1. INTRODUCTION

Over the past several decades, great achievements have been made in optical communication technologies [1–8]. It is well known that optical communication has been widely adopted in long-distance applications such as backbone, metropolitan, and access networks due to its great advantages in information capacity, latency, and power consumption over electrical communication [1–4]. For the same reasons, optical communication is also being adopted in short-distance applications such as rack-to-rack interconnect of high-performance computers and data center networks [7,8].

For all applications, one serious challenge is to continuously increase the information capacity carried in a physical channel to meet the ever-increasing application bandwidth demand [1–6]. Consequently, various multiplexing technologies, such as time-division multiplexing, wavelength-division multiplexing (WDM), and polarization-division multiplexing, have been intensively explored and successfully deployed in optical communication systems [1–4]. Exploding networking traffic growth, however, demands for optical communication and interconnect systems to continue scaling cost-effectively. New forms of optical parallelism are needed. Mode-division multiplexing (MDM) is one of the promising technologies to increase the information capacity seamlessly, allowing multiple channels of information to be transmitted using the orthogonal spatial modes of a fiber or waveguide [9–34]. Various mode multiplexers and de-multiplexers based on optical fiber [9–19], ${\mathrm{Si}}_3{\mathrm{N}}_4$ [20], and silicon waveguides [21–32] have been proposed and demonstrated. Other multimode devices such as waveguide crossings and bends have also been reported [33,34].

Switching information optically is another big challenge in optical communication and interconnect systems [35–47]. Several architectures proposed several decades ago, such as Crossbar, Benes, and Spanke–Benes, constitute the footstone of the optical space switching [35,36]. Various optical switches based on these architectures have been demonstrated on silicon-on-insulator platforms [42–46]. However, most of them are made for single-mode operation, and hence cannot be used for systems with MDM where information switching amongst different spatial modes is required. A great deal of effort has been made to address such a challenge. The first silicon multimode optical switch was reported by Stern et al. [47]. It is based on microrings and capable of $1\times 2$ mode switching. Recently, a silicon $2\times 2$ two-mode dual-polarization optical switch and a silicon $2\times 2$ four-mode optical switch based on Mach–Zehnder interferometers have been demonstrated [48,49]. A silicon high-speed optical mode-selective switch and a reconfigurable optical add–drop multiplexer based on mode multiplexing/de-multiplexing have also been reported [50,51]. In this paper, three general architectures for on-chip optical space and mode switching are proposed, which are optimized for optical space switching, optical space switching plus local optical mode switching, and global optical mode switching, respectively. A silicon thermo-optic $2\times 2$ four-mode optical switch capable of performing the three optical switching functionalities is experimentally demonstrated.

2. GENERAL ARCHITECTURES FOR OPTICAL SPACE AND MODE SWITCHING

A. Type-I $\mathsf{N}\times \mathsf{N}$ Multimode Optical Switch

Figure 1 shows the schematics of the type-I $N\times N$ multimode optical switch composed of $N1\times M$ mode de-multiplexers, $MN\times N$ non-blocking single-mode optical switches, and $NM\times 1$ mode multiplexers. In this architecture, $N$ mode-multiplexed optical signals are injected into $N$ input multimode waveguides. Each mode-multiplexed optical signal is then de-multiplexed into $M$ output single-mode waveguides by the corresponding mode de-multiplexer. The $NM$ outputs of $N1\times M$ mode de-multiplexers are then shuffled to the input ports of $MN\times N$ single-mode optical switches with all mode channels having identical mode order connected to the input ports of one $N\times N$ single-mode optical switch, as depicted in Fig. 1. And the output ports of the $MN\times N$ single-mode optical switches are connected to $NM\times 1$ mode multiplexers in a similar fashion. When the $MN\times N$ single-mode optical switches operate with an identical switching pattern, the entire mode group of an input multimode waveguide can be switched to a specific output multimode waveguide simultaneously. By changing the identical switching pattern of the $MN\times N$ single-mode optical switches, the type-I multimode optical switch is capable of optical space switching of $N$ groups of optical signals from its $N$ input multimode waveguides $(I_1,I_2,\cdots ,I_N)$ to its $N$ output multimode waveguides ($O_1,O_2,\cdots ,O_N$). The type-I multimode optical switch has $N!$ routing states.

