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Two-mode contra-directional coupler based on superposed grating

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Abstract

We propose and demonstrate a novel two-mode grating assisted contra-directional coupler (TGACC), which is capable of filtering two modes channels simultaneously by superposed grating with two superposed grating components. Finite-difference time-domain simulation is employed to study the structure. The influences of main structural parameters are analyzed, and apodization is employed to reduce the band sidelobes, crosstalk and back-reflections. We experimentally present a mode-channel switchable TGACC for 2.54nm-wide wavelength band centered at 1548.0nm by 50K thermal-optic tuning. With two channels combined into one device, the TGACC can help to enrich the functionality and reduce the footprint of mode-division multiplexing (MDM) systems.

© 2017 Optical Society of America

1. Introduction

Silicon photonic circuits based on Silicon-on-insulator (SOI) is regarded as a promising replacement of copper-wire-based electric interconnection to meet the growing bandwidth demand of multicore processors [1]. Various multiplexing technique has been implemented in silicon photonic circuits to increase the data transfer rates, such as wavelength-division multiplexing (WDM), polarization-division multiplexing (PDM), and mode-division multiplexing (MDM) [2]. MDM is an extensively-studied multiplexing technique in optical fiber communication [3, 4] and is getting more and more attentions for on-chip interconnection applications [5, 6]. The channels of MDM are multiplexed on different modes of a waveguide and share the same wavelength, which makes it ready to be combined with established WDM techniques to further increase the network capacity [7]. In recent years, different kinds of (de)multiplexers for MDM has been reported, such as Y-splitter [8], multimode interference [9] and asymmetrical co-directional couplers (ADCs) [6]. Hybrid demultiplexer combining MDM with WDM by using ADCs and arrayed-waveguide gratings (AWGs) has been demonstrated up to 64 channels [10].

Most of the optical components are designed for single-mode operation on SOI platform and incompatible with MDM system. Redesign of those components to be compatible with multimode operation could further increase the functionality of MDM system. Researching efforts has already been put in this direction, for example, two-mode ring resonator [11], higher order-mode pass filter [12], mode exchanger [13], and bandstop filter [14].

Grating assisted contra-directional couplers (GACCs) are bandpass filters with Bragg-grating defined wavelength selective functions, which enabled many applications as a single-mode element [15–18]. Mode (de)multiplexers based on GACCs are also reported, which can achieve mode (de)multiplexing wavelength filtering at the same time [19, 20]. However, those GACCs are all composed of a single grating component and only work in one mode channel, limiting its application in MDM systems.

In this paper, we propose and demonstrate a novel two-mode grating assisted contra-directional coupler (TGACC) based on superposed grating. It can manage filtering of two modes by one single structure rather than cascading two filters or demultiplexing each mode for filtering. The proposed device consists of two parallel multimode waveguides of asymmetric width with superposed gratings formed on the inner sides of the waveguides. The superposed grating is the superposition of two grating components based on sine function. Each grating component couples a waveguide mode to its corresponding in the other waveguide. Both 3D and 2.5D variational finite-difference time-domain (FDTD) simulations are performed to study the proposed structure using software of Lumerical Solutions, Inc [21], and the design is optimized to suppress the crosstalk, back-reflections, and band sidelobes. A TGACC with two mode channels closely configured is demonstrated by experiment. We also show that, by thermal-optic tuning of 50K, mode channel switching is realized for a 2.54nm-wide wavelength band.

2. Device configuration and working principle

Figure 1(a) is the basic configuration of the proposed TGACC based on two parallel placed asymmetric multimode waveguides on silicon-on-insulator (SOI). The superposed gratings are formed symmetrically by sidewall corrugation on both the inner side of the two waveguides, as clearly seen in Fig. 1(b). Figure 1(c) shows the superposed grating composed of two grating components. The SOI has a top silicon layer of 220nm thick. The width of the two multimode waveguides are W1 = 900nm and W2 = 700nm. The waveguides and gratings are formed by a single etching of 220nm depth. The surface of the structure is covered by a SiO2 layer. Throughout this work, the transverse-electric (TE) polarization is concerned. The refractive indices of Si and SiO2 at room temperature are 3.478 and 1.5, respectively. As labeled in Figs. 1(b) and 1(c), the coupling length of the superposed grating is denoted by L. The waveguide gap is denoted by G, and Gh is the minimum gap between the grating tooth in the TGACC region. The pitches, corrugation amplitudes and periods numbers of the grating components composing the superposed grating are denoted by Λi, ti, and Ni, respectively, where the subscript i represent the index of grating components. The gaps and grating corrugation amplitude has the relation as G = Gh + 2(t1 + t2).

 figure: Fig. 1

Fig. 1 Schematic configuration of the proposed TGACC. (a) Top view the structure, and (b) superposed grating profile (blue) composed of two grating components (red and green), when t1 = t2. (c) Superposed grating profile (blue) composed of two grating components (red and green), when t1 = t2.

