Abstract

We design and fabricate silicon vertical slot waveguides for terabit-scale data transmission. The designed silicon photonic device is composed of apodized grating couplers, strip waveguides, strip-to-slot/slot-to-strip mode converters, and slot waveguide. Tight light confinement in the nano-scale air slot region is achieved in the silicon vertical slot waveguide which features relatively lower nonlinearity compared to silicon strip waveguide. Using the fabricated silicon photonic devices, we first demonstrate ultra-wide bandwidth 1.8-Tbit/s data transmission through a 2-mm-long silicon vertical slot waveguide using 161 wavelength-division multiplexing (WDM) channels each carrying 11.2-Gbit/s orthogonal frequency-division multiplexing (OFDM) 16-ary quadrature amplitude modulation (16-QAM) signal. All 161 WDM channels achieve bit-error rate (BER) less than 1e-3 after on-chip data transmission. We further demonstrate terabit-scale data transmission through four silicon vertical slot waveguides with different lengths (1 mm, 2 mm, 3.1 mm, 12.2 mm). The optical signal-to-noise ratio (OSNR) penalties of data transmission through four silicon vertical slot waveguides are 1, 2, 3.2 and 4.5 dB at a BER of 1e-3, respectively. The obtained results indicate that the presented silicon vertical slot waveguide might be an alternative promising candidate facilitating chip-scale high-speed optical interconnections

© 2015 Optical Society of America

1. Introduction

The arrival of the era of bit data has fuelled the rapid development of high-speed data transmission within limited bandwidth resources, ranging from long distance communication links to short-distance access networks and even shorter-reach rack-to-rack, backplanes, chip-to-chip, and on-chip interconnections [1]. Photonic integrated circuits (PICs) or integrated optical circuits using photons rather than electrons to perform a wide variety of optical functions, feature higher data transmission rates compared to traditional electronic integrated circuits [2, 3]. Recent advances in the density and complexity of PICs have facilitated possible integration of complete optical communication systems on a monolithic chip. That is, PICs offer an attractive solution to enable chip-to-chip and on-chip optical interconnection networks [4, 5]. PICs-assisted optical interconnection provides relaxed interconnection latency, wide bandwidth, high resistance to electromagnetic interferences, and low power consumption. Several optical technologies have been developed for optical interconnections, including the use of planar optical circuits [6], silicon photonics [7], photonic crystals [8], and plasmonic circuits [9]. Silicon photonics is considered to be a promising technology to address ever increasing challenges of future chip-scale optical interconnections owing to the compactness for high-density integration and complementary metal-oxide-semiconductor (CMOS) compatible platforms for low-cost mass production [10, 11]. Silicon vertical slot waveguide which confines light in the low-index air slot region could be also an alternative candidate facilitating chip-scale optical interconnections.

Recently, data transmissions of 170-Gbit/s binary on-off keying (OOK) signals in an erbium-doped waveguide amplifier on silicon [12] and 40-Gbit/s binary differential phase-shift keying (DPSK) transmission through a silicon microring switch [13] have been reported. Considering the unprecedented bandwidth scalability with reduced power dissipation enabled by high-performance silicon photonic devices, wavelength-division multiplexing (WDM) technique can be utilized to achieve high transmission rate and make wavelength parallelism available in integrated optics [14, 15]. Most of the previous works on data transmissions in silicon photonic devices showing impressive performance employed signals with binary modulations (e.g. OOK, DPSK). It is well known that advanced modulations with multi-bit information coded in one symbol can harvest high capacity and high spectral efficiency. Not only optical fiber communications also chip-scale optical interconnections show a growing trend of high-speed data transmission using advanced modulations to continue supporting ever-increasing capacity demands. So far high-speed data transmissions with advanced modulations have been reported in optical fiber transmission systems [1618]. In particular, coherent multi-carrier multi-level modulations together with optical multiplexing techniques have also been employed to significantly boost the aggregated transmission capacity and spectral efficiency in fiber optical communications. For instance, orthogonal frequency-division multiplexing (OFDM), advanced multi-level quadrature amplitude modulation (QAM), and WDM have been combined together to increase the transmission capacity and spectral efficiency of optical communication systems [19]. OFDM-based modulation, which offers the potential advantages of robustness to chromatic dispersion and seamless multiplexing of modulated signals, is a more spectrally efficient advanced modulation [20]. In this scenario, one would also expect chip-scale optical interconnections with high-speed data transmissions of WDM OFDM m-QAM signals in silicon photonic devices. Actually, advanced modulations have already been demonstrated using chip-scale PICs. Silicon photonic integrated devices have been used for compact coherent optical transmitters and receivers of advanced modulations [2125]. In addition to transmitter and receiver, network on a chip and system on a chip have also been proposed and demonstrated [26, 27]. Moreover, advanced modulations have also been employed in on-chip optical interconnections [28, 29]. For example, terabit data transmission of chip-scale interconnections have been demonstrated using 105 wavelengths each modulated with a 16-QAM signal [29].

