Group-IV semiconductor compounds with intense optical nonlinearity have emerged as a new branch of all-optical processing materials benefiting from the manufacturing compatibility with silicon electronic and photonic integrated circuits. Due to the chemical reforming on the bonding or precipitating feature of the compositional atoms in the membrane matrix, either the orbital hybridization or the quantum self-assembly of interstitial composites can be employed to reform the electronic and optical characteristics. The recent development on enhancing the nonlinear refractive indices of the group-IV semiconductor materials has revealed significant progress to accelerate the all-optical switching logic, which greatly reduces the energy consumption to enable the constitution of the advanced multi-logic gating and the entry-level photonic computing circuits. This work not only overviews the group-IV semiconductor photonic data processing elements but also prospects for the future direction of optical quantum computation and communication. To date, the nonlinear refractive indices of the group-IV semiconductor materials can be obtained as 10−8 to 10−16 cm2/W in the range between 300 and 10 000 nm in 2022. The wavelength conversion and data switching with bit rate beyond 25 Gbps have been achieved via nonlinear photonic waveguide components. By taking the non-stoichiometric SiC-made micro-ring waveguide as an example, the n2 as high as 3.05 × 10−14 cm2/W of the resonant SiC micro-ring gate is retrieved from the pump–probe analysis. The eye-diagram of the wavelength converted data in the micro-ring achieves its signal-to-noise and on/off-extinction ratios (SNR and ER) of 5.6 and 11.8 dB, while up to 25-Gbps all-optical data-format inversion with 4.8-dB SNR and 10.2-dB ER is also performed during an ultrafast switching within rising and falling time of less than 22 ps. Such all-optical data processing including both wavelength switching and format conversion in the highly nonlinear optical SiC waveguide resonator can achieve error-free operation with corresponding bit-error-ratios of lower than 1 × 10−5 at 25 Gbps after forward error correction.

Due to the rapid development of person to person (P2P), person to machine (P2M), and machine to machine (M2M) with elevating bit rates, the data transmission and communication in the physical layer of cloud data exchanging and computing centers have faced a huge challenge on the transceiving speed not only in the bulk circuit but also in the chip level. This demand becomes an important issue to urge the next-generation transmission architecture initiated for the future. Therefore, the active functional components with high processing speed and low energy consumption are developed. However, the allowable channel speed of the silicon-based electronic integrated circuits is still limited by the transit time of the chip material and bonding wire even when scaling down the chip size. Group-IV semiconductor photonics is emerging as one promising solution to evolutionally overcome the inherent limitations of microelectronic data communication where photonics can take pace with Moore’s law.1–3 The functional photonic waveguide devices made by group-IV elementary and compound semiconductors benefit from the full compatibility with conventional silicon electronic integrated circuits, which can easily achieve a higher processing bit rate and lower propagation loss than bonding wires and transmission lines during chip-level communications. These superiorities also make the group-IV semiconductor waveguide photonics competitive with current solutions for data-center and chip-to-chip interconnections. Numerous implementations controlled with versatile electrical-to-optical or optical-to-electronic mechanisms are performed by assembling fundamental silicon waveguide elements, such as directional couplers,4–6 optical switches,7–9 modulators,10–12 filters,13–15 logic gates,16–19 add/drop multiplexers/demultiplexers,20–22 and photodetectors,23–25 for optical signal processing in a high-speed photonic system on an integrated chip. Nevertheless, the data processing speed is still restricted by the electrical-to-optical mechanism due to the finite resistance–inductance–capacitance (RLC) constants of the electronic integrated circuits at the current stage.

Recently, all-optical switching, modulation, and processing become more popular for high-speed data transmission than ever due to the significant progress achieved in controlling the nonlinear optical properties of group-IV semiconductors.26–32 Typical nonlinear optical effects observed in other materials including two-photon absorption (TPA)-induced free-carrier absorption (FCA),33–35 four-wave-mixing (FWM),36–39 cross-phase modulation (XPM),40–42 and optical Kerr effect43–45 have been gradually explored using the elementary or compound group-IV matrices. By taking the third-order optical nonlinearity (χ(3)) as an example for the wavelength conversion functionality, the FWM is one of the representative effects with a new differential frequency component induced when passing single- or two-tone signals through the group-IV semiconductors, thus providing the non-degenerate (f1, f2, 2f1f2, and 2f2f1) and degenerate (f1, f3, f4) types of the FWM induced wavelength conversion of data carriers as illustrated in Fig. 1(a). However, the FWM modulation, as well as wavelength conversion procedure, is sensitive to phase variation and frequency deviation, which often requires accurate phase matching between two-tone carriers during data transmission when considering the FWM as the all-optical processing mechanism.

FIG. 1.

Schematic diagram of (a) non-degenerate and degenerate FWM and (b) XPM effects.

FIG. 1.

Schematic diagram of (a) non-degenerate and degenerate FWM and (b) XPM effects.

Close modal

Alternatively, the XPM procedure is also correlated with the phase variation of the slave affected by the refractive index change when passing another master carrier through the medium to induce the nonlinear Kerr effect via the third-order optical nonlinearity (χ(3)), as shown in Fig. 1(b). The phase variation of Δϕ = 2π(Δn)L/λ with Δn, L, and λ, respectively, denoting the refractive index change, the active length, and the optical wavelength. The XPM effect needs either intense pumping power or long interaction length to induce sufficiently large phase variation, which is usually operated under pulsed data bit operation to facilitate the peak power enhancement transiently. Moreover, such an effect must rely on an optical delay line interference for coherent detection and decoding. In addition to the FWM and XPM effects, the TPA-induced FCA effect also plays an important role in the all-optical modulation,46–60 which exhibits large isolation between pumped and converted streams as the widely employed nonlinear group-IV semiconductors like Si and SiC provide larger bandgap energy than the pumped photons at telecommunication band. Apparently, the TPA effect must be induced by the intensive pumping to excite free carriers up-transited from valence to conduction band, as shown in Fig. 2(a). All-optical data format inversion occurs when these generated free carriers absorb idler photons in another wavelength channel. However, such a TPA-induced FCA is limited by the carrier lifetime of the group-IV semiconductor host to confine its switching speed, and the carrier lifetime shortening is a crucial process to speed up the FCA modulation up to several Gbit/s.61–70 

FIG. 2.

Schematic diagram of the (a) TPA-induced FCA and (b) nonlinear Kerr effects.

FIG. 2.

Schematic diagram of the (a) TPA-induced FCA and (b) nonlinear Kerr effects.

Close modal

The cross-wavelength intensity modulation (XWIM) via the nonlinear Kerr effect is the simplest approach in view of all candidates for nonlinear all-optical switching. By employing the waveguide micro-ring resonator that generates optical combs periodically in the transmission spectrum, the high-quality-factor transmission notch red-shifts its central wavelength when the seeded data stream induces nonlinear refractive index change in the micro-ring resonator. Such a transiently red-shifted notch varies the transmission power of the idler carrier located at the original notch wavelength, which performs the all-optical XWIM process within one data bit, and the format can be selected to inverse or not via the set of the idler inside or outside the transmission notch originally, as illustrated in Fig. 2(b). The XWIM is not limited by the carrier lifetime such that the data rate can easily approach several tens Gbit/s or higher. The wavelength conversion and the data format following/inversion can be performed by either acquiring the intensive seeding or reducing the waveguide cross-section, both cases would suffer from the beyond damage threshold operation of the host waveguide material. Such a drawback persistently urges the study on reforming the group-IV semiconductor matrix to efficiently improve its optical nonlinearity. Sections II and III summarize the research progress on enhancing the nonlinear refractive index of the group-IV semiconductors and discuss the performance of the all-optical modulation as high as 25 Gbit/s based on the C-rich SiC micro-ring resonator via nonlinear Kerr switching.

