Schematic view of a silicon transceiver chip, comprising a 

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... quantity Á represents the phase mismatch due to group velocity dispersion (GVD) between the signal wave at wavelength s and the converted wave at wavelength c . The quantity D 2 denotes the GVD parameter and p is the wavelength of the pump. Measuring two different samples with nominally identical geometry at two different signal wavelengths, we have obtained nonlinear parameters of 116 000, 107 000, 104 000, and 91 000 W À 1 km À 1 , leading to an average value of 104 000 W À 1 km À 1 [25]. 3) Phase-Matching Over Large Spectral Range: The dependence of the FWM efficiency as a function of wavelength offset between pump and probe signal has been tested as well; see Fig. 7. The group velocity dispersion parameter D 2 was found to be so small that phase-matching over a large 20 nm spectral range could be achieved. Measure- ments of the spectral efficiency were performed on a waveguide with height h 1⁄4 220 nm, width w 1⁄4 216 nm, slot width w slot 1⁄4 157 nm, and geometrical waveguide length L 1⁄4 4 mm. By fitting the measured dependence of as a function of the detuning Á to (7) and (8), the waveguide under test exhibited a group velocity dispersion parameter of D 2 1⁄4 À 6 : 84 fs = ð mm nm Þ and a nonlinearity parameter of 1⁄4 0 : 83 Â 10 5 W À 1 km À 1 . 4) Dynamics and Two-Photon Absorption: The SOH slot waveguide was tested for its phase response in a pump- probe experiment [47]. Fig. 8 shows the phase shift induced by a pump-probe measurement with 100 fs long pulses for various input powers at a wavelength of 1550 nm. The slot waveguide shows an instantaneous Kerr-type response, which has its origin predominantly in the cladding. There are no slow tails due to TPA in silicon with subsequent free- carrier absorption such as seen in nonlinear silicon strip waveguides [47]. The geometry of the slot waveguides in the TPA absorption experiment was identical to the one from the loss characterization. To proof the viability of the concept, all-optical demultiplexing of a 120 Gbit/s data signal to a 10 Gbit/s data stream has been performed. The experimental setup together with the eye diagrams are depicted in Fig. 9. For the data (pump), we used mode-locked fibre lasers operating at repetition rates of 10 GHz and emitting pulses of approxi- mately 3 ps full-width half-maximum. The signal and the pump were synchronized using a tunable optical delay. The 120 Gbit/s data were generated by modulating the 10 GHz pulse train with a pseudorandom bit sequence (2 31 À 1 bit) and by subsequent optical time-division multiplexing. Both the pump and the signal were amplified and coupled into a SOH slot waveguide of height h 1⁄4 220 nm, strip width w 1⁄4 212 nm, and slot width w slot 1⁄4 205 nm. The output signal was bandpass filtered at the converted wavelength and amplified, and the eye diagram was recorded with a digital communication analyzer. By varying the delay between the pump and the signal, different tributaries could be chosen for demultiplexing. Similar performance was found for all the tributaries. From the eye diagram, a quality factor of Q 2 1⁄4 11 : 1 dB was measured for an on-chip pump power of 15.6 dBm (36 mW). Since the power of the converted signal depends quadratically on the pump power, and since the 10 GHz pump exhibits noticeable amplitude fluctuations [see eye diagram (2) in Fig. 9], the Q-factor was mainly limited by the performance of the pump. More recently we have tested slot waveguides for their ability to demulitplex 170.8 to 42.7 Gbit/s [26] and for 40 Gbit/s all-optical wavelength conversion [48]. No pattern dependence or any other speed limitations were observed. In this section, we discuss the potential of the SOH platform for the fabrication of optical modulators with drive voltages around 1 V and bandwidths exceeding 100 Gbit/s [28]. Electrooptic modulators typically are implemented as Mach–Zehnder interferometers (MZIs); see Fig. 1, where both arms of the MZI comprise phase modulator sections. Three phase modulator structures compatible with the SOH approach are depicted in Fig. 10. The phase shifters consist of silicon waveguides (Si) surrounded by a poled electrooptic organic material (EO). The optical strip waveguides are operated in quasi-TE mode. In the traveling-wave strip waveguide scheme of Fig. 10(a), the microwave field is applied via two aluminum conductors running in parallel to the optical strip waveguide. The spacing between the conductors and the optical waveguide is chosen large enough (typically 1 m) to avoid optical loss. For the traveling-wave socket slot waveguide [Fig. 10(b)], both silicon strips are doped and connected to the aluminum conductors by thin silicon sockets. Arsenic doping with a density of n D % 2 Â 10 16 cm À 3 yields sufficient electrical conductivity Si % 10 ð cm Þ À 1 but does not induce relevant optical loss. In Fig. 10(c), a photonic crystal (PhC) line defect waveguide comes with a slot etched into the SOI device layer for exploiting the field enhancement in quasi-TE polarization as described previously. The PhC is a slow-light structure, which significantly increases the interaction time with the microwave field. This in turn allows the construction of ultracompact modulators. The numerous possibilities to arrange the PhC holes allow optimization of the structure so that operation without dispersion is possible within a sufficiently large wavelength range. Details of the PhC design, which resulted