Optical multicasting, which efficiently delivers a stream of information across various channels, plays a pivotal role in enhancing the reconfigurability and non-blocking capacity of future optical networks [1,2]. Its ability to convert data from parallel to serial formats also enables advanced optical computing [3–10] like the acceleration of convolutional computations within optical neural networks. Various physical dimensions of light, such as wavelength [11–15], spatial mode [16–19], and orbital angular momentum [20], have been demonstrated as information channels in optical multicasting. With the widespread application of wavelength division multiplexing (WDM) technology, wavelength multicasting has been extensively studied. Wavelength multicasting has been demonstrated based on different nonlinear processes like self-phase modulation (SPM) in a photonic-crystal fiber (PCF) [21], cross-phase modulation (XPM) in a silicon nanowire [22], cross-absorption modulation (XAM) in an electro absorption modulator (EAM) [23,24], and four-wave mixing (FWM) in nonlinear media [25,26]. Among these, FWM is considered one of the critical nonlinear effects for implementing wavelength multicasting, owing to its advantages in modulation format transparency and parallel processing. A six-channel wavelength multicasting of a 36 Gb/s 16-QAM optical signal based on FWM in a silicon waveguide has been reported [13]. In addition to silicon, various nonlinear material platforms, such as periodically poled lithium niobate (PPLN) [11] and AlGaAs [12], are utilized to achieve wavelength multicasting based on FWM. However, the scheme is limited by the incoherence of the pump lights, making it difficult to achieve wavelength multicasting across more wavelengths. By utilizing coherent pump lights, a 26-channel wavelength multicasting of a 10 Gb/s differential phase-shift keying (DPSK) optical signal has been demonstrated in both a highly nonlinear fiber (HNLF) and a silicon waveguide [14]. Thus, utilizing coherent light sources is a crucial approach to extending wavelength multicasting across a broader range of wavelengths. Mode is another significant physical dimension of light, and studies have also explored the mode multicasting of optical signals. Mode multicasting technologies are primarily divided into FWM methods [17,18] and power splitting methods [19]. FWM-based mode multicasting necessitates the design of waveguide dispersion to fulfill phase matching conditions across different modes at specific wavelengths, presenting challenges for broad bandwidth applications. A three-channel multi-mode multicasting based on FWM, featuring a 3 dB bandwidth of less than 1 nm, has been demonstrated in previous work [18]. Conversely, power-splitting-based mode multicasting is not constrained by phase matching requirements. A mode multicasting scheme based on tapered directional couplers can achieve three-channel mode multicasting at 1540–1560 nm [19].

With the development of Internet of Things (IoT) technologies, 5G and the upcoming 6G networks, artificial intelligence, and big data analytics, the capacity of optical networks is rapidly expanding. However, in the last decade single-mode fiber systems using WDM with coherent detection began to approach their theoretical capacity limits [27]. To satisfy the rapidly growing capacity demand of optical communication systems, mode division multiplexing (MDM) [16] has attracted worldwide research interests recently. Future optical networks utilizing mode and wavelength hybrid multiplexing require multidimensional multicasting technology, tasked with multicasting signals to specific modes and wavelengths. Recently, a five-channel multidimensional multicasting of 40 Gb/s QPSK in a passive multi-mode waveguide has been demonstrated [28]. However, the simultaneous utilization of wavelength and mode multicasting results in higher energy density within the multi-mode waveguide, thereby increasing nonlinear losses due to two-photon absorption (TPA) and free carrier absorption (FCA) [29], which ultimately makes it challenging to increase the total number of multicast channels. To overcome the limitations imposed by FCA, reverse-biased PIN junctions have been introduced in single-mode waveguides, enabling wavelength multicasting of 40 Gb/s OOK signals across seven channels [10]. Therefore, utilizing reverse-biased PIN junctions in multi-mode waveguides has the potential to reduce nonlinear losses, thereby significantly increasing the number of multicast channels by simultaneously multicasting in both modes and wavelengths.

