Abstract

We analyze the impact of aberration on spectral performance of silicon-based arrayed waveguide grating (AWG) router with the conventional design using a constant pitch along the grating circle for the array waveguides near the free propagation region (FPR), and simulation results show that due to existence of large aberration, side lobes occur in spectral responses of peripheral output channels for the center input light while more serious side lobes appear in most output channels within a free spectral range (FSR) for the edge channel input. Therefore, there is a high crosstalk in conventional N × N silicon AWG, which is very detrimental for router applications. In order to address it, a simple design with a constant projected period on a line tangent to the grating at its pole for the array waveguides near the FPR is proposed, and aberrations of all output wavelengths within a FSR are kept at a rather low level both for the center and edge input. Then we fabricate two kinds of AWG routers with the conventional and proposed design respectively on a SOI wafer, and experimental results show that spectral responses of the AWG router with the proposed design are significantly improved compared to those obtained in the conventional design, especially for the edge channel input.

© 2017 Optical Society of America

1. Introduction

Silicon-on-insulator (SOI)-based arrayed waveguide grating (AWG), which can simultaneously process N2 optical channels as a router or N optical channels as a multi/demultiplexer at N different frequencies, plays an important role in high-capacity optical interconnects [1, 2]. Because of the high index contrast between the silicon core and oxide cladding, ultra-compact silicon AWG with superdense integration can be achieved. Furthermore, its fabrication process is compatible with CMOS technology, which can dramatically reduce the cost.

However, due to the sub-micron waveguide dimensions of silicon waveguide and its high light confinement, small variations in geometry will result in significant change in its propagation constant and hence high cross talk level in silicon AWG. An array waveguide layout called “horseshoe-shape” [3] in combination with broad multimode straight waveguide and narrow single mode bend waveguide is employed to decrease the phase error sensitivity to small fluctuation in waveguide width, and consequently the spectral performance of silicon AWG is substantially improved [4, 5]. S. Pathak et al [6] studied the impact of the lithography mask discretization on silicon AWG and showed that a smaller mask grid can dramatically decrease the cross talk level. Although the above-mentioned approaches have drastically improved the performance of silicon AWG, only partial channels (usually 0.5 ~0.6 × FSR/ Δλch) [5, 7] in one FSR are available to obtain optimal spectra. Therefore, it is very hard to meet an ever-increasing requirement on bandwidth in data communication networks, in which silicon AWG with operating channels as many as possible is highly desirable. Especially for AWG routers, all of these channels within the whole FSR should be used and have low cross talk for light coupling at any one of the input channels [8]. On the other hand, for the edge channel light input, it has been demonstrated that there is a large side lobes in its output spectra of silicon AWG in [9, 10]. Thus the design of silicon AWG should be further improved.

In this paper, we firstly study the aberrations in two kinds of silicon AWG routers: one with the conventional design using a constant pitch along the grating circle for the array waveguides near the FPR and the other with the proposed design employing a constant projected period on a line tangent to the grating at its pole for the array waveguides. Theoretical analysis shows that the proposed design has sufficiently small aberration values both for the center and edge channel input while the conventional design has large aberration values in its peripheral output wavelengths for the center input light and much larger aberration values for the edge channel input light, and consequently the conventional design suffers high crosstalk in its output spectra. Then we fabricated these two AWG routers and experimentally verified that the AWG router with the proposed design can significantly improve the spectral performance, especially for the edge channel input. To the best of our knowledge, this is the first time to employ the layout design with constant projected period along a line tangent to the grating pole for array waveguides to improve the performance of silicon-based AWG router, although echelle grating has utilized the similar method for position design of grating facets [11], it is mainly used as a multi/demultiplexer, not a router.

