Abstract

Correlated photon pairs are a fundamental building block of quantum photonic systems. While pair sources have previously been integrated on silicon chips built using customized photonics manufacturing processes, these often take advantage of only a small fraction of the established techniques for microelectronics fabrication and have yet to be integrated in a process that also supports electronics. Here we report the first demonstration of quantum-correlated photon pair generation in a device fabricated in an unmodified advanced (sub-100-nm) complementary metal-oxide semiconductor (CMOS) process, alongside millions of working transistors. The microring resonator photon pair source is formed in the transistor layer structure, with the resonator core formed by the silicon layer typically used for the transistor body. With ultralow CW on-chip pump powers ranging from 4.8 to 400 μW, we demonstrate pair generation rates between 165 Hz and 332 kHz using >80% efficient WSi superconducting nanowire single-photon detectors. Coincidences-to-accidentals ratios consistently exceeding 40 were measured, with a maximum of 55. In the process of characterizing this source, we also accurately predict pair generation rates from the results of classical stimulated four-wave mixing measurements. This proof-of-principle device demonstrates the potential of commercial CMOS microelectronics as an advanced quantum photonics platform with the capability of large volumes and pristine process control, where state-of-the-art high-speed digital circuits could interact with quantum photonic circuits.

© 2015 Optical Society of America

1. INTRODUCTION

Quantum photonic systems often consist of relatively large bulk optical components and can significantly benefit from chip-scale integration [14], similar to the way that large-scale integration of transistors has revolutionized modern digital electronics. The microelectronics industry, dominated by complementary metal-oxide semiconductor (CMOS) technology, remains one of the most successful examples of large-scale integrated systems, benefiting from high-yield and cost-effective fabrication methods while supporting billions of components. Following the success of CMOS, there has been great interest in implementing scalable quantum photonic devices in “CMOS-compatible” platforms to benefit from proven and reliable fabrication techniques. These silicon photonics processes support high-performance classical devices such as filters [57], switches [8,9], and delay lines [1012], which are essential components of a reconfigurable quantum photonic system. At the heart of such a system must lie a source of photons with nonclassical correlations such as entanglement [13]. Quantum-correlated photon pair sources utilizing the relatively large Kerr nonlinearity of silicon (100 times that of fused silica) have been theoretically [1417] and experimentally investigated in silicon waveguides [1822], microresonators [2325], and coupled resonator optical waveguides [2628]. These devices utilize spontaneous four-wave mixing (SFWM), where two pump photons are parametrically converted into a signal and idler photon pair. Recently, time–energy [19,20,2831] and polarization entanglement [22,30] have both been shown between photon pairs generated in silicon sources. Systems have continued to scale to include on-chip interference between multiple integrated photon sources [32], demultiplexing of signal and idler photons [33,34], and multichip high-extinction pump rejection [35]. Many of these “CMOS-compatible” implementations have relied on electron-beam lithography fabrication techniques and often include custom-tailored silicon thicknesses that are typical in silicon photonics but are incompatible with advanced CMOS microelectronics, preventing monolithic integration of electronics and quantum photonics on a single chip. While utilization of CMOS materials and fabrication processes offers certain processing benefits, until now, monolithic integration of quantum photonic sources within a microelectronics platform has not been investigated.

Recently, monolithic integration of classical photonics in commercial CMOS processes has been pursued in the context of enabling energy-efficient optical interconnects between processors and memory [36], resulting in the demonstration of a chip-to-chip optical link [37]. The IBM 12SOI 45 nm CMOS process [38], utilized for the device in this paper, has proven to be a particularly well-suited platform for the integration of photonic devices alongside millions of transistors [39] and has enabled control of photonic components by on-chip digital electronics for an optical transmitter and receiver [40]. In addition, this CMOS node is at the core of the third-, fourth-, and fifth-highest performing supercomputers in the world [41]. High-performance classical photonic components such as 5 fJ/bit modulators [42], record tuning-efficiency filters [43], and highly efficient fiber-to-chip grating couplers [44] have also been demonstrated in this CMOS process. Furthermore, microelectronic circuits in the 45 nm SOI CMOS process used here have been shown to operate at cryogenic temperatures [45], potentially enabling additional integration with cryogenic quantum systems. In this paper, we demonstrate the first source of quantum-correlated photon pairs directly integrated in an unmodified advanced CMOS process.

2. DEVICE DESIGN

As a photon pair source we use a microring resonator [Fig. 1] fabricated in the crystalline silicon (c-Si) CMOS layer typically used for the body of a transistor [Fig. 2(a)]. The fabrication is performed within a CMOS foundry without any processing changes while maintaining compliance with the existing CMOS design rules. Upon delivery from the foundry, the silicon handle wafer is removed as a postprocessing step via a XeF2 etch, as described in [39], to provide confinement for the optical mode, since the buried oxide layer (<200nm) is not sufficiently thick to prevent optical leakage into the silicon substrate. This single postprocessing step has been shown to preserve integrated transistor performance characteristics to within 5% [39]. We note that the sub-100-nm-thick [46] c-Si guiding layer results in a significant portion of the optical mode extending into the SiN and SiO2 cladding, as shown in Fig. 2(b). This not only confines a small fraction of the modal power within the silicon core, the dominant Kerr medium, but also prevents the design of a resonator with zero group velocity dispersion. Four-wave mixing (FWM) is greatly enhanced by the presence of a large density of photonic states, which conserve energy and momentum. When a degenerate pump beam is tuned on resonance, adjacent resonances are intrinsically momentum matched, but dispersion results in a difference between adjacent free spectral ranges (FSRs) introducing an energy mismatch [47]. This effect of dispersion becomes negligible if the difference in FSRs, ΔνFSR, is significantly smaller than the linewidths of the resonances involved. Simulations of ΔνFSR are shown in Fig. 2(c) for a pump wavelength near 1550 nm for various ring widths and radii. A ring width of 1.08 μm and outer radius of 22 μm with a predicted difference in FSRs of 1.4 GHz are chosen in order to obtain a small mode volume while also supporting a suitably small ΔνFSR. A transmission spectrum [Fig. 3(a)] of the CMOS foundry-fabricated device shows a difference in FSRs of 1.8 GHz centered around a pump resonance near 1558 nm. The 0.4 GHz difference between measured and simulated values is likely due to uncertainty in refractive indices and fabricated dimensions. Fitting the passive resonance gives a total quality factor, Qtot, of 31,000, with an intrinsic quality factor of Qo=114,000 due to intrinsic losses such as linear absorption and roughness loss and an external quality factor of Qext=43,000 due to coupling to the waveguide bus. The total Q corresponds to a linewidth of 6.2 GHz, which is significantly greater than the measured 1.8 GHz difference in FSRs. The resonator is overcoupled to provide higher tolerance to dispersion while also providing a higher escape efficiency for generated photon pairs. We note that the absence of a single ring geometry with ΔνFSR=0 does not fundamentally limit the achievable FWM efficiency in this platform, since additional dispersion engineering methods involving coupling multiple resonators can completely compensate for dispersion [48], though at the expense of increased complexity. However, such complex schemes are especially suitable for electronic–photonic integrated circuits enabled by this platform, which can provide feedback control for complex photonic devices [49]. Therefore, it is an intrinsic optical quality factor determined by losses and lithographic line-edge-roughness-induced light scattering that is the fundamental limitation for the FWM efficiency in this process.

