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Abstract
In this theoretical work, we design elemental and higher-order wavelength-division-multiplexed cross-connects (WXCs): nonblocking space-and-wavelength routing switches to be constructed in a monolithic, industry-standard, silicon-on-insulator (SOI) chip operating at a center wavelength of 1550 nm. Each multi-spectral multi-crossbar 2×2 x Mλ “element” of the network switch is an M-fold cascade connection of λ-diverse SOI Mach-Zehnder interferometers (MZIs), each of which utilizes a nanobeam cavity in each MZI arm. Within the element, each MZI has an electro-optically (EO) controlled local PN-junction “depleter” embedded in each cavity. The cavity voltage commands are (0,0) or (V,V) where V is a “small” reverse bias. Each element can be reconfigured in 2 to 5 ps, depending on Q, with few-fJ/bit switching energy. For the M = 3 case, a compact 6-element 4×4×3λ WXC is presented. In addition, compact new designs are given for a 12-element 8×8×3λ WXC and for 16×16×8λ WXCs employing either 56 or 72 elements.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical switch fabrics such as wavelength-division-multiplexed cross-connects (WXCs) play an important role in modern data centers and complex optical communications networks. The goal of the present theoretical work is to advance the WXC art by: minimizing the number of elemental switches, eliminating passive MUX and DEMUX devices in the WXC architecture, handling multiplexed input signals with multi-spectral “element” switches, attaining ultrafast switching speed with ultralow switching energy, minimizing the footprint of the manufacturable silicon-photonics device, and by obtaining a high port count together with low insertion loss and low crosstalk.
The approach here is to present new designs for: (1) a high-transmission single-mode electro-optical (EO) nanobeam (NB) switch manufacturable in an industry-standard datacom platform (2) an ultrafast ∼2 ps PN controller for each NB cavity, (3) a Mach-Zehnder interferometer (MZI) with a stable zero-bias state, plus push-push addressing, that yields high-transmission cross and bar states, (4) a 2 × 2 x Mλ multi-spectral cross-bar made from a series connection of MZI’s that represents M wavelength channels (5) an efficient, nonblocking 4 × 4×3λ WXC using six 2 × 2×3λ elements, (6) an 8 × 8×3λ WXC using only 12 elements, and (7) a small-footprint wide-sense-nonblocking 16 × 16 × 8λ WXC using either 56 or 72 elements.
2. Design of nanobeams and electro-optical Mach-Zehnder Interferometers
The starting point of our investigation is an SiO2-encapsulated single-photonic-mode nanobeam (NB). We shall apply to our NB switch the recent results of Vasco et al., [1] who optimized the air-hole lattice. We adopt their structure in which the Si waveguide has a width of 500 nm and a thickness of 260 nm. Prior to optimization, the lattice parameter was 350 nm and the hole radius 98 nm. Their optimization procedure is to vary the hole-to-hole spacing and the hole radii in a symmetric fashion on each side of the L1 point-defect cavity as shown in Fig. 1(a).
Fig. 1. Top view of proposed SOI nanobeam: (a) point-defect cavity resonator optimized for 98% single-TE-mode transmission, (b) two identical coupled cavities within the same nanobeam.
Because of that lattice, the mode intensity profile of the TE-like fundamental mode has two small lobes in the defect cavity; an ultrasmall mode volume contained within 1.1 µm of length (configuration 1(d) of [1]). This global optimization of both high Q and high transmission for a given number of holes N on each side of the cavity was performed using a particle-swarm algorithm for the 5 holes on each side of the cavity. Of particular interest here is the case N = 8 (16 holes total) where Q = 3200 and the peak transmission is 98%. This is the unloaded Qu discussed below. To give some specifics, this N=8 lattice has a length of 5.8 µm between the outer edges of the two end holes. The 5.8 µm length offers a very compact footprint for the dual-nanobeam interferometer discussed below. The main reason for choosing the low Qu is to provide a large information bandwidth for modulated light entering the switching network as discussed below. For example, if the electro-optical (EO) construction in the intrinsic Si nanobeam cavity region reduces the Qu to a loaded QL of 2000 (spectral bandwidth of 0.78 nm), then at an operation wavelength of 1550 nm, the frequency bandwidth is 97 GHz. However, that bandwidth is reduced, as discussed below, when several element devices are connected in an optical cascade, as is done here in the switches detailed below. The unavoidable and undesired narrowing of the nanobeam cavity’s resonance profile when two or more (same-λ) interferometers are joined in series is related to the Lorentzian shape of the cavity resonance profile.
