Tunable resonance-domain diffraction gratings based on electrostrictive polymers

Ramon Axelrod; Yosi Shacham-Diamand; Michael A. Golub

doi:10.1364/AO.56.001817

Applied Optics
Vol. 56,
Issue 7,
pp. 1817-1825
(2017)
•https://doi.org/10.1364/AO.56.001817

Tunable resonance-domain diffraction gratings based on electrostrictive polymers

Ramon Axelrod, Yosi Shacham-Diamand, and Michael A. Golub

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Ramon Axelrod, Yosi Shacham-Diamand, and Michael A. Golub, "Tunable resonance-domain diffraction gratings based on electrostrictive polymers," Appl. Opt. 56, 1817-1825 (2017)

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Abstract

Critical combination of high diffraction efficiency and large diffraction angles can be delivered by resonance-domain diffractive optics with high aspect ratio and wavelength-scale grating periods. To advance from static to electrically tunable resonance-domain diffraction grating, we resorted to its replication onto 2–5 μm thick P(VDF-TrFE-CFE) electrostrictive ter-polymer membranes. Electromechanical and optical computer simulations provided higher than 90% diffraction efficiency, a large continuous deflection range exceeding 20°, and capabilities for adiabatic spatial modulation of the grating period and slant. A prototype of the tunable resonance-domain diffraction grating was fabricated in a soft-stamp thermal nanoimprinting process, characterized, optically tested, and provided experimental feasibility proof for the tunable sub-micron-period gratings on electrostrictive polymers.

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Characteristic	Value
Young’s modulus (Y)	0.4 GPa
Poisson ratio ( $ν_{P}$ )	0.4
Longitudinal piezoelectric coefficient (d33)	$- 4.66 \cdot 10^{- 4} μm / V$
Traverse piezoelectric coefficient (d13)	$3.33 \cdot 10^{- 4} μm / V$
Refractive index ( $n$ )	1.43
Refractive index dependency on strain: $(d n / d s) / n$	80%
Dielectric constant ( $ε$ , 1 Khz)	55
Traverse saturation strain and associated field	150 V/μm (4.5%)

Parameter	Value (“0” subscript denotes unstrained value)
Period	$Λ (s) = Λ_{0} (1 + s)$
Height	$h (s) = h_{0} (1 + s_{3}) = h_{0} (1 - s / ν_{P})$
Slant	$\tan φ (s) = \tan φ_{0} \frac{1 + s}{1 - s / ν_{P}}$
Duty cycle	$q (s) = q_{0} \frac{1 + 0.47 s}{1 + 1.55 s}$
Refractive index	$n_{M} (s) = n_{M 0} (1 + 0.80 s)$ , $n_{M 0} = 1.43$

ID	Lateral Shift [μm]	Membrane Thickness [μm]	PDMS Grating Substrate Thickness [μm]
C	0–0.1	8.5	50
D	0.1–0.2	7.5	100
E	0–0.1	7	10

Characteristic	Value
Young’s modulus (Y)	0.4 GPa
Poisson ratio ( $ν_{P}$ )	0.4
Longitudinal piezoelectric coefficient (d33)	$- 4.66 \cdot 10^{- 4} μm / V$
Traverse piezoelectric coefficient (d13)	$3.33 \cdot 10^{- 4} μm / V$
Refractive index ( $n$ )	1.43
Refractive index dependency on strain: $(d n / d s) / n$	80%
Dielectric constant ( $ε$ , 1 Khz)	55
Traverse saturation strain and associated field	150 V/μm (4.5%)

Parameter	Value (“0” subscript denotes unstrained value)
Period	$Λ (s) = Λ_{0} (1 + s)$
Height	$h (s) = h_{0} (1 + s_{3}) = h_{0} (1 - s / ν_{P})$
Slant	$\tan φ (s) = \tan φ_{0} \frac{1 + s}{1 - s / ν_{P}}$
Duty cycle	$q (s) = q_{0} \frac{1 + 0.47 s}{1 + 1.55 s}$
Refractive index	$n_{M} (s) = n_{M 0} (1 + 0.80 s)$ , $n_{M 0} = 1.43$

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Applied Optics