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Abstract
The reconfigurable mode demultiplexer is a crucial component for flexibly routing modes into different channels in on-chip multimode photonic systems with enhanced information processing capabilities. In this paper, we present a multichannel reconfigurable mode demultiplexer enabled by ultralow-loss phase-changing Sb2Se3. By harnessing the phase-change-mediated mode coupling in asymmetric directional couplers (ADCs), one or more of the higher-order modes including TE1, TE2 and TE3 modes could be selectively dropped from the bus waveguide with low losses. With an optimized ADCs structure, the proposed mode demultiplexer demonstrates insertion loss less than 0.227 dB in the ON (amorphous) state and the extinction ratios large than 23.28 dB over the C-band. By coupling the access waveguides of the higher-order mode in parallel on both sides of the bus waveguide, the device size can be compact with a footprint of ∼ 7 × 75 µm2, and this design approach can be further extended to enable more higher-order mode multiplexing.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
On-chip mode-division multiplexing (MDM) offers a promising solution to enhance the information carrying and processing capabilities of on-chip optical interconnects [1–3], by enabling the simultaneous multiplexing of multiple distinct orthogonal eigen modes [4]. To address the challenge posed by the increasing demand for information processing and the need for higher transmission capacity, MDM can be combined with wave-division multiplexing (WDM) [5,6], and polarization-division multiplexing (PDM) technologies [7–9], which not only reduces system costs but also saves physical space [10,11]. The development of a mode (de)multiplexer is crucial for constructing a hybrid multiplexing system. It is important to enable the dynamic tunability of mode (de)multiplexer to control the selective switching of different higher-order modes channels.
Traditional signal tuning methods in reconfigurable photonic devices, such as thermo-electric effect [12–14] and carrier dispersion tuning [15–17], have limited refractive index tuning capabilities (usually Δn < 0.01) and require a continuous supply of energy to maintain the changed state because of the volatile property [13,18]. To overcome these limitations and reduce energy consumption, phase-change-materials (PCMs), like Ge2Sb2Te5 (GST), Ge2Sb2Se4Te1 (GSST) and GeTe, have been extensively studied in photonics applications due to their large refractive index variation (usually Δn > 1) between the amorphous and crystalline states and non-volatility [19–22]. A GSST-assisted mode-selective switch enabling converting TE11 to TE21, TE31, or TE41 via three cascaded ADCs was proposed [23]. This method only converts the fundamental mode in the single-mode silicon waveguide into three higher-order modes, which does not truly enable reconfigurable (de)multiplexing of higher-order modes [24]. The GSST-assisted add/drop mode multiplexers has been demonstrated to enable selective adding or dropping of the TE1 and TE2 higher-order modes to/from the multimode bus waveguide, without implementing more higher-order mode channels.
Recently, novel PCMs such as Sb2Se3 and Sb2S3 have been demonstrated to have large (usually Δn > 0.6) refractive index contrast and ultra-low optical loss in the infrared range for both the amorphous and crystalline states, characterized by an extinction coefficient (k) of less than 1 × 10−5 [25]. Although Sb2Se3 requires micro to milliseconds to switch, without fast kinetics like GST only requiring tens of nanoseconds, it is not very relevant for reconfigurable devices which switching event occurs on the time scale of minutes to hours [26]. Crystallization of Sb2Se3 can be achieved by heating it to its crystallization temperature of Tx = 200 °C and heating Sb2Se3 above its melting temperature of Tm = 620 °C followed by rapid cooling can result in amorphization [27]. It can be prepared through thermal evaporation or magnetron sputtering, which exhibits stable phase-change properties, maintaining stability for over 1,000 cycles [25,26,28]. Sb2Se3 has been extensively utilized in the modal field control in various integrated waveguides, such as switches based on directional coupler or multimode interference [29–31], MZI [27,28], micro-ring resonator [32], and Bragg grating filters [33]. This paper specifically focuses on the Sb2Se3-mediated asymmetric mode coupling of higher-order modes. Here, a Sb2Se3-enabled reconfigurable mode demultiplexer is proposed to demultiplex three higher-order modes (TE1, TE2, and TE3) from the bus waveguide into the access waveguide using three cascaded ADCs. By transmitting two higher-order modes in the same bus waveguide section, a compact waveguide device with a length of only 75 µm can be achieved [4,34]. The incorporation of Sb2Se3 material enables low-loss demultiplexing of higher-order modes [25].