In principle, the all-optical FCA modulation based on transient carrier dynamics exhibits a lower modulation speed than the all-optical nonlinear Kerr modulation based on the nonlinear refractive index switching. Such a bottleneck elucidates the transferring research trend from FCA modulation to Kerr switch for group-IV semiconducting materials in recent years. The numerical analysis of nonlinear refractive indices (n2) has been demonstrated via degenerate four-wave-mixing (FWM),71,72 beam distortion,73 nearly degenerate three-wave mixing (TWM),74 nonlinear interferometry,75,76 ellipse rotation,77 self-phase modulation (SPM),78 and Z-scan measurements.79,80 Starting from the crystalline Si,81–98, Fig. 3(a) and Table I summarize the n2 coefficient for the crystalline Si obtained from previous studies, indicating that the n2 of the crystalline Si material is around 10−13 to 10−14 cm2/W at near- and mid-infrared wavelength regions (1220–5500 nm). In particular, Rieger et al. have observed the n2 of silicon as 7 × 10−14 cm2/W at 1.5 µm via the use of a silicon-on-insulator waveguide83 as early as 2004. Boyraz et al. determined the n2 as large as 1.2 × 10−13 cm2/W at 1.8 µm for bulk Si.84 Fukuda et al. utilized the four-wave mixing method to characterize n2 = 7 × 10−14 cm2/W at 1.55 µm for Si wire, and the all-optical wavelength conversion at 10 Gbit/s was also demonstrated in 2005.85 

FIG. 3.

The diagrams for developing progress on the nonlinear refractive indices of (a) the crystalline Si and (b) the amorphous Si.

FIG. 3.

The diagrams for developing progress on the nonlinear refractive indices of (a) the crystalline Si and (b) the amorphous Si.

Close modal
TABLE I.

Table for developing progress on the nonlinear refractive index of the crystalline Si.

GroupWavelength (nm)n2 (cm2/W)Year
CUHK 1540 6 × 10−14 200281  
Bell Lab 1540 4.5 × 10−14 200382  
UBC 1530 7 × 10−14 200483  
UCLA 1559 3.7 × 10−14 200484  
NTT 1546–1547 9 × 10−14 200585  
CU-IBM 1550 4.5 × 10−14 200586  
NEC 1550 1.45 × 10−13 200587  
IBM 1500 5 × 10−14 200688  
UT 1220 4.7 ± 2.0 × 10−14 200789  
UT 1800 1.2 × 10−13 200789  
UR 1200–2400 2.5 ± 1.5 × 10−14 200790  
CIT 1550 1.2 × 10−13 200791  
SU 1064 6.8 × 10−11 200892  
NIAIST 1550 2 × 10−14 201193  
UCSD 2598 3.75 ± 0.75 × 10−15 201194  
UCLA 1550 5.52 × 10−14 201195  
UCLA 2200 6.23 × 10−14 201195  
UCLA 3390 3.67 × 10−14 201195  
UCLA 4260 3.26 × 10−14 201195  
NTU 2100 1.65 × 10−13 201396  
ANU 1550 6.7 ± 0.6 × 10−14 201397  
ANU 3000–5500 2.7 ± 0.5 × 10−14 201397  
ZU 2000 8.9 × 10−14 201898  
GroupWavelength (nm)n2 (cm2/W)Year
CUHK 1540 6 × 10−14 200281  
Bell Lab 1540 4.5 × 10−14 200382  
UBC 1530 7 × 10−14 200483  
UCLA 1559 3.7 × 10−14 200484  
NTT 1546–1547 9 × 10−14 200585  
CU-IBM 1550 4.5 × 10−14 200586  
NEC 1550 1.45 × 10−13 200587  
IBM 1500 5 × 10−14 200688  
UT 1220 4.7 ± 2.0 × 10−14 200789  
UT 1800 1.2 × 10−13 200789  
UR 1200–2400 2.5 ± 1.5 × 10−14 200790  
CIT 1550 1.2 × 10−13 200791  
SU 1064 6.8 × 10−11 200892  
NIAIST 1550 2 × 10−14 201193  
UCSD 2598 3.75 ± 0.75 × 10−15 201194  
UCLA 1550 5.52 × 10−14 201195  
UCLA 2200 6.23 × 10−14 201195  
UCLA 3390 3.67 × 10−14 201195  
UCLA 4260 3.26 × 10−14 201195  
NTU 2100 1.65 × 10−13 201396  
ANU 1550 6.7 ± 0.6 × 10−14 201397  
ANU 3000–5500 2.7 ± 0.5 × 10−14 201397  
ZU 2000 8.9 × 10−14 201898  

Later on, the twofold enhancement of n2 up to 1.65 × 10−13 cm2/W at 2.1 µm in the crystalline Si wafer was observed by Wang and co-workers,96 and the mid-infrared optical nonlinearity analysis of the crystalline Si with n2 = 2.7 ± 0.5 × 10−14 cm2/W at 3–5 µm was delivered by Gai et al.97 In contrast, the amorphous Si (a-Si) has also been studied for nonlinear optical applications.99–113 The developing progress on the n2 of the a-Si is summarized in Fig. 3(b) and Table II. At the early stage, the n2 = 3.2 × 10−16 cm2/W obtained for fused silica is still two orders of magnitude smaller than that of the bulk crystalline observed by Tzortzakis and co-workers in 2001.99 After a long while, Shoji et al. fabricated an a-Si waveguide with n2 = 0.5 × 10−14 cm2/W enlarged by one order of magnitude compared to the previous reports;102 Kuyken and co-workers further enhanced the n2 of the a-Si waveguide to 1.3 ± 0.2 × 10−13 cm2/W.105 Notably, Shen et al. demonstrated the (SPM) to obtain the n2 of the a-Si core fiber as large as 1.75 × 10−13 cm2/W,108 and the highest record of the n2 = 5 × 10−13 cm2/W for the a-Si determined from the four-wave mixing analysis was reported by Li et al. in 2017.112 Most of the reported n2 for the a-Si is around 10−13 to 10−14 cm2/W.

TABLE II.

Table for developing progress on the nonlinear refractive index of the amorphous Si.

