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In future high capacity multicore optical fiber (MCF) networks, signal-processing devices should be able to manipulate data without sacrificing network capacity or MCFs advantages. Thus, it is crucial to have high performance novel devices that can be connected directly to MCFs without conversion to conventional single-core fibers. In this work, a novel Y-splitter for multicore optical fibers is proposed and numerically demonstrated for the first time. The splitter can directly split the power of input MCF cores by 50/50 splitting-ratio into two output MCFs cores. The splitter principle of operation mainly depends on novel double-hump graded-index (DHGI) profile that can space-division split (SDS) optical power by half. Both finite-difference-time-domain and eigenmode-expansion simulations are performed to design, verify, and characterize performance of Y-splitter. It shows wideband operation over the S, C, L, U-bands with polarization insensitivity. It also demonstrates high performance with reasonable insertion-loss, in addition to very low excess-loss and return-loss. Moreover, the splitter shows good performance tolerance to both MCF and design parameters variations.
© 2015 Optical Society of America
1. Introduction
Space division multiplexing (SDM) is considered one of the key solutions in the next generation high capacity optical fiber networks. The current networks capacity is growing exponentially and approaching its final limit despite of using many different solutions such as time-division-multiplexing (TDM), dense-wavelength-division-multiplexing (WDM), polarization-division-multiplexing (PDM), and complex modulation formats [1–5]. Multicore optical fiber (MCF) is considered one of SDM approaches that has a potential to break such capacity limit in future optical networks. A MCF consists of multiple cores arranged in a certain configuration within the same cladding region. Each core can transmit the same set of different TDM, WDM, and/ or PDM channels and thus it can simply multiply the network capacity [6].
However, this MCF potential cannot be fully exploited, unless suitable MCF devices is provided to perform mandatory and conventional signal-processing operations on propagating data during transmission. Relaying on the current traditional solutions of converting back and forth between MCF and single-core single-mode fiber (SMF) to perform such operations imposes a bottle-neck that compromises the high capacity advantages of MCF networks. Therefore, providing novel MCF devices such as couplers, multiplexers, switches, etc. which can be directly connected and integrated with MCF is considered the key solution of such problem.
Several techniques have been already reported on space division multiplexing to couple light to/ from MCF from/ to single-core SMFs. One technique is based on fiber tapered MCF connector (TMC). It couples light from single-mode fibers to MCF by reducing the space among cores from single mode fibers to multi-core fiber [2, 6, 7, 9]. Another SDM multiplexing technique is photonic-lanterns [5, 10, 11]. It functions by propagating several Gaussian modes from SMFs and focusing them to diffraction limit through an adiabatic gradual tapered waveguide. Another technique uses free-space optics such as lenses and collimators to couple the light to/ from MCF [12]. In this technique, the collimated beams coming out of each SMF is imaged on each MCF cores using several ordinary lenses. This free-space SDM technique was utilized for coupling to 19-cores MCF and data transmission with speed up to 305 Tb/s [8, 13]. Other techniques include one dimensional multi-mode-interference (MMI) couplers [14], arrayed waveguide gratings (AWG) [15], and phase matching SDM [16]. Moreover, ultrafast laser inscription has been reported to fabricate waveguides in transparent dielectric materials in order to be used as SDM multiplexers between SMFs and MCF [17].
Here in this work, a novel MCF to MCF Y-splitter (1x2 50:50 coupler) is numerically demonstrated as one step toward the next generation MCFs devices. As already known, Y-splitters are crucial elements in any optical fiber network, especially when signals on optical fibers are required to be distributed (splitted) to other different fibers in order to reach multiple destinations. The Y-splitters can be generally useful in many emerging MCF applications including optical communications, SDM amplification, sensors, and chip interconnection.
The novel MCF Y-splitter demonstrated here is simulated using both finite-difference-time-domain (FDTD) and eigenmode expansion (EME) methods to verify its operation and completely characterize its performance. The Y-splitter shows an excellent performance over the wideband of S, C, L, U wavelength range. It also shows polarization insensitive operation. Its estimated insertion-loss is very reasonable and the excess-loss and return-loss are very small. Moreover, it shows a good performance tolerance to MCF parameter variations, and design parameters variations. All of such excellent characteristics are very attractive for the next generation high capacity MCF networks. To the best of my knowledge, this is the first time to demonstrate such space-division splitter between MCFs.