In this study, we utilized a multi-mode PIN silicon waveguide and mode multiplexers to achieve multidimensional multicasting of an 80 Gb/s QPSK signal across 14 parallel channels: nine channels in the TE0 mode and five channels in the TE1 mode. Using reverse-biased PIN junctions to reduce nonlinear loss and enhance nonlinearity, the output power of the converted light after FWM in three modes, TE0, TE1, and TE2, can be increased by 13 dB, 11.7 dB, and 7.7 dB, respectively. Besides, we experimentally achieved nine-channel, seven-channel, and two-channel wavelength multicasting for TE0, TE1, and TE2 modes, respectively. Notably, all replicated signals demonstrated clear constellation diagrams and error-free performance (BER<3.8×10−3). This research presents a viable solution for multicasting in future mode-wavelength division multiplexing optical networks and responds to the growing demands for computational speeds by expanding the dimensions of multicasting channels.

The schematic diagram of simultaneous multicasting of modes and wavelengths using a multi-mode PIN silicon waveguide is illustrated in Fig. 1(a). The device consists of a 4.5 cm silicon waveguide with PIN junctions and two mode multiplexers based on directional couplers. The silicon waveguide with PIN junctions functions as the nonlinear medium for FWM. The mode multiplexers are utilized to convert TE0 mode into TE1 and TE2 modes, and to reconvert TE2 and TE1 modes back into TE0 mode. It was fabricated using 130 nm CMOS technology at the Chongqing United Microelectronics Center (CUMEC).

The input light, composed of three pump lights (blue) and the signal light (green), is divided into three paths by a coupler, each of which is then launched into different ports. Note that the pump lights used here are three comb teeth of a Kerr frequency comb generated by a SiN microring. As previously mentioned, this ensures coherence among the pump lights, thereby increasing the number of multicast channels and reducing the impact of pump noise on the quality of the multicast signals. Subsequently, the input light from different ports is coupled into the different modes of the multi-mode PIN silicon waveguide via a mode multiplexer [30–34]. Three signal lights are transmitted through the multi-mode PIN silicon waveguide, undergoing intramodal FWM with the pump lights, where the information carried by the signal lights is transferred to different wavelengths (i.e., the wavelength of the idler lights), enabling simultaneous multicasting in both mode and wavelength domains. Compared to wavelength multicasting in a single-mode waveguide, simultaneous multicasting of multiple modes in a multi-mode waveguide increases the pump power within the waveguide. Assuming equal pump power per mode compared to single-mode wavelength multicasting, the total pump power in the multi-mode waveguide will increase proportionally to the number of modes. This increase in pump power leads to greater nonlinear loss in the waveguide, thereby limiting the simultaneous multicasting of additional modes. To mitigate the nonlinear loss caused by the increased power, we apply PIN structures adjacent to the waveguide. By reverse-biasing the PIN junction, carriers generated by TPA in the waveguide can be swept away, thereby reducing FCA. As shown in Fig. 1(a), the output light, in addition to the pump lights and signal lights, includes replicas from 27 channels in total, comprising three different modes and nine different wavelengths. Each replica carries the information originally loaded onto the signal light. The incorporation of PIN structures adjacent to the multi-mode waveguide effectively mitigates nonlinear losses, enabling the simultaneous multicasting of multiple modes and wavelengths with improved FWM efficiency.

The principle of wavelength multicasting for each mode is shown in Fig. 1(b). In this process, the signal light Is and pump lights P1,2,3 undergo FWM, and produce replicas on nine wavelengths. The replicas are sequentially designated as MC1 to MC9, ordered by frequency from the lowest to the highest. Note that the number of replicas M increases with the number of pump lights N, satisfying the relationship M=4N−3 [21]. Consequently, M can be enhanced by adding more pump lights. The frequencies of different replicas are shown in the table in Fig. 1(b), where ωp1, ωp2, and ωp3 represent the frequencies of the three pump lights, and ωs represents the frequency of the signal light. The FWM process responsible for generating the replicas can be deduced from the frequencies of replicas. For example, the frequency of MC1 is 2ωp1−ωs, indicating that two photons from pump P1 are annihilated to generate one signal photon and one MC1 photon. For MC1, MC2, MC4, MC5, MC6, and MC9, only one FWM process is responsible for generating these replicas. Among these replicas, the phases of MC1, MC2, MC4, and MC5 are conjugated with the phase of the signal light, whereas the phases of MC6 and MC9 are identical to that of the signal light. The conversion efficiency of this FWM process is equal to Cγ2Pp12, where C is a constant, γ is the nonlinear coefficient of the silicon waveguide, and Pp1 is the power of P1. The conversion efficiency of these FWM processes is proportional to the power of the associated pump lights and the nonlinear coefficient. The frequency of MC2 is ωp1+ωp2−ωs, indicating that one photon from pump P1 and one photon from pump P2 are annihilated to generate one signal photon and one MC2 photon. Other FWM processes are similar to the generation of MC1 or MC2. On the other hand, there are two different FWM processes involved in the generation of replicas MC3. The same applies to replicas MC7 and MC8. The idler lights generated in two different FWM processes will interfere with each other. Take MC3 for example. The phases of the two idler lights are 2φp2−φs and φp1+φp3−φs, respectively. When the phase relationship between the pump lights satisfies 2mπ−π2<2φp2−φp1−φp3<2mπ+π2, the two idlers interfere constructively and successful multicasting to MC3 can be achieved. Such phase relationship between the pump lights must be satisfied and fixed over time. This requirement is met by the Kerr frequency comb used in this study; detailed device parameters for generating the Kerr frequency comb are provided in Section 3. We utilized the Lugiato–Lefever equation proposed in Ref. [35] to calculate the phase difference of the pump lights. Our simulation result revealed that the phase difference of the pump lights is fixed at around 38π, satisfying the constructive interference condition. Therefore, using the coherent pump can multicast the signal light from a single wavelength to nine wavelength channels through the FWM effect.