2. Principle and design
Figure 1(a) illustrates the top view of the proposed multichannel reconfigurable mode demultiplexer, which is constructed of fully-etched strip waveguides fabricated on a silicon-on-insulator (SOI) wafer with a 220-nm-thick silicon top layer. The refractive indices of Si and SiO2 are 3.477 and 1.444 at 1.55 µm, respectively. The reconfigurable demultiplexer consists of a bus waveguide and three access waveguides, with thin Sb2Se3 layers deposited on the top. The bus waveguide is divided into three sections with waveguide widths of wb1, wb2, and wb3, respectively, and each section is connected by adiabatic tapers to minimize mode loss. The coupling region lengths of the three ADCs are Lc1, Lc2, and Lc3, respectively, and the lengths of the two tapers are Lt1 and Lt2. A cross-sectional view of the ADC region is shown in Fig. 1(b). The widths of the bus waveguide and the access silicon waveguide are wb and ws, and the width and height of the Sb2Se3 on the top of the access silicon waveguide are wg and hg, respectively. The gap between the two parallel silicon waveguides in the coupling section is gc. In the S-type waveguide connecting the output and coupling sections of the access waveguide, the x-span and y-span are taken to be 10 µm and 1.5 µm, respectively, to ensure negligible waveguide bending loss. At the telecommunication wavelength of 1550 nm, the refractive indices of Sb2Se3 in the amorphous and crystalline states are 3.285 and 4.050, respectively [25].
Fig. 1. (a) Top view of the reconfigurable mode multiplexer. (b) Cross view of the coupling region (Cross section indicated in the top view). (c) Schematic of a certain higher-order mode’s coupling process.
From a certain higher-order mode’s coupling process in Fig. 1(c), when Sb2Se3 of the access waveguide is in the amorphous state, the higher-order mode can be coupled into the access waveguide through the ADC; when it is in the crystalline state, the higher-order mode will not be exported from the access waveguide output port due to phase mismatch. Thus, the first section of the bus waveguide propagates TE0, TE1, TE2, and TE3 modes, and three higher-order modes can be selectively coupled into the corresponding access waveguides through three ADCs. Only the TE3 mode could couple into the access waveguide via the ADC3 being converted to the fundamental mode. The TE0, TE1, and TE2 modes propagate through the second section of the bus waveguide, and the TE1 and TE2 modes will couple into the corresponding access waveguides via the ADC1 and ADC2, respectively. Only the TE0 mode could propagates through the third section of the bus waveguide.
As mentioned above, the ADC structure here is to satisfy the phase matching condition to allow the i (i = 1st, 2rd, and 3th) higher-order mode in the multimode bus waveguide coupling to the corresponding access waveguide and evolving to the fundamental mode. This indicates that the access waveguide should have a close modal index to that of the bus waveguide, when Sb2Se3 is in the amorphous state [35]. To achieve the cross-coupling between the two waveguides in the amorphous state, we firstly demonstrate the widths wb1 and wb2, of the first and second sections in the bus waveguide. Figure 2 shows the guided modes as a function of the width of the silicon waveguide with air upper cladding at 1550 nm [8]. When achieving phase matching, it is should be noted that modes with lower effective indices may lead to higher scattering losses during waveguide coupling due to stronger evanescent wave outside the waveguide. Furthermore, the effective indices of the chosen higher-order mode should be carefully selected to reduce the crosstalk with other higher-order modes during the out-coupling process. To realize a compact demultiplexer design, two bus waveguide sections with different widths are utilized, with the second section allowing for the simultaneous propagation of two higher-order modes through the ADC1 and ADC2. Considering the insertion losses and the crosstalk of mode out-coupling, the widths of the first and second waveguide sections are chosen as 1.64 µm and 1.06 µm, respectively, for an optimized performance. The third section is set to be 0.45 µm for single-mode operation. The modal effective refractive indices of the TE1, TE2 and TE3 mode in the bus waveguide are 2.4289, 1.8375 and 2.1157, respectively.
