8 ÿ 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network

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8 × 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network Zhihua Yu a,∗ , Tao Han a , Guangjun Wang a , Guang Qi a , Fengguang Luo b , Bin Li b a b

Teaching Experimental Center for Information Technology, China University of Geosciences (Wuhan), Wuhan, Hubei 430074, China Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

a r t i c l e

i n f o

Article history: Received 20 June 2012 Accepted 12 November 2012

a b s t r a c t We use the transfer matrix method to investigate a 8 × 8 no blocking microring resonator crossbar that can be used to route wavelength division multiplexing (WDM) signals across the chip. The proposed design is no-blocking and reconfigurable and its salient feature is the ability to support multicasting and multiplexing efficiently, which can be satisfied for on-chip interconnects in future many-core processors.

Keywords: On-chip interconnects Microring resonator Transfer matrix method

1. Introduction Recently, photonic networks-on-chip (NoC) for future manycore computing systems have attracted many researchers’ interests. As pointed out in the International Technology Roadmap for Semiconductor (ITRS), optical communications on a chip is one alternative interconnection technology that promises high-datarate signal transmission and low power consumption [1,2]. Several network architectures [3], such as mesh, torus, crossbar, fat tree and clos, have been analyzed to construct efficient photonic NoC [4]. According to the configurability of the routing patterns, they can be divided into two categories. One is wavelength-selective passive network which has the fixed routing pattern defined at the design of the network and the path between the source and the destination is established through the dynamic selection of specific wavelength at the source or the destination, and the other is switching network which dynamically set the routing pattern through an electronic controlled network. It is claimed that the former can exhibit low latency since the routing network is passive, which suggests that the time of selecting specific wavelength is shorter than that of configuring the optical switching network [1]. In this paper, we proposed a 8 × 8 no-blocking microring resonator crossbar that can be used to route wavelength division multiplexing (WDM) signals across the chip. The optical paths between the sources and destinations are established based on the wavelengths that are used. The virtues of this proposed crossbar is

∗ Corresponding author. E-mail address: [email protected] (Z. Yu).

© 2012 Elsevier GmbH. All rights reserved.

no-blocking and reconfigurable. It could allow WDM signals from a single source to be multicast to an arbitrary subset of the output ports. Also, signals from multiple sources can be multiplexed to a single destination through the proposed crossbar without arbitration for the destination, as the incoming signals are distributed over distinct wavelength channels.

2. Photonic network architectures The basic building block for the optical crossbar is an add-drop filter comprising two microring resonator coupled with a waveguide crossing [5,6]. Fig. 1(a) shows the schematic of the basic building block. The two microring structures are identical and they have the same resonance wavelength. The optical signal excited at each input port propagates along the vertical waveguide. When the signal wavelength does not correspond to the resonance wavelength of the microring resonator, the optical signal continues to propagate without tunneling to the other orthogonal (horizontal) waveguide. When the signal wavelength is at the resonance wavelength, the optical signal couples into the microring resonator and tunnels out to the other waveguide. In this way, two channels can be set up (as Fig. 1(a) shows with the red and blue line). The optical signal can be routed to either the through or drop port, depending on its wavelength. The waveguide crossing junction usually causes high scattering loss, lowering signal forward transmission and inducing crosstalk between the two output ports. The optical crossbar exploits multimode interference (MMI) couplers to mitigate this problem. For the MMI coupler, the waveguide mode is self-imaged at the MMI center (crossing center) with no expansion of the wavefront, resulting in smoother forward propagation. Simulations indicate that the

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Please cite this article in press as: Z. Yu, et al., 8 × 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.035

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Table 1 8 × 8 crossbar routing table.

