Silicon nitride three-mode division multiplexing and wavelength-division multiplexing using asymmetrical directional couplers and microring resonators Yue-De Yang,1,2 Yu Li,1 Yong-Zhen Huang,2 and Andrew W. Poon1,* 1

Photonic Device Laboratory, Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong SAR, China State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China * [email protected]

2

Abstract: We demonstrate silicon nitride mode-division multiplexing (MDM) and wavelength-division multiplexing (WDM) using asymmetrical directional couplers and microring resonators. Our experiments reveal three-mode multiplexing and demultiplexing. We demonstrate 30Gb/s open eye diagrams with an extinction ratio of ~9 dB for each of the three modes. We observe the worst-case modal crosstalk of ~-10 dB. Our analysis of the measured transmission spectra suggests three contributions to the observed crosstalks, with the dominant cause being a compromised input-coupling at the directional couplers in the multiplexer. ©2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (060.4230) Multiplexing.

References and links 1.

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#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22172

1. Introduction Optical interconnects using silicon photonics are promising for low-power-consumption and large-data-capacity communications for computercom and datacenter applications [1]. Notably, researchers have demonstrated 90nm complementary metal-oxide-semiconductor (CMOS) photonic optical interconnects using wavelength-division multiplexing (WDM) [2]. However, the number of wavelength channels in a silicon waveguide can be limited by the WDM light sources. In order to increase the data capacity of an integrated waveguide with a single wavelength channel, it has long been proposed that mode-division multiplexing (MDM) [3] offers an extra multiplexing dimension in the spatial domain [4]. Recently, several research groups have demonstrated on-chip MDM using silicon photonics on siliconon-insulator (SOI) substrates, including the use of transformation optics for multimode waveguide bends [5], MDM multiplexers (MUXs) and demultiplexers (DeMUXs) based on asymmetrical directional couplers [6–8], adiabatic coupling [9] and asymmetrical Y-junctions [10]. Combinations of MDM techniques with polarization-division multiplexing (PDM) or WDM techniques have also been recently developed, such as PDM-compatible MDM [11] based on asymmetrical directional couplers and WDM-compatible MDM [12] based on microring resonators. In this paper, we demonstrate a three-mode MDM-WDM circuit on a silicon nitride (SiN)on-silica substrate using CMOS-compatible technology. The circuit comprises a MDM MUX based on WDM-compatible asymmetrical directional couplers and a wavelength-selective mode DeMUX based on microring resonators. Comparing with the SOI platform, SiN waveguides feature two key merits, namely (1) they are low-loss over a relatively wide transparency wavelength range in the visible to near-infrared, enabling 850/1310/1550nm band communications, and (2) SiN as a deposited thin-film device layer enables multilayer integration on bulk silicon substrates without using costly SOI wafers. 2. Principle and device design Figure 1(a) schematically shows the working principle of the MDM-WDM transmission scheme. The number of transmission channels is multiplexed by both the mode number M and the wavelength channel number N. In this paper, we use three different directional couplers (M1, M2 and M3) in the MUX (Fig. 1(b)) to multiplex to the bus waveguide three different modes over a continuous wavelength range, shown as the orange, purple and pink bars in Fig. 1(a). Each mode can contain multiple wavelength channels (denoted in black arrows). In order to demultiplex the M × N MDM-WDM transmission channels, we use microring resonator-based channel drop filters that are phase-matched to different mode orders as basic building blocks in the DeMUX. As a proof of concept, here we use three identically designed microring resonators with different designs of the directional coupling to the bus waveguide (see D1, D2 and D3 in Fig. 1(c)) to demultiplex the three mode transmission channels at a single wavelength channel (N = 1) λ1 (highlighted by the black solid-line squares). In principle, the free spectral range (FSR) of the microring resonators needs to be different from the WDM channel spacing, and desirably wider than the spectral bandwidth of the communications window. This enables the microring resonators to act as a singlewavelength-channel drop filter. We can readily extend the concept to demultiplexing N = 2, 3… by integrating extra sets of microring resonators to match the transmission channels at λ2, λ3 …, and to demultiplex the mode transmission channels accordingly (highlighted by the black dashed-line squares). As each bus waveguide can be coupled to multiple microring resonators of different resonances, and the microring resonators can be closely spaced as long as they are not mutually coupled, the MDM-WDM circuit in this scheme for multiple wavelength channels can remain compact. Figures 1(b) and 1(c) schematically show the MUX and DeMUX principles. We consider only the transverse-electric (TE) polarized modes. For the MUX, directional couplers (M1, M2

