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Abstract
Data exchange between different data channels can offer more flexible and advanced functions for many optical networks. In this paper, we propose a switchable and reconfigurable data exchange device for arbitrary two optical mode channels based on three-waveguide-coupling (TWC) switches in mode-division multiplexing (MDM) networks. The working principle of the TWC switches is numerically analyzed using the coupled supermode theory. As a proof of concept, switchable data exchange between arbitrary two mode channels among the first three-order quasi-transverse electric modes is experimentally demonstrated successfully. The insertion losses of the device are less than 5.6 dB, including the coupling loss of the multiplexer and demultiplexer, while the mode crosstalk is less than -13.0 dB for all functions. The proposed device is expected to offer more flexibility to on-chip MDM networks due to its low loss, low crosstalk and good scalability.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mode-division multiplexing (MDM) is emerging as a new dimension after wavelength-division multiplexing (WDM) and polarization-division multiplexing (PDM) to further increase the data capacity of on-chip optical interconnects, which treats multiple guided modes in a silicon waveguide as independent data channels [1].The optical MDM network has attracted more and more attention due to its low cost, low loss and low inter-modal crosstalk. Recently, a quantity of MDM devices such as mode multiplexer/demultiplexer [2–4], mode switch [5–7], multimode bending [8–10] and multimode crossing [11–13], etc. have been proposed and demonstrated, which improve the flexibility and scale down the size for the MDM system. Data exchange is also an important feature of many optical networks, which provides more flexible and advanced functions by swapping data information between different data channels [14]. Data exchange in MDM system called mode exchange has been investigated based on different structures such as micro-ring resonators (MRR) [15, 16], asymmetric direction coupler (ADC) [17], Mach-Zehnder interferometer (MZI) [18], metamaterial [19] and hybrid plasmonic waveguide [20]. However, most of these approaches cannot perform switchable and reconfigurable functions simultaneously, and here, switchable function means the data information carried on two optical modes can exchange or not, while reconfigurable function means the proposed device can implement data exchange between arbitrary two optical modes. Therefore, a switchable and reconfigurable device is still desired to achieve on-chip mode exchange for MDM system.
The three-waveguide-coupling (TWC) switch was first proposed in [21], where the author shows the mode conversion functionality of this structure briefly. In our previous work [22], we proposed and experimentally demonstrated a mode multiplexer/demultiplexer using multimode interference coupler (MMI) and the TWC switch. With the help of the principle of MMI, the relations between the phase difference of the two light beams input into the upper and lower single-mode waveguide and the parity of the order of the coupled optical modes in the middle bus waveguide were theoretically simulated. However, the reason for which specific phase differences are required for different-order mode coupling is still not revealed.
In this paper, we theoretically and experimentally investigate the switchable and reconfigurable mode exchange between arbitrary two optical modes utilizing the cascaded TWC switches. The working principle of the TWC switches is analyzed using the coupled supermode theory. As a proof of concept, the performance of the device in switchable data exchange for arbitrary two optical mode channels among the first three order quasi-transverse electric (TE) modes is characterized. The experimental results show the proposed device realizes switchable data exchange between arbitrary two modes with low losses and low mode crosstalk successfully. In addition, the device has a good scalability and, thus, it is expected to offer more flexibility to on-chip MDM networks.
2. Device design and working principle
Data information carried on an optical mode channel will enter to another when the mode converted. Consequently, data exchange in a mode-division-multiplexing system can be implemented through swapping different optical modes. Figure 1 shows the schematic of the proposed mode exchange device formed by cascaded TWC switches. Arbitrary two optical signals from different-order TE mode channels i.e. TE0, TE1, TE2 are injected at the input port and output with mode exchanged or not. We indicate the six TWC mode switches as MS1 to MS6 respectively. The structure of proposed device is symmetrical about the y axis. Figure 1(b) shows a top view of the left half of the proposed device, it can be seen that each TWC mode switch comprises two single-mode upper or lower waveguides called the arms and a middle bus waveguide. By designing different widths for the bus waveguides, different TWC mode switches are applied to route and receive different order optical modes. Specifically, MS1 and MS6 with the widest (w3) bus waveguide are used for routing and receiving TE2 mode respectively, MS2 and MS5 with the second wider (w2) bus waveguide are used for routing and receiving TE1 mode respectively while MS3 and MS4 with the narrowest (w1) bus waveguide are used for routing and receiving TE0 mode respectively. The coupling lengths of TE0, TE1 and TE2 mode switches are denoted as L0, L1 and L2 respectively. Bus waveguides with different widths are connected by taper waveguides while the arms with the same width are connected using single-mode transition waveguides. In addition, phase shifters are integrated on the transition waveguides between the upper arms of TWC mode switches. A cross-sectional view of the transition waveguide with titanium (Ti) heater on the top is shown in Fig. 1(c). The detailed device design process and working principle are depicted hereinafter.