2. Principles of operation
The proposed MCF Y-splitter is a three-dimensional (3D) device that mainly depends on space-division splitting (SDS) by double-hump graded-index (DHGI) in rectangular waveguide. It consists of multiple single Y-splitters, each one is dedicated to one MCF core and consists of 3-stages: Expander, DHGI-SDS, and separator. Figure 1(a) shows the 3D schematic diagram of Y-splitter together with MCFs. The selected MCFs here have homogeneous identical step-index single-mode seven cores arranged in triangular-lattice. The core and cladding diameters are 9µm and 125µm, respectively. The separation between adjacent cores is 40µm. The cladding refractive index is 1.45, and the relative refractive index difference is 0.35% resulting in a core refractive index of ≈1.4551 [18, 19].
Fig. 1 The MCF Y-splitter structure. (a) The 3D schematic diagram of Y-Splitter with seven sub-splitters connected between 7-core MCFs, each sub-splitter consists of 3-stages. (b) Schematic front-view of Y-splitter showing transverse cross-section of rectangular waveguides and MCFs cores/ cladding.
The 3D Y-splitter consists of seven single sub-splitters. Each sub Y-splitter connects one of the input MCF cores to corresponding two output MCFs cores. A sub Y-splitter consists of 3-stages of rectangular waveguides (WG) that have dimensions and refractive indices as discussed later in this section. The seven Y-splitters are surrounded everywhere by a cladding region (400x125µm) with 1.45 refractive index that matches the refractive index of MCFs cladding.
Figure 1(b) shows a 2D schematic front-view of the Y-splitter and three connected MCFs. It demonstrates the arrangement of rectangular WGs together with MCFs cores and the cladding region. The separation between output MCFs is selected here to be equal to one MCF diameter (125µm). The seven Y-splitters WGs are shown as rectangles, each comprising an input core in the middle and two output cores on both sides. All rectangular WGs have equal heights of 9µm. The MCFs are rotated by 19° around their longitudinal axis in order to have a line-of-sight view between cores of each single splitter. That results in a vertical separation between adjacent WGs equals to 4µm. In order to ensure vertical de-coupling between those adjacent WGs, a thin isolation layer (2µm) with a lower refractive index (1.44) than the cladding region (1.45) is inserted in the mid-way between each adjacent WGs. This isolation layers (not shown in figures for simplicity) act as trenches [18] that help in reducing cross-talk between WGs as will be discussed latter in section five.
Figure 2(a) illustrates a schematic diagram of single Y-splitter together with its 3-stages showing its dimensions and refractive indices. The first stage acts as a graded-index lens [20] to expand the input core beam slightly. The rectangular WG lens (280x60x9µm) has the index profile:
Where no = 1.46, and ‘y’ dimension is measured in ‘µm’ as shown in Fig. 2(a). This gentle parabolic index is optimized to have a small slope in order to act as a taper that gradually expands the input beam adiabatically and thus reduce the number of excited higher order modes. That would help eventually in matching the fundamental mode of output cores both in size and profile, and thus avoiding too much coupling loss.Fig. 2 A single sub Y-splitter structure and its FDTD simulation. (a) 2D refractive index profile of sub Y-splitter. The inset shows the double-hump graded index profile of the second stage space-division-splitter (SDS). The white arrows indicate approximate locations of total internal reflections occurrence. (b) The FDTD simulation of electric-filed magnitude (|E| a.u.) for a single sub Y-splitter at the wavelength of 1555nm.