In this paper, we design and fabricate silicon vertical slot waveguides which tightly confine light in the low-index air slot region. We study the data transmission performance of the fabricated silicon slot waveguide for WDM OFDM 16-QAM signals in the experiment. Ultra-wide bandwidth 1.8-Tbit/s (161 WDM channels, 11.2-Gbit/s OFDM 16-QAM) data transmissions through 1-mm, 2-mm, 3.1-mm and 12.2-mm-long silicon vertical slot waveguides are demonstrated in the experiment. The bit-error rate (BER) performance is measured for a comprehensive evaluation of the transmission performance.

2. Fabricated silicon vertical slot waveguide

Figure 1 shows the schematic diagram of the proposed silicon vertical slot waveguide which is composed of three key parts, i.e. strip-to-slot mode converter, slot waveguide, and slot-to-strip mode converter. Remarkably, different mode guiding mechanisms cause large mode distribution difference between the strip waveguide and slot waveguide. As a result, direct coupling method would induce large coupling loss. Hence, mode converters are highly preferred to reduce the coupling loss when designing slot waveguides [30, 31]. The strip-to-slot mode converter including two sections is presented in Fig. 1(a). Within the first section with a length of L1, the width of the strip waveguide keeps constant, while the first rail (bottom rail shown in Fig. 1(a)) of the vertical slot waveguide is introduced with an initial width and linearly expanding to the designed rail width. Within the second section with a length of L2, the strip waveguide is gradually narrowed down into the second rail (top rail shown in Fig. 1(a)) of the vertical slot waveguide, while the width of the first rail of the vertical slot waveguide keeps constant. The width of the slot region also keeps unchanged when gradually narrowing the strip waveguide. The quasi-TE mode distributions of the strip waveguide and slot waveguide are simulated by the finite-element method (FEM) software package COMSOL Multiphysics with the scattering bound condition and rectangular perfectly matched layer (PML). A full-vector model that can weigh the contributions of different materials to the nonlinear coefficient is considered to achieve accurate results [32, 33]. From the insets of mode distributions in Fig. 1(a), one can clearly see the mode conversion from the strip mode to slot mode. Figure 1(b) shows the cross-section of the silicon vertical slot waveguide. From the inset of mode distribution in Fig. 1(b), it can be clearly seen that tight light confinement is achievable in the nano-scale air slot region, which could offer relatively lower nonlinearity compared to the strip waveguide. The geometry parameters of the designed silicon vertical slot waveguide are as follows: the width of the slot waveguide rail Wr = 220 nm, the height of the slot waveguide H = 220 nm, and the width of the air slot region Ws = 100 nm. Using given geometric parameters, one can calculate the effective nonlinear coefficient of the waveguide.

 figure: Fig. 1

Fig. 1 Schematic diagram of the proposed silicon vertical slot waveguide. (a) Mode converter. (b) Cross-section of silicon vertical slot waveguide.

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By generalizing the definition of the Aeff as [32]

Aeff=|(eν×hν*)z^dA|2|(eν×hν*)z^|2dA
where eν and hν are modal field distributions, the nonlinear coefficient γν can be expressed by [32]
γν=2πλn2¯Aeff
n2¯=kε0μ0n2(x,y)n2(x,y)(2|eν|4+|eν2|2)dA3|(eν×hν*)z^|2dA
In the calculations, the nonlinear refractive indices n2 used for silicon and silica are 4.5 × 10−18 and 2.6 × 10−20 m2/W, respectively [33]. The width and height of the strip waveguide are 540 nm and 220 nm, respectively. The nonlinear coefficients of the strip waveguide and slot waveguide are calculated to be around 211.6 and 4.1 W−1m−1, respectively. As a consequence, silicon vertical slot waveguide confining light tightly in the air slot region features relatively lower nonlinearity, which could be a promising candidate for chip-scale data transmission.