GroupWavelength (nm)n2 (cm2/W)Year
ENSTA 800 3.2 × 10−16 200199  
UOS 10 000 3.73 × 10−12 2003100  
HU 1 060 6 × 10−12 2006101  
NIAIST 1 550 5 × 10−13 2010102  
RIT 1 550 4.2 × 10−13 2010103  
UOS 1 540 1.8 × 10−13 2010104  
GU-IMEC-ULB 1 535 1.3 ± 0.2×10−13 2011105  
JHU 1 541 7.43 × 10−13 2012106  
UOS 1 540 1.7 × 10−13 2013107  
UOS 1 750 1.75 × 10−13 2013108  
UOS 2 150 1.2 × 10−13 2013108  
UOP 1 550 2.8 × 10−13 2013109  
ANU 1 550 2.2 × 10−12 2014110  
HP Lab 1 550 1 × 10−13 2014111  
JHU 1 550 5 × 10−13 2017112  
UOS 1 550 1.675 ± 0.175 × 10−13 2018113  
UOS 2 400 1.15 ± 0.15 × 10−13 2018113  
GroupWavelength (nm)n2 (cm2/W)Year
ENSTA 800 3.2 × 10−16 200199  
UOS 10 000 3.73 × 10−12 2003100  
HU 1 060 6 × 10−12 2006101  
NIAIST 1 550 5 × 10−13 2010102  
RIT 1 550 4.2 × 10−13 2010103  
UOS 1 540 1.8 × 10−13 2010104  
GU-IMEC-ULB 1 535 1.3 ± 0.2×10−13 2011105  
JHU 1 541 7.43 × 10−13 2012106  
UOS 1 540 1.7 × 10−13 2013107  
UOS 1 750 1.75 × 10−13 2013108  
UOS 2 150 1.2 × 10−13 2013108  
UOP 1 550 2.8 × 10−13 2013109  
ANU 1 550 2.2 × 10−12 2014110  
HP Lab 1 550 1 × 10−13 2014111  
JHU 1 550 5 × 10−13 2017112  
UOS 1 550 1.675 ± 0.175 × 10−13 2018113  
UOS 2 400 1.15 ± 0.15 × 10−13 2018113  

Although the crystalline and amorphous Si materials can provide a high n2 coefficient, their relatively large linear refractive indices inevitably limit the maximal core size as well as the allowable transmission power in the waveguide for single-mode operation. In addition, the crystalline and amorphous silicon materials possess the low bandgap to easily cause the TPA-induced FCA under the telecommunication wavelength operation. The pumping intensity can be relatively low to generate the TPA-induced FCA modulation in crystalline and amorphous silicon materials. However, the carrier lifetimes of the crystalline and amorphous silicon materials still limit the modulation speed of all-optical data processing based on the TPA-induced FCA modulation. In contrast, the nonlinear Kerr effect is mainly dependent on the n2 of the materials, which is suitable for high-speed all-optical data processing as the interaction time of the nonlinear Kerr effect is in the femtosecond scale and is independent with free carriers of silicon materials. Nevertheless, the Kerr coefficient of pure silicon materials is extremely small due to the structural symmetry. These drawbacks in the crystalline and amorphous silicon materials accelerate the research pace toward the stoichiometric SiOx114–128 and SiNx129–144 dielectrics as they all exhibit the lower low refractive indices for allowing the large-core waveguide and high-power operation in single-mode regime over the broadband region covering visible and near-infrared wavelengths. Moreover, the SiOx and SiNx materials also exhibit larger bandgaps to avoid the TPA-induced FCA generation for high-speed all-optical data processing. As early as 1973, Stolen and Ashkin observed the light-induced birefringence in a glass waveguide and obtained its n2 of 5.45 × 10−17 cm2/W.114 Kim and Hutchinson measured the intensity-induced nonlinearity of fused silica to acquire its n2 of 3 × 10−16 cm2/W at 308 nm117 in 1989, and the similar n2 of 2.76 × 10−16 cm2/W at 1.5 µm for the fused silica fiber was determined using cross-phase modulation119 by Kato et al. in 1998. Olivier and co-workers also observed the n2 of 4.9 ± 0.6 × 10−16 cm2/W at 1064 nm and 3.4 ± 0.5 × 10−16 cm2/W at 532 nm for fused silica.123 Kabaciński et al. utilized SPM to obtain n2 = 2.19 ± 0.05 × 10−16 cm2/W at 1030 nm for fused silica.128 

With Fig. 4(a) and Table III summarizing the reported n2 for the SiOx in the recent 50 years, it is concluded that most SiOx materials only provide n2 on the scale of 10−15 to 10−16 cm2/W. Regarding the SiNx material, Ikeda et al. obtained n2 = 2.4 × 10−15 cm2/W from a SiNx micro-ring resonator operated at 1549 nm for the first time,129 and the same value at 1550 nm was confirmed by using the optical parametric oscillator by Levy et al. in 2010.132 Wang and co-workers further employed the SPM to observe the n2 of the silicon-rich (Si-rich) SiNx as large as 2.8 × 10−13 cm2/W.135 Moreover, Ding et al. reformed the SiN via thermal annealing to increase the n2 up to 6.27 × 10−12 cm2/W at 1550 nm.140 Afterward, Hong and co-workers employed the FWM to obtain n2 = 2.6 × 10−15 cm2/W at 1550 nm in the SiNx micro-ring resonator143 in 2021. In recent 15 years, the reported n2 of the SiNx exhibits a relatively broad tuning range from 10−15 to 10−12 cm2/W, as summarized in Fig. 4(b) and Table IV.

FIG. 4.

The diagrams for developing progress on the nonlinear refractive indices of (a) the SiOx and (b) SiNx.

FIG. 4.

The diagrams for developing progress on the nonlinear refractive indices of (a) the SiOx and (b) SiNx.

Close modal
TABLE III.

Table for developing progress on the nonlinear refractive index of the SiOx.

GroupWavelength (nm)n2 (cm2/W)Year
Bell Lab 2360 5.45 × 10−16 1973114  
LLNL, UC 1064 2.73 ± 0.27 × 10−16 1976115  
LLNL, UC 355 2.5 ± 1.2 × 10−16 1984116  
ICL 308 3 × 10−16 1989117  
AT&T Bell Lab 1319 2.52 × 10−16 1994118  
SEI, Ltd. 1550 4.44 × 10−16 1995119  
SEI, Ltd. 1550 2.76 × 10−16 1995120  
LLNL, UC 351 3.6 ± 0.64 × 10−16 1998121  
LLNL, UC 527 3.0 ± 0.35 × 10−16 1998121  
LLNL, UC 1053 2.74 ± 0.17 × 10−16 1998121  
NJIT 1064 2.44 × 10−16 2003122  
IF 532 3.4 ± 0.5 × 10−16 2004123  
IF 1064 4.9 ± 0.6 × 10−16 2004123  
EP 800 3.54 × 10−16 2005124  
FSUJ 800 1.55 ± 0.85 × 10−16 2006125  
UJM 800 2.48 × 10−16 2007126  
NRL 772 2.07 ± 0.52 × 10−16 2015127  
NRL 1030 2.23 ± 0.12 × 10−16 2015127  
NRL 1550 2.42 ± 0.15 × 10−16 2015127  
WUT 1030 2.19 ± 0.05 × 10−13 2019128  
GroupWavelength (nm)n2 (cm2/W)Year
Bell Lab 2360 5.45 × 10−16 1973114  
LLNL, UC 1064 2.73 ± 0.27 × 10−16 1976115  
LLNL, UC 355 2.5 ± 1.2 × 10−16 1984116  
ICL 308 3 × 10−16 1989117  
AT&T Bell Lab 1319 2.52 × 10−16 1994118  
SEI, Ltd. 1550 4.44 × 10−16 1995119  
SEI, Ltd. 1550 2.76 × 10−16 1995120  
LLNL, UC 351 3.6 ± 0.64 × 10−16 1998121  
LLNL, UC 527 3.0 ± 0.35 × 10−16 1998121  
LLNL, UC 1053 2.74 ± 0.17 × 10−16 1998121  
NJIT 1064 2.44 × 10−16 2003122  
IF 532 3.4 ± 0.5 × 10−16 2004123  
IF 1064 4.9 ± 0.6 × 10−16 2004123  
EP 800 3.54 × 10−16 2005124  
FSUJ 800 1.55 ± 0.85 × 10−16 2006125  
UJM 800 2.48 × 10−16 2007126  
NRL 772 2.07 ± 0.52 × 10−16 2015127  
NRL 1030 2.23 ± 0.12 × 10−16 2015127  
NRL 1550 2.42 ± 0.15 × 10−16 2015127  
WUT 1030 2.19 ± 0.05 × 10−13 2019128  
TABLE IV.