The second stage is the main one in splitter operation. It consists of a rectangular WG that has a centered double-hump graded refractive index (DHGI) profile as illustrated in Fig. 2(a) inset. The double-hump center is aligned with the lens central axis. Each hump has a dimension of 995x60x9µm. Each single hump has a parabolic profile:
Where 20 and −20 µm correspond to the left (−60 µm<y<0) and right (0<y<60 µm) hump, respectively. The SDS splitting occurs by using total internal reflection (TIR) phenomenon [20]. The DHGI imposes a low refractive index region at mid of the lens output, which increases gently when moving away from DHGI mid region. Thus, it divides the expanded beam equally in space by TIR, forcing 50% of optical power to deflect to the right-hand side and 50% to deflect to the left-hand side (as indicated by white arrows in Fig. 2(a)). When both splitted beams reach the lower refractive index region at WG other sides, they deflect again by TIR and propagate along the x-direction into the third stage. Therefore the second stage is considered the main part that Y space-division splits (Y-SDS) input beam. To the best of my knowledge this is the first time to demonstrate such 50/50 space-division splitter (SDS) using DHGI rectangular WG.The third stage is used to separate the two splitted beams coming out of the second-stage far apart in order to de-couple them completely and also choose the separation between output MCFs. This stage center is aligned with the second stage central axis. It consists of two rectangular WGs each one (1090x133x9µm) has a graded-index profile:
Where the right and left WGs are centered at 78.5 µm and –78.5 µm, respectively, and the overall separation between output splitted beams is adjusted at 2x125 = 250µm. The WGs act as a beam deflectors. The graded index profile deflect input beam by TIR toward waveguide center and then it continues to reach the WG other side where it deflects again by TIR into the output cores. The amount of separation between output splitted beams can be simply controlled as it is directly proportional to the WGs y-dimension.It is worth mentioning that all graded refractive-indices of the 3-stages are chosen to have parabolic profile in order to minimize intermodal dispersion [20]. Thus, together with the device short length (≈2.4mm), it is expected to have a negligible overall dispersion. Also, it is worth mentioning that the propagating beams are mono-mode across the rectangular WGs z-dimension, as will be demonstrated later through EME simulations.
2.1. Theoretical analysis
It is already known that analytical solution of wave-equations in graded-index waveguides is usually very complicated and sometimes impossible to obtain [20]. Thus, numerical simulations are always the best and simple way to get most accurate and fast solutions. The numerical solutions will be illustrated in details in the next sections. However in this sub-section, a simple theoretical analysis is developed to clarify the principle of operation of a single Y-splitter together with its three stages as illustrated in Fig. 2(a).
The propagating ray trajectory in graded-index waveguides can be simply traced using the Eikonal differential equation [20]:
The parabolic graded indices profiles for each WG stage of Y-splitter can be generally written as:Where m = 1, 2, 3 corresponds to the 1st, 2nd, and 3rd stage, and ‘αm’ is a constant that can be simply deduced from Eqs. (1)-(3), as α1 = 3.31x10−3 µm−1, and α2 = α3 = 2.455x10−3 µm−1. Substituting (5) into (4) and solving for the ray trajectory path, we get the following harmonic solutions that approximately describe each stage output-ray position ‘yo’ and angle ‘θo’as a function of the same stage input-ray position ‘yi’ and angle ‘θi’: Where ‘yc’ is the peak-position of parabolic index profile and it equals to 0, 20, 78.5 µm for the symmetrical right-hand side of the 1st, 2nd, and 3rd stages, respectively. The ‘x’ dimension is measured in ‘µm’ as shown in Fig. 2(a). The input/ output angles are always measured between a ray propagation direction and the normal to a stage input/ output interface. The position of input ray to a stage is always equals to the position of output ray from previous stage:While the input angle to a stage is related to the output angle of previous stage by Snell’s law:As the splitter is symmetrical about its central axis, it has two symmetrical ray paths (left and right) as shown in Fig. 2(a), the right path is picked as an example in the following analysis.Assuming the first stage input angle is θi1 = 2.2°, and the initial position is yi1 = 0 at the center of input core, in addition given that the length of the first stage is X1 = 280 µm, then using Eqs. (6) and (7) the first stage output ray position and angle can be calculated as yo1 = 10.75 µm and θo1 = 1.32°, respectively.
