1.

Introduction

Silicon-on-insulator (SOI) has become a popular choice of material in recent years because of its potential for use in the photonics components manufacturing industry, which uses a monolithic or hybrid integration assembly. Arrayed waveguide gratings (AWG)-based silicon waveguide structures functioning as multiplexers/demultiplexers (mux/demux) are being widely employed in wavelength-division multiplexing (WDM) systems. There are several advantages in using SOI as a platform for photonics integration, such as low manufacturing costs due to the use of existing complementary metal oxide semiconductor fabrication technology,¹ compact devices, and high confinement of the optical mode.² Further, silicon has a high index contrast ($\mathrm{\Delta }n$) and is transparent at infrared wavelengths, making it suitable for optical communication applications. By using these features of SOI materials, we designed and analyzed an SOI-based AWG mux/demux capable of splitting or combining the multiple signals in a single fiber utilized in coarse wavelength-division multiplexing (CWDM) systems.

In this work, we optimized the geometrical rib waveguide structure and characterized the ideal parameters of a linear tapered double S-shaped AWG on an SOI platform to mitigate insertion loss (IL) and adjacent crosstalk (XT) in an 18-channel CWDM device with a channel spacing of 20 nm. The investigations were carried out by selecting the dimensions of the rib waveguide, which allows a single-mode condition where the ratio of the slab height ($h$) to the thickness of the top silicon (Si) guiding layer ($H$) or $h/H$ was in the range of 0.7 to 0.85. For each value of $h/H$, the core width was also varied between 0.5 and $1.2\mu \mathrm{m}$. The range of $H$ values is specific to the 18-channel AWG with broad channel spacings. In previous works, we have achieved IL of $<7\mathrm{dB}$³ and $<4.03\mathrm{dB}$,⁴ respectively. The IL was further reduced to 3 to 6 dB when the commonly used linear tapered waveguide was used in the AWGs.

Due to imperfections in the AWG fabrication process, such as in lithography or in etching, random phase errors of the arrayed waveguides may occur and affect the adjacent XT and IL values. Okamoto⁵ reports that the thickness fluctuation of the top Si layer in the SOI wafer was in the range of 0.5 to 1.0 nm and affected the adjacent XT by $-20\mathrm{dB}$. Meanwhile, a photo-mask resolution of 25 nm causes the adjacent XT to drop to $<-30\mathrm{dB}$.⁶ For a shallow-etched Si nanowire AWG with varied etch depths, the deviation in the core width is in the range of 3 to 8 nm.⁷ Owing to small variations of $\sim 20\mathrm{nm}$ in the etching profile, one linear AWG device with the same core width and different etch depths were carried out to identify the adjacent XT and IL behavior. Using the same size of core width, the effect of birefringence was also analyzed in order to compensate the wavelength shift. Besides the reduction in IL and adjacent XT, we also aim to obtain an AWG with a channel central wavelength that complies with the CWDM grid and with a channel spacing tolerance of $\pm 5\mathrm{nm}$.

2.

AWG Design Parameter

Three different sets of input parameters were considered in the process of designing the AWG device.⁸

Fig. 1

Theoretical values of adjacent crosstalk with respect to the input/output (I/O) waveguide separation width ($D$) for different thicknesses of the top Si guiding layer ($H$). Values of $D$ were chosen so that the adjacent crosstalk (XT) is better than $-35\mathrm{dB}$ in the coarse wavelength-division multiplexing (CWDM) transmission spectrum.

Fig. 2

Theoretical values of nonuniformity are $<1\mathrm{dB}$ for different thicknesses of the top Si guiding layer ($H$).

3.

Optimization on Dimension of Rib Waveguide

The cross-section of the rib waveguide structure was determined using Eqs. (1) and (2) (Ref. 9) for a single-mode condition, where $W$, $H$, and $h$ are the core width, thickness of top Si layer, and slab height, respectively.