A recent investigation of coupled identical cavities within one nanobeam showed that the side-skirts of the spectral profile could be made steeper than those of the Lorentzian profile when the cavities were judiciously coupled by close proximity of the two photonic-crystal lattices. Taking this coupling approach, we present in Fig. 1(b) two N = 8 lattices that are directly adjacent to each other as a technique to sharpen or to make “more rectangular” the joint profile of the resulting resonance curve, in the manner that is illustrated in configuration 2 of [2]. The matrix application of Fig. 1(b) is described in Section 5 below.
Regarding wavelength-division multiplexed (WDM) applications of Fig. 1, the calculations of Vasco [1] show that the nanobeams have a wide frequency “stop band” that extends from 185 to 225 THz, corresponding to a wavelength range of 1330 to 1620 nm, quite adequate for coarse WDM as well as dense WDM within the telecom-datacom bands centered at 1550 nm.
Having chosen the resonators, the next step is to introduce the resonant 2 × 2 MZI structure. To gain perspective on MZI switching, an alternative to the incorporation of NBs is investigated, which is the MZI that has micro-ring-resonator (MRR) assistance. That MRR architecture was employed recently for WDM multi-channel space-and-wavelength selective switching [3]. For each wavelength channel, identical MRRs were deployed, side-coupled to the MZI arms, together with a π/2 phase bias in one arm. Then the resonances of those MRRs were driven in opposite directions about the λ-channel, using push-pull addressing to achieve cross and bar states at the MZI outputs. Arguably, this push-pull requirement is less convenient than push-push addressing because the former requires a DC “push bias” that is cancelled by the pull input, whereas the latter addressing does not need a constant voltage applied.
We propose here a push-push technique for each λ channel. The EO control technique proposed here is to form a vertical PN junction locally within the NB cavity region along the 1.1 µm cavity length in the example described above. A very fast and energy-efficient way to change the effective index of each cavity is to deplete free carriers from the waveguide core mid-region by applying reverse bias to each PN junction. The reverse-bias voltage “V” required to shift the resonance wavelength by one (or more) resonance linewidths is termed “push”, and push-push refers to identical voltage applied to each of two MZI PN junctions due to the electrically parallel connection of those junctions [4]. The push-push approach is generalized to M wavelengths in the present paper.
Considering one particular resonance wavelength, Fig. 2(a) shows a close-up view of the two MZI “arms” showing the identical NBs in each, as well as the lateral PN junction proposed for EO resonance-shifting along the wavelength axis. For convenient electrical contacting of each junction, a localized rib waveguided structure (rather than a strip) is proposed here for the “arms” structure, that is, each 500-nm x 210-nm strip rests upon a very thin 50-nm silicon platform. Localized donor and acceptor impurities are implanted into cavity side-walls of the strip and into the Si slab-wing structure along with P+ and N+ areas for contacting as illustrated in the cross-section (through-cavity) view of Fig. 2(b). The metalized contacts and voltage control circuit are shown. Figure 2(b) illustrates the two identical PN junctions and the carrier-depleted regions in the strips that overlap the TE mode propagating there. The single-mode rib waveguides are assumed to have propagation very similar to that of the strip case.
Fig. 2. (a) close-up top view of MZI rib-waveguide EO arms for a 2 × 2×1λ switch, (b) cross-section view of dual-arm assembly though the center of one 1DPhC cavity.