Using Eq. (9), the input angle to the second stage can be calculated as θi2 = 1.319°. Given the second stage length is X2 = 995 µm, then using Eqs. (6) and (7) the second stage output ray position and angle can be calculated as yo2 = 33.11 µm θo2 = −0.1727°, respectively.
The calculated input angle to third stage using Eq. (9) is θi3 = −0.17369°. Given the third stage length is X3 = 1090 µm, then using Eqs. (6) and (7) the third stage output ray position and angle can be calculated as yo3 = 119.51 µm and θo3 = 2.85°, respectively.
The following Table 1 summarizes the results of this theoretical analysis. These results show a good agreement with the numerical simulations that will be discussed later in the following section and already illustrated in Fig. 2(b).
Table 1. The summary of ray-trajectory theoretical analysis results
3. FDTD simulations
The FDTD simulation of electric field magnitudes (|E|) for one Y-splitter is performed using Lumerical solutions software [21] to verify device operation. Figure 2(b) shows a 2D cross section of the simulated field at operating wavelength of 1555nm. The input core (9µm in diameter) has a fundamental Gaussian mode propagating along x-direction. In the first stage, the graded index lens expands the input beam across y-direction to reach a total width of ≈18µm. In the second stage, the DHGI WG splits the expanded beam into two beams with 50/50 splitting ratio.
As seen, each splitted beam is deflected by TIR at the second stage output to continue propagation along the x-direction. In the third stage, separators deflect the beams away from each other by TIR until they reach the stage output where they deflect again by TIR in order to continue in x-direction to the output MCFs cores. The fundamental mode of input core has a maximum |E| = 1 a.u., while the fundamental modes of output cores have 50/50 splitting ratio with maximum |E| ≈0.64 a.u. corresponding to intensities proportional to |E|2 ≈0.4. The overall separation between output cores is exactly 250µm.
4. EME simulations
The eigenmode expansion (EME) solver by Lumerical solutions [21] is utilized to simulate the 3D field propagation along the entire Y-splitter structure together with the three connected 7-core MCFs. The simulation is carried out at operating wavelength of 1555nm. The EME allows simultaneous propagation of all fundamental modes of input MCF cores through the Y-splitter rectangular WGs up to the two output MCFs cores. Figure 3(a)-3(g) show seven longitudinal cross-sections of propagating modes (|E|) from input cores 1 through 7, respectively, to their corresponding output cores. As seen, the Y-splitters have different y-positions with respect to each other depending on their relative position to the input/ output cores.
Fig. 3 The EME simulations (|E| a.u.) of Y-splitters together with MCFs cores. (a)-(g) show the longitudinal cross-sections of the seven sub Y-splitters connected to input/ output core 1 to 7, respectively.
Figure 4(a)-4(e) show five selected transverse cross-sections of Y-splitter and MCFs along propagation direction. Each cross-section shows seven different beam profiles each corresponds to one splitter element. The cross-sections correspond to input MCF cores, lenses, SDS, separators, and output MCF cores, respectively. Figure 4(a) shows the Gaussian fundamental modes of input single-mode cores. In Fig. 4(e), it is clear that the output has splitting ratio of 50/50 between the two output MCFs, and each output core preserves the fundamental mode distribution exactly as input cores.
Fig. 4 The EME simulations (|E| a.u.) of Y-splitters together with MCFs cores. It shows transverse cross-sections of: (a) Input MCF, (b) Lenses, (c) SDS, (d) Separators, and (e) Output MCFs. The cross-sections correspond to x-positions in Fig. 3 equal to 350, 750, 1750, 2500, and 3500 µm, respectively.
In all these transverse cross-sections, there is no significant sign of cross-coupling across the cladding region between WGs or cores. Which indicates non-significant induced cross-talks and back-reflections among cores and Y-splitter different elements.
