Abstract

We experimentally demonstrate ultrahigh extinction ratio (>65 dB) amplitude modulators (AMs) that can be electrically tuned to operate across a broad spectral range of 160 nm from 1480 – 1640 nm and 95 nm from 1280 – 1375 nm. Our on-chip AMs employ one extra coupler compared with conventional Mach-Zehnder interferometers (MZI), thus form a cascaded MZI (CMZI) structure. Either directional or adiabatic couplers are used to compose the CMZI AMs and experimental comparisons are made between these two different structures. We investigate the performance of CMZI AMs under extreme conditions such as using 95:5 split ratio couplers and unbalanced waveguide losses. Electro-optic phase shifters are also integrated in the CMZI AMs for high-speed operation. Finally, we investigate the output optical phase when the amplitude is modulated, which provides us valuable information when both amplitude and phase are to be controlled. Our demonstration not only paves the road to applications such as quantum information processing that requires high extinction ratio AMs but also significantly alleviates the tight fabrication tolerance needed for large-scale integrated photonics.

© 2017 Optical Society of America

1. Introduction

Silicon integrated photonics has been advancing rapidly recently and promises next generation classical and quantum photonic devices [1–8]. Photonics using coherent photons with intrinsic high frequencies and low propagation losses in waveguides offers opportunities for data communication with ultralow energy consumption [9,10], broad bandwidth, and ultrahigh density [11,12] that are significantly superior to the electrical counterparts. Therefore, silicon photonics has been placed in an advantageous position to significantly reduce the power consumption and greatly enhance the transmission rate for short reach interconnect such as high-performance computing and data centers [13–15]. While tremendous progresses and broad applications have been realized using silicon integrated photonics, tight fabrication tolerance down to sub-10-nm is still significantly limiting the performances of integrated optical components and has become the bottleneck for mass production. For example, 50:50 beam couplers are widely used to provide power, polarization splitting or combining. However, due to the fabrication imperfection, often an exact 50:50 split ratio cannot be achieved at desired wavelengths. As one of the most important building blocks for integrated photonics, on-chip amplitude modulators (AMs) based on optical couplers are directly affected by fabrication variations. Due to the uncertainty in the thicknesses and widths of Si waveguides, the extinction ratios (ERs) of Mach-Zehnder interferometer (MZI) AMs are typically less than 30 dB [16,17] and the operating wavelengths can be tens of nanometers away from the design target. Moreover, the split ratio of a directional coupler [18] is sensitive to wavelength and therefore results in narrow bandwidth operation.

Much effort has been devoted to realizing high ER AMs [17,19–23] or effectively low crosstalk switches [24] over a wide spectral region, so multiple modulators can perform under a same wavelength using a single laser, despite the discrepancy caused by design or fabrication. Adiabatic couplers [25,26] and multimode interference (MMI) couplers [27] have been used for broadband operation. For example, Han Y. et al demonstrated compact and broadband AMs using grating waveguide adiabatic couplers; however, the highest ER of only 26 dB was achieved [16].

More recently, high extinction MZI AMs with ~50 dB [21] and ~60 dB [23] ERs were demonstrated. Nevertheless, neither high speed nor broadband operation was reported. Here, we experimentally demonstrate ~65 dB ultrahigh ER AMs that operates across a broad spectral region of 160 nm from 1480 – 1640 nm and over 95 nm from 1280 nm – 1375 nm in a single device. The operation bandwidth is only limited by the tuning range of our lasers. We also compare the high ER performance of two different AM designs that are composed of either adiabatic or directional couplers. Moreover, we show that our AMs can provide ultrahigh ERs even when employing extremely unbalanced couplers (95:5 split ratio). The insensitivity of our AMs to the fabrication imperfections and operating wavelengths enables design with high tolerance and guarantees high yield. Finally, we theoretically characterize optical phase output of our AMs when the amplitude is modulated. Accessing this information is important when both amplitude and phase need to be controlled. Our broadband AMs with record high ERs pave the road to broad integrated photonic applications including high data rate quantum communication [28], quantum sensing and quantum computing [29,30].

2. Cascaded Mach-Zehnder interferometer design for high ER AMs

Different from a conventional AM based on an MZI that is constructed by two 3-dB couplers and a phase-shifters, our cascaded MZI (CMZI) design employs one extra 3-dB coupler and extra phase shifters. Our CMZIs were fabricated on Sandia National Laboratories’ silicon photonic platform [2,26]. Figure 1(a) shows a microscope image of a fabricated CMZI AM comprising thermal-optical (TO) phase shifters, electro-optical (EO) phase shifters and three directional couplers. The EO phase shifters are integrated for high-speed operation. Figure 1(b) shows a different design that replaces the three directional couplers with three adiabatic couplers. The last adiabatic coupler is cut off from the image due to the limited space. Later, we will compare the performance of these two different AMs in experiment. Figure 1(c) shows a schematic of the CMZI AM for clearer illustration. Transverse-electric polarized laser light is coupled into the CMZI AM from the upper left input port and output from the right side, both using end-facet coupling technique. The optical electric fields (or powers) at different locations of the CMZI AM are noted as E1E6 (or P1P6), with a subscript of ‘b’ or ‘c’ added to note either the bar or cross waveguide, respectively. The combinations of 1—6 and b (or c) are also used to note the locations. For example, 6b indicates the bar output port. Though four TO and two EO phase shifters were integrated in our devices, Fig. 1(c) only shows the phase shifters on the upper branch without losing generality.

 figure: Fig. 1

Fig. 1 Two microscope images of CMZI AMs consisting of (a) directional or (b) adiabatic couplers. Due to the limited space, the third adiabatic coupler is not completely shown in (b). Each CMZI AM is composed of 3 couplers, 4 TO phase shifters and 2 EO phase shifters. (c) Schematic of a CMZI AM. Laser light is coupled into the CMZI AM from the upper left input port and output from the right side.

