Performance Analysis of Multiple Strips to Reduce the Separation of Photonic Waveguides in Photonic Array

In order to construct a dense Photonic Integrated Circuit (PIC) that comprises photonic waveguides, it is vital to consider the necessity of low crosstalk between surrounding waveguides. From past literature, higher coupling length can be obtained by utilizing a silicon – on -insulator (SOI) based photonic waveguide with an acceptable waveguide separation between them. The current research aims to reduce waveguide separation and hence increase photonic integration over PICs. Numerous strips were inserted between the photonic waveguides to achieve this. The impact of modifications in height and width of three, four, and five strips on coupling has been analyzed. This has led to the inference that larger coupling lengths can be achieved. The greatest coupling lengths of 485 µm, 620 µm, and 104,110 µm were reached with end-to-end waveguide separations between the two adjacent waveguides of 175 nm for three strips, four strips and five strips inserted between two photonic waveguides. Achieving a coupling length of 104,110 µm proves that the proposed design is better than previously proposed designs in terms of coupling length. In addition, we have compared the coupling lengths obtained when Ge strips and Si strips were inserted between the photonic waveguides. The method given in this paper can be used to design a variety of photonic applications.


Introduction
The main properties of Photonic Integrated Circuit (PIC) are high bandwidth competence, less propagation delay, and small size. PICs involving different photonic circuits also includes the array of photonic waveguide which transmits signals from source to destination. The photonic waveguide is a key component of the PIC and it can have different structures. The popular structures are slot, ridge and strip type structures. All these structures can be used for different specific applications. However, in the current study, the strip waveguide has been taken into consideration to transmit the signal through the waveguide. In the PICs, there are many photonic waveguides inserted in a single chip/PIC where there may be crosstalk between the adjacent photonic waveguides. To avoid the crosstalk between waveguides, one can keep sufficient separation between the photonic waveguides.
However, this reduces the number of photonic waveguides in a single chip area. To design compact chips, it is highly required to keep smaller distances in between the photonic waveguides. However, as the distance between the photonic waveguide reduces, it decreases the coupling length and correspondingly increases the crosstalk and results in weak signal strength at the destination. Therefore, the ability to achieve compact integration is vital for the efficient design of PICs with a closely spaced waveguide array [1][2][3]. The main reason behind the higher crosstalk in between the photonic waveguide is that some portion of optical field go out from the parent waveguide and goes into adjacent waveguides. Hence, it is necessary to prevent the evanescent field to go out from the parent waveguide as well as to enter adjacent waveguides for compact integration of waveguides. As a result, reducing crosstalk between nearby waveguides is a critical and difficult issue that makes it difficult to produce compact and dense PICs [4]. To make photonic devices more compact, one idea is to swap out conventional photonic components with cutting-edge Nano photonic ones like plasmonic configurations and metamaterial-based structures [5][6][7][8]. Some authors proposed other approaches for reducing crosstalk between photonic waveguides [9,10]. In the literature, the authors describe techniques such as the grating technique in the photonic waveguide array. This technique prevents the evanescent field to enter into the adjacent waveguide in the PICs. Hence this technique eliminates the crosstalk and correspondingly leads to increase in coupling length. In the direction parallel to the communication, a high index is visible in the silicon gratings. This causes the evanescent field to degrade quickly and leak from the waveguide core. Leakage leads to increase in crosstalk between the photonic waveguide that leads to messages being lost before reaching the destination. Thus, leakage is not desired, and the authors in [11][12][13] have focused their study into the investigation of the effects of placing three strips in the middle of two neighboring waveguides and this approach shows the enhanced performances in terms of coupling length. In order to construct a dense Photonic Integrated Circuit (PIC) that comprises photonic waveguides, it is important to keep lower gap between the photonic waveguides. However, due to kept lower separation, there is higher crosstalk/lower coupling length has been reported in literature by some authors. The lowest separation between two photonic waveguides of up to 300 nm has been reported by researchers previously [11]. However, there is further possibilities to reduce the separation between the waveguides while keeping the other required parameter performances at satisfactory level. The investigations looked at the scalability and coupling length performance of the silicon waveguide as well as its mode characteristics. In the current work waveguide spacing of up to 175 nm has been discussed. Previously, the authors claimed that they obtained a coupling length of 1000 µm for the distance of 300 nm between the adjacent photonic waveguides [11], which is not sufficient to propagate the signal up to remarkable distances and suffer very high crosstalk. However, in the current study, coupling lengths of up to 81,578 m were produced for the same waveguide spacing by utilizing three homogeneous germanium strips with height variations. Furthermore, with a reduced waveguide spacing of 200 nm, the coupling length was increased to 66,810 nm, demonstrating very low crosstalk and thus dense photonic integration over the PICs, which is the primary objective of the current study. We obtained larger coupling lengths during our study and have presented the results in this study.