3. Design of the 2 × 2 x Mλ elemental switch
3.1 Architecture of a proposed 2 × 2×3λ element
The 2 × 2 x Mλ switch proposed here is a series waveguide connection of M independent 2 × 2 MZI’s where each MZI in the cascade is dedicated to a particular wavelength of the M-fold wavelength “array.” To give a clearer picture of how the 2 × 2 x Mλ device serves as a “building block” or element of a higher-order WXC, we present in Fig. 3 the specific example of the 2 × 2×3λ “multi-cross-bar” device, a schematic top view of this MZI with the three wavelengths color coded as red, green, and blue. The six air-hole lattices are not shown in order to keep the drawing simple. There are three independent voltage controllers and each of these has two electrical states: (0,0) or (V,V). An important aspect of this WXC architecture is that passive DEMUX and MUX devices are not required at inputs and outputs. Our “building block elements” have two key features: transparency of the element to non-resonant light, and independence of λ-switching, which means that switching of one wavelength does not affect the switching of another wavelength. To illustrate this, consider a particular wavelength signal λ2 that is put into the cascade. If that wavelength is not resonant with the first MZI at λ1 that the signal encounters, then that MZI will entirely reflect the λ2 signal from the NB regions because the signal is within the stop band of that MZI. Then each MZI arm gives total reflection, and because of the interference of those two reflections, there will be constructively “all” of the light transmitted to the bar port and destructively “none” of the light returning to the input port. This will give λ2 input-to-bar transport, irrespective of whether the λ1-MZI is in its (0,0) or (V,V) state. Thus, in the cascade, an input signal will get input-to-bar, input-to-bar, etc, transport until that light encounters its dedicated MZI resonance, at which location that resonant light will interfere constructively at the cross port. Also, that dedicated resonance is EO-shiftable, which means that dedicated (V,V) addressing will switch the cross-port light to the bar port.
Fig. 3. Schematic view of proposed 2 × 2×3λ three-λ-channel WXC cross-bar spatial routing switch. The air hole lattices in the NB waveguides are not shown.
The WDM switching action is illustrated symbolically in Fig. 3 by red, green, and blue columns at input and output of the cascade (a multiplexed data stream) with column width representing independent modulated signals at those wavelengths. The net result is that two switching states are available for each wavelength. There are eight possible “configurations” of the Fig. 3 WDM device, (cross or bar)1 + (cross or bar)2 + (cross or bar)3, four of which are illustrated in Fig. 4. Several possible combinations of cross and bar states for the WDM wavelength channels (green dashed lines) are shown, and Fig. 4 presents the optical power arriving at the cross port in Fig. 3. The Fig. 3 devices apply to coarse WDM. To discuss dense WDM, we define the λ-channel separation as ΔΛ, the 3-dB resonance linewidth as δλ and the available voltage-induced resonance shift as Δλ. The minimum ΔΛ is determined by how much crosstalk (CT) between channels can be tolerated, and CT is governed by both ΔΛ/δλ and Δλ/δλ . Using QL = 10,000 and Δλ/δλ = 1.5, the ΔΛ = 0.64 nm dense-WDM deployed by Kong et al., [5] is feasible, but with a reduced δλ=19 GHz information bandwidth for each switching element. If we demand the large bandwidth of the QL = 2000 example described above, then the WDM system shall have a ΔΛ of several nanometers in the 1550 nm band. For example, taking QL = 2000, a practical ΔΛ would be 3.5 nm which is 4.5 times the 0.78 nm δλ. This, together with an EO shift Δλ = 2 δλ would help keep CT low. The technical issue then is whether Δλ in the 0.78–1.56 nm range is feasible at reasonable applied voltage. Whether such Δλ can be met requires analysis of PN junction tradeoffs. If the single junction is not adequate for the low-Q case, it is quite possible that a U-shaped horizontal junction localized at each NB cavity, such as the NPN described in recent literature [6,7] would provide the needed resonance-shift-per-volt.
Fig. 4. Four addressing configurations of the Fig. 3 device, showing the cross-port optical transmission in the three adjacent wavelength channels.
Returning to Fig. 3, we can perform a Lorentzian mathematical modeling of this multi-spectral switch to predict quantitatively the optical output power from cross and bar ports as a function of λ under certain assumptions of IL, δλ, and Δλ for a given MZI. The IL is included in a cavity-to-waveguides coupling factor Qc that supplements the internal cavity loss Qi, where the total loaded Q of the NB cavity is defined as 1/QL = 1/Qc + 1/Qi. The resonance wavelength is a function of voltage, λR(V), and we define QL = λR(0)/δλ. The key equations for this formulation are then written as:
Because the wavelength of operation for channel-1 in Fig. 5 is 1550 nm, it is seen in Fig. 5(a) that the most limiting factor is the CT observed in the Bar (0,0) state of MZI-1 coming from the Cross (V,V) state of that MZI. It is clear in Fig. 5(b) that the second approach greatly alleviates this problem. Low CT is predicted.