in light propagating at 4% of the speed of light in vacuum, have been published in [28] and [50] and demonstrated in [51]–[54] The slot PhC modulator is covered with an EO material too. Again, the doped PhC regions are electrically connected to the aluminum conductors. The rationale for the slot waveguide modulator approach is as follows. • The SOH allows filling of the slot with a highly nonlinear poled electrooptic material of choice, providing almost instantaneous nonlinearity V rather than direct carrier injection in silicon with its related speed limitations. • The voltage applied across the electrodes drops off almost entirely across the narrow slot w gap . Since the dimension of the slot is as small as 150 nm, one obtains a large electric field E x right in the middle of the slot. • The slot waveguide structure leads to an optical field almost entirely confined to the slot. This results in an extremely efficient optoelectronic effect since now both the electric and optical field are largest inside the slot. • The slow-light slot waveguide PhC approach provides an additional field enhancement of the optical field. This enhancement is due to the long time that the optical field resides in the structure and allows one to further reduce the length of the phase modulator section. In the following, we will discuss important parameters such as modulation bandwidth f mod and drive voltage swing, which are related to the phase shift voltage U . In this section, we estimate the achievable modulation bandwidth under the assumption that the microwave generator is matched to the wave impedance of the coplanar transmission line of the MZI modulator, see Fig. 1. We further make the realistic assumption that the silicon structures are so small that microwave losses are negligible. The modulation bandwidth is then affected by RC effects, the spatial walkoff between the electrical and optical wave, and potential bandwidth limitations from the nonlinear material. However, the latter is negligible as long as there is no TPA and operation speed is not in the terahertz regime. 1) Electrical RC-Limitations: Electrical RC-limitations are negligible for an impedance-matched travelling-wave electrical waveguide as depicted in Fig. 10(a), yet there might be a limiting RC-factor for the two slot waveguide structures of Fig. 10(b) and (c). The doped sections con- necting the metal electrodes and the slot have a finite resistivity R 0 per length, and the voltage across the nonconductive slot has a certain capacitance C 0 per length. As a result, an electrical wave with a constant amplitude U traveling along the electrodes generates a voltage amplitude U gap across the nonconductive gap. The 3 dB bandwidth associated with the phase-shifter section as depicted in Fig. 11 is therefore ...

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... quantity Á represents the phase mismatch due to group velocity dispersion (GVD) between the signal wave at wavelength s and the converted wave at wavelength c . The quantity D 2 denotes the GVD parameter and p is the wavelength of the pump. Measuring two different samples with nominally identical geometry at two different signal wavelengths, we have obtained nonlinear parameters of 116 000, 107 000, 104 000, and 91 000 W À 1 km À 1 , leading to an average value of 104 000 W À 1 km À 1 [25]. 3) Phase-Matching Over Large Spectral Range: The dependence of the FWM efficiency as a function of wavelength offset between pump and probe signal has been tested as well; see Fig. 7. The group velocity dispersion parameter D 2 was found to be so small that phase-matching over a large 20 nm spectral range could be achieved. Measure- ments of the spectral efficiency were performed on a waveguide with height h 1⁄4 220 nm, width w 1⁄4 216 nm, slot width w slot 1⁄4 157 nm, and geometrical waveguide length L 1⁄4 4 mm. By fitting the measured dependence of as a function of the detuning Á to (7) and (8), the waveguide under test exhibited a group velocity dispersion parameter of D 2 1⁄4 À 6 : 84 fs = ð mm nm Þ and a nonlinearity parameter of 1⁄4 0 : 83 Â 10 5 W À 1 km À 1 . 4) Dynamics and Two-Photon Absorption: The SOH slot waveguide was tested for its phase response in a pump- probe experiment [47]. Fig. 8 shows the phase shift induced by a pump-probe measurement with 100 fs long pulses for various input powers at a wavelength of 1550 nm. The slot waveguide shows an instantaneous Kerr-type response, which has its origin predominantly in the cladding. There are no slow tails due to TPA in silicon with subsequent free- carrier absorption such as seen in nonlinear silicon strip waveguides [47]. The geometry of the slot waveguides in the TPA absorption experiment was identical to the one from the loss characterization. To proof the viability of the concept, all-optical demultiplexing of a 120 Gbit/s data signal to a 10 Gbit/s data stream has been performed. The experimental setup together with the eye diagrams are depicted in Fig. 9. For the data (pump), we used mode-locked fibre lasers operating at repetition rates of 10 GHz and emitting pulses of approxi- mately 3 ps full-width half-maximum. The signal and the pump were synchronized using a tunable optical delay. The 120 Gbit/s data were generated by modulating the 10 GHz pulse train with a pseudorandom bit sequence (2 31 À 1 bit) and by subsequent optical time-division multiplexing. Both the pump and the signal were amplified and coupled into a SOH slot waveguide of height h 1⁄4 220 nm, strip width w 1⁄4 212 nm, and slot