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Abstract
We propose an on-chip mode division (de)multiplexer based on asymmetric directional couplers (ADCs) for multi-band operation. In mode-coupling process, the minimum coupling length is wavelength-dependent. The longer the wavelength is, the shorter the minimum coupling length is. A light of longer wavelength can be coupled back and forth multiple times with a total coupling length which equals to the minimum coupling length of a shorter wavelength light, thus realizing multi-band transmission at different wavelengths. As a proof-of-concept experiment, a four-mode (de)multiplexer for joint operation in the C- and O-Bands is designed and experimentally demonstrated. For the four modes (TE0, TE1, TE2 and TE3), the measured insertion losses (ILs) and crosstalk (CT) of the (de)multiplexer are < 4.7 dB and < −10.1 dB respectively from 1290 nm to 1360 nm, and they are < 3.5 dB and < −11.8 dB respectively from 1510 nm to 1580 nm.
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1. Introduction
Driven by the exponential growth of the data traffic, it is highly desired to further scale the transmission capacity of photonic integrated circuits (PICs) by employing multiplexing technologies, such as wavelength division multiplexing (WDM) [1,2], mode division multiplexing (MDM) [3–7] and polarization division multiplexing (PDM) [8]. WDM is the most widely used multiplexing technology, while it needs precise wavelength calibration. Recently, as a promising approach, MDM has attracted great interest and it is capable of scaling the transmission capacity by employing orthogonal modes to multiplex optical signals. In addition, MDM technology can be combined with WDM for capacity scaling [9–14].
Mode (de)multiplexers are the key components for MDM systems on silicon-on-insulator (SOI) platforms [15,16]. There are various approaches to achieve on-chip MDM, such as asymmetric directional couplers (ADCs) [17–20], multimode interference (MMI) couplers [21–24] and Y-junctions [25–27]. Mode (de)multiplexers based on MMIs and Y-junctions have broad operation bandwidths and good fabrication tolerances, while the scalabilities of the devices are limited [24,27]. On the other hand, mode (de)multiplexers based on the ADC architecture can achieve high-order mode multiplexing, while the bandwidths are limited due to the stringent phase matching conditions.
Efforts have been put to realize broadband mode (de)multiplexers with good scalabilities. Researchers have successfully achieved a wide operation bandwidth over 100 nm by using a tapered adiabatic directional coupler [17,18]. In addition, a subwavelength waveguide-based ADC is demonstrated with a wide bandwidth of 120 nm due to the reduced confinement of the field and dispersion [19]. These works effectively scale the bandwidth of the ADC-based mode (de)multiplexer. However, most of these ADCs work exclusively on single wavelength band and fail to operate at two or more widely separated bands, which limit their applications towards future multi-band optical systems. For instance, in passive optical network (PON), upstream wavelength and downstream wavelength usually locate at different wavelength bands to minimize the cost and avoid dispersion compensation [28]. Thus, it is useful to design a mode (de)multiplexer which can operate at different wavelength bands to increase the channel counts of PON systems. To the best of our knowledge, there was only one report on a dual-band (O- and C-bands) (de)multiplexer with two-mode multiplexing using tapered ADCs [20].
In this paper, we propose an on-chip four-mode (de)multiplexer for multi-band operation based on ADCs. It is shown that if the length of the coupling area of an ADC is properly designed, the ADC can realize high transmission efficiency at multi-bands. The basic principle is illustrated as follows: in mode-coupling process, the minimum coupling length is wavelength-dependent. The longer the wavelength is, the shorter the minimum coupling length is. A light of longer wavelength can be coupled back and forth multiple times with a total coupling length which equals to the minimum coupling length of a shorter-wavelength light, thus realizing multi-band transmission at different wavelengths. As a proof-of-concept experiment, we design and experimentally demonstrate the four-mode (de)multiplexer that can operate at both the C- and O-Bands. The measured insertion losses (ILs) and crosstalk (CT) of the (de)multiplexer are less than 4.7 dB and −10 dB respectively, in the wavelength range from 1290 nm to 1360 nm for TE0, TE1, TE2 and TE3 modes. Similarly, the ILs and CT of the (de)multiplexer are lower than 3.2 dB and −11.8 dB, respectively, from 1510 nm to 1580 nm for all the four modes.