As the core unit of an FWM-based multidimensional multicasting chip, the PIN multi-mode waveguide needs to have high FWM conversion efficiency and low intermodal crosstalk. High conversion efficiency requires low loss and a high nonlinear coefficient. As the waveguide width increases, the influence of sidewall roughness on the optical field within the waveguide decreases, thereby reducing waveguide loss. However, widening the waveguide also enlarges the mode field area, which reduces the waveguide’s nonlinear coefficient. The design of low-loss nonlinear waveguides necessitates a trade-off between minimizing loss and maximizing the nonlinear coefficient. To select an appropriate waveguide width, we used simulation software Lumerical to simulate the variations of the nonlinearity coefficient and losses as a function of waveguide width. As illustrated in Fig. 2(a), we found that at a waveguide width of 1500 nm, the nonlinearity coefficient and losses of the waveguide are best balanced. As for the length of the waveguide, we have chosen an optimal waveguide length; increasing or shortening the waveguide length would result in a decrease in conversion efficiency. The relationship between waveguide length and conversion efficiency is determined by CE=γ2Leff2Pp2e−αL, where Leff=1−e−αLα represents the effective length of the waveguide, γ represents the nonlinearity coefficient, and α represents the waveguide loss. According to this formula, we can obtain the relationship between length and conversion efficiency depicted in Fig. 2(b). From the figure, it can be seen that when the length is chosen to be 4.5 cm, the waveguide achieves maximum FWM conversion efficiency. Moreover, the spacing between the doped regions in the PIN junction and the waveguide significantly influences loss, thereby affecting the efficiency of FWM. Reducing this spacing enhances the efficiency of PIN carrier sweep, thereby mitigating the nonlinear loss due to FCA. However, if the spacing between the doped regions and the waveguide becomes too narrow, it may increase waveguide loss. Consequently, after detailed theoretical analysis, we determined the optimal dimensions for the multi-mode PIN waveguide. The schematic diagram of the silicon waveguide cross-section is displayed in Fig. 1(c). Built on a 220 nm SOI platform, the ridge waveguide has a width of 1412 nm, and the etching depth of both the slab area and doping areas is 150 nm. Adjacent to the doping areas, two heavily doped areas serve as ohmic contacts, with the width of the heavily doped area being 2.5 μm. The distance between the doping areas and the ridge waveguide is 0.744 μm. The widths of the P and N regions are 0.3 μm. Additionally, Euler bends are employed to minimize the mode crosstalk in the bending parts of the multi-mode waveguide [36,37]. By carefully designing the curvature of bending waveguides, we have addressed the issue of high crosstalk and losses in multi-mode bending waveguides. This has yielded multi-mode waveguides characterized by a compact footprint, reduced transmission loss, and minimal modal crosstalk.

