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Abstract
We propose and experimentally demonstrate an ultrabroadband and compact 2 × 2 3-dB coupler based on the trapezoidal subwavelength gratings (SWGs). The adiabatic coupling is achieved between a trapezoidal SWG waveguide and a reversely tapered strip waveguide, which contributes to the ultrabroad operation bandwidth and the compact footprint of the coupler. Numerical results prove that our device has a power splitting imbalance of < ± 0.5 dB and an excess loss of < 0.2 dB in the ultrabroad bandwidth of 300 nm from 1400 nm to 1700nm, with a coupling length of 4.4 µm and a total length of 24.4 µm. The fabricated device is characterized in a 270-nm bandwidth from 1400 nm to 1670 nm, showing a measured power splitting imbalance of < ± 0.7 dB and an excess loss of < 0.5 dB.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silicon photonics on the silicon-on-insulator (SOI) platform has attracted considerable research interest in the past decade for its possibility of realizing compact and cost-effective photonic integrated circuits (PICs) with CMOS-compatible processing [1]. Optical power splitters are an essential component of PICs for splitting and combining optical signals, which has various applications in multiplexing systems, optical modulators, optical switches and optical signal processors [2–5]. Directional couplers (DCs) [6] and multimode interference (MMI) couplers [7,8] are widely used as 2 × 2 3-dB couplers on the SOI platform. However, the wavelength sensitivity or the large footprint of these devices hinders their usage in ultrabroadband and densely integrated optical communication systems. Therefore, there is a high demand for compact 2 × 2 3-dB couplers with broader bandwidths, low excess losses (ELs) and imbalances.
Several approaches have been proposed to expand the operation bandwidths of 3-dB couplers, such as adiabatic DCs [9–12], asymmetric DCs (ADCs) [13–15] and subwavelength grating (SWG) assisted DCs [16–22]. Adiabatic DCs are usually insensitive to wavelength variation, but long device lengths are required to preserve the adiabaticity. A short length of 11.7 µm can be achieved in adiabatic DCs using shortcuts to adiabaticity (STA) protocols, but at the cost of a narrower bandwidth of only 75 nm and a power splitting imbalance of ± 1 dB [11]. ADCs can have compact footprints and broad bandwidths thanks to the phase matching between two waveguides of different widths [13,15]. However, the performance is very sensitive to the variations in waveguide and gap widths. Recently, SWGs have emerged as a promising approach to tailoring the refractive indices and engineering the dispersion properties of photonic devices [23,24]. The SWG assisted DCs have been proved to have broad bandwidths as well as short coupling lengths [19–21]. Moreover, the gradient index (GRIN) waveguides can be constructed by using non-uniform SWGs such as trapezoidal SWGs and paraboloidal SWGs [25–30]. For example, the slowly varying trapezoidal SWGs have been employed to implement ultrabroadband power coupling and mode-order conversion within a coupling length of only 12.5 µm, indicating that the trapezoidal SWG based structures show great potential for expanding the bandwidth while shrinking the device size [30].
In this work, we propose and experimentally demonstrate an ultrabroadband and compact 2 × 2 3-dB coupler based on the trapezoidal SWGs working for the fundamental transverse electric (TE) mode. It consists of a gradually varying trapezoidal SWG waveguide coupled to a reversely tapered strip waveguide. The coupling strength varying along the propagation direction reduces the wavelength sensitivity and therefore broadens the bandwidth of the proposed device [13]. Besides, the coupling strength is enhanced due to the modified mode profile in the GRIN waveguide constructed by the trapezoidal SWGs. As a result, the proposed coupler is very compact, having a coupling length of only 4.4 µm and a total length of 24.4 µm. Numerical results prove that our device shows an ultrabroad bandwidth of 300 nm ranging from 1400 nm to 1700nm, with a power splitting imbalance of < ± 0.5 dB and an EL of < 0.2 dB. We have also experimentally demonstrated that the fabricated 3-dB coupler performs well in the wavelength range from 1400 nm to 1670 nm, achieving a measured power splitting ratio within 3 ± 0.7 dB and an EL less than 0.5 dB. To the best of our knowledge, our work has the broadest bandwidth and the shortest coupling length at the same time among the silicon-based 2 × 2 3-dB couplers demonstrated in experiments so far.