2. Principle and design

Figure 1(a) shows the most widely used layout for array waveguides with a constant periodicity da along the grating circle while Fig. 1(b) gives the proposed design layout for array waveguides with a constant periodicity along a projection on a line tangent to the grating at its pole. These two layouts differ slightly, and they will become similar when the input beam divergence in slab waveguide is low and the Rowland circle radius (R) is very large such as in the low-index-contrast silica-on-silicon platform. However, for high-index-contrast platform like silicon-on-insulator platform, there is a very large beam divergence angle for input waveguide and a rather small Rowland circle radius R, thus a large difference for these two layouts. In order to further understand these two layout designs, we will mathematically illustrate them. We take the coordinate system as shown in Fig. 2 and assume that: light input from the point A(xA, yA), after traveling through the first slab waveguide, is coupled into the array waveguides at P(u(w), w), then passes through each array waveguide with length of L(w) and further the second slab waveguide, finally refocused at the point B(xB, yB) and coupled into the output waveguide. It should be noted that (u, w) is the coordinate of end-point P of the array waveguide at the grating circle, which determines the locations of array waveguides, thus the difference between the conventional design and proposed design is actually the difference of coordinate (u, w). If the number of array waveguides is assumed to be 2N + 1 in Fig. 1(a) for the conventional design, u and w can be expressed as

w=2Rsin(ida2R),i=N,...1,0,1,...,N(u2R)2+w2=(2R)2
Similarly, in Fig. 1(b) for the proposed design, u and w can be expressed as
w=ida,i=N,...1,0,1,...,N(u2R)2+w2=(2R)2
It is known from Eqs. (1) and (2) that w will have the same value when the Rowland circle radius is sufficiently large (i.e., 2R >> i·da). Once w is determined, locations of the array waveguides along the grating circle are also determined. Based on Fig. 2, the optical path function of AWG can be written as [12]
F(w)=nsrA(w)+naL(w)+nsrB(w)G(w)mλ
with ns and na effective indices in the slab and array waveguide respectively, m grating order, L(w) length of the array waveguide between P and P’, G(w) (G(w) = i) number of array waveguides counting from the center (G(0) = 0), and rA(w) and rB(w) are distances from point P to point A and B respectively. In Eq. (3), the r(w) and L(w) terms determine the focusing property of the AWG while the G(wm·λ term determines the grating diffraction. Then we define a grating aberration function for the array waveguide with the coordinate (u(w), w) as
ΔF(w)=F(w)F(0)=ns(rAP(w)rAO)+na(L(w)L(0))+ns(rPB(w)rOB)G(w)mλ
where the parameters of rAO, rOB, L(0) and G(0) correspond to the center array waveguide. Actually, ΔF(w) is derived from the grating equation of the AWG, and when ΔF(w) equals to zero, it has the same expression as the grating equation. The grating equation denotes that the difference between the total phase retardations for the two light beams passing through any two adjacent array waveguides must be an integer number of wavelength. Usually for the output wavelengths gradually going outward from the center in conventional AWG layout, the grating equation is only completely satisfied for a part of array waveguides, i.e., middle array waveguides, and slightly unsatisfied for the edge array waveguides. The extent of unsatisfaction for the grating equation can be expressed by the grating aberration function ΔF(w). If there is a perfect imaging at the output Rowland circle (imaging plane), ΔF(w) should be sufficiently small (i.e., ΔF << λ/4) for an arbitrary number G(w) of the array waveguide for all output wavelengths. In low-index-contrast like silica-on-silicon platform, ΔF(w) is generally very small, far less than λ/4, thus conventional layout design of array waveguides in Rowland configuration is effective. However for high index contrast platform, ΔF(w) is often very large for the output wavelengths going far from the center due to the very small Rowland circle radius (~100 μm), thus the conventional layout design of array waveguides is no longer suitable for the edge output wavelengths. According to Eq. (4), in order to keep the value of ΔF(w) at a rather small level for any array waveguide, three parameters rAP(w), L(w) and rPB(w), can be appropriately adjusted to meet the requirement. In our proposed design as shown in Fig. 1(b) for simplicity, the layout of Rowland configuration remains unchanged and compared to the conventional layout design as shown in Fig. 1(a) for array waveguides, we only slightly adjust their locations (u(w), w) along the grating circle. Therefore, only rAP(w) and rPB(w) are changed to obtain a rather small ΔF(w). However, for stigmatic point based design [12] to reduce the aberration, rAP(w), L(w) and rPB(w) are usually simultaneously adjusted, thus the star coupler is no longer the Rowland configuration, which complicates the layout design of AWG.

 figure: Fig. 1

Fig. 1 Location distribution of the array waveguides along the grating circle for Rowland configuration. (a) Conventional design: constant curvilinear period, (b) Proposed design: constant projected period.

