WDM performances of two- and three-waveguide Mach-Zehnder switches assembled into 4 x 4 matrix router.
Chip Multiprocessors that exploit the potentialities of parallel computing are the state of the art solution to face the constant need of increasing computing system efficiency. A chip multiprocessor consists of several smaller processing cores designed and replicated several times. They achieve performance gain through parallel code execution using multiple threads across the cores. As the number of cores in chip multiprocessors continues to scale, the efficient interconnection of these cores is becoming a major challenge to overcome the communication bottleneck, thus obtaining high bandwidth, low-power and low-latency requirements. All these characteristics cannot be matched by traditional point-to-point connections through dedicated wires. Network-on-chips (NoCs) have emerged as a technology enabling a high degree of integration in multi-core systems on chip. The NoCs were introduced to reduce the wiring complexity and to increase the communication efficiency by designing regular topologies. However, an important performance limitation in traditional NoCs, which are mainly made by switching elements, network interfaces and inter-switch links, arises from multi-hop communications based on planar metal interconnects and to the consequent high latency and power consumption. In fact, at the physical level, the metal interconnect is responsible for depressing the on-chip data bandwidth while consuming an increasing percentage of power.
The recent developments in nanotechnology have enabled promising alternatives, such as Photonic Networks on Chip (PhNoC), which are opening new perspectives of performance improvement in Chip Multiprocessor (CMP) architectures. In fact, the integration of a photonic layer into CMPs allows to exploit the advantages of optical data transmission, such as high transmission bandwidth, low latency, low power consumption, etc. .
Among the components necessary for on-chip photonic communication, such as multiplexers/demultiplexers , multiwavelength filters [3,4], modulators [5-9], the switches play a fundamental role for their capability of routing the signals along the network thus connecting the different processors.
A variety of technologies have been proposed for the realization of innovative and integrable photonic components useful for optical data communication such as active switches based on III-V or III-V-N compounds, which conjugate the switching functionality to the signal amplification [10-14], or devices exploiting non-linear materials, liquid crystals, or photonic crystals for multi-channel filtering and narrow-band switching [4, 15-20]. However, the silicon nanotechnology seems to be the one more mature in the context of on-chip integration, thanks to its compatibility with standard CMOS fabrication processes.
Silicon components allow the realization of reconfigurable networks due to the possibility of inducing a refractive index variation by thermo-optic or plasma-optic effects. For example, data rate up to 40 Gb/s has been reached by plasma-optic effect in reversely biased p-n junctions [5-9]. Moreover, the data rate can be enhanced up to Tb/s by the implementation of Wavelength Division Multiplexing (WDM) schemes in the PhNoC.
The WDM, which allows the parallel transmission of multiple channels on the same waveguide, each associated to a different wavelength, requires the exploitation of broadband switches capable of contemporarily routing the different channels. In a previous work  we proposed a broadband Mach-Zehnder switch configuration based on three-waveguide couplers which guarantees a broadband operation compared to the conventional two-waveguide configuration. Here, we discuss the performances of the switches assembled into 4 x 4 matrices which are the basic elements necessary to build up the entire network thus allowing the different processors to exchange sets of data. Moreover, the proposed numerical approach is useful for the integration of the photonic switching elements into network design tools. In fact, on one hand the optimization of the overall photonic NoC requires the simulation of the network architecture by dedicated tools , which can not simulate the optical devices at a physical level. On the other hand, the design of SOI switches needs complex numerical models based on the differential equations for accounting the physical phenomena, such as the carrier dynamics and the electromagnetic propagation. An accurate analysis of the physical phenomena underlying the switching element functionality, allows for describing the optical devices through equivalent black-boxes to be included into the models at the network level.
In this paper, we report the results of the design and the simulations of two configurations of broadband Mach-Zehnder Switch (MZS) exploiting, respectively, two and three waveguides. The switches are based on SOI waveguides assembled into Mach-Zehnder interferometric configurations in which the phase shift is induced by the plasma-optic effect. The simulation of the carrier dynamics was performed by the Finite Element Method (FEM) [23, 24], whereas the electromagnetic propagation was simulated through the Finite Difference Beam Propagation Method (FD-BPM) . By means of these numerical models we obtain the switch transmittance and other relevant parameters, such as the insertion loss and the power consumption, necessary for the black-box description of the devices at the network simulation level. Finally, the performances of the two MZSs assembled into 4 x 4 switch matrices are evaluated.