Table for developing progress on the nonlinear refractive index of the SiNx.

GroupWavelength (nm)n2 (cm2/W)Year
UCSD 1548 2.4 × 10−15 2008129  
UCSB 1550 3.5 × 10−15 2010130  
UCSD 1548 2.4 × 10−15 2010131  
CU 1550 2.5 × 10−15 2010132  
CUT 1550 1.4 × 10−14 2015133  
NTU, TW 1550 1.6 × 10−13 2015134  
SUTD 1550 2.8 × 10−13 2015135  
CUT 1550 1.13 ± 0.13 × 10−14 2017136  
UOS 1550 2 ± 0.15 × 10−14 2017137  
FU 1550 6.94 × 10−15 2018138  
CUT 1542 5 ± 1.6 × 10−15 2019139  
SNU 1064 2 × 10−12 2019140  
SNU 1550 6.27 × 10−12 2019140  
RMIT 1560 5.6 × 10−15 2020141  
SU 2000 3.51 × 10−15 2021142  
WHUT 1550 2.6 × 10−15 2021143  
SUTD 1550 9.8 × 10−14 2021144  
GroupWavelength (nm)n2 (cm2/W)Year
UCSD 1548 2.4 × 10−15 2008129  
UCSB 1550 3.5 × 10−15 2010130  
UCSD 1548 2.4 × 10−15 2010131  
CU 1550 2.5 × 10−15 2010132  
CUT 1550 1.4 × 10−14 2015133  
NTU, TW 1550 1.6 × 10−13 2015134  
SUTD 1550 2.8 × 10−13 2015135  
CUT 1550 1.13 ± 0.13 × 10−14 2017136  
UOS 1550 2 ± 0.15 × 10−14 2017137  
FU 1550 6.94 × 10−15 2018138  
CUT 1542 5 ± 1.6 × 10−15 2019139  
SNU 1064 2 × 10−12 2019140  
SNU 1550 6.27 × 10−12 2019140  
RMIT 1560 5.6 × 10−15 2020141  
SU 2000 3.51 × 10−15 2021142  
WHUT 1550 2.6 × 10−15 2021143  
SUTD 1550 9.8 × 10−14 2021144  

The SiOx and SiNx materials with such low nonlinear refractive indices often require an extremely high pumping intensity to induce a sufficiently large refractive index change, which can hardly be applicable to the photonic system-on-chip for practical communication needs. Enhancing the optical nonlinearity of the group-IV semiconducting materials has gradually relied on doping or mixing with other nano- or poly-structured elementary group-IV semiconductors lately.145–160 One of the recognized examples is to generate the excitons in the Si quantum dots or nanocrystals to enhance the reinforced oscillation magnitude for improving the nonlinear refractive index. In 1998, Vijayalakshmi et al. employed ion-implantation to precipitate dense Si nanoclusters in the SiO2 membrane for obtaining n2 as large as 0.5 ± 0.13 × 10−7 cm2/W at 532 nm.145 Prakash and co-workers also synthesized the Si nanocrystals in the SiO2 host matrix to improve its n2 up to 9.61 × 10−12 cm2/W.147 Torres-Torres et al. observed that the 3.1-nm-large Si nanoclusters could significantly enlarge the n2 of the SiNx to 2.7 × 10−12 cm2/W.149 Motamedi et al. employed the heterodyne pump–probe analysis to clarify the n2 of the Si nanowire waveguide as 0.32 × 10−13 cm2/W153 in 2012. Torres-Torres et al. further improved the n2 of the silica plate with ion-implanted Si quantum dots to 2.11 × 10−10 cm2/W159 in 2018, such large nonlinearity has already approached that of the graphene and its tuning range is as wide as 6 orders of magnitude, as shown in Fig. 5 and Table V. In addition to the aforementioned materials, SiC is also considered for the nonlinear Kerr applications with its superiorities in high thermal stability, large damage threshold energy, and tunable bandgap, which can support broadband high-intensity operation.161–164 In addition, the compatibility of SiC with both group III-V and IV semiconductor platforms for photonic integrated circuits also urges studies on its optical nonlinearity recently.165–184 In 2008, DesAutels and co-workers used the Z-scan technology to observe the n2 of the 6H-SiC at 780 nm as 4.75 × 10−15 cm2/W.165 In 2015, Cheng et al. increased the C content in the SiC matrix to generate the graphite-like C–C bonds for improving the n2 up to 1 ± 0.1 × 10−11 cm2/W at 800 nm.168 In 2018, Martini and Politi observed the four-wave mixing effect in the 3C-SiC ring resonator to evaluate the n2 of 3C-SiC as 5.31 ± 0.04 × 10−15 cm2/W at 1550 nm.174 

FIG. 5.

The diagram for developing progress on the nonlinear refractive indices of the Si nanostructures.

FIG. 5.

The diagram for developing progress on the nonlinear refractive indices of the Si nanostructures.

Close modal
TABLE V.

Table for developing progress on the nonlinear refractive indices of the Si nanostructures.

GroupMaterialWavelength (nm)n2 (cm2/W)Year
NJIT Si nanoclusters in SiOx 355 9.6 ± 2.5 × 10−9 1998145  
NJIT Si nanoclusters in SiOx 532 3.7 ± 0.9 × 10−8 1998145  
UNITN Si nanocrystals in SiOx 813 5.86 ± 1.09 × 10−14 2002146  
UNITN Si nanocrystals in SiOx 813 9.37 ± 1.97 × 10−12 2002147  
UB Si nanocrystals in SiOx 827 10−12 2008148  
UB Si nanocrystals in SiOx 1550 10−8 2008148  
IPN Si nanoclusters in SiNx 820 2.7 × 10−12 2008149  
KU Si nanocrystals in SiOx 752–838 2 × 10−13 2009150  
UNITN Si nanocrystals in SiOx 1550 4.8 ± 0.6 × 10−13 2009151  
CU Si nanowire 1775 1.14 × 10−13 2011152  
CU Si nanowire 2200 8 × 10−14 2011152  
CUT Si nanowire 1500 3.2 × 10−14 2012153  
BU Si nanocrystals in SiOx 800 5 ± 5 × 10−10 2012154  
BU Si nanocrystals in SiNx 800 4.5 ± 4.5 × 10−10 2012154  
NTU, TW Si quantum dots in SiNx 1549 2.17 × 10−13 2015155  
UNITN Si nanocrystals in SiOx 1550 1.2 × 10−12 2016156  
NTU, TW Si quantum dots in SiNx 1550 3 × 10−14 2016157  
NTU, TW Si quantum dots in SiNx 800 9.2 × 10−12 2016158  
IPN Si quantum dots in SiOx 830 2.11 × 10−14 2018159  
UOS Polycrystalline Si 1750 1 × 10−13 2019160  
UOS Polycrystalline Si 2350 7 × 10−14 2019160  
GroupMaterialWavelength (nm)n2 (cm2/W)Year
NJIT Si nanoclusters in SiOx 355 9.6 ± 2.5 × 10−9 1998145  
NJIT Si nanoclusters in SiOx 532 3.7 ± 0.9 × 10−8 1998145  
UNITN Si nanocrystals in SiOx 813 5.86 ± 1.09 × 10−14 2002146  
UNITN Si nanocrystals in SiOx 813 9.37 ± 1.97 × 10−12 2002147  
UB Si nanocrystals in SiOx 827 10−12 2008148  
UB Si nanocrystals in SiOx 1550 10−8 2008148  
IPN Si nanoclusters in SiNx 820 2.7 × 10−12 2008149  
KU Si nanocrystals in SiOx 752–838 2 × 10−13 2009150  
UNITN Si nanocrystals in SiOx 1550 4.8 ± 0.6 × 10−13 2009151  
CU Si nanowire 1775 1.14 × 10−13 2011152  
CU Si nanowire 2200 8 × 10−14 2011152  
CUT Si nanowire 1500 3.2 × 10−14 2012153  
BU Si nanocrystals in SiOx 800 5 ± 5 × 10−10 2012154  
BU Si nanocrystals in SiNx 800 4.5 ± 4.5 × 10−10 2012154  
NTU, TW Si quantum dots in SiNx 1549 2.17 × 10−13 2015155  
UNITN Si nanocrystals in SiOx 1550 1.2 × 10−12 2016156  
NTU, TW Si quantum dots in SiNx 1550 3 × 10−14 2016157  
NTU, TW Si quantum dots in SiNx 800 9.2 × 10−12 2016158  
IPN Si quantum dots in SiOx 830 2.11 × 10−14 2018159  
UOS Polycrystalline Si 1750 1 × 10−13 2019160  
UOS Polycrystalline Si 2350 7 × 10−14 2019160  