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 figure: Fig. 2

Fig. 2 Illustration of the free propagation region based on the Rowland configuration.

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ere a SOI wafer with top silicon layer of 220 nm and buried oxide layer of 2 μm is used and two 400 GHz 15 × 15 AWG routers with the conventional and proposed layout are designed respectively for an example. Horseshoe-shaped layout is employed for the arrayed waveguides, but they have a fixed width due to the defect of e-beam direct writing facility in our lab and operate at TM polarization with low sensitivity to waveguide width fluctuation. The main design parameters are given in Table 1. The conventional design has a constant curvilinear period of da = 2 μm for all arrayed waveguides along the grating circle while the proposed design has a variable curvilinear period to keep a constant pitch of da = 2 μm along a projected line tangent to its grating pole. As is shown in Table 1, length of FPR (radius of the grating circle) is only 101.2 μm, and according to the rule of thumb [13], the number of array waveguides should be three to four times the number of channels within a FSR, thus number of array waveguides is set to be 59 to keep most of the input light diverging in FPR captured. Figure 3 shows location differences along the direction of grating circle for all 59 array waveguides employing the constant curvilinear period design and constant projected period design respectively. It is known that for these two designs, locations of the middle array waveguides along the grating circle are the same while location differences for array waveguides going far from the center array waveguide become much larger.

Tables Icon

Table 1. Design parameters of the exampled AWG router.

 figure: Fig. 3

Fig. 3 Deviation of locations of array waveguides in proposed design from those in conventional design along the grating circle.

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By using Eq. (4), we calculated aberration values of all 59 array waveguides for a given wavelength input from point A and refocused at point B, as illustrated in Fig. 2, and collected its maximum aberration value ΔFmax. Figure 4 shows maximum aberration values of all 15 output wavelengths within a FSR for these two designs when light inputs from the 1st channel and 8th channel respectively. As can be seen from Fig. 4(b) for the 8th channel input, the aberration value is equal to zero for the designed center wavelength of 1550 nm and it increases as the wavelength goes far from the center wavelength. Aberration values for the peripheral output wavelengths in the conventional design have been as large as ~0.8λ, which has exceeded the required value of 0.25λ in perfect imaging, while those are less than 0.1λ inthe proposed design. Therefore in conventional design with a constant curvilinear period for the array waveguides, performance of the marginal channels will be substantially decreased, which in turn results in reduction of the number of available channels within a FSR in multi/ demultiplexer applications [7, 14]. When the light inputs from the 1st channel, as shown in Fig. 4(a), the conventional design suffers more serious aberration for most output wavelengths and the maximum value of aberration is ~1.6λ, significantly larger than 0.25λ, thus the corresponding performance will be greatly degraded, which is undesired in router applications with N input channels including the peripheral input channels. However, in the proposed design with constant projected period for the array waveguides, the aberrations for all output wavelengths are still kept at a low value less than 0.15λ. In order to further illustrate the impact of aberration on spectral responses of these two kinds of AWG routers, an improved analytical simulation method based on Ref. [15]. is employed. Figure 5 shows simulated spectral responses of the 15 × 15, 400 GHz AWG router with the conventional design for the 1st and 8th channel input respectively. It is known from Fig. 5(b) for the center channel input that the passband shape becomes deformed and widened due to existence of large aberration when the output channel gets close to the edge. Because of larger aberrations as shown in Fig. 4(a) for the peripheral channel input, deformations of the corresponding passband shapes in most output channels become more serious, as shown in Fig. 5(a). And meanwhile, we also give simulated spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the proposed design for the 1st and 8th channel input respectively, as shown in Fig. 6. Compared to Fig. 5 with the conventional design, passband shapes for the marginal output wavelengths are significantly improved and all output wavelengths almost have the same spectral shape both for the 1st and 8th channel input in Fig. 6. On the other hand, since the suppressed aberration in the proposed design improves the imaging quality of the output wavelength, the extra loss due to the spectrum widening and the channel spacing fluctuation resulting from the obtained central wavelength deviating from the designed wavelength are eliminated, as compared to the conventional design. As a result, the SOI-based AWG with good performance in terms of low crosstalk and larger channel number can be theoretically obtained by employing the proposed design for the array waveguides. For 1 × N multi/demultiplexer applications, the proposed design can increase the number of channels up to fill up one FSR as shown in Fig. 6(b), and it also can effectively improve the spectral performance for edge channel input, which is very important in N × N router applications.

 figure: Fig. 4

Fig. 4 Aberration values of 15 output wavelengths of two kinds of AWG routers for the 1st channel input (a) and 8th channel input (b), respectively.