2. TWO AND THREE-WAVEGUIDE MACH-ZEHNDER
The designed reconfigurable Mach-Zehnder switches are schematized in Figure 1. They are made of two 50% coupling sections, exploiting two (Figure 1(a)) or three (Figure 1(b)) waveguide couplers and of a phase shifter region in which a [pi] phase shift is achieved by plasma-optic effect in a forward biased p-i-n junction. In both the cases, the signal launched at port 1 is completely transferred at port 4 when no plasma-optic effect is considered ([OFF.sub.i] state), whereas it is transferred at port 3 ([ON.sub.1] state) thanks to the plasma-optic effect and to the consequent change in carrier concentration, which induces a [pi] phase shift between the active and the reference arms of the MZS. Similar behaviour occurs for the input signal launched at port 2. In this case, the input signal is transferred to port 3 in the [OFF.sub.2] state and to port 4 in the [ON.sub.2] state.
The waveguides, whose cross section is shown in Figure 1(c), are silicon ribs embedded in Si[O.sub.2] having core thickness [d.sub.c] = 0.05 [micro]m, rib thickness [d.sub.r] = 0.20 [micro]m, rib width w = 0.50 [micro]m, silicon and silicon dioxide refractive indices [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively, at the wavelength [lambda] = 1.55 [micro]m. The separation gap between the coupled waveguides is equal to 0.30 [micro]m. In the phase shifter region, a forward biased p-i-n diode is formed by the intrinsic silicon core and by two highly doped [p.sup.+] and [n.sup.+] regions, having carrier density [N.sub.e] = [N.sub.h] = [10.sup.20] [cm.sup.-3].
The refractive effective index change and the losses induced by the free-carrier plasma dispersion effect depends on the variation of the electron and hole distributions. The FEM is an efficient and accurate numerical technique to solve partial differential equations or systems modelling physical phenomena essential to investigate a wide spectrum of optical components. FEM transforms a very complicated problem into small elements, each solved in relation to the other, by approximating each element with suitable polynomial approximation functions. In substance, the procedure consists of eliminating the spatial derivatives by reducing the partial differential equation in a system of algebraic equations for steady state problems and in a system of ordinary differential equations for transient problems. Recently, the FEM technique has been efficiently applied to different architectures of silicon plasma dispersion modulators. In fact, the electron and the hole distribution can be easily calculated either in static analysis or dynamic analysis by using the FEM to solve the 2- D drift-diffusion equation [23,24]. Then, from the 2-D free-carrier distribution, silicon refractive index and absorption coefficient changes due to applied voltage are calculated using the well-known Soref-Bennett formulas .
The calculated average silicon refractive index change [DELTA]n and the loss coefficient [alpha] are [DELTA]n = -5.282 x [10.sup.-3] and [alpha] = 27.80 [cm.sup.-1], respectively, for an applied voltage V = 1V. According to the refractive index variation, the length of the phase shifting region [L.sub.phS] = 147.54 [micro]m was chosen to achieve the required [pi] phase shift at the wavelength [lambda] = 1.55 [micro]m. Moreover, a power consumption of 2.6 mW and a switching time [t.sub.s] [congruent to] 4 ns were evaluated by means of the FEM time dependent simulations.