More recently, Yu et al. also used the Z-scan method to measure the n2 as 7.15 × 10−11 cm2/W at 1064 nm in the as-grown SiOxCy materials.179 In 2013, Chang et al. used the direct-current (DC) Kerr effect to obtain the n2 of the Si-rich SiC as 2.54 × 10−13 cm2/W at 1550 nm.184 In view of previous reports on exploring the n2 of the SiCx materials listed in Fig. 6(a) and Table VI, it is notable that changing the stoichiometry of the SiC allows the tuning of its n2 from 10−15 to 10−9 cm2/W when operated in near- and mid-infrared wavelengths. In addition, the SiGe material is also applied to the mid-infrared application.185–192 Hammani and co-workers measured the n2 of 1.119 × 10−13 cm2/W for the SiGe material with 30% Ge content185 in 2013. Carletti et al. observed the nonlinear optical response of the SiGe waveguide to extract its n2 as 1.75 × 10−14 cm2/W at 3.75 µm and 1.5 × 10−14 cm2/W at 4.162 µm.187 In the meantime, Ettabib et al. estimated the n2 of 1.1 × 10−13 cm2/W for the SiGe waveguide.189 In 2018, Sinobad and co-workers obtained the n2 of the SiGe waveguide as 2.5 × 10−14 cm2/W at a wavelength ranging from 3.0 to 8.5 µm.191  Figure 6(b) and Table VII summarize the research results in recent 10 years on the n2 of the SiGe to show its relative narrow distribution within 10−14 to 10−12 cm2/W as compared to other group-IV materials.

FIG. 6.

The diagrams for developing progress on the nonlinear refractive indices of (a) the SiC and (b) the SiGe.

FIG. 6.

The diagrams for developing progress on the nonlinear refractive indices of (a) the SiC and (b) the SiGe.

Close modal
TABLE VI.

Table for developing progress on the nonlinear refractive indices of the SiC.

GroupWavelength (nm)n2 (cm2/W)Year
AT&T GS 780 4.75 × 10−15 2008165  
FU-NTU 800 1.678 × 10−15 2010166  
UR 1550 5.9 ± 0.7 × 10−15 2010167  
NTU 800 1 ± 0.1 × 10−11 2015168  
NTU 800 3.86 × 10−11 2015169  
CU 2360 8.5 ± 1.1 × 10−15 2015170  
CAS 532 1.88 × 10−15 2016171  
NTU 1552 3.14 × 10−13 2016172  
NTU 1550 1.37 × 10−12 2017173  
UOS 1550 5.31 ± 0.04 × 10−15 2018174  
NTU 1550 2.44 × 10−12 2019175  
SUTD 1550 4.8 × 10−14 2019176  
DTU 1545 6 ± 0.6 × 10−15 2019177  
SNU 1064 1.23 × 10−12 2019178  
SNU 1064 7.15 × 10−11 2020179  
SUST 530 3.9 × 10−15 2021180  
SUST 780 3.69 × 10−15 2021180  
SUST 800 3.88 × 10−15 2021180  
CAS 1545 8 × 10−15 2021181  
CAS 1565 1.31 × 10−14 2021182  
UNSW-SUST 820 2.68 × 10−9 2021183  
UCSD 1542 2.54 × 10−13 2022184  
GroupWavelength (nm)n2 (cm2/W)Year
AT&T GS 780 4.75 × 10−15 2008165  
FU-NTU 800 1.678 × 10−15 2010166  
UR 1550 5.9 ± 0.7 × 10−15 2010167  
NTU 800 1 ± 0.1 × 10−11 2015168  
NTU 800 3.86 × 10−11 2015169  
CU 2360 8.5 ± 1.1 × 10−15 2015170  
CAS 532 1.88 × 10−15 2016171  
NTU 1552 3.14 × 10−13 2016172  
NTU 1550 1.37 × 10−12 2017173  
UOS 1550 5.31 ± 0.04 × 10−15 2018174  
NTU 1550 2.44 × 10−12 2019175  
SUTD 1550 4.8 × 10−14 2019176  
DTU 1545 6 ± 0.6 × 10−15 2019177  
SNU 1064 1.23 × 10−12 2019178  
SNU 1064 7.15 × 10−11 2020179  
SUST 530 3.9 × 10−15 2021180  
SUST 780 3.69 × 10−15 2021180  
SUST 800 3.88 × 10−15 2021180  
CAS 1545 8 × 10−15 2021181  
CAS 1565 1.31 × 10−14 2021182  
UNSW-SUST 820 2.68 × 10−9 2021183  
UCSD 1542 2.54 × 10−13 2022184  
TABLE VII.

Table for developing progress on the nonlinear refractive indices of the SiGe.

GroupWavelength (nm)n2 (cm2/W)Year
UOS 1 550 1.119 × 10−13 2013185  
UOS 2 000 1.28 × 10−13 2014186  
UDL 3 250 7.5 × 10−15 2015187  
UDL 3 750 1.75 × 10−14 2015187  
UDL 4 162 1.5 × 10−14 2015187  
UDL 4 750 2 × 10−14 2015187  
UDL 4 000 5.25 × 10−14 2015188  
UOS 2 400 1.1 × 10−13 2015189  
UPS 3 000 2.2 × 10−13 2017190  
UPS 10 000 1.8 × 10−13 2017190  
UDL 4 000 2.5 × 10−14 2018191  
CAS 3 000 5.25 × 10−14 2020192  
GroupWavelength (nm)n2 (cm2/W)Year
UOS 1 550 1.119 × 10−13 2013185  
UOS 2 000 1.28 × 10−13 2014186  
UDL 3 250 7.5 × 10−15 2015187  
UDL 3 750 1.75 × 10−14 2015187  
UDL 4 162 1.5 × 10−14 2015187  
UDL 4 750 2 × 10−14 2015187  
UDL 4 000 5.25 × 10−14 2015188  
UOS 2 400 1.1 × 10−13 2015189  
UPS 3 000 2.2 × 10−13 2017190  
UPS 10 000 1.8 × 10−13 2017190  
UDL 4 000 2.5 × 10−14 2018191  
CAS 3 000 5.25 × 10−14 2020192  