Fig. 5. Lorentzian model of power at the cross and bar output ports of the Fig. 3 device as a function of wavelength for (0,0) and (V,V) addressing (a) channel spacing of 2.5 nm and Δλ = δλ =0.78 nm; (b) channel spacing of 3.5 nm and Δλ = 2 δλ = 1.56 nm. Only the λ1 and λ2 channels are shown.
Considering the general M-channel Fig. 3 device, the WDM input signals arrive at λ1, λ2,…λM. If we denote λR as the resonance wavelength of one MZI within Fig. 3, then considering the “compound MZI” device, we require a close alignment or actual matching of the Fig. 3 resonances to the corresponding wavelengths of the optical “wavelength-comb” source; that is, λR1 = λ1, λR2 = λ2,…λRM = λM. In practice, it is not easy to attain this matching because the device must be manufactured with very precise control of the NB air-hole lattice dimensions. One solution to this fabrication control problem is to provide on each MZI a “trimmer” for finely adjusting the nominal λR after the fabrication has taken place. To modify λR, we propose thermo-optical (TO) tuning of each NB cavity. An example is to deposit an indium-tin oxide “heater stripe” at one end of each cavity region. This would be a single ITO stripe about 50 nm in width that would appear as a vertical stripe in Fig. 2(a) (not shown). By controlling the heater current, the λR value could be controlled in 0.01 nm increments because a small temperature rise in the Si cavity induces a small change in its effective index.
3.2 MUX and DEMUX functions
Another aspect of Fig. 3 is its application as either a passive wavelength-division multiplexer or as a passive wavelength-division demultiplexer, obtained when the junction dopings and the voltage-control signals are absent. This passive use is sketched in Fig. 6, and the unused ports are terminated in absorbers, as indicated. The Fig. 6 arrangement was discussed earlier [8]. The 1 x N x Mλ architecture of [8] uses solely 1 × 2 NB MZI elements (one of four ports is dangling) and the element count is higher for the “tree” WXC of [8] than in the corresponding portion of the present N x N x Mλ’s. (The labels M and N were interchanged in [8]).
Fig. 6. Passive MUX and DEMUX operation provided by M-cascade connection of different resonance NB MZIs.
3.3 Proposed M-channel electro-optical wavelength multiplexer
We should note in passing that the Fig. 3 2 × 2 x Mλ could be modified to create a special-purpose 1 × 1 x Mλ EO modulator for “terabit” WDM modulation applications. Looking at each constituent MZI in Fig. 3, we propose to terminate each “second input” port, making Fig. 3 an array of 1 × 2 switches. Then we might consider the rather extreme example of M = 16 to illustrate the multiplexing of 16 high-speed electrical data signals onto the one “optical carrier” sent into an optical fiber. Then the EO data transmitter would look like the schematic multi-spectral arrangement of Fig. 7, where we shall assume that 16 closely spaced equal-height spectral emission lines are attained from a frequency comb laser as in Kong et al., [5] and that the FC light is sent into one waveguide that feeds the proposed 1 × 1×16 λ modulator. The Fig. 7 operation is explained as follows: First, the MZI’s resonance wavelengths are designed to be mapped to the comb wavelengths (λR1 = λ1, λR2 = λ2,…λR16 = λ16 as discussed earlier). Looking at the input, bar, and cross ports of each MZI in Fig. 7, we make a waveguide interconnection of input-to-bar-to-input-to-bar, leading to one “final output port” labeled “WDM optical signal 2” in Fig. 7. In addition, we connect all 16 of the cross ports to one bus waveguide, as shown, which then produces a second “alternative final output” labeled “WDM optical signal 1” in Fig. 7. Now we can detail the constituent EO modulation effects. When an electrical logic signal of “0” is applied to a given MZI, an optical logic signal of “0” exits the bar port; and if electric logic “1” is then applied, the result is an optical “1” at the bar port. The complimentary logical signals are produced at the cross port of this same MZI, with electrical “0” giving optical “1” and electrical “1” giving optical “0”. For that reason, the user of Fig. 7 has a choice of optical wave-train outputs: ordinary and inverted. But in either case, the device offers “automatic multiplexing” of 16 optical signals, that is 16 independent optical data streams are combined onto one waveguide output: WDM 1 and its compliment WDM 2. If we assume that each MZI is capable of 50 Gb/s EO switching, then the WDM output signal has a data rate of 0.8 Tb/s. This NB approach offers a rather small overall footprint for its photonic integrated circuit realization. Another aspect of Figs. 3 and 7 is the possible application of the present MZI devices to ultrafast multi-spectral EO logic [9].