5. Performance evaluations
In order to assess the Y-splitter performance, FDTD simulations are performed over the S, C, L, U wavelength bands covering a wideband range from 1.46 µm to 1.675 µm. Let’s define the input power to splitter as ‘Pi’, splitter outputs powers as ‘Po1’ & ‘Po2’, and the back-reflected power from input as ‘PBR’. Then the splitter characterization parameters in decibels can be defined as: Insertion-loss (IL) = −10log10 (Po/Pi), excess-loss (EL) = −10log10 {(Po1 + Po2)/Pi}, splitting-ratio (SR) = IL - EL, power-imbalance (PI) = −10log10 (Po2/Po1), polarization-dependent-loss (PDL) = ILTE - ILTM, and return-loss (RL) = −10log10 (PBR/Pi).
Figure 5(a) shows the fundamental mode IL of Y-splitter over the entire wavelength range for each core. The IL is the total splitter loss due to both EL and SR. For same wavelength, the maximum variation in IL is less than ≈0.1dB. For all cores, the IL varies slightly by less than ≈0.12dB over the entire wavelength range, indicating almost same performance among different cores.
Fig. 5 The wideband performance evaluation parameters of Y-Splitter for each core. (a) Insertion-loss, (b) Excess-loss, (c) Splitting-ratio, (d) Power-imbalance, (e) Polarization-dependent-loss, and (f) Return-loss.
In Fig. 5(b), the EL of Y-splitter for each core varies slightly by less than ≈0.13dB over the entire wavelength range. The maximum EL is ≈0.81dB (i.e. less than 1dB). The EL arises mainly from coupling losses among splitter stages in addition to coupling between splitter and MCF cores.
In Fig. 5(c), the SR of Y-splitter for each core varies slightly by less than ≈0.1dB over the entire wavelength range. The SR fluctuates slightly around ≈3.01dB, which indicates an excellent and fixed 50/ 50 splitting ratio over a wideband wavelength range. The SR small vitiations among different cores is due to cores offset positions within MCF cladding that result in asymmetric cladding thickness around cores and thus slightly different splitting ratios.
In Fig. 5(d), it is shown that the PI between each Y-splitter two outputs is less than ≈0.09dB. For each core, it varies slightly by less than ≈0.08dB over the entire wavelength range. This indicates an excellent balance (50:50) between splitter outputs over a wideband wavelength range.
In Fig. 5(e), the PDL of different cores is very small with a worst case value of less than ≈0.02 dB. Therefore, the splitter can be considered polarization insensitive.
In Fig. 5(f), the RL values is almost the same for all cores with a worst case value ≈35.8 dB around the wavelength of 1525nm.
As stated earlier, the separation between adjacent WGs along z-direction is 4µm, which may allow for vertical (along z-direction) coupling between WGs. However, the shifts in y-position among central axis of different WGs, in addition to isolation layers (trenches) in the mid-way between WGs along z-direction, result in a worst case cross-talk (XT) at WGs output cores ≈-26 dB. The XT here is defined as the ratio between leaking power from an exciting waveguide to a neighbor waveguide divided by propagating power in the exciting waveguide, where both powers are estimated at the waveguides output cores. It is worth to mention that this XT value could be reduced by using more isolating trenches. Also, it is expected to have less XT value in case of MCFs with larger cores-to-core separation, where the z-separation in between adjacent WGs can be designed to become wider.
It is worth mentioning that the space-division splitter by DHGI is based on splitting of input beam power rather than interference between input beam modes like conventional optical fiber directional couplers or multimode-interference couplers. Thus, such conventional couplers/ splitters performance is considerably dependent on the operating wavelength. However, the SDS Y-splitter technique maintains an excellent performance with very small variations over wideband wavelength range.
6. Tolerances
In this section the splitter performance tolerances to some critical design parameters are investigated. These tolerances in general can be used to set the margins and sensitivity of device fabrication errors too. In addition, the tolerances to input/ output MCFs parameters variations are also investigated.
In the previous section, the splitter PDL and RL are shown to be negligible. The IL is always equal to summation of EL and SR. The SR is almost 3dB for all cores. In addition, the differences in performance among cores are small. Thus, the EL and PI can be considered the most two crucial figure of merits that can be utilized to judge on Y-splitter performance tolerance. To maintain a good performance of Y-splitter, the maximum values of EL and PI are usually preferred to be around 1dB and 0.1dB, respectively. All the following tolerance simulations are performed at a single wavelength of 1555nm on center-core of MCF.