By overviewing the developing progress on the optical nonlinearity of the group-IV semiconductors in different structural forms, the enhancement of the nonlinear refractive index for these group-IV materials via new synthesizing techniques is sufficiently large to enable their practical applications in all-optical communication networks and computation logic fields. As the Si integrated photonics becomes more important for data-center transmission and optical quantum computing at the current stage, the all-optical switching, logic-gating, modulation, and data-processing will be soon considered to involve as the key elements in the Si photonic platform for next-generation heterogeneous networks. By taking the SiC micro-ring resonator as an example, the all-optical data processing at 25 Gbps in the resonant SiC micro-ring element via the utilization of the enhanced nonlinear Kerr effect is detailed in Sec. III. To detail the all-optical modulation via the nonlinear Kerr effect, the SiC micro-ring resonator carrying the pulsed return-to-zero on-off keying (PRZ-OOK) data format was taken as the example device and the data format for a demonstration in this Tutorial.

To fabricate a SiC micro-ring resonator waveguide, the thermal silicon oxide (SiO2) with the 3-µm thickness was grown on the silicon substrate to be a button cladding of the waveguide. In previous research, the nonlinear refractive index coefficient of the SiC is enhanced with a lot of carbon content in the film due to the sp2-orbital C–C bonds in SiC film to reduce the effective mass and shorter lattice of the whole SiC material. The SiC with the 380-nm thickness was deposited by a plasma-enhanced chemical vapor deposition (PECVD). The fluence ratio to grow the SiC was controlled as 0.94 with the gas mixture of methane (CH4, 161 SCCM) and the diluted silane (SiH4, 200 SCCM) composed of silane (8%) and argon (Ar, 92%). The temperature, pressure, and radio-frequency power were set as 550 °C, 0.12 torr, and 120 W, respectively. E-beam lithography was used to determine the pattern of the micro-ring resonator waveguide on the photoresistor (PR, ZEP-520). The determined photoresistor pattern was developed by the developer (ZED-N50) because the photoresistor is a positive photoresistor to make the patterned area soft to wash away. Chromium (Cr) was deposited on the determined pattern by the e-gun evaporator as a hard mask to protect the SiC to be etched via a reactive ion etching (RIE). After removing the photoresistor on the chip, the protective hard mask was determined and the un-patterned SiC thin film was etched to be a micro-ring resonator waveguide by an RIE process. The residual Cr hard mask was wet-etching by a Cr remover (CR-7) with a high Cr-etching rate and a small SiC-etching rate to remove the Cr and avoid etching the SiC. To protect the micro-ring resonator waveguide, the SiO2 was deposited upon the device.

The structure of the micro-ring resonator waveguide was designed, as shown in Fig. 7. The inverted taper structure with the waveguide width broadening from 200 to 500 nm within a total length of 200 µm was designed to reduce the coupling loss between the waveguide and the lensed fiber due to different optical coupling fields between each other. By inserting the inverted taper structure, the coupling loss between the waveguide and lensed fiber can be reduced to 3 dB/facet. The cross-section of the waveguide with the size of 500 × 380 nm2 was designed by the simulated result from the commercial R-soft CAD to ensure a fundamental mode in the waveguide without the high-order mode operation at 1550 nm. The radius of the micro-ring resonator was designed as 150 µm for the free spectral range of about 1 nm, and the gap spacing between the waveguide and the micro-ring resonator was simulated by the R-soft CAD to make the coupling ratio of 5% with a better quality factor (Q).

FIG. 7.

(a) The schematic diagram and (b) cross-section of the micro-ring resonator waveguide.

FIG. 7.

(a) The schematic diagram and (b) cross-section of the micro-ring resonator waveguide.

Close modal
The refractive index (orange dot line) of the SiC is measured by an ellipsometer, as shown in Fig. 8(a). From Fig. 8(a), the refractive index of the SiC at 1550 nm is measured as 2.14. The Sellmeier equation can be defined as the following formula to fit the refractive index (blue line):
(1)
where n is the refractive index of the SiC material as a function of wavelength (λ). B1, B2, B3, C1, C2, and C3 are fitting parameters. In this case, B1, B2, B3, C1, C2, and C3 are obtained as 0.85, 2.60, 0.05, 0.06, 0.2, 0, and 0, respectively. The material dispersion (red line) of the SiC film defined as a function of Dmaterial = d2n/dλ2 can be obtained from the refractive index.
FIG. 8.

(a) The dispersion and the refractive index of the SiC micro-ring resonator waveguide. (b) The XPS spectrum of the non-stoichiometric SiC film.

FIG. 8.

(a) The dispersion and the refractive index of the SiC micro-ring resonator waveguide. (b) The XPS spectrum of the non-stoichiometric SiC film.

Close modal

From the fitting parameters of the Sellmeier equation, the effective group index of the waveguide can be simulated by a commercial R-soft CAD, and the waveguide dispersion of the device is proportional to the secondary differential of the effective group index. The material dispersion of the SiC and the waveguide dispersion of the device are obtained as −254 and −959 ps nm−1 km−1 at 1550 nm, respectively. By combining the material dispersion and the waveguide dispersion to form the chromatic dispersion, the chromatic dispersion of the SiC micro-ring resonator waveguide is calculated as −1213 ps nm−1 km−1 at 1550 nm, as shown in Fig. 8(a). As a result, the negative chromatic dispersion for the SiC micro-ring resonator waveguide induces the positive group velocity delay with a value of 1546 ps2/km. By using an Mg K-line radiation x-ray photoelectron spectroscopy (XPS), the composition of the non-stoichiometric SiC was measured with the relative binding energy of C1s and Si2p orbital electrons at 101.6 and 284.0 eV, respectively. The atom ratio of the carbon and silicon content for the non-stoichiometric SiC is measured as 50.7% and 49.3%, respectively, with the corresponding molar factor of 1.03 as shown in Fig. 8(b).

To build up the 25 Gbps pumping system to generate a pulse stream, the programmable pattern generator (PPG) was used to produce a pulse stream with the pulsewidth of 40 ps, as shown in Fig. 9. The electrical pulse stream generated from PPG was amplified by an electrical amplifier (AMZ-40). The amplified pulse stream externally modulated the CW tunable laser to be an optical data stream via an MZM. To enhance the peak power of the pulse stream, an erbium-doped fiber amplifier (EDFA) was used to amplify the optical data stream. Because of the amplified spontaneous emission (ASE) of EDFA, the ASE noise degrades the signal-to-noise ratio (SNR) of the pumping data stream. Therefore, the optical bandpass filter (OBPF) was utilized to filter the noise of the pumping stream.

FIG. 9.

The pump–probe system for all-optical 25 Gbps nonlinear Kerr switching in the SiC-based micro-ring resonator waveguide.

FIG. 9.

The pump–probe system for all-optical 25 Gbps nonlinear Kerr switching in the SiC-based micro-ring resonator waveguide.