The designed silicon vertical slot waveguide is fabricated on a silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon layer and a 3-um-thick buried oxide layer. The device layout is transferred to ZEP520A photoresist by electron-beam lithography (Vistec EBPG5000 + ES). Using electron-beam lithography (EBL) followed by induced coupled plasma (ICP) etching (Oxford Instruments Plasmalab System 100), the designed silicon vertical slot waveguide is formed by the upper silicon layer which is etched downward to 220 nm. The designed silicon photonic device is composed of grating couplers, strip waveguides, strip-to-slot/slot-to-strip mode converters, and slot waveguide. Vertical grating couplers are used to couple light in and out of the bus waveguides and they prohibit transmitting TM mode and ensure operation with TE-polarized light only. A fully etched apodized grating coupler is employed to simplify the fabrication progress and tolerate the sensitivity of the etching depth [34]. The scanning electron microscope (SEM) images of the apodized grating coupler are shown in Figs. 2(b) and 2(c). To improve the fiber to waveguide coupling efficiency, a nominal 1200 nm wide strip waveguide is linearly tapered to 500 nm between the vertical grating coupler and mode converter. Figures 2(d) and 2(e) depict the SEM images of the mode converter between strip waveguide and slot waveguide. We choose the parameters of mode converter to be L = 15 μm, L1 = 5 μm and L2 = 10 μm. The mode conversion loss between the strip waveguide and slot waveguide is assessed to be less than 0.5 dB. We also consider the bending region for long waveguide. Figures 2(f) and 2(g) show the bending region of a 4-mm long slot waveguide. The SEM images of slot region are depicted in Figs. 2(h) and 2(i). Shown in Fig. 2(i) is the cross-section of slot waveguide. The rail width of the slot waveguide is 220 nm, and the width and height of the air slot region are 100 and 220 nm, respectively. The slot waveguide propagation loss is assessed to be ~5 dB/cm. In general, the overall loss of the fabricated silicon vertical slot waveguide could be ascribed to the sidewall quality (roughness) of the slot, mode confinement loss, waveguide bending loss, material loss, substrate leakage, mode conversion loss between the strip waveguide and slot waveguide, fiber-to-waveguide and waveguide-to-fiber vertical grating coupling loss. For the slot waveguide propagation loss, the main contribution is from the sidewall quality (roughness) of the slot.

 figure: Fig. 2

Fig. 2 SEM images of (a) silicon photonic device (grating couplers, strip waveguides, slot waveguides, and strip-to-slot/slot-to-strip mode converters), (b)(c) apodized grating coupler, (d)(e) mode converter between strip waveguide and slot waveguide, (f)(g) bending region, and (h)(i) slot region.

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3. Experimental setup

Figure 3 shows the experimental setup for terabit-scale ultra-wide bandwidth WDM OFDM 16-QAM data transmission through silicon vertical slot waveguides. At the transmitter, 7 external cavity lasers (ECLs) at 1536.0, 1540.5, 1545.1, 1549.7, 1554.3, 1558.9 and 1563.6 nm are combined by two 4x1 polarization maintaining optical couplers (PMOCs) with the optical spectrum shown in Figs. 4(a) and 4(b), and then injected into two phase modulators (PMs). We employ 7 ECLs and 2 PMs to generate 161 optical carriers (WDM channels). The PMs are driven by a strong radio-frequency (RF) sine wave with a 25-GHz repetition frequency. After passing through PMs, each ECL can generate 23 optical frequency combs with a 25-GHz frequency spacing. In such fashion, 161 (23 x 7) optical carriers with a channel spacing of 25 GHz are generated with the optical spectrum shown in Figs. 4(c) and 4(d). A programmable wavelength selective switch (WSS) is then employed to couple, reshape and flatten the generated optical carriers which are amplified by erbium-doped fiber amplifiers (EDFAs). From Fig. 4(e), one can see that flattened optical carriers are generated. The generated 161 optical carriers are launched into an optical I/Q modulator to carry 11.2-Gbit/s OFDM 16-QAM signal. An arbitrary waveform generator (AWG) running at 10 GS/s is employed to produce single-side-band OFDM signal. After the optical I/Q modulator, the generated 161 WDM 11.2-Gbit/s OFDM 16-QAM signals shown in Fig. 4(f) are amplified by an EDFA and then fed into the fabricated silicon vertical slot waveguide assisted by vertical coupling via a grating coupler and mode conversion between the strip waveguide and slot waveguide. After data transmission through the silicon vertical slot waveguide, mode conversion between the slot waveguide and strip waveguide, and vertical coupling via a grating coupler, the output signals are sent into another EDFA which is followed by a WSS to select each single wavelength channel. A variable optical attenuator (VOA) is employed to adjust the optical signal-to-noise ratio (OSNR) before the receiver. At the receiver, a local oscillator (LO) is used to beat with the received signal in a coherent receiver. The two RF signals corresponding to I/Q components are fed into a Tektronix real-time scope and processed off-line with a Matlab program. The offline digital processing of the received signal includes: 1) carrier frequency offset estimation and OFDM window synchronization; 2) fast Fourier transform (FFT); 3) channel estimation; 4) phase noise estimation (crucial to m-QAM signal); 5) constellation decision and bit-error rate (BER) calculation.