2. Structure and design
The 3-dB coupler is designed based on a SOI wafer with a 220-nm-thick silicon top layer, a 3-µm-thick buried oxide layer and a 1-µm-thick silica upper cladding layer, as shown in Fig. 1. It contains three regions in which all the SWGs share the same period Λ [see Fig. 1(a)]. In Region I, a S-bend constitutes the upper branch with a lateral length of Ls and its width linearly tapered from w4 to w1. A transition taper is used in the lower branch to connect the input strip waveguide of width w4 and the SWG waveguide of width w3. The SWG waveguide in this region is composed of N1 uniform rectangular silicon blocks of which the duty cycle is η = d0/Λ. In Region II, the adiabatic coupling occurs between a trapezoidal SWG waveguide and a reversely tapered strip waveguide. Different from the uniform SWGs, the SWGs here consist of a series of slowly varying trapezoidal silicon blocks [see Fig. 1(b)]. The length of the upper side of the trapezoids is fixed at d0 while that of the lower side satisfies the following relationship:
where di is the length of the lower side of the ith trapezoidal silicon block, N is the number of periods in the coupling region, and the order i increases from 1 to N along the propagation direction. The coupling length is thereby Lc = NΛ. The width of the upper straight waveguide is reversely tapered from w1 to w2, and the gap between the strip waveguide and the SWG waveguide is g. In Region III, the upper branch consists of a S-bend similar to that at the input end, but this time the width is reversely tapered from w2 to w4. For the lower branch, a transition taper is also used to connect the output strip waveguide and the trapezoidal SWG waveguide as in Region I. Similar to the trapezoidal silicon blocks in Region II, the length of the upper side of the trapezoids in Region III is also fixed at d0, and that of the lower side follows the relationship below: where di is the length of the lower side of the ith trapezoidal silicon block, N1 is the number of periods, and the order i increases from 1 to N1 along the propagation direction.
Fig. 1. (a) 3D schematic and (b) top view of the ultrabroadband 2 × 2 3-dB coupler based on the trapezoidal SWGs.
Since our device is designed for the fundamental TE mode, we choose w4 = 500 nm to keep the single mode operation. In Regions I and III, the lateral length of the S-bends is chosen to be Ls = 10 µm and the number of periods of the SWGs is N1 = 35 in order to reduce the ELs. The period of the SWGs is Λ = 220 nm, which is well below the guided half-wavelength for the Bragg reflection in the wavelength range considered here [19]. For the SWG waveguides, the material refractive index n can be calculated by the effective medium theory (EMT) [23,24]:
where nSi and nSiO2 are the refractive indices of silicon and silica, respectively, and the duty cycle η and the refractive index n are both position-dependent for the trapezoidal SWGs, as we have illustrated in Ref. [30]. The trapezoidal SWG waveguides can also be viewed as GRIN waveguides, in which the guided wave deflects from the waveguide center to the sidewall where the effective index n is higher. This will increase the mode overlap between the SWG waveguide and the reversely tapered strip waveguide in Region II and result in a much shorter coupling length. To reach the ultrabroad bandwidth, the phase matching condition should be met between the reversely tapered strip waveguide and the trapezoidal SWG waveguide. In Fig. 2(a), we calculate and plot the effective index of the Bloch mode at 1550 nm in the uniform SWG waveguide when the waveguide width w3 and the duty cycle η vary around 650 nm and 68%, respectively. As we can see, the effective index matches that of the strip waveguide mode in Fig. 2(b) where the waveguide width changes from 350 nm to 365 nm. Thus, we choose w3 = 650 nm, d0 = 150 nm (corresponding to η = 68%), w1 = 350 nm, and w2 = 365 nm for our design. The gap between the reversely tapered strip waveguide and the trapezoidal SWG waveguide in Region II is set to g = 80 nm to ensure the efficient coupling. To obtain a slowly varying coupling strength, the length of the lower side of the trapezoidal silicon blocks in Region II changes from d0 = 150 nm to dN = 64 nm according to Eq. (1) with N = 20. The coupling length is hence Lc = 4.4 µm, and the total length of the device is Lc + 2 Ls = 24.4 µm. In Region III, however, the length of the lower side of the trapezoidal silicon blocks increases from dts = 107 nm to d0 = 150 nm along the propagation direction. In this way, we gradually convert the trapezoidal SWGs back to normal SWGs with which a transition taper is used to connect the output strip waveguide.Fig. 2. Calculated effective indices of the fundamental TE modes at 1550 nm in (a) an uniform SWG waveguide as functions of duty cycle η and waveguide width w3 and (b) a strip waveguide as a function of waveguide width Wstrip.
