1State Key Laboratory for Modern Optical Instrumentation, Center for Optical & Electromagnetic Research, College of Optical Science and Engineering, International Research Center for Advanced Photonics, Zhejiang University, Hangzhou 310058, China
2Jiaxing Key Laboratory of Photonic Sensing & Intelligent Imaging, Jiaxing 314000, China
3Intelligent Optics & Photonics Research Center, Jiaxing Research Institute, Zhejiang University, Jiaxing 314000, China
4Ningbo Research Institute, Zhejiang University, Ningbo 315100, China
Chirped Bragg grating is a powerful dispersion compensator. It has the advantages of a broad working bandwidth, a simple structure, and a compact footprint. However, previously reported integrated silicon chirped Bragg gratings relying on the transverse electric (TE) modes fail to achieve a large time delay because the TE modes are hypersensitive to sidewall roughness and fabrication errors. Here, we propose and demonstrate a dispersion compensator utilizing a transverse magnetic (TM) type silicon chirped multimode waveguide grating (CMWG), which exhibits a broad working bandwidth of 30.3 nm, an extensive dispersion of 25.1 ps/nm, and a recorded large group delay of 812.6 ps.
【AIGC One Sentence Reading】:A TM-type chirped multimode waveguide grating in silicon offers large dispersion compensation with 812.6 ps delay over 30.3 nm bandwidth.
【AIGC Short Abstract】:A TM-type chirped multimode waveguide grating (CMWG) in silicon is proposed as a dispersion compensator, overcoming limitations of TE-mode gratings affected by sidewall roughness. It offers a broad bandwidth of 30.3 nm, high dispersion of 25.1 ps/nm, and a large group delay of 812.6 ps.
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The velocity of light varies with wavelength as it passes through a medium known as chromatic dispersion[1], which is critical in many photonic applications. For example, a large-capacity and long-haul communication system requires a dispersion compensator to compensate for the chromatic time delay after traveling a long fiber[2]. Nonlinear wavelength conversion needs precise dispersion control to satisfy a phase-matching condition, ensuring efficient and new broadband wavelength generation[3]. Moreover, dispersion management enables the control of multiwavelength independently, contributing to complex signal processing, such as arbitrary waveform generation and beam forming[4,5]. Therefore, large-scale and precise dispersion control is one of the key issues for developing many photonics systems.
Silicon photonics compatible with complementary metal–oxide–semiconductor (CMOS) technology has shown many advantages over photonic systems based on separated optical devices in many aspects, such as scalability, stability, and power consumption[6]. Consequently, large-scale and precise dispersion control on a silicon-on-insulator (SOI) chip is needed to realize functional integrated photonic systems. Various structures such as Mach–Zehnder interferometers (MZIs)[7], microring resonators (MRRs)[8], contra-directional couplers (contra-DCs)[9], and Bragg gratings[10] have been proposed to manage dispersion. The MZI-based dispersion compensators, requiring long interference arms, have a narrow working bandwidth (e.g., ) and large footprints[7]. The working bandwidth of cascaded MRRs is also limited by their quality factors by having a narrow bandwidth (e.g., ), and complex thermal tuning is required to compensate for the resonance shift caused by imperfect fabrications[8]. Integrated chirped Bragg gratings have been proposed to provide a broad working bandwidth for dispersion management[10], and the circulator can be eliminated with the assistance of asymmetric chirped multimode waveguide grating (CMWG) by reflecting the input into modes[11]. The footprint can be shrunken using Archimedean spiral structures[12]. However, CMWGs utilizing TE modes are more sensitive to fabrication errors due to their higher effective index compared to TM modes. This necessitates more periods for the same amount of group delay value and introduces more deviations, thus restricting their ability in large-scale dispersion control.
In this Letter, we introduce a TM-type CMWG, which is much less sensitive to fabrication errors than a TE-type CMWG, to realize large-scale dispersion compensation on a 220-nm SOI platform. Particularly, a detailed simulation of the fabrication sensitivity difference between the two polarization types is provided. The device with an asymmetric CMWG induces wavelength-dependent group delay and simultaneously reflects the into the modes. The mode (de)multiplexer drops the mode from the input waveguide with low loss and low crosstalk to separate input and reflected signals. Group delay ripples (GDRs) are suppressed by a fabrication-friendly lateral-shift apodization. Experimentally, a maximal 30-mm-long CMWG with a footprint of only was fabricated, exhibiting a recorded large group delay of 812.6 ps, a dispersion of 25.1 ps/nm, and a working bandwidth of 30.3 nm.