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 figure: Fig. 5

Fig. 5 Simulated spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the conventional design for the 1st channel input (a) and 8th channel input (b), respectively.

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 figure: Fig. 6

Fig. 6 Simulated spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the proposed design for the 1st channel input (a) and 8th channel input (b), respectively.

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It should be pointed out that in the proposed design with a constant projected period for the array waveguides, as shown in Fig. 3, the pitch between adjacent middle array waveguides along the grating circle is equal to that of the conventional design, while the pitch between the peripheral array waveguides increases gradually and is slightly larger than that of the conventional design. On the other hand, the middle array waveguides receive most power of the input light and only partial power is coupled to the peripheral array waveguides. Therefore, the slightly larger pitch between the peripheral array waveguides, which corresponds to a larger gap, will slightly increases the loss, however according to the simulation results in Figs. 5(b) and Fig. 6(b), the extra loss is only about 0.1 dB, which can be acceptable in practical applications.

3. Fabrication

For fabrication of these two devices, an initial SOI chip with 220 nm thick top silicon layer and 2 μm BOX is firstly cleaned and spin-coated with a layer of photoresist ma-N-2403. Then, the designed AWG patterns are written to the photoresist by electron-beam-lithography. After development of the photoresist, reactive ion etching with SF6 and C4F8 gases is employed to etch through the silicon layer. Subsequently, a mixed solution of H2SO4 and H2O2 (H2SO4: H2O2 = 2:1) is used to remove the residual resist. And finally, a layer of SU-8 polymer with a thickness of 1.5μm is spin-coated on the chip to protect the AWG patterns. Figure 7(a) shows optical microscope images of the fabricated devices, and the changed part between the proposed and conventional design is also denoted in Fig. 7(b).

 figure: Fig. 7

Fig. 7 (a) Optical microscope images of the fabricated 15 × 15 AWG router. Insets: Enlarged view of array waveguides (b) and I/O waveguides (c) near the FPR.

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4. Experimental results and discussions

To characterize the fabricated devices, deeply etched (220 nm) focused grating couplers working at TM polarization with period of 988 nm and duty cycle of 0.7 are connected into the input and output waveguides, as shown in Fig. 7(a). The coupling efficiency of above 30% with a standard single mode fiber is obtained. Figure 8 shows experimentally measured results of the 15 × 15 AWG router with a constant curvilinear period along the grating circle for the array waveguides when the light inputs from the 1st and 8th channel respectively. These results are normalized by the transmission of a straight waveguide with a same length beside the corresponding AWG router. Due to the difference between the fabricated and designed array waveguide width, center wavelength of the fabricated AWG router slightly deviates from the designed value. It is known from Fig. 8(b) that deformation of the spectral shapes occurs at the peripheral output channels and consequently exhibits a large crosstalk, which agrees well with the simulated results as shown in Fig. 5(b). However as shown in Fig. 8(a) for the 1st channel input, the spectral shapes of most output channels become badly deformed and widened, also in a good agreement with the simulation results as shown in Fig. 5(a). Therefore, the existence of aberration in silicon-based AWG routers with the conventional design is experimentally verified and it considerably influences the spectral performance. Figure 9 shows measured spectra of the 15 × 15 AWG router with the proposed design for the 1st and 8th channel input respectively. It is known that spectral performance of all output wavelengths is drastically improved, especially for the marginal wavelengths. As is shown in Fig. 9(a), due to the fact that ch-15 and ch-1 working at the border of two adjacent free spectral ranges (FSR) and a slight difference between FSR and 15 times of the designed channel spacing, the channel spacing between these two channels is a little different from the other channels. In order to further observe the performance improvement, three output channels including the 1st, 8th, and 15th channel are chosen to make a comparison for the 1st and 8th channel input respectively, and similarities and differences are obtained by overlapping the channel spectra by shifting them by multiples of channel spacing. The comparison results of these three output channels are shown in Fig. 10 for the conventional design and Fig. 11 for the proposed design, respectively. It is known from Fig. 10 that spectra differences among these three output channels are substantially large especially for the 1st channel input. However, as shown in Fig. 11, spectra of these three output channels overlap very well both for the 1st and 8th input, which validates the reduction of aberration in silicon-based AWG router with the proposed design.

