1. Introduction

The recent theoretical work of Huang et al. [1] shows that a wavelength-specific 2×2 add-drop filter having high performance can be realized in the 1550-nm SOI platform by using a nanobeam (NB) waveguide segment that is coupled on both sides to bus waveguides, forming a localized three-waveguide coupler (3W-NB). This device has a unique aspect: the nanobeam supports TE₀, TE₁ and TE₂ modes, while the bus waveguides have only TE₀ propagation. The nanobeam lattice reflectors are optimized using photonic crystal engineering, and the gaps between waveguides are properly chosen to create a new traveling-wave-like Fabry Perot (FP) resonance in the 2×2. The fundamental bus waveguide mode (TE₀) is partially coupled to the higher mode in the Fabry-Perot cavity (TE₂). Then, the forward-propagating TE₂ is converted to the backward TE₀ from the right-side NB reflector (or from TE₀ to TE₂ from left-side NB reflector), which, in turn, cannot be coupled out to the Bus waveguides due to the phase mismatch. Therefore, the fields in the resonator and bus waveguides are coupled only in the forward direction, resulting in a traveling-wave-like FP resonator. In this context, the main difference between the present architecture and those based on traveling-wave microring or microdisk is that cross and bar signals can be observed from the same directions. Moreover, a smaller mode volume and better metrics are expected with respect to microring or microdisk based architecture.

At a particular resonance wavelength, a phase-matched TE₀-to-TE₂-to-TE₀ coupling was attained, and that condition produced the low-loss, low-crosstalk add-drop function, showing improved metrics with respect to the devices proposed in [2] and [3].

Looking at prior-art metrics in SOI, the add-drop filter of [2] used a single nanobeam and employed an anti-symmetric multimode periodic waveguide structure to implement mode conversion and degenerate resonant states. The results were: insertion loss ($IL$) of −1.1 dB at the drop port and crosstalk ($CT$) at the add port of −14.7 dB. In the work of [3] the building-block element consists of a 2×2 Mach-Zehnder interferometer (MZI) switch based upon dual nanobeam cavities tuned by means of the thermo-optical (TO) effect. The $CT$ at the drop port and the $IL$ at the through port were evaluated as −16.8 dB and −1.5 dB, respectively. By comparison, the resonant 2×2 3W-NB switch detailed here can be considered as even more efficient. We believe that the 3W-NB is a key candidate for the “building blocks” used to create wavelength-division-multiplexed cross-connects (WXCs) for modern data centers and complex optical communications networks.

The TO controllers do not offer the very fast switching speeds provided by the electro-optical nanobeam techniques proposed in [4–5]. However, in the context of N × N matrix switching, the reconfiguration rates given by the TO approach are generally considered to be adequate. Another nanobeam reconfiguration technique includes an indium-tin-oxide gate [6], but that method suffered from relatively high IL. A hybrid integration technique can be used for NB switching; for example, thin-film lithium niobate was integrated on SOI [7] where a resonance shift of 16 pm/V was found for high-Q modes. However, this becomes problematic in the “lower Q” context that offers the wider information bandwidth that is targeted here.

Focusing on NB Q ∼ 2000, we have engineered the 3W-NB to perform as a 2 × 2 spatial-routing switch for telecom-datacom applications in three silicon-based platforms: 1550-nm SOI, 2000-nm GeON and 2000-nm GeSON. In addition to optical communications at 2000 nm [8–10] where low-loss fibers are available [10], the Ge 3W-NB 2 × 2s are motivated generally by potential applications in chemical, medical, biological and physical sensing over the 2 to 5 µm wavelength mid-infrared (MIR) range. [11–13].

The TO approach taken here is to position a nanoscale resistance-type heater strip in the oxide cladding at a sub-micron distance above the NB cavity region. When the strip is addressed with electric current, it induces change in the NB index. The zero-power initial condition $\mathrm{\Delta }T$ = 0 is a stable state where the 2×2 is in its cross state. When the 2 × 2 is current-addressed, such as $\mathrm{\Delta }T$ = 30K, the index change induces a useful shift of the NB resonance along the wavelength axis, thereby changing the $\mathrm{\Delta }T$ = 0 cross state into the $\mathrm{\Delta }T$ = 30K bar state. To quantify this TO switching, we have applied 3D FDTD simulations to the 3W-NB structure as detailed below. The sections of this paper present the TO switch structure engineering, numerical simulation results and potential photonic-integrated-circuit switching applications.

