Multi-Channel Spectral Filters Based On Sampled Fiber Bragg Gratings

With the fast development of optical communications industry, fiber Bragg gratings, as a novel type of passive fiber components in optical communication systems and the optical sensing system, are attracting more and more attentions due to its superior characteristics of explosion-proof, immue of electromagnetic interference, anti-radiation, surviving in high temperature, small size, light weight, and all-fiber flexibility.Chirped and sampled fiber Bragg gratings are taking attention by its capabilities of generating multi-channel and dispersion compensation. It was found that the multichannel reflection peaks shift from the corresponding uniform sampled FBG when either the grating period or the sampling function or both is chirped. The amount of the shifts were usually obtained numerically using the T-matrix calculation. In view of the importance of the accurate prediction or determination of the wavelength shift, (subsequently, the precise wavelength position of each channel) due to the chirp introduced in the grating parameters, there is a need to develop an analytical, rather than a numerical tool, to characterize the channel wavelength. In this paper, we present an analytical expression for the sampled FBGs with arbitrary chirps in sampling function or grating period or combination of both using Fourier theory. The relationship among the wavelength of each channel, the chirp coefficient of the sampling function and the grating period, and the length of the grating is explicitly given. The calculated results based on the analytical expression are examined with the conventional numerical results, which are found to be in excellent agreement. This analytical tool can provide insight into the designs of more-complex sampled grating structures and into ways to tailor the parameters properly to obtain a specific performance. As the increasing requirement of the wavelength channel numbers, finding a simple and flexible manufacturing method for multi-channel fiber optical filters with wide wavelength range and clear isolation is always the goal of designers. Two types of sampled fiber Bragg gratings are most frequently employed in practice, i.e., amplitude sampled fiber Bragg grating (ASFBG) and phase-only sampled fiber Bragg grating (PSFBG). The main drawback of the conventional ASFBG is the trade-off between the spectral range and the channel energy efficiency according to Fourier transform in which the spectral range in frequency domain is inversely proportional to the duty cycle in each sampling period. The more the output channel, the smaller the duty cycle, which directly results in the very low energy efficiency when an ASFBG is employed in a conventional way since a large portion of the fiber is absent of the grating. Recently, it has been shown that the multi-channel generation can be implemented by exploiting Talbot effect in sampled and chirped FBGs, in which the channel density (or free spectral range, FSR) can be effectively multiplied by changing the chirp coefficient with no need to change the sampling period as the case in conventional SFBGs. However, when we examine the structure of an ASFBG used under condition of Talbot effect, it is found that the duty cycle of each sampling period must also be kept small in order to obtain clean multi-channel outputs, which also results in low energy efficiency and the practical application is thus very limited. The most attractive feature of phase-only sampled FBGs (PSFBGs) is the high energy efficiency. The Talbot effect in PSFBGs for multi-channel generation has also been proposed to enhance the energy efficiency with a limited fiber length. It is shown that, under the Talbot condition, the PSFBGs using less phase transitions is capable of generating superior high-count DWDM channels with high energy efficiency. Nonetheless, the manufacturing difficulty of PSFBGs still remians. In this paper, we propose a novel amplitude sampled FBG structure that has a full duty cycle (=1) for efficient generation of broadband high-count channels operated under spectral Talbot effect. This structure integrates advantages of amplitude sampled FBGs (easy and straightforward making), phase-only sampled FBGs (high energy efficiency and short fiber length) and Talbot effect (inherit high efficiency in high-count channel output and arbitrily FSR tuning). It is shown that the energy efficiency of the structure is comparable to that of the PSFBGs with the same fiber length. The direct use of a simple Gaussian beam profile or combination of Gaussian profile yields high uniformity, high isolation and high-count channel outputs.