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2. Structure and Design
The proposed device is designed on a 220-nm-thick SOI platform with a cladding. Figure 1(a) shows the schematic illustration of the proposed device, including the grating couplers, the mode (de)multiplexer, and the asymmetric spiral CMWG. Specifically, the mode, coupled with the TM-type grating coupler, transmits through the TM mode (de)multiplexer and then is reflected by the CMWG. The CMWG can not only impose dispersion on the light but also reflect the input mode into the mode. The reflected mode is dropped into the output port through the TM mode (de)multiplexer.
Figure 1.Schematic configurations. (a) Top view of the TM-type CMWG. Zoom-in top view of (b) the grating corrugations and (c) the grating transition taper.
The key component of the proposed device is the CMWG. At first, the phase-matching condition between the input mode and the reflected mode is satisfied by where is the reflected Bragg wavelength, Λ is the grating period, and and are the effective refractive indices of the and modes, respectively. The effective refractive indices of the and modes increase with the waveguide width, so the operating wavelength spectrum can be designed by linearly increasing the width of the CMWG from to along the spiral, as shown in Fig. 1(a). The different input wavelengths reflect at different positions along the propagation direction. Hence, the wavelength-dependent group delays are produced. The maximal group delay is decided by the total grating length . The larger waveguide width variation corresponds to the broader operating wavelength spectrum but with a smaller dispersion. Here, the waveguide width , waveguide width variation , and grating period are chosen as 1.5 µm, 500 nm, and 402 nm, respectively to ensure that the CMWG operates at around 1550 nm with a low loss and a large wavelength spectrum. Then, the superposition of the grating teeth is modulated with a cosine function in the propagation direction, as shown in Fig. 1(b). Here, the apodization is realized by gradually transiting the lateral shift from to in the front section of the grating[13]. The modulated transition length is , where () is the modulation length ratio, and the rest of the grating remains asymmetric. The modulated lateral shift is given as
Compared to the usual lateral corrugation apodization of the teeth depth, the superposition modulation used for the present long spiral grating has a lower fabrication requirement[13]. Despite that the corrugation depth should be as small as possible to minimize loss and the GDRs, when the grating length is long enough to totally reflect the input light, is chosen considering fabrication limitation. An Archimedean spiral structure that decreases the radius of the waveguide linearly along the propagation direction is utilized to reduce the footprint of the CMWG. In order to avoid bending loss and crosstalk between adjacent waveguides, the designed CMWG has a minimum radius of 50 µm and a gap between adjacent grating waveguides of 5 µm. Accordingly, the maximal radius of a 30-mm-long CMWG is 224 µm, and it only occupies a compact footprint of . At last, a taper section is adopted to connect the straight waveguide and the symmetric corrugations in the front section of the CMWG to suppress the undesired reflection between the straight waveguide and the CMWG. The taper section includes times the period Λ in which the corrugation depth linearly increases from zero to , as shown in Fig. 1(c).
The transmission spectrum and group delay response are simulated using the transfer matrix method (TMM)[14]. The propagation loss is set as 2.7 dB/cm according to the measured results. Figures 2(a) and 2(b) show the reflectivity and group delay spectrum for various values of the modulated length ratios (, , , , and ) for a 30-mm-long CMWG, exhibiting a maximum group delay of 883 ps, an operation bandwidth of 32.5 nm, and a dispersion of 27.17 ps/nm. The longer wavelength light has a larger loss because it experiences a longer propagation distance. In addition, the reflected light with a flat spectrum at the short wavelength range does not introduce dispersion because the light in the range is reflected at the same position. Figure 2(c) plots the zoom-in group delay spectrum, which indicates that GDRs greatly decrease with modulation length ratio . Here, the average GDR is defined as the average deviation between the simulated value of the group delay and the target value fitted linearly[12]. To further investigate the relationship between the GDRs and the modulation length ratio , average GDRs evaluated from a wavelength range of 1541–1558 nm as a function of is shown in Fig. 2(d). A significant reduction of the average GDRs is observed as increases from to , and then one has an average GDR of when grows from to 0.1. Thus, is chosen as 0.1. As a result, the proportion of the GDRs amplitude in the apodized grating is only 0.51% of the total group delay, while that of the unapodized grating is as large as 13.26%.