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To understand the working principle of a CMZI AM, we first briefly review the working mechanisms of a conventional AM, which can be treated by truncating the CMZI AM (Fig. 1(c)) right after the second coupler. Therefore, the optical electric field input from the upper left port is E1 and the output optical fields are E4b and E4c. To simplify the derivation, lossless light propagation is considered. Light is input from the upper left port with an optical field of E1. Considering the fabrication imperfection or intentionally different designs, split ratios for the two couplers are different with the bar and cross power split ratios of R1b and R1c for the first coupler and R2b and R2c for the second coupler, respectively. Neglecting the propagation loss,R1b+R1c=1 and R2b+R2c=1. Considering directional couplers are used, 90 degrees phase difference is introduced between the bar and cross ports,

E4b=E1R1bR2beiα+E1R1cR2ceiπ.
E4c=E1R1bR2cei(π2α)+E1R1cR2beiπ2.
where the propagation phase is not included and α is the extra phase introduced by TO1. To achieve high ERs for the bar output port (P4b), R1c=R2b and R1b=R2c need to be satisfied; and to achieve high ERs for cross output port (P4c), R1c=R2c andR1b=R2b need to be satisfied. In other words, high ERs from bar or cross output port only occur at stringent conditions when the two directional couplers are either identical or have complementary split ratios, respectively. These tight conditions are often difficult to achieve due to the high accuracy requirements in waveguide widths, gaps, and thicknesses. Therefore, often either targeting wavelengths or device performance are compromised when fabricated dimensions deviate from designs. Moreover, the only way to achieve high ERs for both output ports is to fabricate two identical couplers with exact 50:50 split ratios.

Therefore, we employ an additional coupler so the power distribution at 5b and 5c can be adjusted to match or compensate the split ratio of the 3rd coupler for high ER outputs from P6b or P6c, respectively. First, we investigate the optical output from a CMZI AM when all the three couplers have the same 60:40 split ratio. Figure 2(a) shows the calculated optical intensity at location 5b and 5c when the TO1 phase shifter is modulated between 0 and 2π. Since almost full coverage of amplitude modulation between 0 and 1 can be achieved at 5b and 5c, high ERs are expected at 6b and 6c. Indeed, Figs. 2(b) and 2(c) show optical output power contour images for both the bar and cross output ports when the TO phase shifters provide phase shift between 0 and 2π. >60 dB ultrahigh ERs at both the bar and cross output ports are observed. The upper limit of the calculated ERs constrained by the computational increment step size of the phase shifters. In reality, the experimental ERs will only be limited by the resolution and stability of electrical bias. Note that although directional couplers are used for the above calculations, similar conclusions can be drawn for CMZI AMs comprising adiabatic couplers.

 figure: Fig. 2

Fig. 2 (a) Normalized optical intensity at 5b and 5c when the TO1 phase shifter is biased to provide phase shift between 0 and 2π. Contour images of the optical power outputs from the (b) bar and (c) cross output ports of the CMZI AM showing high ERs.

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As we have shown that the ER of our CMZI AM relies on the couplers’ power split ratio which can be adjusted by varying the optical phase. Therefore, ultrahigh ERs for TM polarized light can be expected from our AM with similar designs. Although the TO phase shifters function similarly for both TE and TM polarized light, due to the integrated vertical p-n junction structure of our carrier depletion EO phase shifter, the TM polarized light experiences significant propagation loss. This propagation loss acts as a filter for TM light and helps the realization of ultrahigh ER for TE polarized light. Therefore, achieving ultrahigh ER for TM polarized light is feasible using a CMZI AM that comprises only TO phase shifters. For high speed operation of TM light, design modifications of the EO phase shifter are needed.