width w slot 1⁄4 205 nm. The output signal was bandpass filtered at the converted wavelength and amplified, and the eye diagram was recorded with a digital communication analyzer. By varying the delay between the pump and the signal, different tributaries could be chosen for demultiplexing. Similar performance was found for all the tributaries. From the eye diagram, a quality factor of Q 2 1⁄4 11 : 1 dB was measured for an on-chip pump power of 15.6 dBm (36 mW). Since the power of the converted signal depends quadratically on the pump power, and since the 10 GHz pump exhibits noticeable amplitude fluctuations [see eye diagram (2) in Fig. 9], the Q-factor was mainly limited by the performance of the pump. More recently we have tested slot waveguides for their ability to demulitplex 170.8 to 42.7 Gbit/s [26] and for 40 Gbit/s all-optical wavelength conversion [48]. No pattern dependence or any other speed limitations were observed. In this section, we discuss the potential of the SOH platform for the fabrication of optical modulators with drive voltages around 1 V and bandwidths exceeding 100 Gbit/s [28]. Electrooptic modulators typically are implemented as Mach–Zehnder interferometers (MZIs); see Fig. 1, where both arms of the MZI comprise phase modulator sections. Three phase modulator structures compatible with the SOH approach are depicted in Fig. 10. The phase shifters consist of silicon waveguides (Si) surrounded by a poled electrooptic organic material (EO). The optical strip waveguides are operated in quasi-TE mode. In the traveling-wave strip waveguide scheme of Fig. 10(a), the microwave field is applied via two aluminum conductors running in parallel to the optical strip waveguide. The spacing between the conductors and the optical waveguide is chosen large enough (typically 1 m) to avoid optical loss. For the traveling-wave socket slot waveguide [Fig. 10(b)], both silicon strips are doped and connected to the aluminum conductors by thin silicon sockets. Arsenic doping with a density of n D % 2 Â 10 16 cm À 3 yields sufficient electrical conductivity Si % 10 ð cm Þ À 1 but does not induce relevant optical loss. In Fig. 10(c), a photonic crystal (PhC) line defect waveguide comes with a slot etched into the SOI device layer for exploiting the field enhancement in quasi-TE polarization as described previously. The PhC is a slow-light structure, which significantly increases the interaction time with the microwave field. This in turn allows the construction of ultracompact modulators. The numerous possibilities to arrange the PhC holes allow optimization of the structure so that operation without dispersion is possible within a sufficiently large wavelength range. Details of the PhC design, which resulted in light propagating at 4% of the speed of light in vacuum, have been published in [28] and [50] and demonstrated in [51]–[54] The slot PhC modulator is covered with an EO material too. Again, the doped PhC regions are electrically connected to the aluminum conductors. The rationale for the slot waveguide modulator approach is as follows. • The SOH allows filling of the slot with a highly nonlinear poled electrooptic material of choice, providing almost instantaneous nonlinearity V rather than direct carrier injection in silicon with its related speed limitations. • The voltage applied across the electrodes drops off almost entirely across the narrow slot w gap . Since the dimension of the slot is as small as 150 nm, one obtains a large electric field E x right in the middle of the slot. • The slot waveguide structure leads to an optical field almost entirely confined to the slot. This results in an extremely efficient optoelectronic effect since now both the electric and optical field are largest inside the slot. • The slow-light slot waveguide PhC approach provides an additional field enhancement of the optical field. This enhancement is due to the long time that the optical field resides in the structure and allows one to further reduce the length of the phase modulator section. In the following, we will discuss important parameters such as modulation bandwidth f mod and drive voltage swing, which are related to the phase shift voltage U . In this section, we estimate the achievable modulation bandwidth under the assumption that the microwave generator is matched to the wave impedance of the coplanar transmission line of the MZI modulator, see Fig. 1. We further make the realistic assumption that the silicon structures are so small that microwave losses are negligible. The modulation bandwidth is then affected by RC effects, the spatial walkoff between the electrical and optical wave, and potential bandwidth limitations from the nonlinear material. However, the latter is negligible as long as there is no TPA and operation speed is not in the terahertz regime. 1) Electrical RC-Limitations: Electrical RC-limitations are negligible for an impedance-matched travelling-wave electrical waveguide as depicted in Fig. 10(a), yet there might be a limiting RC-factor for the two slot waveguide structures of Fig. 10(b) and (c). The doped sections con- necting the metal electrodes and the slot have a finite resistivity R 0 per length, and the voltage across the nonconductive slot has a certain capacitance C 0 per length. As a result, an electrical wave with a constant amplitude U traveling along the electrodes generates a voltage amplitude U gap across the nonconductive gap. The 3 dB bandwidth associated with the phase-shifter section as depicted in Fig. 11 is therefore ...