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22173

and M3) enable phase-matching between the fundamental mode (TE0) in the input-coupled singlemode waveguide and the TE0 mode, the first-order mode (TE1), and the second-order mode (TE2) in the bus waveguide, respectively. Based on the coupled-mode theory, we can tailor the interaction length and the coupling gap spacing of directional couplers for efficient coupling between different phase-matched mode orders. Likewise, for the DeMUX, we use asymmetrical directional couplers as the input couplers between the multimode bus waveguide and the singlemode microring resonators, as shown in Fig. 1(c).

Fig. 1. (a) Working principle of the MDM-WDM transmission scheme. (b) and (c) Working principles of the three-mode MUX and DeMUX. (b) MUX based on directional couplers for the TE0 mode in the input waveguide coupling to the TE0, TE1, and TE2 modes in the bus waveguide. (c) DeMUX based on microring resonators for the TE0, TE1, and TE2 modes in the bus waveguide coupling to the TE0 mode in the microring.

Figure 2 schematically shows the three-mode MDM-WDM circuit. For the MUX (Fig. 2(a)), we cascade three different directional couplers with a fixed interaction length of 120 μm but with different waveguide widths and gap spacing. The interaction length is constrained by a relatively wide gap spacing. We launch from input-port I1 to the TE0 mode in the bus waveguide, from input-port I2 to the TE1 mode and from input-port I3 to the TE2 mode, with the latter two couplings through asymmetrical directional couplers. There are 200μm-long adiabatic tapers (T1 and T2) each with a tapering angle of < 0.2° connecting between adjacent bus waveguide segments of different widths in order to adiabatically vary the bus waveguide width.

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22174

Fig. 2. Schematics of a three-mode MDM-WDM circuit. (a) MUX based on asymmetrical directional couplers, and (b) DeMUX based on microring resonators. Inset: Cross-sectional schematic of the SiN waveguide.

For the wavelength-selective mode DeMUX (Fig. 2(b)), we use a mirror-symmetric design for the bus waveguide, with taper T3 identical with taper T2, and taper T4 identical with taper T1. We use identically designed singlemode microring resonators input-coupled from different segments of the bus waveguide with different widths, and output-coupled to singlemode waveguides. In principle, the microring resonators should have a circumference smaller than 40 μm in order to obtain a FSR wider than the 30nm-wide spectral bandwidth of the communications window around 1550 nm. However, limited by the minimum coupling gap spacing and the microring we can reliably fabricate in our current fabrication process (detailed in Sections 3 and 4), we choose a relatively large microring for our proof-of-concept demonstration. The racetrack microrings have an arc radius of 30 μm and a coupling length of 30 μm. We keep the three microrings identical in order to align the transmission resonances for output-coupling the TE0 mode to output-port O1, the TE1 mode to output-port O2 and the TE2 mode to output-port O3. The inset of Fig. 2(b) schematically shows the cross-section of the SiN waveguide, with a 400nm-thick SiN device layer surrounded by silica cladding. For device simulation and modeling, we adopt the refractive indices of SiN and SiO2 as nSiN = 2.08 and nSiO2 = 1.45, respectively, according to ellipsometry measurements of our deposited thin-film samples. We calculate the effective refractive indices (neff) of the TEpolarized modes in the SiN waveguides of different widths using beam-propagation method (BPM). We only consider the TE-polarized modes but not the transverse-magnetic (TM)polarized modes because the latter exhibit a relatively large waveguide bending loss in the thin SiN waveguide according to our simulations (0.2 dB/cm for the TE fundamental mode, 2.6 dB/cm for the TM fundamental mode), and thus lead to low quality (Q) factors for SiN microring resonators in the TM polarization. Figures 3(a)-3(c) show the BPM-simulated mode intensity profiles of the TE0, TE1 and TE2 modes in different bus waveguide segments. We choose the bus waveguide width (wb) to be 1, 2.25 and 3.5 μm for the TE0, TE1 and TE2 modes, respectively. Figures 3(d)-3(f) depict the BPM-simulated mode intensity profiles of the asymmetrical directional coupler designs