Methodology
A photonic array consists of a number of photonic waveguides. The focus of this study was on one of the pair of photonic waveguides from the waveguide array. The proposed structure's design is seen in Fig. 1 and comprises of two adjacent ridge waveguides with many strips positioned in between the waveguides. Figure 1a consists of three strips in between the two adjacent photonic waveguides. Similarly, Fig. 1b, c presents the four strips and five strips respectively, which has been inserted in between the two adjacent photonic waveguides. The photonic waveguide consists of core and lower clad, which are filled with the materials of silicon and silica respectively. The photonic waveguide has the dimensions of 500 nm, and 220 nm corresponding to the core width and core height which is of silicon material. At the operating wavelength of 1.55 µm, the refractive indices of silicon and silica are 3.45 and 1.45 respectively. Also, there are multiple strips that has been used in the design strategy which is of germanium material in the current study. At a wavelength of 1.55 µm, the refractive index of germanium is 4.21 [14][15][16]. However, the width and height of all the strips were changed throughout the study to estimate the better performance of the design structures. The end-to-end distance between the inner edges of the two adjacent waveguides were considered as 200 nm in one case and 175 nm in second case. Furthermore, the height of the strips were adjusted for the different modal analysis of the design. Moreover, due to the presence of germanium strips, it can be observed that the combination of multiple strips is able to prevent the Fig. 1 Basic design structure of photonic waveguide with (a) three strips, (b) four strips, and (c) five strips placed between neighboring waveguides evanescent field from entering any adjacent waveguide, because it has higher refractive index. The absorption of germanium is beneficial for the current study, as the mode will propagate through the silicon waveguide and germanium is used to prevent the mode interchanged from one silicon waveguide to another silicon waveguide. Since, the main reason behind the higher crosstalk in between the photonic waveguide is that some portion of optical field go out from the parent waveguide and goes into adjacent waveguides. Hence, it is necessary to prevent the evanescent field to go out from the parent waveguide as well as to enter adjacent waveguides for compact integration of waveguides. As a result, reducing crosstalk between nearby waveguides is a critical and difficult issue that makes it difficult to produce compact and dense PICs. To prevent the evanescent field the germanium strip has been used and due to its high absorption in the operating wavelength it can able to prevent significantly and hence light only passes through the silicon waveguide, which is required to obtain the higher coupling length. This is advantageous for establishing greater coupling lengths.
In the photonic waveguide array, it is possible to transfer the propagating power from parent waveguide to adjacent waveguide up to a certain extent. It becomes necessary to limit the power transfer from one waveguide to another waveguide. This is done by keeping a suitable gap between adjacent waveguides. However, it will limit the number of photonic waveguides in the photonic array. Furthermore, it may require more space to design the required number of waveguides. To decide the level of power transfer from parent waveguide to adjacent waveguide, the parameter of coupling length (Lc) is considered. It can be characterized as the distance over which optical power is fully transferred from parent waveguide to the adjacent waveguide [17,18].
It is defined in Eq. 1 where n s and n a are the real parts of the effective refractive indices for symmetric and antisymmetric modes respectively while is the operational wavelength. It is noted that, for the sufficient amount of coupling length, there will be lower crosstalk for the proper level of propagation distance. In fact, the coupling length and crosstalk between the waveguides are inversely proportional to each other. Hence the primary goal of this research is to achieve higher coupling length. It can be observed from the Eq. (1) that to achieve higher coupling length, the differences between the effective refractive indices of symmetric and antisymmetric mode should be smaller. However, the crosstalk performances also depend on the propagation distance of the waveguide which limits the crosstalk values.