3. Experimental demonstration of high ER CMZI AMs across a wide spectral range

Next, we show experimental results on spectrally dependent ER of CMZI AMs. We end-facet coupled light from tunable fiber lasers into a CMZI circuit from the upper left port and measured the output power from either the bar or the cross output port. TE polarized light was used throughout this work. To demonstrate high ER performance across a wide spectral range, we measured optical output power as a function of the electrical power dissipated on TO1 and TO2 when the wavelength was tuned from 1480 to 1640 nm, the range of which is limited by our Santec TSL-710 laser. First, we measured an AM consisting of adiabatic couplers. The adiabatic couplers employ an asymmetric structure consisting of two 230 nm thick and 100 μm long waveguides with a 280 nm gap in the interaction region. One waveguide has a constant width of 280 nm while the other waveguide has width that is tapered from 320 to 280 nm. Therefore, the two waveguides are identical at the end of the interaction region. Two representative contour images of the optical output power are shown in Figs. 3(a) and 3(b) at 1540 and 1600 nm, respectively. Figure 3(c) plot a slice of data extracted from Fig. 3(a) showing that a highest ER of ~65 dB was observed as we swept the voltage applied on the TO2 while keeping the TO1 power constant. The measured ultrahigh ERs indicate high purity TE polarization of the transmitted light due to the strong suppression of TM polarized light by the long EO phase shifters. Figure 3(c) also shows that ER over 30 dB could be achieved within a power window ~3 mW dissipated on the TO2 phase shifter. Although the adiabatic couplers were designed to have a broadband 50:50 split ratio, due to the fabrication imperfection, our measurements on control samples showed that the split ratio deviated significantly away from 50:50 (from approximately 60:40 to 40:60). Despite this deviation, Fig. 3(d) shows that ultrahigh ERs were observed within a 160 nm bandwidth for both the bar and cross output ports. Note that the presented data only shows the lower limits of the ER of our CMZI AMs due to the limited sensitivity of the power meter (−80 dBm), as well as the resolution/stability of electric power supplies. Although different biasing voltages on the TO shifters are needed for different operating wavelengths, a self-optimization algorithm can be developed for auto-configuration [23].

 figure: Fig. 3

Fig. 3 Experimental demonstration of ultrahigh ER achieved between 1480 and 1640 nm. Output optical power contour images at (a) 1540 nm and (b) 1600 nm when voltage bias is swept across both the TO phase shifters. (c) An output optical power curve extracted from (a) by varying the TO2 bias while keeping the TO1 bias constant. (d) Measured ERs of a CMZI AM comprising adiabatic couplers covering the spectral regime of 1480-1640 nm. (e) Measured ERs of a CMZI AM comprising directional couplers covering the spectral regimes of 1280-1375 nm and 1480-1640 nm. (f) Experimentally measured (blue dots) and calculated (red curves) ERs of a CMZI AM when the laser is detuned away from the optimum wavelength.

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In comparison, we also measured the ER of a CMZI AM consisting of three directional couplers, whose split ratios are wavelength sensitive. The interaction region of the direction couplers consists of two identical straight waveguides that are 10 μm long, 230 nm thick, 350 nm wide with a gap width of 350 nm. To prove that our CMZI AM can achieve ultrahigh ER for a broader spectral range, we used another laser that is tunable between 1280 and 1375 nm. Figure 3(e) shows the ERs measured for both the bar and cross output ports with distinct behavior from the AM consisting of adiabatic couplers. Between 1480 and 1640 nm, the cross output port shows strongly wavelength dependent ERs ranging from ~1.8 to ~66 dB. In contrast, between 1280 and 1375 nm, the cross output port provides ultrahigh ERs while the bar output port exhibits low ERs. Nonetheless, ultrahigh ERs were observed from at least one of the two output ports across the whole tuning range of both lasers. Although we were not able to characterize the CMZI AM between 1375 and 1480 nm, it is expected that this device can achieve ultrahigh ERs over 360 nm bandwidth despite that different output ports need to be employed. As discussed above, the key of achieving a high ER for an output port is to obtain desired optical power distribution at location 5b and 5c to match the split ratio of the third coupler. Therefore, lower ERs will be measured when certain power distribution cannot be satisfied. This is why the two ports in Fig. 3(e) show distinct behaviors and details will be explored below.

Although demonstrating ultrahigh dynamic ER is of great interest, it is not feasible to measure the dynamic ER at high speeds because we had to use AC coupling since our high speed photodetectors with integral transimpedance amplifiers had a high DC output voltage of 3 V. The dynamic ER is ultimately limited by the optical bandwidth of our AMs. Therefore, we measured the ERs when the laser wavelength is detuned away from the optimum wavelength while maintaining the constant biasing voltages across the phase shifters. Figure 3(f) shows that over 50 dB or 40 dB ERs can be achieved across bandwidths of ~0.4 nm or ~2 nm, respectively, corresponding to ~50 GHz or 250 GHz bandwidths. Ideally, these large optical bandwidths allow high ERs at high data rates. However, practical limitations of providing exact voltage drive signals at high speed in the presence of impedance mismatches are likely to limit the ER to a lower value than the high DC ER values that we measured.

For comparison, we simulated the spectral dependent ER by considering the wavelength dependent coupling strength. The coupling strength directly controls the power split ratio of directional couplers and in turn modifies the ERs of CMZI AM. The coupling strength of two waveguides next to each other is calculated based on Ref [31]:

S2=δ2+κ2.
where κ is the coupling strength; 2δ=β2β1, where β1 and β2 are the propagation constants of uncoupled waveguide modes; and 2S=βevenβodd, where βeven and βodd are the propagation constant of even and odd supermodes, respectively. Since two identical waveguides are used to compose the directional coupler, so δ=0. To retrieve S, we simulated the wavelength dependent effective index for both the odd and even optical modes using Lumerical MODE solution. The ER is calculated based on Fig. 2 that the TO shifters introduce constant optical phases of which the highest ER is obtained. As the wavelength changes, the power split of directional couplers deviate away from 60:40, resulting in a degraded ER. The calculation also takes into account the fact that the phase introduced by the TO shifters is inversely proportional to the wavelengths since the optical path change is the same. Overall, the simulated ER agrees well with the experimentally results, especially at the lower ER region. The disagreement at the high ER region is likely contributed by the instability of electrical biasing source.