A mode multiplexer serves to convert lower-order modes into higher-order modes and consists of two directional couplers [30–34]. Optical signals of different modes are multiplexed through different ports, transmitted through multi-mode waveguides, and then demultiplexed to corresponding output ports. The first coupler, which converts the TE0 mode to the TE1 mode, consists of a single-mode narrow waveguide and an intermediate waveguide. The second coupler, which converts the TE0 mode to the TE2 mode, comprises a single-mode narrow waveguide and a wide waveguide. The widths of the waveguides in the coupling region are strategically designed based on phase matching conditions among different modes. That is, the propagation constants for the TE0 mode in the narrow waveguide, the TE1 mode in the intermediate waveguide, and the TE2 mode in the wide waveguide are closely aligned. To optimize mode conversion efficiency, the narrow waveguide is designed with a width of 400 nm, the intermediate waveguide with a width of 904 nm, and the primary component of the multi-mode waveguide spans 1412 nm. For more details, refer to our previous work [38]. The coupling distance and coupling length of the two couplers are 185 nm and 10.5 μm, respectively.

To test the effect of reverse-biased PIN junctions in reducing waveguide losses and enhancing waveguide nonlinearity, an experimental setup was constructed as shown in Fig. 3(a). For brevity, the polarization controllers (PCs) are not depicted, which are required to maximize the fiber to chip coupling efficiency in the actual experimental setup. Two lasers generate 1547 nm probe light and 1550 nm continuous wave light, which are then amplified by an EDFA before entering the 5:5 coupler. Subsequently, lights are coupled into the mode multiplexer through grating couplers. At the output, lights are also extracted by grating couplers and the output spectra are measured by an optical spectrum analyzer (OSA). It should be noted that lights are transmitted through the waveguide in TE0, TE1, and TE2 modes for the purpose of nonlinear efficiency characterization in this experiment. The probe light and continuous wave light undergo degenerate FWM, generating an idler light. The conversion efficiency of FWM is defined as the power ratio of the output idler light to the output probe light, characterizing the nonlinear efficiency of the waveguide.

Figure 3(c) illustrates the output spectra of TE0 mode, with the red and blue curves representing conditions with and without a 15 V reverse bias applied to the PIN junction, respectively. The figure demonstrates that applying a reverse bias voltage to the PIN junction increases the output power of the signal light by 6.6 dB; this effect is due to the reverse-biased PIN junction removing the carriers generated by TPA, which reduces nonlinear losses in the waveguide. As a result, the power of both the pump and signal within the nonlinear waveguide increases. Consequently, the power of the idler light generated by FWM has also increased. One can see that the output power of the TE0 idler light increased by 13.1 dB. To test the power increase of the idler light in the TE1 and TE2 modes, the input light was injected into the TE1 or TE2 port, and the output light was received at the corresponding output port. It was observed that the idler light power in the TE1 and TE2 modes increased by 11.7 dB and 7.7 dB, respectively. The FWM conversion efficiency for the TE0, TE1, and TE2 modes can reach as high as −10dB, −12.4dB, and −19.4dB, respectively. These findings indicate that a reverse-biased PIN junction enhances nonlinearity of the waveguide effectively. Figure 3(d) presents the measured conversion efficiency of the probe light in the TE0 mode across various wavelengths with and without a 15 V reverse bias applied to the PIN junction, revealing that the 3 dB bandwidth of FWM in the waveguide is approximately 17 nm and the reverse-biased PIN junction enhances FWM efficiency without significantly impacting the FWM bandwidth. Figure 3(b) illustrates the power of the output idler light in the TE0 mode as a function of reverse bias voltage for input probe light powers of 16 dBm, 18 dBm, 20 dBm, and 22 dBm. The leftmost point of each curve indicates when the PIN is in an open circuit state. The figure shows that the power of the output idler light increases with the reverse bias voltage. However, the increase in idler light power saturates after the reverse bias voltage reaches 5 V. Specifically, compared to the case without reverse bias, the output power of the idler light with a 5 V reverse bias voltage increases by 4.5 dB at an input probe power of 16 dBm, 7.7 dB at 18 dBm, 9 dB at 20 dBm, and 8.1 dB at 22 dBm.

Figure 3(e) displays the transmission spectra for different input-output combinations; for instance, TE0-TE0 represents the transmission from and to the TE0 port. It can be seen that crosstalk between TE0 and TE1 remains below 10 dB across most wavelengths except near 1545–1555 nm, enabling effective multi-mode FWM. Furthermore, it is noted that TE1-TE1 experiences additional losses near 1540–1560 nm, attributed to the larger mode area of the TE1 mode. This may due to several reasons including higher transmission losses in TE1 mode due to larger mode overlap with doping regions and side-wall scattering effects.