 figure: Fig. 8

Fig. 8 Measured spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the conventional design for the 1st channel input (a) and 8th channel input (b), respectively.

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 figure: Fig. 9

Fig. 9 Measured spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the proposed design for the 1st channel input (a) and 8th channel input (b), respectively.

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 figure: Fig. 10

Fig. 10 Overlapped spectra of the 1st, 8th and 15th output channel of the fabricated AWG router with the conventional design for the 1st (a) and 8th (b) input, respectively.

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 figure: Fig. 11

Fig. 11 Overlapped spectra of the 1st, 8th and 15th output channel of the fabricated AWG router with the proposed design for the 1st (a) and 8th (b) input, respectively.

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Figure 12 shows cyclic property of the fabricated AWG router. Since the side channels experience 3 dB extra loss compared to the center channel, the combination of the side input and side output channel will experience up to 6 dB extra loss compared to the combination of the center input and center output channel for an N × N router. Therefore as shown in Fig. 12(a), the measured insertion loss varies from −8 dB to −3.5 dB. For the central input and central output channel, the loss is about 3.5 dB, which mainly originates from the large mode mismatch between the slab mode and array waveguide mode due to a deep etch shown in Fig. 0.7(b) at the junction between the slab waveguide and array waveguides and a gap of 0.5 μm between adjacent array waveguides, and it can be reduced by the combination of deep and shallow etch and using a smaller gap at the junction [7, 14]. On the other hand, the crosstalk performance is mainly determined by fabrication technology and aberration in silicon AWG. In our designed AWG, although the aberration value is sufficiently low theoretically, crosstalk level resulting from the phase error due to imperfect fabrication technology is dominant in the fabricated device. Therefore, the crosstalk results are slightly different for different input channel, ranging from −19 dB to −24 dB, as shown in Fig. 12(b), and they can be further improved by optimizing the fabrication technology and mask layout design [3, 6, 14].

 figure: Fig. 12

Fig. 12 Spectral responses of the fabricated 15 × 15 AWG router. (a) Insertion loss, (b) Crosstalk level.

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5. Conclusion

In this paper, we have theoretically and experimentally demonstrated that spectral performance of all output wavelengths within a FSR in the AWG router with the proposed design having a constant projected period in a line tangent to the grating for the array waveguides near the FPR, can be significantly improved, while the conventional AWG router with a constant curvilinear period along the grating circle for the array waveguides suffers high crosstalk in its peripheral output wavelengths, especially for the edge channel input light, due to a large aberration. The proposed AWG router, having a good crosstalk level regardless of the light input channel, will play an important role in future high capacity on-chip optical interconnect applications.

Funding

National High-Tech R and D Program of China (2013AA014401); National Science Foundations of China (61605172); Public Project of Zhejiang Province (2016C33074); Scientific Research Projects of the Department of Education of Hebei Province (QN2016090); Natural Science Foundation of Hebei Province (F2017402068).