I1 I2 I3 I4 I5 I6 I7 I8

(a)

O1

O2

O3

O4

O5

O6

O7

O8

4 5 3 6 2 7 1 8

5 6 4 7 3 8 2 1

3 4 2 5 1 3 8 7

6 7 5 8 4 1 3 2

2 3 1 4 8 5 7 6

7 8 6 1 5 2 4 3

1 2 8 3 7 4 7 5

8 1 7 2 6 3 5 4

illustrates the input–output routing table for a 8 × 8 crossbar with eight-column different microrings, whose resonances are at 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8 independently. From the chart, we can see that the whole switch network is no-blocking. 3. Modeling

(b)

We first analyze the basic switch element, which is a microring resonator coupled with a waveguide crossing. Fig. 1(a) shows the schematic of the basic building block. The waveguideto-microresonator coupling efficiency is one key parameter that determines the microresonator-based filter transmission and bandwidth. For microring resonator-based filters, the coupling efficiency depends on the bus waveguide dimensions, the waveguide-to-microring interaction length, and the gap spacing between the bus waveguide and the microring. Given the coupling efficiency (in terms of field coupling and transmission coefficients), we can model the field transmission coefficients of the microresonator coupled with a waveguide crossing. Fig. 1(b) shows the numerically simulated transmission spectra using transfer matrix method. In this way, the optical signal can be routed to either the through or drop port, depending on its wavelength (Fig. 2). The modeling process is based on applying the transfer matrix method [8]. The first step in the process is to deduce the electric field transmission functions for the two output ports of the basic building block. The electric field transmission through the input coupler of the microring resonator can be expressed as:



b1



=

b2



d1



(c) Fig. 1. Matrix switch configuration of (a) 2 × 2 optical crossbar, (b) 4 × 4 optical crossbar, and (c) 8 × 8 optical crossbar. (For interpretation of the references to color in the text, the reader is referred to the web version of the article.)

junction insertion loss can be as low as 0.1 dB per junction and crosstalk can be suppressed to −40 dB using a carefully designed MMI coupler [7]. Larger-scale crossbar designs require cascading multiple basic building blocks in a matrix form. Fig. 1(b) shows 4 × 4 matrix switch configuration and Fig. 1(c) shows 8 × 8 matrix switch configuration. Eight WDM signals (1 , 2 , . . ., 8 ) from one input-port are demultiplexed at the output after passing through the crossbar and the wavelength assignment is cyclic for different input ports. In this sense, the crossbar is functionally similar to arrayed waveguide gratings (AWG), except that it uses optical resonance rather than optical phase coherence to separate WDM channels. Table 1

c2 d2

 =

d2







 =

t1

−ik1

ik1

t1



a1



(1)

a2

t2

−ik2

−ik2

t2



c1

 (2)

c2

A1/4 ei

0

0

A1/4 ei



a2

 (3)

b2

where kx and tx (x = 1, 2) are the field coupling and transmission coefficients of the input/output couplers (for lossless coupling, kx 2 + tx 2 = 1). We relate to the microring round-trip length  as  = 2neff Lr /, neff is the waveguide effective refractive index and  is the free-space wavelength. The term A0.25 exp(i0.25) represents the field component that propagates a quarter of the microring between the horizontal and vertical bus waveguides. The microring round-trip amplitude transmission factor A as A = exp((1/2) · (˛dB /4.34) · 2r), where ˛dB is the microring transmission loss (A = 1 means lossless microresonator) and r is the microring radius. Solving (1)–(3), we can get the formal expressions of the electric field transmissions at the throughput- and rop-ports Tt and Td : 2

Tt =

Et t1 − t1 2 t2 A exp(i) − k1 t2 A exp(i) = Ein 1 − t1 t2 exp(i)

(4)

Please cite this article in press as: Z. Yu, et al., 8 × 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.035

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3 8x8 Microring Array

(a) 1 O1 O2 O3 O4 O5 O6 O7 O8

0.9 0.8

Normalized Power

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.545

1.55

(a)

1.555 1.56 Wavelength (μm)

1.565

1.57

8x8 Microring Array 1

O1 O2 O3 O4 O5 O6 O7 O8

0.9

Pthroughput

0.9 0.8

0.8

0.7

0.7 Normalized Power

Normalized Intensity

1

(b)

0.6

A=0.993,k0=k1=0.3 0.5 0.4 0.3

0.6 0.5 0.4 0.3

0.2

0.2

Pdrop

0.1

0.1 0 1.55

1.555

1.56

1.565

1.57

1.575

0 1.545

Wavelength (μm)

1.55

(b) Fig. 2. (a) The basic switch element using a microring resonator side-coupled to a MMI waveguide crossing; (b) the throughput- and drop-port numerically simulated transmission spectra using transfer matrix method.

