Open Access
Add to BibSonomy
Abstract
A reconfigurable mode (de)multiplexer/switch (RMDS) is a pivotal component for the mode routing in mode-division multiplexing (MDM) networks. Here, we propose a three-dimensional (3D) RMDS via a triple-waveguide directional coupler, consisting of a lower doped silicon waveguide, a central plasmonic horizontal-slot waveguide with indium-tin-oxide (ITO) and an upper doped polycrystalline-silicon waveguide. The enhanced light-matter-interactions can be achieved via the central plasmonic metal-oxide-semiconductor (MOS) mode. The multiplexing states of the proposed 3D-RMDS can be switched by adjusting the applied voltage bias on the ITO layer. The simulation results reveal that a 3D quasi-TM0 and quasi-TM1 RMDS is with a compact length of 8.429 μm, the mode crosstalk of −20.3 dB (−9.2 dB) and the insertion loss of 0.06 dB (1.47dB) at the wavelength of 1550 nm for the “OFF” (“ON”) state, respectively. The proposed 3D-RMDS can be applied in future 3D on-chip MDM networks to achieve a flexible mode-routing and further enhance the transmission capacity.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past decades, many multiplexing technologies have been proposed and developed to meet the demand of the exponentially increasing data traffic, such as wavelength-division multiplexing (WDM), polarization-division multiplexing (PDM) technologies and so on [1,2]. Recently, the mode-division multiplexing (MDM) technology has been attracting great attention to enhance the communication capacity by using the high-order modes of multimode waveguides [3,4]. The MDM network is well compatible with the WDM and PDM systems, which can easily expand the existing network to achieve a large system capacity [5]. A mode multiplexer (MUX)/demultiplexer (DeMUX) is one of the most pivotal components for the MDM networks. In order to realize a MDM network on-chip, several kinds of silicon based mode (De)MUXs have been proposed, which can provide very compact, easy-fabrication and cost-effective devices, owing to silicon waveguides with the high refractive index-contrast and complementary metal-oxide-semiconductor (CMOS) compatible fabrication-process [6,7].
Several approaches to constructing a mode (De)MUX have been reported, including the adiabatic couplers (ACs), multimode-interference (MMI) waveguides, Y-branches, and asymmetrical directional couplers (ADCs) [8–11]. Although the mode (De)MUXs based on the ACs, MMI waveguides and Y-branches are with broad bandwidths and high extinction ratios (ERs), these devices suffer from relatively long lengths of > 100 μm. A more compact mode (De)MUX can be obtained by using the ADCs structures, but the traditional ADCs are with narrow bandwidths and tight fabrication-tolerances due to the critical phase-matching conditions. The tapered and taper-etched ADCs have been proposed to relax the tolerance of the mode (De)MUXs, but the fabrication-processes would be more complicated [12,13].
A reconfigurable MDM network would provide the ability to switch and route different mode signals in different channels, which is one of the main trends of the future MDM systems [14]. A reconfigurable mode (De)MUX/switch (RMDS) is an essential component for the reconfigurable MDM networks. A few RMDSs have been reported for future MDM networks, mainly including the Mach-Zehnder interferometers (MZIs) and micro-ring resonators (MRRs) [15]. A reconfigurable photonic integrated mode (De)MUX has been reported by using two balanced MZIs with two 2 × 2 MMIs and two phase-shifters [16]. This reported mode (De)MUX is with a mode excitation crosstalk (CT) of −20 dB and a measured bandwidth of > 10 nm. However, the device length of this mode (De)MUX is more than 400 μm owing to large sizes of the MMIs and phase-shifters. Another approach could be the use of two Y-junctions and a phase-shifter based MZI. C. Sun et al. reported a reconfigurable mode-MUX via a MZI assisted by a phase-shifter, which can achieve a measured ER of ∼24 dB over the C band for OFF–ON switchover [17]. Nevertheless, owing to the weak nonlinear thermo-optic (TO) effect of silicon material, the MZIs based reconfigurable mode (De)MUXs suffer from the large footprints. Another approach could be the use of the MRRs based MDM (De)MUXs. A 1 × 2 multimode switch based on the silicon MRRs has been proposed and experimentally developed, which can provide the low CT of < −16.8 dB, bit-error below 10−9 and power penalties below 1.4 dB, while routing 10 Gb/s data [18]. But, the spectral bandwidth of a MRR is limited, which should be circumvented in many optical communication systems. Therefore, a RMDS allowing for fast tunable states is relatively challenging with respect to the footprint and switching-speed.