4. High ER performance of CMZI AMs under extreme conditions

Next we will investigate in details on why high ERs were not observed both for the cross output port between 1520 – 1620 nm and for the bar output port between 1280 – 1375 nm when the CMZI AM is composed of directional couplers. These studies will help us to understand the working mechanism of the CMZI AMs.

We calculate the ERs of CMZI AMs consisting of three identical couplers. Since Fig. 1 already shows the results of 60:40 split ratio couplers, we will discuss more unbalanced couplers of 74:26, 75:25, 95:5, and 5:95 split ratios. Figure 4(a), 4(d), 4(g) and 4(j) show optical intensity at the locations of 5b and 5c when the TO1 phase shifter is modulated between 0 and 2π. As the couplers become more unbalanced, the coverages of the optical power at both locations are reduced. As emphasized that high ERs at the cross or bar output ports can only be achieved if the power split at 5b and 5c matches (P5bP5c=R3bR3c) or is complementary (P5bP5c=R3cR3b) to the split ratio of the third coupler, respectively. Figure 4(a) shows that when the couplers have a split ratio of 74:26, the optical powers at 5b and 5c can be tuned between 0.23−1 and 0−0.77, respectively. Therefore, high ERs can still be achieved at both the cross and bar output ports with two satisfied conditions shown in Fig. 4(b) and 4(c). In contrast, Fig. 4(d) shows that, when the split ratio is 75:25, optical power coverages at 5b and 5c are 1−0.25 and 0−0.75, respectively. Due to this smaller coverage, Fig. 5(e) shows that high ER at the bar output port can only be achieved at one condition (the black dots in Fig. 5(d)) when the power split at 5b and 5c are 0.25 and 0.75, respectively. If the couplers deviate further from the balanced condition, high ERs can no longer be achieved for the bar output port. Indeed, Fig. 4(h) shows that, when the couplers’ split ratio is 95:5, only 2 dB ER was observed for the bar output port. On the contrary, Fig. 4(f) and 4(i) show that ultrahigh ERs can still be measured from the cross output port. This is because the power split ratios at 5b and 5c can match the split ratio of the 3rd coupler. For a similar reason, Fig. 4(j)− and 4(l) show that high ERs is only observed for the bar output port when the couplers have power split ratios of 5:95. With the theoretical support, we now understand that the low ERs measured from the cross and bar output port shown in Fig. 3(d) is caused by the extremely unbalanced coupler as Fig. 4(l) and 4(i) show, respectively.

 figure: Fig. 4

Fig. 4 Simulated optical output power from both the bar and cross output ports when the directional coupler’s split ratios are 74:26, 75:25, 95:5 and 5:95. (a), (d), (g) and (j) Optical power distribution achieved at the locations of 5b and 5c when the TO1 phase shifter is tuned between 0 and 2π. (b), (e), (h) and (k) Optical output power from the bar output port of 6b when the TO phase shifters are tuned between 0 and 2π. (c), (f), (i) and (l) Optical output power from the cross output port of 6c when the TO phase shifters are tuned between 0 and 2π. The black dots and circles in (d) show the conditions when the ultrahigh ERs are observed for bar and cross output ports, respectively.

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 figure: Fig. 5

Fig. 5 2D contour images of simulated results of the optical output powers from the (a) bar and (b) cross ports when the three directional couplers have different split ratios of 30:70, 60:40 and 85:15. Different light propagation losses of −0.5 dB, −0.35 dB, −0.17 dB and −0.65 dB are also incorporated in the calculation to simulate the fabrication imperfection at different waveguide sections.

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Next, we show that high ERs can be achieved even when a CMZI AM comprises three randomly designed couplers each with drastically different split ratios. Figure 5(a) and 5(b) show the output power from the bar and cross output ports when the split ratios of the directional couplers are 30:70, 60:40 and 85:15. Moreover, we intentional added different propagation losses for different sections of the waveguides to simulation the optical losses introduced by the material absorption, sidewall roughness, bending, etc. The losses at different sections are −0.5 dB (from input to 3b), −0.35 dB (from input to 3c), −0.17 dB (from 3b to 5b) and −0.65 dB (from 3c to 5c). Despite of these unbalanced conditions, ultrahigh ERs are still observed from both the bar and cross output ports. Therefore, our results indicate that 1) fabrication robustness to fabrication variation, 2) the guaranteed high ERs from our CMZI AMs over a broad spectral range.