After determining the widths of the bus waveguide sections and the effective indices corresponding to the three higher-order modes, it is necessary to design appropriate access waveguides for the different higher-order modes of TE1, TE2, and TE3 in the bus waveguide. These access waveguides should enable selective demultiplexing in the ON/OFF (amorphous/crystalline) state. Due to the lower extinction coefficient of Sb2Se3 in the amorphous state, the higher-order modes in the bus waveguide will be coupled into the corresponding access waveguides and exit as the fundamental mode at the output ports. Conversely, in the crystalline state, the higher-order modes will not exit from the access waveguide output ports. Therefore, in the Sb2Se3 amorphous state, the effective refractive indices (neff) of the fundamental mode in the access waveguide is equivalent to that of the corresponding higher-order mode in the bus waveguide, enabling effective mode cross-coupling in the ADC. The refractive index changes of the Sb2Se3 thin film in the crystalline state cause a slight modal index mismatch between the two waveguides. Therefore, the coupling efficiency between the two waveguides in the crystalline state is significantly lower compared to the nearly 100% coupling efficiency achieved in the amorphous state. As a consequence, higher-order mode optical signals are allowed to be recoupled back into the bus waveguide in the crystalline state. This implies that the coupling lengths in ADCs in the amorphous state are common multiples of the coupling lengths in the crystalline state [36].
The height of the Sb2Se3 thin film in the access waveguide is assumed to be 40 nm. Additionally, the remaining access waveguide parameters are as follows: wg and ws. To ensure easy achievement within the alignment precision of electron beam lithography (EBL), wg is set to be 80 nm smaller than ws [37]. wg and ws are then optimized accordingly to satisfy the phase matching condition in the amorphous state, and neff of the access waveguides are calculated. The variations of neff of the fundamental mode in the access waveguide with ws and wg is given in Fig. 3, in which ws for the TE1, TE2, and TE3 modes are set to be 0.476 µm, 0.333 µm, and 0.379 µm, respectively, and wg are 0.345 µm, 0.221 µm, and 0.284 µm, respectively.
The coupling gap (gc) of the ADCs need to be optimized to ensure the coupling lengths of the amorphous state to be common multiples of the coupling lengths of the crystalline state, considering the minor refractive index differences between the crystalline and amorphous state of Sb2Se3 [36]. This allowed the optical signals to couple back into the bus waveguide in the fully crystallized state. The optical field intensity patterns in the amorphous and crystalline state for the TE1, TE2, and TE3 modes are given in Fig. 4. It can be observed that in the amorphous state, the higher-order modes in the bus waveguide are coupled into the access waveguide. Similarly, in the crystalline state, a portion of the higher-order modes are also coupled into the access waveguide. By selecting appropriate coupling region lengths, the higher-order modes would be output from the access waveguide output ports in the ON state while not output from the access waveguide output ports in the OFF state. The coupling length, Lc,am, in the amorphous state, is calculated using the coupled wave theory equation [35,37]:
where λ is the wavelength, and n1 and n2 are neff of the odd and even supermodes in a two-waveguide system. In the crystalline state, the change in neff of the access waveguide results in a phase mismatch, and the crystalline coupling length, Lc,cr, can be derived to be [38]:Fig. 3. Phase-matching conditions for TE1, TE2 and TE3 modes. Variations of neff with ws for (a) TE1, (c) TE2 and (e) TE3 modes. Variations of neff with wg for (b) TE1, (d) TE2 and (f) TE3 modes.
Fig. 4. Optical field intensity propagation for (a), (c) and (e) amorphous and (b), (d) and (f) crystalline Sb2Se3 when Lc,am ≈ 2m·Lc,cr, where m ∈ Z+ for TE1, TE2, and TE3 modes.
