Design of a Reconfigurable Optical Filter Based on Triple-ring-assisted Mach-Zenhnder Interferometer with Large Bandwidth Tuning Capability

Jia JIANG; Minming GENG; Qiang LIU; Zhenrong ZHANG

doi:10.3788/gzxb20215007.0713002

Abstract

A compact reconfigurable optical filter based on silicon-on-insulator with large bandwidth tuning capability is designed in this paper. The device is based on triple-ring-assisted Mach-Zehnder interferometer. The bandwidth and center wavelength of the device can be tuned at the same time by reasonably changing the phases of the microring resonators through the thermo-optic effect of silicon. The performance of the proposed device is simulated by finite difference time domain method. The simulation results show that the tuning range of the bandwidth is 1.4 nm to 10.6 nm， which accounts for 11.5% to 85% of the free spectrum range. The stopband extinction ratio is greater than 20 dB， and the passband loss is 0.4 dB to 0.7 dB， the footprint of the device is about 40 μm×60 μm.

Keywords

Mach-Zehnder interferometer Microring resonator Optical filter Silicon-on-insulator Tunable bandwidth

0 Introduction

In the past decades， especially in the twenty years of the new century， the silicon photonics has been developing extremely rapidly， due to its superiorities in many aspects， such as fabrication technology， integration density， excellent performance， application diversity and so on^［1-4］. Many devices and circuits based on silicon photonics have been proposed and demonstrated^［5-6］， which can be widely used in optical fiber communications^［7］， optical interconnect^［8］， microwave photonics^［9］， optical sensing^［10］， optical neural network^［11］， quantum communication^［12］， etc. As various applications become more and more intelligent， the reconfigurability is a key performance for the devices and circuits to meet the requirements of different applications^［13］. As the most fundamental element， the reconfigurable optical filters based on silicon photonics have been reported with different schemes， e.g.， AWG， Bragg-grating， Mach-Zehnder Interferometer （MZI）， Microring Resonators （MRR）， etc. The schemes based on AWG^{［14， 15］} have advantages in multi-wavelength alignment and translation of all channels. But to some extent， the flexibility of the filters based on AWG is relatively weak when dealing with single channel is required. The schemes based on Bragg-grating^{［16， 17］} can be Free Spectrum Range （FSR） free which is desired in ultra-wideband applications of fiber communications and microwave photonics. But the footprint of the devices based on Bragg-grating is relatively large， which makes the tuning power consumption quite high. The schemes based on MZI， MRR or a mixture of the two structures^［18-28］ have advantages in flexibility， scalability， footprint and power consumption. To tune both the bandwidth and wavelength， the optical filters based on cascaded high-order microring resonators or ring-assisted MZI have been proposed^［20-28］. The bandwidth tunability performance of the proposed filters is limited. In the proposed filters， the maximum Bandwidth Tuning Range （BTR） is about 1.44 nm reported in Ref.［22］， which may be not large enough for the applications in the 400 Gbps/1 Tbps flexible optical communication networks^［29］. In this paper， a compact silicon reconfigurable optical filter based on triple-ring-assisted MZI with ultra-large bandwidth tuning range is proposed.

1 Selection and optimization of scheme

As mentioned above， there are mainly two kinds of schemes to design the bandwidth-tunable optical filter. One is based on ring-assisted MZI， the other is based on multiple cascaded microring resonators. The performance parameters of the optical filters based on the two schemes are summarized in Table 1. The BTRs of the two schemes are almost the same. But in general， the filters based on ring-assisted MZI have an edge in terms of the proportion of BTR in the whole FSR， which is more suitable for designing optical filter with large BTR. Thus， the scheme based on ring-assisted MZI is selected in this paper.