In order to reduce the footprint, switching-time and power-consumption, the light-matter-interaction must be enhanced inside the RMDS. Recently, many silicon modulators and switches have been reported by using CMOS-compatible transparent conducting oxides (TCOs) [e.g. indium tin oxide (ITO), graphene, gallium zinc oxide and vanadium dioxide (VO2)] [19–22] as a result of their unique properties of epsilon-near-zero (ENZ) effect and electrically tunable permittivity, which can achieve the high switching-speed (ps), compact footprint (λ-size), ultra-bandwidth and ultra-low power-consumption (several fJ/bit). Using a metal-oxide semiconductor (MOS) plasmonic hybrid waveguide with ITO, C. Ye et al. proposed and optimized a compact 2 × 2 electro-optic (EO) switch with a footprint of only 4.8 µm2 and allowing for sub-fJ per bit power efficiency [19]. H. Zhao et al. numerically designed a broadband electro-absorption modulator by using an ITO based MOS type structure with a high absorption loss of 9.8 dB/μm [23]. λ-size ITO and graphene based EO modulators have been reported to achieve a 3 λ-short device, and a 0.78 λ-short device respectively [24]. Moreover, both ITO and graphene based compact switches and modulators are capable of broad bandwidth since no resonator is implemented. Among them, optical switches are capable of data routing, which is indispensable in WDM networks. However, above reported devices are based on single-mode waveguides, which only consider fundamental modes. For the MDM networks, it is essential to implement switching and (de)multiplexing for multimode waveguides since the photonic structures required to perform the switching and (de)multiplexing differ greatly from mode to mode.
Inspired by the MOS-type hybrid plasmonic waveguide with TCO materials, we propose a three-dimensional (3D) RMDS via a triple-waveguide ADC, consisting of a lower doped silicon waveguide, a central plasmonic horizontal-slot waveguide with ITO and an upper doped polycrystalline-silicon (Poly-Si) waveguide. By introducing the 3D scheme, the limitation of the integration density for 2D photonic integrated circuits (PICs) would be addressed and the operating modes can be simultaneously routed between different layers and different channels, which may find applications in future 3D integrated MDM systems. By introducing a nano-ITO layer, a high switching-speed can be achieved due to the high carrier mobility in ITO and the strong confinement of both electrical and optical fields, thereby enhancing the light-matter-interaction. The output mode-states can be adjusted by electrically tuning the free carrier concentration in the intermediate ITO layer. In this work, the ITO layer is sandwiched by two SiO2 layers to achieve dual bias operation, while biasing it simultaneously from both the top and the bottom to achieve two accumulation layers at each ITO-SiO2 surface. For the conventional two-waveguide based plasmonic devices, the main issue is the high loss due to the lossy metal-based plasmonic structure [25]. In this paper, the lossy plasmonic waveguide is placed in between two outer silicon waveguides as an aid-waveguide, which can significantly reduce the propagation loss. The characteristics of the carrier accumulation layer of the ITO are studied by using the Thomas-Fermi approximation, which are fundamental and important to the operation of the proposed structure. The proposed 3D-RMDS is optimized by using the full-vectorial finite element method (FV-FEM) and 3D full-vectorial finite difference time domain (3D-FV-FDTD) method.
2. Structure and principle
The schematic diagram of the proposed 3D-RMDS is shown in Fig. 1(a) based on a triple-waveguide ADC, which is comprised of a lower doped silicon waveguide (input waveguide), an upper doped Poly-Si waveguide (bus waveguide) and a central plasmonic horizontal-slot waveguide. The central plasmonic waveguide consists of a thin ITO layer sandwiched by two silicon dioxide (SiO2) layers and two doped silicon layers, in which a MOS-type plasmonic hybrid mode can be supported. The BAR- and CROSS-ports are denoted by the ports O1 and O2, respectively. The proposed structure is compatible with the CMOS process, thereby the (de)multiplexing states can be switched by electrically tuning the carrier concentration of the thin ITO layer. The operation principle of the proposed 3D-RMDS can be explained in details: (i) for the “OFF” state, the central plasmonic waveguide is without an external electric field. A phase-matching condition would be achieved for this triple-waveguide ADC. A quasi-TM0 mode launching at lower port I1 can be completely converted to the quasi-TM1 mode in the bus waveguide after propagating along a coupling length of Lc and outputs at upper CROSS-port O2; (ii) for the “ON” state, an optimized voltage bias is applied on the central plasmonic waveguide, thereby the carrier concentration at the ITO-dielectric interface is increased and the part of the plasmonic hybrid mode is concentrated into a nanometer-thin region. The output quasi-TM0 mode can be switched to stay at the BAR side via adjusting the effective indices of the supermodes through tuning the complex refractive index of the ITO.
Fig. 1 Schematic of 3D reconfigurable mode (De)MUX/switch: (a) Schematic diagram for the proposed device. (b) Cross-section of triple-waveguide ADC based 3D reconfigurable mode (De)MUX/switch.