First we start with performance tolerances to variations in MCF parameters. Figure 6(a) shows the tolerance of Y-splitter PI and EL to relative misalignment between input MCF and splitter first-stage. The ‘Δy’ and ‘Δz’ represent the offset in ‘y’ and ‘z’ direction, respectively, between the center axes of input core and splitter first-stage WG. In y-direction, the misalignment tolerance is found to be Δy ≈ ± 0.43µm to keep |PI| ≤ 0.1dB, while the EL in this case is already below ≈0.76dB. While in z-direction, the misalignment tolerance is found to be Δz ≈ ± 0.4µm to keep EL ≤ 1dB, while the |PI| in this case is already below ≈0.034dB.
Fig. 6 The EL and PI performance tolerance to variations in MCF parameters. (a) Input MCF misalignment in ‘y’ and ‘z’ directions, (b) Output MCF misalignment in ‘y’ and ‘z’ directions, (c) Variations in MCF core diameters, (d) Variations in MCF core refractive indices.
Figure 6(b) shows the tolerance of Y-splitter PI and EL to relative misalignment between output MCF and the splitter third-stage. The ‘Δy’ and ‘Δz’ represent the offset in ‘y’ and ‘z’ direction, respectively, between the center axes of fiber core and splitter third stage WG. In y-direction, the misalignment tolerance is found to be Δy ≈ ± 1.2µm to keep |PI| ≤ 0.1dB, while the EL in this case is already below ≈0.86dB. In z-direction, the misalignment tolerance is found to be Δz ≈ ± 0.85µm to keep EL ≤ 1dB, while the |PI| in this case is maintained below ≈0.01dB. It is worth to mention that other types of misalignments between input/ output MCFs and the device such as rotational, diagonal, or combination of both can be decomposed and expressed in terms of ‘y’ and ‘z’ misalignments in order to get rough estimation of EL and PI in this case.
Figure 6(c) shows the tolerance of Y-splitter PI and EL to variations in MCF cores diameters. As long as the splitter is usually located at some fixed point along MCF piece, it is expected to have the same diameter variation for the same core at both input and output of splitter. The ‘ΔΦ’ represents the change in core diameter relative to the 9µm diameter value. To maintain a single mode operation, the maximum core diameter should not exceed ≈9.78µm. Therefore, the ‘ΔΦ’ is kept within the symmetric range of ± 0.76µm. As shown in the figure, the EL and PI can well tolerate the entire range of ΔΦ ≈ ± 0.76µm with acceptable performance. The best EL value occurs at the core diameter of 9µm, where mode-matching between WGs and cores is already optimized during the design. However, the EL asymmetrically changes with ΔΦ due to degradation in mode-matching especially when the cores diameters become smaller, as expected.
Figure 6(d) shows the tolerance of Y-splitter PI and EL to variations in MCF relative refractive index difference ‘Δ’. The ‘Δ’ represents the change in core refractive index relative to the 1.45 cladding refractive index. As long as the splitter is usually located at certain fixed point along MCF piece, it is expected to have same ‘Δ’ variation for the same core at both input and output of splitter. To maintain single mode operation, the maximum ‘Δ’ value should be ≈0.43%. As shown, the EL and PI can well tolerate the entire tested range of Δ ≈0.27% to 0.43% with acceptable performance.
In the following the tolerance to variations in splitter design parameters are investigated. Those variations can set the maximum margins for possible fabrication errors. In other words, having a large design tolerance means relaxed constraints on fabrication error margins and ease of fabrication.
Figure 7(a) shows the tolerance of Y-splitter EL to variations in different stages lengths (ΔL). The PI is not included here as it is found to remain constant with length variation and equals to the same value in Fig. 6(c) and 6(d). The EL is examined at different lengths around its optimum value and the collected points are plotted and then best curve-fitted. It is found that the tolerance to variation in lens-stage is ≈ ± 60µm. The tolerance to variation in SDS-stage is ≈ ± 180µm. The tolerance to variation in separator-stage is ≈ ± 135µm. These are considered wide margins that can tolerate large design and fabrication errors.