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... photonics is likely to become a key technology for highly integrated optics, such as it has been for electronics for more than 60 years. The main advantages of silicon as a platform for integrated optics are the availability of a mature silicon technology, the compatibility with complementary metal–oxide–semiconductor (CMOS) electronics, low costs, and the availability of a high-resolution lithography with 35 nm resolution [1]–[5]. Consequently, a whole industry has worked on providing a complete library of optical components. Some of these components are lowest loss waveguides [6], [7], tapers [8] and grating couplers [9], filters [10], [11], or photonic crystal devices offering dispersion and slow light functionalities [12], [13], to name just a few. While all of the aforementioned devices are passive building blocks, active devices such as lasers, amplifiers, and modulators are needed to comple- ment the library of multifunctional optoelectronic silicon circuits. And indeed, by wafer-bonding III–V hetero- structures onto silicon-on-insulator (SOI) waveguides, continuous-wave (cw) lasers [14]–[16], mode-locked lasers [17], and optically and electrically pumped amplifiers [18]–[20] have been realized. Yet, electrical and optical modulation is still an issue. As a matter of fact, electrical and optical signal processing suffer from two-photon absorption (TPA) and free-carrier absorption (FCA) related speed limitations [21]. While research in silicon concentrates on solving these speed issues, polymer optics have achieved remarkable results long since. Already in 1997, nonlinear polymer devices demonstrated modulation over the whole W-band up to 110 GHz [22], and thus indicated the potential of organic materials for even highest speed. This has triggered the development of a big set of novel nonlinear organic materials [23]. A logical next step in the development was thus to combine the silicon and organic technologies in order to create a new silicon-organic hybrid (SOH) platform that combines the advantages of silicon with the ultrafast performance of organic materials. Indeed, potential operation in excess of 1 THz can be inferred [24], and only recently, high-quality 120 Gbit/s signal processing was performed [25], [26]. In addition, ultralow power electrooptic switching has been shown as well [27]. In this paper, we review the SOH platform. It relies on CMOS technology for fabricating silicon wire waveguides and exploits nonlinear organic materials for the cladding. While the silicon wire provides the guiding of the optical mode, the organic material provides the necessary nonlinearity to perform electrical and optical modulation up to highest speed. We first discuss approaches with structures for performing Kerr-based ultrafast ð 3 Þ -nonlinear signal processing and show that it is feasible to fabricate a slot waveguide structure, which provides a nonlinearity parameter on the order of 1⁄4 100 000 W À 1 km À 1 . This is V to the best of our knowledge V the largest nonlinearity ever shown for a Kerr-effect based waveguide. We then demonstrate experimentally the demultiplexing of optical data signals from 120 to 10 Gbit/s in one compact device of 6 mm length [25]. Lastly, we give design guidelines that will lead the technology towards 100 Gbit/s/1 V modulators with dimensions of 80 m [28]. This paper is organized as follows. In Section II, we outline two major applications areas, the state-of-the art, and issues with current approaches. In Section III, we discuss structures and design principles for waveguides that will enable all-optical signal processing at bit rates beyond 100 Gbit/s. Section IV gives design guidelines for next-generation electrooptical SOH modulators. This paper ends with conclusions. The ability to electrically process optical signals is key for the fabrication of high-speed optoelectronic modulators. Modulators are needed for the fabrication of small form factor transceivers, which preferentially should comprise all the electrical and optical circuitry on a single low-cost silicon chip. Fig. 1 shows the outline of such a chip with an integrated transmitter and receiver module. The chip could potentially be smaller than 2 Â 10 mm 2 . It could comprise a III–V wafer-bonded laser diode, a high-speed electro-optic modulator to encode data onto an optical carrier provided by the laser diode, passive optical waveguides, a silicon-germanium photodiode, and CMOS compatible electronic circuitry. However, electrical modulation of optical signals in silicon is not straightforward