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We propose a photonic crystal slab-based 1 × 3 power splitter with high output transmission and equal power distribution. It is designed by cascading an asymmetric 1 × 2 power splitter and a symmetric 1 × 2 power splitter. Desired equal power splitting is achieved by introducing and optimizing the splitting region of the 1 × 2 power splitters with flexible structural defects. Simulations were carried out by using 3-D Finite Difference Time Domain method showing equal normalized power distributions of 29.6%, 28.9% and 30.5% at 1550 nm optical wavelength. In addition, equal power splitting also takes place at 1561 nm.
© 2014 Optical Society of America
1. Introduction
Photonic crystal (PhC) has been used to design various optical applications due to its photonic bandgap (PBG) effect which is not observed in conventional planar waveguide. PBG effect arises from the periodic modulation of refractive index in PhC. PBG forbids some wavelength bands to propagate through the PhC in all directions. Nevertheless, by introducing a line defect into the PhC, a photonic crystal waveguide (PhCW) is created where the light is now allowed to exist and propagate inside the PBG region. PhCW is commonly created by removing exactly one row of air holes, known as W1 PhCW. The light propagation in the PhCW is guided laterally by the PBG effect and confined vertically by index guiding (e.g. total internal reflection (TIR)). Since the light confinement in PhCW is mainly due to the PBG effect without experiencing the constrain by TIR, propagation through sharp bend with high output transmission is possible [1]. Furthermore, waveguides or optical devices based on PhC can be realized in micron size, and eventually favors the use of PhC for ultra-dense photonic integrated circuits (PICs).
In PICs, PhCW can be used to guide and route the electromagnetic wave between different functional blocks. In the situation where the power distribution to multiple outputs is intended, waveguide with splitting ability (e.g. power splitter) is needed to perform the task. The simplest 1 × 2 power splitter (also known as Y-branch power divider) has been investigated and demonstrated by many researchers [2–7]. In addition to 1 × 2 power splitter, 1 × 3 power splitter is another important splitting component in PICs. Planar based splitters are widely used in passive optical networks for signal distributions. The 1 × 3 splitter can find its applications in all kind of optical interconnects as the third port can be a monitoring port for 1 × 2 connections. Recently, there have been growing interests in designing 1 × 3 power splitters. By applying techniques such as coupling [8,9], multimode interference (MMI) [10], structural tuning [11], and magneto optical properties [12], researchers had been able to demonstrate 1 × 3 power splitter theoretically and experimentally.
The design of 1 × 3 power splitter is commonly based on directional couplers. Coupled mode theory is employed to calculate the interaction length needed for complete power transfer from one waveguide to another waveguide. The interaction length, or the coupling length, equal to ( and are the propagation constant for even and odd modes), is adjusted to control the amount of power to be coupled to adjacent waveguides [13]. Djavid et al. [8] proposed a 1 × 3 power splitter by deploying directional couplers and ring resonators in the design. Output transmission efficiency near to 33% at 1594 nm wavelength was numerically obtained from 2-D finite difference time domain (FDTD) simulation. In another attempt, Liu [9] reported a W1 PhCW combined with two directional couplers in designing a 1 × 3 power splitter with transmission loss of ~10%. Their proposed splitter operates in the visible light region of 532 nm wavelength, which is not suitable for the applications in optical communication. Zhang et al. [10] employed MMI technique to design a 1 × 3 power splitter. They proposed MMI based 1 × 3 power splitter with normalized output transmittance of around −7.5 dB obtained numerically for each branch at 1567.4 nm wavelength. The drawback for designing 1 × 3 power splitter based on directional coupler or MMI is the equal power distribution normally occurs at only single wavelength depends to the coupling length. Furthermore, longer coupling length increases the size of the integrated device, and hence reduces the compactness of the PICs.