Then, we confirmed that this rib waveguide provided single-mode propagation by simulating the structure using the OptiBPM simulator performing under the quasi-TE mode solver. To achieve 18-channels’ transmission with a 20 nm channel spacing using a double S-shaped AWG design, the thickness of the top Si layer should be in the range of 0.4 to $1.0\mu \mathrm{m}$. We found that if the thickness was $<0.4\mu \mathrm{m}$, an 18-channel transmission spectrum could not be achieved. Moreover, if the thickness exceeded $1.0\mu \mathrm{m}$, the larger bending radius with a high loss and large device footprint was produced. Thus, the minimum and maximum thicknesses for the top Si layer were set to 0.4 and $1.0\mu \mathrm{m}$, respectively. We used WDM-Phasar software to optimize the value of the ratio $h/H$. Values in the range of 0.75 to 0.8 resulted in the best performance for simulations under single-mode propagation. The simulation was run using the optimized value of the ratio $h/H$ along with different values of the top Si layer thickness. Figure 3 displays the cross-section and profile pattern for single-mode propagation in the rib waveguide structure operating in the TE mode with a 1431 nm AWG channel central wavelength for the top Si layer thickness in the range of 0.4 to $1.0\mu \mathrm{m}$.

Fig. 3

The single-mode profile in the cross section of the arrayed waveguide grating rib waveguide for different thicknesses of the top Si layer ($H$).

4.

Optimization of AWG Design Layout

Figure 4 shows a schematic of the SOI-based AWG computer aided design (CAD) layout with a rib waveguide structure, which was designed using the WDM-Phasar simulator, for 18 channels of the CWDM transmission spectrum. The architecture of the AWG device consists of 18 I/O ports, 72 arrayed waveguides with constant optical path length increments ($\mathrm{\Delta }L$) between neighboring waveguides, and two symmetrical free propagation regions (FPR). The layout pattern is the same for all thicknesses of the top Si layer, but other parameters, such as the modal index, $\mathrm{\Delta }L$, FPR, free spectral region, and nonuniformity, were different. Four geometrical parameters of the AWG structure that must be calculated in order to get the correct AWG demultiplexing properties are the length of the FPR (or focus length, $f$), the minimum waveguide separation width between two neighboring waveguides in the phased array ($d$) and at the I/O waveguides ($D$), as well as the constant optical path length increment ($\mathrm{\Delta }L$). For example, the FPR for a $1.0\text{-}\mu \mathrm{m}\text{-}\text{thick}$ top Si layer was $794.019\mu \mathrm{m}$ long on both sides of the AWG. Using the equation $\mathrm{\Delta }L={\lambda }_0·m/n_c$ for the same thickness of the top Si layer, $\mathrm{\Delta }L$ is $0.823\mu \mathrm{m}$ when $m=2$, ${\lambda }_0=1.431\mu \mathrm{m}$ (2930 GHz), and $n_c=3.4763235$ were chosen. Three parameters play a critical role in optimizing the AWG device to achieve a low loss, smaller footprint, and good performance in terms of adjacent XT and IL. These parameters are the bending radius, the total number of arrayed waveguides, and the initial length increment. The initial length increment is a special parameter in the AWG-Phasar tool that allows change in the bending of the waveguides in the phased array and it is defined as the difference between the distance span of the path and the length along the path. With an increase in the number of arrayed waveguides, the AWG experienced a high optical loss, especially in the arrayed waveguide region, due to the large S-bending radius. On the other hand, when the number of arrayed waveguides increased, the possibility of coherent interference, in which identical wavelengths with the same phase order pass through each $i$’th arrayed waveguide, was increased. Therefore, for this model 72 arrayed waveguides were used. The initial length increment depends on the thickness of the top Si layer. The maximum ($1.0\mu \mathrm{m}$) and minimum ($0.4\mu \mathrm{m}$) thicknesses of the top Si layer results in initial length increments of 1500 and $3200\mu \mathrm{m}$, respectively. Furthermore, the total device size and bending radius were different for different thicknesses of the top Si layer. For example, for a $1.2\mu \mathrm{m}$ core width with a $1.0\mu \mathrm{m}$ top Si layer thickness, the first arrayed waveguide produced a total bending radius of $829.404\mu \mathrm{m}$ with a total loss of 0.097 dB over a total AWG device length of $7466\mu \mathrm{m}$, while the last arrayed waveguide produced a total bending radius of $1025.628\mu \mathrm{m}$ with a 0.065 dB loss over a total AWG device length of $7524\mu \mathrm{m}$. In accordance with Pearson et al.,¹⁰ the bending radius obtained from this simulation is within the fundamental mode regime. Moreover, the minimum bending radius reported for high-index contrast materials is $<2\mathrm{mm}$,¹¹ and this indicates that our design results in an improved bending radius. For the example mentioned above, the total size of the AWG on chip is $48\mathrm{mm}\times 9\mathrm{mm}$.

