Static phase change in a fiber optic coil hydrophone

V. S. Sudarshanam; K. Srinivasan

doi:10.1364/AO.29.000855

Static phase change in a fiber optic coil hydrophone

V. S. Sudarshanam and K. Srinivasan

Applied Optics
Vol. 29,
Issue 6,
pp. 855-863
(1990)
•https://doi.org/10.1364/AO.29.000855

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V. S. Sudarshanam and K. Srinivasan, "Static phase change in a fiber optic coil hydrophone," Appl. Opt. 29, 855-863 (1990)

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- Original Manuscript: May 3, 1989
- Published: February 20, 1990

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Abstract

For low acoustic frequencies, the acoustooptic interaction in a fiber optic interferometric coil hydrophone has been modeled on assumptions of hydrostatic and radial stress. However, an inherent ambiguity exists in the way by which the correct model has been chosen. It is established through unambiguous experimental determination of the sign of the induced static phase change that the hydrostatic model alone is valid. The method involves the use of a phase modulator constructed by bonding an optical fiber onto a piezoelectric PVF₂ film. Theoretical considerations which also favor the hydrostatic model are presented.

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Hypothesis	Change in fiber length	Stress configuration	Strain matrix	Sensitivity ΔΦ/PL (rad/Pa m)	Sign of phase change
Axially constrained radial pressure	Zero	$\begin{array}{l} α_{x} = σ_{y} = - P \\ σ_{x} = ν (σ_{x} + σ_{y}) \end{array}$	$[\begin{matrix} - P (1 - ν - 2 ν^{2}) / E \\ - P (1 - ν - 2 ν^{2}) / E \\ 0 \end{matrix}]$	$\begin{array}{l} \frac{β n^{2}}{2 E} (1 - ν - 2 v^{2}) (p_{11} + p_{12}) \\ = 6.74 \times 10^{- 5} rad / Pa m \end{array}$	Positive
Axially unconstrained radial pressure (RPH)	Elongation	$\begin{array}{l} σ_{x} = σ_{y} = - P \\ σ_{x} = 0 \end{array}$	$[\begin{array}{l} - P (1 - ν) / E \\ - P (1 - ν) / E \\ + P (2 ν) / E \end{array}]$	$\begin{array}{l} \frac{2 β ν}{E} + \frac{β n^{2}}{2 E} [(1 - ν) (p_{11} + p_{12}) - 2 ν p_{12}] \\ = 13.92 \times 10^{- 5} rad / Pa m \end{array}$	Positive
Hydrostatic pressure (HPH)	Contraction	$σ_{x} = σ_{y} = σ_{z} = - P$	$[\begin{matrix} - P (1 - 2 ν) / E \\ - P (1 - 2 ν) / E \\ - P (1 - 2 ν) / E \end{matrix}]$	$\begin{array}{l} \frac{- β}{E} (1 - 2 ν) + \frac{β n^{2}}{2 E} (1 - 2 ν) (2 p_{12} + p_{11}) \\ = - 4.06 \times 10^{- 5} rad / Pa m \end{array}$	Negative

Element	Parameter	Value
FPF composite	(a) Phase shifting coefficient	1.77 rad/V_peak m
	(b) Fiber interaction length	1.04 m
Piezofilm	(a) Strain per unit applied voltage	0.82 × 10⁻⁶/V
	(b) Thickness	28 μm
	(c) Length	14 cm
Optical fiber	(a) Core radius	4 μm
	(b) Cladding radius	125 μm
	(c) Coating (Jacket) radius	230 μm
	(d) Longitudinal strain sensitivity	1.25 × 10⁷ rad/m (per unit strain)

Hypothesis	Change in fiber length	Stress configuration	Strain matrix	Sensitivity ΔΦ/PL (rad/Pa m)	Sign of phase change
Axially constrained radial pressure	Zero	$\begin{array}{l} α_{x} = σ_{y} = - P \\ σ_{x} = ν (σ_{x} + σ_{y}) \end{array}$	$[\begin{matrix} - P (1 - ν - 2 ν^{2}) / E \\ - P (1 - ν - 2 ν^{2}) / E \\ 0 \end{matrix}]$	$\begin{array}{l} \frac{β n^{2}}{2 E} (1 - ν - 2 v^{2}) (p_{11} + p_{12}) \\ = 6.74 \times 10^{- 5} rad / Pa m \end{array}$	Positive
Axially unconstrained radial pressure (RPH)	Elongation	$\begin{array}{l} σ_{x} = σ_{y} = - P \\ σ_{x} = 0 \end{array}$	$[\begin{array}{l} - P (1 - ν) / E \\ - P (1 - ν) / E \\ + P (2 ν) / E \end{array}]$	$\begin{array}{l} \frac{2 β ν}{E} + \frac{β n^{2}}{2 E} [(1 - ν) (p_{11} + p_{12}) - 2 ν p_{12}] \\ = 13.92 \times 10^{- 5} rad / Pa m \end{array}$	Positive
Hydrostatic pressure (HPH)	Contraction	$σ_{x} = σ_{y} = σ_{z} = - P$	$[\begin{matrix} - P (1 - 2 ν) / E \\ - P (1 - 2 ν) / E \\ - P (1 - 2 ν) / E \end{matrix}]$	$\begin{array}{l} \frac{- β}{E} (1 - 2 ν) + \frac{β n^{2}}{2 E} (1 - 2 ν) (2 p_{12} + p_{11}) \\ = - 4.06 \times 10^{- 5} rad / Pa m \end{array}$	Negative

Element	Parameter	Value
FPF composite	(a) Phase shifting coefficient	1.77 rad/V_peak m
	(b) Fiber interaction length	1.04 m
Piezofilm	(a) Strain per unit applied voltage	0.82 × 10⁻⁶/V
	(b) Thickness	28 μm
	(c) Length	14 cm
Optical fiber	(a) Core radius	4 μm
	(b) Cladding radius	125 μm
	(c) Coating (Jacket) radius	230 μm
	(d) Longitudinal strain sensitivity	1.25 × 10⁷ rad/m (per unit strain)

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