Moreover, an efficient 1 × 3 power splitter was proposed by Wang et al. by deploying magneto-optical materials [12]. Numerical simulation shows 33% splitting ratio at microwave frequency of 4.3 GHz and less than 1% difference at the output for each branch within frequency ranging from 4.248 GHz to 4.357 GHz. However, the required materials for their proposed design to operate in optical regime do not exist. Recently, we reported a high output transmission and ultra-compact 1 × 3 power splitter based on structural tuning method [11]. By introducing flexible structural defects into the splitting region, we numerically showed that nearly 33% power distribution was obtained for each branch at 1550 nm (optical C-band), 1470 nm (optical S-band) and 1388 nm (optical E-band) wavelengths to suit into different applications in different optical wavelength bands
Instead of using the aforementioned methods, a simple method based on cascading two Y-splitters, an asymmetric output distribution 1 × 2 power splitter and a symmetric output distribution 1 × 2 power splitter together with structural tuning, the design of 1 × 3 power splitter can be realized. The diagram showing the idea of cascaded 1 × 3 power splitter is indicated in Fig. 1. The percentage on each output branch is the desired power splitting ratio of the power splitter. In this manuscript, we report the numerical investigation on cascaded 1 × 3 power splitter with equal power splitting ratio at 1550 nm and 1561 nm wavelengths which is formed by connecting an asymmetric output distribution 1 × 2 power splitter to a symmetric output distribution 1 × 2 power splitter. This paper is organized as follows. Section 2 describes the design and simulation results of symmetrical 1 × 2 power splitter. In Section 3, the analysis and discussion of asymmetrical 1 × 2 power splitter is presented. The simulation results for the cascaded 1 × 3 power splitter are discussed in Section 4. Finally, conclusion of this work is presented in Section 5.
Fig. 1 Diagram of the proposed cascaded 1 × 3 power splitter based on an asymmetric 1 × 2 power splitter and a symmetric 1 × 2 power splitter. Percentage on each output branch indicates the desired power splitting ratio.
2. Symmetrical 1 × 2 power splitter
Optical splitter is a vital component in photonic integrated circuits (PICs) to route and split optical signal into different functional blocks. The simplest 1 × 2 PhC slab-based power splitter (Y-splitter) has been widely investigated by many researchers by using methods such as directional coupler [14] and MMI [15]. In addition, signal splitting also can be achieved by proper modification or tuning of the structure at the splitting region (junction region). By adding two air holes in gradually increasing size into the splitting region, 40% power transmission for each branch is obtained from 2-D simulation [3]. Furthermore, lossless output power distribution was shown by varying the dimension of air holes surrounding the splitting region [4]. Recently, topology optimization method is being used to modify the structural distribution at the splitting region in order to obtain 46.7% output power transmission for each output branch [16]. In this section, we design a symmetrical output distribution 1 × 2 power splitter by introducing flexible structural defect in the splitting region in order to equally divide the input signal.
2.1 Design of symmetry output power distribution 1 × 2 power splitter
Figure 2 illustrates the schematic drawing of a conventional unmodified PhC slab-based 1 × 2 power splitter. The splitter is formed by three straight W1 waveguides connected at 120° in triangular lattice air holes PhC slab. The background material indicated by green color is silicon with refractive index of 3.4, whereas white color represents air region. The computational region is truncated by perfectly matched layers (PMLs) as depicted by the blue color frame. The layout of the design is lying in the in-plane x-z axes with y-axis pointing the out-of-plane direction. The input excitation position (Input), the output transmission measurement locations for upper output branch (P1), and lower output branch (P2) are indicated in Fig. 2. The input signal is excited at several lattice distances after the left-side boundary in order to visually observe any reflected light (if any) from the discontinuity splitting region. The magnified box shows the modified power splitter with single Drop Hole (DH) structural defect inserted into the splitting region. Since the only difference between the layout of the modified and unmodified power splitters is at the splitting region, only the splitting region for the modified power splitter is shown in the magnified box for simplicity. The Xdown parameter is used in the design of asymmetric output power distribution 1 × 2 power splitter which will be presented in Section 3.