Close modal

To further amplify the peak power of the signal, a second-stage amplifier was employed to enhance the pumping pulse. The pumping pulse was polarized by polarization controllers (PCs) and a fiber-based in-line polarizer was used to decide the polarization direction of the device. Similar to the pumping pulse generator system, the CW probe was amplified by the EDFA and polarized by the PCs and an in-line polarizer. The pumping pulse stream and the CW probe were coupled by a 50/50 coupler and injected into the micro-ring resonator waveguide through a lensed fiber. Then, the pumping pulse stream was filtered by an OBPF to separate the modulated probe. The modulated probe was detected by a photodetector (Newport, Model 1014), and the received signal was left by a DC block to reduce the DC component. With the AC component of the signal amplified by an electrical amplifier (AMP, Picosecond 5882), the signal was analyzed by the sampling scope (Agilent, 83485). Finally, all-optical 25 Gbps data transmission is demonstrated by using a SiC micro-ring resonator waveguide.

At first, the basic parameters of the micro-ring resonator should be discussed. Figure 10 shows the TE- and TM-mode transmission spectra of the micro-ring resonator waveguide. With the asymmetric cross-section of the waveguide, the effective refractive indices of TE and TM modes are different. Because of the different effective refractive indices of the TE and TM modes, the TE- and TM-mode transmission dips have different free spectral ranges to make the TE- and TM-mode transmission dips separated on some wavelength and overlapped on the other wavelength. Therefore, the transmission spectrum of the micro-ring resonator waveguide with different polarizations should be, respectively, discussed. By fitting the TE-mode transmission spectrum, the effective refractive index, free spectral range, coupling factor, and magnification factor of the device with the gap spacing of 1300 nm are obtained as 1.875, 1.38 nm, 0.91, and 1.15, respectively, as listed in Table VIII. In addition, the linewidth of transmission dip is evaluated as 0.1506 nm to acquire the corresponding quality factor and mode extinction ratio (ER) of 10 500 and 10.7 dB, respectively. For the TM-mode transmission spectrum, the device possesses its effective refractive index, free spectral range, coupling factor, and magnification factor of 1.790, 1.43 nm, 0.89, and 1.73, respectively. Moreover, the quality factor and mode extinction ratio of the TM-mode transmission spectrum are calculated as 10 000 and 6.6 dB, respectively, by the linewidth of transmission dip of 0.1559 nm. From the above-mentioned result, this asymmetric structure of the micro-ring resonator waveguide prefers the TE-mode light.

FIG. 10.

The (a) TE- and (b) TM-mode transmission spectra of the SiC micro-ring resonator waveguide with gap spacing of 1300 nm.

FIG. 10.

The (a) TE- and (b) TM-mode transmission spectra of the SiC micro-ring resonator waveguide with gap spacing of 1300 nm.

Close modal
TABLE VIII.

The simulated parameters for the TE- and TM-mode transmission spectra of the SiC micro-ring resonator waveguide with gap spacing of 1300 nm.

Polarization modeTE-modeTM-mode
Gap spacing (nm) 1300 
N, group index 1.875 1.790 
ΔλFSR (nm) 1.38 1.43 
y, coupling factor 0.91 0.89 
M, magnification factor 1.15 1.73 
ΔλFWHM (nm) 0.150 6 0.155 9 
Q, quality factor 10 500 10 000 
MER, mode extinction ratio (dB) 10.7 6.6 
Polarization modeTE-modeTM-mode
Gap spacing (nm) 1300 
N, group index 1.875 1.790 
ΔλFSR (nm) 1.38 1.43 
y, coupling factor 0.91 0.89 
M, magnification factor 1.15 1.73 
ΔλFWHM (nm) 0.150 6 0.155 9 
Q, quality factor 10 500 10 000 
MER, mode extinction ratio (dB) 10.7 6.6 

To perform the 25 Gbps all-optical nonlinear Kerr switching, the Kerr modulation of a single-bit signal under different probe wavelengths from 1560.64 to 1560.88 nm is measured. The wavelength of the intensive pumping is set at a transmission dip of 1550.60 nm to make the pumping pulse resonate in the micro-ring resonator, which enhances the intensity to induce the nonlinear Kerr effect. With the refractive index variation of SiC, the transmission spectrum of the device is red-shifted due to the wavelength of the standing wave red-shifted by the lengthened effective optical path of the micro-ring resonator. Because of the red-shifted spectrum of the device, the probe can be converted by the pumping pulse when the probe wavelength is set at the shorter wavelength from the transmission dip. However, the probe is inverted by the pumping pulse when the probe wavelength is located at a longer wavelength from the transmission dip. With different probe wavelengths, the modulated probe has a different modulation depth because the probe has a different transmission variation under the same spectral shift. As a result, the maximal modulation depth of data conversion is produced at 1560.70 nm, and the maximal modulation depth of data inversion is located at 1560.82 nm. With different probe wavelengths, the data conversion and inversion can be demonstrated, as shown in Fig. 11. Under a peak power of 0.8 W to inject the device, the transmission spectrum of the SiC micro-ring resonator is red-shifted by 0.12 nm to obtain the transient refractive index change of 1.48 × 10−4, as shown in Figs. 11(b) and 11(c). According to the refractive index change of Δn = n2 × M × I with the M and I, respectively, denoting the magnification factor and the peak intensity, the n2 of the SiC micro-ring resonator can be obtained as 3.05 × 10−14 cm2/W.

FIG. 11.

(a) The Kerr modulation probe signal at different wavelengths. (b) The intensity of the Kerr modulated signal at different probe wavelengths. (c) The transmission comb red-shifted by an excessively intense pump pulse for the SiC micro-ring resonator.

FIG. 11.

(a) The Kerr modulation probe signal at different wavelengths. (b) The intensity of the Kerr modulated signal at different probe wavelengths. (c) The transmission comb red-shifted by an excessively intense pump pulse for the SiC micro-ring resonator.

Close modal

To demonstrate an all-optical modulator, the 25-Gbps pumping with the data stream of “01010010” is generated to induce the nonlinear Kerr effect in the SiC micro-ring resonator, as shown in Fig. 12(a). The peak power of the pumping is achieved at 0.8 W to make red-shift the transmission spectrum of the device. With the red-shifted spectrum following the pumping pulse stream, the CW probe can be modulated with the modulated stream of “01010010.” The probe wavelength is an important factor to determine the data conversion or inversion for the modulated probe signal.

FIG. 12.

The pumping pulse with the data stream of (a) “01010010” and (b) “01010110.” The probe stream at 1560.70 nm modulated by the pumping pulse with the data stream of (c) “01010010” and (d) “01010110.” The probe stream at 1560.82 nm modulated by the pumping pulse with the data stream of (e) “01010010” and (f) “01010010.”

FIG. 12.

The pumping pulse with the data stream of (a) “01010010” and (b) “01010110.” The probe stream at 1560.70 nm modulated by the pumping pulse with the data stream of (c) “01010010” and (d) “01010110.” The probe stream at 1560.82 nm modulated by the pumping pulse with the data stream of (e) “01010010” and (f) “01010010.”

Close modal

With the probe wavelength at 1560.70 nm, the CW probe can be modulated to a conversion data stream as a cross-wavelength data converter, as shown in Fig. 12(c). On the other hand, changing the probe wavelength to 1560.82 nm makes the modulated probe steam a data inversion as a cross-wavelength data inverter, as shown in Fig. 12(e). To observe the capability of modulation of the device, the other pumping pulse stream of “01010110” is produced, as shown in Fig. 12(b). With the pumping pulse stream of the “01010110,” the probe at 1560.70 nm can be converted to a modulated probe data stream of “01010110,” as shown in Fig. 12(d). The probe at 1560.82 can be modulated to “10101001” as a data inverter by the pumping pulse stream of “01010110,” as shown in Fig. 12(f). From the above-mentioned results, the SiC-based micro-ring resonator waveguide can be demonstrated as a 25 Gbps all-optical modulator with the PRZ-OOK data stream. The eye diagram of 25 Gbps all-optical nonlinear Kerr switching with PRZ-OOK data stream is shown in Fig. 13.

