Defect-Photonic Crystal Fiber structure of Zero Chromatic Dispersion and very low Confinement loss

Photonic crystal fibers are being designed with promising results owing to design flexibility and structure geometry. A four-ring structure with ring defects has been proposed. The results show that Photonic crystal fiber with the third ring removed has very low confinement loss of 1.17x10-4dB/km at 1.55μm, chromatic dispersion of 69ps/km.nm at 0.75μm and zero chromatic dispersion at 0.86μm. The results also show that removing only the third ring reduces chromatic dispersion at shorter wavelengths than at longer wavelengths. Vectorial Finite element method is used for this work. The proposed fiber can be used for short and medium transmission applications.


Introduction
Photonic bandgap effect came to light from the works of Yablonovitch and John (Yablonovitch, 1987) in the study of spontaneous emission control and confinement of light in periodic materials (Bjarklev, Broeng, & Bjarklev, 2012). Dielectric materials are arranged in a periodic form. If total photonic bandgap is considered, the frequencies obtained does not allow any propagation when the photonic crystal is infinite. Certain frequencies propagate, should a defect be introduced into the infinite photonic crystal. This defect could be a point defect which changes the periodicity in the crystal but allowing for light confinement in the area of the defect as the light comes from the defect. Another defect which also confines the light at the area of the defect and allow for propagation along the defect is the linear defect. Guiding light under the condition of linear defect can also occur in a two dimensional periodicity. Holes are inserted in a silica material to create a lower refractive index called the cladding as oppose to the core with high refractive index. Cladding which is holy, is made of two dimensionally periodic array of holes. Photonic crystal fiber (PCF) could be either holy core or of solid core type. The type that is widely used is the solid core due to its ease of fabrication. Defects can be done at the preform stage of fabrication with ease which makes creating defects in photonic crystal fiber of less fabrication difficulty. (d ric Zolla, 2005) A paper by (Biswas et al., 2019) have proposed a circular air holes type of PCF and created a defect in the core by eliminating a single hole and has achieved a chromatic dispersion of -1044ps/km.nm at a wavelength of 1.55µm but the work has not been extended to investigate confinement loss property. Rabiul Hasan et al (Hasan, Islam, Rifat, & Hasan, 2017), increased birefringence by removing two holes in a circular air hole photonic crystal fiber structure to create artificial defects within the core. The results indicates an ultra-high birefringence of 2.64 x 10 -2 and negative dispersion values from -242.22ps/km.nm to -762.6ps/km.nm at a wavelength of 1.3µm to 1.67µm.
Further to this work, another research by Lee et al (Lee, Lee, Jung, Oh, & Kim, 2016) implemented two line defects inside the core to obtain birefringence in the order of 10 -2 with an improvement of dispersion from -400ps/km.nm at a wavelength of 1.26µm and a confinement loss of 10 -3 dB/km. In another PCF structure, tiny holes have been introduced into the core to create a defect (Talukder, Isti, Nuzhat, & Biswas, 2020). In all the research papers mentioned, the defects have been created in the core by adding or eliminating a hole. However, none shows the effect of a removal of one or two rings on the optical properties of the structure especially with all circular air holes PCF structure. Also some PCF structures with circular air holes have been replaced by elliptical holes in order to create some sort of defects in (Ghunawat, Chandra, & Singh, 2017;Halder & Hossain, 2016).
In this paper a four ring PCF structure with circular air holes and three conditions of ring defect has been designed to achieve a very low confinement loss of 1.17x10 -4 dB/km at 1.55µm, chromatic dispersion of -69ps/km.nm at 0.75µm and zero chromatic dispersion at 0.96µm is proposed. Propagation properties of the proposed PCFs have been analyzed using full vectorial Finite Element Method

Design methodology of proposed PCF structure
Proposed Hexagonal PCF structures; PCF1, PCF2 and PCF3's cross-sectional view are shown in figures 1.1, 1.2 and 1.3 respectively. The designs consist of a cladding of circular air holes and solid core. For the background material, silica is used, which is industrially available. The refractive index considered for the cladding is 1. The 98 proposed designs are progressive and consist of three air hole rings in PCF 1, two air hole rings in PCF 2 and PCF 3. A perfectly matched layer has been provided to absorb radiated waves with small reflections light. This design is made up of four rings. All the three PCF's have air filling fraction of d/˄=0.6. The rings are designed such that the pitch is kept at 2.3µm for all the PCF structures. In PCF1 the air hole radius for each hole in ring one is given by 1.035µm and ring two except 'a' and 'b' is given by 0.8625µm. The fourth ring have holes with radii of 0.5175µm.
The PCF structures have been designed to study the effect of the defect created by the removal of some rings. In PCF1 the third ring has been removed. In PCF2 the first and the second ring have been removed. Also, in PCF3 the first, second and third ring has been replaced with one ring with a pitch of 4µm. The hole labelled 'c' and 'd' are given by a radii of 1.725µm and 2.07µm respectively.