Once the 2-D distribution of refractive index and absorption coefficient is known, the electromagnetic field distribution along the switch has been evaluated by the FD-BPM, which is a numerical method suitable for the analysis of strongly guiding structures. By the FD-BPM the Helmholtz wave equation:
[[nabla].sup.2] E(x, y, z) + [k.sup.2.sub.0][n.sup.2] (x, y, z)E(x, y,z) = 0 (1)
is solved by applying a finite-difference scheme by which the continuous 3-D space is discretized into a grid defined in the computation region, thus reducing the wave Equation (1) to an algebraic system. In Equation (1) [k.sub.0] is the wavenumber in vacuum and n(x, y, z) is the refractive index of the structure. A split-step algorithm was used to optimize the computation time and the transparent boundary conditions were introduced to absorb the waves outgoing from the computation window. In order to evaluate the performances of the conventional 2WG MZS and of the proposed 3WG MZS, we consider two figures of merit, i.e., the crosstalk CT and the insertion loss IL, calculated according to the following formulas:
[CT.sub.ij] = 10 x [log.sub.1o] ([T.sub.i]/[T.sub.j]) (2)
[IL.sub.ij] = 10 x [log.sub.1o] (1/[T.sub.j]) (3)
where [T.sub.i] and [T.sub.j] are the transmittances at the ports i and j when the signal is launched in input at the same waveguide corresponding to the port i.
Owing to the refractive index dispersion, the switch performances worsen as the operating wavelength is detuned from the design value, i.e., [lambda] = 1.55 [micro]m. Therefore, a spectral analysis is required to evaluate the switch bandwidth, defined as the wavelength range in which the crosstalk CT and the insertion loss IL are both below the reference values [CT.sub.R] = -15dB and [IL.sub.R] = 1.1 dB, respectively [21,27].
Figure 2 shows the crosstalk and the insertion loss in the wavelength range where both the conditions CT < -15 dB and IL < 1.1 dB are fulfilled, for the 2WG MZS in the OFF (solid curves) and in the ON (dashed curves) states. In particular, Figures 2(a) and (b) refer to the case of input signal launched at port 1, whereas Figures 2(c) and (d) refer to the case of input signal launched at port 2.
Since the 2WG-MZS becomes asymmetric in the ON state (dashed curves), owing to the refractive index change in the phase shifter, the CT and the IL spectra calculated when the input signal is launched at port 1 (Figures 2(a) and (b)) are slightly different from those calculated when the input signal is launched at port 2 (Figures 2(c) and (d)).
Figure 3 shows the crosstalk (Figure 3(a)) and the insertion loss (Figure 3(b)) for the 3WG MZS in the OFF (solid curves) and in the ON (dashed curves) states in the wavelength range where both the conditions CT < -15 dB and IL < 1.1 dB are fulfilled. In this case, the spectral behavior of the 3WG MZS remains unchanged either when the input signal is launched at port 1 or at port 2, since the device is anyway symmetric.
We have calculated that the MZS bandwidth is equal to [DELTA][lambda] = 60 nm and [DELTA][lambda] = 115 nm in the cases of two-and three-waveguide configurations, respectively. Therefore, the three-waveguide MZS exhibits an almost doubled bandwidth useful for the WDM transmission on optical NoCs.
3. 4 X 4 MACH-ZEHNDER SWITCH MATRIX
The above-mentioned analysis, through the combination of the FEM drift-diffusion model and the FD-BPM model of the electromagnetic propagation, provides a description at the physical level of the MZSs which characterizes the device behavior at the ports (as shown in Figures 2 and 3). From the knowledge of these spectra it is possible to consider the MZSs as black boxes that allow the implementation of reliable numerical models at the network level.
In this way, the behavior of the switch matrixes and of the overall network can be predicted by suitably multiplying the transfer functions according to the switch connections within the network.
As schematized in Figure 4, we focus on the analysis of a 4 x 4 switch matrix in which six MZSs are connected according to the Benes configuration . We have chosen this classical and simple configuration of switch matrix to compare the performances of the conventional 2WG MZS with those of the proposed 3WG MZS. However, for more efficient and more complex configurations the analysis would be similar .
Table 1 reports the eight states of the switch matrix that allow the connection of each input port [I.sub.i], i = 1, 2, 3, 4 with all the output ports [O.sub.j], j = 1, 2, 3, 4, with two different paths. The ON and OFF conditions, denoted respectively by 1 and 0, are also reported in Table 1 for the six MZSs.