The cross-section of the proposed triple-waveguide ADC based 3D-RMDS is shown in Fig. 1(b). The proposed device is based on the silicon-on-isolator (SOI) platform, in which the refractive indices of the silicon, SiO2 and Poly-Si are taken as 3.47548, 1.46 and 3.48, respectively at the operating wavelength of 1550 nm. The whole structure is embedded in the SiO2 upper-cladding. The gap between the central plasmonic waveguide and the doped silicon/Poly-Si waveguides is denoted by g. The heights of the lower silicon and upper Poly-Si layers are identical and denoted by h. The widths of the input and bus waveguides are represented by W1 and W2, respectively. The size of the input waveguide is chosen as W1 × h = 400 nm × 220 nm, which is a common size of a silicon waveguide. For the central plasmonic slot waveguide, the width is denoted by Wp and the heights of the ITO and SiO2 layers are represented by hi and hs, respectively. It can be observed from Fig. 1(b) that the active material of the ITO is sandwiched by two silica layers and the voltage bias is applied between both the upper/lower doped silicon-layers and the ITO layer, which can achieve a dual-bias operation. Due to a reasonably thin (< 5 nm) accumulation layer of the ITO, the height of the ITO layer is appropriately chosen to be hi = 10 nm.
3. Electrical simulation
The characteristic of the ITO is the key to the proposed 3D-RMDS. The permittivity of the ITO layer is calculated based on the Drude-Lorentz model [26]:
where ε∞ = 3.9 is the high-frequency ITO permittivity; γ = 1.84 × 1014 rad/s is the electron scattering rate; ω is the angular momentum in rad/s. The plasma frequency, ωp is determined by:where ε0 is the vacuum permittivity; m* = 0.35m0 is the effective mass of the electron; e and m0 are the elementary electron charge and the rest mass of the electron, respectively; nc is the voltage-tunable carrier concentration of the ITO layer, which can be calculated based on the Thomas-Fermi approximation [27]:where h is Planck’s constant; φ(y) is the local potential; the Fermi energy, EF is determined by:where n0 is the bulk free electron concentration at the applied voltage bias, Vg = 0, which can be calculated via n0 = ε0m*ωp/e2. According to the Thomas-Fermi approximation, the Thomas-Fermi screening length of ITO is estimated to be 1.27 nm, which is calculated by using the formula:In order to double the carrier-accumulation speed, a plasmonic structure of an ITO layer sandwiched by two SiO2 layers is used in this case. According to the Drude-Lorentz model, variations of the complex permittivity and refractive index of the ITO layer are calculated and shown in Fig. 2. Variations of the real and imaginary parts of the complex permittivity of the ITO as a function of frequency (lower x-axis) and wavelength (upper x-axis) for different carrier concentrations are shown in Figs. 2(a) and 2(b), respectively. Variations of the refractive indices and extinction coefficients of the ITO with frequency (lower x-axis) and wavelength (upper x-axis) for different carrier concentrations are shown in Figs. 2(c) and 2(d), respectively. It can be noted that with the change of the carrier concentration of ITO from 1020 to 1021 cm−3, the permittivity at the wavelength of 1550 nm changes dramatically. With the increase of the carrier concentration inside two accumulation layers of the ITO, the material would become more metallic, which can achieve an ENZ effect [23].
Fig. 2 ITO optical parameters from the Drude-Lorentz model: (a) real part and (b) imaginary part of the complex permittivity of ITO as a function of frequency (lower x-axis) and wavelength (upper x-axis) for different carrier concentrations. (c) Refractive indices and (d) extinction coefficients of ITO with different carrier concentrations.
In this case, the operating wavelength of 1550 nm is chosen for the proposed 3D-RMDS. Variations of the real part (left y-axis) and imaginary part (right y-axis) of the complex permittivity of the ITO with different carrier concentrations are shown in Fig. 3 at the wavelength of 1550 nm. It can be noted that in order to achieve an ENZ effect by tuning the ITO material from dielectric to quasi-metallic, a carrier concentration of < 6.5 × 1021 cm−3 is needed. The ENZ effect can bring the real part of index of the ITO material close to zero, thereby can induce significantly large modal effective-index changes of the central plasmonic waveguide.
Fig. 3 (a) Real part (left y-axis) and (b) imaginary part (right y-axis) of the complex permittivity of ITO with different carrier concentrations at the wavelength of 1550 nm.
Next, the effects of the applied voltage are studied for the central plasmonic waveguide. For the electrical simulation of the ITO based MOS-type structure, the proposed plasmonic structure is simplified to a 2D structure model shown as an inset in Fig. 4(a). According to the Thomas-Fermi approximation, variation of the carrier concentration with the applied voltage at the wavelength of 1550 nm is calculated and shown in Fig. 4(a). It can be noted that the accumulated carrier concentration of the ITO is increased with the increase of the applied voltage. Then, by using the Drude-Lorentz model, variations of the real part (left y-axis) and imaginary part (right y-axis) of the complex permittivity of the ITO with the applied voltage can be calculated and shown in Fig. 4(b). It can be noted that the real part of the complex permittivity is decreased with the increase of the applied voltage, while the imaginary part is increased. In order to achieve an ENZ condition, the applied voltage is chosen to be Vg = 2.4 V. The refractive index of the ITO would be changed from 1.960 + 0.003i at Vg = 0 V to 0.479 + 0.646i at Vg = 2.4 V, which are corresponding to the dielectric and quasi-metallic states, respectively.
