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Abstract
A silicon waveguide mode selective switch based on optical phase-change material Ge2Sb2Se4Te1(GSST) is theoretically demonstrated. The mode switch formed by three cascaded asymmetric directional couplers (ADCs) allows the input TE11 mode to be selectively converted to TE21, TE31 or TE41 mode based on the state of GSST. Each ADC consists of the single-mode silicon waveguide and the GSST film covered multimode silicon waveguide. The phase change of GSST could adjust the effective index of GSST/Si hybrid waveguide, thereby implementing the mode conversion. The three-dimensional finite-difference time-domain (3D-FDTD) method is adopted for performance optimization. The simulation results show that the mode conversion efficiencies of TE11 to TE21, TE31 and TE41 mode are 89.96%, 92.87% and 90.94%, respectively. The proposed mode selective switch has good potentials in on-chip signal multiplexing.
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1. Introduction
Over past few decades, photonic devices based on different platforms, such as silicon-on-insulator (SOI), have held promise due to compactness, low power and compatibility with CMOS technology-based microelectronic circuits [1–4]. Due to the intrinsic physical limitation, current communication technology is unable to satisfy the fast-growing transmission demand. Therefore, multiplexing technologies, such as wavelength division multiplexing (WDM), have been used to improve the transmission capacity [5–7]. Compared with WDM technology, mode division multiplexing (MDM) technique could enhance the transmission capacity by multiplexing several modes in one wavelength channel [8,9]. In addition, the simultaneous application of WDM and MDM technologies can further increase the communication capacity [9,10]. In practical MDM application, mode converters, mode multiplexers and demultiplexers, mode filters and mode switches are key components for mode signal processing. Among these functional devices, the mode switch is a key device for mode exchange.
Optical phase change material (OPCM) could realize the reversal conversion between the amorphous state and the crystalline state, during which the refractive index would greatly change (Δn > 1). OPCM has been applied in optical modulators and optical switches [11,12], working principle of which is different from the traditional electro-optic effect [13–15] or thermo-optic effect [16–18]. As a novel OPCM, Ge2Sb2Se4Te1(GSST) has attracted extensive attention due to its remarkable refractive index change at different states [19,20]. Compared with the well-known OPCM of Ge2Sb2Te5 (GST), GSST has a quality factor improvement over two orders of magnitude, as well as the broadband optical transparency [21]. The low extinction coefficient of GSST at amorphous state is only 0.00018, which is more than 200 times smaller than that of GST. Hence, the combination of GSST with SOI technology is promising for the design of low-loss, nonvolatile integrated waveguide switches [22–24]. Unlike from the electro-optic effect or thermo-optic effect-based switch, GSST is self-retaining, which means energy consumption is only required during the period of state conversion. The avoid of constant power supply offers GSST-assisted optical devices favorable characteristic of power saving [25,26].
Y. Wei et al. have demonstrated the GSST-assisted add/drop mode multiplexers. With the introduction of ADC structure, the filtering of TE11 and TE21 modes can be implemented at the coupling lengths of 49 µm and 8.5 µm, respectively [27]. With the help of GSST, the mode multiplexing from TE11 to TE21 within the length of 17.65 µm can be realized by the co-operation of two asymmetric waveguide couplers [28]. P. Xu proposed a GST-assisted three-waveguide directional coupler, constructing as a 2×2 switch unit. [29]. W. Jiang proposed a vertical mode switch, in which the double-layer silicon structure is prepared by depositing polysilicon on the top silicon of a SOI wafer. GSST is introduced on the upper silicon layer, by which the mode coupling from TM11 mode to TM21 mode can be implemented. The coupling length is less than 25 µm [30]. In comparison, the GSST-assisted ADC has merits of simple structure and lower loss. However, the mode channel and switching performance are still deserved to be improved.
In this paper, a GSST-assisted silicon waveguide mode switch is proposed to selectively convert TE11 mode to TE21, TE31 or TE41 mode. The mode switch is constructed by cascading three asymmetric directional couplers (ADCs). Each ADC is composed of the single-mode silicon waveguide and the GSST covered multimode silicon waveguide. By three-dimensional finite-difference time-domain (3D-FDTD) optimization, the fundamental mode can be effectively converted to the targeted high-order mode by changing the state of GSST. The proposed mode switch has good potentials in on-chip signal multiplexing.