References and links

1. P. Dong, “Silicon photonic integrated circuits for wavelength-division multiplexing applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 6100609 (2016). [CrossRef]  

2. R. Proietti, Z. Cao, C. J. Nitta, Y. Li, and S. J. B. Yoo, “A scalable, low-latency, high-throughput, optical interconnect architecture based on arrayed waveguide grating routers,” J. Lightwave Technol. 33(4), 911–920 (2015). [CrossRef]  

3. W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006). [CrossRef]  

4. D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008). [CrossRef]  

5. J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Low-loss and low-crosstalk 8 × 8 silicon nanowire AWG routers fabricated with CMOS technology,” Opt. Express 22(8), 9395–9403 (2014). [CrossRef]   [PubMed]  

6. S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014). [CrossRef]  

7. J. Park, G. Kim, H. Park, J. Joo, S. Kim, and M.-J. Kwack, “Performance improvement in silicon arrayed waveguide grating by suppression of scattering near the boundary of a star coupler,” Appl. Opt. 54(17), 5597–5602 (2015). [CrossRef]   [PubMed]  

8. S. Kamei, M. Ishii, A. Kaneko, T. Shibata, and M. Itoh, “N × N cyclic-frequency router with improved performance based on arrayed-waveguide grating,” J. Lightwave Technol. 27(18), 4097–4104 (2009). [CrossRef]  

9. J. Zou, T. Lang, Z. Le, and J.-J. He, “Ultracompact silicon-on-insulator-based reflective arrayed waveguide gratings for spectroscopic applications,” Appl. Opt. 55(13), 3531–3536 (2016). [CrossRef]   [PubMed]  

10. B. Gargallo, P. Muñoz, R. Baños, A. L. Giesecke, J. Bolten, T. Wahlbrink, and H. Kleinjans, “Reflective arrayed waveguide gratings based on Sagnac loop reflectors with custom spectral response,” Opt. Express 22(12), 14348–14362 (2014). [CrossRef]   [PubMed]  

11. J. Brouckaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonics silicon-on-insulator platform,” J. Lightwave Technol. 25(5), 1269–1275 (2007). [CrossRef]  

12. D. Wang, G. Jin, Y. Yan, and M. Wu, “Aberration theory of arrayed waveguide grating,” J. Lightwave Technol. 19(2), 279–284 (2001). [CrossRef]  

13. S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

14. S. Pathak, D. Van Thourhout, and W. Bogaerts, “Design trade-offs for silicon-on-insulator-based AWGs for (de)multiplexer applications,” Opt. Lett. 38(16), 2961–2964 (2013). [CrossRef]   [PubMed]  

15. E. Kleijn, M. K. Smit, and X. J. M. Leijtens, “New analytical arrayed waveguide grating model,” J. Lightwave Technol. 31(20), 3309–3314 (2013). [CrossRef]  

References

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  1. P. Dong, “Silicon photonic integrated circuits for wavelength-division multiplexing applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 6100609 (2016).
    [Crossref]
  2. R. Proietti, Z. Cao, C. J. Nitta, Y. Li, and S. J. B. Yoo, “A scalable, low-latency, high-throughput, optical interconnect architecture based on arrayed waveguide grating routers,” J. Lightwave Technol. 33(4), 911–920 (2015).
    [Crossref]
  3. W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
    [Crossref]
  4. D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
    [Crossref]
  5. J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Low-loss and low-crosstalk 8 × 8 silicon nanowire AWG routers fabricated with CMOS technology,” Opt. Express 22(8), 9395–9403 (2014).
    [Crossref] [PubMed]
  6. S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
    [Crossref]
  7. J. Park, G. Kim, H. Park, J. Joo, S. Kim, and M.-J. Kwack, “Performance improvement in silicon arrayed waveguide grating by suppression of scattering near the boundary of a star coupler,” Appl. Opt. 54(17), 5597–5602 (2015).
    [Crossref] [PubMed]
  8. S. Kamei, M. Ishii, A. Kaneko, T. Shibata, and M. Itoh, “N × N cyclic-frequency router with improved performance based on arrayed-waveguide grating,” J. Lightwave Technol. 27(18), 4097–4104 (2009).
    [Crossref]
  9. J. Zou, T. Lang, Z. Le, and J.-J. He, “Ultracompact silicon-on-insulator-based reflective arrayed waveguide gratings for spectroscopic applications,” Appl. Opt. 55(13), 3531–3536 (2016).
    [Crossref] [PubMed]
  10. B. Gargallo, P. Muñoz, R. Baños, A. L. Giesecke, J. Bolten, T. Wahlbrink, and H. Kleinjans, “Reflective arrayed waveguide gratings based on Sagnac loop reflectors with custom spectral response,” Opt. Express 22(12), 14348–14362 (2014).
    [Crossref] [PubMed]
  11. J. Brouckaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonics silicon-on-insulator platform,” J. Lightwave Technol. 25(5), 1269–1275 (2007).
    [Crossref]
  12. D. Wang, G. Jin, Y. Yan, and M. Wu, “Aberration theory of arrayed waveguide grating,” J. Lightwave Technol. 19(2), 279–284 (2001).
    [Crossref]
  13. S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).
  14. S. Pathak, D. Van Thourhout, and W. Bogaerts, “Design trade-offs for silicon-on-insulator-based AWGs for (de)multiplexer applications,” Opt. Lett. 38(16), 2961–2964 (2013).
    [Crossref] [PubMed]
  15. E. Kleijn, M. K. Smit, and X. J. M. Leijtens, “New analytical arrayed waveguide grating model,” J. Lightwave Technol. 31(20), 3309–3314 (2013).
    [Crossref]