2. Resonant 3W-NB TO 2 × 2 crossbar switch architectures

We examined both Si and Ge structures. Before going into detail, we would like to explain the choice of Si₃N₄ in the Ge MIR platform. Silicon nitride gives high MIR transmission [14] and is a CMOS-compatible material with refractive index ∼2. Therefore, as detailed in [15], silicon-on-nitride (SON) becomes a promising alternative to SOI by replacing the lossy SiO₂ bottom cladding with silicon nitride. Khan et al. [16] demonstrated the first MIR waveguide on an SON platform by bonding a silicon handling die to a low-stress silicon-nitride-coated SOI die and by subsequently removing the SOI substrate. We believe that Ge-on-SON can represent a good candidate to realize tunable MIR photonic switches by guaranteeing low losses and lower power consumption due to the 3x-higher TO coefficient that Ge offers with respect to Si.

Figures 1(a) and 1(b) show the 2 × 2 TO switch architecture. It consists of a central Fabry-Perot (FP) resonator and two symmetrically side-coupled bus waveguides. The device is physically realized in strip waveguides having height, H, and widths, ${W_b}$ and W, for bus and FP waveguides, as sketched in Figs. 1(c), 1(d) and 1(e) for SOI, Ge-on-SON and GON platforms, respectively. The surface of device is covered by a SiO₂ (SOI) or Si₃N₄ cladding layer (Ge-on-SON and GON). Electrical contacts to the nano-heater stripe are made through vertical vias that are etched into the oxide (or nitride). The strip waveguides have the width and height for single-mode and multi-mode operation, for the bus and FP waveguides, respectively. Bent S-shaped directional couplers (DCs) are used as input and output waveguides, where G represents the minimum gap between the bus and FP waveguides. Figure 1(b) indicates our NB design. The FP resonator consists of two identical mode-conversion Bragg grating reflectors with the distance L representing the cavity length. Each grating reflector is formed by fully etching a row of periodic circular holes, having constant period a. Moreover, each Bragg grating consists of two adjacent sub-sections: Mirror and Taper, where the mirror section is comprised of ${N_M}$ uniform holes with radius r and the taper section is obtained by means of ${N_T}$ holes having radii adiabatically changed by amount $\mathrm{\Delta }r$. The cavity length L and the grating period a are chosen in order to induce resonant modes near 1550 nm for SOI and near 2000 nm for Ge-on-SON (or GON) platforms. In addition, the grating period is designed to optimize the back reflection between the fundamental TE mode and the higher-order TE mode (TE₀/TE₂ in the following analysis). As mentioned, resonance tuning is actuated by a TO heater strip deposited, with micro-spacing, over the FP resonator [the orange stripes in Figs. 1(c), 1(d) and 1(e)]. As outlined in [17], the TO technique can be considered as an efficient tool to induce refractive index changes ($\mathrm{\Delta }n$) with low-power consumption. Indeed, due to silicon’s or germanium’s thermo-optic coefficient $dn/dT$=1.86×10⁻⁴ K⁻¹ or 5.85×10⁻⁴ K⁻¹, the $\mathrm{\Delta }T$ required to achieve a $\mathrm{\Delta }n$ value that is able to shift the resonance of about one linewidth is not excessive.

 

Fig. 1. (a) Schematic 3D view of the 2 × 2 crossbar switch based on three coupled waveguides with central nanobeam (3W-NB); (b) Schematic top view of the 2 × 2 crossbar switch showing NB mirrors, hole tapers and point-defects cavity; (c) Cross section of the 3W-NB based on the SOI platform; (d) Cross section of the 3W-NB based on the Ge-on-SON platform; (e) Cross section of the 3W-NB based on the GON platform.