2. Principle
In coupled-mode theory (CMT), the fundamental mode in the access waveguide can be coupled to a high-order mode in a bus waveguide when the phase matching condition is satisfied, which can be expressed as:
where nTE0_access and nTEi_bus are the effective refractive indices of the fundamental mode in the access waveguide and the i-th order mode in the bus waveguide, respectively. The effective index of the guided mode is related to the geometry of the waveguide. The thickness of the waveguide is usually fixed to 220 nm for a commercial SOI wafer. For a given width of access waveguide (waccess = 350 nm in this case), the dimension of the bus waveguide is fixed in order to satisfy the phase matching condition. However, the effective refractive index of the guided mode varies with the operating wavelength. It means that the width of the bus waveguide needs to be changed when the operating wavelength varies which limits the bandwidth of the ADC. Table 1 shows the calculated bus waveguide widths for different modes to couple with a 350-nm-width access waveguide at λ1 = 1310 nm and λ2 = 1550 nm, respectively. It can be noted that the optimal waveguide widths for the two wavelengths are different but the deviation is minor. We set the width of the bus waveguide between the optimal widths for 1310 nm and 1550 nm. Thus, the designed ADC can realize the mode coupling at both wavelengths at the cost of an acceptable performance degradation.
Table 1. Calculated optimal widths (nm) of the bus waveguide for TE1∼TE4 modesa
The coupling length is the main factor that affects the operation bandwidth of the ADC. In CMT, the mode coupling can be a periodic phenomenon which means that the light will be periodically coupled back and forth between the access waveguide and the bus waveguide. The optimal coupling length Lc is not unique which is denoted by [29]:
In a conventional ADC, light is usually coupled from the access waveguide to the bus waveguide in the first period (m = 0) to minimize the footprint of the device. If we do not limit the length of the device, it may happen that a light of one wavelength can be coupled from the access waveguide to the bus waveguide with m = m1 and another light of a different wavelength can show different periods (m = m2) over the same total length:
where Lc1 and Lc2 are the total coupling lengths for two different wavelengths, L01 and L02 are minimum coupling lengths for the two wavelengths, m1 and m2 are the numbers of periods. If there are m1 and m2 values that satisfy Eq. (5), the designed ADC can operate at two wavelengths, consequently increasing the available operation band of the ADC at the cost of increased length of the device. Using the method, we design a four-mode (de)multiplexer operating at both C- and O-bands as shown in the following.3. Design and simulation
In this work, we choose λ1 = 1310 nm and λ2 = 1550 nm as the operating wavelengths because the two wavelengths are widely used in optical communication systems [30]. The structure of the designed ADC for TE1 mode is illustrated in Fig. 1. The width of the access waveguide is narrower than a conventional single-mode waveguide, which helps to strengthen the coupling and shorten the coupling length [14]. The gap between the access waveguide and the bus waveguide is set to be 100 nm. The widths of the bus waveguide for TE1, TE2 and TE3 modes are set to be 730 nm, 1100 nm and 1500 nm, respectively, referring to Table 1.