To verify the wavelength multicasting capability of the multi-mode PIN silicon waveguide, we multicast an 80 Gb/s QPSK signal light to different wavelengths through FWM with an optical frequency comb. In the current characterization, we multicast the TE0, TE1, and TE2 modes from a single wavelength to nine, seven, and two different wavelengths, respectively. Simultaneous multicasting results in two modes are presented in the next session.

Figure 4 presents a schematic diagram of the experimental setup for wavelength multicasting. An integrated microring resonator made by a silicon nitride platform at LIGENTEC is used to generate an optical frequency comb that serves as the wavelength multicasting pump light [39–44]. This microring resonator has a radius of 150 μm and a cross-section of 800nm×1650nm, which establishes a second-order dispersion coefficient of 93ps2/km at 1550 nm. The loaded quality (Q) factor of the microring resonator is approximately 5×105, and its free spectral range (FSR) is about 151 GHz. These parameters set the microring’s parametric oscillation threshold at 70 mW, with the primary comb spaced 12 FSRs from the pump light. A tunable laser generates a continuous light, which is amplified by an EDFA and passes through a WDM over the ITU C44–C49 channels to filter out the amplified spontaneous emission (ASE) noise outside of the passband. The continuous light then enters a Si3N4 microring to generate a Kerr frequency comb. Subsequently, three frequency comb teeth are filtered out by a band-pass filter to serve as wavelength multicasting pump lights. Therefore, the frequency spacing between adjacent pumps equals the FSR of the microring resonator. To ensure all the generated idlers are located in the C band, we selected the wavelength of the continuous light to be 1538.16 nm, positioning the primary comb wavelength at 1552.67 nm. Subsequently, we chose the primary comb and the two adjacent combs as the pump lights. These pump lights and an 80 Gb/s QPSK signal light generated by a QPSK transmitter are combined using a 5:5 coupler and then coupled from fiber to chip via grating couplers. As depicted in Fig. 4(b), the input spectrum includes P1, P2, and P3 as the pump lights at 1551.43 nm, 1552.64 nm, and 1553.87 nm, respectively, alongside the 80 Gb/s QPSK signal Is at 1558.17 nm to ensure that the replicas do not interfere with others or the pump lights. The input light passes through the silicon waveguide, and the output light is extracted at the grating coupler that demultiplexes the same mode as the grating coupler used at the input port. The output light is split by a 9:1 coupler, where 90% of this output, after passing through a tunable band-pass filter, an attenuator (ATT), and a low-noise EDFA, is channeled into an optical modulation analyzer (OMA) to assess signal quality. The remaining 10% is analyzed using an OSA to measure the spectrum of the output light.

