Coupling-Strength-Independent Long-Period Grating Designs for THz-Bandwidth Optical Differentiators

A novel design of THz-bandwidth all-optical arbitrary-order temporal differentiators using long period fiber/waveguide gratings (LPGs) is proposed and numerically demonstrated. The proposed technique is based on the first-order Born approximation approach in LPGs. We show that an N th-order optical differentiator can be implemented based on an LPG incorporating N π-phase shifts along its length and operating in the cross-coupling mode. The proposed design has a strong tolerance against practical fluctuations in the grating parameters, e.g., as induced during the fabrication process or by environmental fluctuations. In particular, this LPG design solution is essentially insensitive to variations in the grating coupling strength.