Each signal path, connecting the input [I.sub.i] with the output [O.sub.j], involves three MZSs which can be either in the ON or in the OFF conditions. As an example, when the switch matrix is in the state 1, that is [MZS.sub.i] and [MZS.sub.5] in OFF condition and the other ones in the ON condition, the input port [I.sub.i] is directly linked to the output port [O.sub.i], for i = 1, 2, 3, 4. Therefore, for example, the signal launched at port [I.sub.1] will be transmitted at port [O.sub.i] passing through the switches [MZS.sub.i], [MZS.sub.4], and [MZS.sub.5] which are in the OFF, ON, and OFF conditions, respectively. On the other hand, the signal launched at the port [I.sub.2] will emerge from the port [O.sub.2] through [MZS.sub.1], [MZS.sub.3], and [MZS.sub.5], in the OFF, ON, and OFF conditions, respectively. Similar behavior occurs for the other two links [I.sub.3] [right arrow] [O.sub.3] and [I.sub.4] [right arrow] [O.sub.4].
In the evaluation of the switch matrix performance, the most relevant parameter is the insertion loss. In fact, the cascade of multiple devices does not significantly change the crosstalk CT, calculated as the ratio between the transmittances at the switch output ports. Conversely, the total insertion loss is the sum in dB of the IL contributions of the three MZSs encountered by the signal along the generic path.
Figures 5 and 6 show the IL spectra for the 2WG-MZS (Figure 5) and for the 3WG-MZS (Figure 6) configurations assembled into 4 x 4 switch matrix calculated at the four output ports [O.sub.1] (solid curve), [O.sub.2] (dashed curve), [O.sub.3] (dotted curve), and [O.sub.4] (dash-dotted curve) when the input signal is launched at: (a) [I.sub.1], (b) [I.sub.2], (c) [I.sub.3], and (d) [I.sub.4] input ports.
The IL curves reported in Figures 5 and 6, calculated by Equation (3) from the FD-BPM transmittance spectra, correspond to the states from 1 to 4 in Table 1. The spectra in Figures 5 and 6 are limited to the MZS bandwidth in the case of the two-and the three-waveguide configurations, respectively.
We can see that the IL spectra change according to the signal path and to the switching condition of the three switches encountered by the signals along the paths. In particular, in the case of 2WG-MZS matrix, the loss is minimum when all the three MZSs are in the OFF condition along the path, i.e., when the signal is launched at port [I.sub.1] and collected at port [O.sub.3] (dotted curve in Figure 5(a)) or when it is launched at port [I.sub.2] and collected at port [O.sub.4] (dash-dotted curve in Figure 5(b)). In fact, as shown in Figure 2 (b), the insertion loss is lower for the 2WG-MZS in the OFF state, whereas in the ON state the loss is higher, due to the propagation losses induced in the phase shifter by the plasma-optic effect.
In the case of the 3WG-MZS switch matrix, most of the signal paths are characterized by a maximum value of the IL at the edges of the considered wavelength range and a minimum value at the central wavelength [lambda] = 1.55 nm. This behavior is due to the presence of at least one MZS in the OFF state along the considered paths. In fact, in the case of a single 3WG-MZS switch in the ON state, as shown in Figure 3(b) (dashed curve), the insertion loss spectrum is almost constant, whereas in the OFF state (solid curve in Figure 3(b)) it is maximum at the edges of the considered wavelength range, reaching its minimum value at the central wavelength [lambda] = 1.55 [micro]m. This loss mechanism is mainly due to the part of the signal remaining in the central waveguide when the wavelength is detuned from the operation value [lambda] = 1.55 [micro]m.
Moreover, from Figure 6 we can see that only the signal paths with all the three MZSs in the ON state are characterized by an almost constant trend of the IL spectrum, i.e., the paths connecting ports [I.sub.3] with [O.sub.3] (dotted curve in Figure 6(c)) and port [I.sub.4] with [O.sub.4] (dash-dotted curve in Figure 6(c)). In these cases, the dominant loss mechanism is the plasma-optic effect in the phase shifter.
To better compare the performances of the 2WG-MZS and of the 3WG-MZS matrices, we report in Tables 2 and 3 the maximum insertion loss for the different inputs [I.sub.i] and outputs [O.sub.j] corresponding to the curves in Figures 5 and 6. The Tables 2 and 3 also specify the MZSs being in the ON state along the signal path from the input [I.sub.i] to the output [O.sub.j].