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22175

adopted in the MUX. We choose the gap spacing to be 0.5 μm for the symmetrical directional coupling for the TE0 mode (Fig. 3(d)). For the asymmetrical directional coupling, we choose the gap spacing to be 0.45 μm for the TE0 mode coupling to the TE1 mode (Fig. 3(e)), and 0.40 μm for the TE0 mode coupling to the TE2 mode (Fig. 3(f)). Our BPM simulation results suggest a relatively long coupling length of approximately 90-110 μm for the three different mode couplings. The small index contrast of the SiN/SiO2 platform (~2.08/1.45) results in a relatively long coupling length and therefore leads to a large circuit size compared with that in the SOI platform [11]. This is one trade-off in using the SiN/SiO2 platform over SOI.

Fig. 3. (a)–(c) BPM-simulated mode intensity profiles of the (a) TE0, (b) TE1 and (c) TE2 modes in different bus waveguide segments. (d) – (f) BPM-simulated mode intensity profiles of the three directional couplers, including (d) a symmetrical directional coupling for the TE0 mode, (e) an asymmetrical directional coupling from the TE0 mode to the TE1 mode, and (f) an asymmetrical directional coupling from the TE0 mode to the TE2 mode.

3. Modeling Here, we detail the modeling results that motivate the device design parameters. Figure 4(a) shows the calculated neff of the TE modes as a function of the waveguide width. We adopt the widths of the input- and output-waveguides and of the microring resonators to be 1 μm, which support only the TE0 mode. The neff for the TE0 mode is 1.7. The bus waveguide width (wb) values at different segments are determined according to the phase-matching condition (shown by the dotted line) for directional coupling to different transverse mode orders. We therefore choose wb to be 1, 2.25 and 3.5 μm in the coupling regions for the TE0, TE1 and TE2 modes, respectively. Figure 4(b) shows the numerically calculated field coupling coefficients of the three directional couplers at different coupling gap spacing (g) values at a fixed interaction length (L = 120 μm) for the coupling of the TE0 mode in the input-waveguide to different mode orders in the bus waveguide of different widths. The values are numerically calculated according to the coupled-mode theory, assuming the BPM-simulated waveguide mode-field amplitude profiles. We vary the coupling gap spacing instead of the interaction length in order to keep the coupling spacing values consistent with those designed for the microring resonators (of a shorter interaction length) in the DeMUX. The minimum g value of 350 nm examined is limited by our photolithography resolution. Our simulation results suggest that at L = 120 μm we obtain a field coupling coefficient of ~0.8 upon g = 500, 450 and 400 nm for coupling to the TE0, TE1 and TE2 modes, respectively. Figure 4(c) shows the numerically calculated field coupling coefficients of the three 30μm-long bus-to-microring coupling at different g values. With g = 500, 450 and 400 nm for coupling from the TE0, TE1 and TE2 modes, respectively, we obtain a field coupling coefficient of ~0.5 for all three modes. A transfer-matrix modeling calculation for a microring add-drop configuration assuming a field coupling coefficient of 0.5, lossless input- and

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22176

output-coupling and a waveguide propagation loss of 2 dB/cm suggests a loaded resonance Q factor of around 4000 (a bandwidth of ~50 GHz), which is compatible to a high-data-rate transmission.