Figure 2.(a) Simulated reflectivity and (b) the group delay spectrum for the case with different apodization length ratios η = 0, 10−3, 10−2, and 10−1. (c) Zoom-in group delay spectrum at 1542–1542.5 nm. (d) Average GDR variation as a function of modulated length ratio η.
Considering the fabrication process, period deviation and polygon misalignment are inevitable for the fabricated devices, as depicted in Figs. 3(a) and 3(b), respectively. Hence, the effective indices of the TM modes [, , and when μ] are smaller than those of the TE modes [, , and when μ] on a 220 nm SOI platform, so the corresponding period of a TM-type CMWG is larger than that of a TE-type CMWG according to Eq. (1). However, the maximal group delay is , where is the vacuum speed of light. The average group refractive indices of the TM modes [, , and , when μ] are slightly larger than those of the TE modes [, , and , when μ]. Considering that the period of the TM-type CMWG is much larger than that of the TE-type CMWG with the same waveguide width, a TM-type CMWG has a smaller number of periods than a TE-type CMWG with the same length. As a result, a TM-type CMWG is less sensitive to the period deviation and has a fewer number of polygon misalignments.
Figure 3.(a) Schematic configuration of period perturbation and (b) polygon misalignment. Simulated group delay spectrum with (black) and without (red) 0.1 nm period perturbation of (c) TE-type and (d) TM-type CMWGs. Simulated group delay spectrum with (black) and without (red) 2 nm polygon misalignment of (e) TE-type and (f) TM-type CMWGs.
The influence of fabrication errors on dispersion compensation is analytically evaluated using the TMM. In order to show the advantage of TM-type CMWG over TE-type CMWG in fabrication tolerance, both TE-type and TM-type CMWGs are explored under the same fabrication errors. The designed TM-type CMWG has a waveguide width of μ, a waveguide width variation of , a corrugation depth of , and a grating period of . The TE-type has the same structural parameters as the TM-type, except the period of the TE-type is reset as to work at the same center wavelength. Figures 3(c) and 3(d) plot the group delay as a function of the wavelength with a normally distributed period perturbation (mean and standard deviation of 0 and 0.1 nm). The GDRs caused by period perturbation are and for the TE-type and TM-type CMWGs, respectively. Figures 3(e) and 3(f) plot group delay as a function of wavelength with a 2 nm polygon misalignment per 1024 periods. The GDRs caused by polygon misalignment are and for the TE-type and TM-type CMWGs, respectively. The comparison indicates that the TM-type CMWG shows better resistance against fabrication errors.
The TM mode (de)multiplexer is designed based on an adiabatic dual-core taper coupler (ADC) [Fig. 4(a)] using the method given in our previous work[15]. The core widths at the input/drop ends of waveguides A and B are and , respectively. By gradually increasing the core width of waveguide A from 900 to 1150 nm and decreasing the core width of waveguide B from 500 to 200 nm, we can drop backward signals with low insertion loss and low crosstalk in a broadband spectrum. The gap between waveguides A and B is 200 nm to balance the fabrication tolerance and coupling strength. The taper length is chosen as 30 µm to avoid mode hybridization. The simulated propagation field of the designed mode (de)multiplexer is depicted in Fig. 4(b) at a wavelength of 1538 nm, showing that the reflected mode launched from the right side is efficiently converted to the mode. Figure 4(c) indicates that the designed mode (de)multiplexer has crosstalk below over the whole C band.
Figure 4.(a) Schematic configuration of the mode (de)multiplexer consisting of an adiabatic dual-core taper coupler. (b) Simulated light propagation in the designed adiabatic dual-core taper when operating at the wavelength of 1538 nm. (c) Simulated transmission spectrum for the dropped TM0 mode in waveguide B (blue) and the residual TM1 mode (red) in waveguide A.
We fabricated the TM-type CMWGs on 220 nm silicon on a 2-µm buried oxide platform. The first step of electron-beam lithography (EBL) was adopted to define the device patterns, and the patterns were transferred to the top silicon layer by 220 nm reactive-ion etching (RIE). The second step of EBL and 70 nm RIE were adopted to fabricate grating couplers. Last, a 1.1-µm-thick layer was deposited as an upper cladding layer by plasmon-enhanced chemical vapor deposition (PECVD).