2. Principle and design
As has been reported, amorphous GSST (a-GSST) has a similar refractive index to that of silicon [21]. However, the crystallization of GSST that could be completed within microseconds and the re-amorphization of GSST that could be completed within nanoseconds would greatly change the refractive index, making GSST an ideal alternative for optical switching [31]. To be noted, the mode field distribution, propagation constant and absorption of GSST/Si hybrid waveguide are different from those of conventional silicon waveguide. Therefore, it is necessary to study the mode coupling and propagation of hybrid waveguide.
2.1 Device structure
The top view of proposed selective mode switch is shown in Fig. 1. The bus waveguide with a width Wd only supports the propagation of fundamental mode TE11. ADC1, ADC2, and ADC3 cascade along the bus waveguide. The widths of multimode waveguide in ADC1, ADC2, and ADC3 are W1, W2, and W3, respectively. Each multimode waveguide is covered by GSST thin film. ADC1, ADC2, and ADC3 can support the existence of high-order modes of TE21, TE31 and TE41, respectively. Specific designed coupling lengths of L1, L2, L3, as well as waveguide gaps of D1, D2 and D3 allow the mode coupling when GSST is in a certain state. For each ADC, when GSST is in the amorphous state, the fundamental mode that propagates along the bus waveguide will be coupled into the GSST/Si hybrid waveguide and converted to a high-order mode due to the refractive index match between two modes. When GSST is in the crystalline state, the effective refractive index of GSST/Si hybrid waveguide changes due to the index increment of GSST, which breaks the refractive index match between two neighbored waveguides. The fundamental mode would continue propagate along the bus waveguide with no coupling. Therefore, the proposed device can selectively convert the input TE11 mode into TE21, TE31 or TE41 mode as required.
Fig. 1. Schematic diagram of the top view of mode selective switch constructed by three cascaded ADCs. The gold color section corresponds to the GSST covered silicon waveguide.
As shown in Fig. 2, when GSST films in all three ADCs are in the crystalline state, the input TE11 would directly output from the port Output 1. When GSST in ADC1 is in the amorphous state, TE11 in the bus waveguide will be completely converted to TE21 mode and output from the port Output 2. Similarly, when GSST in ADC2 or ADC3 is in the amorphous state, TE11 in the bus waveguide will be converted to TE31 mode or TE41 mode, and output from Output 3 or Output 4.
Fig. 2. TE11 mode is selectively converted to TE21, TE31 or TE41 mode at ADC1, ADC2, and ADC3, respectively, when GSST is in the amorphous state.
2.2 Design optimization
In this work, the silicon waveguide is constructed on the SOI platform with 340 nm-thick top silicon layer and 2 µm-thick buried silicon oxide. The constructed device is covered by silica for protection and stable working. At the optical wavelength of 1550 nm, refractive indices of silicon and silicon dioxide are 3.467 and 1.444, respectively. The refractive indices of amorphous GSST and crystalline GSST (c-GSST) are 3.375 + 0.00018i and 5 + 0.42i, respectively. Since the imaginary part relates to the light absorption, the GSST/Si hybrid waveguide has higher optical loss compared with the silicon waveguide. Therefore, it is deserved to study the mode propagation in ADC at different scenarios.
2.2.1 Single and multimode waveguides
As mentioned above, the ADC structure here is to satisfy the phase matching condition to allow the fundamental mode coupling to the adjacent multimode waveguide and evolving to a high-order mode. This implies that the GSST/Si waveguide should have close refractive index to that of the Si waveguide, when GSST is in the amorphous state. To find out the correct geometric dimension of ADCs, 3D-FDTD method is adopted to calculate the effective refractive index and mode coupling. The effective refractive index neff of TE11 mode in silicon waveguide as a function of waveguide width Wd is shown in Fig. 3. It can be seen that neff of TE11 mode is 2.7458 at Wd = 0.5 µm, which could be set as the width of single mode waveguide. The inset shows the TE11 mode distribution in the silicon waveguide.