 

Fig. 1. Optical micrograph of the (a) top and (b) bottom of the CMOS chip with (c) zoom-in of the ring resonator pair source and grating couplers.

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Fig. 2. (a) Schematic of a typical transistor composed of a crystalline silicon (c-Si) body and a polysilicon gate, (b) cross section illustration of the microring resonator pair source showing how the sub-100-nm c-Si transistor body layer can be used to confine light after removal of the Si handle wafer. The fundamental resonator mode contours are superimposed in red to illustrate how the majority of the modal field extends into the cladding. (c) Simulated difference in FSR ΔνFSR at 1550 nm due to dispersion with the chosen design predicted to be a negligible 1.4 GHz.

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Fig. 3. (a) Passive wavelength sweep of the three interacting resonances showing a difference in FSRs of 1.8 GHz and an intrinsic quality factor of 114,000, (b) measured stimulated four-wave mixing efficiency with fit to Eq. (1). Horizontal (vertical) error bars correspond to uncertainty in input (output) coupling. Deviation from theory at higher pump powers is a result of parasitic nonlinear and thermal effects.

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3. STIMULATED FOUR-WAVE MIXING

In order to characterize the photon pair source, we first measure stimulated FWM where a seed laser is used in addition to the pump to stimulate the FWM process. The efficiency of classical FWM is commonly defined as the ratio of idler power in the output bus to seed power in the input bus. Measuring FWM with pump powers ranging from 21 to 2dBm results in efficiencies of 70 to 42dB, respectively, as shown in Fig. 3(b). The efficiencies with a pump power below 10dBm follow an expected quadratic dependence on pump power. At higher pump powers, parasistic nonlinearities such as two-photon absorption (TPA), free-carrier absorption (FCA), and self- and cross-phase modulation, in addition to thermal heating of the resonator due to linear absorption, result in a deviation from the quadratic trend. Assuming that the pump and seed lasers are both placed on resonance, in the limit of negligible nonlinear loss, the efficiency of the stimulated FWM is well described by [48,50,51]

ηstim=Pp2ω2βfwm2(2rextrtot2)32rext(2πΔνFSR)2+rtot2.
Here, ΔνFSR is the difference in adjacent FSRs due to dispersion, Pp is the pump power in the waveguide at optical angular frequency ω, and βfwm is a parameter containing the nonlinearity of silicon and is inversely proportional to the mode volume. The decay rates rtot (total energy amplitude decay rate due to all mechanisms) and rext (decay rate due to coupling to waveguide only) are related to the measured quality factors Qtot=ω/2rtot and Qext=ω/2rext. The decay rates in the resonator presented here are treated as equal for the pump, signal, and idler resonances. Fitting the measured efficiencies in the region of pump powers before parasitic nonlinearities are present (below 10dBm) to Eq. (1), we find βfwm=5.32×106J1. The βfwm parameter is related to the Kerr nonlinearity, denoted n2, of the silicon core by
βfwm=n2cnSi2Veff,
where c is the speed of light, nSi is the refractive index of silicon, and Veff=18.5μm3 is an effective mode volume [52] calculated using a numerical mode solver [53]. Here, the fitted βfwm corresponds to n2=3.96×1014cm2/W, well within the uncertainties of previously measured values for crystalline silicon [54,55].

4. PHOTON PAIR GENERATION

SFWM is tested by performing coincidence measurements between generated photon pairs. A schematic of the experimental setup is illustrated in Fig. 4. A continuous-wave (CW) telecom pump laser is passed through a series of two C-band (1530–1565 nm) separators and two 1nm wide telecom bandpass filters to remove laser spontaneous emission noise at the signal and idler wavelengths. The pump is subsequently coupled to the input waveguide via a grating coupler and tuned to the pump resonance near 1558 nm. The generated photon pairs are coupled from the output grating and then individually filtered by cascaded telecom filters with an estimated 180 dB total isolation from the pump. The signal and idler photons are sent to 81% and 87% efficient WSi superconducting nanowire single-photon detectors (SNSPDs) [56], respectively. While microring resonator sources of photon pairs generally generate a comb of signal–idler pairs [57], since FSRs multiple mode orders away from the pump resonance are often also phase matched, we use 5nm bandwidth telecom filters at the signal (1552nm) and idler (1564nm) wavelengths to ensure the measurement of pairs only at the FSRs immediately adjacent to the pump. A time interval analyzer records counts as a relative time delay between the two detectors.

 

Fig. 4. Simplified schematic of the pair generation measurement. The pump light is passed through two C-band (1530–1565 nm) separators and two telecom filters to eliminate noise from the laser. A fiber polarization controller (FPC) is used to optimize coupling efficiency. The signal and idler photons are then filtered individually and sent to high-efficiency superconducting nanowire single-photon detectors (SNSPDs). A time interval analyzer is then used to count coincidences. The pump power is monitored by a classical photodetector to ensure the pump light is on resonance.

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From here, the coincidence rate versus estimated pump power in the waveguide is measured, as shown in Fig. 5(a). Measurements at each pump power are performed with a sufficiently long integration time to accumulate the same number (approximately 200 counts) of coincidences at the zero-delay time bin. The integration times range from 2 s at the highest pump power to 1 h at the lowest pump power. The on-chip pair rate shown in Fig. 5(b) is estimated by subtracting out the losses (in decibels) of each mode from the measured coincidence rate [24]. Since both the signal and idler modes experience approximately 15 dB of loss after the detection efficiency and loss from the output waveguide to the detectors are taken into account, the measured coincidence rate (which relies on the joint probability of both photons of a pair being detected) will be 30dB lower than the on-chip pair rate. Measurements of grating coupler loss are performed immediately after each coincidence measurement in order to account for potential drift in the coupling to the waveguide. The uncertainty of individual grating coupler loss is visible in the error bars in Fig. 5, because only the combination of both input and output gratings, which we assume to be identical, can be directly measured.