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The superposed grating is a superposition of grating profiles in sine function. As shown in Fig. 1(b), two sine grating profiles combine into one superposed grating profile P(x), which can be expressed as:

P(x)=t1sin(K1x)Π1(x)+t2sin(K2x)Π2(x)whereΠi(x)={1x[0,NiΛi]0x[0,NiΛi]

where K1 = 2π/Λ1 and K2 = 2π/Λ2 are the coupling vectors of the two grating components. Unlike conventional grating which has only one coupling vector, the superposed grating can have multiple coupling vectors, each supported by one of its grating components. In the proposed TGACC, each coupling vector contributes to the grating assisted mode coupling as long as a phase-match condition is satisfied:

βjm+βkn=Ki

where βjm and βkn stands for the propagation constants of the j-th and k-th order mode in two multimode waveguides (represented by m, n) of the TGACC. Ki represents the coupling vector of the i-th grating component. For the TGACC illustrated in Fig. 1 with a waveguide gap of G = 220nm, the Ey field distributions of two 0th modes (TE01, TE02) and two 1st order mode (TE11, TE12) are shown in Fig. 2(a). The calculated propagation constants of the modes coupling are sketched in Fig. 2(b). The tilted lines are the plots of the left-hand side of the Eq. (2), as a function of the wavelength. We choose the values of K1 and K2 at the wavelength of 1550nm, for effective mode coupling from TE01 to TE02 (0th modes channel), and from TE11 to TE12 (1st modes channel), respectively. The grating component pitches can be calculated from the definition of K. It is noted that on the red side of 1550nm, both coupling vectors also match the phase condition for self-reflection of TE01 and TE11 mode. The reflection coupling of TE01 and TE11 is located at the blue side of 1500nm. Furthermore, the crosstalk coupling of TE01 to TE12 is found to be located at wavelength shorter than 1500nm, and TE11 to TE02 at wavelength longer than 1600nm.

 figure: Fig. 2

Fig. 2 (a) The Ey field distributions of two 0th modes TE01, TE02 and two 1st order mode TE11, TE12. (b) Calculated propagation constants of the modes with the phase-match condition. The mode coupling of TE01 to TE02 and TE11 to TE12 are highlighted by solid lines. The crosstalk coupling of TE01 to TE12 and TE11 to TE02 are represented by dashed lines. The self-reflection of TE01 to TE01 and TE11 to TE11, and the reflection coupling between TE01 and TE11 are represented by dot-dashed lines.

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The superposed grating in TGACC couples each mode channel simultaneously. A 3D FDTD simulation is performed to illustrate the device behavior. The results are shown in Figs. 3(a) and 3(b). In the 3D FDTD simulations, non-uniform meshing with Δxmin = Δymin = Δzmin = 25nm is used. The calculation region is surrounded by perfectly matched layer (PML) absorbing boundaries. The simulated structure has t1 = 73nm, t2 = 7nm, G = 220nm and Gh = 60nm. The grating pitches are Λ1 = 288nm and Λ2 = 358nm. The waveguide sections with superposed grating curve is constructed using polygons with point spacing of 10nm in x-direction. Since the 3D-FDTD simulation is extremely time and memory consuming, we set the coupling length to be 50μm to make the simulation executable on our computer and the coupling profiles strong enough to be recognized. Figures 3(a) and 3(b) show that the TGACC can manage the contra-directional coupling of TE01 to TE02 and TE11 to TE12 at the same time. Although the coupling length in the simulation is insufficient for complete power transfer, the operation principle of the device is proved.

 figure: Fig. 3

Fig. 3 3D-FDTD simulations of the TGACC for (a) TE01 to TE02 and (b) TE11 to TE12 around the wavelength of 1550nm. TE01 and TE11 mode source are injected from waveguide 1 respectively. The waveguides are outlined by the black lines.