Fig. 7. 16-channel electrical data multiplexing onto one optical carrier by means of 1 × 1×16λ EO MZI modulator driven by a matched CW frequency-comb laser.
3.4 Data bandwidth and switching time
The effective bandwidth B of each EO NB cavity is a function of the junction’s electrical bandwidth Be and the cavity’s optical bandwidth Bo, namely B = BeBo/sqrt(Be2 + Bo2). If Be is much larger than Bo (which it is here) then B = Bo to a good approximation. In frequency terms, we have Q = ν/B where ν is the 193.6 THz frequency corresponding to the 1550 nm wavelength, and B is the FWHM of the resonance lineshape. In fact, B is the information bandwidth of the switch elements. The switching time or reconfiguration time “t” of the WXC is readily found as t = 1/2πB. The reason for high Be is the short RC time constant of the junction which has a reverse bias capacitance around 1 fF. Also, a junction voltage analysis [4,10,11] reveals that the switching energy for each MZI in Fig. 3 is about 3 fJ/b. The loaded QL of the cavity refers to the Q of a fully fabricated junction in Fig. 2 where “loaded” refers to optical losses introduced by doping and scattering. Taking QL = 2000, then the optical bandwidth of the cavity Bo = 97 GHz. Our estimate of optical loss introduced by ion implants into the L1 cavity region suggests that the unloaded-Q will be reduced by about 40% from that of undoped silicon, indicating that Qu = 3200 as utilized above. In the present example, the switching time is extremely short: 1.6 ps, which suggests extremely high EO bit rates in Fig. 7 and ultrafast WXC reconfiguration generally.
4. Design of N x N x Mλ wavelength cross-connects (WXCs)
4.1 Proposed 4 × 4×3λ WXC
There are many architectures given in the literature for monochromatic N x N matrix switches, constructed usually from 2 × 2 elements. The basic idea of this paper is to substitute 2 × 2 x Mλ elements into those designs in order to achieve N x N x Mλ WXCs. The concept here is that this substitution will achieve the desired WDM result because the cross-bar switching of the N x N x λi network does not block the N x N x λj network switching. Input signals travel with little attenuation to-and-from their “λ-dedicated” MZIs. Wavelength-multiplexed signals flow into each input of the matrix (perhaps from optical fibers), and a total number of M x N independent modulated optical signals goes into the N x N x Mλ device. The total output number is also M x N. The important point here about matrix architecture is that any practical, nonblocking monochromatic N x N configuration is suitable for upgrading to our N x N x Mλ WXC. The constraint on our approach comes in for high-radix devices in which the composite bandpass of the WXC becomes unacceptably small when any input light signal passes through “too large a number” of stages.
To show, in principle, that the Fig. 3 device is an important element for higher-order nonblocking switch arrays, we have adopted the architecture of Yang et al., [12]. They showed a 6-element monochromatic architecture where four inputs transfer data to four outputs in parallel. Taking that as a foundation, we expanded the network to a 4 × 4×3λ WXC, and we deployed the Fig. 3 devices to realize in principle this higher-order network, as specified in Fig. 8. This simple, ultrafast-switching WXC has 12 input signals and 12 output signals as well as 18 control “wires.” It is based upon EO carrier depletion in our case. The Fig. 8 router is, in principle, easy to build in a silicon photonics foundry, and the photonic integrated circuit has a compact footprint. As M is increased from 3 to 8, for example, the insertion loss (IL) of each 2 × 2 x Mλ will increase, and it is an application-specific judgement call as to how much IL can be tolerated. Also, there is a burden of “precise fabrication” placed upon the 2 × 2 x Mλ elements, and the feasibility will depend upon the accuracy and expense at which the devices can be fabricated. Note that this WXC approach uses no wavelength demultiplexers at the input and no wavelength multiplexers at the output. The avoidance of DEMUX and MUX holds throughout this paper. Another aspect of Fig. 8 and subsequent figures is the fiber-optic scenario in which each input source and each output “receiver” is a λ-multiplexed fiber.