 

Fig. 5. (a) Coincidence rate of photon pairs at the detectors with (b) the estimated on-chip rate after subtracting out losses to the detectors. The solid line is the rate expected based on the stimulated four-wave mixing measurements in Fig. 3(b).

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Pair generation rates were measured over 3 orders of magnitude with on-chip rates ranging from 165 Hz to 332 kHz. The rate of photon pairs in the output waveguide can be described by [58]

Icoinc=ηescPp2ω2βfwm2(2rextrtot2)24rext(2πΔνFSR)2+(2rtot)2,
where ηesc is the escape efficiency for photons generated in the ring defined as rext/rtot. The escape efficiency takes into account the photon pairs generated within the cavity where one of the photons is lost due to loss mechanisms such as sidewall roughness scattering and absorption. Use of the fitted βfwm from the classical FWM measurements to predict the pair generation rate provides excellent agreement with the measured data, as seen in Fig. 5(b). Similar to the case of classical measurements, at higher pump powers the pair rate experiences a deviation from theory due to parasitic nonlinear [25,59,60] and thermal effects.

Coincidence measurements also provide a coincidences-to-accidentals ratio (CAR), often used as a figure of merit characterizing the noise of a photon pair source. The coincidence peak has a finite width resulting from a combination of timing jitter of the detectors (105 and 130ps for the signal and idler, respectively) and the temporal width of the photon pairs determined by the linewidth of the resonator. Here, we perform a Gaussian fit to the coincidence peak and use the full width at half-maximum (FWHM) as the delay window [inset of Fig. 6(a)] for a comparison to previously demonstrated photon pair sources. The measured CARs are shown versus pump power in Fig. 6(a). CARs greater than 40 were consistently measured, with a maximum CAR of 55 at a pump power of 12.4dBm. The choice of FWHM as the timing window is somewhat arbitrary [25,61], though useful for comparison to other demonstrations in the literature. A larger coincidence window results in a larger pair rate but a lower CAR, while a smaller coincidence window results in a higher CAR at the expense of the pair rate. Since the measured coincidence rates in Fig. 5 include all true coincidences, we provide the corresponding CARs in Fig. 6(b), where the timing window is chosen to cover ±3 standard deviations (611ps) of the fitted Gaussian. We note that choosing the larger window results in about 50% lower CARs compared to using the FWHM. The SNSPDs display negligible intrinsic dark count rates (<1 count per second [56]) with device background count rates (measured with the pump laser off) for the signal and idler detectors of 400 and 980 counts per second, respectively, resulting from room-temperature thermal radiation reaching the detectors. The pump power dependence of the CAR displayed in Fig. 6 can be explained by categorizing the CAR into three regimes: (1) In the very low pump power regime, the CAR is dominated by noise sources that do not vary with laser power (i.e., device background count rates) and increased pump power will yield more coincidences with a negligible increase in accidentals. (2) In the optimal pump power regime for peak CAR, higher pump power results in increased coincidences but also increased accidentals from system background counts due to noise sources depending linearly on pump power such as leakage of pump light through the filters and spontaneous Raman emission generated in the device’s cladding. (3) In the higher pump power regime, multipair emission along with nonlinear loss due to TPA and FCA limit the CAR.

 

Fig. 6. Coincidences-to-accidentals ratio (CAR) for various pump powers where the coincidence peaks were fit to a Gaussian function (insets) and delay windows selected at (a) the full width at half-maximum and (b) ±3 standard deviations.

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5. DISCUSSION

Despite a device geometry limited by implementation in a 45 nm node CMOS microelectronics process, the pair source presented here demonstrated high generation rates up to 332 kHz and CARs exceeding 50. These pair rates and CARs are on the same order as many custom-fabricated Si sources [23,24,26,33,35]. CARs can be improved by increased rejection of background emission from the pump laser and by the use of a pulsed pump [61] or an on-chip modulator [42] to control pair generation time windows. While the CMOS process does not support a completely dispersionless single-ring design, we showed that the dispersion could be minimized, resulting in a mere 1.8 GHz difference in adjacent FSRs. Equations (1) and (3) can be used to quantify the effect of dispersion as a decrease in efficiency of 14.6% and 7.5% for stimulated and spontaneous FWM, respectively.

The relationship between stimulated and spontaneous FWM has been a subject of recent investigation [62,63], as it is useful to determine the effectiveness of predicting pair generation rates from classical FWM measurements. In fact, classical measurements have recently been demonstrated for fast and efficient characterization of entangled photon sources [64]. In the limit of no dispersion, Eqs. (1) and (3) give a simple formula relating pair generation rate to seeded FWM efficiency of

Icoinc=ηesc2(2rextrtot2)1ηstim.
Until recently [58], a complete description of SFWM in lossy microcavities was not available, leading to a significant discrepancy in measured pair rates and theoretical predictions [23]. Here we accurately predict the SFWM-based coincidence rates from classical FWM measurements of the CMOS-integrated microresonator. To our knowledge, this is the first demonstration of using classical FWM measurements of a microresonator to accurately predict the nonclassical correlations revealed by coincidence counting of photon pairs generated by SFWM. In addition, these results confirm the findings of [63], where classical FWM measurements were first used to predict the optical powers generated by parametric fluorescence from a microring resonator.

Pair generation rates near 165 Hz with on-chip pump powers as low as 4.8 μW were demonstrated, which is, to the best of our knowledge, the lowest pump power used to produce photon pairs in silicon. This was primarily enabled by the use of highly efficient SNSPDs for coincidence measurements of pairs generated in a Si microring source, despite the significant loss from the output grating coupler to the detectors. These losses can be greatly reduced in future implementations by integration with on-chip filters and highly efficient grating couplers, which have already been demonstrated in this process [44], potentially enabling heralded single-photon sources with high heralding efficiency, which is necessary to compete with parametric downconversion-based sources [65].