Scheme	BW_max / FSR	Tunable BW / nm	Ref.
MRRs in an MZI	0.88 nm / 9 nm	0.46~0.88	［21］
MRRs in an MZI	1.44 nm / 1.6 nm	0.16~1.44	［22］
MRRs in an MZI	1.12 nm / 8.5 nm	0.37~1.12	［23］
MRRs in an MZI	0.113 nm / 0.256 nm	0.033~0.113	［24］
Cascaded rings	1 nm / 7.2 nm	0.0928 ~1	［25］
Cascaded rings	1.2 nm / 70.8 nm	0.3~1.2	［26］
Cascaded rings	0.16 nm / 16 nm	0.12~0.16	［27］
Cascaded rings	0.64 nm / 1.8nm	0.056~0.64	［28］

Table 1. The summarization of performance of different schemes

View all Tables

To meet the requirements of optical fiber communication systems^［30］， the Stopband Extinction Ratio （SER） should be larger than 20 dB and the passband loss lower than 1 dB during the reconstruction of the wavelength and bandwidth of the optical filter. The number of microring resonator in a ring-assisted MZI is the key to the performance of the optical filters based on it. The optical filters based on double-ring-assisted MZI are reported in Ref.［21-24］， but the SER or PL may deteriorate when changing the phase of the microring resonator to tune the bandwidth or wavelength of the filter， which makes the performance of the filter unstable. To enlarge the BTR and make the filter more stable， one more microring resonator is added to the double-ring-assisted MZI to form an asymmetric phase control structure.

2 Theoretical analysis and optimization of key parameters

The structure of the designed optical filter， which is based on triple-ring-assisted MZI， is shown in Fig.1. The inputs are denoted by X₁ and X₂， and the outputs are denoted by Y₁ and Y₂. X₂ is zero during the process of design and simulation. The power coupling ratios of the 3-dB couplers named K₁ and K₂ are k₁and k₂， respectively. The three MRRs are the key phase control units in the filter. The MRR called R_A is coupled with the upper arm of the MZI， and R_B as well as R_Cis coupled with the lower arm. Thus， the structure of the optical filter is asymmetric， which makes the bandwidth of the filter can be tuned. In order to control the coupling strength and phase conveniently， the race-track structure is selected. The three yellow areas in Fig.1 are used to change the phases of the MRRs， named θ_A， θ_B and θ_C， respectively， to tune the center wavelength of the optical filter by thermo-optic or electro-optic effect of silicon^［1］. The electro-optic effect usually induces extra loss caused by the absorption of the free carriers^［31］ whereas the thermo-optic effect does not induce any extra loss. Thus， the thermo-optic effect is selected in this paper.

Figure 1.Schematic of the proposed device based on triple-ring-assisted MZI

According to the transfer-matrix method^［31-32］， the relationship between the inputs and outputs of the filter meets the following equation.

\begin{array}{l} [\begin{matrix} Y_{1} \\ Y_{2} \end{matrix}] = [\begin{matrix} c_{2} \\ - j s_{2} \end{matrix} \begin{matrix} - j s_{2} \\ c_{2} \end{matrix}] [\begin{matrix} H_{1} (z) \\ 0 \end{matrix} \begin{matrix} 0 \\ H_{2} (z) \end{matrix}] [\begin{matrix} c_{1} \\ - j s_{1} \end{matrix} \begin{matrix} - j s_{1} \\ c_{1} \end{matrix}] [\begin{matrix} X_{1} \\ X_{2} \end{matrix}] \\ = [\begin{matrix} c_{1} c_{2} H_{1} (z) - s_{1} s_{2} H_{2} (z) \\ - j (c_{1} s_{2} H_{1} (z) + s_{1} c_{2} H_{2} (z)) \end{matrix} \begin{matrix} - j (s_{1} c_{2} H_{1} (z) + c_{1} s_{2} H_{2} (z)) \\ - s_{1} s_{2} H_{1} (z) + c_{1} c_{2} H_{2} (z) \end{matrix}] [\begin{matrix} X_{1} \\ X_{2} \end{matrix}] \end{array}

In Eq. （1）， the parameters of c_l and s_l （l = 1 and 2） satisfy the following equations.

c_{l} = \sqrt[]{1 - k_{l}}, s_{l} = - j \sqrt[]{k_{l}}, l = 1, 2

To make the performance of the proposed filter better， the power coupling ratios of K₁， as well as K₂， is equal to 1∶1， which means the structures of the two 3-dB couplers are the same and the subscript of k， c and s can be omitted. The system transfer functions of the proposed filter， which are the keys to analyze the performance of the filter， are obtained as follows when X₂ is zero.