To verify the ultrabroadband performance, a 3D finite-difference time-domain (FDTD) method is used to perform the full-wave numerical simulations of the 3-dB coupler. Figures 3(a) and (b) show the simulated electric field distributions at the wavelength of 1550 nm when the light is launched from the Input 1 and Input 2 ports, respectively. It can be seen that the input light is split equally between two output ports. The power splitting ratio and the EL of the device are also calculated and plotted in Fig. 3(c) over a wavelength range of 1400 nm - 1700nm. The power splitting ratio is better than 3 ± 0.5 dB and the EL is lower than 0.2 dB in the 300-nm bandwidth discussed here.
Fig. 3. Simulated propagation profiles (Ey) for the 2 × 2 3-dB coupler when light is launched from (a) the Input 1 port and (b) the Input 2 port. (c) Simulated power splitting ratio and EL as a function of wavelength.
3. Fabrication and measurement
Our device was fabricated on a SOI wafer with a 220-nm-thick silicon top layer and a 3-µm-thick buried oxide layer. Firstly, a number of devices including grating couplers, strip and SWG waveguides were patterned using electron beam lithography (EBL, Vistec EBPG 5200+). Then inductively coupled plasma (ICP, SPTS DRIE-I) dry etching was used to transfer the patterns onto the top silicon layer. Finally, a 1-µm-thick silica cladding layer was deposited over the whole device using plasma enhanced chemical vapor deposition (PECVD, Oxford Plasmalab System 100). Figure 4(a) shows the scanning electron microscope (SEM) image of the fabricated 3-dB coupler. To evaluate the power splitting imbalance of the device, we integrated two such couplers into an unbalanced Mach-Zehnder interferometer (MZI) [17,20] where there is a length difference of ΔL = 200 µm between two arms, as shown in the microscope picture of Fig. 4(b). In Fig. 4(c), we present the 20 cascaded 3-dB couplers which are used for the evaluation of the average EL of a single device [10].
Fig. 4. (a) SEM image of the fabricated 2 × 2 3-dB coupler. Optical microscope photos of (b) the unbalanced MZI based on the proposed 3-dB couplers and (c) the 20 cascaded 3-dB couplers.