6. CONCLUSION

We have demonstrated the first source of quantum-correlated photons in an advanced microelectronics process, opening the door for the integration of quantum states of light with photonic circuits and high-speed digital electronics on a single chip. In addition, this is the first measurement, to our knowledge, of photon pairs from a silicon microresonator using highly efficient (>80%) single-photon detectors, allowing record low pump power pair generation. This work also provides an accurate prediction of pair generation rates of a microresonator photon pair source from classical FWM measurements. The results presented here are a proof-of-principle demonstration that quantum sources of light can be integrated within a standard CMOS platform. Combined with previously demonstrated classical components, the CMOS process may provide an attractive platform for quantum photonic circuits controlled by state-of-the-art electronics, even at cryogenic temperatures [45]. For example, previously demonstrated on-chip classical detectors [66] could monitor the power of a pump laser from the through port of a microresonator photon pair source like that demonstrated in this paper, while digital circuits could actively compensate for drift in the resonance frequency caused by environmental factors such as temperature fluctuations, thereby enabling a highly stable source of photon pairs. One can also imagine a reconfigurable feed-forward system [13,67] where detection of a heralding signal photon can be processed by digital logic on chip and subsequently route the corresponding idler photon for a specific operation. The results presented here extend beyond the simple integration of photonic circuits in “CMOS compatible” materials or widely used customized photonics processes by implementing a source directly in an unmodified commercial CMOS process.

Funding

Office of Naval Research (ONR) (N000141410259).

Acknowledgment

We would like to thank Gil Triginer Garcés, Scott Glancy, L. Krister Shalm, and Tim Bartley for helpful discussions related to this work.

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36. C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. Holzwarth, M. A. Popović, H. Li, H. Smith, J. Hoyt, F. Kärtner, R. Ram, V. Stojanović, and K. Asanovic, “Building manycore processor-to-DRAM networks with monolithic silicon photonics,” in 16th IEEE Symposium on High Performance Interconnects (IEEE, 2008), pp. 21–30.

37. C. Sun, M. Georgas, J. Orcutt, B. Moss, Y.-H. Chen, J. Shainline, M. Wade, K. Mehta, K. Nammari, E. Timurdogan, D. Miller, O. Tehar-Zahav, Z. Sternberg, J. Leu, J. Chong, R. Bafrali, G. Sandhu, M. Watts, R. Meade, M. Popović, R. Ram, and V. Stojanović, “A monolithically integrated chip-to-chip optical link in bulk CMOS,” IEEE J. Solid-State Circuits 50, 828–844 (2015).

38. S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS technology,” in IEEE International Electron Devices Meetings, Digest of Technical Papers (IEEE, 2007), pp. 255–258.

39. J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. M. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. A. Popović, R. J. Ram, and V. Sojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20, 12222–12232 (2012). [CrossRef]  

40. M. Georgas, B. R. Moss, C. Sun, J. Shainline, J. S. Orcutt, M. Wade, Y. H. Chen, K. Nammari, J. C. Leu, A. Srinivasan, R. J. Ram, M. A. Popović, and V. Stojanović, “A monolithically-integrated optical transmitter and receiver in a zero-change 45  nm SOI process,” in VLSI Circuits Symposium (IEEE, 2014), paper 247.

41. See http://www.top500.org for Pos. 1: Tianhe-2 (MilkyWay-2), Guangzhou, China; Pos. 2: Titan, Oak Ridge National Lab, DOE, USA; Pos. 3: Sequoia, DOE, USA; Pos. 4: K computer, RIKEN, Japan; and Pos. 5: Mira, DOE, USA, June 2015, Top500.

42. J. M. Shainline, J. S. Orcutt, M. T. Wade, K. Nammari, B. Moss, M. Georgas, C. Sun, R. J. Ram, V. Stojanović, and M. A. Popović, “Depletion-mode carrier-plasma optical modulator in zero-change advanced CMOS,” Opt. Lett. 38, 2657–2659 (2013). [CrossRef]  

43. M. T. Wade, J. M. Shainline, J. S. Orcutt, C. Sun, R. Kumar, B. Moss, M. Georgas, R. J. Ram, V. Stojanović, and M. A. Popović, “Energy-efficient active photonics in a zero-change, state-of-the-art CMOS process,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2E.7.

44. M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Stojanović, and M. A. Popović, “75% efficient wide bandwidth grating couplers in a 45  nm microelectronics CMOS process,” in 2015 IEEE Optical Interconnects Conference (OI) (IEEE, 2015), pp. 46–47.

45. I. V. Vernik, T. A. Ohki, M. B. Ketchen, and M. Bhushan, “Performance characterization of PD-SOI ring oscillators at cryogenic temperatures,” in 2010 IEEE International SOI Conference(IEEE, 2010).

46. Exact layer dimensions are available in the IBM 12SOI Process Design Kit under nondisclosure agreement [38].

47. C. M. Gentry, X. Zeng, and M. A. Popović, “A discrete, resonance, all-order dispersion engineering method for microcavity design for four-wave mixing,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2014), paper FTu5D.3.

48. C. M. Gentry, X. Zeng, and M. A. Popović, “Tunable coupled-mode dispersion compensation and its application to on-chip resonant four-wave mixing,” Opt. Lett. 39, 5689–5692 (2014). [CrossRef]  

49. C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.

50. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554–556 (2000). [CrossRef]  

51. X. Zeng, C. M. Gentry, and M. A. Popović, “Four-wave mixing in silicon coupled-cavity resonators with port-selective, orthogonal supermode excitation,” Opt. Lett. 40, 2120–2123 (2015). [CrossRef]  

52. X. Zeng and M. A. Popović, “Design of triply-resonant micro-optical parametric oscillators based on Kerr nonlinearity,” Opt. Express 22, 15837–15867 (2014). [CrossRef]  

53. M. A. Popović, “Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures,” in Proceedings of Integrated Photonics Research (Optical Society of America, 2003), paper ITuD4.

54. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003). [CrossRef]  

55. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007). [CrossRef]  

56. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013). [CrossRef]  

57. C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22, 6535–6546 (2014). [CrossRef]  

58. Z. Vernon and J. E. Sipe, “Spontaneous four-wave mixing in lossy microring resonators,” Phys. Rev. A 91, 053802 (2015). [CrossRef]  

59. C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

60. L. G. Helt, M. J. Steel, and J. E. Sipe, “Parasitic nonlinearities in photon pair generation via integrated spontaneous four-wave mixing: critical problem or distraction?” Appl. Phys. Lett. 102, 201106 (2013). [CrossRef]  

61. S. Dyer, B. Baek, and S. W. Nam, “High-brightness, low-noise, all-fiber photon pair source,” Opt. Express 17, 10290–10297 (2009). [CrossRef]  

62. L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? Comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29, 2199–2212 (2012). [CrossRef]  

63. S. Azzini, D. Grassani, M. Galli, L. C. Andreani, M. Sorel, M. J. Strain, L. G. Helt, J. E. Sipe, M. Liscidini, and D. Bajoni, “From classical four-wave mixing to parametric fluorescence in silicon microring resonators,” Opt. Lett. 37, 3807–3809 (2012). [CrossRef]  