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3. Filter spectral responses

The spectral responses of the TGACC are calculated by 2.5D variational FDTD simulation, which, in the case of SOI-based slab waveguide structures, provides results comparable to 3D FDTD using only the simulation time and memory of a 2D FDTD simulation [22]. Although the results of 2.5D variational FDTD simulation may differ from experiment to some extent, it is still a good choice for initial design. The simulation setup is non-uniform meshing with Δxmin = Δymin = 10nm in the grating region, and Δzmin = 1nm. The grating pitches are Λ1 = 287nm and Λ2 = 348nm. The other structure parameters are the same as in the previous 3D FDTD with L = 200μm, i.e. N1 = 697, N2 = 575. Figures 4(a) and 4(b) show the through and drop ports spectra of 0th modes channel and 1st modes channel. The spectral responses are obtained by separately injecting TE01 mode and TE11 mode from the input port. For the drop port, the central wavelength, 3dB bandwidth, and insert loss are (1547.7nm, 4.6nm, −0.12dB) and (1549.7nm, 4.8nm, −0.16dB), respectively. It is shown that the TGACC manage the filtering of both channels simultaneously. The crosstalk spectra are also drawn in the Figs. 4(a) and 4(b). The signal-to-crosstalk ratio (SXR) is found to be 12.6dB for 0th modes channel and 12.8dB for 1st modes channel. The self-reflection and reflection coupling of TE01 and TE11 mode are plotted in Figs. 4(c) and 4(d), which are found to be (−12.2dB, −16.1dB) in 0th modes channel band and (−8.2dB, −16.1dB) in 1st modes channel band, respectively. We will show in the next section that both the crosstalk and back reflections can be suppressed by apodization.

 figure: Fig. 4

Fig. 4 The through-port, drop-port, and crosstalk spectral responses of (a) 0th modes channel (TE01 to TE02) and (b) 1st modes channel (TE11 to TE12). The self-reflection and reflection coupling of (c) TE01 and (b) TE11.

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Among the structure parameters, the influence of the grating component pitch Λi and superposed grating inner gap Gh are straightforward: Increasing Λi results in redshift of the corresponding mode channel and increasing Gh leads to decrease of coupling coefficient of both channels resulting in bandwidth narrowing. The influence of waveguide gap and corrugation amplitudes are much more implicit. To reveal the effect of those parameters, we simulate and investigate the spectral responses of both channels by varying G, t1, and t2 when keeping Λ1 = 287nm, Λ2 = 348nm, Gh = 60nm, and L = 200μm. We define Δt<(G-Gh)/4 so that t1 = (G-Gh)/4 + Δt and t2 = (G-Gh)/4-Δt. The results are summarized in Fig. 5.

 figure: Fig. 5

Fig. 5 The central wavelength of (a) 0th modes channel and (b) 1st modes channel; the 3dB bandwidth of (c) 0th modes channel and (d) 1st modes channel. All are as a function of Δt at different value of G.

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Figures 5(a) and 5(b) shows the influence of G and Δt on the central wavelength of 0th modes channel and 1st modes channel respectively. It is seen that as G increases, the central wavelength of both channels shift to short wavelength, since increasing G leads to decrease of effective index of each mode and results in blueshift of the coupling wavelength of each grating component. While keeping G unchanged, the central wavelength of 0th modes channel also blueshift by increasing Δt. It can be explained through the superposed grating profile at Δt = 0nm in Fig. 1(c). As Δt increases, the superposed grating profile approaches to sine function with fixed amplitude which results in a decrease of effective index of the 0th waveguide modes, as most of the 0th modes are confined in the waveguides. For the 1st modes channel, the blueshift of central wavelength is less effective than the 0th modes channel, since significant amount of energy of the 1st modes are in the waveguide gap. It also shows a redshift at high Δt values in Fig. 5(b). It is due to the increase of effective index caused by positive corrugation exceeds the decrease of effective index caused by negative corrugation. A finer parameter sweep of high Δt values at G = 220nm also shows a trend of redshift, excluding the possible causation of simulation error.

The influences of structure parameters G and Δt on 3dB bandwidth are shown in Figs. 5(c) and 5(d). At Δt = 0nm, the bandwidth of 1st channel is much larger than 0th channel due to the stronger interaction with sidewall corrugation of 1st modes. It is well known that the coupling bandwidth of a grating component is positively related to its coupling strength [23] and the coupling strength is positively related to its corrugation amplitude ti. It is also the case for superposed grating. When keeping G and increasing Δt, the bandwidth of 0th channel increases as t1 increases and the bandwidth of 1st channel decreases as t2 decreases. On the other hand, at fixed Gh and Δt, increasing G results in two kinds of opposite influences on the coupling strength: weakening due to separation of waveguides and enhancing due to increase of corrugation amplitude. As shown in Figs. 5(c) and 5(d), the weakening is more effective for 0th modes since the mode energy is mostly confined in waveguides. The enhancing is more effective for the 1st modes due to the high interaction between the sidewall corrugation and mode energy in the waveguide gap.