Fig. 4

Schematic of a double S-shaped arrayed waveguide grating (AWG) using a rib-waveguide structure. The left and right arms of the array of waveguides result in a symmetric value of bending radius and single-mode propagation under TE polarization is launched at the input waveguide.

Existing AWG devices use a U-shaped pattern.^12,13 However, for broad channel spacing (20 nm), where $\mathrm{\Delta }L$ is very small, the WDM-Phasar simulator is incapable of connecting all the arrayed waveguides for an AWG with a U-shaped pattern. Therefore, the double S-shaped pattern was used for the AWG, where the higher losses incurred in this pattern are compensated with the usage of a high-index contrast material. Optical light beams couple if the distance between adjacent waveguides in the arrayed waveguide region is $<3\mu \mathrm{m}$. AWGs with an S-shaped pattern have also been used in other practical devices,¹⁴ such as in broadband InP AWGs. However, the arrayed waveguide region was different when an antisymmetric S-shaped pattern was used. In this work, the commonly used linear tapered waveguide design was also used in the FPR for the incoming and outgoing waveguides to reduce the IL and adjacent XT as shown in Fig. 5. The diffraction loss is influenced by the value of the minimum arrayed waveguide separation, $d$. For the linear tapered region, the entrance width $W_1$, exit width $W_0$, tapered length $L_{\text{tap}}$, and tapering angle $\delta$ are related as $W_0=W_1-2L_{\text{tap}}\tan \delta$.¹⁵ This relationship is illustrated in Fig. 5, where $Z$ is the direction of the propagation of light. Table 1 lists the values of each parameter for different thicknesses of the top Si layer.

Fig. 5

Schematic of free propagation region showing the position of linear tapered, minimum input/output waveguide separation ($D$), focus length ($f$), minimum arrayed waveguide separation ($d$), entrance tapered width ($W_1$), and exit tapered width ($W_0$).

Table 1

Parameter for tapered waveguide at free propagation region (FPR).

5.

Simulation Results and Discussion

Figures 6(a) and 6(b) plot the IL and adjacent XT as functions of the channel number for different values of the top Si layer thickness between 0.4 and $1.0\mu \mathrm{m}$, over 18 channels ranging from 1271 to 1611 nm. These data were extracted from the original transmission spectrum as shown in Fig. 7. The lowest IL was observed at the central channel (channel number 9 with a wavelength of 1431.6 nm), while the highest IL was observed in the peripheral channels which are far apart from the central channel. This distribution pattern occurs because the far-field intensity of each individual waveguide is reduced with the distance away from the origin of the central wavelength. The nonuniformity between the central channel and the peripheral channels is $\sim 1$ to 5 dB for different values of the top Si layer thickness. This value is high when compared with the theoretical data presented in Fig. 2 where the IL was $<1\mathrm{dB}$. When the thickness of the top Si layer was decreased, the IL increased in the range of 1.0 to 3.0 dB at the central wavelength. This is because the core width ($W$) decreases with a decrease in the top Si guiding layer thickness, and when $W$ becomes smaller than the minimum arrayed waveguide separation width ($d$), a high diffraction loss is observed at the first FPR. To overcome this issue, a standard tapered design was included at both FPRs, which is a common method used to reduce IL.¹⁶ As shown in Fig. 6(b), the usage of a tapered design produced similar adjacent XT values of $-13.5\mathrm{dB}$ for top Si layer thicknesses of 0.4 and $1.0\mu \mathrm{m}$ for channel number 9. The lowest adjacent XT of $-38.83\mathrm{dB}$ was observed in the same channel for a top Si guiding layer thickness of $0.7\mu \mathrm{m}$. This value exhibits the best result for the adjacent XT. Adjacent XT values of $-35.45$, $-26.28$, $-19.69$, and $-15.92\mathrm{dB}$ were obtained for the top Si layer thicknesses of 0.9, 0.8, 0.5, and $0.6\mu \mathrm{m}$, respectively. For the top Si guiding layer of $1.0\mu \mathrm{m}$, the adjacent XT exhibits a large value of $-12.67\mathrm{dB}$ due to the effect of side lobes. Note that the adjacent XT can be reduced by decreasing the value of $d$ and increasing the value of $D$.¹⁷ However, our proposed design uses the same values for both $d$ and $D$ in order to maintain the adjacent XT to be $>-35\mathrm{dB}$. Besides, the values of $d$ and $D$ can be adjusted depending on the design parameters. The plot in the graph shows that no direct relationship exists between the adjacent XT and the thickness of the top Si layer. However, the AWG design results in values comparable with those produced by existing practical devices that have different channel spacing but are fabricated using the same material (SOI).^13,17,18 The lowest IL, with a higher adjacent XT, was obtained for an AWG design with a top Si layer thickness of $1.0\mu \mathrm{m}$ and a core width of $1.2\mu \mathrm{m}$. The complete transmission spectrum of an 18-channel AWG is shown in Fig. 7. It has a central wavelength close to that of the CWDM wavelength grid with an average channel spacing of $\sim 2500\mathrm{GHz}$ (19.9 nm). For example, a central wavelength of $1431.6\pm 5\mathrm{nm}$ is obtained at the center of the spectrum. Furthermore, for a top Si guiding layer thickness of $1.0\mu \mathrm{m}$, the relationship among the entrance tapered waveguide width ($W_1$) and the adjacent XT as well as the IL values for a complete CWDM channel was investigated. When the taper width was increased, the adjacent XT is predicted to be higher due to a higher evanescent coupling between the output waveguide with reduced IL. Thus, as predicted, when the maximum entrance tapered waveguide width was increased from 2.2 to $3\mu \mathrm{m}$, the IL is reduced but the adjacent XT is increased. For example, in channel number 9, the IL is reduced to 2 dB and the XT increased to 16 dB, respectively, as illustrated in Fig. 8.