Simulation Analysis
The modal investigations of the current design were carried out using the COMSOL Multiphysics simulation programme. The Finite Element Method (FEM) is used in the modal investigations. In the current geometry as shown as in Fig. 1, the incredibly tiny mesh size was considered when discretizing the waveguide geometry model to investigate the performances of the structure, which has the combination of waveguides and strips. The estimation of propagation distance is a vital parameter and hence, the scattering boundary condition has also been used to alleviate losses during mode propagation [19,20] through the waveguide in the current design. For all of the studies considered, the modal performance for both symmetric and antisymmetric modes was acquired along with the corresponding coupling length. The width and height of the ridge waveguides were taken as standard dimensions of 500 nm and 220 nm, respectively. However, the strip width and height have been changed during the analysis. Strip widths of 15 nm and 25 nm have been used most frequently while strip height has been adjusted widely up to 400 nm. However, in some cases of suitability, the strip

Influence of three strips in between photonic waveguide
To investigate the performance of coupling length, an initial end-to-end waveguide separation of 200 nm was assumed and two different strip widths have been considered to analyses its performances. In this section, the study focused on the tentative simulation analysis for strip widths of 15 nm and 25 nm with the combinations of different strip height, under the influence of three strips. The strip heights of all the three strips were evenly altered to obtain the values of effective refractive indices for symmetric and antisymmetric mode. Figure 2 shows the mode profile by using 3-strips for the symmetric and assymetric modes. The Figs. 3 and 4, shows the different plots, while the strip heights has been varied up to 400 nm. Figure 3a shows the differences in effective refractive indices for symmetric and antisymmetric modes for three strips of germanium material, which has inserted in between two ridge waveguides. Moreover, the results have also obtained with the silicon strip to observe the comparison between the influence of silicon strips and germanium strips. The estimation of coupling length has been carried out by using Eq. (1). Where, it can be observed that the dependency of effective refractive indices of symmetric and antisymmetric propagation mode on coupling length, which has shown in Fig. 3. In the Fig. 3, the discontinuity shows the mode shifting from symmetrical mode to antisymmetric mode and vice versa as with the variations in the strip height and correspondingly changes in the effective refractive indices. After the estimation of mode indices corresponding to symmetric and antisymmetric mode, corresponding coupling length can be computed. For both the investigated strip widths (15 nm and 25 nm), the equivalent coupling length in terms of height has been computed and its variations has been shown in Fig. 4. The Fig. 4 shows the variation of coupling length as the changes occurs in effective refractive indices of symmetrical and antisymmetric mode as observed in Fig. 4. The values of the coupling length increase with increase in strip height and reach to a peak value at strip height of 400 nm and width of 25 nm for germanium strip, as shown in Fig. 4b. However, with the same dimension the values of the coupling length have obtained a lower value, while considering the silicon strips. Further, when germanium strips are considered in the study, the results show their peak coupling lengths of 485 µm, and 1412 µm, respectively of end-to-end separation of 175 nm and 200 nm. As a result, it is obvious that three germanium strips can obtain a very high coupling length for end-to-end waveguide separation of 200 nm. However, the research has continued for a smaller end to end separation of 175 nm, and as shown in Fig. 4b, with the combination of three strips, we were unable to obtain the larger coupling length. As a result, the research has been continued by analyzing the influence of four strips to achieve the better performance.

Influence of four strips in between photonic waveguide
In this sub-section, the performance of coupling length has been analyzed by using the greater number of strips to enhance its performances. Again, the strip heights of all considered four strips were evenly altered to obtain the values of effective refractive indices for symmetric and antisymmetric mode. Figure 5 shows the mode profile by using 4-strips for the symmetric and assymetric modes. The Figs. 6 and 7, shows the different plots, while the strip heights has been varied up to 400 nm. Figure 6a shows the differences in effective refractive indices for symmetric and antisymmetric modes for three strips of germanium material, which has been inserted in between two ridge waveguides. Similar to the previous case, the obtained results with the germanium strips has been compared with the silicon strips as shown in the Fig. 6. The coupling length has been estimated with the help of different mode indices. The dependency of effective refractive indices of symmetric and antisymmetric propagation mode on coupling length as shown in Fig. 6. For both the investigated strip widths (15 nm and 25 nm), the equivalent coupling length with respect to height has been computed and its variations has been shown in Fig. 7. The values of the coupling length increase with increase in strip height and reach a peak value at strip height of 400 nm  and width of 25 nm for the germanium strip, as shown in Fig. 7b. However, with the same dimensions, the values of the coupling length were lower while considering the silicon strips.The jump in coupling length has been observed in coupling length because of strip height has been tuned to disable the evanescent field to enter into neighboring waveguides. With the increase in the strip height, the coupling length changes and can attains a peak value by tunning the strip height. Since, corresponding to the peak value of coupling length, the strip height able to prevent the evanescent field sufficiently. In the current study, germanium strips are considered and the results show their peak coupling lengths of 78,200 µm for the end-to-end separation of 200 nm. Also, the similar results have been reported by some of the authors. However, the study has been continued for lower end to end separation of 175 nm and as seen from Fig. 7a, it can be observed that it is not possible to achieve the higher coupling length with four strips. Therefore, the study has been continued to achieve the higher coupling length by using five strips.