Fig. 4. (a) Calculated neff values of the TE modes of 400nm-thick SiN waveguides. Black squares: TE0, red circles: TE1, blue triangles: TE2, green triangles: TE3 and purple triangles: TE4. (b) Calculated field coupling coefficients of the three directional couplers in the MUX. Blue triangles: TE0-to-TE2, red squares: TE0-to-TE1, and black crossings: TE0-to-TE0. (c) Calculated field coupling coefficients of the bus-to-microring coupling in the DeMUX. (d) Calculated field cross-coupling coefficients of the undesired modes in bus-to-microring coupling. Black circles: the TE0 mode cross-couples from a bus waveguide with wb = 2.25 μm, red stars: the TE1 mode cross-couples from a bus waveguide with wb = 3.5 μm, and purple crossings: the TE0 mode cross-couples from a bus waveguide with wb = 3.5 μm.

Figure 4(d) shows the numerically calculated field cross-coupling coefficients of the lower-order modes in the bus waveguide coupling to the singlemode waveguide (of the microring resonators) at different g values. The lower-order modes refer to the TE0 and TE1 modes in a 3.5μm bus waveguide, and the TE0 mode in a 2.25μm waveguide. Such crosscouplings contribute to undesirable modal crosstalks. The modeling results suggest low field cross-coupling coefficients below 0.05. The numerical modeling results in Figs. 4(b)-4(d) suggest that the directional couplers with the long interaction length of 120 μm used in the MUX exhibit a higher sensitivity of the coupling coefficient values to the coupling gap spacing variations. In our current design, with a coupling coefficient centered about 0.8 for all the three directional couplers in the MUX, we note that a 10nm reduction in the coupling gap spacing reduces the coupling coefficient values to ~0.7 (Fig. 4(b)). This leads to a modeled transmission intensity drop of ~1 dB in the MUX. For the directional couplers with the short interaction length of 30 μm used in the DeMUX, we note that a 10nm variation in the coupling gap spacing only varies the coupling coefficient values by about 0.02 (Fig. 4(c)) and the cross-coupling coefficient values by the order of 10−3 (Fig. 4(d)). Thus, based on our numerical modeling, we expect that a 1dB transmission intensity drop can be related to a 10nm fabrication error. In principle, by tailoring the bus waveguide width, the coupling spacing and the interaction length, one can scale the MDM-WDM circuit to transmit more higher-order modes. For example, according to our modeling (Fig. 4(a)), with a bus waveguide width of 4.75 μm, the TE3 mode also satisfies the phase-matching condition. With an interaction length of 30 μm for the microring resonator and a coupling gap spacing of 0.35 μm, we can obtain a #217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22177

field coupling coefficient of ~0.5 with a maximum field cross-coupling coefficient of 0.038 (not shown). However, in principle, modal crosstalks incur due to the residual couplings upon partial phase-matching between the fundamental mode of a singlemode waveguide and the lowerorder modes of the multimode waveguide. In general, the dominant modal crosstalk is due to the residual coupling with the next-highest-order mode. The maximum amount of dominant modal crosstalk depends on how close the partial phase matching is. Our numerical studies of the multimode waveguides and asymmetric directional couplers using BPM (not shown here) suggest that the waveguide propagation constants of TE5 and TE4 modes in a 6-mode waveguide become close enough to obtain similar coupling lengths. Thus, we believe that in practice this kind of platform can support approximately up to 6 modes for relatively low modal crosstalk over the shortest coupling length to the highest-order mode. One way to further increase the number of modes for relatively low modal crosstalk is to tradeoff the shortest coupling length, such that we may employ a longer interaction length to suppress the next-highest-order mode. Besides, in order to further extend on the platform, it has been shown in the literature [11] that polarization-multiplexing can be employed. Table 1. Designed field coupling coefficients at each coupling region MUX O1 I1 I2 I3