Upon stipulating the design requirements and calculations, the coupling gap, gc, and coupling length, Lc, of each higher-order mode TE1, TE2, and TE3 are then determined according to Fig. 5. Figure 5(a), (c) and (e) show the corresponding Lc of each higher-order mode in different states as gc increases. For clarity, we represent the Lc of the two structural states as a ratio i.e. Lc ratio = Lc,am / Lc,cr. The variations of the Lc ratio with the ADC coupling gap gc for the three higher-order modes is given in Fig. 5(b), (d), and (f). Considering the actual manufacturing accuracy of the coupling gap and compact footprint, the Lc ratio of the three higher-order modes of TE1, TE2 and TE3 are chosen as m = 2, 1 and 2, respectively. The final dimensions of the three higher-order modes ADCs are then given in Table 1.
Fig. 5. Coupling length and coupling length ratio of Sb2Se3 for (a), (b) TE1, (c), (d) TE2, and (e), (f) TE3 modes.
Table 1. Device dimension of the reconfigurable mode demultiplexer
The optimization for the design of the tapers is also investigated by using the 3D-FDTD method. Figure 6(a) shows the variations of the insertion losses (ILs) with the taper length of the first taper between the first and second sections of the bus waveguide. The ILs of the TE0 ∼ TE2 modes are calculated due to these modes supported in the second bus waveguide section. In this case, the maximum IL of two tapers is set as IL ≤ 0.05 dB and then the taper lengths can be optimized. It can be noted from Fig. 6(a) that the ILs of the TE0 ∼ TE2 modes are decreased with the increasing taper length and are lower than 0.05 dB after the taper length is larger than 3.07 µm. Considering the compact structure, the length of the first taper is set to be Lt1 = 3.07 µm, and the field propagation pattern for the TE2 mode is shown as the inset in Fig. 6(a). Similarly, the second taper length is also investigated and shown in Fig. 6(b), with the field propagation pattern for the TE0 mode shown as the inset. The second taper length is determined to be Lt2 = 1.31 µm.
Fig. 6. Variations of the insertion losses with the taper lengths of (a) the first taper between the first and second sections and (b) the second taper between the second section and the single-mode strip waveguide.
3. Results and discussions
Figure 7 illustrates the selective demultiplexing of the higher-order TE1, TE2, and TE3 modes in the ON/OFF state. In the amorphous state of Sb2Se3, the higher-order mode is effectively coupled from the bus waveguide to the corresponding access waveguide. Due to the refractive index matching, the higher-order mode TE1 in the bus waveguide will evolve to the fundamental mode of the corresponding access waveguide, as shown in Fig. 7(a). On the other hand, in the crystalline state, the effective index matching for the TE1 mode in the ADC1 is disrupted by the refractive index increment of Sb2Se3, resulting in weaker coupling. As a result, the TE1 mode in the access waveguide couples back into the bus waveguide again, as shown in Fig. 7(b). Similar results of TE2 mode in ADC2 and TE3 mode in ADC3 can be observed in Fig. 7(c), (d), (e) and (f), respectively.
Fig. 7. Normalized electric field distribution of ADCs with (a), (c) and (e) amorphous and (b), (d) and (f) crystalline Sb2Se3 for TE1, TE2, and TE3 modes.
Figure 8 presents the corresponding insertion losses (ILs) and extinction ratios (ERs) of the TE1, TE2, and TE3 modes in the telecommunication band (1530 nm to 1565 nm) at the output ports of the access waveguides. In the amorphous state of Sb2Se3, the maximum insertion losses of the three higher-order modes, TE1, TE2, and TE3, are respectively 0.086 dB, 0.227 dB, and 0.108 dB, respectively in the C-band. In the crystalline state, the maximum transmission of the three higher-order modes, TE1, TE2, and TE3, are -28.91 dB, -23.51 dB, and -29.31 dB, respectively. At the access waveguide output ports, the insertion loss is less than 0.24 dB and the extinction ratio is more than 23.28 dB in the C-band for the TE1, TE2, and TE3 modes.
Fig. 8. Transmission spectra of the ADCs in the ON (amorphous) and OFF (crystalline) state at the access waveguide output ports for (a) TE1, (b) TE2, and (c) TE3 modes.