Influence of five strips in between photonic waveguide
The current sub-section focuses on the performance of coupling length using the five strips. The simulation has been carried out with the end-to-end waveguide separations of 200 nm and 175 nm with various strip widths. Strip heights of all five strips were consistently altered to get closer values of effective refractive indices for symmetric and antisymmetric modes. Figure 8 shows the mode profile by using 5-strips for the symmetric and assymetric modes. Figure 9 shows the differences in effective refractive indices when the height has been varied up to 400 nm for symmetric and antisymmetric modes for five strips of germanium material and it has also been compared with the silicon strips which were inserted in between the two ridge waveguides. For both of the considered strip widths, the equivalent coupling length in terms of height has also been computed. Figure 9a shows the differences in effective refractive indices for symmetric and antisymmetric

Discussion and comparison
The crosstalk of a photonic waveguide is inversely proportional to the coupling length. Therefore, the primary goal of this research is to achieve a higher coupling length with a lower waveguide spacing. Three, four, and five strips were employed between neighboring photonic waveguides to create a longer coupling length, and the effect of their height modifications was studied. Taking the waveguide separation as 175 nm in between to photonic waveguide of a photonic array, we achieved the highest coupling lengths of 485 µm, 620 µm, and 104,110 µm respectively for three strips, four strips and five strips. So, by using the five number of germanium strips, it is possible to achieve a very high coupling length up to 104,110 µm by tuning the height and width of the strips. Since, the higher coupling length has been achieved at a lower gap of 175 nm, there will be corresponding lower crosstalk in between two photonic waveguides in the photonic waveguide array. Hence, it is useful to design a larger number of waveguides in the same chip of PICs. As a result, the current technique of inserting multiple germanium strips can be used to decrease crosstalk between   [21] 332,000 µm 3 Si strips with gap of 500 nm, 2018 [7] 4000 µm 5 Si strips with gap of 500 nm and width of 475 nm 2020 [11] 1000 µm 3 Si strips with gap of 300 nm, 2021 [13] 81,578 µm 3 Ge strips with gap of 300 nm, Proposed Work 104,110 µm 5 Ge-strips with gap of 175 nm, width of 19 nm and height of 452 nm two photonic waveguides. Thus, we can accomplish higher density photonic integration over the PICs. Table 1 shows the comparison between coupling lengths of previous and current work for different dimensions.

Conclusion
The current work was done using multiple strips, which are inserted between photonic waveguides to estimate crosstalk performances in order to get dense photonic integration. The impact of three, four, and five strips between neighboring integrated photonic waveguides on achieving decreased crosstalk for compact photonic devices has been illustrated in this study. Maximum coupling lengths of 104,110 µm has been attained at waveguide separations of 175 nm, which demonstrates the considerable improvement over previously reported research. The proposed waveguide structure may achieve decreased crosstalk, which is advantageous for achieving the dense photonic integrated platform. In addition, the methodology for determining the coupling length for Ge-strip was compared to silicon strips. The presented analysis shows that the five-strip combination has a longer coupling length than the three-and four-strip combinations. Furthermore, the suggested structure's dimensions can be tweaked leading to crosstalk being reduced and coupling length being improved which in turn improves the device. The method proposed in this paper could be useful in the development of a variety of applications, including integrated photonic switches. The proposed waveguide structure reduces crosstalk, which is advantageous for achieving the dense photonic integrated platform.