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The resonant 2 × 2 crossbar switch design and simulations require very robust mathematical models to be as flexible and accurate as possible. For that purpose, in the following section we have adopted the three-dimensional (3D) finite-difference time-domain (FDTD) method. This approach allows us to determine the overall device operation even if it is well known to be time- and memory-consuming.

3. Numerical results

The 2×2 crossbar switch is investigated in this section, and after that an analysis of tunable operation is given. For all devices, the wavelength of operation λ(op) = λ(res) = ${\lambda _R}$ is near 1550 nm (SOI) or 2000 nm (Ge) . We start by adopting the structural parameters reported in Ref. [1] for an SOI 3W-NB. This represents our benchmark in order to design the crossbar switch operating at 2000 nm based on the Ge-on-SON (GON) platform.

The design rules for both SOI and Ge platforms, are oriented toward using the resonant 3W-NB as a building block for a 2 × 2 × M$\lambda $ switch consisting of a series waveguide connection of M independent 2×2 3W-NB’s where each 3W-NB in the cascade is dedicated to a particular wavelength of the M-fold wavelength “array.” In turn, the 2 × 2 × M$\lambda $ device serves as a fundamental element of a higher-order WXC. In the context of dense WDM, we define the $\lambda $-channel separation as $\Delta \mathrm{\Lambda }$, the 3-dB resonance linewidth of a 2×2 as $\delta \lambda $ and the available thermally-induced resonance shift as $\Delta {\mathrm{\lambda }_R}$. As detailed in [18], the minimum $\Delta \mathrm{\Lambda }$ is determined by how much $CT$ between channels can be tolerated, and $CT$ is governed by both $\Delta \mathrm{\Lambda }/\delta \lambda $ and $\Delta {\mathrm{\lambda }_R}/\delta \lambda $. In a recent work, Soref [18] outlined that taking a resonance quality factor $Q$ = 2000 (bandwidth 96.7 GHz), a practical $\Delta \mathrm{\Lambda }$ would be 3.5 nm in the 1550 nm resonance case, a spacing that is 4.5 times the 0.78 nm $\delta \lambda $ . In this context, a shift $\Delta {\mathrm{\lambda }_R}$ = $2\cdot \delta \lambda $ would be considered in order to keep $CT$ low. The above- mentioned requirements lead us to modify the dense-WDM deployed by Kong et al. [19], where $Q$ = 10000, $\Delta \mathrm{\Lambda }$=0.64 nm and $\Delta {\mathrm{\lambda }_R}/\delta \lambda $=1.5 were used. The technical issue then is whether $\Delta {\mathrm{\lambda }_R}$ in the $\delta \lambda $-$2\cdot \delta \lambda $ range is feasible at reasonable induced $\Delta T$ in the presence of resonant modes having quality factor Q in the 1000-to-2000 range. This represents the goal of the following analysis. With reference to Figs. 1(b) and 1(c), the 3W-NB crossbar switch is physically realized in SOI wire waveguides having $H$=220 nm, $W$=1000 nm and ${W_b}$ = 340 nm. The Bragg grating sections are created by using the following structural parameters: $r$=80 nm, $a$=360 nm, $\Delta r$=10 nm, ${N_M}$=36, and ${N_T}$=7. Moreover, the cavity length L is assumed to be 4.04 µm. Hereinafter we focus the design and analysis on the TE polarization, specifically the TE₀ fundamental optical mode represents the input mode, and the Bragg grating period a has been designed to reflect TE₀/TE₂. In this context, 3D FDTD simulations record a resonance wavelength ${\lambda _R}$=1551.72 nm (Cross state: $\Delta T$=0 K) and $d{\lambda _R}/dT$ = 0.0738 nm K⁻¹. In our simulations we have considered a distributed heating effect, i.e., the induced $\Delta T$ is also assumed applied at the S-shaped waveguides of the DCs. On the basis of these results, a temperature change $\Delta T$ of 50K, which induces $\Delta {\mathrm{\lambda }_R}$ =3.69 nm, can help to meet the condition $\Delta {\mathrm{\lambda }_R} \ge \; 2\cdot \delta \lambda $ for Q values ranging between 1000 and 2000. Considering the Fig. 1(a) micro-heater, we estimate that the thermal power required for DT = 50 K is in the 0.1 to 1.0 mW range, judging from the experimental nanobeam results of Zhang et al. [20]. The total quality factor Q takes into account a cavity-to-waveguides coupling factor ${Q_c}$ that supplements the intrinsic factor $ {Q_i}$ (loss depending, mainly scattering loss from the holes), where the total Q is defined as $1/Q = 1/{Q_c} + 1/{Q_i}$ of the NB cavity.