Structure in which two gratings with different pitches are designed separately on the inner side of two waveguides has been reported recently to offer two wavelength channels for the single-mode contra-directional coupler [24]. The structure may also be used for two-mode filtering. Compared to the separated grating, the superposed grating has the advantage of having corrugation on both side of the two waveguide. The overlap between the corrugation and mode energies in both waveguides is higher than the separated grating, making it more efficient to adjust coupling coefficient by adjusting corrugation amplitude. The 0th modes channel with highly confined mode profile can also achieve a wider bandwidth compared to the case of separated grating.

4. Suppression of the crosstalk, back reflections and sidelobes

Low channel crosstalk, small back reflection and weak sidelobes are of great importance for the TGACC. In this section, we aim to optimize the design to suppress the crosstalk, back reflections and sidelobes. According to the phase-match condition in Fig. 2(b), the crosstalk come from the sidelobes of TE01 to TE12 coupling and TE11 to TE02 coupling. The back-reflections in the passing bands come from the sidelobes of TE01 self-reflection, TE11 self-reflection and reflection coupling between TE01 and TE11. Therefore, by suppressing the sidelobes, we can achieve low crosstalk and back reflections at the same time.

Here, we use a TGACC with t01 = 73nm, t02 = 7nm, and L = 350μm for example. Gaussian apodization on both grating components of the superposed grating is used to suppress the sidelobes. The Gaussian profile for the corrugation amplitude of i-th grating component is described by:

ti(x)=t0iexp[12(xL/2σL/2)2]0xL

where σ denotes the apodization coefficient and t0i is the maximum corrugation amplitude. Figure 6(a) shows the Gaussian profile for different apodization coefficient. As σ decrease, the corrugation amplitude at the grating ends approach zero. The drop-port spectral responses of the uniform and apodized TGACCs are shown in Fig. 6(b) for 0th modes channel and Fig. 6(c) for 1st modes channel. The stop sidebands become flat and the sidelobes are greatly suppressed as the apodization is used. The insert loss of each channel is (−0.04dB, −0.05dB), (−0.11dB, −0.07dB), and (−0.35dB, −0.28dB) for σ = 1, σ = 1/2 and σ = 1/3, respectively. The corresponding 3dB bandwidths are (4.0nm, 3.9nm), (4.7nm, 4.3nm), and (5.2nm, 4.9nm). The increase of bandwidth as σ decreasing is due to the grating chirp introduced by apodization. It is shown that the TGACC with smaller apodization coefficient has better sidelobes suppression, but suffers deterioration of band-top flatness and insert loss. It is also noted that, at σ = 1/3, the sidelobes suppression of 0th modes channel is less effective on the red side and the sidelobes suppression of 1st modes channel is less effective on the blue side. This is due to the non-uniform “dc” effective index change of the waveguides [25]. Better filter shape can be achieved by cascading two identical TGACC with high apodization coefficient [15].

 figure: Fig. 6

Fig. 6 (a) Gaussian apodization profile of corrugation amplitude with different apodization coefficients. The drop-port spectral responses of the uniform and apodized TGACCs for (b) 0th modes channel and (c) 1st modes channel. The spectra are shifted horizontally to be clearly shown.

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The effect of the apodization on crosstalk, self-reflection and reflection coupling of each channel are shown in Fig. 7. It is shown that all three spectra within the channel bands are suppressed as σ decreases. With apodization of σ = 1/2, the crosstalk is suppressed under −20dB for both channels. The self-reflection is suppressed under −17dB for 0th modes channel and −20dB for 1st modes channel. The reflection coupling is suppressed under −20dB for both channels. Therefore, it is concluded that apodization is effective for simultaneous suppression of crosstalk, back reflections and sidelobes, though it will deteriorate the band-top flatness and insert loss to some degree.

 figure: Fig. 7

Fig. 7 The crosstalk (a) and (b), self-reflection (c) and (d), and reflection coupling (e) and (f) of uniform and apodized TGACCs for 0th modes channel and 1st modes channel respectively. The 3dB band range of each channel for the TGACCs are shown by dashed vertical line of corresponding color.

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5. Experiment results

The proposed TGACCs were fabricated on a SOI wafer with 220nm thick top silicon and 2μm thick buried oxide. The layout of the device with components used for testing are shown in Fig. 8(a). Photonics crystal grating couplers designed for TE polarization are used for vertical fiber coupling test. The input, drop and through port each has a pair of grating couplers for 0th modes channel and 1st modes channel, respectively. Multiplexing and Demultiplexing of the two modes channels are performed by tapered asymmetrical directional couplers (ADCs) whose design parameters are shown in Fig. 8(b) for 700nm wide multimode waveguide and in Fig. 8(c) for 900nm wide multimode waveguide. The single mode waveguides in the ADCs are 400nm wide. All the components were patterned using electron beam lithography (EBL, Vistec EBPG 5000 Plus) with beam step size of 5nm. Inductively coupled plasma (ICP) etch were then performed to transfer the pattern from photoresist to the SOI wafer. Spin coating of a layer of 558nm thick Hydrogen silsesquioxane (HSQ) followed by 2-hour baking on 200°C hotplate were carried out to make sure the gaps of the devices are filled with silicon oxide. At last, 700nm silicon dioxide was deposited by plasmas enhanced chemical vapor deposition (PECVD) to cover the wafer. The scanning electron microscope (SEM) micrographs of different parts of the fabricated TGACC are shown as insets in Fig. 8(a). The superposed grating profile in the SEM picture looks like uniform since t02 is much smaller compared to t01.