64. L. A. Rozema, C. Wang, D. H. Mahler, A. Hayat, A. M. Steinberg, J. E. Sipe, and M. Liscidini, “Characterizing an entangled-photon source with classical detectors and measurements,” Optica 2, 430–433 (2015). [CrossRef]  

65. P. B. Dixon, D. Rosenberg, V. Stelmakh, M. E. Grein, R. S. Bennink, E. A. Dauler, A. J. Kerman, R. J. Molnar, and F. N. C. Wong, “Heralding efficiency and correlated-mode coupling of near-IR fiber-coupled photon pairs,” Phys. Rev. A 90, 043804 (2014). [CrossRef]  

66. L. Alloatti, S. A. Srinivasan, J. S. Orcutt, and R. J. Ram, “Waveguide-coupled detector in zero-change complementary metal-oxide-semiconductor,” Appl. Phys. Lett. 107, 041104 (2015). [CrossRef]  

67. R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007). [CrossRef]  

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  38. S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS technology,” in IEEE International Electron Devices Meetings, Digest of Technical Papers (IEEE, 2007), pp. 255–258.
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  41. See http://www.top500.org for Pos. 1: Tianhe-2 (MilkyWay-2), Guangzhou, China; Pos. 2: Titan, Oak Ridge National Lab, DOE, USA; Pos. 3: Sequoia, DOE, USA; Pos. 4: K computer, RIKEN, Japan; and Pos. 5: Mira, DOE, USA, June 2015, Top500.
  42. J. M. Shainline, J. S. Orcutt, M. T. Wade, K. Nammari, B. Moss, M. Georgas, C. Sun, R. J. Ram, V. Stojanović, and M. A. Popović, “Depletion-mode carrier-plasma optical modulator in zero-change advanced CMOS,” Opt. Lett. 38, 2657–2659 (2013).
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  43. M. T. Wade, J. M. Shainline, J. S. Orcutt, C. Sun, R. Kumar, B. Moss, M. Georgas, R. J. Ram, V. Stojanović, and M. A. Popović, “Energy-efficient active photonics in a zero-change, state-of-the-art CMOS process,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2E.7.
  44. M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Stojanović, and M. A. Popović, “75% efficient wide bandwidth grating couplers in a 45  nm microelectronics CMOS process,” in 2015 IEEE Optical Interconnects Conference (OI) (IEEE, 2015), pp. 46–47.
  45. I. V. Vernik, T. A. Ohki, M. B. Ketchen, and M. Bhushan, “Performance characterization of PD-SOI ring oscillators at cryogenic temperatures,” in 2010 IEEE International SOI Conference(IEEE, 2010).
  46. Exact layer dimensions are available in the IBM 12SOI Process Design Kit under nondisclosure agreement [38].
  47. C. M. Gentry, X. Zeng, and M. A. Popović, “A discrete, resonance, all-order dispersion engineering method for microcavity design for four-wave mixing,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2014), paper FTu5D.3.
  48. C. M. Gentry, X. Zeng, and M. A. Popović, “Tunable coupled-mode dispersion compensation and its application to on-chip resonant four-wave mixing,” Opt. Lett. 39, 5689–5692 (2014).
    [Crossref]
  49. C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.
  50. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554–556 (2000).
    [Crossref]
  51. X. Zeng, C. M. Gentry, and M. A. Popović, “Four-wave mixing in silicon coupled-cavity resonators with port-selective, orthogonal supermode excitation,” Opt. Lett. 40, 2120–2123 (2015).
    [Crossref]
  52. X. Zeng and M. A. Popović, “Design of triply-resonant micro-optical parametric oscillators based on Kerr nonlinearity,” Opt. Express 22, 15837–15867 (2014).
    [Crossref]
  53. M. A. Popović, “Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures,” in Proceedings of Integrated Photonics Research (Optical Society of America, 2003), paper ITuD4.
  54. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003).
    [Crossref]
  55. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
    [Crossref]
  56. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
    [Crossref]
  57. C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22, 6535–6546 (2014).
    [Crossref]
  58. Z. Vernon and J. E. Sipe, “Spontaneous four-wave mixing in lossy microring resonators,” Phys. Rev. A 91, 053802 (2015).
    [Crossref]
  59. C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).
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  64. L. A. Rozema, C. Wang, D. H. Mahler, A. Hayat, A. M. Steinberg, J. E. Sipe, and M. Liscidini, “Characterizing an entangled-photon source with classical detectors and measurements,” Optica 2, 430–433 (2015).
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2015 (8)

D. Grassani, S. Azzini, M. Liscidini, M. Galli, M. J. Strain, M. Sorel, J. E. Sipe, and D. Bajoni, “Micrometer-scale integrated silicon source of time-energy entangled photons,” Optica 2, 88–94 (2015).
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J. Suo, S. Dong, W. Zhang, Y. Huang, and J. Peng, “Generation of hyper-entanglement on polarization and energy-time based on a silicon micro-ring cavity,” Opt. Express 23, 3985–3995 (2015).
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R. Wakabayashi, M. Fujiwara, K.-I. Yoshino, Y. Nambu, M. Sasaki, and T. Aoki, “Time-bin entangled photon pair generation from Si micro-ring resonator,” Opt. Express 23, 1103–1113 (2015).
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C. Sun, M. Georgas, J. Orcutt, B. Moss, Y.-H. Chen, J. Shainline, M. Wade, K. Mehta, K. Nammari, E. Timurdogan, D. Miller, O. Tehar-Zahav, Z. Sternberg, J. Leu, J. Chong, R. Bafrali, G. Sandhu, M. Watts, R. Meade, M. Popović, R. Ram, and V. Stojanović, “A monolithically integrated chip-to-chip optical link in bulk CMOS,” IEEE J. Solid-State Circuits 50, 828–844 (2015).