Fig. 7 The performance tolerance to variations in Y-splitter design parameters. (a) The EL tolerance to variations in different stages lengths, (b) The EL and PI tolerances to misalignment between stages positions and/ or graded-indices profiles.
As mentioned earlier, one of the design rules of splitter is to have the center-axes of all stages aligned together along the center axis of input core. Figure 7(b) shows the tolerance of Y-splitter EL and PI to errors in relative position (i.e. misalignment) between lens stage and SDS stage (ΔY12). Also, it shows the misalignment between the SDS stage and separator stage (ΔY23). These misalignments may also account for relative shifting errors between centers of GI profiles of successive stages during fabrication. It is found that the misalignment tolerance ΔY12 is ≈ ± 0.2µm, and the EL in this case is below ≈0.76dB. While the misalignment tolerance ΔY23 is ≈ ± 0.8µm, and the EL in this case is below ≈0.85dB. That indicates that axial misalignment between the first and second stages is more critical to splitter performance and fabrication errors than misalignment between the second and third stages.
Although the presented work here is mainly concerned with numerical simulations of Y-splitter in order to verify its operation and evaluate its performance, it is worth to give a hint about the device fabrication. The key issue in device fabrication is the practical implementation of different graded refractive indices profiles, shown in Fig. 2(a), in addition to cladding and trenches step refractive index profiles in between rectangular WGs. The silica-glass (SiO2) is the best material to realize different refractive indices of this device. One suggested technique for refractive indices implementation is flame hydrolysis deposition (FHD) method [22, 23]. The FHD is a simple technique that has high precision and excellent reproducibility. It can be used for deposition of different silica-glass layers of splitter whether it is cladding, cores, or trenches. Using FHD the glass particles can be deposited point-by-point in the X, Y, and Z directions by scanning a flame torch. The torch has a controllable raw material vapor composition and flow rate that can be easily used to adjust refractive index and thickness of each deposited film [24]. The device can be implemented by depositing layers in the x-y plane, one after another while moving along the z-direction. In each layer (x-y plane) the flame gases composition (i.e. mixing-ratio) and flow-rate can be pre-programed and modulated to achieve the desired graded refractive indices distribution spanning the splitter entire three stages and its surrounding cladding, as shown in Fig. 2(a). The refractive index profile changes within each layer could be used to define the WGs boundaries and dimensions as well. Also, that can be applied to deposit trenches and cladding layers with constant step refractive indices in between WGs layers.
7. Conclusions
For the first time, a novel Y-splitter for MCFs is numerically demonstrated. The splitter mainly depends on space-division-splitting of input power by a double-hump graded-index profile. It consists of three stages to expand, split, and separate multicore fiber input beams. The refractive indices of Y-splitter are selected to allow input/ output MCFs to be directly attached to the device. The overall length of the device (≈2.4mm) is considered short and compact in size when compared to other conventional fiber couplers. The selected parabolic refractive indices profiles together with the device short length is expected to introduce a negligible overall dispersion to propagating signals. The Y-splitting can be generally applied to MCF fibers with different core-lattice configurations given that MCFs could be rotated in such a way to allow each single sub-splitter input and output cores to have a line-of-sight view in order to place the rectangular WG stages. The splitter shows excellent performance over a wideband wavelength range (S, C, L, and U bands) with polarization insensitive operation. The performance variations from one core to another can be considered small. The simulations show good performance tolerance to MCF parameter variations such as core diameters and refractive indices, which may exist in practical transmission systems to mitigate transmission impairments. Also the splitter shows good performance tolerance to design parameters variations, which in turn indicate relaxed constraints on fabrication errors margin and sensitivity. All these features are considered very attractive for the next generation high capacity MCF networks, in addition to other emerging MCF different applications.
Acknowledgments
The author would like to gratefully acknowledge the technical and financial support of the Research Center at College of Engineering and the Deanship of Scientific Research at King Saud University.
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