In the ADC section, the top side of 340 nm-thick multimode silicon stripe is covered by a 20 nm-thick GSST layer. Refractive indices of TE21, TE31 and TE41 mode in the GSST/Si hybrid waveguides as the function of waveguide width are shown in Fig. 4(a), (b) and (c), respectively. To match the refractive index of TE11 mode in the single-mode bus waveguide, W1, W2, and W3 are accordingly selected to be 0.99 µm, 1.49 µm and 2 µm, respectively.
Fig. 4. Effective refractive index of (a) TE21, (b) TE31 and (c) TE41 mode in the GSST/Si hybrid waveguides as the function of waveguide width W1, W2, and W3. The inset shows the mode field distribution of TE21, TE31 and TE41 mode in the hybrid waveguide.
2.2.2 Gap
As shown in Fig. 1, to implement the mode conversion from the fundamental mode to the targeted high-order mode, the gap between two the single mode waveguide and hybrid waveguide, as well as the coupling length of ADC, are supposed to be optimized according to the mode conversion efficiency. The even-like supermode and the odd-like supermode emerge when the mode coupling happens in ADC. When the mode phase difference between two waveguides is 180°, an odd-like supermode will be generated. When no phase difference between two waveguides exists, an even-like supermode will be generated. With the enlargement of gap, the chance of waveguide to support the transmission of both the odd-like supermode and the even-like supermode decreases until the cut-off happens. Meanwhile, the ADC structure is unable to implement the mode conversion.
The effective refractive indices as a function of gap width in ADC1, ADC2, and ADC3 have been calculated by the finite element method (FEM), as shown in Fig. 5. The odd-like supermodes and the even-like supermodes at different coupling gap widths can be observed in the insets. Based on the relationship L=λ/2△n, when the wavelength is fixed, the refractive index difference between the odd-like supermode and the even-like supermode is negatively correlated with the coupling length. Though a small refractive index difference could ensure the favorable mode conversion efficiency, it requires an excessively long coupling length and large device size. Therefore, it is necessary to reduce the coupling length as much as possible, while ensuring the mode conversion efficiency. Since the relationship between the coupling length and the supermodes can be described by a correlation function, the approximate optimal coupling length can be found. With comprehensive consideration, D1, D2, and D3 are chosen to be 0.15 µm, 0.195 µm, and 0.2 µm, respectively.
Fig. 5. Effective index of the even-like supermodes and the odd-like supermodes as a function of gap width in (a) ADC1, (b) ADC2, and (c) ADC3.
2.2.3 Coupling length
According to the principle of directional coupler, except for the gap between waveguides, the coupling length has great influence on the mode exchange, too. Therefore, the coupling length L1, L2, and L3 of ADCs are investigated at fixed waveguide gap. Figure 6 presents the mode conversion efficiency as a function of coupling lengths of L1, L2, and L3 of ADCs, respectively. As mentioned in Section 2.2.2, D1, D2, and D3 of ADCs have been confirmed to be 0.15, 0.195 and 0.20 µm, respectively. Due to the diversity of refractive index difference between the fundamental mode and high-order modes, the optimized coupling length depends on the targeted mode conversion. For compactness, L1, L2, and L3 of three ADCs are selected as 32.5, 82 and 110 µm, respectively. For low loss propagation, the bending radius of the bend waveguide is selected as 5 µm. The induced optical loss is estimated to be 0.004 dB. The mode conversion efficiencies of TE11 mode to TE21, TE31 and TE41 mode are 89.96%, 92.87% and 90.94%, respectively. The complete size of three-mode selective switch is 280 µm ×53 µm.
Fig. 6. Mode conversion efficiency as a function of coupling lengths of L1, L2, and L3 of ADCs at 1550 nm, respectively.
3. Result and discussion
With above optimized geometric parameters, TE11 to TE21, TE11 to TE31 and TE11 to TE41 mode switching at ON state (a-GSST) and OFF state (c-GSST) are shown in Fig. 7. When GSST is in the amorphous state, TE11 mode is effectively coupled from the Si waveguide to the GSST/Si hybrid waveguide. Due to the refractive index matching, the fundamental mode will evolve to the high-order mode TE21 in the hybrid waveguide, as shown in Fig. 7 (a). In contrast, when GSST is in the crystalline state, the effective index matching in ADC1 is broken by the refractive index increment of GSST and no mode evolvement happens. The TE11 mode will stay and continue propagating along the bus waveguide, as shown in Fig. 7(b). Similar scenario of TE11 to TE31 mode in ADC2 and TE11 to TE41 mode in ADC3 can be observed in Fig. 7 (c) and (e), respectively.