Fig. 4 (a) Variation of the carrier concentration with the applied voltage bias at the wavelength of 1550 nm; the inset is the schematic diagram for the electrical simulation. (b) Variations of real part (left y-axis) and imaginary part (right y-axis) of the complex permittivity of ITO with the applied voltage bias.
In order to study the mode-evolution characteristics of the central ITO based plasmonic slot waveguide, the changes of the effective index and the leakage loss are calculated with respect to the applied voltage bias. Variations of the effective index (left y-axis) and the leakage loss (right y-axis) with the applied voltage bias are shown in Fig. 5(a). It can be noted that the effective index is decreased with the increase of the applied voltage bias, whereas the leakage loss is increased. This phenomenon can be explained by the fact that with the increase of the applied voltage bias, the real part of the index of the ITO is reduced and the ITO material reaches to the quasi-metallic state, which would result in an increasing plasmonic loss. The Poynting vectors, Pz (x, y) of the quasi-TM0 mode of the central plasmonic slot waveguide are calculated by using the FV-FEM for Vg = 0 and 2.4 V and shown in Figs. 5(b) and 5(c), respectively. It can be observed that without an applied voltage, the mode field of the quasi-TM0 mode is mainly confined in two low-index SiO2 layers. The central waveguide can be equivalent to a horizontal two-slot waveguide. When Vg = 2.4 V is applied, it can be noted from Fig. 5(c) that the plasmonic hybrid mode of the quasi-TM0 polarization is concentrated into a nanometer-thin region of the ITO layer. The central waveguide can be equivalent to a horizontal single-slot waveguide, which can dramatically change the effective index of the central waveguide compared to the horizontal two-slot waveguide.
Fig. 5 (a) Variations of the effective index (left y-axis) and the leakage loss (right y-axis) with the applied voltage bias. (b) and (c) are the Poynting vectors, Pz (x, y) of the quasi-TM0 mode in the central slot waveguide without an external electric field and under the applied voltage bias of Vg = 2.4 V, respectively.
4. Optical simulation
The optical simulation for the proposed 3D-RMDS is carried out by using the FV-FEM and 3D-FV-FDTD. As the proposed device based on a triple-waveguide ADC, the phase-matching condition is firstly investigated by using the FV-FEM. For the “OFF” state without an external voltage bias, the phase-matching condition between these three waveguides should be satisfied to achieve a maximum mode (de)multiplexing. The effective index of the upper bus waveguide should be equal to that of the lower input waveguide. Variations of the effective index with the width of the doped silicon waveguide are shown in Fig. 6(a). The effective index of the quasi-TM0 mode of the doped silicon waveguide is denoted by a dash-dotted green line, while that of the quasi-TM1 mode of the doped Poly-Si waveguide is shown by a solid pink line. The effective index of the quasi-TM0 mode of the input waveguide with the size of W1 × h = 400 nm × 220 nm is calculated to be neff = 1.71, as shown by a dash-dotted black line in Fig. 6(a). In order to achieve the phase-matching condition, the width of the bus waveguide is chosen to be W2 = 1.06 μm. The Ey fields of the quasi-TM0 and quasi-TM1 modes of the phase-matched input and bus waveguides are shown in Figs. 6(b) and 6(c), respectively.
Fig. 6 (a) Variations of the effective index with the width of the doped silicon waveguide. (b) Ey field of the quasi-TM0 mode in the lower doped silicon waveguide. (c) Ey field of the quasi-TM1 mode in the upper doped Poly-Si waveguide.
For a triple-waveguide based ADC, there are five supermodes supported in this structure, including three TM-supermodes and two TE-supermodes. The Ey field of the TM-A supermode, Pz field of the TM-B supermode and Ey field of the TM-C supermode are shown in Figs. 7(a), 7(b), and 7(c), respectively. The Ey components were selected for the TM-A and TM-C supermodes due to their mode fields mainly confined in the horizontal slot regions. Owing to the mode fields mainly confined in two outer waveguide, the Poynting vector, Pz component is selected for the TM-B supermode, which can represent the power distribution of this mode. In order to achieve a maximum mode conversion efficiency (MCE) at the CROSS state, the effective indices of the TM-A, TM-B and TM-C supermodes (nA, nB and nC) should meet the following condition [19]:
Fig. 7 Supermode field profiles of three-waveguide based 3D reconfigurable mode (De)MUX/switch: (a) Ey field of TM-A. (b) Pz field of TM-B. (c) Ey field of TM-C.