Fig. 2 Schematic drawing of the conventional unmodified 1 × 2 power splitter. Magnified box shows the modified power splitter with single Drop Hole structural defect at the splitting region. Light is excited at the location indicated by “Input” and the transmissions are measured at locations indicated by P1 and P2.
The design layout of the proposed flexible structural defect which is named as Drop Hole is indicated in Fig. 3. The shape of the DH defect is designed similarly to the wave breaker of a ship, so that the incoming electromagnetic (EM) wave is perturbed, guided and split adiabatically as the EM wave propagates through the tip to the center hole of the DH. In the simulation, the DH defect is treated as an air defect etched in the dielectric material similar to the air holes etched in the dielectric slab. There are three main parameters for the DH defect, “r1” represents the radius of the DH, “L” denotes the length of the DH from tip to the center of hole, and “θ” is the bending angle of the DH. In the simulation, the DH defect is pointing to the input direction, or in other words, the bending angle of the DH is always fixed at θ = 0°, thus, the bending angle of the DH is not taken into consideration in the optimization process. In addition, we have previously reported the use of the DH defect in designing an ultra-compact 180° PhCW bend [17] and lossless structure tuned 1 × 3 power splitter [11] with 2-D analysis.
Fig. 3 Design layout of the proposed flexible structural defect (Drop Hole) with three main defect parameters of r1, L and θ.
For the structure with simple threefold rotational symmetry such as Y-junction, the maximum output transmission of the unmatched Y-junction is 44.4% per output branch [18]. Therefore, minimum output transmission for each output branch of the proposed modified 1 × 2 power splitter is targeted to be at least 44.4%. As shown by Wilson et al. [3], by placing two air holes with increasing size at the splitting region could split the signal effectively. In addition, by introducing air defect into the splitting region reduces the size of the junction region, and prevents the excitation of higher-order modes. The schematic layout of the splitting region for the proposed modified symmetrical output distribution 1 × 2 power splitter is shown in the magnified box in Fig. 2. The tip of the DH defect is pointing to the propagation direction of the input signal, similar to the arrangement of adding air holes in increasing size as proposed by Wilson et al. [3]. Furthermore, the DH defect is inserted exactly at the center of the junction region in order to maintain the symmetry of the upper and lower output branches. Therefore, equal output power distribution can be acquired at both output branches.
In this work, 3-D FDTD method is used to compute the output transmission (output power) of the proposed power splitters. The FDTD simulation is based on the in-house developed FORTRAN language compiler built in Microsoft Visual Studio software. The basic design parameters of the PhC slab are lattice constant of Λ = 440 nm, air hole radius of r = 135 nm and slab thickness of 230 nm. Calculation by using 3-D Plane Wave Expansion Method [19] indicates that this structure exhibits large transverse electric (TE) -like bandgap ranging from normalized frequency, Λ/λ = 0.2689 to 0.3348. Therefore, TE polarized continuous wave with electric field in the in-plane x-z axes (Ex and Ez) and magnetic field in out-of-plane direction (Hy) is launched into the proposed structure to analyze the transmission performance of the power splitter. The resolution of the mesh size used in the 3-D FDTD simulation for all x-y-z directions is Δx = Δy = Δz = Λ/32 = 13.75 nm. The mesh size was determined within the fabrication resolution based on Helium Focused Ion Beam (HeFiB) technology to ensure the feasibility of device fabrication. Up to date, HeFiB technology has been used to fabricate 5 nm square hole drilled on Au Film [20] and 3.5 nm gaps in gold layer [21]. Since the fabricated 5 nm square hole [20] is much smaller than the 13.75 nm square mesh that was used in discretizing the DH defect in our simulation, therefore, it is presumed that the DH defect with its smallest possible dimension of 13.75 nm is possible to be fabricated using HeFiB technology. In the simulation, the output transmission of the power splitter is normalized to the output transmission of a straight W1 PhCW with identical waveguide length to accurately acquire the output transmission efficiency. Furthermore, the normalized reflected power and normalized out-of-plane losses are calculated by subtracting losses of the power splitter with the losses of the straight W1 PhCW.