Take the design of the ADC for TE1 mode as an example. The following simulations and optimizations are carried out by Lumerical FDTD solutions. The simulated coupling lengths L01 for 1310 nm and L02 for 1550 nm are 13.2 µm and 4.9 µm, respectively. If m1 = 0 and m2 = 1, Eq. (5) can be approximately satisfied. In other words, the light at 1550-nm wavelength can be coupled to the bus waveguide during the second period and the light at 1310-nm wavelength can be coupled to the bus waveguide in the first period as shown in Fig. 2(a) and (b). Therefore, the coupling length Lc of the ADC is set to be 13.5 µm. The simulated transmission response of the designed ADC is shown in the Fig. 3(a). We can notice that there are two obvious peaks in the transmission spectrum which prove the feasibility of the ADC for multi-band operation. At λ1 = 1310 nm and λ2 = 1550 nm, the ILs are 0.35 and 1.02 dB, respectively. Figure 3(a) illustrates that the transmission efficiency is not high and the bandwidth is limited around λ2 = 1550 nm because the coupling length Lc is not the optimal for the wavelengths around 1550 nm. In order to further improve the performance, we taper the access waveguide and the bus waveguide and the simulated transmission spectrum is shown in Fig. 3(b). At λ1 = 1310 nm and λ2 = 1550 nm, the ILs are 0.64 and 0.72 dB, respectively. The bandwidth increases greatly around λ1 = 1310 nm and λ2 = 1550 nm. The light around λ1 = 1310 nm cannot be coupled back due to the phase mismatch resulting from the counter-tapered ADC [17], leading to a broader bandwidth. The coupling strength of the light around λ2 = 1550 nm is stronger than that of the light around λ1 = 1310 nm so the light around λ2 = 1550 nm can still be periodically coupled between the waveguides. The counter-tapered ADC can relax the phase matching condition for the light around λ2 = 1550 nm and make the light easier to be coupled to the bus waveguide.
Fig. 2. Simulated power distributions of the counter-tapered ADC for (a) TE1 mode at λ1 = 1310 nm, (b) TE1 mode at λ2 = 1550 nm, (c) TE2 mode at λ1 = 1310 nm, (d) TE2 mode at λ2 = 1550 nm, (e) TE3 mode at λ1 = 1310 nm, (f) TE3 mode at λ2 = 1550 nm.
Fig. 3. Simulated transmission spectra of (a) the conventional ADC for TE1 mode, (b) the designed ADC for TE1 mode, (c) the designed ADC for TE2 mode, (d) the designed ADC for TE3 mode.
According to this method, we also design the ADCs for TE2 and TE3 modes, respectively. The simulated power distributions of the designed ADCs are shown in Fig. 2 and the simulated transmission spectra are shown in Fig. 3(c) and (d), respectively. The ILs are 0.59 dB and 0.78 dB for TE2 mode and the ILs are 0.80 dB and 0.75 dB for TE3 mode at λ1 = 1310 nm and λ2 = 1550 nm. During the design and simulation process, we find that the transmission around λ2 = 1550 nm can be improved by accurately extending the length of the device to the coupling length Lc when m2 = 2, which means that the light at 1550-nm wavelength can be coupled to the bus waveguide during the third period, as shown in Fig. 2(d) and (f). And the transmission around λ1 = 1310 nm can also be improved by extending the length of the device due to the counter-tapered ADC structure. The parameters of the designed ADCs are shown in Table 2.
Table 2. Parameters of the designed ADCs for TE1, TE2 and TE3 modes
To investigate the fabrication-error tolerance of the proposed ADC, transmission spectra of the ADC for TE1 mode with different waveguide widths and coupling gaps are shown in Fig. 4. The simulation results show that the ILs are < 2.33 dB and the CT values are < −19.2 dB in the two wavelength ranges (1290 nm∼1360 nm & 1510 nm∼1580 nm) with the variation of the waveguide width by ±10 nm and ±20 nm. And the ILs are < 2.62 dB and the CT values are < −18.4 dB in the two wavelength ranges if the coupling gap varies by ±10 nm and ±20 nm. In summary, the proposed ADCs exhibit a good fabrication-error tolerance. Fabrication errors are major challenges for achieving integrated photonic devices with stable performances. While one can mitigate the fabrication variation effects by means of post-fabrication adjustments, such as post-fabrication trimming [31–33] to enhance the performance of the fabricated device.
Fig. 4. Simulated transmission spectra of the designed ADCs for TE1 mode with variations in (a) the access and the bus waveguide widths ΔW and (b) the coupling gap Δg. Dashed lines indicate crosstalk.