 

Fig. 1. Schematics of the type-I $N\times N$ multimode optical switch (M-DEMUX, mode de-multiplexer; M-MUX, mode multiplexer; SM-OS, single-mode optical switch).

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B. Type-II $\mathsf{N}\times \mathsf{N}$ Multimode Optical Switch

Figure 2 shows the schematics of the type-II $N\times N$ multimode optical switch composed of $N1\times M$ mode de-multiplexers, $NM\times M$ non-blocking single-mode optical switches (shown in rectangles), $MN\times N$ non-blocking single-mode optical switches (shown in rounded rectangles), and $NM\times 1$ mode multiplexers. On the base of the type-I architecture, the type-II $N\times N$ multimode optical switch adds $NM\times M$ non-blocking single-mode optical switches between the $N1\times M$ mode de-multiplexers layer and the $MN\times N$ single-mode optical switches layer. The $M$ spatial modes from an input multimode waveguide are converted to $M$ fundamental modes by the corresponding mode de-multiplexer, and are then space switched to $M$ output single-mode waveguides by the follow-on $M\times M$ single-mode optical switch. If $NM\times M$ single-mode optical switches operate with an identical switching pattern, the type-II $N\times N$ multimode optical switch performs the same functionalities as the type-I switch. If $NM\times M$ single-mode optical switches operate with different switching patterns, optical mode switching will occur. In other words, the type-II $N\times N$ multimode optical switch is capable of not only optical space switching amongst its $N$ input multimode waveguides and $N$ output multimode waveguides, but also optical mode switching amongst different spatial mode channels within the optical link $I_m\to O_n$, where $m$, $n$ denote the input and output multimode waveguide number, respectively. The local optical mode switching makes the type-II multimode optical switch more powerful in functionality than the type-I switch. The type-II $N\times N$ multimode optical switch has $N!$ routing states for optical space switching. In each of these routing states, there are an additional ${(M!)}^N$ optical mode switching states enabled by the addition of $NM\times M$ non-blocking single-mode optical switches. Together, a type-II $N\times N$ multimode optical switch has a total of ${(M!)}^{N}N!$ routing states.

 

Fig. 2. Schematics of the type-II $N\times N$ multimode optical switch.

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C. Type-III $\mathsf{N}\times \mathsf{N}$ Multimode Optical Switch

Figure 3 shows the schematics of the type-III $N\times N$ multimode optical switch composed of $N1\times M$ mode de-multiplexers, one $MN\times MN$ non-blocking single-mode optical switch, and $NM\times 1$ mode multiplexers. It is a completely non-blocking architecture that can switch any mode channel in the input multimode waveguides to any mode channel in any of the output multimode waveguides without blocking. The type-III $N\times N$ multimode optical switch has $(MN)!$ routing states.

 

Fig. 3. Schematics of the type-III $N\times N$ multimode optical switch.

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It should be noted that the aforementioned three types of multimode optical switches are optimized for different functionalities. The type-I multimode optical switch is capable of optical space switching only. The type-II multimode optical switch is improved with local optical mode switching in addition to optical space switching. It enables a lot more routing states than the type-I multimode optical switch, but it is not a completely non-blocking yet. The type-III multimode optical switch is truly non-blocking global optical mode switching. It is the most powerful in functionalities but the largest in footprint and the highest in power consumption. If all single-mode optical switches are based on a Spanke–Benes network, the total number of $2\times 2$ switch units needed is $MN(N-1)/2$, $MN(M+N-2)/2$, and $MN(MN-1)/2$ for type-I, type-II, and type-III multimode optical switches, respectively. If a Benes network is used instead, the total number of $2\times 2$ switch units needed is $MN({\log }_{2}N-1/2)$, $MN({\log }_2(MN)-1)$, and $MN({\log }_2(MN)-1/2)$ for type-I, type-II, and type-III multimode optical switches, respectively.