 figure: Fig. 3

Fig. 3 Experimental setup for terabit-scale ultra-wide bandwidth WDM OFDM 16-QAM data transmission through silicon vertical slot waveguides.

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 figure: Fig. 4

Fig. 4 Measured optical spectra of signals at the transmitter.

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4. Experimental results

We first demonstrate terabit-scale data transmission through a 2-mm-long silicon vertical slot waveguide using 1.8-Tbit/s (161 WDM 11.2-Gbit/s OFDM 16-QAM) signals. Figure 5(a) shows measured output spectrum after transmitting through the fabricated silicon vertical slot waveguide. The measured BER performance for all 161 WDM channels through the fabricated vertical slot waveguide is shown in Fig. 5(b). One can clearly see that all 161 WDM channels can achieve BER less than 1e-3 (7% forward error correction (FEC) threshold). Figure 6(a) shows the received RF spectrum of the demodulated OFDM signal at the offline digital signal processor with a bandwidth of 3.2 GHz. Single channel measurements of three typical wavelengths (1533.82 nm, 1549.27 nm, and 1565.84 nm) for 2-mm-long silicon vertical slot waveguide are shown in Fig. 6(b). The observed OSNR penalties of data transmission through 2-mm-long silicon vertical slot waveguides are less than 2 dB at a BER of 1e-3.

 figure: Fig. 5

Fig. 5 (a) Output spectrum of ultra-wide bandwidth 1.8-Tbit/s (161 WDM OFDM 16-QAM) signals after transmitting through the silicon vertical slot waveguide. (b) BER performance for all 161 WDM channels.

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 figure: Fig. 6

Fig. 6 (a) Received RF spectrum of OFDM 16-QAM signal after demodulation; (b) Measured BER versus received OSNR for data transmission through a 2-mm silicon vertical slot waveguide at three typical wavelengths.

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We then study the BER performance for ultra-wide bandwidth 1.8-Tbit/s data transmission through 1-mm, 2-mm, 3.1-mm and 12.2-mm-long silicon vertical slot waveguides (slot 1 to slot 4), respectively. Typical single channel measurement for each silicon vertical slot waveguide is shown in Fig. 7. Four wavelengths of 1539.1 nm (slot 1), 1549.3 nm (slot 2), 1558.5 nm (slot 3) and 1565.8 nm (slot 4) are selected for four silicon vertical slot waveguides with different lengths. The observed OSNR penalties of data transmission through four silicon vertical slot waveguides are 1, 2, 3.2 and 4.5 dB at a BER of 1e-3, respectively. Figure 7(b) shows measured constellations of different wavelengths for four slot waveguides with different lengths.

 figure: Fig. 7

Fig. 7 (a) BER versus received OSNR and (b) constellations for data transmission through 1-mm (slot 1), 2-mm (slot 2), 3.1-mm (slot 3), and 12.2-mm-long (slot 4) silicon vertical slot waveguides, respectively.

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Remarkably, the slot waveguide has relatively lower nonlinearity owing to the tight mode confinement in the air slot region. That is, a large part of the guided mode is in the air slot region and a small part of the guided mode is in the silicon region. Despite reduced nonlinearity, the partial mode distribution in the silicon region still contributes to the nonlinear interactions. The observed OSNR penalty under a long waveguide could be ascribed to the nonlinear distortion contributed from the partial mode distribution in the silicon region. The assessed signal power threshold of nonlinear distortion is within 10 to 15 mW.