because the second-order ð 2 Þ -susceptibility is non-existent in principle in monocrystalline silicon, and thus simple electrooptic modulation of the optical phase is not possible. As a consequence, injection of free carriers can be used instead. These carrier-injection operated modulators have already shown operation up to 40 Gbit/s [29]. However, free carriers lead to increased losses, and it is not clear to what extent speed can be further increased due to the limited mobility and the relatively long carrier lifetime. The situation is similar for all-optical signal processing in silicon. To optically modulate optical signals, a sufficiently strong third-order ð 3 Þ -susceptibility is needed. While third-order nonlinearities in silicon nanophotonic waveguides exist, the effect is impeded by TPA and by TPA-induced FCA. For instance, all-optical signal regeneration has been demonstrated at 10 Gbit/s [30], but for data rates of 40 Gbit/s, free carriers generated by TPA have to be removed by appropriate technological measures for preventing excessive absorption [29], [31], and this becomes actually difficult at bit rates beyond 40 Gbit/s. While all-optical technologies are already of interest at both lower and highest speeds due to the small footprint and the resulting energy efficiency, they are, however, most attractive at speeds beyond the present limits of electronics, i.e., at speeds beyond 40 Gbit/s. At those speeds, ð 3 Þ -nonlinearities allow manifold applications. For instance, four-wave mixing (FWM) [30] is frequently used for all-optical high-speed demultiplexing [25], for wavelength conversion, or for optical sampling. Fig. 2(a) shows a typical FWM setup, in which a high-speed data signal at in ; 1 is demultiplexed by a strong clock signal clk ; 2 , resulting in an idler signal at idler ; 3 . In this example, the clock signal maps every second bit of the input signal onto an idler by means of the ð 3 Þ -nonlinearity. The spectrum behind the ð 3 Þ -nonlinear device is depicted on the right- hand side of Fig. 2(a). A filter is typically used to separate the new signal at idler 3 from the input and the clock signal. For other applications, cross-phase modulation (XPM) might be used to perform wavelength conversion; see Fig. 2(b). In this process, a strong input signal in 1 changes the refractive index of the ð 3 Þ -nonlinear material. This affects the phase of a second signal, e.g., a cw signal at 2 . This can actually be exploited in an interferometric configuration by transfer of the original information at in 1 onto a new wavelength at 2 . XPM nonlinearity is attractive because it allows wavelength conversion over the largest possible spectral range since the phase-matching condition is always fulfilled. Finally, self-phase modulation (SPM) may be used to perform all-optical signal regeneration; see Fig. 2(c). SPM- based signal regeneration usually follows the so-called Mamyshev scheme [32], in which the intensity-induced refractive index change is exploited to spectrally broaden a signal. A subsequent filter selects only those parts of the spectrum that were caused by moderate signal powers. The noisy low-power contributions will not have sufficient power to broaden the signal and thus will not make it into the filter passband. Conversely, signals with large amplitude will experience stronger broadening and thus generate spectral components beyond the filter passband. These additional spectral components will be rejected. As a result, both the noisy low-power parts of the signal and the high-power parts will be suppressed, thus regenerating the signal. The motivation behind the SOH approach is to combine the advantages of silicon technology with the versatility offered by the numerous options with organic materials. In the SOH approach, all passive components, i.e., waveguides, couplers, and filters, are fabricated in silicon. The high refractive index of silicon ð n % 3 : 5 Þ leads to strongly guided light. The nonlinear optical functionality, however, is taken over by the organic cladding. For choosing this material, one takes advantage of the many organic molecules and polymers that have been developed in the last years. Their nonlinear refractive index virtually reacts instantaneously, and so the bandwidth is almost unlimited [24]. Organic materials typically have small linear refractive indexes on the order of 1.4–2.5. Examples of electrooptically active nonlinear organic molecules and polymers and their electrooptic coefficients r are summarized in Table 1. Electrooptic coefficient r and second-order susceptibility ð 2 Þ are interrelated ...