κI1 κI2 κI3

0.8 0.8 0.8

κO1 0.5 Nil Nil

κ'O1 0.5 Nil Nil

DeMUX O2 κΟ2 0.04 0.5 Nil

κ'Ο2 0.5 0.5 Nil

O3 κΟ3 0.01 0.03 0.5

κ'Ο3 0.5 0.5 0.5

Table 1 summarizes the designed field coupling coefficients at each coupling region of the MDM-WDM circuit. For the MUX, κIi (i = 1, 2, 3) represents the field coupling coefficient at each directional coupling region, where the light launched from input-port Ii couples to the bus waveguide. We design κIi = 0.8 for all the three coupling regions (see Fig. 4(b)). For the DeMUX, κOj (j = 1, 2, 3) represents the field coupling coefficient at each bus-to-microring coupling region for output-port Oj, and κ'Oj represents the field coupling coefficient at the microring-to-drop-waveguide coupling region (TE0-to-TE0 only) for output-port Oj. For the desired transmission channel, where i = j, we design κOj = κ'Oj = 0.5 for all three modes (see Fig. 4(c)). For the undesired crosstalk channel, where i < j, we limit κOj to be less than 0.05 (see Fig. 4(d)), while κ'Oj remains at 0.5. For the case that i > j, we ignore κOj and κ'Oj, assuming that the high-order modes are spatially filtered by the taper(s) and the following bus waveguide segment(s). 4. Device fabrication We fabricate the MDM-WDM circuit on a SiN-on-silica substrate using CMOS-compatible processes. In brief, a bulk silicon wafer is first thermally oxidized to form a 1.5μm-thick silica under-cladding layer. A 400nm-thick low-stress SiN device layer is then deposited using lowpressure chemical-vapor deposition (LPCVD) at 700 °C. The device structures are defined by photolithography (i-line stepper, 365 nm) and CF4-based inductively coupled plasma reactive ion plasma etching (ICP-RIE) process. The etch depth is about 400 nm, with the SiN layer totally etched. A 1.2μm-thick silica layer is deposited on top using LPCVD as an uppercladding layer. A 500nm-thick Al is sputtered through a 500nm-wide window on top of the microring to form a microheater for thermal-optically aligning the microring resonators. Figure 5(a) shows the scanning-electron microscope (SEM) image of the fabricated SiN MDM-WDM circuit, including the metal pads. The circuit spans a total length of ~2 mm. Figures 5(b), 5(c) and 5(d) show from a different device the zoom-in-view SEM images of the input-waveguide coupled to the bus waveguide of the MUX for coupling to the TE0, TE1, and TE2 modes, respectively. The images are taken after removing the metal and the uppercladding silica layer by wet etching. We caution that the measured waveguide widths and gap spacing can marginally deviate from the actual fabricated values as the wet etching process

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22178

slightly etches the SiN layer. The fabricated coupling gap spacing values measured from the SEM images are about 490, 430 and 340 nm, which are narrower than the designed values of 500, 450 and 400 nm, respectively. We attribute the relatively large deviation of 60 nm from the designed value for the narrowest gap spacing to our lithography resolution. The three fabricated input-waveguide widths are consistently ~0.98 - 0.99 μm. The three fabricated bus waveguide widths are 0.98, 2.22 and 3.47 μm, which are consistent with the designed values of 1.00, 2.25 and 3.50 μm, all within a fabrication imperfection of 30 nm. The fabricated 1μm-wide waveguide propagation loss is ~2 dB/cm according to cutback measurements. We attribute the relatively high waveguide loss of our LPCVD SiN waveguides to unoptimized growth and fabrication processes. The latter have introduced significant sidewall roughness.

Fig. 5. (a) SEM image for the fabricated SiN MDM-WDM circuit. (b) - (d) SEM images of the coupling regions between the input waveguides and the bus waveguides with a designed bus waveguide width of (b) 1 μm, (c) 2.25 μm, and (d) 3.5 μm.

5. Device characterization In the experiment, we use a lensed polarization-maintaining singlemode fiber to butt-couple the TE-polarized laser light separately to the input-waveguide ports (I1 to I3) or directly to the bus waveguide. We use a 40 × microscope objective lens (NA of 0.65) to collect the light from the output end facet of the MUX bus waveguide for MUX characterization or from the DeMUX output-waveguide ports (O1 to O3) and bus waveguide output end facet for MUXDeMUX circuit characterization. We use a polarization analyzer to filter the TE polarization.