To demonstrate the performance of our device, two tunable laser sources (EXFO T100S-HP-ES and T100S-HP-CLU) were employed to cover the wavelength range from 1400 nm to 1670 nm. The TE-polarized light was coupled into and out of the chip using grating couplers. The output light was coupled into the optical power meter and the photodetector (EXFO CTP10) for optical alignment and power measurement, respectively. Since the bandwidth of a single grating coupler is limited [21,30], we used three different kinds of grating couplers to measure the transmission spectra in the wavelength ranges of 1400 nm - 1505 nm, 1505 nm - 1620 nm, 1620 nm - 1670 nm, respectively. Since different tilted angles will lead to different central wavelengths, we can obtain the transmission spectrum in a broader bandwidth with one pair of grating couplers by adjusting the tilted angles. For each grating coupler, two tilted fiber angles of θfiber = 14° and θfiber = 5° were used with each configuration covering approximately 50 nm. Thus, five measurements were conducted for each device to obtain the spectral response over a 270-nm bandwidth of 1400 nm - 1670 nm, as shown in Fig. 5. Figures 5(a)-(e) present the transmission spectra of the unbalanced MZI normalized to those of the reference grating couplers fabricated on the same chip. The extinction ratios (ERs) from both output ports are larger than 17 dB in the entire bandwidth. The power splitting ratios of the 3-dB coupler K can be extracted from the ERs of the measured MZI responses using the following equation [9,17]:
Fig. 5. (a)-(e) Measured MZI transmission spectra in the wavelength ranges of (a) 1400 nm - 1450 nm, (b) 1450 nm - 1505 nm, (c) 1505 nm - 1560 nm, (d) 1560 nm - 1620 nm and (e) 1620 nm - 1670 nm. The tilted fiber angles θfiber with which the transmission spectra are measured are indicated in the figures. (f)-(j) Power splitting ratios for the 2 × 2 3-dB coupler extracted from the ERs in (a)-(e), respectively.
The results are displayed in Figs. 5(f)-(j) as a function of wavelength. It is obvious that the trapezoidal SWG coupler can achieve 3-dB power splitting ratios with < ± 0.7 dB imbalance over the wavelength range of 270 nm. The deviations between the measured and simulated results can be attributed to the imperfections introduced during fabrication.
Using the same measurement methods, one can measure the Els of 20 cascaded 2 × 2 3-dB couplers [as shown in Fig. 4(c)] in the ultrabroad band. The total ELs of 20 cascaded couplers are below 10 dB in the 270-nm bandwidth, which means average ELs of < 0.5 dB for each coupler. The ELs of a single 3-dB coupler are presented in Figs. 6(a)-(e) as a function of wavelength. The measured ELs are a bit higher than the predicted values due to the inevitable fabrication errors.
Fig. 6. Measured ELs of the 2 × 2 3-dB coupler in the wavelength ranges of (a) 1400 nm - 1450 nm, (b) 1450 nm - 1505 nm, (c) 1505 nm - 1560 nm, (d) 1560 nm - 1620 nm and (e) 1620 nm - 1670 nm. The tilted fiber angles θfiber with which the transmission spectra are measured are indicated in the figures.
Table 1 summarizes the most recent experimental demonstrations of the broadband 2 × 2 3-dB couplers built on the SOI platform. It is obvious that our design has the broadest bandwidth and the shortest coupling length compared to the experimentally demonstrated devices reported so far. Since the strip-to-SWG transition tapers are 20 µm long, the total length of the proposed device is a little larger than that in Ref. [21].
Table 1. Comparison of the state-of-the-art broadband 2 × 2 3-dB couplers
4. Conclusion
In conclusion, we have proposed and experimentally demonstrated an ultrabroadband and compact 2 × 2 3-dB coupler based on the trapezoidal SWGs. Thanks to the efficient adiabatic coupling enabled by the trapezoidal SWG and reversely tapered strip waveguides, the coupling length of the proposed device is only 4.4 µm with the total length being 24.4 µm. The simulation results indicate that the imbalance of the 3-dB coupler is no more than ± 0.5 dB and the EL is lower than 0.2 dB over the 300-nm bandwidth of 1400 nm - 1700nm. The performance was further verified in the experiments employing unbalanced MZI and cascaded structures. The measured power splitting ratio is better than 3 ± 0.7 dB and the average EL is less than 0.5 dB in the wavelength range from 1400 nm to 1670 nm. Given the ultrabroad bandwidth and the compact footprint, our device should find numerous applications in on-chip optical communication systems.
Funding
National Key Research and Development Program of China (2019YFB1803903); National Natural Science Foundation of China (61835008, 61860206001, 62005134, 62035016, 62105200).
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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