2016 (2)

P. Dong, “Silicon photonic integrated circuits for wavelength-division multiplexing applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 6100609 (2016).
[Crossref]

J. Zou, T. Lang, Z. Le, and J.-J. He, “Ultracompact silicon-on-insulator-based reflective arrayed waveguide gratings for spectroscopic applications,” Appl. Opt. 55(13), 3531–3536 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (4)

S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Low-loss and low-crosstalk 8 × 8 silicon nanowire AWG routers fabricated with CMOS technology,” Opt. Express 22(8), 9395–9403 (2014).
[Crossref] [PubMed]

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

B. Gargallo, P. Muñoz, R. Baños, A. L. Giesecke, J. Bolten, T. Wahlbrink, and H. Kleinjans, “Reflective arrayed waveguide gratings based on Sagnac loop reflectors with custom spectral response,” Opt. Express 22(12), 14348–14362 (2014).
[Crossref] [PubMed]

2013 (2)

2009 (1)

2008 (1)

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

2007 (1)

2006 (1)

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

2001 (1)

Absil, P.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

Baets, R.

Baets, R. G.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Baños, R.

Beckx, S.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Bogaerts, W.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

S. Pathak, D. Van Thourhout, and W. Bogaerts, “Design trade-offs for silicon-on-insulator-based AWGs for (de)multiplexer applications,” Opt. Lett. 38(16), 2961–2964 (2013).
[Crossref] [PubMed]

J. Brouckaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonics silicon-on-insulator platform,” J. Lightwave Technol. 25(5), 1269–1275 (2007).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Bolten, J.

Brouckaert, J.

Cao, Z.

Dong, P.

P. Dong, “Silicon photonic integrated circuits for wavelength-division multiplexing applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 6100609 (2016).
[Crossref]

Dumon, P.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

J. Brouckaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonics silicon-on-insulator platform,” J. Lightwave Technol. 25(5), 1269–1275 (2007).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Gan, F.

Gargallo, B.

Giesecke, A. L.

He, J.-J.

Ishii, M.

Itoh, M.

Jaenen, P.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Jin, G.

Joo, J.

Kamei, S.

Kaneko, A.

Kim, D.-J.

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

Kim, G.

J. Park, G. Kim, H. Park, J. Joo, S. Kim, and M.-J. Kwack, “Performance improvement in silicon arrayed waveguide grating by suppression of scattering near the boundary of a star coupler,” Appl. Opt. 54(17), 5597–5602 (2015).
[Crossref] [PubMed]

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

Kim, S.

Kleijn, E.

Kleinjans, H.

Kwack, M.-J.

Lang, T.

Le, Z.

Lee, J.-M.

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

Leijtens, X. J. M.

Lepage, G.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

Li, L.

Li, W.

Li, Y.

Muñoz, P.

Nitta, C. J.

Pang, A.

Park, H.

Park, J.

Pathak, S.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

S. Pathak, D. Van Thourhout, and W. Bogaerts, “Design trade-offs for silicon-on-insulator-based AWGs for (de)multiplexer applications,” Opt. Lett. 38(16), 2961–2964 (2013).
[Crossref] [PubMed]

Proietti, R.

Pyo, J.

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

Qi, M.