Fig. 6. Near-field images of the MUX bus waveguide output facet with the light input-coupled from ports (a) I1, (b) I2, and (c) I3.

5.1 MUX characterization We first image the mode intensity profiles from the output end facet of the MUX bus waveguide. Figures 6(a), 6(b) and 6(c) show the measured near-field images with the laser

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22179

light at 1550 nm launched to ports I1, I2 and I3, respectively. The images reveal the coupling to the TE0 mode from I1, to the TE1 mode from I2 and to the TE2 mode from I3. Table 2. Measured transmissions and extracted field coupling coefficients of the MUX at 1550 nm Transmission (dB) Coupling coeff.

Input Bus −19 ± 1 –

I1(κI1) −19 ± 1 0.8(0.8)

I2(κI2) −28 ± 1 0.4(0.7)

I3(κI3) −28 ± 1 0.4(0.4)

Table 2 lists the measured transmissions from the MUX output with the laser light separately launched at ports I1, I2, I3 and the bus input end facet. We estimate a fiber-to-chip alignment variation of ± 1 dB based on measuring the bus-input-to-bus-output transmission. The measured transmissions exhibit a variation of less than 3 dB within a wavelength span between 1540 nm and 1556 nm. Using the measured bus waveguide transmission as a reference and assuming lossless coupling for the directional couplers, we can extract the field coupling coefficients κI1, κI2 and κI3 to be 0.8, 0.4 and 0.4, respectively. The extracted κI1 and κI3 values are consistent with the estimated values of 0.8 and 0.4 (values in brackets), respectively. We obtain the estimated values from our modeling using the measured coupling gap spacing and waveguide widths from a representative device (see Figs. 5(b) and 5(d)). The extracted κI2 value of 0.4 is, however, smaller than the estimated value of 0.7. We attribute the mismatch to fabrication variances among different devices on the same wafer. 5.2 MUX-DeMUX circuit characterization We measure the drop-port transmission spectra of the three-mode MDM-WDM circuit at output-ports O1 (for TE0), O2 (for TE1) and O3 (for TE2) after aligning the microring resonances to match the TE0 mode transmission resonances. We thermally tune the microring resonator coupled to O2 with a 0.5V-bias applied to the microheater (inducing a 0.1nm redshift) and the microring resonator coupled to O3 with a 1V-bias (inducing a 0.2nm redshift). The measured tuning efficiency is 30 pm/mW. Figures 7(a)–7(c) show the measured TE-polarized transmission spectra at output-ports O1, O2 and O3 and the bus output, with the laser light input-coupled from ports I1, I2 and I3. The measured linewidths for the resonance around 1550 nm are 0.50, 0.40 and 0.39 nm for the transmissions from I1-to-O1 (Fig. 7(a)), I2-to-O2 (Fig. 7(b)) and I3-to-O3 (Fig. 7(c)), respectively. The resonance Q factors are ~3000 to ~4000, which are consistent with the designed value of 4000 (see Sec. 3). We also measure the TM-polarized transmission, which reveals a low Q of only ~700 (data not shown). We observe a dominant modal crosstalk of ~24 dB in the I1-to-O1 transmission from I2-to-O1 (Fig. 7(a)), of ~-10 dB in the I2-to-O2 transmission from I1-to-O2 (Fig. 7(b)), and of ~-15 dB in the I3-to-O3 transmission from I2to-O3 (Fig. 7(c)). The relatively flat transmission at off-resonance wavelength of the throughput spectra indicates a wide transmission band of the directional couplers of 30 μm long in the DeMUX. Given the >16 nm 3dB bandwidth of the directional couplers in the MUX, the bandwidth of the directional couplers with 30 μm interaction length can only be wider than 16 nm.

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22180

Fig. 7. (a)-(c) Measured and fitted transmission spectra from the bus output and outputs of (a) O1, (b) O2, and (c) O3 with input light from I1, I2 and I3. (d) - (f) Measured eye diagrams of the three transmission channels at 30 Gb/s.