Variations of the effective indices of the TM supermodes with the width of the central slot waveguide are shown in Fig. 8 for both the “OFF” and “ON” states. The effective index of the TM-B supermode is denoted by a dash black line, which is constant with the change of the Wp due to the mode field confined in two outer silicon waveguides. The effective indices of the TM-A and TM-C supermodes at "OFF" state are denoted by the solid red and blue lines, respectively, while those at “ON” state under Vg = 2.4 V are shown by the dash-dotted red and blue lines, respectively. The values of (nA + nC)/2 are denoted by the solid and dash-dotted black lines for the "OFF" and "ON" states, respectively. It can be noted from Fig. 8 that the phase-matched Wp are chosen as Wp = 140 and 190.3 nm for the “OFF” and “ON” states, respectively.
Fig. 8 Variations of the effective indices of the TM supermodes with the width of the central slot waveguide. The solid and dash-dotted lines are for the “OFF” state (without an external electric field) and “ON” state (under the applied voltage bias of 2.4 V), respectively.
The proposed design operates at two states: the input quasi-TM0 mode at port I1 (a) converted to the quasi-TM1 mode on the CROSS side corresponding to the “OFF” state; (b) propagating along the BAR side corresponding to the “ON” state. For the proposed design, the physical length of the device is depended on the coupling length at the CROSS state. In order to achieve a compact device with a high ER, the coupling length at the CROSS state is expected to be shorter, while that at the BAR state is expected to be longer. The coupling length of a triple-waveguide ADC can be calculated by using the formula [19]:
where βA and βC are the propagation constants of the TM-A and TM-C supermodes, respectively; λ0 is the operating wavelength.A coupling length ratio between the “ON” and “OFF” states is denoted by Lc ratio (ON/OFF) = Lc (ON)/Lc (OFF). Variations of the coupling length (left y-axis) and the coupling length ratio (right y-axis) with the gap, g and the height of the silica layer, hs, are shown in Figs. 9(a) and 9(b), respectively. The coupling lengths for the “ON” and “OFF” states are denoted by the solid red and blue lines, respectively. The Lc ratio (ON/OFF) is denoted by a dash-dotted black line. It can be noted from Fig. 9(a) that the coupling lengths for both the “ON” and “OFF” states are increased with the increase of the gap, g. Therefore, with a narrower gap, a shorter coupling length can be achieved due to a stronger interaction, while a higher CT would also be induced. It can also be noted from Fig. 9(a) that the Lc ratio (ON/OFF) is increased as a function of the increase of the gap, g. It can be noted from Fig. 9(b) that the coupling length for the “OFF” state is increased with the increase of the height of the silica layer, hs. For the “OFF” state, the mode field of the central slot waveguide is mainly confined in two silica layers, which is affected significantly by the change of hs. The Pz fields of the TM-A and TM-C supermodes at “OFF” state are shown in Fig. 10 since the Pz component is more typical representative of these two supermodes compared to the Hx and Ey components. While for the “ON” state, the plasmonic hybrid mode field is concentrated into the nano-thin ITO layer, which is less affected by the change of hs. The Pz fields of the TM-A and TM-C supermodes at “ON” state are shown in Fig. 10. It can also be verified from Fig. 9(b) that the coupling length for the “ON” state is slightly decreased with the increase of the hs from 10 nm to 25 nm, and then reaches to a constant value after hs = 25 nm. The Lc ratio (ON/OFF) is decreased with the increase of the hs. In this case, the optimal parameters are chosen as: hs = 10 nm, hi = 10 nm, Wp = 140 nm, and g = 300 nm. The coupling length ratio and the coupling length for the “OFF” state are calculated to be Lc ratio (ON/OFF) = 5.02 and Lc (OFF) = 8.429 μm, respectively. If the gap is increased to be g = 400 nm, the coupling length ratio is significantly increased to Lc ratio (ON/OFF) = 31.50 with a slightly longer Lc (OFF) = 12.955 μm.
Fig. 9 Variations of the coupling length (left y-axis) and coupling length ratio (Lc ratio, right y-axis) with (a) gap, g and (b) height of the silica layer, hs, respectively.
Fig. 10 Pz fields of the TM-A and TM-C supermodes at “OFF” state (without an external electric field) and “ON” state (under the applied voltage bias of 2.4 V), respectively.