5. High speed modulation

TO phase shifters typically have slow response time of ~10 µs [21] which limits the modulation frequency to dozens of kHz. Therefore, as Fig. 1 shows, we incorporate EO phase modulators in our CMZI AMs for high speed operation. We carried out an eye-diagram measurement by applying a non-return-to-zero (NRZ) signal on EO1. We measured the optical power from the cross output port using a high speed photodiode, which was connected to an oscilloscope triggered by the clock of the NRZ signal. Figure 6 shows eye-diagrams of a CMZI AM modulated at 1, 5, and 10 Gb/s data-rate. Measurements at higher speed were not performed due to the fact that traveling wave modulator design was not implemented in our devices. Although high ER (>30 dB) measurements are not possible due to the limitation of instruments, clear eye-diagrams indicate ultrahigh ER at high speed is possible. Note that, as shown in Fig. 3(f), the ultrahigh speed operation will eventually limit the ER of our AMs, or to achieve high ER, operation speed may need to be compromised. If it were possible to achieve high accuracy voltage drive, then Fig. 3(f) indicates that for a 10 GHz (~0.08 nm) offset from the carrier frequency, the modulation depth is greater than 50 dB. This serves as a rough bound for the extinction ratio achievable at high bit rates.

 figure: Fig. 6

Fig. 6 Eye-diagrams of high speed amplitude modulation of CMZI AM at 1, 5, and 10 Gb/s.

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6. Phase response of the CMZI AMs

While we have emphasized on the amplitude modulation of our CMZI AMs, it is also highly interesting to explore the phase response since many applications require both amplitude and phase control, such as continuous variable quantum key distribution [28]. The study of the coupling between amplitude and phase modulators is critical for accurate control. Here we show theoretically that the output optical phase is indeed modulated as we change the amplitude. Figure 7(a) shows a 2D contour plot of the cross port output optical phase as a function of the TO1 and TO2 phase shifters when all three couplers have splitting ratio of 60:40 (the same CMZI AM design as shown in Fig. 1). The output phase changes gradually at most locations in the 2D image, with abrupt phase changes around the two points where the highest ERs are achieved. To look into the output phase behavior around these particular conditions, Fig. 7(b) shows the output phase (unwrapped) along the white and black dashed lines that cross one of the two high ER points. Note that the two lines also mimic how the CMZI AMs will be used in reality that high ERs are achieved by sweeping the voltage across only one phase shifter (either TO1 or TO2) while applying a constant voltage to the other phase shifter. The output phases jump abruptly with an amplitude of π when the ultrahigh ER is achieved. Therefore, due to this intrinsic coupling of phase and amplitude modulations, care must be taken for applications requiring the control of both quantities. While only the simulated results are provided here, we will verify this phase behavior using self-referenced homodyne detection technique [28] and present experimental results in future publications.

 figure: Fig. 7

Fig. 7 (a) 2D contour images of simulated output optical phase when TO1 and TO2 phase shifters are modulated. The white and black dashed lines cross one of the two conditions that ultrahigh ER is achieved. (b) Output optical phase curves along the white or black dashed line shown in (a).

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7. Conclusions

In conclusion, we experimental demonstrated ultrahigh ERs over a broad spectral range using CMZI AMs consisting of either directional or adiabatic couplers. The highest measured ER of ~66 dB is not limited by our device but by other factors such as power meter sensitivity and the stability and resolution of power supply. Moreover, we demonstrated that ultrahigh ERs can be achieved from at least one output port (bar or cross) regardless the splitting ratios of the couplers. We also demonstrated high speed AM modulation using the integrated EO phase shifters, which potentially enables ultrahigh ER AMs with Gb/s data rate. Finally, we showed that the output optical phase is modulated strongly especially when the ultrahigh ERs are achieved. We envision that our demonstration significantly relaxes the fabrication tolerance, increases the compatibilities between different devices, and paves the road to high performance classical and quantum optical devices using integrated photonics.

Funding

U.S. Department of Energy National Nuclear Security Administration contract DE-NA0003525.

Acknowledgments

We acknowledge the technical assistance from Lilian Casias, Mottaleb Hossain and Changyi Li at the early stage of this work. Parts of this work were supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering and performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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18. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005). [CrossRef]  

19. D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]  

20. T. Goh, A. Himeno, M. Okuno, H. Takahashi, and K. Hattori, “High-extinction ratio and low-loss silica-based 8×8 strictly nonblocking thermooptic matrix switch,” J. Lightwave Technol. 17(7), 1192–1199 (1999). [CrossRef]  

21. K. Suzuki, G. Cong, K. Tanizawa, S.-H. Kim, K. Ikeda, S. Namiki, and H. Kawashima, “Ultra-high-extinction-ratio 2 × 2 silicon optical switch with variable splitter,” Opt. Express 23(7), 9086–9092 (2015). [CrossRef]   [PubMed]  

22. K. Suzuki, K. Tanizawa, T. Matsukawa, G. Cong, S.-H. Kim, S. Suda, M. Ohno, T. Chiba, H. Tadokoro, M. Yanagihara, Y. Igarashi, M. Masahara, S. Namiki, and H. Kawashima, “Ultra-compact 8 × 8 strictly-non-blocking Si-wire PILOSS switch,” Opt. Express 22(4), 3887–3894 (2014). [CrossRef]   [PubMed]  

23. C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach-Zehnder interferometer,” Opt. Lett. 41(22), 5318–5321 (2016). [CrossRef]   [PubMed]  

24. Y. Shoji, K. Kintaka, S. Suda, H. Kawashima, T. Hasama, and H. Ishikawa, “Low-crosstalk 2 x 2 thermo-optic switch with silicon wire waveguides,” Opt. Express 18(9), 9071–9075 (2010). [CrossRef]   [PubMed]  

25. Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photon. Res. 2(3), A41–A44 (2014). [CrossRef]  

26. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010). [CrossRef]  