Fig. 6

Simulation results of (a) insertion loss and (b) adjacent XT for different thicknesses of top silicon layer for all 18 channels of the CWDM AWG demultiplexer.

Fig. 7

Simulation results for transmission spectrum of 18-channel AWG demultiplexer obtained from a $1.0\text{-}\mu \mathrm{m}\text{-}\text{thick}$ top silicon layer with core width of $1.2\mu \mathrm{m}$.

Fig. 8

The comparative results of insertion loss (IL) and adjacent XT as a function of channel spacing/number when the entrance tapered waveguide width ($W_1$) is increased from 2.2 to $3.0\mu \mathrm{m}$ for a top Si layer thickness of $1.0\mu \mathrm{m}$.

When the thickness of the top Si guiding layer of the CWDM AWG was varied, no significant relationship was observed for the insertion loss and the adjacent XT as many AWG design parameters were also simultaneously varied. Therefore, in order to investigate the effect of imperfections in the CWDM AWG fabrication processes, such as in lithography or in etching, the top Si guiding layer thickness ($H$) was varied by $\sim 20\mathrm{nm}$ while maintaining the core width ($W$) at $0.6\mu \mathrm{m}$ and the slab height ($h$) at $0.4\mu \mathrm{m}$. The top Si guiding layer thickness ($H$) was varied from 0.5, 0.52, 0.54, and $0.56\mu \mathrm{m}$, which corresponds to etching depths of 0.1, 0.12, 0.14, and $0.16\mu \mathrm{m}$, respectively. When compared to the AWG design parameters listed in Table 1, a small modification was made to the tapered length, $L_{\text{tap}}$, and the entrance tapered width ($W_1$) for a $0.5\mu \mathrm{m}$ top Si guiding layer as tabulated in Table 2, where $L_{\text{tap}}$ was expanded from 91.75 to $103.22\mu \mathrm{m}$, while ${\mathrm{W}}_1$ was changed from 2.81 to $3.1\mu \mathrm{m}$. These values were consistently used for all the subsequent AWG designs in order to effectively evaluate the effect of imperfections in the CWDM AWG fabrication processes. A summary of the AWG design parameters for the waveguide cross-section values, entrance tapered waveguide width, exit tapered waveguide width, and the tapered length is tabulated in Table 2. Other AWG design parameters are the same as discussed in Sec. 2. Figure 9 presents the IL and adjacent XT as a function of the channel spacing/number for incremental etch depths from 0.1 to $0.16\mu \mathrm{m}$, which was extracted from the 18-channel CWDM transmission spectrum as illustrated in Fig. 10. At the central waveguide channel, for etch depths of 0.1, 0.12, 0.14, and $0.16\mu \mathrm{m}$, IL values increased from 1.36, 1.72, and 1.97 dB to 2.59 dB, respectively. Meanwhile, the adjacent XT for the same central waveguide also decreased with values of $-19.87$, $-17.37$, $-15.51$, and $-14.95\mathrm{dB}$, respectively. Therefore, when the etch depth is increased, the IL and adjacent XT decreased. Therefore, the best design parameter combination for a CWDM SOI-based AWG in order to obtain a low insertion loss and adjacent XT is reached the top Si thickness is $0.5\mu \mathrm{m}$ for each $0.1\mu \mathrm{m}$ of depth and core width of $0.6\mu \mathrm{m}$.