2.2 Analysis of symmetry output power distribution 1 × 2 power splitter
In order to show the advantages of adopting DH defect in the design of splitter, conventional unmodified 1 × 2 power splitter is first simulated by using FDTD method. Figure 4 shows the steady-state magnetic field (Hy) distribution of the unmodified 1 × 2 power splitter at 1550 nm wavelength. Before any structural defect is introduced into the splitting region, the reflected power is high as indicated by the backward propagating EM wave. From the numerical simulation, the normalized output transmission efficiency for P1 and P2 are found to be 19.65% respectively. This means that the total normalized output transmission efficiency of Ptot = P1 + P2 = 39.3% only. The normalized reflected power, Pref is as large as 57.1% and the normalized out-of-plane loss, Pofp is about 2.43%. Therefore, optimization is needed to reduce the reflection and increasing the output transmission efficiency.
Fig. 4 Steady-state magnetic field (Hy) distribution of the conventional unmodified 1 × 2 power splitter at 1550 nm wavelength. Black solid-line indicates the input excitation location.
The optimization processes for the DH parameters are carried out by varying one parameter while fixing another parameter to achieve high output transmission and negligible reflected power. Figure 5 depicts the transmission performances of the modified 1 × 2 power splitter at fixed DH length, L = 2.0Λ versus the DH radius, r1. The total normalized output transmission, Ptot is higher than 92.5% within the DH radius considered in the simulation. The maximum Ptot occurs at r1 = 0.325r. The effect of changing the DH radius to the output transmission can be explained by the concept of perfect impedance matching [22]. At fixed DH length, L = 2.0 Λ, increasing the DH radius improves the impedance matching between input channel and output branches. The output transmission increases while Pref reduces until the maximum Ptot is achieved (r1 = 0.325r in this case). Further increasing the DH radius causes a drop in Ptot due to impedance mismatch.
Fig. 5 Normalized output transmission and losses (in percentage, %) versus DH radius, r1 at DH length, L = 2.0Λ and 1550 nm wavelength.
On the other hand, the output performances of the modified power splitter at fixed DH radius, r1 = 0.325r with respect to the changes in DH length, L, is shown in Fig. 6. Simulation results show that optimum DH parameters for the symmetrical 1 × 2 power splitter occur at r1 = 0.325r and L = 2.0Λ with 96.3%, −0.48% and 3.73% for Ptot, Pref and Pofp respectively. The negative value in Pref is because we normalized the reflected power by subtracting reflection of the power splitter to the reflection of straight W1 PhCW as mentioned in Section 2.1. The output transmission efficiency of the modified power splitter is highly depending on the DH length. By varying the DH length from L = 1.0Λ to L = 2.0Λ, the output transmission efficiency improves dramatically from 69% to 96%. This suggests that DH with long interaction length is crucial to increase the impedance matching and perturb the incoming signal slowly while dividing it.
Fig. 6 Normalized output transmission and losses (in percentage, %) versus DH length, L, at DH radius, r1 = 0.325r and 1550 nm wavelength.
The tolerance analyses of the optimum DH parameters for the symmetric 1 × 2 splitter to study the allowable fabrication error are presented in Fig. 5 (DH radius changes at fixed L = 2.0Λ) and Fig. 6 (DH length changes at fixed r1 = 0.325r). Figure 5 shows that at fixed DH length, L = 2.0Λ, Ptot is higher than 94% within the range of DH radius from r1 = 0.15r to 0.6r. On the other hand, Fig. 6 indicates that at fixed DH radius, r1 = 0.325r, Ptot is also > 94% when the DH length is changing from L = 1.9Λ to 2.15Λ.