H_{Y_{1}} (z) = |\frac{Y_{1} (z)}{X_{1} (z)}| = c^{2} H_{1} (z) - s^{2} H_{2} (z)

H_{Y_{2}} (z) = |\frac{Y_{2} (z)}{X_{1} (z)}| = c s H_{1} (z) + s c H_{2} (z)

Here， H₁（z） is the transfer function of the upper arm coupled with R_A， and H₂（z） is the transfer function of the lower arm coupled with R_B and R_C. Both H₁（z） and H₂（z） can be obtained by transfer-matrix method and shown below.

H_{1} (z) = \frac{ρ_{A} - z^{- 1} e^{- j θ_{A}}}{1 - ρ_{A} z^{- 1} e^{- j θ_{A}}}

H_{2} (z) = \frac{ρ_{B} ρ_{C} - (ρ_{B} e^{- j θ_{C}} + ρ_{C} e^{- j θ_{B}}) z^{- 1} + e^{- j (θ_{B} + θ_{C})} z^{- 2}}{1 - (ρ_{B} e^{- j θ_{B}} + ρ_{C} e^{- j θ_{C}}) z^{- 1} + ρ_{B} ρ_{C} e^{- j (θ_{B} + θ_{C})} z^{- 2}}

Here， the power coupling ratios and transmission coefficients between the resonators and straight waveguides are denoted by k_i and ρ_i （i=A， B and C）， respectively. The relationship between k_i and ρ_iis shown below.

ρ_{i} = \sqrt[]{1 - k_{i}}, i = A, B a n d C

In order to get the system transfer functions， take Eqs. （5） and （6） into Eqs. （3） and （4）. To simplify the results， let ρ_B = ρ_C， and θ_B = -θ_C， and the system transfer functions are obtained as follows.

H_{Y_{1}} (z) = \frac{0.5 (M_{1} - M_{2} z^{- 1} + M_{3} z^{- 2} + M_{1} e^{- j θ_{A}} z^{- 3})}{1 - (2 ρ_{B} c o s θ_{B} + ρ_{A} e^{- j θ_{A}}) z^{- 1} + (ρ_{B}^{2} + 2 ρ_{A} ρ_{B} c o s θ_{B} e^{- j θ_{A}}) z^{- 2} - ρ_{B}^{2} ρ_{A} e^{- j θ_{A}} z^{- 3}}

Here， $M_{1} = ρ_{A} - ρ_{B}^{2}$ ， $M_{2} = 2 ρ_{A} ρ_{B} c o s θ_{B} + e^{- j θ_{A}} - 2 ρ_{B} c o s θ_{B} - ρ_{A} ρ_{B}^{2} e^{- j θ_{A}}$ and $M_{3} = 2 ρ_{B} c o s θ_{B} e^{- j θ_{A}} + ρ_{A} ρ_{B}^{2} - 2 ρ_{A} ρ_{B} c o s θ_{B} e^{- j θ_{A}} - 1 .$

H_{Y_{2}} (z) = \frac{0.5 (N_{1} - N_{2} z^{- 1} + N_{3} z^{- 2} - N_{1} e^{- j θ_{A}} z^{- 3})}{1 - (2 ρ_{B} c o s θ_{B} + ρ_{A} e^{- j θ_{A}}) z^{- 1} + (ρ_{B}^{2} + 2 ρ_{A} ρ_{B} c o s θ_{B} e^{- j θ_{A}}) z^{- 2} - ρ_{B}^{2} ρ_{A} e^{- j θ_{A}} z^{- 3}}

Here， $N_{1} = ρ_{A} + ρ_{B}^{2}$ ， $N_{2} = 2 ρ_{B} c o s θ_{B} + ρ_{B}^{2} ρ_{A} e^{- j θ_{A}} + 2 ρ_{A} ρ_{B} c o s θ_{B} + e^{- j θ_{A}}$ and $N_{3} = 2 ρ_{B} c o s θ_{B} e^{- j θ_{A}} + ρ_{A} ρ_{B}^{2} + 2 ρ_{A} ρ_{B} c o s θ_{B} e^{- j θ_{A}} + 1$ .