Fig. 7. Optical conversion of (a) TE11 to TE21 mode in ADC1, (c) TE11 to TE31 mode in ADC2, and TE11 to TE41 mode in ADC3, when GSST is in the amorphous state and the switch is in the “ON” state. (b), (d) and (e) present the “OFF” state of proposed mode switch, when GSST is in the crystalline state.
The insertion loss (IL) and mode crosstalk (CT) of three ADCs are studied as a function of wavelength, as shown in Fig. 8 below. When the switch is in “ON” state, IL is less than 1 dB within the wavelength range from 1523 to 1565 nm. In the “OFF” state, IL is no larger than 0.7 dB within the wavelength range from 1500 to 1600 nm, which is favorable to the construction multistage cascading. The different variation in Fig. 8(e) mainly comes from the width of hybrid waveguide that is much larger than that of the optical wavelength. All mode CTs are less than -10 dB within the wavelength range from 1540 to 1555 nm, when three switch units are in “ON” state. All mode CTs are lower than -21 dB, when three switch units are in the “OFF” state. Since ADC1, ADC2, and ADC3 will not be in the “ON” state simultaneously, no optical interruption between switch units will exist. At the operation wavelength of 1550 nm, when ADC1 is working, the insertion loss is 0.29 dB, and the crosstalks at output port 1, 3 and 4 are -13.51 dB, -37.92 dB, and -37.45 dB, respectively. When ADC2 is working, the insertion loss is 0.41 dB, and the crosstalks at output port 1, 2, and 4 are -11.58 dB, -32.93 dB and -35.55 dB, respectively. When ADC3 is working, the insertion loss is 0.53 dB, and the crosstalks at output port 1, 2, and 3 are -10.65 dB, -32.11 dB and -35.58 dB, respectively. When no ADC is working, the insertion loss is 1.38 dB, and the crosstalks at output port 2, 3, and 4 are -22.34 dB, -25.49 dB, and -24.87 dB, respectively.
Fig. 8. Insertion loss of (a) ADC1, (c) ADC2, and (e) ADC3 is investigated as a function wavelength. Mode crosstalk of (b) ADC1, (d) ADC2, and (f) ADC3 is studied as a function of wavelength.
For regular operation, one key issue for proposed mode switch is to effectively change the phase state of GSST. As has been reported, optical radiation and electrical heating may be applied to implement the phase transition of GSST. The optical radiation is conducted by focusing the amplified light from an external laser onto the GSST film via a single-mode fiber [27,28,32]. Electrical heating can implement the phase transition by introducing an ITO heater onto the GSST film. The driving voltage on ITO heater increases the temperature over the threshold of phase transition [22,33–35]. In comparison, the electrical driving is a more reliable and convenient switching method. Especially, compared to using ITO as the electrode, the doped-Si switching is a more promising alternative for electrical switching of on-chip PCM-based devices [36].
4. Conclusion
A GSST-assisted silicon waveguide mode selective switch is theoretically demonstrated. The switch is constructed by three cascaded ADCs, which could implement the optional mode switching from TE11 to TE21, TE31 or TE41 mode. 3D-FDTD method is used in the design optimization. By the quantitative study of phase matching and mode coupling, the proposed switch shows the insertion loss less than 1 dB within the wavelength range from 1523-1565 nm. The mode conversion efficiencies of TE11 to TE21, TE31 or TE41 mode are 89.96%, 92.87% and 90.94%, respectively. Due to the non-volatile nature of GSST, no excess power is required to maintain the switching state. The proposed mode selection switch has good penitential in low power, fast response on-chip signal routing.
Funding
National Key Research and Development Program of China (2019YFB2203001).
Acknowledgments
We thank the Ministry of Science and Technology of People’s Republic of China for financial support.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon request.
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