Figure 7(a) presents the steady-state magnetic field (Hy) distribution of the modified 1 × 2 power splitter at optimum DH parameters of L = 2.0Λ and r1 = 0.325r and wavelength of 1550 nm. The magnetic field plot clearly indicates that the EM wave is split equally into two outputs with similar intensity and negligible reflection. Figure 7(b) shows the amplitude of the power at the locations indicated by dashed-lines “i” (before interact with DH defect), “ii” (contact with DH defect), and “iii” (interacting with DH defect) in Fig. 7(a). From Fig. 7(b), we see that the power-field profile is evolved from single Gaussian distribution shape (“i”) to a field profile with two lower amplitude shapes (similar to Gaussian profile) which is separated by a high power-field enhancement (“iii”). The high power-field enhancement takes place inside the DH defect. This is owing to the fact that the normal component of electric flux density (D = εE) has to be continuous across the high index contrast interface [23]. Therefore, inside the low index DH region with sub-wavelength size, the electric field intensity will be higher than the surrounding electric field in the high index region. Owing to the continuity of D across the high index contrast interface, the presence of the DH defect in the splitting region assists the EM wave to split into two waves gradually across the entire DH defect before it reaches the end of the splitting region.
Fig. 7 (a) Steady-state magnetic field (Hy) distribution of the modified 1 × 2 power splitter at optimum DH parameters of L = 2.0Λ and r1 = 0.325r, and at 1550 nm wavelength. (b) Amplitude of the power at dashed-lines indicated as “i” (before interact with DH defect), “ii” (contact with DH defect) and “iii” (interacting with DH defect) in (a). The power amplitude is only plotted along the red dashed-line.
Output transmission performances of both conventional unmodified and modified 1 × 2 power splitters at optical C-band wavelengths are depicted in Fig. 8. From the result, the performances of the modified power splitter are greatly improved over the conventional unmodified power splitter. The Ptot of the modified power splitter is higher than 94% within the entire optical C-band. The consistent output transmission over the C-band is due to the effective refractive index at the splitting region is almost wavelength independent. From the Maxwell-Ampere equation, the time varying electric field depends on the curl of magnetic field and also the permittivity of the material. The permittivity of the material varies insignificantly within a short range of wavelengths. Therefore, it is expected the magnitude of the output transmission is consistent within a short range of the wavelengths. Besides that, the Pref is suppressed below 2%. Such high output transmission and low reflection loss power splitter is useful as an efficient symmetrical 1 × 2 power divider in ultra-dense PICs.
Fig. 8 Normalized output transmission and reflection power for conventional unmodified and modified 1 × 2 power splitters at optical C-band wavelengths.
3. Asymmetrical 1 × 2 power splitter
1 × 2 power splitter with asymmetric output power distribution plays the main role in realizing the idea of forming cascaded 1 × 3 power splitter in this work. Ideally, the ratio of the output power distribution for the asymmetry 1 × 2 power splitter has to be 1/3 and 2/3 of the total output power. For example, P1 is 33.3% and P2 is 66.6%. By doing this, a symmetric 1 × 2 power splitter (splitter with equal (50%) output power distribution) can be connected to the 66.6% output branch to yield a cascaded 1 × 3 power splitter with equal output power distribution of 33.3% per output branch.
From our understanding, there is no literature or well-known equation such as coupling length for designing asymmetric output distribution 1 × 2 power splitter based on structural tuning in the splitting region. Therefore, the design of asymmetric power splitter is started by modifying the DH defect from the proposed optimized symmetric output distribution 1 × 2 power splitter which has been discussed in Section 2. In order to obtain symmetrical 1 × 2 power splitter with equal output power distribution, the DH defect is introduced at the center of the splitting region to maintain the symmetry of the splitter structure. On the contrary, asymmetric or unequal output distribution 1 × 2 power splitter is possible by making the structure asymmetry, i.e. by shifting the entire DH defect downwards or upwards at DH bending angle of θ = 0° (pointing to the input direction). To clearly define the position of the DH defect, a new term – Xdown – is introduced to represent the DH defect location when it is shifted downward in the direction of x-axis. In addition, b (b = () is used to represent displacement of the DH defect (see Fig. 2 for the definition of Xdown and b).