For the designed silicon vertical slot waveguides, the challenges of fabrication are as follows. 1) Perfectly forming a narrow slot region with high quality sidewalls. The slot region has a small width (~100 nm), so it is challenge to fabricate a smooth sidewall of the slot with high quality. The roughness of the sidewalls would induce propagation loss. With further improvement, thermal oxidation might be used in the smoothening of the slot sidewalls. 2) Precisely controlling the slot width. Considering the linewidth limits of the lithography, it is challenge to keep the fabricated slot width the same value as the designed one. In this case, one could consider the deviation between the measured slot width and designed one and compensate such deviation during the waveguide design.

For adopted advanced modulations, despite improved capacity and spectral efficiency, OFDM 16-QAM is relatively complicated and power consuming. With future improvement, for some cost sensitive applications, direct detection optical OFDM based on amplitude modulation could be more attractive because of the reduced complexity and power consuming of the transceiver compared with coherent optical OFDM [22, 35].

5. Conclusion

In summary, we design and fabricate silicon vertical slot waveguides which could tightly confine light into nano-scale air slot region. Compared to the nonlinearity of strip waveguide, silicon vertical slot waveguide might be a promising candidate facilitating chip-scale data transmission. Using the fabricated silicon photonic devices formed by apodized grating couplers, strip waveguides, strip-to-slot/slot-to-strip mode converters, and slot waveguide, we first demonstrate 1.8-Tbit/s (161 WDM OFDM 16-QAM) signal transmission through a 2-mm-long silicon vertical slot waveguide. All 161 WDM channels achieve BER less than 1e-3 after propagating through the waveguide. We then demonstrate ultra-wide bandwidth 1.8-Tbit/s data transmission through four silicon vertical slot waveguides with different lengths (1 mm, 2 mm, 3.1 mm, 12.2 mm). The OSNR penalties of data transmission through four silicon vertical slot waveguides are 1, 2, 3.2 and 4.5 dB at a BER of 1e-3, respectively. The obtained results imply that silicon vertical slot waveguides could be used to facilitate terabit chip-scale optical interconnections.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) under grants 61222502, the Program for New Century Excellent Talents in University (NCET-11-0182), the Wuhan Science and Technology Plan Project under grant 2014070404010201, the Fundamental Research Funds for the Central Universities (HUST) under grants 2012YQ008 and 2013ZZGH003, and the seed project of Wuhan National Laboratory for Optoelectronics (WNLO). The authors thank Jinsong Xia, Yong Zhang and Zengzhi Huang in the Center of Micro-Fabrication and Characterization (CMFC) of WNLO for the support in the manufacturing process of silicon vertical slot waveguides. The authors also thank the facility support of the Center for Nanoscale Characterization and Devices of WNLO.

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35. W.-R. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100 Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol. 30(12), 2025–2034 (2012). [CrossRef]  

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2014 (4)

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20, 6100108 (2014).

C. Weimann, P. C. Schindler, R. Palmer, S. Wolf, D. Bekele, D. Korn, J. Pfeifle, S. Koeber, R. Schmogrow, L. Alloatti, D. Elder, H. Yu, W. Bogaerts, L. R. Dalton, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission,” Opt. Express 22(3), 3629–3637 (2014), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-3-3629 .
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Z. Zhou, Z. Tu, T. Li, and X. Wang, “Silicon photonics for advanced optical interconnections,” J. Lightwave Technol. 33(4), 928–933 (2014).
[Crossref]

2013 (2)

2012 (5)

2011 (2)

2010 (2)

2009 (5)

2008 (3)

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-20-15915 .
[Crossref] [PubMed]

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

2007 (2)

2006 (2)

2005 (3)

M. Lipson, “Guiding, modulation, and emitting light on silicon challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005).
[Crossref]

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

2003 (1)

2000 (1)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728–749 (2000).
[Crossref]

Afshar V, S.

Alasaarela, T.

Alloatti, L.

Aroca, R.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20, 6100108 (2014).

Balthasar, G.

Barwicz, T.

Beausoleil, R. G.

Bekele, D.

Beling, A.

Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product,” Nat. Photonics 3(1), 59–63 (2009).
[Crossref]

Bergman, K.