Confinement Loss
In PCF, the mode leak from the core to the finite holes in the cladding. This occurs in-between the holes. The

Change of wavelength with respect to Effective Refractive Index
Effective refractive index values were obtained from the simulation. The variation of refractive index with wavelength is shown in Figure 1.7. The graph shows that as effective refractive index decreases, wavelength also increase, which is in agreement with (Akowuah, Ademgil, & Haxha, 2012) for all the defects created.
The graph in figure 1.7 of effective refractive index indicates that PCF 1 has the lowest refractive index of 1.39µm at 1550 nm wavelength. The results in figure 1.7 show that light is confined well in core region at shorter wavelengths. Removing the third ring only to create defect, reduced the real effective refractive index as compared to the case where the first and second ring are removed. Also removing entirely, the first, second and third ring and replacing it with the single ring with larger holes also increased the real effective part of the complex wave.
This shows that removing the inner rings makes room for increase in the real refractive index.

Change of wavelength with respect to Chromatic dispersion
The change of chromatic dispersion with wavelength for the proposed PCFs is shown in Figure 1.8 which shows that chromatic dispersion increases as wavelength increases. The dispersion of 89ps/km.nm, around 100 ps/km.nm is obtained for PCFs 2 and 3 respectively and 176 ps/nm.km for PCF 1 at 1550 nm. The chromatic dispersion is better for PCF2 in which the first and third ring is removed. Minimum dispersion of -140ps/km.nm for PCF 2, -132 ps/km.nm for PCF 3 and -69 ps/km.nm for PCF 1 is obtained at the value of 750nm. Zero chromatic dispersion has been obtained for all the proposed PCF structures from 0.85 to 1.1 ps/km.nm which is also in agreement with (Barrientos- García et al., 2016;García et al., 2015). results show that PCF1 has the lowest confinement loss and this is attributed to the presence of more air holes than the rest of the PCFs since only the third ring is removed. The confinement loss in order of 10 -2 dB/m is obtained at the telecommunication wavelength of 1550 nm for PCFs 2 and 3, as shown in Figure 1.9. PCF 1 shows a significantly less confinement loss of less than 1.17x10 -4 dB/m at 1550nm which is better than (Hasan et al., 2017;Islam et al., 2019;Lee et al., 2016). It is worth noting that, considering the spectral range of 750 nm to 1500 nm, confinement loss for all the designed PCFs, gradually increases as wavelength increases. A key focus of the proposed design is to ensure the ease of fabrication. Some techniques which are being adopted for fabrication of PCFs are stack and draw method (Pysz et al., 2014) conventional drilling, (Ghosh, Bose, Roy, & Bhadra, 2015), and sol-gel casting (Bise & Trevor, 2005). The shape of the core along with the cladding is controlled utilizing stack and draw method and Sol-gel casting. It has been reported in (Liu, Wu, Vincent Tse, Lu, & Tam, 2013) and (Bise & Trevor, 2005) that complex structures of PCFs can be fabricated utilizing stack and draw methods and sol-gel techniques. Circular air holes, has been employed for the proposed designs and the number of rings, are also less bulky with the introduction of the defects. The proposed designs can be fabricated using stack and draw method.

Conclusion
It has been demonstrated that ring defects affect the chromatic dispersion and confinement loss. The proposed fibers show low Closs and single zero chromatic dispersion for all the PCFs. The PCF 2 has given a negative chromatic dispersion of -140 ps/km.nm at 890nm wavelength. The PCF1 shows very low confinement loss of 1.17x10 -4 dB/km at 1.55µm, chromatic dispersion of -69ps/km.nm at 0.75µm and zero chromatic dispersion at 0.86µm which would be convenient for usage in short and medium transmission.