As reported in Table 2, in the case of 2WG-MZS matrix, the maximum insertion loss assumes the lowest value IL = 0.61 dB for all the switches along the path in the OFF state (i.e., from port [I.sub.1] to port [O.sub.3] and from port [I.sub.2] to port [O.sub.4]), whereas the maximum insertion loss assumes the greatest value IL = 3.18dB for the three switches in the ON state. Conversely, as reported in Table 3, in the case of the 3WG-MZS matrix all the possible paths from port [I.sub.i] to port [O.sub.j] have comparable losses, reaching a maximum insertion loss value IL = 3.32 dB.
Although the 2WG-MZS matrix exhibits some lower-loss signal paths, the maximum IL is comparable to that of the 3WG-MZS matrix. Therefore, to parity of maximum insertion loss and, consequently, of required input optical power, the 3WG-MZS configuration is considerably advantageous in terms of bandwidth. In fact, the three-waveguide configuration exhibits a bandwidth equal to [DELTA][lambda] = 115 nm, whereas the bandwidth of the two-waveguide one is equal to [DELTA][lambda] = 60 nm. Therefore, to parity of maximum insertion loss, considering a WDM channel spacing of 2 nm, 30 channels can be allocated in the 60-nm bandwidth of the two-waveguide MZS, whereas 57 channels can be allocated in the 115-nm bandwidth of the three-waveguide one.
Moreover, if the data rate of each transmission channel is assumed equal to 10Gb/s, the overall data rate achievable with the 2WGMZS matrix is 300Gb/s, whereas it becomes 570Gb/s for the three-waveguide configuration. This is a considerable increase in the transmission data rate which leads also to an improvement of the power efficiency in terms of energy per bit, owing to the increased number of WDM channels that can be contemporarily routed to parity of switching power . In fact, the power consumption depends only on the phase shifter operation which is the same for both the two-and the three-waveguide configurations. As estimated by the FEM model, the power required by a single switch in the ON state is 2.6 mW which corresponds to an energy per bit value for the two- and three-waveguide configurations equal to 8.7fJ/b and 4.6fJ/b, respectively.
A three-waveguide Mach-Zehnder switch configuration was proposed and analyzed through numerical simulations based on the FEM and FD-BPM models. These numerical models are used to obtain the relevant parameters necessary for the modelling and the simulation of the devices at the network level.
Compared to the conventional two-waveguide configuration, the proposed switch shows an almost doubled bandwidth thus giving enhanced performances for the WDM transmission in photonics networks on chip. In particular, considering a WDM channel spacing of 2 nm, 57 channels can be allocated in the 115-nm bandwidth of the three-waveguide MZS, whereas 30 channels are allowed in the 60-nm bandwidth of the two-waveguide conventional configuration.
This behavior also leads to an improvement of the switch efficiency in terms of energy-per-bit which is equal to 8.7 fJ/b and 4.6 fJ/b for the two- and the three-waveguide configurations, respectively. Moreover, considering the arrangement of the two MZS configurations into 4 x 4 switch matrixes, the overall insertion losses were evaluated showing that the maximum insertion losses are comparable in the two cases (i.e., IL = 3.18dB and IL = 3.38 dB, respectively, for the 2WG-MZS and 3WG-MZS assembled into 4 x 4 switch matrixes).
The research has been conducted in the framework of the European Cooperation in Science and Technology ("COST") Action MP0805 and has been supported by the Photonic Interconnect Technology for Chip Multiprocessing Architectures ("PHOTONICA") project under the Fondo per gli Investimenti della Ricerca di Base 2008 ("FIRB") program, funded by the Italian government and by the project "Regional laboratory for synthesis and characterization of new organic and nanostructured materials for electronics, photonics, and advanced technologies" funded by the Apulia Region.
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Giovanna Calo * and Vincenzo Petruzzelli
Dipartimento di Ingegneria Elettrica e dell'Informazione, Politecnico di Bari, Via Re David n. 200, Bari 70125, Italy
Received 30 November 2012, Accepted 30 January 2013, Scheduled 26 February 2013
* Corresponding author: Giovanna Calo (firstname.lastname@example.org).