L. Xu, W. Zhang, Q. Li, J. Chan, H. L. R. Lira, M. Lipson, and K. Bergman, “40-Gb/s DPSK data transmission through a silicon microring switch,” IEEE Photon. Technol. Lett. 24(6), 473–475 (2012).
[Crossref]

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-20-15915 .
[Crossref] [PubMed]

A. Shacham, K. Bergman, and L. P. Carloni, “On the design of a photonic network-on-chip,” in Pro. Int. Symp. Networks-on-chip (NOCS), Princeton, NJ (2007).
[Crossref]

Bi, H.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[Crossref]

Biberman, A.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-20-15915 .
[Crossref] [PubMed]

Bogaerts, W.

Bowers, J. E.

Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product,” Nat. Photonics 3(1), 59–63 (2009).
[Crossref]

Bradley, J. D.

Bramerie, L.

Brasch, V.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Buhl, L. L.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20, 6100108 (2014).

Byun, H.

Campbell, J. C.

Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product,” Nat. Photonics 3(1), 59–63 (2009).
[Crossref]

Carloni, L. P.

A. Shacham, K. Bergman, and L. P. Carloni, “On the design of a photonic network-on-chip,” in Pro. Int. Symp. Networks-on-chip (NOCS), Princeton, NJ (2007).
[Crossref]

Chan, J.

L. Xu, W. Zhang, Q. Li, J. Chan, H. L. R. Lira, M. Lipson, and K. Bergman, “40-Gb/s DPSK data transmission through a silicon microring switch,” IEEE Photon. Technol. Lett. 24(6), 473–475 (2012).
[Crossref]

Chandrasekhar, S.

Chen, H.-W.

Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product,” Nat. Photonics 3(1), 59–63 (2009).
[Crossref]

Chen, L.

Chen, R.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[Crossref]

Chen, X.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

Chen, Y. M.

Chen, Y.-K.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20, 6100108 (2014).

Cheng, Z. Z.

Choi, J.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[Crossref]

Chou, C.-Y.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

Chow, C.-W.

Costa e Silva, M.

Dadap, J. I.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

Dai, D.

Dalton, L. R.

Ding, Y.

Dong, P.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20, 6100108 (2014).

Driessen, A.

Elder, D.

Essiambre, R.

Fontaine, N. K.

Freude, W.

Gan, F.

Gay, M.

Geis, M.

Gnauck, A. H.

Green, W. M. J.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20(6), 398–400 (2008).
[Crossref]

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

Grein, M.

Hartinger, K.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

He, S.

Herr, T.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Hillerkuss, D.

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of the proposed silicon vertical slot waveguide. (a) Mode converter. (b) Cross-section of silicon vertical slot waveguide.
Fig. 2
Fig. 2 SEM images of (a) silicon photonic device (grating couplers, strip waveguides, slot waveguides, and strip-to-slot/slot-to-strip mode converters), (b)(c) apodized grating coupler, (d)(e) mode converter between strip waveguide and slot waveguide, (f)(g) bending region, and (h)(i) slot region.
Fig. 3
Fig. 3 Experimental setup for terabit-scale ultra-wide bandwidth WDM OFDM 16-QAM data transmission through silicon vertical slot waveguides.
Fig. 4
Fig. 4 Measured optical spectra of signals at the transmitter.
Fig. 5
Fig. 5 (a) Output spectrum of ultra-wide bandwidth 1.8-Tbit/s (161 WDM OFDM 16-QAM) signals after transmitting through the silicon vertical slot waveguide. (b) BER performance for all 161 WDM channels.
Fig. 6
Fig. 6 (a) Received RF spectrum of OFDM 16-QAM signal after demodulation; (b) Measured BER versus received OSNR for data transmission through a 2-mm silicon vertical slot waveguide at three typical wavelengths.
Fig. 7
Fig. 7 (a) BER versus received OSNR and (b) constellations for data transmission through 1-mm (slot 1), 2-mm (slot 2), 3.1-mm (slot 3), and 12.2-mm-long (slot 4) silicon vertical slot waveguides, respectively.

Equations (3)

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A eff = | ( e ν × h ν * ) z ^ dA | 2 | ( e ν × h ν * ) z ^ | 2 dA
γ ν = 2π λ n 2 ¯ A eff
n 2 ¯ =k ε 0 μ 0 n 2 (x,y) n 2 (x,y)(2 | e ν | 4 + | e ν 2 | 2 ) dA 3 | ( e ν × h ν * ) z ^ | 2 dA

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