After attaining the above results, a parametric investigation of the switching mechanism in terms of $IL$ and $CT$ as a function of the DC gap G was carried out, assuming the Bar state for $\mathrm{\Delta }T$=50 K. The main features of the 2×2 3W-NB crossbar switch operating at ${\mathrm{\lambda }_R}$=1551.72 nm, having $Q$=1222.4, ${Q_c}$ = 1290.9 and ${Q_i}$=23055, are then summarized in Table 1, where the insertion loss and crosstalk parameters are extracted considering the spectra simulated by means of 3D-FDTD at the Bar-1 and Cross-1 ports [see Fig. 1(a)]. Thus, Table 1 indicates that a good trade-off between low $IL$ and low $CT$ can be obtained for $G$=250 nm. In this context, Fig. 2(a) shows the transmission spectra for $\mathrm{\Delta }T$=0 K (Cross state) and for $\mathrm{\Delta }T$=50 K (Bar state). Moreover, the y-component of the mode electric field at ${\mathrm{\lambda }_R}$=1551.72 nm is plotted in Figs. 2(b) and 2(c) for $\mathrm{\Delta }T$=0 K and $\mathrm{\Delta }T$=50 K, respectively.

 

Fig. 2. (a) Transmission spectra for Cross-1 state and Bar-1 states; (b) y-component of mode electric field at ${\lambda _R}$=1551.72 nm for Cross state (zoom-in); (c) y-component of mode electric field at ${\lambda _R}$=1551.72 nm for Bar state (zoom-in). Parameters: $H$=220 nm, $W$=1000 nm, ${W_b}$ = 340 nm, $G$=250 nm, $r$=80 nm, $a$=360 nm, $\Delta r$=10 nm, ${N_M}$=36, ${N_T}$=7, and $L$ = 4.04 µm.

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Table 1. Calculated 2 × 2 switching performance for 3W-NB crossbar switch in the SOI platform.

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Turning now to the 3W-NB crossbar switch based upon the Ge-on-SON platform, we performed parametric investigations with results presented in Figs. 3(a)–3(b), and Figs. 4(a)–4(b). Moreover for a given value of the grating period, we have selected, among all the resonant cavity modes, the one with highest metrics. In this context, we indicate with m^th and (m+1)^th the resonant cavity modes with resonance wavelengths (depending on the parameter $a$) ranging from 1970nm to 1978nm and from 2024nm to 2044nm, respectively. In particular for the paramters used in our simulations, we record three different resonant modes in the wavelength range 1910nm-2100 nm. The first resonant mode at lowest resonance wavelength shows always lower metrics, then hereafter we set m=2.

 

Fig. 3. (a) Quality factor and resonance wavelength as a function of the grating period in the Cross state condition; (b) Switch metrics in terms of insertion loss and crosstalk as a function of grating period and for both Cross and Bar states. Parameters: $H$=200 nm, $W$=1200 nm, $G$ = 200 nm, ${W_b}$ = 420 nm, $r$=80 nm, $\Delta r$=10 nm, ${N_M}$=36, ${N_T}$=7, and $L$ = 4.04 µm (Ge-on-SON).

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Fig. 4. (a) Quality factor in Cross state and insertion losses in both Cross and Bar states as a function of bus waveguide width (Ge-on-SON); (b) Crosstalk as a function of the bus waveguide width, for both Cross and Bar states (Ge-on-SON). Parameters: $H$=200 nm, $W$=1200 nm, $t$=50 nm, $G$ = 200 nm, $a$=362 nm, $r$=80 nm, $\Delta r$=10 nm, ${N_M}$=36, ${N_T}$=7, and $L$ = 4.04 µm.