X. Zeng, C. M. Gentry, and M. A. Popović, “Four-wave mixing in silicon coupled-cavity resonators with port-selective, orthogonal supermode excitation,” Opt. Lett. 40, 2120–2123 (2015).
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Z. Vernon and J. E. Sipe, “Spontaneous four-wave mixing in lossy microring resonators,” Phys. Rev. A 91, 053802 (2015).
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L. A. Rozema, C. Wang, D. H. Mahler, A. Hayat, A. M. Steinberg, J. E. Sipe, and M. Liscidini, “Characterizing an entangled-photon source with classical detectors and measurements,” Optica 2, 430–433 (2015).
[Crossref]

L. Alloatti, S. A. Srinivasan, J. S. Orcutt, and R. J. Ram, “Waveguide-coupled detector in zero-change complementary metal-oxide-semiconductor,” Appl. Phys. Lett. 107, 041104 (2015).
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2014 (6)

C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22, 6535–6546 (2014).
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P. B. Dixon, D. Rosenberg, V. Stelmakh, M. E. Grein, R. S. Bennink, E. A. Dauler, A. J. Kerman, R. J. Molnar, and F. N. C. Wong, “Heralding efficiency and correlated-mode coupling of near-IR fiber-coupled photon pairs,” Phys. Rev. A 90, 043804 (2014).
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X. Zeng and M. A. Popović, “Design of triply-resonant micro-optical parametric oscillators based on Kerr nonlinearity,” Opt. Express 22, 15837–15867 (2014).
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N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems,” Phys. Rev. X 4, 041047 (2014).

C. M. Gentry, X. Zeng, and M. A. Popović, “Tunable coupled-mode dispersion compensation and its application to on-chip resonant four-wave mixing,” Opt. Lett. 39, 5689–5692 (2014).
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H. Takesue, N. Matsuda, E. Kuramochi, and M. Notomi, “Entangled photons from on-chip slow light,” Sci. Rep. 4, 3913 (2014).

2013 (11)

N. Matsuda, H. Takesue, K. Shimizu, Y. Tokura, E. Kuramochi, and M. Notomi, “Slow light enhanced correlated photon pair generation in photonic-crystal coupled-resonator optical waveguides,” Opt. Express 21, 8596–8604 (2013).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. I. Izuka, M. Ezaki, R. Hadfield, G. D. Marshall, V. Z. Willer, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8, 104–108 (2013).
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R. Kumar, J. R. Ong, J. Recchio, K. Srinivasan, and S. Mookherjea, “Spectrally multiplexed and tunable-wavelength photon pairs at 1.55  μm from a silicon coupled-resonator optical waveguide,” Opt. Lett. 38, 2969–2971 (2013).
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M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, M. J. Steel, T. F. Krauss, A. S. Clark, and B. J. Eggleton, “Integrated spatial multiplexing of heralded single-photon sources,” Nat. Commun. 4, 2582 (2013).

E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbox, V. Zwiller, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, J. L. O’Brien, and M. G. Thompson, “Photon pair generation in silicon micro-ring resonator with reverse bias enhancement,” Opt. Express 21, 27826–27834 (2013).
[Crossref]

B. J. Metcalf, N. Thomas-Peters, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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J. R. Ong, R. Kumar, and S. Mookherjea, “Ultra-high-contrast and tunable-bandwidth filter using cascaded high-order silicon microring filters,” IEEE Photon. Technol. Lett. 25, 1543–1546 (2013).
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J. M. Shainline, J. S. Orcutt, M. T. Wade, K. Nammari, B. Moss, M. Georgas, C. Sun, R. J. Ram, V. Stojanović, and M. A. Popović, “Depletion-mode carrier-plasma optical modulator in zero-change advanced CMOS,” Opt. Lett. 38, 2657–2659 (2013).
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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

L. G. Helt, M. J. Steel, and J. E. Sipe, “Parasitic nonlinearities in photon pair generation via integrated spontaneous four-wave mixing: critical problem or distraction?” Appl. Phys. Lett. 102, 201106 (2013).
[Crossref]

2012 (9)

L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? Comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29, 2199–2212 (2012).
[Crossref]

S. Azzini, D. Grassani, M. Galli, L. C. Andreani, M. Sorel, M. J. Strain, L. G. Helt, J. E. Sipe, M. Liscidini, and D. Bajoni, “From classical four-wave mixing to parametric fluorescence in silicon microring resonators,” Opt. Lett. 37, 3807–3809 (2012).
[Crossref]

S. Tanzilli, A. Martin, F. Kaiser, M. P. De Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143 (2012).
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H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).

R. M. Camacho, “Entangled photon generation using four-wave mixing in azimuthally symmetric microresonators,” Opt. Express 20, 21977–21991 (2012).
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M. Davanço, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett. 100, 261104 (2012).
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S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, and D. Bajoni, “Ultra-low power generation of twin photons in a compact silicon ring resonator,” Opt. Express 20, 23100–23107 (2012).
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N. Matsuda, H. L. Jeannic, H. Fukuda, T. Tsuchizawa, W. J. Munro, K. Shimizu, K. Yamada, Y. Tokura, and H. Takesue, “A monolithically integrated polarization entangled photon pair source on a silicon chip,” Sci. Rep. 2, 817 (2012).

J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. M. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. A. Popović, R. J. Ram, and V. Sojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20, 12222–12232 (2012).
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2011 (4)

2010 (3)

L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, “Spontaneous four-wave mixing in microring resonators,” Opt. Lett. 35, 3006–3008 (2010).
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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, 6–22 (2010).
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A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. 2, 181–194 (2010).
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2009 (4)

J. L. O’Brien, A. Furusawa, and J. Vucković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
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A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
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S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558–16570 (2009).
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S. Dyer, B. Baek, and S. W. Nam, “High-brightness, low-noise, all-fiber photon pair source,” Opt. Express 17, 10290–10297 (2009).
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2008 (2)

K.-I. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S.-I. Itabasha, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368–20373 (2008).
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Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
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2007 (4)

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express 15, 11934–11941 (2007).
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H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-I. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
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A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
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2006 (2)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003).
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2000 (1)

Absil, P. P.

Agha, I.

M. Davanço, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett. 100, 261104 (2012).
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Agrawal, G. P.

Alibart, O.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143 (2012).
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Alloatti, L.

L. Alloatti, S. A. Srinivasan, J. S. Orcutt, and R. J. Ram, “Waveguide-coupled detector in zero-change complementary metal-oxide-semiconductor,” Appl. Phys. Lett. 107, 041104 (2015).
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C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.

Andreani, L. C.

Aoki, T.

Asanovic, K.

C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. Holzwarth, M. A. Popović, H. Li, H. Smith, J. Hoyt, F. Kärtner, R. Ram, V. Stojanović, and K. Asanovic, “Building manycore processor-to-DRAM networks with monolithic silicon photonics,” in 16th IEEE Symposium on High Performance Interconnects (IEEE, 2008), pp. 21–30.

Assefa, S.

M. Davanço, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett. 100, 261104 (2012).
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Atabaki, A.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.

M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Stojanović, and M. A. Popović, “75% efficient wide bandwidth grating couplers in a 45  nm microelectronics CMOS process,” in 2015 IEEE Optical Interconnects Conference (OI) (IEEE, 2015), pp. 46–47.