The optimization process for obtaining asymmetric 1 × 2 power splitter with 1/3: 2/3 power distribution is started by adopting the optimum DH parameters of L = 2.0Λ and r1 = 0.325r from the symmetrical 1 × 2 power splitter (Section 2) and then the DH defect is shifted downward. Figure 9 shows the normalized output of the asymmetric 1 × 2 power splitter as the DH defect is shifted downward. The insets indicate the layout and steady-state magnetic field distribution when the DH defect is shifted downward with (a) Xdown = 0.2b and (b) Xdown = 0.4b. The horizontal black solid-line in the insets shows the center of the splitting region is for reference. Shifting the DH defect downwards within Xdown = 0.1b to 0.35b produces Pref lower than 2% with different ratio of output power distributions. At Xdown = 0.2b, the output power distribution ratio is closer to 1/3: 2/3 (P1 = 31.9%, P2 = 62.6%) and the Pref is as low as 1.1%. Consequently, the output performances when Xdown = 0.2b meet with the targeted output performances (1/3: 2/3 power distribution) for the asymmetric 1 × 2 power splitter. Therefore, the second optimization step is proceeded with Xdown fixed to 0.2b.
Fig. 9 Normalized output transmission and losses versus Xdown, (b) at L = 2.0Λ and r1 = 0.325r. Insets show the layout and magnetic field distribution at Xdown = 0.2b (a) and Xdown = 0.4b (b) at the splitting region of the proposed asymmetric 1 × 2 power splitter. Horizontal black solid-line in the insets indicates the center of the splitting region is for illustration purpose only.
Figure 10 illustrates the output performances of the asymmetric power splitter versus the DH length at Xdown = 0.2b, r1 = 0.325r and 1550 nm wavelength. The most desirable output performances for the third optimization step occur at L = 1.95Λ, where the simulated output power transmission are 30.9% and 64% for P1 and P2 respectively. In addition, the Pref is 0.4% only. Thus, when the asymmetric 1 × 2 power splitter is cascaded with a symmetric 1 × 2 power splitter, the resulted cascaded 1 × 3 power splitter will has output power transmissions of 30.9%, 32% and 32% for each output branch. Nevertheless, one also has to remember that the symmetric 1 × 2 power splitter possess some reflection and out-of-plane losses. Therefore, in the cascaded 1 × 3 power splitter (to be discussed later in Section 4), the ideally 32% output power for each branch of the symmetric 1 × 2 power splitter will be reduced and it is possibly matches with the P1 value of the asymmetric 1 × 2 power splitter.
Fig. 10 Normalized output transmission and losses versus DH length, L, at Xdown = 0.2b and r1 = 0.325r at 1550 nm wavelength.
The third optimization step is then proceeded by changing the DH radius at fixed L = 1.95Λ and Xdown = 0.2b. The result of the simulation is shown in Fig. 11. The desired output power occurs at DH radius, r1 = 0.33r, where the P1 = 31.2%, P2 = 63.8%, Pref = 0.25% and Pofp = 4.4%. From the simulation, power distribution to the upper branch (P1) increases while the DH radius is increased. This can be explained by using TIR phenomena and by referring to the insets (a) and (b) in the same figure. Increasing the DH radius enlarges the size of the DH defect. This causes the slope of the index difference interface (indicated by the blue solid-line in the insets) between the body of the DH defect and the silicon slab material become steeper. Thus, the amount of input power flows into the upper branch increases due to the TIR (higher amount of light density being reflected towards the upper branch when the light reaches the index difference interface) as indicated by the red arrows in the insets. In addition, the out-of-plane losses increase linearly with the size of the DH radius. This is due to the increases of the air defect in the splitting region reduces the strength of the light confinement in vertical direction, lead to higher leakage to the out-of-plane direction.