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With reference to Figs. 1(b) and 1(d), the 3W-NB crossbar switch is physically realized in Ge wire waveguides having $H$=200 nm, $W$=1200 nm, $t$ = 50 nm, $r$=80 nm, $\Delta r$=10 nm, ${N_M}$=36, ${N_T}$=7 and $L$=4.04 µm. Figure 3(a) shows the quality factor Q and the resonance wavelength ${\lambda _R}$ as a function of the grating period a, assuming ${W_b}$ = 420 nm and $G$=200 nm. In the plot we have selected ${\lambda _R}$ inducing minimum $IL$ in the Cross state. The plot indicates that a Q factor ranging between 1000 and 2000 can be obtained by changing a between 350 nm and 365 nm. Moreover, our thermal investigations indicate that the resonance wavelength change with temperature has a slope of $d{\lambda _R}/dT$=0.22 nm K⁻¹, inducing the condition $\Delta {\mathrm{\lambda }_R} \ge \; 2\cdot \delta \lambda $ with just $\Delta T$=30 K assumed hereinafter as Bar state. The switch metrics in terms of $IL$ and $CT$ are shown in Fig. 3(b) for both Cross and Bar states. The data record that a very good trade-off between low $IL$ and low $CT$ can be obtained with a grating period $a$=362 nm. With the aim of optimizing the 3W-NB crossbar design, we performed parametric simulations changing the bus waveguide width ${W_b}$ in the 350 nm-500 nm range and assuming $a$=362 nm. In particular, Fig. 4(a) shows Q in the Cross state and $IL$ for both Cross and Bar states as a function of ${W_b}$, while the $CT$ metrics are plotted in Fig. 4(b) under the same conditions. The curves indicate that ${W_b}$=460 nm can represent the best trade-off choice. In the simulations the resonance wavelength has been calculated as ${\lambda _R}$=2024nm, and the quality factors as $Q$=1576.9, ${Q_c}$ = 1637.1 and $ {Q_i}$=42866.

After attaining the above results, Fig. 5(a) shows the transmission spectra for $\Delta T$=0 K (Cross state) and $\Delta T$=30 K (Bar state). Moreover, the y-component of the electric field at ${\lambda _R}$=2024 nm is plotted in Figs. 5(b) and 5(c) for $\Delta T$=0 K and $\Delta T$=30 K, respectively, and showing the switch crossbar behavior. Under this hypothesis, the calculated metrics are: −0.32 dB $IL$ and −20.97 dB $CT$ and −0.26 dB $IL$ and −17.66 dB $CT$ for the Cross and Bar states, respectively. Moreover, the simulation data record $Q$=1577.2, $\delta \lambda $=1.283 nm, and $\Delta {\mathrm{\lambda }_R}$=6.6 nm (at $\Delta T$=30 K).

 

Fig. 5. (a) Transmission spectra for Cross state and Bar state (Ge-on-SON); (b) y-component of mode electric field at ${\mathrm{\lambda }_R}$=2023.8 nm for Cross state (zoom-in); (c) y-component of mode electric field at ${\mathrm{\lambda }_R}$=2023.8nm for Bar state (zoom-in). Parameters: $H$=200 nm, $W$=1200 nm, ${W_b}$ = 460 nm, $G$=200 nm, $t$=50 nm, $ r$=80 nm, $a$=360 nm, $\mathrm{\Delta }r$=10 nm, ${N_M}$=36, ${N_T}$=7, and $L$ = 4.04 µm (Ge-on-SON).

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Finally, we performed similar investigations on the GON platform, assuming the same structural parameters as in Ge-on-SON except for the strip height fixed here as $H$=250 nm. Here, the simulations indicate that the optimum resonance wavelength in the Cross state is ${\lambda _R}$=2057 nm, which changes with the temperature with a slope of about $d{\lambda _R}/dT$=0.24 nm/K. Thus, $\Delta {\mathrm{\lambda }_R}$=7.2 nm is obtained for $\Delta T$=30 K. After attaining the above results, a parametric investigation of the switching mechanism in terms of $IL$ and $CT$ as a function of the bus waveguide width ${W_b}$ was carried out, assuming the Bar state for $\Delta T$=30 K. The main features of the 2×2 3W-NB crossbar switch operating at ${\lambda _R}$=2057 nm are then summarized in Table 2.