Fig. 1. (a) The schematic of the proposed optical mode exchange device. (b) The top view of the left half of the proposed device. (c) The cross-sectional view of the transition waveguide with Ti heater on the top.
According to the phase matching condition, the input optical modes in the bus waveguide should in principle couple to two fundamental modes in the upper and lower arms if the effective refractive index (ERI) of the input mode in the bus waveguide matches the ERI of the fundamental mode in the single-mode arm [23]. To do so, the ERI of different order optical modes in channel waveguides with different widths is calculated using a full-vector eigenmode solver based on mode-matching method [24], as shown in Fig. 2. First, the widths of the single-mode waveguides are fixed to 0.45 µm to meet the single-mode condition. The ERI of TE0 mode in the single-mode waveguide is calculated to be about 2.36 at the wavelength of 1550 nm. For efficient mode coupling in the TWC mode switches, we set w1, w2 and w3 to be 0.45 µm, 0.933 µm and 1.419 µm respectively to meet the phase matching condition between the TE0 mode in the single-mode arm and different-order modes i.e. TE0, TE1, TE2 in the bus waveguide. To control variables, we designed the coupling gap between the arm and bus waveguide in all TWC switches to be 200 nm. In order to investigate the phase difference between the two TE0 modes in the upper and lower arms coupled from different-order modes in the bus waveguide, the local supermodes in the TWC structure are simulated by finite difference time domain (FDTD) method [25]. Figure 3 shows the electric fields Ey of local supermodes at the y-z cross section in the TWC structure with different width bus waveguides. As shown in Figs. 3(a)-(c), TE0 mode switch with a 0.45 µm bus waveguide support three local supermodes including two even modes and one odd mode. The amplitude dynamics of local supermodes along the propagation direction in a coupling system can be written as:
Where aj and ak are amplitudes of different supermodes, the supermode coupling coefficients Cjk can be expressed by the coupled supermode theory [26]:Fig. 2. The simulated effective refractive index of different optical modes versus waveguide widths.
Fig. 3. The simulated localized supermodes in (a)-(c) TE0 mode switch with a 0.45 µm bus waveguide, (d)-(f) TE1 mode switch with a 0.933 µm bus waveguide and (g)-(i) TE2 mode switch with a 1.419 µm bus waveguide. (neff, effective refractive index).
where ε0 is the vacuum permittivity, µ0 is the vacuum permeability, k0 is the wavenumber in free space, βj and βk are the propagation constants of different supermodes, ej and ek are the electric fields of the supermodes, n(x, y, z) is the refractive index. According to the coupled supermode theory, the two even modes localized in the whole system can be regarded as that generated from the effective mutual coupling between the TE0 supermode in the bus waveguide and the even supermode confined in the two arms due to the phase matching. The odd supermode is then only confined in the two arms without coupling with the TE0 mode in the bus waveguide since the overlap integral of the electric fields of these two supermodes is zero. Then, Figs. 3 (d)-(f) show another three orthogonal local supermodes including two odd modes and one even mode in the TE1 mode switch of which the bus waveguide is 0.933 µm. Different from the case of TE0 mode switch, the two odd modes localized in the whole system are induced by the mode coupling between the TE1 supermode in the bus waveguide and the odd supermode confined in the two arms due to the phase matching. The coupling coefficients between the even supermode confined in the two arms and the TE1 supermode in the bus waveguide is zero. Finally, three local supermodes in the TE2 mode switch of which the bus waveguide is 1.419 µm are shown in Figs. 3 (g)-(i) with two even modes localized in the whole system and one odd mode confined in the two arms, similar to the case of TE0 mode switch.
From the simulation results above, it can be predicted that the two TE0 modes in the upper and lower arms coupled from even-order modes in the bus waveguide will be in-phase while those coupled from odd-order modes will be anti-phase once the signal input into the bus waveguide. To confirm this prediction, the FDTD method is again used to analyze the behavior of TWC mode switch. The simulation results are presented in Fig. 4. Figures 4(a) and 4(b) show the electric field profile Ey at the x-y cross section of TE0 mode switch when a TE0 mode signal input into the bus waveguide or two anti-phase TE0 mode signals input into the two arms respectively. It can be seen from the result that the aforementioned two even supermodes are excited when a TE0 mode signal input into the bus waveguide. The TE0 mode finally couples to two in-phase TE0 modes confined in the upper and lower arms respectively since a π phase difference generated between these two even supermodes due to different propagation constants. The coupling length can be expressed as:
Fig. 4. The simulated transmission of (a) TE0 mode switch when a TE0 mode input into the bus waveguide, (b) TE0 mode switch when two anti-phase TE0 modes input into the two arms, (c) TE1 mode switch when a TE1 mode input into the bus waveguide, (d) TE1 mode switch when two in-phase TE0 modes input into the two arms, (e) TE2 mode switch when a TE2 mode input into the bus waveguide, (f) TE2 mode switch when two anti-phase TE0 modes input into the two arms.