Figures 5(a)–5(c) present the output light spectra across different modes. Specifically, Fig. 5(a) illustrates the output spectrum of the TE0 mode, signifying that the input light is coupled into the TE0 port and extracted from the output port that demultiplexes the TE0 mode. The spectrum clearly demonstrates that the QPSK signal is replicated across nine distinct wavelengths, i.e., 1544.8 nm, 1546 nm, 1547.22 nm, 1548.43 nm, 1549.62 nm, 1555.7 nm, 1556.94 nm, 1559.4 nm, and 1560.64 nm. These replicas are designated as MC1 to MC9, respectively. The conversion efficiencies for these replicas, defined as the ratio of the replicas’ output power to the output signal light power, are −35.1dB, −25.8dB, −24.6dB, −22.1dB, −32.2dB, −28dB, −23.7dB, −23.3dB, and −28.5dB for MC1 to MC9, respectively. Note that the differences in the conversion efficiencies of replicas are primarily attributed to differences in pump light powers. Since P2 is a primary comb of a Kerr frequency comb, while P1 and P3 are secondary combs, the power of P2 is approximately 10 dB higher than that of the other two pump lights, as shown in Fig. 4(b). As previously explained, the conversion efficiency of replicas is proportional to the power of the associated pump lights. For instance, the conversion efficiencies of MC1 and MC2 are −35.1dB and −25.8dB, respectively, resulting in a 10 dB difference in conversion efficiencies due to the 10 dB difference in pump light power. The difference in conversion efficiency, caused by the power differences among the pump lights, leads to notably lower signal quality in MC1 compared to MC2. By using pump lights with the same power, the gap in conversion efficiency between channels can be reduced, thus improving the performance of our system. The constellation diagrams for QPSK signals from various replicas are displayed by the insets of the figure. Notably, MC2, MC3, MC4, MC7, and MC8, which exhibit higher conversion efficiencies, demonstrate superior signal quality with densely packed sampling points, although all replicas effectively replicate the signal light. Figure 5(b) presents the output spectrum for the TE1 mode. The conversion efficiencies for MC1 to MC9 are as follows: −39dB, −28dB, −23.2dB, −24.6dB, −36.6dB, −31.4dB, −20.3dB, −20.2dB, and −31.9dB, respectively. The constellation diagrams for MC2, MC3, MC4, MC6, MC7, MC8, and MC9 in the TE1 mode have been recorded. In the TE2 mode, as illustrated in Fig. 5(c), the conversion efficiencies for MC2 to MC4 and MC6 to MC9 are as follows: −31.1dB, −31.7dB, −29.5dB, −36.6dB, −30.4dB, −30.4dB, and −37.1dB. However, only the constellation diagrams for MC7 and MC8 are provided. This limitation is mainly attributed to the overall low conversion efficiency in TE2 mode, as well as increased doping-related losses within the 1540–1555 nm range, as previously mentioned. Figure 5(d) shows the error vector magnitude (EVM) of different replicas, with the red/blue/yellow points representing the TE0/TE1/TE2 modes, respectively.

Figures 6(a) and 6(b) show the BER curves for QPSK signals in different replicas of the TE0 and TE1 modes, respectively, with the points representing experimental data and the curves being fitting lines. It can be seen that for TE0 mode the replicas MC2, MC3, MC4, MC7, and MC8 exhibit lower bit error rates and power penalty due to higher conversion efficiencies. The measured power penalty of these replicas is less than 2 dB for TE0 mode and less than 4 dB for TE1 mode at a BER of 10−4.

Building on the separate wavelength multicasting of the three modes, we conducted further experiments to verify the simultaneous multicasting of two modes across 14 channels using the proposed PIN multi-mode waveguide. The experimental setup is similar to the one shown in Fig. 4(a), with an additional 5:5 splitter connected after the initial 5:5 splitter. The spectra from both output ports of the second splitter are depicted in Fig. 4(b). One output is directly connected to the TE0 port of the chip, while the other output is connected to the TE1 port via a 1 km SMF. The SMF is used to decohere the two paths. As shown in Fig. 4(b), the input light was introduced simultaneously from both the TE0 and TE1 ports. After traversing the waveguide, the signal light in the TE0 and TE1 modes was replicated into nine distinct channels, measured at the corresponding demultiplexing port. The signal quality of the replicated light across different channels is presented in Fig. 7, showing simultaneous multicasting within the TE0 and TE1 modes of the waveguide. Figure 7(a) exhibits the EVM and constellation diagrams for the multicast signal in TE0 and TE1 modes, at a received signal power level of −33dBm. The figure reveals that the signal light in the TE0 mode is multicast into nine channels, with channel wavelengths matching those during single-mode multicasting. Owing to previously mentioned variations in pump power, the EVM in channels MC2, MC3, MC4, MC7, and MC8 is relatively lower. For the TE1 mode, the signal was converted from a single wavelength to five distinct wavelengths, with the EVM and eye diagram quality demonstrating comparable performance across all the five channels. Figure 7(b) displays the BER for the multicast signal of the TE0 and TE1 modes at different wavelengths, at a received signal power level of −33dBm. Similar to the EVM, BER in MC2, MC3, MC4, MC7, and MC8 is relatively lower compared to other channels, and within the same wavelength, the error rate in TE0 mode is lower than that in TE1 mode. However, the error rates for all replicas below 3.8×10−3 have been demonstrated, indicating that we have successfully conducted simultaneous multicasting of an 80 Gb/s QPSK signal for 14 channels in two modes. Compared with multicasting separately in each mode, the channel number that has been successfully broadcasted in TE1 mode when multicast in TE0 mode simultaneously reduces to two due to the mode crosstalk shown in Fig. 3(e). Actually, to reduce the impact of mode crosstalk, 1 km SMF is added to de-correlate two modes, as described earlier. Although Euler bends have been used to reduce mode crosstalk at the bending region, fabrication errors in the mode multiplexer and demuliplexer are inevitable and might deteriorate mode crosstalk performances. Improvement can be expected with more robust device design [45].