Table 3 summarizes the transmissions at the resonance wavelength around 1550 nm for ports O1, O2 and O3 and the bus output and at an off-resonance wavelength around 1547.5 nm for the bus output. The measured transmissions for I1-to-O1, I2-to-O2, and I3-to-O3 are −20, −29 and −29 dB, respectively. Comparing with the respective MUX transmissions of −19, −28 and −28 dB (see Table 2), we thus attribute the observed MUX-DeMUX circuit transmission variation to the MUX transmission variation and that the DeMUX transmission loss for each channel is −1 dB ( ± 1 dB). Table 3. Transmissions (dB) of the MDM-WDM circuit I1 I2 I3

O1 −20 ± 1 −44 ± 1 −51 ± 1

O2 −39 ± 1 −29 ± 1 −53 ± 1

O3 −47 ± 1 −44 ± 1 −29 ± 1

Bus output (on-resonance) −27 ± 1 −45 ± 1 −52 ± 1

Bus output (off-resonance) −20 ± 1 −41 ± 1 −47 ± 1

We characterize the data transmission of the MDM-WDM circuit by measuring eye diagrams of the three transmission modes separately with individual inputs at a data rate of 30 Gb/s, as shown in Fig. 7(d) for I1-to-O1, (e) for I2-to-O2, and (f) for I3-to-O3. We use an erbium-doped fiber amplifier (EDFA) before and after the chip in order to compensate the relatively large transmission loss. The open eye diagrams exhibit an extinction ratio (ER) of #217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22181

~9 dB at a pseudorandom binary sequence of 231-1. We attribute the noise to the amplified spontaneous emission (ASE) noise of the EDFAs. Thus we expect that the output extinction ratio can be degraded compared to the transmitter output due to the ASE noise in our experimental setup. The measured extinction ratio of the signal can be under-estimating the performance of the device. We attribute the long rise/fall times in the eye diagrams mainly to the rise/fall times of the measurement system. 6. Field coupling coefficients and crosstalk analysis Here we analyze in detail the field coupling coefficients and the crosstalk contributions for the DeMUX based on fitting the measured MUX-DeMUX transmission spectra around the 1550nm resonance using the transfer-matrix method. Table 4 summarizes our fitting results. We first fit the I1-to-O1 transmission and the I1-to-bus throughput (Fig. 7(a)). For the MUX transmission, we adopt the extracted κI1 of 0.8 (see Table 2). We assume lossless couplings for both the MUX and the DeMUX. Our fitting results suggest κO1 = 0.45 and κ'O1 = 0.65. These values, however, deviate from our estimated values of 0.5 (values in brackets) assuming a coupling gap spacing of 490 nm and symmetrical waveguide widths of 0.99 μm according to our SEM image (see Fig. 5(b)). We attribute the variations between the fitted values and the estimated values to the fabrication variances among devices on the same wafer. Table 4. Fitted field coupling coefficients of the DeMUX O1 I1 I2 I3

κO1 0.45 (0.5) -

O2 κ'O1 0.65(0.5) -

κΟ2 0.04 (0.03) 0.35 (0.5) -

O3 κ'Ο2 0.60 (0.5) 0.60 (0.5) -

κΟ3 0.03 (0.01) 0.05 (0.03) 0.35 (0.6)

κ'Ο3 0.55 (0.5) 0.55 (0.5) 0.55 (0.5)

