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

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.

© 2011 Optical Society of America

Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer

Thomas X. H. Huang, Xiaoke Yi, and Robert A. Minasian
Opt. Lett. 36(22) 4440-4442 (2011)

Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings

Reza Ashrafi and José Azaña
Opt. Lett. 37(13) 2604-2606 (2012)

Tunable, nondispersive optical filter using photonic Hilbert transformation

Hamed Pishvai Bazargani, María del Rosario Fernández-Ruiz, and José Azaña
Opt. Lett. 39(17) 5232-5235 (2014)

All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis

Mohammad H. Asghari and José Azaña
Opt. Lett. 34(3) 334-336 (2009)

Fractional Hilbert transform

Adolf W. Lohmann, David Mendlovic, and Zeev Zalevsky
Opt. Lett. 21(4) 281-283 (1996)