3. PROOF OF CONCEPT OF THE MULTIMODE OPTICAL SWITCH

A. Device Architecture and Design

Since the type-III multimode optical switch is capable of the functionalities of both type-I and type-II switches, we choose to implement a type-III $2\times 2$ four-mode optical switch for proof of concept. It is composed of two $1\times 4$ mode de-multiplexers, one $8\times 8$ single-mode optical switch, and two $4\times 1$ mode multiplexers, as depicted in Fig. 4(a). The propagation loss and optical crosstalk of the waveguide crossings can be very low with proper design and implementation as reported previously [44,46]. The $8\times 8$ single-mode optical switch is based on Benes network as it has fewer $2\times 2$ switch units than other networks such as Spanke–Benes and crossbar [35,36]. Two auxiliary mode multiplexers and two auxiliary mode de-multiplexers are integrated with the type-III $2\times 2$ four-mode optical switch for the purpose of performance characterization. Several structures have been utilized to realize mode multiplexing and de-multiplexing, such as the adiabatic coupler [21], multimode interference coupler [22,23], asymmetric Y-junction [24,25], and asymmetric directional coupler (ADC) [26–29]. The chosen mode multiplexer and de-multiplexer are based on ADCs as they are more compact and more scalable. Considering the compatibility with the electro-optic tuning scheme in the future, a silicon rib waveguide with 70 nm slab thickness is used to construct the ADCs. The rib waveguides carrying the ${\mathrm{TE}}_0$, ${\mathrm{TE}}_1$, ${\mathrm{TE}}_2$, and ${\mathrm{TE}}_3$ modes are 400, 916, 1416, and 1916 nm in width, respectively. The optimized coupling lengths for the ${\mathrm{TE}}_1$, ${\mathrm{TE}}_2$, and ${\mathrm{TE}}_3$ modes are 13, 15, and 19 μm, respectively. Adiabatic tapers connecting the waveguides with different widths are 10 μm in length. Previous work indicates that the optical bandwidths of the mode multiplexer/de-multiplexer based on ADCs are relatively large, which makes them suitable for WDM application [28,31,32]. Although both Mach–Zehnder optical switches and microring optical switches are capable of manipulating WDM signals, the former has a larger tolerance to imperfect fabrication and a lower temperature sensitivity [43,44,52]. Two MMI couplers that are 6 μm in width and 43 μm in length and one thermo-optic phase shifter with 200 μm length are utilized to construct the Mach–Zehnder optical switches. A silicon inverse taper covered by an air-bridge $6\mathrm{\mu m}\times 6\mathrm{\mu m}$ silicon dioxide waveguide is used to reduce the coupling loss between the silicon waveguide and the normal single-mode fiber [53,54] to about $3\mathrm{dB}/\text{facet}$.

 

Fig. 4. (a) Schematics and (b) micrograph of a type-III $2\times 2$ four-mode optical switch.

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Several notations are adopted to facilitate the following description. $I_m^i$ ($i=0$, 1, 2, 3 and $m=1$, 2) denotes the input single-mode waveguide for the $i$th-order spatial mode of the auxiliary mode multiplexer $m$. ${(I_m^i)}^{\prime }$ denotes the output single-mode waveguide for the $i$th-order spatial mode of the mode de-multiplexer $m$. $O_m^i$ denotes the output single-mode waveguide for the $i$ th-order spatial mode of the auxiliary mode de-multiplexer $m$. ${(O_m^i)}^{\prime }$ denotes the input single-mode waveguide for the $i$th-order spatial mode of the mode multiplexer $m$. The optical link from the input single-mode waveguide $I_m^i$ to the output single-mode waveguide $O_n^j$ is denoted as $I_m^i\to O_n^j$. The switch unit in the “bar” state is denoted as $S^B$, and that in the “cross” state is denoted as $S^C$.