Azzini, S.

Baehr-Jones, T.

N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems,” Phys. Rev. X 4, 041047 (2014).

Baek, B.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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S. Dyer, B. Baek, and S. W. Nam, “High-brightness, low-noise, all-fiber photon pair source,” Opt. Express 17, 10290–10297 (2009).
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Baets, R. G.

Bafrali, R.

C. Sun, M. Georgas, J. Orcutt, B. Moss, Y.-H. Chen, J. Shainline, M. Wade, K. Mehta, K. Nammari, E. Timurdogan, D. Miller, O. Tehar-Zahav, Z. Sternberg, J. Leu, J. Chong, R. Bafrali, G. Sandhu, M. Watts, R. Meade, M. Popović, R. Ram, and V. Stojanović, “A monolithically integrated chip-to-chip optical link in bulk CMOS,” IEEE J. Solid-State Circuits 50, 828–844 (2015).

Baghban, M. A.

Bajoni, D.

Barbieri, M.

B. J. Metcalf, N. Thomas-Peters, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

Batten, C.

C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. Holzwarth, M. A. Popović, H. Li, H. Smith, J. Hoyt, F. Kärtner, R. Ram, V. Stojanović, and K. Asanovic, “Building manycore processor-to-DRAM networks with monolithic silicon photonics,” in 16th IEEE Symposium on High Performance Interconnects (IEEE, 2008), pp. 21–30.

Bennink, R. S.

P. B. Dixon, D. Rosenberg, V. Stelmakh, M. E. Grein, R. S. Bennink, E. A. Dauler, A. J. Kerman, R. J. Molnar, and F. N. C. Wong, “Heralding efficiency and correlated-mode coupling of near-IR fiber-coupled photon pairs,” Phys. Rev. A 90, 043804 (2014).
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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, 6–22 (2010).
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Bhushan, M.

I. V. Vernik, T. A. Ohki, M. B. Ketchen, and M. Bhushan, “Performance characterization of PD-SOI ring oscillators at cryogenic temperatures,” in 2010 IEEE International SOI Conference(IEEE, 2010).

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, 6–22 (2010).
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Bogaerts, W.

Böhi, P.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
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Bonneau, D.

E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbox, V. Zwiller, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, J. L. O’Brien, and M. G. Thompson, “Photon pair generation in silicon micro-ring resonator with reverse bias enhancement,” Opt. Express 21, 27826–27834 (2013).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. I. Izuka, M. Ezaki, R. Hadfield, G. D. Marshall, V. Z. Willer, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8, 104–108 (2013).
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Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
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Broome, M. A.

B. J. Metcalf, N. Thomas-Peters, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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Camacho, R. M.

Canciamilla, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. 2, 181–194 (2010).
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Caspani, L.

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, 6–22 (2010).
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Chen, J.

Chen, T.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).

Chen, Y. H.

M. Georgas, B. R. Moss, C. Sun, J. Shainline, J. S. Orcutt, M. Wade, Y. H. Chen, K. Nammari, J. C. Leu, A. Srinivasan, R. J. Ram, M. A. Popović, and V. Stojanović, “A monolithically-integrated optical transmitter and receiver in a zero-change 45  nm SOI process,” in VLSI Circuits Symposium (IEEE, 2014), paper 247.

Chen, Y.-H.

C. Sun, M. Georgas, J. Orcutt, B. Moss, Y.-H. Chen, J. Shainline, M. Wade, K. Mehta, K. Nammari, E. Timurdogan, D. Miller, O. Tehar-Zahav, Z. Sternberg, J. Leu, J. Chong, R. Bafrali, G. Sandhu, M. Watts, R. Meade, M. Popović, R. Ram, and V. Stojanović, “A monolithically integrated chip-to-chip optical link in bulk CMOS,” IEEE J. Solid-State Circuits 50, 828–844 (2015).

Cho, P. S.

Chong, J.

C. Sun, M. Georgas, J. Orcutt, B. Moss, Y.-H. Chen, J. Shainline, M. Wade, K. Mehta, K. Nammari, E. Timurdogan, D. Miller, O. Tehar-Zahav, Z. Sternberg, J. Leu, J. Chong, R. Bafrali, G. Sandhu, M. Watts, R. Meade, M. Popović, R. Ram, and V. Stojanović, “A monolithically integrated chip-to-chip optical link in bulk CMOS,” IEEE J. Solid-State Circuits 50, 828–844 (2015).

Chou, A.

S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS technology,” in IEEE International Electron Devices Meetings, Digest of Technical Papers (IEEE, 2007), pp. 255–258.

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Clark, A. S.

C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, M. J. Steel, T. F. Krauss, A. S. Clark, and B. J. Eggleton, “Integrated spatial multiplexing of heralded single-photon sources,” Nat. Commun. 4, 2582 (2013).

E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbox, V. Zwiller, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, J. L. O’Brien, and M. G. Thompson, “Photon pair generation in silicon micro-ring resonator with reverse bias enhancement,” Opt. Express 21, 27826–27834 (2013).
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C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, M. J. Steel, T. F. Krauss, A. S. Clark, and B. J. Eggleton, “Integrated spatial multiplexing of heralded single-photon sources,” Nat. Commun. 4, 2582 (2013).

Combrié, S.

C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

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M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

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P. B. Dixon, D. Rosenberg, V. Stelmakh, M. E. Grein, R. S. Bennink, E. A. Dauler, A. J. Kerman, R. J. Molnar, and F. N. C. Wong, “Heralding efficiency and correlated-mode coupling of near-IR fiber-coupled photon pairs,” Phys. Rev. A 90, 043804 (2014).
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C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, M. J. Steel, T. F. Krauss, A. S. Clark, and B. J. Eggleton, “Integrated spatial multiplexing of heralded single-photon sources,” Nat. Commun. 4, 2582 (2013).

C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, J. G. Rarity, and B. J. Eggleton, “Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide,” Opt. Lett. 36, 3413–3415 (2011).
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N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems,” Phys. Rev. X 4, 041047 (2014).

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E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbox, V. Zwiller, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, J. L. O’Brien, and M. G. Thompson, “Photon pair generation in silicon micro-ring resonator with reverse bias enhancement,” Opt. Express 21, 27826–27834 (2013).
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N. Matsuda, H. L. Jeannic, H. Fukuda, T. Tsuchizawa, W. J. Munro, K. Shimizu, K. Yamada, Y. Tokura, and H. Takesue, “A monolithically integrated polarization entangled photon pair source on a silicon chip,” Sci. Rep. 2, 817 (2012).

