All-optical temporal fractional order differentiator using an in-fiber ellipsoidal airmicrocavity

An all-optical temporal fractional order differentiator with ultrabroad bandwidth （-1.6 THz） and extremely simple fabrication is proposed and experimentally demonstrated based on an in-fiber ellipsoidal air-microcavity. The ellipsoidal air-microcavity is fabricated by splicing a single mode fiber （SMF） and a photonic crystal fiber （PCF） together using a simple arc-discharging technology. By changing the arc-discharging times, the propagation loss can be adjusted and then the differentiation order is tuned. A nearly Gaussian-like optical pulse with 3 dB bandwidth of 8 nm is launched into the differentiator and a 0.65 order differentiation of the input pulse is achieved with a processing error of 2.55%.