B. Device Fabrication

The device is fabricated on an 8-inch silicon-on-insulator wafer with a 220-nm-thick top silicon layer and a 3-μm-thick buried silicon dioxide layer at the Institute of Microelectronics, Singapore. 248-nm deep ultraviolet photolithography is used to define the patterns, and inductively coupled plasma etching is employed to form the silicon waveguides. The single-mode rib waveguide is 400 nm in width, 220 nm in height, and 70 nm in slab thickness. A 1500-nm-thick silica layer is deposited on the silicon layer by plasma-enhanced chemical vapor deposition (PECVD) to minimize the metal absorption. Then a 150-nm-thick titanium nitride is sputtered on the separate layer, and 1-μm-wide titanium nitride metal is fabricated on one arm of the Mach–Zehnder optical switch as the micro-heater for thermal tuning. Via holes are etched after depositing a 300-nm-thick silica layer by PECVD. Finally, aluminum wires and pads are fabricated. Figure 4(b) shows the micrograph of the fabricated device, which is $3000\mathrm{\mu m}\times 1700\mathrm{\mu m}$ in footprint.

C. Optical Transmission Spectra Characterization

The experimental setup for characterizing the device is shown in Fig. 5. The spectrum response of the device is measured using an amplified spontaneous emission source (HY-ASW-C-N-19-B-FA) and an optical spectrum analyzer (Yakogawa AQ6370). All switch units are designed to be in the “cross” state with no driving voltage applied. So the optical signal at the input single-mode waveguide $I_m^i$ should be guided to the output single-mode waveguide $O_n^i$ ($i=0$, 1, 2, 3; $m$, $n=1$, 2 and $m\ne n$). However, the original states of the switch units deviate from the designed ones due to the imperfect fabrication. Current injection to the micro-heater is used to initialize the state of each switch unit. Each optical link has five switch units. Except for the last one, each has two cascaded switch units. We chose the optical link $I_1^0\to O_2^0$ as an example to illustrate the initialization method. Due to the imperfect fabrication, the optical signal at the input waveguide $I_1^0$ can be guided to the output waveguide $O_2^0$ through more than one routing path. But it must pass through the switch unit $S_{11}$ and at least one of the cascaded switch units ($S_{12}$ and $S_{32}$). We can adjust the driving voltages of the switch units $S_{11}$ and $S_{32}$ and monitor the optical power at the output waveguide $O_2^0$. If the optical power at the output waveguide $O_2^0$ does not change, it means that the optical signal is guided to the switch unit $S_{12}$ and the switch unit $S_{11}$ is in the “bar” state. Or we can adjust the driving voltages of the switch units $S_{11}$ and $S_{12}$ and monitor the optical power at the output waveguide $O_2^0$. If the optical power at the output waveguide $O_2^0$ does not change, it means that the optical signal is guided to the switch unit $S_{32}$ and the switch unit $S_{11}$ is in the “cross” state. Using this method, we can determine the state of any switch unit and its driving voltages. For a larger-scale single-mode or multimode optical switch, an automatic initialization process based on closed-loop control is preferred and a series of integrated monitoring channels is also helpful for the characterization process.

 

Fig. 5. Experimental setup for characterizing the device (ASE, amplified spontaneous emission; TL, tunable laser; PC, polarization controller; DCP, direct-current power; AFG, arbitrary function generator; DUT, device under test; PPG, pulse pattern generator; OSA, optical spectrum analyzer; DCA, digital communication analyzer; EDFA, erbium-doped fiber amplifier; MD, modulator; RTO, real-time oscilloscope).

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1. Optical Space Switching

The type-III $2\times 2$ four-mode optical switch has two routing states for optical space switching. Figure 6(a) shows the established optical links and the states of all switch units in one of the two routing states. All switch units are in the “cross” state, and the optical links $I_1^i\to O_2^i$ and $I_2^i\to O_1^i$ are established.