 figure: Fig. 8

Fig. 8 (a) The layout of TGACC used for fabrication. The SEM images of the TGACCs are shown by insets. The schematic configuration of the ADC multiplexers with design parameters for (b) 700nm wide multimode waveguide and (b) 900nm wide multimode waveguide.

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An amplified spontaneous emission (ASE) light source was used as input source. For each modes channel, the spectral responses of drop and through port were measured from the corresponding grating couplers. The crosstalk in 0th (1st) modes channel was measured from the drop port of 0th (1st) modes channel with light injected from the input port of 1st (0th) modes channel. In order to eliminate the spectral response of grating coupler and ADCs from the results, three reference structures were also fabricated on the same wafer, as shown in Fig. 9. Spectral responses of a straight waveguide with two cascaded ADC-900nm (Ref1) were measured for normalization of the through port response. Spectral responses of a tapered waveguide with cascaded ADC-900nm and ADC-700nm (Ref2) were measured for normalization of the drop port response. A straight waveguide with two back-to-back grating couplers (Ref3) was measured to get the spectral response of the grating coupler. Together with the previous two structures, the multiplexing spectral responses of the ADCs can also be calculated. The crosstalk of TGACC in 0th (1th) modes channel was normalized by the spectral response of two grating couplers, one ADC-900nm (ADC-700nm), and the spectrum of light source.

 figure: Fig. 9

Fig. 9 Layout of reference structures used in the measurement.

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The normalized spectral response of through port, drop port and crosstalk at different temperature are shown in Fig. 10 and the experiment properties of the TGACC are summarized in Table 1. The insertion loss of ADCs have been excluded from the figure and the table. If including the ADCs loss, the insertion loss will be −2.20dB for 0th channel and −4.26dB for 1st channel at room temperature. The design parameters of the fabricated TGACC are W1 = 900nm, W2 = 700nm, L = 360μm, G = 220nm and Gh = 60nm. The structure is apodized by Gaussian profile with σ = 0.4. The spectral dip around 1562nm at the through port of 0th modes is due to self-reflection of the TGACC. Filtering channels can be clearly seen at the drop port of 0th mode and 1st mode, proving that the TGACC can manage the filtering of two modes by one device. At room temperature, two channels are closely configured by using grating pitches of Λ1 = 290nm and Λ2 = 366nm, resulting in a band center distance of 4.9nm. Comparable 3dB bandwidths of two modes channels are achieved with parameters of t01 = 75nm and t02 = 5nm. We measured the signal-to-crosstalk ratios (SXR) at ΔT = 0K. We note that the SXR of 1st modes channel is apparently smaller than that of the 0th modes channel and the crosstalk in the band of 1st modes channel is larger than what we expected from Fig. 7(b). This may due to the mode coupling of 0th modes to 1st modes caused by fabrication imperfections such as deformed grating tooth, waveguide sidewall roughness and write field stitching error of the EBL system. The minimum loss of the 1st modes channel is slightly larger than the 0th modes channel, since the 1st modes encounters more waveguide sidewall roughness scattering than the 0th modes.

 figure: Fig. 10

Fig. 10 (a) The through-port (dashed lines), drop-port (solid lines), and crosstalk (dotted lines) normalized spectral responses of the fabricated TGACCs at room temperature (ΔT = 0K). (b) The drop port normalized responses at ΔT = 50K. Shadowed region shows the overlapped 3dB band of 1st modes channel at ΔT = 0K and 0th modes channel at ΔT = 50K.

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Tables Icon

Table 1. Experiment properties of 0th and 1st modes channel in the fabricated TGACC.

With this configuration of TGACC, mode-channel switching can be realized by thermal-optic tuning. Figure 10 shows that, as the temperature increases by 50K, both modes channels redshift and the 2.51nm-wide wavelength band (shadowed region) centered at 1548.0nm switches from 1st modes channel to 0th modes channel. It is noted that the extinction ratios of both channels at ΔT = 50K are lower that at ΔT = 0K. This is because Silicon has a larger thermal-optic coefficient than Silicon dioxide and the 0th modes has more energy confined in the silicon core than 1st modes. Therefore, as the temperature increases, the 0th modes channel redshifts more than the 1st modes channel. The distance between two channels decreases, leading to degradation of the extinction ratio.

