![]() Where j = − 1 is the imaginary unit, ν is the baseband frequency, i.e., ν = ν o p t − ν 0, ν o p t is the optical frequency, and ν 0 is the carrier optical frequency of the signal. have shown all-optical temporal differentiation based on a Moiré fiber grating (MFG) operated in reflection, where first-order temporal differentiation is obtained with one crossover point, and second-order temporal differentiation with two symmetrical crossover points along the MFG length. Consequently, in order to perform photonic fractional differentiation, Liu et al. ![]() proposed and demonstrated the feasibility of writing a Moiré grating in a standard telecommunication optical fiber (SMF-28) using stretching and double exposure to ultraviolet fringes. This last feature is one of the most important in its comparison to PS-FBGs. It has some peculiarities, such as a perfect apodization with a cosine profile, and it has an intrinsic π phase shift at the crossover point, i.e., it is not necessary to post-process the grating in order to introduce the phase shift. They are created by superimposing two Bragg gratings with slightly different periods. In that work, the technique produces broadband filters whose structures depend only on an intermediate stretch between two identical UV exposures.Īs an alternative to FBGs and LPGs, Moiré gratings are one of the important structures first proposed by Reid et al. ![]() reported the fabrication of in-fiber Moiré filters by double exposure of a non-dedicated chirp phase mask. The second uses a double-grating writing technique by introducing a path-length difference across the wavefront of one of the two beams of the writing interferometer. In the first method, the constant average effective refractive index along the grating is obtained by exploiting the finite coherence length of the marking laser. In 1998, Fröhlich and Kashyap proposed two new methods for apodizing FBGs. Although this technique provides a robust means that enables the fabrication of the PS-FBG with higher quality and repeatability, the fabrication cost of the phase mask is high. were the first to propose the phase-shift phase mask technique, where the desired phase shift was pre-inscribed in a phase mask and the phase shift as well as the FBG itself are produced at the same time. Although they have many applications, their manufacture is acknowledged as one of the difficulties in creating new sensors or communication subsystems consisting of a grating, where a discrete phase shift is introduced at particular locations. The reader can find more information about these gratings in, and references therein.įurthermore, phase-shifted fiber Bragg gratings (PS-FBG) have been created and employed as intricate filters, including flat-top band-pass/band-stop filters, triangle filters, ultra-narrow filters, and filters with large channel counts. Photonic differentiation can also occur in planar waveguides such as silicon-on-chips, but here we limit ourselves to optical fibers due to their inherent compatibility with already established fiber optic systems. Instead, long-period gratings (LPGs) are more suitable for higher bandwidths (>100 GHz). ![]() Fiber Bragg gratings (FBGs) are preferable when requiring small bandwidths (i.e., the tens-of-gigahertz range). Depending on the operating bandwidths, two different types of fiber gratings were mainly used. The performance of all-optical integer-order temporal differentiation was demonstrated in several papers. ![]() However, the previously mentioned order n of differentiation was typically restricted to an integer. This device works with the field envelope, and converts a given signal into its n-th order derivative. Among other advantages, they are fully compatible with fiber optic systems and independent of polarization. Temporal differentiator devices play an important role in photonics, as they are simple, have a low fabrication cost, and have a low insertion loss. When operating in the optical domain, these devices offer a greater bandwidth and higher operating speeds than devices operating with the traditional electronics-based system. In recent years, due to the exponential development of photonic technologies, all-optical circuits have been implemented for signal processing. ![]()
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