Similarly, we fit the I2-to-O2 transmission and the I2-to-bus throughput (Fig. 7(b)). We adopt the extracted κI2 of 0.4 (see Table 2) for the directional coupler in the MUX. The bus throughput sees an additional loss for the TE1 mode due to taper T4 and the following bus waveguide segment, as both do not propagate the TE1 mode. Our fitting results suggest κO2 = 0.35 and κ'O2 = 0.60. Likewise, we fit the I3-to-O3 transmission and the I3-to-bus throughput (Fig. 7(c)). We adopt the extracted κI3 = 0.4 (see Table 2) for the directional coupler in the MUX. The bus throughput sees an additional loss for the TE2 mode due to tapers T3 and T4 and the following bus waveguide segments that do not propagate the TE2 mode. Our fitting results suggest κO3 = 0.35 and κ'O3 = 0.55. We analyze the worst-case crosstalk of ~-10 dB in the I2-to-O2 transmission from I1-toO2 (Fig. 7(b)). Following a similar fitting analysis, we obtain κO2 = 0.04 for input at I1, which is consistent with the designed field cross-coupling coefficient of 0.04 for the TE0 mode coupling from a 2.25μm bus waveguide (see Fig. 4(d), circles). Therefore, we attribute the relatively large −10dB crosstalk to the compromised I2-to-O2 transmission due to the reduced field coupling coefficient of κI2 in the MUX (see Tables 1 and 2). With an improved κI2 to the designed value of 0.8, we expect an increased I2-to-O2 transmission to −20 dB and a reduced crosstalk of −19 dB from I1-to-O2. Therefore, a compromised input-coupling of the directional coupler in the MUX constitutes a major contribution to the crosstalk of the MDMWDM circuit. Similarly, we analyze the crosstalk of ~-15 - ~-18 dB in the I3-to-O3 transmission from I2-to-O3 and I1-to-O3, respectively (Fig. 7(c)). We obtain from our fitting analysis κO3 = 0.05 for input at I2 and κO3 = 0.03 for input at I1. They are consistent with the designed crosscoupling coefficients of 0.03 for the TE1 mode coupling from a 3.5μm bus waveguide to a 1μm waveguide (Fig. 4(d), stars), and of 0.01 for the TE0 mode coupling from a 3.5μm bus waveguide to a 1μm waveguide (Fig. 4(d), crosses). With an improved κI3 to the designed value of 0.8, we expect an increased I3-to-O3 transmission to −20 dB and a reduced crosstalk of −27 dB from I1-to-O3. However, assuming an improved κI2 to 0.8, we expect the crosstalk #217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22182

from I2-to-O3 to remain at −15 dB. The remaining crosstalk mainly has two contributions, namely the compromised κO3 for the I3-to-O3 transmission and the raised κO3 for the I2-to-O3 cross-coupling (see Tables 1 and 3). We remark that the low crosstalk contributions from I2 and I3 to O1 (~-23 dB - ~-31 dB), as shown in Table 3, are suppressed by the higher-order mode propagation loss in tapers T3 and T4 and the following bus waveguide segments. Likewise, the low crosstalk from I3 to O2 (~-24 dB), as shown in Table 3, is suppressed by the higher-order mode propagation loss in taper T3 and the following bus waveguide. 7. Conclusions We have designed and fabricated a three-mode MDM-WDM circuit on a SiN-on-silica substrate using asymmetrical directional couplers and microring resonators. Our experiments revealed three-mode multiplexing and demultiplexing, with the worst-case modal crosstalk of ~-10 dB at the WDM channel wavelength of around 1550 nm. We have observed data transmissions with open eye diagrams at 30 Gb/s for each of the three modes separately. Our analysis suggested three contributions to the observed modal crosstalks, namely (i) a compromised input-coupling of the directional couplers in the MUX, (ii) a compromised input-coupling of the microring resonators in the DeMUX, and (iii) a raised cross-coupling of the microring resonators in the DeMUX, with (i) being the dominant cause. However, one should note that in the case of simultaneously propagating all the three modes, the presence of an unoptimized accumulated modal crosstalk can cause significant signal distortion, and thereby limit the aggregated data transmission bandwidth. Acknowledgments The authors thank Nanoelectronics Fabrication Facilities (NFF) of HKUST for support in the device fabrication. Yue-De Yang acknowledges The Hong Kong Scholars Program 20112013.

#217364 - $15.00 USD Received 18 Jul 2014; revised 24 Aug 2014; accepted 26 Aug 2014; published 5 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.022172 | OPTICS EXPRESS 22183

Silicon nitride three-mode division multiplexing and wavelength-division multiplexing using asymmetrical directional couplers and microring resonators.

We demonstrate silicon nitride mode-division multiplexing (MDM) and wavelength-division multiplexing (WDM) using asymmetrical directional couplers and...
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