Fig. 8. Proposed structure of 4 × 4×3λ EO SOI WXC with nonblocking ultrafast reconfiguration. Each green rectangle represents a Fig. 3 device.
4.2 Design of an 8 × 8 x Mλ WXC
Next, we propose an 8 × 8 Clos-type matrix design for WDM use, and we will take the example of M=3 to illustrate the layout clearly. Figure 9 presents the 8 × 8×3λ structure: here there are 36 control wires and 12 elements in this nonblocking network switch.
Fig. 9. Schematic top view of 8 × 8×3λ WXC handling 24 signals. Each green rectangle is a Fig. 3 device.
5. Two designs for 16 × 16 × 8λ WXCs
Let us assume, as an upper limit, that a cascade of eight MZIs in the Fig. 3 configuration can be constructed with adequate control of the lattice and directional-coupler dimensions. Then we can use those 2 × 2×8λ elements in two ways to build higher-order WDXCs- by using 2 × 2’s as elements, or by using 4 × 4’s as elements. Taking the first approach, we show in the Fig. 10 block diagram a 7-stage Clos-Benes architecture that uses only 56 elemental 2 × 2×8λ devices and only 448 control wires.
Fig. 10. Proposed 16 × 16 x 8λ nonblocking WXC where each green rectangle represents a 2 × 2×8λ EO switch related to Fig. 3. Control wires not shown.
Several features of Fig. 10 are beneficial or advantageous: (1) it is non-blocking in the wide sense, (2) the element count and the wire count are both relatively low, (3) the overall footprint or area of the foundry-compatible switch is relatively small, around 0.5 mm x 0.7 mm, (4) the switch has functionality similar to that of a 128 × 128 matrix switch because there are 128 optical input signals and 128 optical output signals, (5) the insertion loss is relatively low because each signal passes through only 7 elements in cascade (7 “stages”). Generally, the total IL(dB) across any path is S x M x ILm (dB), where S is the number of stages and ILm is the IL of a one monochromatic 2 × 2 constituent, giving a total of 56 ILm in Fig. 10.
Next, we illustrate the advanced capability of Fig. 8 when taken as a WXC component for a higher-radix WXC by applying Fig. 8 to the Clos-Benes matrix architecture. Taking again eight λ-channels, and using a “perfect shuffle” of waveguide interconnections to join “quartets” of 4 × 4×8λ elements, we obtain the WXC for the 16 × 16 × 8λ presented in the block diagram of Fig. 11.
Fig. 11. Proposed 16 × 16 × 8λ WDMCC in which each green rectangle represents a 4 × 4×8λ EO matrix quite similar to the one in Fig. 8. Wavelength multiplexed signals are used in each switch input, and the multiplexing at the switch outputs can be totally controlled.
For both Figs. 10 and 11, we adopt labeling of each input signal according to its row number and its wavelength-channel number. In Fig. 11, the total number of 2 × 2×8λ elemental switches is only 72, and the total number of electrical addressing wires is only 576.
Resonant WXC devices face the fundamental problem of a reduction in information bandwidth that happens as the optical signal traverses a sequence of “narrow-spectrum” devices. Assuming identical elemental switches, the composite spectral profile narrows as light travels through switch-after-switch, which places a constraint upon the number of stages can be used. The problem is noticeable for the Lorentzian lineshapes that are found in the Fig. 1(a) NBs. To give an example, if B is the 3-dB spectral bandpass of an elemental 2 × 2 switch in frequency space, then the output bandwidth is 0.64 B for two stages, 0.44 B for 4 stages, 0.35 B for 6 stages, and 0.32 B for 7 stages. In the QL = 2000 scenario, the 7th stage bandwidth (as per Fig. 10) would be 31 GHz. If we had chosen QL = 5000, where B = 38 GHz, the 7th stage would have B = 12 GHz.
The 4 × 4 Fig. 8 modules used in Fig. 11 present a “variability” problem because the number of 2 × 2s that light passes through in Fig. 8 is either one or three, depending upon addressing. Taking the 3-stage worst-case, the Fig. 10 WXC has an S=7 advantage over the S=9 in Fig. 11. In other words, Fig. 10 has less B-narrowing and less IL.