A wide range of applications are available for the TGACC. The independence of each grating component in the superposed grating provides good flexibility to the filter design. For example, the TGACC can be configured to filter two modes of the same wavelength by adjusting the pitches of each grating component. The bandwidth of each channel can also be different by adjusting the grating tooth. Together, a TGACC can be designed to filter one mode in certain wavelength band and both modes in another wavelength band. Furthermore, filters with more functionality can be achieved when combined with thermal-optic tuning, such as the mode-channel switching demonstrated above.

6. Conclusion

In summary, we have proposed a novel TGACC capable of filtering two modes channels by superposed grating at the same time. We have studied the proposed structure systematically using 3D and 2.5D variational FDTD simulations. The numerical results show that the grating component in the superposed grating can manage the filtering of its corresponding modes simultaneously. The crosstalk, back-reflections and sidelobes of both modes channels can be suppressed together by applying Gaussian apodization. The proposed structure is validated by experiment and mode-channel switching is realized by thermal-optic tuning of the fabricated TGACC. This device can reduce the footprint of MDM systems, since it can manage filtering two modes in a single structure rather than cascading two filters or demultiplexing each mode for filtering.

Funding

National Natural Science Foundation of China (Grant 61335002, 11574102); the Major State Basic Research Development Program of China (Grant 2013CB632104, 2013CB933303); the “863” project (Grant 2015AA016904); Specialized Research Fund for the Doctoral Program of Higher Education (Grant 20110142120059).

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20. H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013). [CrossRef]   [PubMed]  

21. Lumerical Solutions Inc, “FDTD and MODE solutions,” https://www.lumerical.com/.

22. Lumerical Solutions Inc, “Lumerical 2.5D FDTD Propagation Method,” https://www.lumerical.com/support/whitepaper/2.5d_fdtd_propagation_method.html.

23. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Process calibration method for designing silicon-on-insulator contra-directional grating couplers,” Opt. Express 23(8), 10573–10588 (2015). [CrossRef]   [PubMed]  

24. M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Two-period contra-directional grating assisted coupler,” Opt. Express 24(20), 22865–22874 (2016). [CrossRef]   [PubMed]  

25. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]  

References

  • View by:

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  11. B. A. Dorin and W. N. Ye, “Two-mode division multiplexing in a silicon-on-insulator ring resonator,” Opt. Express 22(4), 4547–4558 (2014).
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  12. X. Guan, Y. Ding, and L. H. Frandsen, “Ultra-compact broadband higher order-mode pass filter fabricated in a silicon waveguide for multimode photonics,” Opt. Lett. 40(16), 3893–3896 (2015).
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  13. 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).
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  14. Q. Huang, K. Jie, Q. Liu, Y. Huang, Y. Wang, and J. Xia, “Ultra-compact, broadband tunable optical bandstop filters based on a multimode one-dimensional photonic crystal waveguide,” Opt. Express 24(18), 20542–20553 (2016).
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  15. J. St-Yves, H. Bahrami, P. Jean, S. LaRochelle, and W. Shi, “Widely bandwidth-tunable silicon filter with an unlimited free-spectral range,” Opt. Lett. 40(23), 5471–5474 (2015).
    [Crossref] [PubMed]
  16. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Grating-assisted silicon-on-insulator racetrack resonator reflector,” Opt. Express 23(20), 25509–25522 (2015).
    [Crossref] [PubMed]
  17. W. Shi, H. Yun, C. Lin, M. Greenberg, X. Wang, Y. Wang, S. T. Fard, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, “Ultra-compact, flat-top demultiplexer using anti-reflection contra-directional couplers for CWDM networks on silicon,” Opt. Express 21(6), 6733–6738 (2013).
    [Crossref] [PubMed]
  18. H. Qiu, Y. Su, P. Yu, T. Hu, J. Yang, and X. Jiang, “Compact polarization splitter based on silicon grating-assisted couplers,” Opt. Lett. 40(9), 1885–1887 (2015).
    [Crossref] [PubMed]
  19. G. F. R. Chen, T. Wang, K. J. A. Ooi, A. K. L. Chee, L. K. Ang, and D. T. H. Tan, “Wavelength selective mode division multiplexing on a silicon chip,” Opt. Express 23(6), 8095–8103 (2015).
    [Crossref] [PubMed]
  20. H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013).
    [Crossref] [PubMed]
  21. Lumerical Solutions Inc, “FDTD and MODE solutions,” https://www.lumerical.com/ .
  22. Lumerical Solutions Inc, “Lumerical 2.5D FDTD Propagation Method,” https://www.lumerical.com/support/whitepaper/2.5d_fdtd_propagation_method.html .
  23. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Process calibration method for designing silicon-on-insulator contra-directional grating couplers,” Opt. Express 23(8), 10573–10588 (2015).
    [Crossref] [PubMed]
  24. M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Two-period contra-directional grating assisted coupler,” Opt. Express 24(20), 22865–22874 (2016).
    [Crossref] [PubMed]
  25. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
    [Crossref]