Fig. 11 Normalized output transmission and losses versus DH radius, r1, at Xdown = 0.2b and L = 1.95Λ at 1550 nm wavelength. Insets show the layout and magnetic field (Hy) distribution at r1 = 0.3r (a) and r1 = 0.6r (b). Blue solid-line indicates the slope of the index difference interface between the DH defect and the surrounding high index silicon material.
Up to this stage, optimization of the DH parameters have been completed by considering the effect of shifting the DH defect downwards, Xdown, DH length, L, and DH radius, r1. The obtained optimum DH parameters for the design of the asymmetric output distribution 1 × 2 power splitter are L = 1.95Λ, r1 = 0.33r and Xdown = 0.2b. The allowable fabrication error for the optimized asymmetric 1 × 2 power splitter is considered by analyzing the DH length and DH radius. The sensitivity of the DH radius to the fabrication error is depicted in Fig. 11 which was presented previously. Figure 11 shows that when the DH radius is varied from r1 = 0.315r to 0.345r at optimum DH length, L = 1.95Λ, the ratio of the power distribution, P1/P2 is ranging from 0.48 to 0.5. On the other hand, sensitivity of the DH length to the asymmetric 1 × 2 power splitter is depicted in Fig. 12. At fixed DH radius, r1 = 0.33r, the upper output branch power distribution, P1, changes from 30.3% to 32.1%, whereas lower output branch power distribution, P2 varies from 65% to 62.6% when the DH length, L is changed from 1.9 Λ to 2.0 Λ. These tolerance analyses suggest that high fabrication accuracy using HeFiB technology [20] is crucial to fabricate our proposed splitter.
Figure 13 shows the output performances of the modified asymmetric 1 × 2 power splitter over the entire optical C-band wavelengths under optimum parameters of L = 1.95Λ, r1 = 0.33r and Xdown = 0.2b. The modified asymmetric 1 × 2 power splitter exhibits different power splitting ratios at different wavelengths. Therefore, the proposed design can be implemented as wavelength dependent asymmetric 1 × 2 power splitter to unequally divide the power at different wavelengths within C-band. Besides the relatively large value of the Ptot (P1 + P2), the Pref is suppressed below 0.9% within the entire C-band region too. In PICs, low reflection is important to prevent crosstalk with input light. On the other hand, the Pofp is around 4.4% within the entire C-band region. The out-of-plane losses are due to the air type DH defect which reduces the light confinement whenever the light interacts with the DH defect. Finally, the steady-state magnetic field (Hy) distribution of the optimized asymmetric 1 × 2 power splitter at 1550 nm wavelength is presented in Fig. 14. The magnified box shows the splitting region with the proposed DH defect shifted 0.2b downwards, making the structure becomes asymmetry. The magnetic field intensity at the lower output branch is found higher than the upper output branch, indicating higher power density is flowed into the lower output branch.
Fig. 13 Normalized output transmission and losses over optical C-band wavelengths at optimum DH parameters of L = 1.95Λ, r1 = 0.33r and Xdown = 0.2b.
Fig. 14 Steady-state magnetic field (Hy) distribution of the modified asymmetric power distribution 1 × 2 power splitter at 1550 nm wavelength, L = 1.95Λ, Xdown = 0.2b and r1 = 0.33r. Magnified box shows the position of the DH defect when it is shifted 0.2b downwards. The horizontal solid-line in the magnified box indicates the center of the splitter structure.
4. Cascaded 1 × 3 power splitter
In this section, the optimized asymmetry 1 × 2 power splitter from Section 3 and the optimized symmetry 1 × 2 power splitter from Section 2 are cascaded to form a 1 × 3 power splitter with equal output power distribution.