1.555 1.56 Wavelength (μm)

1.565

1.57

Fig. 3. Calculated transmission spectra for a 8 × 8 crossbar with various resonance bandwidths: (a) 50 GHz and (b) 100 GHz. The channel spacing is fixed at 250 GHz.

4. Discussion

Td =

Ed k0 k1 A0.25 exp(i0.25) = Ein 1 − t1 t2 A exp(i)

(5)

where Et and Ed are the electric field amplitude at the throughput port and drop port, Ein is the electric field at the input-port, and  is the microring round-trip phase change. The basic building blocks are interconnected to form higherorder crossbars [9,10]. In an N × N crossbar, each optical routing path between the input and output ports has N sequentially cascaded basic building blocks. As these basic building blocks are located in different columns, the microrings have different resonance wavelengths, and we denote their through and drop transmission functions as Ttl and Tdl (l is the column number). The crossbar output electric field transmission function Tij (i, j = 1, 2, . . ., N for input and output port numbers) is therefore the product of several transmission functions Ttl and Tdl . For instance, in the 8 × 8 crossbar, T11 = Tt1 Tt2 Tt3 Td4 Tt5 Tt6 Tt7 , T12 = Tt1 Tt2 Tt3 Tt4 Td5 Tt6 Tt7 Tt8 , T13 = Tt1 Tt2 Td3 Tt4 Tt5 Tt7 Tt8 , T14 = Tt1 T t2 Tt3 Tt4 Tt5 Td6 Tt7 Tt8 , T15 = Tt1 Td2 Tt3 Tt5 Tt6 Tt7 Tt8 , T16 = Tt1 Tt3 Tt4 Tt5 Tt6 Td7 Tt8 , T17 = Td1 Tt3 Tt4 Td5 Tt6 Tt7 Tt8 and T18 = Tt1 Tt2 Tt3 Tt4 Td5 Tt6 Tt7 . Fig. 3(a) and (b) shows simulated output transmission spectra for 8 × 8 crossbars. The channel bandwidths are 50 GHz and 100 GHz independently, the channel spacing 250 GHz, and the resulting crosstalk −20 dB. Note that passband shapes with broader bandwidths and sharper roll-offs can be achieved by using series-coupled microring resonators instead of the single microring resonator in the basic building block.

In order to transfer more power to the drop waveguide at resonance wavelengths, we should calculate the throughput-port transmission spectrum and resonance linewidth (3-dB bandwidth) as a function of  and ˛. According to the definition of 3-dB bandwidth: P = (1/2)Pmax , we can get the value of :



 = arccos

(1 + A2 t12 t22 )(t1 − At2 )2 + 4At1 t2 (t12 + A2 t22 ) 2At1 t2 [2 + 2A2 t12 t22 − (t1 − At2 )2 ]



(6)

Then, using the relation of wavelength and phase delay, we can get:  = 2 = (2)2 Nef f

 2

(7)

Then, the 3-dB bandwidth is: 3 dB =

2  22 rNeff

(8)

Fig. 4(a) shows the resonance 3-dB bandwidth (BW) as a function of  and ˛. It is inversely proportional to the resonance Q-factor: BW = f0 /Q. Hence, small ˛ (large A) and large  tend to have large Q but small resonance bandwidth. Fig. 4(b) shows the throughput transmission spectrum extinction ratio (ER) as a function of  and A (ER = −10 log(Pmin /Pmax )), large  and large A (means low transmission loss) can get large ER. Therefore, just as Fig. 4(c) shows, microring resonators with high coupling coefficients () and low transmission loss (˛) would be the best choice to this crossbar.