Next, the propagation characteristics of the proposed 3D-RMDS are investigated by using the 3D-FV-FDTD method. The propagation fields of the optimal design with the parameters of hs = 10 nm, hi = 10 nm, Wp = 140 nm, and g = 300 nm are calculated and shown in Fig. 11 at the operating wavelength of 1550 nm. The mesh sizes were set as 10, 10, and 20 nm for the x, y and z directions, respectively. A refined mesh of Δy = 2 nm was used for the ITO and inner silica layers of the central slot waveguide. As the longitudinal xz-plane shown in Fig. 11, the y-coordinate was set to be y = 0.36 μm, which is corresponding to the horizontal centerline of the cross-section of the upper Poly-Si waveguide. The coupling length of the proposed device, Lc = Lc (OFF) = 8.429 μm is shown in Fig. 11(a). When launching the quasi-TM0 mode at port I1 of the input waveguide, the CROSS (“OFF”) and BAR (“ON”) states are switched by applying Vg = 0 V and 2.4 V, respectively. It can be noted from Figs. 11(a) and 11(b) that for the CROSS state, a high efficient 3D-RMDS can be achieved, in which the input quasi-TM0 mode is completely transferred from the lower input waveguide to the quasi-TM1 mode of the upper bus waveguide. The Hx fields were chosen to describe the mode coupling between the lower and upper layers since the Ey fields have larger evanescent fields between these two layers. When applying a gate voltage of Vg = 2.4 V on the ITO, the input quasi-TM0 mode would propagate along the lower input waveguide without mode-coupling, which can be revealed in Figs. 11(c) and 11(d), respectively. It should be important to note that the light in the input-waveguide section is shown in Fig. 11(d), which is the evanescent field of the Ey component monitored at the upper layer. We calculated the Ey field of the quasi-TM0 mode in the lower input waveguide, as shown in Fig. 6(b). It can be noted that the light will get through the interface and enter closer in the silica medium. This part of the Ey field named evanescent field is to exponentially decrease. For y = 0.36 μm, the amplitude of the evanescent field is about half of the maximum, which is large enough to be monitored at the upper layer. Compared to the Ex field at the lower layer shown in Fig. 11(c), the evanescent field shown in Fig. 11(d) is slightly widened due to the wider field profile of the evanescent field than the field confined in the core. This Ey field should be carefully examined for the crosstalk induced by evanescent fields for 3D-PICs devices. For a mode (De)MUX, a quasi-TM0 mode launching at port I2 of the bus waveguide should propagate along the bus waveguide without any mode-coupling loss for both the “ON” and “OFF” states, which can be verified by the propagation field shown in Fig. 11(e).
Fig. 11 Propagation fields along z direction at the operating wavelength of 1550 nm. For quasi-TM0 mode launching at port I1: Hx fields at (a) lower and (b) upper layers for “OFF” state. Ey fields at (c) lower and (d) upper layers for “ON” state. (e) Ey field at upper layer for quasi-TM0 mode launching at port I2.
In order to evaluate the performance of the optimal 3D-RMDS, the mode CT, MCE, and insertion loss (IL), are calculated based on the formulas:
where PI1 is the input power at port I1; PO1 and PO2 are the output powers at ports O1 and O2, respectively. These Eqs. (8), (9) and (10) are for the CROSS state, while the output ports used in the formulas should be changed according to the BAR state. For the CROSS (“OFF”) state, the mode CT, MCE and IL are calculated to be −20.3 dB, 95.4% and 0.06 dB, respectively at the wavelength of 1550 nm. For the BAR (“ON”) state, the mode CT and IL are calculated to be −9.2 and 1.47 dB, respectively.Next, the performances of the proposed 3D-RMDS are studied with respect to the wavelength, the applied voltage bias, and the width of the central waveguide, respectively. Variations of the transmittance with the operating wavelength for the quasi-TM0 mode launching at ports I1 and I2 are shown in Figs. 12(a) and 12(b), respectively. It can be observed that the transmittances at “OFF” state are denoted by the dash-dot-dotted and solid red lines for the BAR and CROSS ports, respectively, while those at “ON” state are shown by the dash and dash-dotted blue lines, respectively. It can be noted from Fig. 12(a) that the 1 dB bandwidth at “OFF” state is over 92 nm from 1508 to 1600 nm. The mode ER is larger than 15 dB in between 1500 nm and 1600 nm. For the “ON” state, the 3 dB bandwidth is 90 nm from 1500 to 1590 nm. Although the mode ER at “ON” state is decreased with the increase of the operating wavelength, an acceptable mode ER of > 7 dB can still be achieved over a broad bandwidth of 100 nm. When launching a quasi-TM0 mode at port I2 of the bus waveguide, the transmittance is insensitive to the variations of the operating wavelength. It can be noted from Fig. 12(b) that with a ± 50 nm change of the wavelength, the mode ER is lower than 33 dB and the IL can be neglected for both the “OFF” and “ON” states, which can enable a high performance for the optimal device.
Fig. 12 Variations of the transmittance with the operating wavelength for the quasi-TM0 mode launching at (a) port I1 and (b) port I2, respectively.