27. K. Hamamoto and H. Jiang, “Active MMI devices: concept, proof, and recent progress,” J. Phys. D Appl. Phys. 48(38), 383001 (2015). [CrossRef]  

28. D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015). [CrossRef]  

29. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001). [CrossRef]   [PubMed]  

30. D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95(1), 010501 (2005). [CrossRef]   [PubMed]  

31. X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett. 34(3), 280–282 (2009). [CrossRef]   [PubMed]  

References

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  12. P. Pepeljugoski, J. Kash, F. Doany, D. Kuchta, L. Schares, C. Schow, M. Taubenblatt, B. J. Offrein, and A. Benner, “Low power and high density optical interconnects for future supercomputers,” in Optical Fiber Communication Conference, 2010 OSA Technical Digest (Optical Society of America, 2010), paper OThX2.
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  16. H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, and N. A. F. Jaeger, “Broadband 2 × 2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides,” Opt. Lett. 41(13), 3041–3044 (2016).
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  19. D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
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  20. T. Goh, A. Himeno, M. Okuno, H. Takahashi, and K. Hattori, “High-extinction ratio and low-loss silica-based 8×8 strictly nonblocking thermooptic matrix switch,” J. Lightwave Technol. 17(7), 1192–1199 (1999).
    [Crossref]
  21. K. Suzuki, G. Cong, K. Tanizawa, S.-H. Kim, K. Ikeda, S. Namiki, and H. Kawashima, “Ultra-high-extinction-ratio 2 × 2 silicon optical switch with variable splitter,” Opt. Express 23(7), 9086–9092 (2015).
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  22. K. Suzuki, K. Tanizawa, T. Matsukawa, G. Cong, S.-H. Kim, S. Suda, M. Ohno, T. Chiba, H. Tadokoro, M. Yanagihara, Y. Igarashi, M. Masahara, S. Namiki, and H. Kawashima, “Ultra-compact 8 × 8 strictly-non-blocking Si-wire PILOSS switch,” Opt. Express 22(4), 3887–3894 (2014).
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  23. C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach-Zehnder interferometer,” Opt. Lett. 41(22), 5318–5321 (2016).
    [Crossref] [PubMed]
  24. Y. Shoji, K. Kintaka, S. Suda, H. Kawashima, T. Hasama, and H. Ishikawa, “Low-crosstalk 2 x 2 thermo-optic switch with silicon wire waveguides,” Opt. Express 18(9), 9071–9075 (2010).
    [Crossref] [PubMed]
  25. Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photon. Res. 2(3), A41–A44 (2014).
    [Crossref]
  26. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
    [Crossref]
  27. K. Hamamoto and H. Jiang, “Active MMI devices: concept, proof, and recent progress,” J. Phys. D Appl. Phys. 48(38), 383001 (2015).
    [Crossref]
  28. D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
    [Crossref]
  29. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001).
    [Crossref] [PubMed]
  30. D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95(1), 010501 (2005).
    [Crossref] [PubMed]
  31. X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett. 34(3), 280–282 (2009).
    [Crossref] [PubMed]

2016 (4)

2015 (4)

K. Suzuki, G. Cong, K. Tanizawa, S.-H. Kim, K. Ikeda, S. Namiki, and H. Kawashima, “Ultra-high-extinction-ratio 2 × 2 silicon optical switch with variable splitter,” Opt. Express 23(7), 9086–9092 (2015).
[Crossref] [PubMed]

C. Doerr, “Silicon photonic integration in telecommunications,” Front. Phys. 3, 37 (2015).
[Crossref]

K. Hamamoto and H. Jiang, “Active MMI devices: concept, proof, and recent progress,” J. Phys. D Appl. Phys. 48(38), 383001 (2015).
[Crossref]

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

2014 (2)

2013 (2)

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

J. R. Ong and S. Mookherjea, “Quantum light generation on a silicon chip using waveguides and resonators,” Opt. Express 21(4), 5171–5181 (2013).
[Crossref] [PubMed]

2010 (4)

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-Performance Modulators and Switches for Silicon Photonic Networks-on-Chip,” IEEE J. Sel. Top. Quantum Electron. 16(1), 6–22 (2010).
[Crossref]

Y. Shoji, K. Kintaka, S. Suda, H. Kawashima, T. Hasama, and H. Ishikawa, “Low-crosstalk 2 x 2 thermo-optic switch with silicon wire waveguides,” Opt. Express 18(9), 9071–9075 (2010).
[Crossref] [PubMed]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

2009 (2)

X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett. 34(3), 280–282 (2009).
[Crossref] [PubMed]

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

2006 (2)

B. Jalali and S. Fathpour, “Silicon Photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[Crossref]

R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

2005 (2)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95(1), 010501 (2005).
[Crossref] [PubMed]

2001 (1)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001).
[Crossref] [PubMed]

1999 (1)

Arakawa, Y.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Bergman, K.

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-Performance Modulators and Switches for Silicon Photonic Networks-on-Chip,” IEEE J. Sel. Top. Quantum Electron. 16(1), 6–22 (2010).
[Crossref]

Biberman, A.