Table 2. Calculated 2 × 2 switching performance for 3W-NB crossbar switch in the GON platform^a.

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For the case with ${W_b}$=460 nm, the simulations record $Q$=1673, ${Q_c}$ = 1753.2 and $ {Q_i}$=36691.

If we consider the geometric features of the crossbar switch discussed in this paper, we see that all the sections of the nanobeam have nanometer-scale features that require high precision in the fabrication of the device. In practice, there will always be fabrication errors related to dimensional inaccuracies in the hole spacing and size. Such errors will give rise to unwanted increases in the IL and resonance wavelength shift with respect to the designed values. In this sense, we have performed a number of simulations by increasing the hole spacing and radius, starting from the designed values. The results of our simulations indicate that for SOI platform we record $d{\lambda _R}/da$=0.15 nm/nm, $dIL/da$=-0.21 dB/nm, $d{\lambda _R}/dr$=-0.49 nm/nm, $dIL/dr$=-0.24 dB/nm. Similarly for Ge-on-SON platform, we obtain $d{\lambda _R}/da$=1.88 nm/nm, $dIL/da$=-0.02 dB/nm, $d{\lambda _R}/dr$=-0.378 nm/nm, $dIL/dr$=-0.11 dB/nm (GON gives very close values).

4. Integrated-photonic switching circuit applications

Having found very good 2 × 2 metrics, we want to examine “higher-order opportunities” for the integrated-photonic devices. Our first proposal, Fig. 6(a), shows the cascade structure of a multi-wavelength 2 × 2×3$\lambda $ multi-cross-bar switching “element” that represents the general 2 × 2 × M$ \lambda $ element. The specific addressing here is for the cross-${\lambda _1}$, cross-${\lambda _2}$, bar-${\lambda _3}$ configuration. Heaters are voltage-addressed as (0,0,V). This 3W-NB’s element is functionally equivalent to the MZI element in Fig. 3 of Soref [18]. These M$\lambda $ 3W-NB elements can be immediately interconnected to create the 8 × 8 × M$\lambda $ and 16 × 16 × M$\lambda $ wavelength-multiplexed cross-connect switches presented in Figs. 9 and 10 of [18]. Figure 6(b) illustrates the application of Fig. 6(a) in a coarse WDM system that has three channels. For (0,0,0) heaters, if the wavelength of operation is the resonance wavelength for each channel, then “off-resonance light” traveling within Fig. 6(a) is in the bar state for every channel; whereas an on-resonance signal experiences the cross state—a state that can be changed to bar, if desired, by TO heating. There is no bandwidth narrowing within Fig. 6(a).

 

Fig. 6. (a) Schematic view of proposed 2 × 2×3$\lambda $ three-$\lambda $-channel WXC cross-bar spatial routing switch. The air hole lattices in the NB waveguides are not shown. (b) Transmission spectra in Cross and Bar states, for each channel.

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Next, in order to illustrate the “matrix” capability of the Fig. 6(a) devices, we propose in Fig. 7 a specific WXC. This figure shows how a 16 × 16 × 4$\lambda $ Benes non-blocking WXC with wavelength-multiplexed inputs and outputs is constructed. At the outputs of Fig. 7, the available information bandwidth is 32% of the element bandwidth.

 

Fig. 7. Schematic view of 16 × 16 × 4$\lambda $ Benes non-blocking wavelength division cross-connect with multiplexed inputs and outputs. A close-up view of four “elements” within the 7-stage matrix is also shown.