The layout and the steady-state magnetic field (Hy) distribution of the cascaded 1 × 3 power splitter at 1550 nm wavelength are shown in Fig. 15. In this design, a DH defect (DH3) is added to form a 60° PhCW bend which is connecting both asymmetric and symmetric 1 × 2 power splitters. The output power distributions at steady-state are P1 = 29.6%, P2 = 28.9% and P3 = 30.5%. The trivial unequal power distribution in P2 and P3 is due to the discretization mesh that used in the FDTD simulation do not share the central axis of symmetry with the structure. Since the absorption loss for pure silicon in the wavelength range that was considered in our work is negligible [24], therefore, the propagation loss of the cascaded power splitter is mainly due to the out-of-plane losses. The calculated out-of-plane losses is equal to Pofp = 7.7%. It may be reduced by sandwiching the PhC slab with 3-D woodpile PhCs as reported in [25]. On the other hand, the loss due to the reflected wave can be minimized by again optimizing the DH defects (DH1-3) of the cascaded 1 × 3 power splitter. However, this further optimization process is not considered because the idea of this proposed cascaded 1 × 3 power splitter is to design an equal power distribution cascaded 1 × 3 power splitter by directly combining two optimized 1 × 2 power splitters.
Fig. 15 Steady-state magnetic field (Hy) distribution for the cascaded 1 × 3 power splitter with three DH defects (DH1-3) at 1550 nm wavelength. Red dashed-line used to indicate the asymmetric and symmetric 1 × 2 power splitters in the design is for illustration purposes only.
Finally, the output performances of the proposed cascaded 1 × 3 power splitter within the entire optical C-band wavelengths are shown in Fig. 16. Besides the equal power distribution that can be achieved at 1550 nm as mentioned previously, it is also happened at 1561 nm wavelength with P1 = 29.8%, P2 = 28.9% and P3 = 30.1%. Therefore, the proposed cascaded 1 × 3 power splitter is able to divide the input power equally into three outputs at two distinct wavelengths inside optical C-band region. Compared to the reported 1 × 3 power splitters [8–10], equal power distribution only happen at a distinct wavelength depends on the coupling length. Our proposed structural tuning method by using flexible DH defect offers more bandwidth for equal power distribution 1 × 3 power splitter, thus overcomes the limitation of single operating frequency for equal power distribution by using coupling length (directional coupler) and MMI methods [8–10].
Fig. 16 Normalized output transmission and losses over optical C-band wavelengths for cascaded 1 × 3 power splitter with three DH defects (DH1-3). Vertical lines indicate equal power splitting at 1550 nm and 1561 nm are for illustration purposes only.
5. Conclusion
We have numerically investigated an equal power distribution 1 × 3 PhC slab-based power splitter by cascading asymmetric and symmetric 1 × 2 power splitters. Both asymmetric and symmetric 1 × 2 power splitters are optimized by tuning the parameters of the Drop Hole structural defect. At 1550 nm wavelength, the symmetric 1 × 2 power splitter achieves normalized output transmission of 48.15% for both output branches, whereas, the asymmetric 1 × 2 power splitter has unequal power distribution of 31.2% and 63.8% for each branch. Cascading the aforementioned two power splitters resulting in a 1 × 3 power splitter with almost equal power distribution of 29.6%, 28.9% and 30.5% at 1550 nm wavelength. Besides, it was shown that the proposed cascaded 1 × 3 power splitter is also capable to operate at 1561 nm wavelength with 29.8%, 28.9% and 30.1% power distributions, thus, providing more bandwidths for equal power distribution in PICs. As shown from our analysis, this DH integrated PhC can be utilized in PIC devices which offers better design flexibility and compactness and also feasible solution with current fabrication technologies. This work can be further explored by infiltrating electro-optic materials into the Drop Hole structural defect to perform active functionalities as reported in [26–28]
Acknowledgments
The authors would like to thank Professor Toshio Kambayashi from Nagaoka University of Technology, Japan for his technical help. This work was funded by MOHE High Impact Research grant (A000007-50001). D. C. Tee acknowledges, as well, the PPP grant (PV137-2012A) given by University of Malaya.
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