Variations of the transmittance with the applied voltage bias and the width of the central slot waveguide are shown in Figs. 13(a) and 13(b), respectively at the operating wavelength of 1550 nm. It can be noted from Fig. 13(a) that the output power at the CROSS port is monotonically decreased with the increase of the applied voltage bias, while that at the BAR port is monotonically increased. This phenomenon can be revealed by the voltage-tunable carrier concentration of the ITO layer as shown in Fig. 4(b). With the increase of the applied voltage bias, the carrier concentration of the ITO is correspondingly increased, which causes a gradually increasing phase-mismatching. It can also be noted from Fig. 13(a) that after the voltage passes the ENZ point (Vg = 2.4 V), the transmittance for the BAR state will saturate with slight improvements. The insertion losses are calculated to be 1.47, 0.68, and 0.23 dB for Vg = 2.4, 3, and 5 V, respectively and the corresponding mode ERs are calculated to be 9.2, 12.1, and 15.6 dB, respectively. Therefore, for the “ON” state, a higher mode ER can be obtained with a higher voltage, which leads to a sacrificing the power-consumption. As shown in Fig. 13(b), with a ± 10 nm change of the Wp, the mode ER is higher than 11 dB and the IL is lower than 0.82 dB for the “OFF” state. The transmittance at “ON” state is almost constant with the change of the Wp.
Fig. 13 Variations of the transmittance with (a) the applied voltage bias and (b) the width of the central slot waveguide, respectively at the operating wavelength of 1550 nm.
A high operation speed of the proposed 3D-RMDS is essential to the mode routing for the MDM networks. The reconfigurable speed is limited to the RC delay. A device capacitance is calculated based on the formula [19]:
where εSiO2 = 3.9; the width and length of the MOS-type plasmonic waveguide are taken as W = 140 nm and L = 8.429 μm, respectively; the height of the capacitor is denoted by h = hs. Assuming an internal impedance of R = 50 Ω, a typical RC time is calculated as 0.2 ps. The reconfigurable speed can be calculated as f = 1/(2π × RC) = 0.781 THz. We can see that the operation speed of the proposed design can be achieved to be in the THz range with very low- picosecond switching-times. In addition, the power-consumptions per bit can be calculated based on the formula: E/bit = CVg2/2 = 11.74, 18.34, and 50.95 fJ/bit for Vg = 2.4, 3, and 5 V, respectively. The proper voltage bias should be adopt to balance the power-consumptions and the insertion loss/mode ER. Compared to the Y-junction and MMIs based structures [15], the switching-time is decreased from 2.5 ns to only 0.2 ps. The device length is significantly decreased from > 400 μm to only 8.429 μm, compared with the conventional MZIs based structures [16].5. Conclusion
In conclusion, we have proposed and optimized a 3D-RMDS based on a triple-waveguide ADC, consisting of a lower doped-silicon waveguide, a central plasmonic horizontal-slot waveguide with the ITO and an upper doped Poly-Si waveguide. The output mode states can be switched by adjusting the applied voltage bias on the ITO layer. The proposed device has been optimally designed by using the FV-FEM and the 3D-FV-FDTD. The numerical results reveal that the proposed 3D-RMDS is with a compact length of 8.429 μm, an ultra-high switching-speed of 0.781 THz and a low power-consumption of 11.74 fJ/bit for ENZ point at Vg = 2.4 V. The mode ERs and ILs are calculated to be 20.3 dB (9.2 dB) and 0.06 dB (1.47 dB) at the wavelength of 1550 nm for the “OFF” (“ON”) state, respectively. By applying a larger voltage bias of Vg = 5 V, the ILs and mode ERs are calculated to be 0.23 dB and 15.6 dB, respectively with a larger power-consumption of 50.95 fJ/bit. The 1 dB and 3dB bandwidths at “OFF” and “ON” states are 92 nm and 90 nm, respectively covering the C-band. The proposed 3D-RMDS enables high-speed, low-power and flexible mode-routing for 3D on-chip MDM networks.
Funding
Natural Science Foundation of Jiangsu Province (BK20180743); NUPTSF (NY218108); the Research Center of Optical Communications Engineering & Technology, Jiangsu Province.
Acknowledgments
The author would like to thank Prof. B. M. Azizur Rahman at City, University of London for the insightful discussion, constructive comments and rigorous numerical algorithm.
References
1. H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express 25(3), 1618–1628 (2017).
2. M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing-polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Lett. 39(4), 758–761 (2014).
3. A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
4. H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
5. Y. Chen, J. Li, P. Zhu, Z. Wu, P. Zhou, Y. Tian, F. Ren, J. Yu, D. Ge, J. Chen, Y. He, and Z. Chen, “Novel MDM-PON scheme utilizing self-homodyne detection for high-speed/capacity access networks,” Opt. Express 23(25), 32054–32062 (2015).
6. C. Sun, Y. Yu, G. Chen, and X. Zhang, “Silicon mode multiplexer processing dual-path mode-division multiplexing signals,” Opt. Lett. 41(23), 5511–5514 (2016).