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-Performance Modulators and Switches for Silicon Photonic Networks-on-Chip,” IEEE J. Sel. Top. Quantum Electron. 16(1), 6–22 (2010).
[Crossref]

Boeuf, F.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Bowers, J. E.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Briegel, H. J.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001).
[Crossref] [PubMed]

Brif, C.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Browne, D. E.

D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95(1), 010501 (2005).
[Crossref] [PubMed]

Camacho, R. M.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Cassan, E.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Chan, J.

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-Performance Modulators and Switches for Silicon Photonic Networks-on-Chip,” IEEE J. Sel. Top. Quantum Electron. 16(1), 6–22 (2010).
[Crossref]

Chen, A.

G. Denoyer, A. Chen, B. Park, Y. Zhou, A. Santipo, and R. Russo, “Hybrid silicon photonic circuits and transceiver for 56Gb/s NRZ 2.2km transmission over single mode fiber,” in 2014 The European Conference on Optical Communication (ECOC), 2014, pp. 1–3.
[Crossref]

Chiba, T.

Chrostowski, L.

Chu, T.

Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photon. Res. 2(3), A41–A44 (2014).
[Crossref]

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Coles, P. J.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Cong, G.

Crozat, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Denoyer, G.

G. Denoyer, A. Chen, B. Park, Y. Zhou, A. Santipo, and R. Russo, “Hybrid silicon photonic circuits and transceiver for 56Gb/s NRZ 2.2km transmission over single mode fiber,” in 2014 The European Conference on Optical Communication (ECOC), 2014, pp. 1–3.
[Crossref]

Doerr, C.

C. Doerr, “Silicon photonic integration in telecommunications,” Front. Phys. 3, 37 (2015).
[Crossref]

Fathpour, S.

Fedeli, J. M.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Fédéli, J.-M.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Fu, Y.

Fujita, T.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Goh, T.

Halbwax, M.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Hamamoto, K.

K. Hamamoto and H. Jiang, “Active MMI devices: concept, proof, and recent progress,” J. Phys. D Appl. Phys. 48(38), 383001 (2015).
[Crossref]

Hartmann, J.-M.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Hasama, T.

Hattori, K.

Himeno, A.

Igarashi, Y.

Ikeda, K.

Ishida, S.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Ishikawa, H.

Jaeger, N. A. F.

Jalali, B.

Jiang, H.

K. Hamamoto and H. Jiang, “Active MMI devices: concept, proof, and recent progress,” J. Phys. D Appl. Phys. 48(38), 383001 (2015).
[Crossref]

Kawashima, H.

Kim, S.-H.

Kintaka, K.

Komljenovic, T.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Laval, S.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Le Roux, X.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Lee, B. G.

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-Performance Modulators and Switches for Silicon Photonic Networks-on-Chip,” IEEE J. Sel. Top. Quantum Electron. 16(1), 6–22 (2010).
[Crossref]

Lentine, A. L.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

Lin, S.

Liu, H.-C.

Lo, H.-K.

Lu, Z.

Lupu, A.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Lütkenhaus, N.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Lyan, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Ma, C.

Maine, S.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Marris-Morini, D.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Marshall, G. D.

Masahara, M.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Mashanovich, G. Z.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Matsukawa, T.

Mikkelsen, J. C.

Miller, D. A. B.

Mookherjea, S.

Nakamura, T.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

Namiki, S.

Nedeljkovic, M.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

O’Brien, J. L.

O’Brien, P.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Ohno, M.

Okuno, M.

Ong, J. R.

Paesani, S.

Park, B.

G. Denoyer, A. Chen, B. Park, Y. Zhou, A. Santipo, and R. Russo, “Hybrid silicon photonic circuits and transceiver for 56Gb/s NRZ 2.2km transmission over single mode fiber,” in 2014 The European Conference on Optical Communication (ECOC), 2014, pp. 1–3.
[Crossref]

Poon, J. K. S.

Qiang, X.

Rasigade, G.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Raussendorf, R.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001).
[Crossref] [PubMed]

Reed, G. T.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Rivallin, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Rudolph, T.

D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95(1), 010501 (2005).
[Crossref] [PubMed]

Russo, R.

G. Denoyer, A. Chen, B. Park, Y. Zhou, A. Santipo, and R. Russo, “Hybrid silicon photonic circuits and transceiver for 56Gb/s NRZ 2.2km transmission over single mode fiber,” in 2014 The European Conference on Optical Communication (ECOC), 2014, pp. 1–3.
[Crossref]

Sacher, W. D.

Santagati, R.

Santipo, A.

G. Denoyer, A. Chen, B. Park, Y. Zhou, A. Santipo, and R. Russo, “Hybrid silicon photonic circuits and transceiver for 56Gb/s NRZ 2.2km transmission over single mode fiber,” in 2014 The European Conference on Optical Communication (ECOC), 2014, pp. 1–3.
[Crossref]

Sarovar, M.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Schmid, J. H.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Shoji, Y.

Soh, D. B. S.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Soref, R.

R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Suda, S.

Sun, X.

Suzuki, K.

Tadokoro, H.

Takahashi, H.

Tang, W.

Tang, Z.

Tanizawa, K.

Thiessen, T.

Thompson, M. G.

Thomson, D.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Trotter, D. C.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

Urayama, J.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Urino, Y.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

Virot, L.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Vivien, L.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

Wang, J.

Wang, Y.