As shown in Fig. 9, the fabrication process of the proposed multichannel reconfigurable mode demultiplexer can be as follows. The device is fabricated on a SOI wafer with a 220 nm-thick top silicon layer and a 2 µm-thick buried-oxide layer. The positive photoresist is spin-coated onto the silicon layer by a spin coater and the silicon waveguide layer is defined using an EBL process and etched by inductively coupled plasma (ICP) dry etching. Next, the positive photoresist (PMMA) is spin-coated onto the silicon layer again. The desired Sb2Se3 windows are patterned by the second EBL process. By using thermal evaporation, the Sb2Se3 layer film can be deposited and then the Sb2Se3 pattern on the access waveguide sections is achieved by the lift-off process. Finally, a thin silicon dioxide capping layer can be deposited on top of the Sb2Se3 to enhance long-term stability and prevent loss and oxidation of selenium [29]. The structural parameters in this work are designed for an air capping layer on the PCM. However, the same device performance can be achieved by adjusting the structural parameters of the device after adding a thin silicon dioxide capping layer.
It should be noted that during the phase-change process, due to atomic rearrangement, the PCM layer undergoes changes in thickness [39]. Specifically, the Sb2Se3 material experiences a 30% reduction in thickness during the thermal evaporation process [33]. Consequently, we analyzed the transmission responses of the proposed device when the Sb2Se3 thickness varies between ±10% from the designed thickness (hg = 40 nm) in Fig. 10. It could be observed that larger Δhg values lead to increased ILs and decreased ERs, and within the varying range of Δhg = ±2 nm, the extinction ratios for the TE1, TE2, and TE3 modes remained ∼15 dB. When the variation range of Δhg is within ±4 nm, the extinction ratios for the three higher-order modes decreased to ∼10 dB and insertion losses increased to ∼1.5 dB. These results demonstrate that the device performance is sensitive to film thickness, underscoring the need for fine thickness control for achieving a satisfactory device performance. To quantify the fabrication tolerance of the present device with the ADCs for the TE1, TE2, and TE3 modes, here we consider the dimensional deviations of ±5 nm on the widths of wg. The simulation results are shown in Fig. 11. In the ON and OFF state, the insertion losses and extinction ratios at the access waveguide output ports are < 0.3 dB and > 13 dB in the C-band, respectively, which is still acceptable.
Fig. 10. Calculated transmission responses of (a) TE1, (b) TE2, and (c) TE3 mode channels considering dimensional deviations on the Sb2Se3 strip thickness at the access waveguide output ports. The working wavelength is 1550 nm.
Fig. 11. Calculated transmission responses of (a) TE1, (b) TE2, and (c) TE3 mode channels considering dimensional deviations on the Sb2Se3 strip width at the access waveguide output ports.
4. Conclusion
In conclusion, we have proposed a compact multichannel reconfigurable mode demultiplexer enabled by phase change material Sb2Se3. By incorporating a Sb2Se3 layer on top of narrow single-mode access waveguides interacting with evanescent wave of guided modes, one or more of the higher-order TE1, TE2 and TE3 modes can be selectively dropped from the bus waveguide. The parameters for the ADCs are chosen carefully to ensure precise phase matching between different modes, and the designed mode demultiplexer shows low insertion losses (< 0.227 dB) in the ON state and high extinction ratios (> 23.28 dB) over the C-band for all mode channels. In particular, the maximum insertion loss for the TE1, TE2 and TE3 modes is less than 0.16 dB, and the minimum extinction ratio is larger than 31 dB, in the ON state at the wavelength of 1550 nm. The proposed compact multi-channel reconfigurable mode demultiplexer potentially paves the way for mode-division multiplexing in on-chip optical communication links and interconnect networks.
Funding
Natural Science Foundation of Zhejiang Province (No. LD22F040002, No. LY23F050008); National Natural Science Foundation of China (No. 62105172); Natural Science Foundation of Ningbo Municipality (No. 2022J105); K. C. Wong Magna Fund in Ningbo University.
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 reasonable request.
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