7. T. Uematsu, Y. Ishizaka, Y. Kawaguchi, K. Saitoh, and M. Koshiba, “Design of a compact two-mode multi/demultiplexer consisting of multimode interference waveguides and a wavelength-insensitive phase shifter for mode-division multiplexing transmission,” J. Lightwave Technol. 30(15), 2421–2426 (2012).
8. Z. Zhang, Y. Yu, and S. Fu, “Broadband on-chip mode-division multiplexer based on adiabatic couplers and symmetric Y-junction,” IEEE Photonics J. 9(2), 6600406 (2017).
9. R. Tang, T. Tanemura, and Y. Nakano, “Integrated reconfigurable unitary optical mode converter using MMI couplers,” IEEE Photonics Technol. Lett. 29(12), 971–974 (2017).
10. J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, and R. M. Osgood, “Asymmetric Y junctions in silicon waveguides for on-chip mode-division multiplexing,” Opt. Lett. 38(11), 1854–1856 (2013).
11. D. Guo and T. Chu, “Silicon mode (de)multiplexers with parameters optimized using shortcuts to adiabaticity,” Opt. Express 25(8), 9160–9170 (2017).
12. Y. Ding, J. Xu, F. Da Ros, B. Huang, H. Ou, and C. Peucheret, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21(8), 10376–10382 (2013).
13. Y. Sun, Y. Xiong, and W. N. Ye, “Experimental demonstration of a two-mode (de)multiplexer based on a taper-etched directional coupler,” Opt. Lett. 41(16), 3743–3746 (2016).
14. N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, R. Maruyama, N. Kuwaki, K. Takenaga, H. Uemura, S. Matsuo, and K. I. Kitayama, “Mode-unbundled ROADM and bidirectional mode assignment for MDM metro area networks,” J. Lightwave Technol. 33(24), 5055–5061 (2015).
15. Y. Xiong, R. B. Priti, and O. Liboiron-Ladouceur, “High-speed two-mode switch for mode-division multiplexing optical networks,” Optica 4(9), 1098–1102 (2017).
16. D. Melati, A. Alippi, and A. Melloni, “Reconfigurable photonic integrated mode (de)multiplexer for SDM fiber transmission,” Opt. Express 24(12), 12625–12634 (2016).
17. C. Sun, Y. Yu, G. Chen, and X. Zhang, “Integrated switchable mode exchange for reconfigurable mode-multiplexing optical networks,” Opt. Lett. 41(14), 3257–3260 (2016).
18. B. Stern, X. L. Zhu, C. P. Chen, L. D. Tzuang, J. Cardenas, K. Bergman, and M. Lipson, “On-chip mode-division multiplexing switch,” Optica 2(6), 530–535 (2015).
19. C. Ye, K. Liu, R. A. Soref, and V. J. Sorger, “A compact plasmonic MOS-based 2 × 2 electro-optic switch,” Nanophotonics 4(3), 261–268 (2015).
20. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
21. V. E. Babicheva, N. Kinsey, G. V. Naik, M. Ferrera, A. V. Lavrinenko, V. M. Shalaev, and A. Boltasseva, “Towards CMOS-compatible nanophotonics: ultra-compact modulators using alternative plasmonic materials,” Opt. Express 21(22), 27326–27337 (2013).
22. J. T. Kim, “CMOS-compatible hybrid plasmonic modulator based on vanadium dioxide insulator-metal phase transition,” Opt. Lett. 39(13), 3997–4000 (2014).
23. H. Zhao, Y. Wang, A. Capretti, L. D. Negro, and J. Klamkin, “Broadband electroabsorption modulators design based on epsilon-near-zero indium tin oxide,” IEEE J. Sel. Top. Quantum Electron. 21(4), 3300207 (2015).
24. C. Ye, S. Khan, Z. R. Li, E. Simsek, and V. J. Sorger, “λ-size ITO and graphene-based electro-optic modulators on SOI,” IEEE J. Sel. Top. Quantum Electron. 20(4), 3400310 (2014).
25. J. T. Kim, “Silicon optical modulators based on tunable plasmonic directional couplers,” IEEE J. Sel. Top. Quantum Electron. 21(4), 3300108 (2015).
26. Z. Ma, Z. Li, K. Liu, C. Ye, and V. J. Sorger, “Indium-tin-oxide for high-performance electro-optic modulation,” Nanophotonics 4(1), 198–213 (2015).
27. A. Melikyan, N. Lindenmann, S. Walheim, P. M. Leufke, S. Ulrich, J. Ye, P. Vincze, H. Hahn, T. Schimmel, C. Koos, W. Freude, and J. Leuthold, “Surface plasmon polariton absorption modulator,” Opt. Express 19(9), 8855–8869 (2011).