Sheng, Z.

Shibata, T.

Smit, M. K.

Song, J. H.

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

Taillaert, D.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Thourhout, D. V.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

Van Thourhout, D.

Vanslembrouck, M.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

Verheyen, P.

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

Wahlbrink, T.

Wang, D.

Wang, J.

Wang, X.

Wiaux, V.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Wouters, J.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Wu, A.

Wu, M.

Yan, Y.

Yoo, S. J. B.

Zou, J.

Zou, S.

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (2)

P. Dong, “Silicon photonic integrated circuits for wavelength-division multiplexing applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 6100609 (2016).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (2)

D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, “Crosstalk reduction in a shallow-etched silicon nanowire AWG,” IEEE Photonics Technol. Lett. 20(19), 1615–1617 (2008).
[Crossref]

S. Pathak, M. Vanslembrouck, P. Dumon, D. V. Thourhout, P. Verheyen, G. Lepage, P. Absil, and W. Bogaerts, “Effect of mask discretization on performance of silicon arrayed waveguide gratings,” IEEE Photonics Technol. Lett. 26(7), 718–721 (2014).
[Crossref]

J. Lightwave Technol. (5)

Opt. Express (2)

Opt. Lett. (1)

Photonics J. (1)

S. Pathak, P. Dumon, D. V. Thourhout, and W. Bogaerts, “Comparison of AWGs and echelle gratings for wavelength division multiplexing on silicon-on-insulator,” Photonics J. 6(5), 4900109 (2014).

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Figures (12)

Fig. 1
Fig. 1 Location distribution of the array waveguides along the grating circle for Rowland configuration. (a) Conventional design: constant curvilinear period, (b) Proposed design: constant projected period.
Fig. 2
Fig. 2 Illustration of the free propagation region based on the Rowland configuration.
Fig. 3
Fig. 3 Deviation of locations of array waveguides in proposed design from those in conventional design along the grating circle.
Fig. 4
Fig. 4 Aberration values of 15 output wavelengths of two kinds of AWG routers for the 1st channel input (a) and 8th channel input (b), respectively.
Fig. 5
Fig. 5 Simulated spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the conventional design for the 1st channel input (a) and 8th channel input (b), respectively.
Fig. 6
Fig. 6 Simulated spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the proposed design for the 1st channel input (a) and 8th channel input (b), respectively.
Fig. 7
Fig. 7 (a) Optical microscope images of the fabricated 15 × 15 AWG router. Insets: Enlarged view of array waveguides (b) and I/O waveguides (c) near the FPR.
Fig. 8
Fig. 8 Measured spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the conventional design for the 1st channel input (a) and 8th channel input (b), respectively.
Fig. 9
Fig. 9 Measured spectral responses of the 400 GHz channel spaced 15 × 15 AWG router with the proposed design for the 1st channel input (a) and 8th channel input (b), respectively.
Fig. 10
Fig. 10 Overlapped spectra of the 1st, 8th and 15th output channel of the fabricated AWG router with the conventional design for the 1st (a) and 8th (b) input, respectively.
Fig. 11
Fig. 11 Overlapped spectra of the 1st, 8th and 15th output channel of the fabricated AWG router with the proposed design for the 1st (a) and 8th (b) input, respectively.
Fig. 12
Fig. 12 Spectral responses of the fabricated 15 × 15 AWG router. (a) Insertion loss, (b) Crosstalk level.

Tables (1)

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Table 1 Design parameters of the exampled AWG router.

Equations (4)

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w = 2 R sin ( i d a 2 R ) , i = N , ... 1 , 0 , 1 , ... , N ( u 2 R ) 2 + w 2 = ( 2 R ) 2
w = i d a , i = N , ... 1 , 0 , 1 , ... , N ( u 2 R ) 2 + w 2 = ( 2 R ) 2
F ( w ) = n s r A ( w ) + n a L ( w ) + n s r B ( w ) G ( w ) m λ
Δ F ( w ) = F ( w ) F ( 0 ) = n s ( r A P ( w ) r A O ) + n a ( L ( w ) L ( 0 ) ) + n s ( r P B ( w ) r O B ) G ( w ) m λ

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