2016 (3)

2015 (6)

2014 (4)

2013 (4)

2012 (2)

2011 (1)

2008 (1)

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic networks-on-chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

1982 (1)

Ang, L. K.

Bahrami, H.

Berdagué, S.

Bergman, K.

Boeck, R.

Bolle, C. A.

Boroojerdi, M. T.

Bowers, J. E.

D. X. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects,” Nanophotonics 3(4-5), 283–311 (2014).
[Crossref]

Carloni, L. P.

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic networks-on-chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

Caverley, M.

Chee, A. K. L.

Chen, C. P.

Chen, G.

Chen, G. F. R.

Chen, S.

Chrostowski, L.

Da Ros, F.

Dadap, J. I.

Dai, D.

Dai, D. X.

D. X. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects,” Nanophotonics 3(4-5), 283–311 (2014).
[Crossref]

Ding, Y.

Dorin, B. A.

Driscoll, J. B.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

Essiambre, R.-J.

Facq, P.

Fard, S. T.

Flueckiger, J.

Frandsen, L. H.

Gnauck, A. H.

Greenberg, M.

Grote, R. R.

Guan, X.

Hu, T.

Huang, B.

Huang, Q.

Huang, Y.

Ishizaka, Y.

Jaeger, N. A. F.

Jean, P.

Jiang, G.

Jiang, X.

Jie, K.

Kawaguchi, Y.

Kirk, A. G.

Koshiba, M.

LaRochelle, S.

Lin, C.

Lingle, R.

Liu, Q.

Love, J. D.

Lu, M.

McCurdy, A.

Ménard, M.

Ooi, K. J. A.

Osgood, R. M.

Ou, H.

Peckham, D. W.

Peucheret, C.

Qiu, H.

Randel, S.

Riesen, N.

Ryf, R.

Saitoh, K.

Shacham, A.

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic networks-on-chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

Shao, H.

Shi, W.

Shi, Y.

Sierra, A.

Souhan, B.

Stein, A.

St-Yves, J.

Su, Y.

Sun, C.

Tan, D. T. H.

Uematsu, T.

Wang, J.

Wang, T.

Wang, X.

Wang, Y.

Winzer, P. J.

Xia, J.

Xu, J.

Yang, J.

Ye, W. N.

Yu, H.

Yu, P.

Yu, Y.

Yun, H.

Zhang, X.

Appl. Opt. (1)

IEEE Trans. Comput. (1)

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic networks-on-chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

J. Lightwave Technol. (3)

Nanophotonics (1)

D. X. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects,” Nanophotonics 3(4-5), 283–311 (2014).
[Crossref]

Opt. Express (11)

S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

B. A. Dorin and W. N. Ye, “Two-mode division multiplexing in a silicon-on-insulator ring resonator,” Opt. Express 22(4), 4547–4558 (2014).
[Crossref] [PubMed]

Q. Huang, K. Jie, Q. Liu, Y. Huang, Y. Wang, and J. Xia, “Ultra-compact, broadband tunable optical bandstop filters based on a multimode one-dimensional photonic crystal waveguide,” Opt. Express 24(18), 20542–20553 (2016).
[Crossref] [PubMed]

R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Grating-assisted silicon-on-insulator racetrack resonator reflector,” Opt. Express 23(20), 25509–25522 (2015).
[Crossref] [PubMed]

W. Shi, H. Yun, C. Lin, M. Greenberg, X. Wang, Y. Wang, S. T. Fard, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, “Ultra-compact, flat-top demultiplexer using anti-reflection contra-directional couplers for CWDM networks on silicon,” Opt. Express 21(6), 6733–6738 (2013).
[Crossref] [PubMed]

G. F. R. Chen, T. Wang, K. J. A. Ooi, A. K. L. Chee, L. K. Ang, and D. T. H. Tan, “Wavelength selective mode division multiplexing on a silicon chip,” Opt. Express 23(6), 8095–8103 (2015).
[Crossref] [PubMed]