Please cite this article in press as: Z. Yu, et al., 8 × 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.035

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1

0.7

=2nm

Neff=2.650 Neff=2.647

0.9

0.6

0.8

k=0.3

Normalized Power

λ3dB(nm)

0.5

0.4

k=0.25

0.3

0.2

k=0.2

0.7 0.6 0.5 0.4 0.3 0.2

0.1

0.1 0 0.8

0.82

0.84

0.86

0.88

0.9 A

0.92

0.94

0.96

0.98

1

0 1.55

Crosstalk 1.552

1.554

1.556

1.558

1.56

1.562

1.564

Wavelength( m)

(a)

Fig. 5. Different resonance wavelength with different refractive index.

90 A=0.998 0.988 0.978

80

1

70

2

3

4 O1

I1

ER(dB)

60 O2

I2

50

I3

40

O3 O4

I4

30 20

(a)

10 0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1

k (b)

2

3

4 O1

I1

1 k1=k2=0.3, A=0.9993 k1=k2=0.15, A=0.9993 k1=k2=0.3, A=0.978 k1=k2=0.15, A=0.978

0.9

Normalized Intensity

0.8

O2

I2 I3

0.7

O3 O4

I4

0.6 (b)

0.5

Fig. 6. Schematic diagrams of (a) single-to-multiple transmission and (b) multipleto-single transmission.

0.4 0.3 0.2 0.1 0 1.554

1.556

1.558

1.56

1.562

1.564

1.566

1.568

Wavelength (μm) (c)

Fig. 4. (a) The resonance 3-dB bandwidth BW as a function of  and A; (b) the throughput transmission spectrum extinction ratio (ER) as a function of  and A; and (c) the normalized intensity of the drop waveguide at resonance wavelengths with different  and A.

regions with p-type or n-type dopants (e.g., boron and phosphorus) is also able to change the refractive index [11,12]. In addition to functioning as a one-to-one cross-connect network, this crossbar has the unique ability to support many-to-one (multiplexing) and one-to-many (multicasting) transmissions that arise in many applications, without additional cost or complexity. Fig. 6 demonstrates the schematic diagrams of 4 × 4 crossbar. This opens up opportunities for the proposed crossbar design in future multicore processors [7]. 5. Conclusion

In order to form cascaded microresonator-based matrix switch, the microrings should have different resonance wavelengths. According to the definition:  = 2neff Lr /, when  = 2m (m = 1,2 . . .), the microring satisfied the resonance conditions. Hence, resonance wavelengths are related with neff and Lr . Fig. 5 shows the corresponding resonance blue-shifted 2 nm using different refractive index. Fabrication-induced phase error in the microring resonators can cause resonance shift from the desired values. In order to compensate for this error, post-fabrication trimming techniques, such as electron beam trimming, can be used to accurately control the resonance wavelengths. Alternatively, doping the desired waveguide

Large scale low latency crossbars are very desirable in on-chip interconnect networks. However, crossbars with a large number of ports and wide data paths are not practical in an electronic implementation because of wiring complexity and the large and power hungry drivers and repeaters needed to support low latency operation. We propose and demonstrate a microring resonator-based arbitration-free optical crossbar that can be used for on-chip WDM based interconnection networks. The proposed crossbar design supports multicasting and multiplexing efficiently, which can be useful in many applications in future multicore processors. The crossbar design is modeled using the transfer matrix method to

Please cite this article in press as: Z. Yu, et al., 8 × 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.035

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study the effect of several key parameters on its transmission performance. Acknowledgment This work has been supported by the National Natural Science Foundation of China (NSFC) under grant 61205089, and by the Fundamental Research Funds for the Central Universities,China University of Geosciences (Wuhan) under grant CUGL100245. References [1] R. Ji, L. Yang, L. Zhang, Five-port optical router for photonic networks-on-chip, Opt. Express 19 (21) (2011) 20258–20268. [2] N. Sherwood-Droz, H. Wang, L. Chen, Optical 4 × 4 hitless slicon router for optical networks-on-chip (NoC), Opt. Express 16 (20) (2008) 15915–15922. [3] Z. Yu, F. Luo, X. Di, Highly reliable optical interconnection network on printed circuit board for distributed computer systems, Opt. Laser Technol. 42 (2010) 1332–1336.

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Please cite this article in press as: Z. Yu, et al., 8 × 8 passive noblocking microring resonator crossbar for on-chip WDM-based interconnection network, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.035