Multidimensional optical multicasting using FWM in multi-mode PIN silicon waveguides has been experimentally demonstrated. To further highlight the originality of our work, we compare our work with other relevant studies. According to Table 1, most previous multicasting work based on nonlinear processes usually multicasts signals in a single mode. The effort to multicast signals of two modes was constrained by FCA, limiting the number of channels to only 10. Our work, benefiting from the use of a PIN junction to mitigate the impact of the FCA and thereby improve the FWM efficiency, can achieve an FWM efficiency of −10dB for the TE0 mode. This enables the multicasting of three different modes, with up to 18 channels in total being multicast. There is significant application potential in the fields of optical communication and optical computing for the future.Table. 1.

Comparison of Key Parameters between This Work and Other Multicast Works

Apart from improving the performance of optical networks, the proposed multidimensional multicasting scheme has the potential to significantly enhance the computational power of optical computing systems. By increasing the number of spatial channels, this scheme can substantially improve the parallelism of computational data channels [3,5,10]. For example, in the optical convolution computing system shown in Fig. 8, duplicating the data information into two different modes enables 6-bit convolution computation across three wavelengths. This scheme leverages the spatial mode dimension of light, doubling the number of multicast channels and improving spectral efficiency.

The optical vector convolutional accelerator (VCA) principle based on this multicasting scheme is illustrated in Fig. 8. It primarily utilizes the multidimensional multicast chip for information duplication, combined with dispersion delay to perform convolution computation. Data input at a single wavelength is multicast to three wavelengths in TE0 and TE1 modes using the proposed multidimensional multicast chip. Different colored replicated light represents various wavelength channels, while different mode field distributions signify distinct spatial modes. After multicasting, the replicas are modulated by wave shapers according to kernel weights, with the kernel weights’ dimension equaling the number of channels. The data in the TE0 mode passes through a delay line, creating a time interval with the data in the TE1 mode that is three times the single-bit period. This multiple equals the number of wavelength channels. These weighted replicas are delayed by dispersion, with the delay step between adjacent channels corresponding to the cycle time. Note that the dispersion elements are placed before MDM to avoid mode-dependent dispersion. Finally, high-speed photodetection sums the delayed and weighted replicas to obtain the convolution result between the input data and kernel weights.

Therefore, compared to multicasting schemes that utilize only the wavelength dimension, the multidimensional multicasting that simultaneously processes signals in both mode and wavelength dimensions can increase the number of computational channels, thereby enhancing the computational power of the VCA. Furthermore, due to the utilization of the mode dimension, which enables the use of delay lines to introduce delays, the requirements for the dispersion component in this scheme are reduced. Consequently, increasing the number of multiplexing modes in the multidimensional multicast chip through multidimensional multicasting technology provides new approaches and pathways for enhancing the computational power of optical computing systems, such as the VCA.

In summary, we propose a multidimensional multicasting scheme that uses simultaneous mode and wavelength multicasting with FWM in multi-mode PIN silicon waveguides. The feasibility of this approach has been experimentally confirmed, demonstrated by a multidimensional multicasting strategy to simultaneously multicast an 80 Gb/s QPSK signal across 14 channels in both mode and wavelength. Further addressing and mitigating the issues of loss and crosstalk may further elevate the limit of nonlinear waveguides with respect to multicasting capabilities. The signals of all 14 channels, nine channels in the TE0 mode and five channels in the TE1 mode, have clear constellation diagrams. These achievements are enabled by introducing a reverse-biased PIN junction in the multi-mode waveguide to reduce nonlinear loss and carefully balancing design restrictions among linear loss, dispersion, nonlinear coefficient, as well as modal crosstalk. Attributed to the multi-mode PIN silicon waveguide, the 80 Gb/s QPSK signal can multicast in three modes, TE0, TE1, and TE2, and from only one wavelength channel to nine, seven, and two wavelength channels, respectively. All channels demonstrated clear constellation diagrams and BER performance below 3.8×10−3. This multidimensional multicasting is of significant importance for future applications in mode division multiplexing optical networks and advanced optical computing.