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 ±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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