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The Fig. 6(a) “elements” can also be used to realize a multi-spectral, multi-resonant TO-reconfigurable, programmable hexagonal “mesh” (integrated circuit) as sketched in Fig. 8(a). The optical inputs and outputs are two wavelength-channels multiplexed in one waveguide. For each $\lambda $-channel this mesh is configured simultaneously and independently by a λ-dedicated group of TO heater addressing currents. Bandwidth narrowing limits the scale of this mesh to a small scale. Another opportunity that is afforded by the architecture of Fig. 6(a) is to realize a reconfigurable, programmable multi-$\lambda $ “diamond mesh” for computational and inverse-design applications, as sketched in Fig. 8(b). Simultaneous and independent computation at two wavelengths is offered. The overall circuit performance in Fig. 7 is estimated by selecting the specific elements; for example, the G = 250-nm elements in Table 1 above. Then the Fig. 7 output bandwidth is 32% of 158 GHz or 50.5 GHz, while the worst-case overall CT is 7 × 0.49 dB or 3.3 dB.

 

Fig. 8. (a) Schematic view of multi-spectral, multi-resonant TO-reconfigurable, programmable hexagonal mesh based upon Fig. 6(a); (b) Schematic view of a reconfigurable, programmable, multi-resonant diamond mesh based upon Fig. 6(a) (inter-element TO phase shifters are not shown).

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The G = 300 nm element choice offers 32 GHz bandwidth and 6.4 dB IL with improved CT performance. In the circuit of Fig. 8(a) the number of hexagonal “cells” would probably be limited in practice to 5 or 6 by bandwidth narrowing and the build-up of IL and CT as an optical signal traverses the circuit. For these reasons, the diamond size in the Fig. 8(b) circuit would probably be limited in practice to 5 × 5.

5. Conclusions

In this paper the 3D-FDTD approach has been applied to quantify the TO-switching-performance metrics of compact resonant 2 × 2 cross-bar switches comprised of three coupled waveguides with central nanobeam (3W-NB) deployed in SOI and Si-based Ge-on-SON and GON platforms that operate around 1550 nm and 2000 nm, respectively. The TE-polarized routing switch has one stable state (cross) that does not require any holding power. Simulations indicate that the electrically addressed TO effect is an efficient way of inducing the bar state, preserving low-power control and low insertion loss. The reconfiguration time is judged as sufficiently short for most matrix-switch applications; for example, a TO transient-response time in the 5 to 10 µsec range has been measured in 2×2 TO MZI element switches [21].

Taking the TE₀ polarization for input light and designing the NB waveguide in order to optimize the coupling between TE₀ and TE₂, output spectra at the Cross and Bar ports have been computed, and the $IL$ and $CT$ metrics are found to be excellent at both low and medium TO drive levels. For example, at 158.16 GHz bandwidth (Q = 1222), −0.47 dB $IL$ and −25 dB $CT$ and −0.35 dB $IL$ and −13.4 dB $CT$ have been recorded for the SOI platform in the Cross and Bar states, respectively, assuming $\Delta T$=50 K. Similarly, the metrics for Ge-on-SON (GON) platform have been evaluated as: −0.32 (−0.40) dB $IL$ and −20.97(−27.1) dB $CT$ and −0.26(−0.195) dB $IL$ and −17.66(−18.91) dB $CT$ for the Cross and Bar states, respectively, assuming $\Delta T$=30 K. In this example, the bandwidth was 93.98 GHz at Q = 2200, and 87.17 GHz at Q = 1673 for Ge-on-SON (GON), respectively. Finally, we have presented a set of applications for the compact resonant 2×2 3W-NB switch in higher-order photonic-integrated-circuit “matrix/mesh” applications. First, we form a 2 × 2 × M$\lambda $ “multi-spectral cross-bar element” using an M-fold cascade connection of $\lambda $-diverse 3W-NBs. Within an element, each 3W-NB is independently thermo-optically controlled by means of its heater-voltage commands (0) or (V) for state selection. Those elements are deployed, for example, as building blocks in higher-order wavelength-division-multiplexed cross-connects (WXCs). Specifics are presented for realizing a 16 × 16 × M$\lambda $ WXC, which is a compact, nonblocking space-and-wavelength routing switch amenable for manufacture in the monolithic, industry-standard SOI platform and in the two, related Si-based MIR platforms. We have also proposed here architectures for reconfigurable, multi-resonant, programmable hexagonal and diamond meshes.