Table 1. Eight states of the 4x4 switch matrix with the corresponding ON and OFF conditions, denoted respectively by 1 and 0, for the six MZSs and the input/output paths. State ON/OFF conditions for the MZSs MZS[sub.i] [MZS.sub.2] [MZS.sub.3] 1 0 1 1 2 0 0 1 3 0 1 0 4 0 1 0 5 1 0 1 6 1 1 1 7 1 0 0 8 1 0 0 ON/OFF conditions for the MZSs State [MZS.sub.4] [MZS.sub.5] [MZS.sub.6] 1 1 0 1 2 1 1 1 3 0 1 0 4 1 0 1 5 1 1 0 6 1 0 1 7 0 0 1 8 0 1 0 State I/O paths [I.sub.1] [I.sub.2] [I.sub.3] [I.sub.4] 1 [O.sub.1] [O.sub.2] [O.sub.3] [O.sub.4] 2 [O.sub.2] [O.sub.1] [O.sub.4] [O.sub.3] 3 [O.sub.3] [O.sub.4] [O.sub.1] [O.sub.2] 4 [O.sub.4] [O.sub.3] [O.sub.2] [O.sub.1] 5 [O.sub.1] [O.sub.2] [O.sub.3] [O.sub.4] 6 [O.sub.2] [O.sub.1] [O.sub.4] [O.sub.3] 7 [O.sub.3] [O.sub.4] [O.sub.1] [O.sub.2] 8 [O.sub.4] [O.sub.3] [O.sub.2] [O.sub.1] Table 2. Maximum insertion loss IL [dB] for different inputs [I.sub.i] and outputs [O.sub.j] in the case of 4 x 4 2WG-MZS switch matrix. The MZSs, which are in the ON state to allow the optical signal to be routed from input [I.sub.i] to output [O.sub.j], are also reported. OUT/IN [O.sub.1] [O.sub.2] [O.sub.3] [O.sub.4] [I.sub.1] [MZS.sub.4] [MZS.sub.4] -- [MZS.sub.6] 1.44 [MZS.sub.5] 0.61 1.46 2.06 [I.sub.2] [MZS.sub.3] [MZS.sub.3] [MZS.sub.6] -- [MZS.sub.5] 1.42 1.42 0.61 2.27 [I.sub.3] [MZS.sub.2] [MZS.sub.2] [MZS.sub.2] [MZS.sub.4] [MZS.sub.5] 1.41 [MZS.sub.3] [MZS.sub.6] 2.29 [MZS.sub.6] 2.32 2.84 [I.sub.4] [MZS.sub.2] [MZS.sub.2] [MZS.sub.3] [MZS.sub.2] 1.46 [MZS.sub.5] [MZS.sub.6] [MZS.sub.4] 2.33 2.89 [MZS.sub.6] 3.18 Table 3. Maximum insertion loss IL [dB] for different input [I.sub.i] and output [O.sub.j] conditions in the case of 4 x 4 3WG-MZS switch matrix. The MZSs, which are in the ON state to allow the optical signal to be routed from input [I.sub.i] to output [O.sub.j], are also reported. OUT/IN [O.sub.1] [O.sub.2] [O.sub.3] [O.sub.4] [I.sub.1] [MZS.sub.4] [MZS.sub.4] -- [MZS.sub.6] 3.01 [MZS.sub.5] 3.32 3.01 2.70 [I.sub.2] [MZS.sub.3] [MZS.sub.3] [MZS.sub.6] -- [MZS.sub.5] 2.30 2.30 3.32 2.70 [I.sub.3] [MZS.sub.2] [MZS.sub.2] [MZS.sub.2] [MZS.sub.4] [MZS.sub.5] 2.30 [MZS.sub.3] [MZS.sub.6] 2.70 [MZS.sub.6] 2.70 2.77 [I.sub.4] [MZS.sub.2] [MZS.sub.2] [MZS.sub.3] [MZS.sub.2] 3.01 [MZS.sub.5] [MZS.sub.6] [MZS.sub.4] 2.70 2.70 [MZS.sub.6] 2.77
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|Title Annotation:||wavelength-division multiplexing|
|Author:||Calo, Giovanna; Petruzzelli, Vincenzo|
|Publication:||Progress In Electromagnetics Research Letters|
|Date:||Mar 1, 2013|
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