r_{13} E$
= 0		$n_{3}^{'} = n_{e} - ½ n_{e}^{3} r_{33} E$	$θ_{x 3} = - \frac{π}{λ} n_{e}^{3} l E (r_{33} - \frac{2}{n_{e}^{2}} d_{31})$

Applied Electric Fields	Rectangular Coordinate Axes	Refractive Indices	Induced Phase Shifts	Configurations

E₁ = E₂	$x_{1}^{'} = \frac{x_{1} - x_{2}}{\sqrt{2}}$	$n_{1}^{'} = n_{o}$	$θ_{x 1}^{'} = \frac{π}{λ} n_{o} d_{14} l E$
$= \frac{E}{\sqrt{2}}$	$x_{2}^{'} = \frac{x_{1} + x_{2}}{2} - \frac{x_{3}}{\sqrt{2}}$	$n_{2}^{'} = n_{o} + ½ n_{o}^{3} r_{41} E$
E₃ = 0	$x_{3}^{'} = \frac{x_{1} + x_{2}}{2} + \frac{x_{3}}{\sqrt{2}}$	$n_{3}^{'} = n_{o} - ½ n_{o}^{3} r_{41} E$	$θ_{x 2}^{'} = \frac{π}{λ} n_{o}^{3} l E (r_{41} + \frac{d_{14}}{n_{o}^{2}})$

E₁ = E₂ = E₃		$n_{1}^{'} = n_{o} - \frac{1}{\sqrt{3}} n_{o}^{3} r_{41} E$	$θ_{x 1}^{'} = - \frac{2 π}{\sqrt{3} λ} n_{o}^{3} l E (r_{41} - \frac{d_{14}}{2 n_{o}^{2}})$
	$x_{1}^{'} = \frac{x_{1} + x_{2} + x_{3}}{\sqrt{3}}$	$n_{2}^{'} = n_{3}^{'}$
$= \frac{E}{\sqrt{3}}$		$= n_{o} + \frac{1}{2 \sqrt{3}} n_{o}^{3} r_{41} E$	$θ_{x 2}^{'} = \frac{π}{\sqrt{3} λ} n_{o}^{3} l E (r_{41} + \frac{d_{14}}{n_{o}^{2}})$

E₃ = E	$x_{1}^{'} = \frac{x_{1} - x_{2}}{\sqrt{2}}$	$n_{1}^{'} = n_{o} + ½ n_{o}^{3} r_{41} E$	$θ_{x 1}^{'} = \frac{π}{λ} n_{o}^{3} l E (r_{41} + \frac{d_{14}}{n_{o}^{2}})$	Same configuration as (b) in Table 1
E₁ = E₂	$x_{2}^{'} = \frac{x_{1} + x_{2}}{\sqrt{2}}$	$n_{2}^{'} = n_{o} - ½ n_{o}^{3} r_{41} E$
= 0	$x_{3}^{'} = x_{3}$	$n_{3}^{'} = n_{o}$	$θ_{x 3}^{'} = \frac{π}{λ} n_{o} d_{14} l E$

	Present Results		Published Data

	KDP	ADP	KDP	ADP
r₆₃ (pm/V)	\|10.6\|	\|8.60\|	−10.7	−8.5
d₃₆ (pm/V)	\|23.5\|	\|42.8\|	+20.4	+44.6
$\| r_{63} + d_{36} / n_{o}^{2} \| (p m / V)$	Very small	9.90	–	–
r₆₃/d₃₆	−0.451	−0.201	−0.525	−0.191
λ (nm)	633	633	546	546

Applied Electric Fields	Rectangular Coordinate Axes	Refractive Indices	Induced Phase Shifts

E₁ = E	$x_{1}^{'} = x_{1}$	$n_{1}^{'} = n_{o}$	$θ_{x 1}^{'} = \frac{π}{λ} n_{o} d_{14} l E$
E₂ = E₃	$x_{2}^{'} = \frac{x_{2} + x_{3}}{\sqrt{2}}$
= 0	$x_{3}^{'} = \frac{- x_{2} + x_{3}}{\sqrt{2}}$	$n_{3}^{'} = n_{o e} + ½ n_{o e}^{3} r_{41} E$	$θ_{x 3}^{'} = \frac{π}{λ} n_{o e}^{3} l E (r_{14} + \frac{d_{14}}{n_{o e}^{2}})$

E₁ = E₂	$x_{1}^{'} = \frac{x_{1} - x_{2}}{\sqrt{2}}$	$n_{1}^{'} = n_{o} + ½ n_{o}^{3} r_{63} E$	$θ_{x 1}^{'} = \frac{π}{λ} n_{o}^{3} l E (r_{63} + \frac{d_{36}}{n_{o}^{2}})$
= 0	$x_{2}^{'} = \frac{x_{1} + x_{2}}{\sqrt{2}}$	$n_{2}^{'} = n_{o} - ½ n_{o}^{3} r_{63} E$
E₃ = E	$x_{3}^{'} = x_{3}$	$n_{3}^{'} = n_{e}$	$θ_{x 3}^{'} = \frac{π}{λ} n_{e} d_{36} l E$

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