 

Fig. 6. (a) Established optical links and states of the switch units in a specific routing state, (b) transmission spectra of the optical links $I_m^i\to O_1^1$ ($m=1$, 2 and $i=0$, 1, 2, 3) and the silicon waveguide, and (c) transmission spectra for the signals and noises of the optical links in the shown routing state (OSNR: optical signal-to-noise ratio).

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We choose the optical link $I_2^1\to O_1^1$ as an example to explain how to characterize the insertion loss and optical signal-to-noise ratio (SNR) of the device. Although the optical signal injected to the input waveguide $I_2^1$ should be guided to the output waveguide $O_1^1$, a part of the optical signal is likely leaked to other output waveguides $O_n^j$ ($n$ and $j$ are not 1 meanwhile) due to the imperfect mode multiplexers/de-multiplexers, waveguide crossings, and switch units. The leaked optical signal becomes the noise to the output waveguide $O_n^j$. To characterize the insertion loss of the optical link $I_2^1\to O_1^1$, we only need to measure its transmission spectra, as the bold blue line shows in Fig. 6(b). To measure its optical SNR, however, we also need to measure the transmission spectra of the optical links $I_1^0\to O_1^1$, $I_1^1\to O_1^1$, $I_1^2\to O_1^1$, $I_1^3\to O_1^1$, $I_2^0\to O_1^1$, $I_2^2\to O_1^1$, and $I_2^3\to O_1^1$, as the normal lines show in Fig. 6(b). Note that these optical links are not established in the routing state shown [Fig. 6(a)]; thus their transmission spectra reflect the noise from other input waveguides to the optical link $I_2^1\to O_1^1$. The sum of the transmission spectra of the optical noise links represents the noise leaked from all possible optical links to the optical link $I_2^1\to O_1^1$, as the bold red line shows in Fig. 6(b). We can determine the optical SNR of the optical link $I_2^1\to O_1^1$ by the difference between the transmission spectra of the signal and the noise. The transmission spectra of a silicon waveguide with the same coupling structures are shown by the bold green line in Fig. 6(b), which indicates that the coupling loss between the device and the single-mode fiber is $\sim 3\mathrm{dB}/\text{facet}$.

Using the same method, we can measure the transmission spectra for the signals and noises of the other seven optical links, as shown in Fig. 6(c). Slight wavelength dependence is observed, which is mainly caused by the dispersion of the Mach–Zehnder interferometer based switch units and the ADC based mode multiplexers/de-multiplexers. The silicon waveguide dispersion also contributes to this phenomenon. Moreover, imperfect fabrication makes the central wavelengths of the switch units and the mode multiplexers/de-multiplexers deviate from the theoretical values, which contributes to wavelength dependence as well.

The minimum and maximum insertion losses of the eight optical links in this routing state are 15.2 and 22.5 dB, respectively, for the wavelength range of 1525–1565 nm. The insertion loss includes the coupling loss between the device and the single-mode fibers, which is about 6.0 dB for all optical links. It also includes the propagation losses of the mode multiplexers/de-multiplexers, switch units, and waveguide crossings (0.3 dB) along the way. The propagation loss of the switch unit is 0.5–1.2 dB for the wavelength range of 1525–1565 nm, which is a little larger than the simulated value of 0.4 dB at 1550 nm. The propagation losses of the mode multiplexer/de-multiplexer are 0.6–1.7 dB, 0.7–1.8 dB, 0.8–2.0 dB, and 1.2–2.8 dB for the ${\mathrm{TE}}_0$, ${\mathrm{TE}}_1$, ${\mathrm{TE}}_2$, and ${\mathrm{TE}}_3$ modes, respectively, for the wavelength range of 1525–1565 nm, which are much larger than the simulated values of $\sim 0.03\mathrm{dB}$ for the ${\mathrm{TE}}_0$ mode, 0.04–0.16 dB for the ${\mathrm{TE}}_1$ mode, 0.05–0.16 dB for the ${\mathrm{TE}}_2$ mode, and 0.05–0.16 dB for the ${\mathrm{TE}}_3$ mode. Clearly mode multiplexers/de-multiplexers based on ADCs are more sensitive to imperfect fabrication than the switch units and waveguide crossings. Given that the device is fabricated at a 180 nm CMOS foundry of IME, these deviations are expected. In order to reduce the insertion loss of the optical link, we need to further optimize the building blocks including the coupling structure, mode multiplexer/de-multiplexer, switch unit, and waveguide crossing. Furthermore, a 40 nm or even 28 nm CMOS foundry process should be considered for device fabrication [46] so that the structural parameters of the fabricated device are more in agreement with the design targets. As the optical switch matrix is based on a Benes network, each optical link has the same number of switch units. The fact that the insertion losses of the optical links are different is mainly caused by the loss differences of different spatial modes of the mode multiplexer/de-multiplexer and different numbers of waveguide crossings in the path.