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Galli, M.

Gan, F.

M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

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M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Stojanović, and M. A. Popović, “75% efficient wide bandwidth grating couplers in a 45  nm microelectronics CMOS process,” in 2015 IEEE Optical Interconnects Conference (OI) (IEEE, 2015), pp. 46–47.

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J. M. Shainline, J. S. Orcutt, M. T. Wade, K. Nammari, B. Moss, M. Georgas, C. Sun, R. J. Ram, V. Stojanović, and M. A. Popović, “Depletion-mode carrier-plasma optical modulator in zero-change advanced CMOS,” Opt. Lett. 38, 2657–2659 (2013).
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M. T. Wade, J. M. Shainline, J. S. Orcutt, C. Sun, R. Kumar, B. Moss, M. Georgas, R. J. Ram, V. Stojanović, and M. A. Popović, “Energy-efficient active photonics in a zero-change, state-of-the-art CMOS process,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2E.7.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.

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C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. Holzwarth, M. A. Popović, H. Li, H. Smith, J. Hoyt, F. Kärtner, R. Ram, V. Stojanović, and K. Asanovic, “Building manycore processor-to-DRAM networks with monolithic silicon photonics,” in 16th IEEE Symposium on High Performance Interconnects (IEEE, 2008), pp. 21–30.

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M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

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B. J. Metcalf, N. Thomas-Peters, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

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H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-I. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. I. Izuka, M. Ezaki, R. Hadfield, G. D. Marshall, V. Z. Willer, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8, 104–108 (2013).
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N. Matsuda, H. L. Jeannic, H. Fukuda, T. Tsuchizawa, W. J. Munro, K. Shimizu, K. Yamada, Y. Tokura, and H. Takesue, “A monolithically integrated polarization entangled photon pair source on a silicon chip,” Sci. Rep. 2, 817 (2012).

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S. Tanzilli, A. Martin, F. Kaiser, M. P. De Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143 (2012).
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M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

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P. B. Dixon, D. Rosenberg, V. Stelmakh, M. E. Grein, R. S. Bennink, E. A. Dauler, A. J. Kerman, R. J. Molnar, and F. N. C. Wong, “Heralding efficiency and correlated-mode coupling of near-IR fiber-coupled photon pairs,” Phys. Rev. A 90, 043804 (2014).
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C. A. Husko, A. S. Clark, M. J. Collins, A. D. Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

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C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.

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M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Stojanović, and M. A. Popović, “75% efficient wide bandwidth grating couplers in a 45  nm microelectronics CMOS process,” in 2015 IEEE Optical Interconnects Conference (OI) (IEEE, 2015), pp. 46–47.

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C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, and M. A. Popović, “A 45  nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in 2015 Symposium on VLSI Circuits (IEEE, 2015), pp. C122–C123.

M. Georgas, B. R. Moss, C. Sun, J. Shainline, J. S. Orcutt, M. Wade, Y. H. Chen, K. Nammari, J. C. Leu, A. Srinivasan, R. J. Ram, M. A. Popović, and V. Stojanović, “A monolithically-integrated optical transmitter and receiver in a zero-change 45  nm SOI process,” in VLSI Circuits Symposium (IEEE, 2014), paper 247.

See http://www.top500.org for Pos. 1: Tianhe-2 (MilkyWay-2), Guangzhou, China; Pos. 2: Titan, Oak Ridge National Lab, DOE, USA; Pos. 3: Sequoia, DOE, USA; Pos. 4: K computer, RIKEN, Japan; and Pos. 5: Mira, DOE, USA, June 2015, Top500.

C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. Holzwarth, M. A. Popović, H. Li, H. Smith, J. Hoyt, F. Kärtner, R. Ram, V. Stojanović, and K. Asanovic, “Building manycore processor-to-DRAM networks with monolithic silicon photonics,” in 16th IEEE Symposium on High Performance Interconnects (IEEE, 2008), pp. 21–30.

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M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” in European Conference on Optical Communication (ECOC) (2007), paper 1.2.3.

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Figures (6)

Fig. 1.
Fig. 1. Optical micrograph of the (a) top and (b) bottom of the CMOS chip with (c) zoom-in of the ring resonator pair source and grating couplers.
Fig. 2.
Fig. 2. (a) Schematic of a typical transistor composed of a crystalline silicon (c-Si) body and a polysilicon gate, (b) cross section illustration of the microring resonator pair source showing how the sub-100-nm c-Si transistor body layer can be used to confine light after removal of the Si handle wafer. The fundamental resonator mode contours are superimposed in red to illustrate how the majority of the modal field extends into the cladding. (c) Simulated difference in FSR ΔνFSR at 1550 nm due to dispersion with the chosen design predicted to be a negligible 1.4 GHz.
Fig. 3.
Fig. 3. (a) Passive wavelength sweep of the three interacting resonances showing a difference in FSRs of 1.8 GHz and an intrinsic quality factor of 114,000, (b) measured stimulated four-wave mixing efficiency with fit to Eq. (1). Horizontal (vertical) error bars correspond to uncertainty in input (output) coupling. Deviation from theory at higher pump powers is a result of parasitic nonlinear and thermal effects.
Fig. 4.
Fig. 4. Simplified schematic of the pair generation measurement. The pump light is passed through two C-band (1530–1565 nm) separators and two telecom filters to eliminate noise from the laser. A fiber polarization controller (FPC) is used to optimize coupling efficiency. The signal and idler photons are then filtered individually and sent to high-efficiency superconducting nanowire single-photon detectors (SNSPDs). A time interval analyzer is then used to count coincidences. The pump power is monitored by a classical photodetector to ensure the pump light is on resonance.
Fig. 5.
Fig. 5. (a) Coincidence rate of photon pairs at the detectors with (b) the estimated on-chip rate after subtracting out losses to the detectors. The solid line is the rate expected based on the stimulated four-wave mixing measurements in Fig. 3(b).
Fig. 6.
Fig. 6. Coincidences-to-accidentals ratio (CAR) for various pump powers where the coincidence peaks were fit to a Gaussian function (insets) and delay windows selected at (a) the full width at half-maximum and (b) ±3 standard deviations.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ηstim=Pp2ω2βfwm2(2rextrtot2)32rext(2πΔνFSR)2+rtot2.
βfwm=n2cnSi2Veff,
Icoinc=ηescPp2ω2βfwm2(2rextrtot2)24rext(2πΔνFSR)2+(2rtot)2,
Icoinc=ηesc2(2rextrtot2)1ηstim.

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