Using the system transfer functions， the response of the proposed optical filter can be calculated and optimized. The bandwidth can be tuned continuously by tuning θ_B and θ_Cwhile keeping θ_A equal to 0， θ_B equal to -θ_C and ρ_i constant. According to the system transfer functions， ρ_i and θ_iare the key parameters affecting the performance of the filter. Here， the impact of ρ_iis analyzed first and the results are shown in Figs.2 （a）~（e）， respectively. First， the relationship between ρ_A， ρ_B and the Stopband Extinction Ratios （SER） of two outputs are analyzed and depicted in Figs.2 （a） and （b）. In both pictures， there are some blank areas， in which the response curve of the filter will be distorted and the corresponding parameters cannot be used to design the filter. The SER may fluctuate during the process of bandwidth adjustment. The minimum value of the SER， denoted by SER_min， should be larger than 20 dB to meets the requirement of optical fiber communication systems^［30］. The effective regions meeting the condition mentioned above are the lower right region of Fig. 2 （a） and the lower left region of Fig.2 （b）， which are marked with a single white dotted line in both pictures. The coordinates of the intersections between the coordinate axis or boundary and the white dotted line are indicated. The overlapping part of the effective regions of Figs. 2 （a） and （b）， marked with A， is exactly the effective region in Fig.2 （b）， which is the key to the subsequent analysis and design.

Figure 2.The influence of ρ_A and ρ_Bon the performance of the optical filter

The relationship between ρ_A， ρ_B and the maximum loss of passband of the two outputs named PL_max is analyzed and shown in Figs.2 （c） and （d）. It can be seen that the PL_max in the region A is smaller than 1 dB in both pictures， which meets the performance requirement.

The relationship between ρ_A， ρ_B and BTR is shown in Fig. 2 （e）. The BTR is normalized by the proportion of the whole FSR. The BTRs of the two outputs are the same and will get larger in the direction of the black arrow and reach the maximum value in the region A.

According to the analysis above， in order to ensure the performance of SER and maximize the BTR， the ideal parameter combination of （ρ_A， ρ_B） is （0， 0.46）， labeled with P₁ in Fig. 2 （e）.

The phases of the microring resonators can be used to tune the central wavelength of the filter. Here， the output of Y₂is selected to make a detailed explanation. The system transfer function of Y₂ is rewritten as follows and an extra phase θ is applied to the three resonators simultaneously.

H_{Y_{2}} (z) = \frac{0.5 (N_{1} - N_{2} z^{- 1} e^{- j θ} + N_{3} z^{- 2} e^{- j 2 θ} - N_{1} e^{- j θ_{A}} z^{- 3} e^{- j 3 θ})}{1 - (2 ρ_{B} c o s θ_{B} + ρ_{A} e^{- j θ_{A}}) z^{- 1} e^{- j θ} + (ρ_{B}^{2} + 2 ρ_{A} ρ_{B} c o s θ_{B} e^{- j θ_{A}}) z^{- 2} e^{- j 2 θ} - ρ_{B}^{2} ρ_{A} e^{- j θ_{A}} z^{- 3} e^{- j 3 θ}}

The response of Eq. （10） is plotted in Fig. 3， and the results show that the normalized central frequency of the filter will shift θ/2π. When θ = 2π， the shifting range of the central frequency will be the whole FSR， which makes the two curves （θ = 0 and θ = 2π） coincide. The situation of Y₁ is the same as that of Y₂.

Figure 3.Normalized central frequency is shifted with the change of the extra phase θ applied on the three resonators

3 Simulation and optimization

3.1 Structure design and optimization

According to the analysis above， the structure of the proposed optical filter is designed and optimized using Finite Difference Time Domain （FDTD） method. The channel-type waveguide with height of 250 nm is chosen. The race-track resonator named R_i shown in Fig.4 is consisted of four arcs with radius of r_i， two vertical straight waveguides with length of L_mi and two horizontal straight waveguides with length of L_ni （i=A， B and C）.