FIG. 13.

The eye diagrams of the 25 Gbps (a) data conversion and (b) data inversion.

FIG. 13.

The eye diagrams of the 25 Gbps (a) data conversion and (b) data inversion.

Close modal

From the eye diagram of data conversion, the SNR and ER are obtained as 5.6 and 11.8 dB, respectively, with the corresponding rising and falling times of 20.9 and 21.9 ps, respectively, as shown in Fig. 13(a). In addition, the 25 Gbps all-optical data inversion has an SNR of 4.8 dB and an ER of 10.2 dB with the rising and falling time of 20.9 and 21.2 ps, respectively, as shown in Fig. 13(b). The bit error ratio (BER) of the 25 Gbps all-optical data conversion and inversion by the micro-ring resonator waveguide is achieved at 2.52 × 10−6 and 1.13 × 10−5, respectively.

By summarizing the reported n2 of the group-IV semiconductor materials from previous studies, the n2 vs the operating wavelength is shown in Fig. 14 to demonstrate the possibility of all-optical modulations in silicon photonic applications. From Fig. 14, the most reported n2 of the group-IV semiconductor materials can be obtained 10−16 to 10−8 cm2/W in the range between 300 and 2000 nm to apply the telecommunication. For the crystalline and amorphous Si, the large refractive index needs a smaller device size to support single-mode operation. This phenomenon hardly injects the signal into the device and induces a larger coupling loss even though these materials demonstrate the large n2. However, the SiO2 material exhibits a low n2, insufficient for many practical applications. Therefore, the SiNx material is regarded as one of the most promising candidates to perform all-optical switching. In addition, the Si nanostructures also can improve the n2 of the group-IV semiconductor materials. Because the SiC material can combine with the III-V compound devices to employ silicon photonics, the SiC material has become popular in recent years. Moreover, the SiGe material has a smaller bandgap to usually demonstrate the nonlinear optical applications in near- and mid-infrared regions. To date, some preliminary works related to quantum computation and communication have been performed by using the nonlinear Kerr effect.193–199 In 2008, Azuma employed the nonlinear Kerr effect in a one-dimensional photonic crystal to demonstrate the nonlinear sign-shift quantum logic gate.193 In addition, Amiri et al. utilized the micro-ring resonator to generate the GHz soliton pulses via the nonlinear Kerr effect for the applications of the quantum repeater and quantum entangled photon source.194 In 2010, Yupapin used a Mach–Zehnder interferometer and a set of micro-ring resonators to construct the generalized quantum key distribution.196 The time delay and nonlinear Kerr effects in each micro-ring resonator can be induced for the qubit (quantum key) generation.196 In 2012, Shahidinejad et al. employed the micro-ring resonator to generate controlled chaotic signals. Then, these controlled chaotic signals passed through the polarizer beam splitter to generate the quantum binary codes.197 In 2016, Okawachi et al. further used a microresonator-based Kerr oscillator to generate the quantum random number.198 All these pioneered reports have exhibited the applicability of the micro-ring resonators for performing the optical quantum computation and communication through the nonlinear Kerr effect.

FIG. 14.

Benchmarks of the nonlinear refractive index vs wavelengths for group-IV semiconductor materials reported in previous studies.

FIG. 14.

Benchmarks of the nonlinear refractive index vs wavelengths for group-IV semiconductor materials reported in previous studies.

Close modal

Group-IV semiconductor compounds with intense optical nonlinearity have emerged as a new branch of all-optical processing materials benefiting from the manufacturing compatibility with silicon electronic and photonic integrated circuits. Due to the chemical reforming on the bonding or precipitating feature of the compositional atoms in the membrane matrix, either the orbital hybridization or the quantum self-assembly of interstitial composites can be employed to reform the electronic and optical characteristics. The recent development on enhancing the nonlinear refractive indices of the group-IV semiconductor materials has revealed significant progress to accelerate the all-optical switching logic, which greatly reduces the energy consumption to enable the constitution of the advanced multi-logic gating and the entry-level photonic computing circuits. This work not only overviews the group-IV semiconductor photonic data processing elements but also prospects for the future direction of optical quantum computation and communication. To date, the nonlinear refractive indices of the group-IV semiconductor materials can be obtained as 10−8 to 10−16 cm2/W in the range between 300 and 10 000 nm in 2022.

The wavelength conversion and data switching with bit rate beyond 25 Gbps have been achieved via nonlinear photonic waveguide components. The atom ratio of the carbon and silicon content for the non-stoichiometric SiC is measured as 50.7% and 49.3%, respectively, with the corresponding molar factor of 1.03. For the basic characteristics of the SiC micro-ring resonator waveguide, the negative chromatic dispersion induces the positive group velocity delay with a value of 1546 ps2/km. For the TE-mode transmission spectrum, the effective refractive index, free spectral range, coupling factor, and magnification factor of the SiC micro-ring resonator with the gap spacing of 1300 nm are obtained as 1.875, 1.38 nm, 0.91, and 1.15, respectively. For the TM-mode transmission spectrum, the device possesses its effective refractive index, free spectral range, coupling factor, and magnification factor of 1.790, 1.43 nm, 0.89, and 1.73, respectively. By taking the non-stoichiometric SiC-made micro-ring waveguide as an example, the n2 as high as 3.05 × 10−14 cm2/W of the resonant SiC micro-ring gate is retrieved from the pump–probe analysis. The eye-diagram of the wavelength converted data in the micro-ring achieves its signal-to-noise and on/off-extinction ratios (SNR and ER) of 5.6 and 11.8 dB, while up to 25-Gbps all-optical data-format inversion with 4.8-dB SNR and 10.2-dB ER is also performed during an ultrafast switching within rising and falling time of less than 22 ps. Such all-optical data processing including both wavelength switching and format conversion in the highly nonlinear optical SiC waveguide resonator can achieve error-free operation with corresponding bit-error-ratios of lower than 1 × 10−5 at 25 Gbps after forward error correction.

This work was supported by the Ministry of Science and Technology, Taiwan (Grant Nos. MOST 109-2221-E-002-184-MY3, MOST 110-2221-E-002-100-MY3, MOST 110-2124-M-A49-003-, MOST 110-2224-E-992-001-, and MOST 111-2119-M-002-009). Chih-Hsien Cheng was supported by the International Research Fellow of the Japan Society for the Promotion of Science [Postdoctoral Fellowships for Research in Japan (Standard), Grant No. 20F20374].

The authors have no conflicts to disclose.

Chih-Hsien Cheng: Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Cai-Syuan Fu: Data curation (lead); Formal analysis (lead); Investigation (lead); Writing – original draft (lead). Huai-Yung Wang: Data curation (supporting); Formal analysis (supporting). Sze Yun Set: Formal analysis (supporting). Shinji Yamashita: Formal analysis (supporting). Gong-Ru Lin: Conceptualization (lead); Data curation (supporting); Formal analysis (supporting); Funding acquisition (lead); Supervision (supporting); Writing – original draft (supporting); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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