As another even-order mode, the situation of TE2 mode switch is similar to that of TE0 mode switch of which the two TE0 modes coupled from the bus waveguide are in-phase. Figures 4(e) and 4(f) show the coupling length L2 of TE2 mode switch is about 29 µm. To sum up, the simulation results agree the prediction well. We can conclude that even-order modes input into the bus waveguide will couple to two in-phase TE0 modes in the arms and vice versa while two anti-phase TE0 mode signals input into the two arms will pass through the two arms without coupling to the bus waveguide in TWC mode switches designed for even-order modes. Besides, odd-order modes input into the bus waveguide will couple to two anti-phase TE0 modes in the arms and vice versa while two in-phase TE0 mode signals input into the two arms will pass through the two arms without coupling to the bus waveguide in TWC mode switches designed for odd-order modes.
As can be seen from the simulated results, the TWC structure has a good performance in mode switch by rigorously controlling the phase difference between the two TE0 modes input into the upper and lower arms. If we connect different TWC switches together and tune the phase difference of the two TE0 modes in the transition waveguides between two switches, it then provides possibilities for mutual conversion between arbitrary two optical modes, which realize the reconfigurable function. Moreover, the input optical signals can also output by keeping the original modes, which realize the switchable function.
3. Fabrication and experimental results
3.1. Fabrication of the proposed device
Figure 5(a) shows the micrograph of the mode exchange device fabricated on a silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon layer and 3-µm-thick buried oxide layer. E-beam lithography (EBL) and inductively coupled plasma etching (ICP) are used to form the waveguide structure. A 2-µm-thick SiO2 separation layer is then deposited on the silicon layer using plasma-enhanced chemical vapor deposition (PECVD). The Ti heater which is 100-nm-thick, 5-µm-wide and 100-µm-long is finally formed by the EBL, e-beam evaporation deposition, and lift-off processes. The length of the taper waveguide connecting the bus waveguides with different widths are set to be 150 µm which is sufficiently long to reduce the inter-modal crosstalk when the optical modes transport along the bus waveguide. For further experimentally demonstrate the performance of the proposed device, ADC-based mode multiplexer (MUX) and demultiplexer (DMUX) are fabricated at two sides of the device for input and output respectively, as shown in Fig. 5(b). Though ADC can be replaced by many other structures such as MRR, Y-junction and MMI, the direction coupler structure is the most commonly used due to its broadband, scalability and compact size. According to the simulated results in section 2, the widths of the multimode waveguides for TE1 and TE2 mode conversion are chosen to be 0.933 µm and 1.419 µm respectively to meet the phase matching condition. The coupling lengths are then designed to be 27 µm and 33.5 µm for efficient conversion to TE1 and TE2 mode while the coupling gaps are fixed to 200 nm. Input and output grating couplers are fabricated for coupling light into and out of the device. This chip is manufactured by Australian Silicon Photonics (www.siliconphotonics.com.au).
Fig. 5. The micrograph of the fabricated (a) mode exchange device and (b) ADC-based mode multiplexer/demultiplexer.
3.2. Experimental results
We employ the amplified spontaneous emission source (ASE), tunable voltage source (TVS) and optical spectrum analyzer (OSA) for characterization of the proposed device. The input grating coupler will couple the broadband continuous light generated by the ASE from an off-chip single-mode fiber to the chip. The TVSs then apply voltages to the micro-heaters to control the phase difference of TE0 modes in the upper and lower transition waveguides between TWC switches. Finally, optical mode signals with data exchanged or not will be couple out to the OSA for analysis via the output grating coupler and another off-chip single-mode fiber.