H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013).
[Crossref] [PubMed]

J. B. Driscoll, C. P. Chen, R. R. Grote, B. Souhan, J. I. Dadap, A. Stein, M. Lu, K. Bergman, and R. M. Osgood., “A 60 Gb/s MDM-WDM Si photonic link with < 0.7 dB power penalty per channel,” Opt. Express 22(15), 18543–18555 (2014).
[Crossref] [PubMed]

R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Process calibration method for designing silicon-on-insulator contra-directional grating couplers,” Opt. Express 23(8), 10573–10588 (2015).
[Crossref] [PubMed]

M. T. Boroojerdi, M. Ménard, and A. G. Kirk, “Two-period contra-directional grating assisted coupler,” Opt. Express 24(20), 22865–22874 (2016).
[Crossref] [PubMed]

Opt. Lett. (6)

Other (2)

Lumerical Solutions Inc, “FDTD and MODE solutions,” https://www.lumerical.com/ .

Lumerical Solutions Inc, “Lumerical 2.5D FDTD Propagation Method,” https://www.lumerical.com/support/whitepaper/2.5d_fdtd_propagation_method.html .

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Figures (10)

Fig. 1
Fig. 1 Schematic configuration of the proposed TGACC. (a) Top view the structure, and (b) superposed grating profile (blue) composed of two grating components (red and green), when t1 = t2. (c) Superposed grating profile (blue) composed of two grating components (red and green), when t1 = t2.
Fig. 2
Fig. 2 (a) The Ey field distributions of two 0th modes TE01, TE02 and two 1st order mode TE11, TE12. (b) Calculated propagation constants of the modes with the phase-match condition. The mode coupling of TE01 to TE02 and TE11 to TE12 are highlighted by solid lines. The crosstalk coupling of TE01 to TE12 and TE11 to TE02 are represented by dashed lines. The self-reflection of TE01 to TE01 and TE11 to TE11, and the reflection coupling between TE01 and TE11 are represented by dot-dashed lines.
Fig. 3
Fig. 3 3D-FDTD simulations of the TGACC for (a) TE01 to TE02 and (b) TE11 to TE12 around the wavelength of 1550nm. TE01 and TE11 mode source are injected from waveguide 1 respectively. The waveguides are outlined by the black lines.
Fig. 4
Fig. 4 The through-port, drop-port, and crosstalk spectral responses of (a) 0th modes channel (TE01 to TE02) and (b) 1st modes channel (TE11 to TE12). The self-reflection and reflection coupling of (c) TE01 and (b) TE11.
Fig. 5
Fig. 5 The central wavelength of (a) 0th modes channel and (b) 1st modes channel; the 3dB bandwidth of (c) 0th modes channel and (d) 1st modes channel. All are as a function of Δt at different value of G.
Fig. 6
Fig. 6 (a) Gaussian apodization profile of corrugation amplitude with different apodization coefficients. The drop-port spectral responses of the uniform and apodized TGACCs for (b) 0th modes channel and (c) 1st modes channel. The spectra are shifted horizontally to be clearly shown.
Fig. 7
Fig. 7 The crosstalk (a) and (b), self-reflection (c) and (d), and reflection coupling (e) and (f) of uniform and apodized TGACCs for 0th modes channel and 1st modes channel respectively. The 3dB band range of each channel for the TGACCs are shown by dashed vertical line of corresponding color.
Fig. 8
Fig. 8 (a) The layout of TGACC used for fabrication. The SEM images of the TGACCs are shown by insets. The schematic configuration of the ADC multiplexers with design parameters for (b) 700nm wide multimode waveguide and (b) 900nm wide multimode waveguide.
Fig. 9
Fig. 9 Layout of reference structures used in the measurement.
Fig. 10
Fig. 10 (a) The through-port (dashed lines), drop-port (solid lines), and crosstalk (dotted lines) normalized spectral responses of the fabricated TGACCs at room temperature (ΔT = 0K). (b) The drop port normalized responses at ΔT = 50K. Shadowed region shows the overlapped 3dB band of 1st modes channel at ΔT = 0K and 0th modes channel at ΔT = 50K.

Tables (1)

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Table 1 Experiment properties of 0th and 1st modes channel in the fabricated TGACC.

Equations (3)

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P ( x ) = t 1 sin ( K 1 x ) Π 1 ( x ) + t 2 sin ( K 2 x ) Π 2 ( x ) w h e r e Π i ( x ) = { 1 x [ 0 , N i Λ i ] 0 x [ 0 , N i Λ i ]
β j m + β k n = K i
t i ( x ) = t 0 i exp [ 1 2 ( x L / 2 σ L / 2 ) 2 ] 0 x L

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