A broad-band amplified spontaneous emission (ASE) light source and an optical spectrum analyzer (OSA) are used to measure the spectrum. TM-type grating couplers were utilized to couple light in and out of the chip. The fabricated mode (de)multiplexer has an insertion loss of less than 0.5 dB and a low crosstalk of less than over a wavelength range of 1520–1570 nm, as shown in Fig. 5. Next, the TM-type CMWGs with different lengths were fabricated to compare their performance. Figures 6(a)–6(c) show the microscope images of the fabricated TM-type CMWGs with different lengths of 5, 15, and 30 mm, respectively. Figures 6(d)–6(f) illustrate the measured reflected transmission spectrum of the CMWGs with different lengths of 5, 15, and 30 mm, respectively. The TM-type CMWG keeps working when the maximal length is 30 mm, achieving a bandwidth of 30.3 nm and a propagation loss of 2.71 dB/cm (20 dB/ns). Here, the bandwidth is denoted as the range between the 3-dB decreased points away from the highest value at the outermost falling edge. The dips in the reflectivity spectrum are caused by transversal modal field misalignment between adjacent polygons. The dip defects can be significantly reduced using the deep ultraviolet (DUV) photolithography process.
Figure 5.(a) Microscope images of the fabricated mode (de)multiplexer. (b) Measured multiplexer transmission spectrum for the TM1 mode input for the dropped port and the through port.
Figure 6.Microscope images of the fabricated CMWGs, including TM-type CMWGs with different lengths of (a) 5, (b) 15, and (c) 30 mm, respectively. Measured reflected transmission spectra for the TM-type CMWGs with different lengths of (d) 5, (e) 15, and (f) 30 mm, respectively.
The measurement setup of the group delay and dispersion is based on our previous work[16]. Light from a tunable laser source was sent into an electro-optic (EO) modulator through a polarization controller. The EO modulator was modulated by an 8–40 GHz radio frequency signal generated by a microwave analog signal generator. The modulated light was injected into the compensator after being amplified by erbium-doped fiber amplifiers (EDFAs). Finally, a digital communication analyzer (DCA) detected the dropped signal from the compensator.
Figure 7 shows the group delay spectrum of the fabricated spiral CMWGs. The maximal group delay values of the 5, 15, and 30 mm CMWGs are 167.7, 488.5, and 812.6 ps, respectively. As a result, the dispersion values are calculated to be 4.9, 13.1, and 25.1 ps/nm. The corresponding GDRs are calculated as , , and for the respective CMWGs. Table 1 summarizes a comparison of various integrated chirped spiral Bragg gratings. Our demonstrated TM-type CMWG is circulator-free and produces the largest group delay and working bandwidth among these silicon structures.
Figure 7.Measured group delay spectra of the fabricated spiral TM CMWGs with different lengths of 5, 15, and 30 mm.
Table 1. Comparison of On-chip Chirped Spiral Bragg Gratings
Ref.
Polarization
Platform
Circulator-free
Length (mm)
Maximal delay (ps)
Bandwidth (nm)
Loss (dB/ns)
Dispersion (ps/nm)
Footprint (mm × mm)
[17]
TM
Silicon
—
4
∼120
11.7
>30
−11
0.13 × 0.13
[18]
TM
Silicon
—
3
∼50
8.8
>50
−11
—
[19]
TE
Silicon
—
27
628
22.5
6
−27.7
0.3 × 0.3
[12]
TE
Silicon nitride
—
138
1440
9.2
1.875
−156.5
2.8 × 2.8
[20]
TE
Silicon nitride
√
201.1
2864
23
1.57
158
2 × 2
[16]
TE
Silicon
√
5
150
23
33.3
6.49
0.21 × 0.21
This work
TM
Silicon
√
30
812.6
30.3
20
25.1
0.6 × 0.46
4. Conclusion
In conclusion, we have proposed and demonstrated a dispersion compensator using spiral TM CMWG, which offers a working bandwidth of 30.3 nm, a dispersion of 25.1 ps/nm, and a recorded large group delay of 812.6 ps. The CMWG is easily integrated with other on-chip devices without requiring a circulator. Despite TE modes being much more popular in silicon PICs, polarization rotation can be achieved with the assistance of high-performance polarization rotators[21,22]. Therefore, the proposed device offers a reliable on-chip large dispersion management solution for microwave photonics, photonic signal processes, and optical communications.
[8] Y. Liu, L. Lu, Z. Ni et al. Silicon integrated continuously tunable dispersion compensator based on cascaded micro-ring resonators. Asia Communications and Photonics Conference (ACP)(2022).