According to the theoretical analysis and simulated results in section 2, even-order modes in the bus waveguide can couple to two in-phase TE0 modes in the arms while odd-order modes in the bus waveguide can couple to two anti-phase TE0 modes. At the same time, two in-phase TE0 modes input into the arms can excite even-order mode in the bus waveguide or pass through the switch without exciting odd-order mode, while two anti-phase TE0 modes input into the arms can excite odd-order mode in the bus waveguide or pass through the switch without exciting even-order mode. Table 1 shows the states of the phase shifters for specific functions of the device in experimental demonstration, where “ON” state means a kπ (k = 1, 2, …, N) phase shift induced by the applied voltage and “OFF” state means a 2mπ (m = 0, 1, …, N) phase shift. It can be seen from the table that PS1 and PS5 are OFF for all functions. However, compensatory voltage is still needed since the phase shifter changed the ERI of TE0 mode in the upper arm. In the experiment, the applied voltages are 2.8 V, 2.1 V, 1.7 V, 1.8 V and 2.5 V for “OFF” state of phase shifters from PS1 to PS5 and the applied voltages are 2.8 V, 2.3 V and 2.4 V for “ON” state of phase shifters from PS2 to PS4. The voltages are applied to the chip by using probe array. The resistance of the fabricated phase shifters from PS1 to PS5 are measured to be 184 Ω, 206 Ω, 201 Ω, 194 Ω and 195 Ω. The resistance variation is due to the imperfect fabrication. The lengths of the wires connected the pads and microheaters are different, which is another reason for this difference. Thus, the power consumption for a π phase shift of the fabricated phase shifters from PS2 to PS4 is calculated to be 16.6 mW, 11.9 mW and 12.9 mW respectively.
Table 1. States of phase shifters for specific functions
Figure 6 shows the measured results of data exchange between arbitrary two optical modes including TE0-TE1 mode exchange (Figs. 6(a)–6(b)), TE0-TE2 mode exchange (Figs. 6(c)–6(d)) and TE1-TE2 mode exchange (Figs. 6(e)–6(f)). Figure 7 shows the measured results of the same device when the data exchange functions are switched off. The switchable function is as important as the reconfigurable function of a mode exchange device for optimizing network performance. The experimental results are normalized by the transmission of a straight waveguide with grating couplers on the same chip. It can be seen from the results that the proposed and fabricated device realizes switchable data exchange between arbitrary two modes successfully. The insertion losses (IL) of the device for all functions are less than 5.6 dB (the highest IL can be found in TE1-to-TE2 mode conversion for TE1-TE2 mode exchange) including the coupling loss of the MUX and DMUX. We also fabricated the MUX/DEMUX element with the same structure parameters as the reported device on the same wafer. The IL of the MUX/DMUX are measured to be 0.90-1.06 dB and 1.04-1.16 dB for TE1 and TE2 modes respectively within the wavelength range of 1545-1565 nm. Therefore, the proposed device performs low losses even for high-order mode exchange. In addition, the mode crosstalk is less than -13.0 dB for all functions. The mode crosstalk can be further reduced through some optimizations such as using a taper-based ADC as the MUX/DMUX [2] to improve the fabrication tolerance of the conventional ADC which we used in this work or employing ridge waveguide rather than channel waveguide to reduce the sensitivity of ERI of optical modes to the parameters of waveguides [27] in the future. Besides, even though we only characterized the performance for arbitrary two mode channels among the first three order modes using the device we fabricated, the device has a good scalability based on which the proposed scheme can further realize data exchange between arbitrary two modes by cascading more TWC switches.
Fig. 6. The measured results of the fabricated mode exchange device for (a)-(b) TE0-TE1 mode exchange, (c)-(d) TE0-TE2 mode exchange and (e)-(f) TE1-TE2 mode exchange.
Fig. 7. The measured results of the fabricated mode exchange device when the mode exchange functions are switched off.
4. Conclusion
In summary, we propose and demonstrate switchable and reconfigurable data exchange between arbitrary two optical mode channels using cascaded TWC switches. The performance of the TWC structure in mode switch is numerically validated. As a proof of concept, the fabricated device realizes switchable data exchange between arbitrary two mode channels among the first three order TE modes successfully. The proposed device shows low insertion losses which are measured to be less than 5.6 dB including the coupling loss of the MUX and DMUX, while the mode crosstalk is less than -13.0 dB for all functions. The mode crosstalk can be further reduced by using a taper-based ADC as the MUX/DMUX to improve the fabrication tolerance of the conventional ADC used in this work or employing ridge waveguide to reduce the sensitivity of ERI of optical modes to the parameters of waveguides. The proposed device has low loss, low crosstalk and good scalability based on which it is expected to be used to flexible MDM networks in the future.
Funding
National Natural Science Foundation of China (61405082); State Key Laboratory on Integrated Optoelectronics (IOSKL2016KF14); Fundamental Research Funds for the Central Universities (lzujbky-2019-84).
Acknowledgments
The authors acknowledge the facilities, and the scientific and technical assistance, of the Micro Nano Research Facility (MNRF) and the Australian Microscopy & Microanalysis Research Facility at RMIT University. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF).
Disclosures
The authors declare no conflicts of interest.
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