The optical SNRs are larger than 15.3 dB for all optical links. In principle, the noise of an optical link is mainly determined by the optical inter-mode crosstalk and the optical inter-path crosstalk. With respect to the optical link $I_2^1\to O_1^1$, there are seven optical links contributing to the noise. The optical signals injected into the input waveguides $I_2^0$, $I_2^2$, and $I_2^3$ are likely leaked to the optical link $I_2^1\to O_1^1$ by mode de-multiplexer 2 and/or mode multiplexer 1. So the noise induced by optical links $I_2^0\to O_1^1$, $I_2^2\to O_1^1$, and $I_2^3\to O_1^1$ is mainly caused by the optical inter-mode crosstalk. The optical signals injected into the input waveguides $I_1^0$, $I_1^1$, $I_1^2$, and $I_1^3$ are likely leaked to the optical link $I_2^1\to O_1^1$ by the switch units and waveguide crossings in the path. So the noise induced by the optical links $I_1^0\to O_1^1$, $I_1^1\to O_1^1$, $I_1^2\to O_1^1$, and $I_1^3\to O_1^1$ is mainly caused by the optical inter-path crosstalk.

The optical crosstalk is less than $-35.0$, $-30$, and $-28.3\mathrm{dB}$ for the waveguide crossings, the switch unit in the “cross” state, and that in the “bar” state, respectively, for the wavelength range of 1525–1565 nm, while the optical crosstalk of the cascaded mode multiplexer and de-multiplexer is less than $-25.7$, $-24.4$, $-21.4$, and $-21.1\mathrm{dB}$ for the ${\mathrm{TE}}_0$, ${\mathrm{TE}}_1$, ${\mathrm{TE}}_2$, and ${\mathrm{TE}}_3$ modes, respectively. Moreover, the mode multiplexers/de-multiplexers are more sensitive to imperfect fabrication than the switch units and waveguide crossings. So the optical crosstalk from the optical links $I_2^0\to O_1^1$, $I_2^2\to O_1^1$, and $I_2^3\to O_1^1$ is larger than that from the optical links $I_1^0\to O_1^1$, $I_1^1\to O_1^1$, $I_1^2\to O_1^1$, and $I_1^3\to O_1^1$ (Table 1).

Table 1. Insertion Losses and Optical Signal-to-Noise Ratios of the Optical Links of the Type-III $2\times 2$ Four-Mode Optical Switch