Table 2

New parameter values for cross-section of rib waveguide and tapered waveguide at FPR.

Fig. 9

The comparative results of IL and adjacent XT as a function of channel spacing/number when the etching depth is increased from 0.1 to $0.16\mu \mathrm{m}$ with a constant core width of $0.60\mu \mathrm{m}$ for TE mode polarization.

Fig. 10

Simulation results for transmission spectrum of 18-channel AWG demultiplexer obtained from a $0.5\text{-}\mu \mathrm{m}\text{-}\text{thick}$ top silicon layer with core width of $0.6\mu \mathrm{m}$.

Using the best design parameter combination for the CWDM AWG, the effect of birefringence was analyzed in order to evaluate the polarization-dependent wavelength shift ($\mathrm{PD}\lambda$), which is given by $\mathrm{PD}\lambda =\lambda (n_{\mathrm{TE}}-n_{\mathrm{TM}})/n$, where $n_{\mathrm{TE}}$ is the refractive index in the TE mode and $n_{\mathrm{TM}}$ is the refractive index in the transverse magnetic (TM) mode. Figure 11 shows the calculated effective index and $\mathrm{PD}\lambda$ as a function of the Si etch depth for the CWDM AWG. When the etch depth is gradually decreased from 0.16 to $0.1\mu \mathrm{m}$, the birefringence ($n_{\mathrm{TE}}-n_{\mathrm{TM}}$) was completely reduced and almost nullified for an etch depth of $0.1\mu \mathrm{m}$ with a core width of $0.6\mu \mathrm{m}$. As for the calculated $\mathrm{PD}\lambda$, a core width of $0.6\mu \mathrm{m}$ and Si etch depth of $0.1\mu \mathrm{m}$ causes the $\mathrm{PD}\lambda$ to be $<0.0005\mathrm{nm}$. For confirmation purposes, the calculated values were compared with a simulated CWDM AWG with an Si etch depth of $0.1\mu \mathrm{m}$ and a core width of $0.6\mu \mathrm{m}$. The spectral response at the central wavelength channel of $1431\mu \mathrm{m}$ for both polarization modes was then compared and illustrated in Fig. 12, where the value of the $\mathrm{PD}\lambda$ is $\sim 0.0004\mathrm{nm}$ and agrees with the calculated value.

Fig. 11

Calculated birefringence ($n_{\mathrm{TE}}-n_{\mathrm{TM}}$) and polarization-dependent wavelength shift ($\mathrm{PD}\lambda$) for a rib waveguide silicon-on-insulator-based CWDM AWG when the etching depth is varied from 0.1 to $0.16\mu \mathrm{m}$ with a constant core width of $0.6\mu \mathrm{m}$.

Fig. 12

Simulated spectral response of 18-channel CWDM AWG demultiplexer with a core width of $0.6\mu \mathrm{m}$ and ratio $h/H=0.80$ exhibiting an almost nullified $\mathrm{PD}\lambda$, where both the TM and TE spectrums tend to overlap at the central wavelength channel of 1431 nm.

6.

Conclusion

We successfully developed an SOI-based linear tapered double S-shaped rib-AWG demultiplexer using beam propagation method under TE mode polarization with average channel spacing of 2485 GHz. We obtained the lowest IL and adjacent XT after inserting tapered regions at the I/O waveguide and arrayed arms in the FPR, for a top Si layer thickness of $0.7\mu \mathrm{m}$ with a core width of $0.8\mu \mathrm{m}$. Fabrication intolerances causing an increment in etch depths of the top Si layer of the AWG rib waveguide by 20 nm deteriorated the IL, adjacent XT, and birefringence. Moreover, the complete transmission spectrum obtained using a $1.431\mu \mathrm{m}$ central wavelength launch was close to the standard CWDM wavelength grid for which this device successfully performed as a demultiplexer.