On the interrelations between an optical differentiator and an optical Hilbert transformer

Nam Quoc Ngo; Yufeng Song

doi:10.1364/OL.36.000915

On the interrelations between an optical differentiator and an optical Hilbert transformer

Nam Quoc Ngo and Yufeng Song

Optics Letters
Vol. 36,
Issue 6,
pp. 915-917
(2011)
•https://doi.org/10.1364/OL.36.000915

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Nam Quoc Ngo and Yufeng Song, "On the interrelations between an optical differentiator and an optical Hilbert transformer," Opt. Lett. 36, 915-917 (2011)

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Table of Contents Category
- Ultrafast Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Continuous optical signal processing (070.6020)
- Optical processing (200.4740)

About this Article
History
- Original Manuscript: August 19, 2010
- Revised Manuscript: November 29, 2010
- Manuscript Accepted: December 28, 2010
- Published: March 10, 2011

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Abstract

We show analytically and numerically that a practically realizable first-order optical Hilbert transformer (OHT) can simultaneously function as a negative/positive first-order temporal optical differentiator (OD) in the stopband and a broadband $\pm 90 °$ phase shifter in the passbands. An integrated-optic OHT based on a four-tap finite impulse response filter is designed using the Remez iteration algorithm and is numerically verified.

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Coupling Coefficients $k_{n}$	Phase Shifts $ϕ_{n}$ [rad]	Output Phase Angles $θ_{n}$ [rad]	Phase Shift $Φ_{n}$ [rad]
$k_{0} = 0.0055$	$ϕ_{0} = 2.9934$	$θ_{0} = - 0.0741$	$Φ_{0} = 3.2157$
$k_{2} = 0.3299$	$ϕ_{2} = 1.9180$	$θ_{2} = - 0.6118$	$Φ_{2} = 3.8275$
$k_{4} = 0.4923$	$ϕ_{4} = 1.5862$	$θ_{4} = - 0.7777$	$Φ_{4} = 1.4636$
$k_{6} = 0.0162$	$ϕ_{6} = 2.8864$	$θ_{6} = - 0.1276$	$Φ_{6} = 1.5912$

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