Figure 4.The structure of the race-track microring resonator

As the discussion on the Fig. 2 （e）， the smaller the ρ_A， the larger the BTR. In Fig. 4， W_idth， G_apand L_n_A are the key structural parameters that affect ρ_A. To find out the minimum value of ρ_A named ρ_Amin， FDTD method is used to calculate the value of ρ_Amin in different combinations of these structural parameters and the results are shown in Fig. 5. The optimum combination of the three structural parameters is labeled with black circle in the picture， which means ρ_Amin will be 0.008 when W_idth is 0.4 μm， G_ap is 130 nm and L_n_A is 5.85 μm. A black line where ρ_A equals 0.008 is drawn in Fig. 2 （e） and it intersects with the white dotted line at P₂（0.008， 0.45）. Here， P₂ can meet the requirements of SER and PL， and make the BTR largest. But there is about 5% error in the fabrication of waveguide. This factor is taken into account in the simulation， and P₃ （0.008， 0.43） is selected. Thus， the value of ρ_B as well as ρ_C is 0.43， and L_n_Band L_n_C are calculated to be 3.69 μm， while keeping W_idth equal to 0.4 μm and G_ap equal to 130 nm.

Figure 5.The value of ρ_Amin with different W_idth， G_ap and L_n_A

The transmission coefficient ρ_r will change with the wavelength， which will influence the performance of the filter. The dispersion effect is introduced into the Eqs. （8） and （9）. The relationship between FSR and SER is discussed to take into account the influence mentioned above and the results are shown in Fig. 6. The larger the FSR， the smaller the minimum SER. To make sure the performance of the filter stable， the value of FSR is selected to be 12.5 nm. Using the resonance condition， L_m_A is calculated to be 0.37 μm， L_m_Bas well as L_m_Cto be 2.75 μm and r_i to be about 5 μm （i=A， BandC）.

Figure 6.The relationship between the FSR and the minimum SER of the two outputs

During the analysis in Section 2， the phase θ_C or θ_B is negative （θ_C = -θ_B）， which is difficult to realize. To overcome this difficulty， the initial phase values of the three resonatorsshould be π but not 0. The initial phase π can be realized by changing the refractive index of the resonators through the thermo-optic effect. Around 1 550 nm， and when the temperature is between 300 K to 550 K， the empirical formula of the relationship between the thermo-optic coefficient and temperature of silicon is shown below ^［33］.

\frac{d n}{d T} = 9.48 \times 10^{- 5} + 3.47 \times 10^{- 7} \times T - 1.49 \times 10^{- 10} \times T^{2} K^{- 1}

The relationship between the initial phase and the change of the refractive index Δn is simulated and shown in Fig. 7. It means that the initial phase can be π when Δn is 0.008， and the temperature change of the waveguide is about 40 K according to the Eq. （11）. When tuning the bandwidth of the filter， R_B can be heated and R_C can be cooled， or vice versa， to keep θ_Cequal to 2π-θ_B， which is the same as θ_Cequal to -θ_B from the perspective of phase.

Figure 7.The relationship between the initial phase and Δn

To lower the power consumption of the device， the initial phase of R_A can be realized by inserting a phase shifter into the straight waveguide of R_A. The phase shifter is composed by two linear tapers as plotted in Fig. 8. The values of W_s and L_s are determined by FDTD method， which are 0.54 μm and 5 μm， respectively.

Figure 8.The structure of the phase shifter

3.2 Simulation of the optical filter with large bandwidth tuning capability

The structure parameters of the proposed filter are listed in Table 2 and its footprint is about 40 μm×60 μm. The performance of the device is simulated by FDTD method and only TE mode is considered. The results are shown in Fig. 9. The bandwidth of the two ports is continuously changed with θ_Band θ_C. The SER is better than 20 dB and the PL is 0.4 dB to 0.7 dB.