4. Fabrication and characterization
In the experiment, two identical four-mode (de)multiplexers operating at both C- and O-bands were fabricated on an SOI wafer with a 220-nm silicon layer on top of a 3-µm silica bottom layer. The structures and grating couplers were patterned by e-beam lithography (Vistec EBPG 5200+) and fully etched by inductively coupled plasma (ICP) etching. Then, a 1-µm SiO2 cladding layer was deposited by plasma-enhanced chemical vapor deposition (PECVD, Oxford). The microscope images and SEM images of the fabricate device are shown in Fig. 5. Due to the limited bandwidths of the grating couplers, we designed identical mode (de)multiplexers on the same chip with O-band and C-band grating couplers, respectively, to characterize the performance of the device. Accordingly, two tunable continuous wave (CW) laser (Keysight 81960A & Santec TSL-550) were used as C-band and O-band light sources, respectively. An optical power meter (Keysight N7744A) was used to characterize the devices.
Fig. 5. Microscope images of the four-mode (de)multiplexers with (a) C-band grating couplers and (b) O-band grating couplers, (c)-(e) SEM images of the coupling areas for TE1-TE3, respectively.
Figure 6(a)-(d) show the measured transmission spectra at four output ports (TE0∼TE3) of the mode (de)multiplexers when the O-band signal is launched from the TE0, TE1, TE2 and TE3 input ports, respectively. Figure 6(e)-(h) show the measured transmission spectra at four output ports (TE0∼TE3) of the mode (de)multiplexers when the C-band light is launched from TE0, TE1, TE2 and TE3 input port, respectively. The measured transmission spectra are normalized to the same grating couplers fabricated on the same wafer. As shown in Fig. 6(a)-(d), the ILs are < 1.2 dB, 3.8 dB, 2.7 dB and 4.7 dB and the CT values are < −15.6 dB, −10.9 dB, −12.0 dB and −10.1 dB in the wavelength range of 1290 nm ∼ 1360 nm for TE0∼TE3 mode channels. As shown in Fig. 6(e)-(h), the ILs are < 0.9 dB, 2.3 dB, 3.5 dB and 3.2 dB and the CT values are < −20.0 dB, −14.7 dB, −12.6 dB and −11.8 dB in the wavelength range of 1510 nm ∼ 1580 nm for TE0∼TE3 mode channels, respectively. In Fig. 3, the simulation results show that the ILs are < 1.01 dB and the CT values are < −19.5 dB from 1290 nm to 1360 nm for all four mode channels. The ILs are < 2.28 dB and the CT values are < −13.4 dB from 1510 nm to 1580 nm for four mode channels, respectively. The measured results are in good agreement with the simulation results in the wavelength range from 1510 nm to 1580 nm. From 1290 nm to 1360 nm, the measured results deteriorate obviously compared with the simulation results which can be contributed to the waveguide dimension deviation caused by fabrication errors.
Fig. 6. Measured transmission spectra at the four output ports of the mode demultiplexers when O-band light is launched from input port (a) TE0, (b) TE1, (c) TE2, (d) TE3 and when C-band light is launched from input port (e) TE0, (f) TE1, (g) TE2, (h) TE3.
Finally, Table 3 summarizes the performances of several recently reported four-mode (de)multiplexers. Our proposed structure shows the widest operation bandwidth with reasonable insertion loss, crosstalk, and footprint out of four-mode on-chip (de)multiplexers.
Table 3. Comparison of the reported four-mode (de)multiplexers
5. Conclusion
In conclusion, we proposed and experimentally demonstrated an on-chip mode division (de)multiplexer for multi-band operation. The (de)multiplexer leverages the periodicity of the mode coupling to realize high transmission efficiency at separated bands. In addition, the (de)multiplexer uses the counter-tapered ADC to improve the transmission efficiency and bandwidth. The measured results show that the CT values are below −10.1 dB from 1290 nm to 1360 nm and less than −11.8 dB from 1510 nm to 1580 nm for four mode channels covering C-band, most part of the O-band and small portions of S- and L-bands. The total measured bandwidth of the (de)multiplexer is 140 nm with an IL of < 4.7 dB and a CT of < −10.1 dB. The designed ADC is expected to be further extended to higher orders.
Funding
National Natural Science Foundation of China (61835008, 61860206001).
Acknowledgment
We thank the Center for Advanced Electronic Materials and Devices (AEMD) of Shanghai Jiao Tong University for the support in device fabrications.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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