An alternative strategy to prevent significant narrowing of B is to employ coupled cavities in each MZI as illustrated in Fig. 12. In this connection, the work of Hendrickson [2] shows that the resulting Fig. 12 resonance profile will have steeper side-skirts than those of the Lorentzian shape and will be also steeper than Gaussian with an appearance illustrated in configuration 2 of [2] where the 6-dB bandwidth was 0.45 nm for Lorentzian and 0.28 nm for two coupled cavities That’s why the Fig. 12 decrease in information band as a function of S will be more gradual than for Lorentzian NBs–motivating the use of the Fig. 12 technique for large-port-number WXCs.
Fig. 12. Close-up view of two MZI arms for the single-wavelength case of two identical NB coupled cavities resulting in a “more rectangular” spectral profile for the MZI composite-cavity resonance.
Returning to Fig. 10, an important metric is the electric power consumed by the fully addressed WXC. We begin this power estimate by calculating the energy per bit consumed by one constituent MZI within the 2 × 2×8λ element when a reverse bias of 2.5 volts (typically needed for full shift of resonance) is applied to each MZI within the element. This energy is ¼ CV2 where C is the capacitance of one EO cavity. Taking C conservatively as 1 fF, we find an energy of 3.1 fJ/b for one MZI. Multiplying this by 448, the number of MZIs, gives 1.4 pJ/b for the WXC. If we then assume a conservative data rate of 15 Gb/s applied to every electrical addressing lead in the WXC, we find a total power consumption of 21 mW for the WXC.
The CT performance of these WXCs requires further quantitative analysis beyond the scope of this paper. Speaking in qualitative terms, we can say that CT suppression is quite good in the WXCs of Figs. 3, 9 and 10. The Fig. 11 WXC is different because it relies upon the 4 x4 CT performance of Fig. 8, CT that depends upon the specific 4 × 4 configuration chosen. In [12] the 4 × 4 CT is reported as -25 dB to -9 dB at a given wavelength.
Returning to Figs. 8–11, a key question is: What are the potential applications of these WXCs? The primary potential applications of these WXCs are in three areas: (1) optical interconnection networks for high-performance systems [13], (2) spatial channel cross-connect architectures for spatial channel networks [14], and (3) disaggregated data-center networks based upon distributed fast optical switches [15] including reconfigurable architectures [16].
6. Conclusion
In conclusion, we have presented a set of new optimized L1-cavity EO nanobeam designs for elemental and higher-order wavelength-division-multiplexed cross-connects. The proposed waveguided devices are compact, nonblocking space-and-wavelength routing switches to be constructed in a monolithic, industry-standard, silicon-on-insulator (SOI) chip operating at a center wavelength of 1550 nm. Each 2 × 2 x Mλ “multi-spectral cross-bar element” of the network switch is an M-fold cascade connection of λ-diverse SOI Mach-Zehnder interferometers (MZIs), where each interferometer utilizes a nanobeam cavity in each MZI arm. Within the element, each MZI within has an independently electro-optically controlled local PN-junction “depleter” embedded in each cavity. The voltage commands are (0,0) or (V,V) (push push) where V is a “small” reverse bias. Each element can be reconfigured in about 2 to 5 ps, depending upon the QL chosen, and the switching energy is in the few-fJ/bit range. For the M = 3 case, a compact 6-element 4 × 4×3λ WXC is presented. The N x N switches considered here have WDM inputs and WDM outputs (M signals per input or output). The insight here is that if the 2 × 2 elements offer nonblocking cross-bar switching for all M λ-channels, then any N x N nonblocking architecture using those elements will give the desired nonblocking WXC operation. Specifically, new designs are given for a 12-element 8 × 8×3λ WXC and for 16 × 16 × 8λ WXCs employing either 56 or 72 elements. Low insertion loss and low crosstalk are anticipated for these architectures.
Funding
Air Force Office of Scientific Research (FA9550-17-1-0354, FA9550-19-1-0341).
Acknowledgements
The author wishes to thank Prof. Francesco De Leonardis for helpful discussions.
Disclosures
The author declares no conflict of interest.
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