Watts, M. R.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

Wilkes, C. M.

Xu, D.-X.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Xu, F.

Yamada, H.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Yanagihara, M.

Yang, Y.

Yariv, A.

Ye, T.

Young, R. W.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

Yun, H.

Zhang, F.

Zhou, X.

Zhou, Y.

G. Denoyer, A. Chen, B. Park, Y. Zhou, A. Santipo, and R. Russo, “Hybrid silicon photonic circuits and transceiver for 56Gb/s NRZ 2.2km transmission over single mode fiber,” in 2014 The European Conference on Optical Communication (ECOC), 2014, pp. 1–3.
[Crossref]

Zilkie, A.

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
[Crossref]

Zortman, W. A.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

Front. Phys. (1)

C. Doerr, “Silicon photonic integration in telecommunications,” Front. Phys. 3, 37 (2015).
[Crossref]

IEEE Commun. Mag. (1)

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-Performance Modulators and Switches for Silicon Photonic Networks-on-Chip,” IEEE J. Sel. Top. Quantum Electron. 16(1), 6–22 (2010).
[Crossref]

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-Voltage, Compact, Depletion-Mode, Silicon Mach-Zehnder Modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. (1)

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18(7), 073003 (2016).
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K. Hamamoto and H. Jiang, “Active MMI devices: concept, proof, and recent progress,” J. Phys. D Appl. Phys. 48(38), 383001 (2015).
[Crossref]

Nat. Photonics (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

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Opt. Lett. (3)

Optica (1)

Photon. Res. (1)

Phys. Rev. Lett. (2)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001).
[Crossref] [PubMed]

D. E. Browne and T. Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95(1), 010501 (2005).
[Crossref] [PubMed]

Phys. Rev. X (1)

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-Referenced Continuous-Variable Quantum Key Distribution Protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent Progress in High-Speed Silicon-Based Optical Modulators,” Proc. IEEE 97(7), 1199–1215 (2009).
[Crossref]

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P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based Quantum Key Distribution,” https://arxiv.org/abs/1509.00768 (2015).

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Figures (7)

Fig. 1
Fig. 1 Two microscope images of CMZI AMs consisting of (a) directional or (b) adiabatic couplers. Due to the limited space, the third adiabatic coupler is not completely shown in (b). Each CMZI AM is composed of 3 couplers, 4 TO phase shifters and 2 EO phase shifters. (c) Schematic of a CMZI AM. Laser light is coupled into the CMZI AM from the upper left input port and output from the right side.
Fig. 2
Fig. 2 (a) Normalized optical intensity at 5b and 5c when the TO1 phase shifter is biased to provide phase shift between 0 and 2π. Contour images of the optical power outputs from the (b) bar and (c) cross output ports of the CMZI AM showing high ERs.
Fig. 3
Fig. 3 Experimental demonstration of ultrahigh ER achieved between 1480 and 1640 nm. Output optical power contour images at (a) 1540 nm and (b) 1600 nm when voltage bias is swept across both the TO phase shifters. (c) An output optical power curve extracted from (a) by varying the TO2 bias while keeping the TO1 bias constant. (d) Measured ERs of a CMZI AM comprising adiabatic couplers covering the spectral regime of 1480-1640 nm. (e) Measured ERs of a CMZI AM comprising directional couplers covering the spectral regimes of 1280-1375 nm and 1480-1640 nm. (f) Experimentally measured (blue dots) and calculated (red curves) ERs of a CMZI AM when the laser is detuned away from the optimum wavelength.
Fig. 4
Fig. 4 Simulated optical output power from both the bar and cross output ports when the directional coupler’s split ratios are 74:26, 75:25, 95:5 and 5:95. (a), (d), (g) and (j) Optical power distribution achieved at the locations of 5b and 5c when the TO1 phase shifter is tuned between 0 and 2π. (b), (e), (h) and (k) Optical output power from the bar output port of 6b when the TO phase shifters are tuned between 0 and 2π. (c), (f), (i) and (l) Optical output power from the cross output port of 6c when the TO phase shifters are tuned between 0 and 2π. The black dots and circles in (d) show the conditions when the ultrahigh ERs are observed for bar and cross output ports, respectively.
Fig. 5
Fig. 5 2D contour images of simulated results of the optical output powers from the (a) bar and (b) cross ports when the three directional couplers have different split ratios of 30:70, 60:40 and 85:15. Different light propagation losses of −0.5 dB, −0.35 dB, −0.17 dB and −0.65 dB are also incorporated in the calculation to simulate the fabrication imperfection at different waveguide sections.
Fig. 6
Fig. 6 Eye-diagrams of high speed amplitude modulation of CMZI AM at 1, 5, and 10 Gb/s.
Fig. 7
Fig. 7 (a) 2D contour images of simulated output optical phase when TO1 and TO2 phase shifters are modulated. The white and black dashed lines cross one of the two conditions that ultrahigh ER is achieved. (b) Output optical phase curves along the white or black dashed line shown in (a).

Equations (3)

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E 4b = E 1 R 1b R 2b e iα + E 1 R 1c R 2c e iπ .
E 4c = E 1 R 1b R 2c e i( π 2 α ) + E 1 R 1c R 2b e i π 2 .
S 2 = δ 2 + κ 2 .

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