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Periodic oscillation is also observed in the transmission spectra of the optical noise links $I_2^0\to O_1^1$, $I_2^2\to O_1^1$, and $I_2^3\to O_1^1$, which is mainly caused by the interference between the noise leaked to the output waveguide $O_1^1$ by mode multiplexer 2A and de-multiplexer 2 and the noise leaked to the output waveguide $O_1^1$ by mode multiplexer 1 and de-multiplexer 1A. For example, with respect to the optical noise link $I_2^2\to O_1^1$, the routing path for the noise leaked by mode multiplexer 2A and de-multiplexer 2 is $I_2^2\to {(I_2^1)}^{\prime }\to S_{31}^C\to S_{22}^C\to S_{23}^C\to S_{14}^C\to S_{15}^C\to {(O_1^1)}^{\prime }\to O_1^1$, and the routing path for the noise leaked by mode multiplexer 1 and de-multiplexer 1A is $I_2^2\to {(I_2^2)}^{\prime }\to S_{41}^C\to S_{42}^C\to S_{33}^C\to S_{34}^C\to S_{25}^C\to {(O_1^2)}^{\prime }\to O_1^1$. The two noises are mainly caused by the optical inter-mode crosstalk of the mode multiplexers/de-multiplexers, and hence have similar power levels. Their interference results in the periodic oscillation in the transmission spectra of the optical noise link $I_2^2\to O_1^1$, as the red line shows in Fig. 6(b).

2. Optical Space Switching Plus Local Optical Mode Switching

The type-III $2\times 2$ four-mode optical switch has 1152 routing states for optical space switching plus local optical mode switching. Figure 7(a) shows the established optical links and the states of all switch units in one of its routing states. Figure 7(b) shows the transmission spectra of both the signal and noise for its eight optical links in the shown routing state. The minimum and maximum insertion losses of the eight optical links are 16.0 and 20.9 dB, respectively, for the wavelength range of 1525–1565 nm (Table 2). The optical SNRs of the eight optical links are larger than 17.1 dB (Table 2). As the optical mode switching only occurs in a specific optical circuit, the noise of each optical link is caused by not only the optical inter-mode crosstalk but also the optical inter-path crosstalk.

 

Fig. 7. (a) Established optical links and states of the switch units in a specific routing state. (b) Transmission spectra for the signal and noise of the optical links in the shown routing state.

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Table 2. Insertion Losses and Optical Signal-to-Noise Ratios of the Optical Links of the Type-III $2\times 2$ Four-Mode Optical Switch

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3. Global Optical Mode Switching

The type-III $2\times 2$ four-mode optical switch has 40320 routing states for global optical mode switching. Figure 8(a) shows the established optical links and the states of all switch units in one of its routing states. Figure 8(b) shows the transmission spectra for the signal and noise of the eight optical links in the shown routing state. The minimum and maximum insertion losses of the eight optical links are 15.3 and 21.5 dB, respectively, for the wavelength range of 1525–1565 nm (Table 3). The optical SNRs are larger than 16.9 dB for all optical links (Table 3). As the optical mode switching occurs amongst different optical circuits, the noise of a specific optical link is determined either by the optical inter-mode crosstalk and the optical inter-path crosstalk or by the optical inter-path crosstalk.

 

Fig. 8. (a) Established optical links and states of the single-mode optical switches in a specific routing state. (b) Transmission spectra for the signal and noise of the optical links in the shown routing state.

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Table 3. Insertion Losses and Optical Signal-to-Noise Ratios of the Optical Links of the Type-III $2\times 2$ Four-Mode Optical Switch

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Based on the analysis above, we reach a general conclusion on the origin of the noise of an optical link $I_s^p\to O_t^q(s,t\in \{1,2,\dots ,N\};p,q\in \{1,2,\dots ,M\})$ in a specific routing state. In addition to the considered optical link, other $(NM-1)$ optical links $I_m^i\to O_n^j$ are also established in this routing state. If $m\ne s$ and $n\ne t$, the noise from the input waveguides $I_m^i$ to the optical link $I_s^p\to O_t^q$ is mainly caused by the optical inter-path crosstalk. In other conditions, the noise from the input waveguides $I_m^i$ to the optical link $I_s^p\to O_t^q$ is caused not only by the optical inter-path crosstalk but also by the optical inter-mode crosstalk.

