DiscussionNarrowband optical filter design for DWDM communication applications based on Generalized Aperiodic Thue–Morse structures
Introduction
In recent years, wavelength filters and demultiplexers play important roles in enhancing the capacity of optical communication. There is a tremendous interest in expanding more compact devices. Nowadays, researchers have paid much attention to one-dimensional (1D) aperiodic structures. Advancements in Dense Wavelength Division Multiplexing (DWDM) systems have made designers and engineers engrossed in narrowband and multiband optical filters [1], [2], [3]. The most important characteristics of optical filters are wide tuning range with a large number of selective channels, fast tuning, low insertion loss, stability with respect to environmental changes, cost effectiveness, and ease of integration, that allows easy splicing to other devices, e.g., coupler, amplifier. DWDM filters are multichannel filters with several pass or stop bands with adjacent channels covering large range of wavelength in the DWDM domain [4], [5], [6], [7]. One of the most suitable choices for DWDM filters is to utilize the multilayer structures. Large multiband periodic filters based on superimposed chirped Fiber Bragg Gratings (FBGs) have already been designed for DWDM to have flat top responses [9]. Demultiplexing a large number of channels in a DWDM communication system would require a large number of filters in series. The main disadvantage of gratings with periodic refractive index is that they have a single stop or a pass band that behaves as a filter.
Since the fundamental discovery of quasicrystals, much attention has been paid to the investigation of structures and physical properties of aperiodic systems [8]. Rostami et al. studied the properties of phonon transmission in random and aperiodic superlattices [7]. Transmission of light through an optical quasiperiodic multilayer has been also extensively studied. Kohmoto et al. investigated the optical transmission through Fibonacci (FC(1)) dielectric multilayer and their theoretical results are confirmed by their experimental ones [11]. As an extension of FC(1), generalized Fibonacci (GF(m, n)) has been also investigated [6], [7]. On the other hand, being a bridge of linking periodic systems with quasiperiodic ones in a geometrical structure, Thue–Morse (TM) systems have attracted much attention over the past years. The electronic and phonon properties of TM lattices are widely studied [9], [10]. Designing a multi narrowband filter is also possible by means of aperiodic Thue–Morse structures [5]. Ring resonators have also been studied actively due to their application in all-optical buffer, optical filters, and dispersion management.
In this paper the possibility of designing DWDM filters with aperiodic generalized Thue–Morse structures is shown. Also demonstrated in this paper are the various effects of parameters on filtering properties such as refractive indices, number of layers and their thickness. We have also shown how we can reach to a bandwidth of 0.1 nm, and also different peak spaces near 1550 nm. For the first time, we have shown that by varying m and n simultaneously in the Thue–Morse structure (BmAn), the most useful properties of the filter can be achieved. Our numerical results of transmittance show that this proposed filter structure has ultra high efficiency and has the most useful properties for filter application. Our simulations have been done in Matlab7. The organization of our paper is as follows.
In Section 2, we present the theoretical background for the Thue–Morse structure. In Section 3, we show that it is possible to design a multichannel filter based on this structure. We select m = 3 and n = 2 for our final designed structure; it means that we generalized the Thue–Morse structure with m = 3 and n = 2 in BmAn. It is also shown that the filtering properties are to impress the structure parameters, such as central wavelength of each channel, bandwidth of them, number of channels that is unlimited and the space between adjacent channels. In this section simulations of the proposed structure have been shown; also, all of filter properties changing due to parameters of structure are shown in this section and the optimum response of final designed filter is selected. Finally, in Section 4, the conclusion of our paper is discussed and we show that based on our simulation results, this filter is completely proper for DWDM communication systems.
Section snippets
Theoretical background of Thue–Morse structures
The theory of light propagation on reflectance and transmittance surfaces of TM(m, n) multilayer systems can be expressed as shown in Fig. 1.
A Thue–Morse (TM) sequence is generated following the growth rule A → AB (AB replacing as A) and B → BA (BA replacing as B). The first five generations of a Thue–Morse structure are shown in the relations below [11].
Or in other words the generation of a Thue–Morse structure is generally
Design and simulation of GATM structure
In the generalized case that we used in this paper, we select m = 3 and n = 2 (A → AnBm, B → BmAn where Bm denotes a string of m Bs and An denotes a string of n As). A generalized Thue–Morse (TM) sequence is generated following the growth rule A → AABBB (AABBB replacing as A) and B → BBBAA (BBBAA replacing as B). The generalized Thue–Morse structure with m = 3 and n = 2 for the first generation is shown in Fig. 2. As shown in this figure, in the first layer and last layer of the generalized structure, we chose
Conclusion
In this paper we proposed a narrowband multichannel DWDM filter by Generalized Aperiodic Thue–Morse(GATM) structures. The channel space and bandwidth of each channel is according to the ITU-T standard. We can control the central wavelength of each channel, the number of channels, and the distance between adjacent channels. Also, the efficiency of each channel is high, thus this filter is suitable for DWDM communication applications. If we want to convert transmission wavelength to reflection
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