D. Eye Diagrams and Bit Error Rate Characterization

A 40 Gbps pseudo-random binary sequence with a length of $2^{31}-1$ is generated by a pulse pattern generator (SHF 12104A) and then used to drive a ${\mathrm{LiNbO}}_3$ optical modulator. Continuous-wave light generated by a tunable laser (Agilent 86164B) is first modulated by the ${\mathrm{LiNbO}}_3$ optical modulator and then coupled into and out of the device by normal single-mode fibers. The output optical signal from the device is amplified by an erbium-doped fiber amplifier (KPS-CUS-BT-C-33-PB-SM-111-FA-FA) followed by a tunable filter (OTF-350) to reduce the background ASE noise. The output optical signal is then sent to a digital communication analyzer (Agilent 86100D) for eye diagrams and a real-time oscilloscope (Tektronix DPO70000) with a receiver for bit error rate (BER) measurements. A square-wave electrical signal from an arbitrary function generator (Tektronix AFG3102) is applied to the switch unit, and its response time can be measured directly by a real-time oscilloscope (Tektronix TDS 2012B). Eye diagrams and BERs for the 40 Gbps data transmission through the optical links for optical space switching, optical space switching plus local optical mode switching, and global optical mode switching in the wavelength range of 1525–1565 nm were all measured. For clarity, only the results measured at 1545 and 1565 nm are shown here.

Figures 9(a) and 9(b) show the eye diagrams and BERs of the optical links for optical space switching and optical space switching plus local optical mode switching at a data rate of 40 Gbps. Clean open “eyes” were obtained for all links. The received optical power penalties at a BER of ${10}^{-9}$ are 1.3 dB and 1.3 dB for $I_2^0\to O_1^0$, 2.2 dB and 2.4 dB for $I_2^1\to O_1^1$, 3.0 dB and 3.3 dB for $I_2^2\to O_1^2$, 4.2 dB and 5.6 dB for $I_2^3\to O_1^3$, 2.9 dB and 3.6 dB for $I_2^0\to O_1^3$, 2.1 dB and 2.7 dB for $I_2^1\to O_1^2$, 1.9 dB and 2.5 dB for $I_2^2\to O_1^1$, and 3.2 dB and 4.0 dB for $I_2^3\to O_1^0$ at 1545 and 1565 nm, respectively. Figure 9(c) shows the eye diagrams and BERs of the optical links for global optical mode switching. The received optical power penalties at a BER of ${10}^{-9}$ are 1.2 dB and 1.0 dB for $I_2^0\to O_1^1$, 1.7 dB and 1.7 dB for $I_2^1\to O_1^0$, 2.4 dB and 2.5 dB for $I_2^2\to O_2^3$, and 3.6 dB and 4.3 dB for $I_2^3\to O_2^2$ at 1545 and 1565 nm, respectively.

 

Fig. 9. Eye diagrams and bit error rates for 40 Gbps data transmission through the optical links for (a) optical space switching, (b) optical space switching plus local optical mode switching, and (c) global optical mode switching.

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E. Power Consumption and Switching Time Characterization

The power consumptions of the 20 switch units are measured. The power consumption variation is due to different initial phase differences between the two arms of different switch units resulting from imperfect fabrication. The minimum and maximum power consumptions of the type-III $2\times 2$ four-mode optical switch are 430 and 1018 mW, respectively. The response time of the type-III $2\times 2$ four-mode optical switch is determined by the slowest switch unit. We characterized all switch units and found that their response times are around 20 μs.

4. CONCLUSION

In conclusion, three general architectures for on-chip optical space and mode switching are proposed, which are optimized for optical space switching, optical space switching plus local optical mode switching, and global optical mode switching, respectively. A silicon thermo-optic $2\times 2$ four-mode optical switch is demonstrated. The minimum and maximum insertion losses of the optical links are 16.0 and 20.9 dB (including $\sim 6\mathrm{dB}$ coupling loss), respectively, for the wavelength range of 1525–1565 nm. An optical SNR of larger than 15.3 dB is achieved for all optical links. The received optical power penalty at a BER of ${10}^{-9}$ varies from 1.0 to 5.6 dB at a data rate of 40 Gbps. This work provides a systematic solution to on-chip information switching for different physical and mode channels.