Item	Value
Waveguide type	Channel
Waveguide height	0.25 μm
r_A， r_B and r_C	5 μm
W_idth	0.4 μm
G_ap	130 nm
Refractive index of silicon	3.507
Refractive index of silica	1.447
Polarization	TE
L_n_A/ L_n_B and L_n_C	5.85 μm/3.69 μm
L_m_A / L_m_B and L_m_C	0.37 μm/2.75 μm

Table 2. The simulation settings of the filter

View all Tables

Figure 9.The performance of the optical filter with different θ_B and θ_C

Both the bandwidth and wavelength can be reconstructed at the same time by tuning the phase of the resonators. The bandwidth is controlled by θ_Band θ_C， and the wavelength is controlled by an extra phase θ applied to the three resonators simultaneously. The results simulated by FDTD method are shown in Fig. 10. The extra phase θ is changed between 0 to 2π with step of π， and θ_Bchanged between 0 to π with step of π/2 while keeping θ_Cequal to 2π-θ_B. It can be seen that the wavelength shifted about 12.5 nm to the right， meanwhile， the bandwidth is changed from 1.4 nm to 10.6 nm. Thus， the maximum phase shift of the resonators is 3π， which corresponds to the change of waveguide temperature about 120°.

Figure 10.The reconfigurations of the wavelength and the bandwidth of the filter

Both the bandwidth and wavelength can be reconstructed at the same time by tuning the phase of the resonators. The bandwidth is controlled by θ_Band θ_C， and the wavelength is controlled by an extra phase θ applied to the three resonators simultaneously. The results simulated by FDTD method are shown in Fig. 10. The extra phase θ is changed between 0 to 2π with step of π， and θ_Bchanged between 0 to π with step of π/2 while keeping θ_C equal to 2π-θ_B. It can be seen that the wavelength shifted about 12.5 nm to the right， meanwhile， the bandwidth is changed from 1.4 nm to 10.6 nm. Thus， the maximum phase shift of the resonators is 3π， which corresponds to the change of waveguide temperature about 120°.

4 Conclusion

In this paper， a reconfigurable optical filter based on triple-ring-assisted MZI with large bandwidth tuning capacity is designed. The system transfer function of the filter is derived using transfer-matrix method. The performance and the structure of the device are analyzed and optimized using the FDTD method. The SER is better than 20 dB， and the PL is less than 0.7 dB. The footprint of the device is about 40 μm×60 μm. By changing the refractive index of the resonators through thermo-optic effect， the center wavelength and the bandwidth can be reconstructed at the same time. The bandwidth of the filter can be tuned between 1.4 nm to 10.6 nm， which accounts for 11.5% to 85% of the FSR.

References

[1] R SOREF. The past， present， and future of silicon photonics. IEEE Journal of selected topics in quantum electronics, 12, 1678-1687(2006).

[2] P P ABSIL, P VERHEYEN, P DE HEYN et al. Silicon photonics integrated circuits： a manufacturing platform for high density， low power optical I/O’s. Optics Express, 23, 9369-9378(2015).

[3] Z LU, J JHOJA, J KLEIN et al. Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability. Optics Express, 25, 9712-9733(2017).

[4] Y ZHANG, A SAMANTA, K SHANG et al. Scalable 3D silicon photonic electronic integrated circuits and their applications. IEEE Journal of Selected Topics in Quantum Electronics, 26, 1-10(2020).

[5] P DONG, Y K CHEN, G H DUAN et al. Silicon photonic devices and integrated circuits. Nanophotonics, 3, 215-228(2014).

[6] R HELKEY, A A M SALEH, J BUCKWALTER et al. High-performance photonic integrated circuits on silicon. IEEE Journal of Selected Topics in Quantum Electronics, 25, 1-15(2019).

[7] Jianhui LI, Yongtang ZHANG, Fang WANG. The design of a high quality and minimum wavelength of ultra-low-loss tapered optical fiber. Acta Photonica Sinica, 45(2016).

[8] H JIA, T ZHOU, X FU et al. Four-port mode-selective silicon optical router for on-chip optical interconnect. Optics Express, 26, 9740-9748(2018).

[9] Dong WANG, Bo DAI, Liqing REN et al. A modulation sheme to generate 24-GHz-Band millimeter-wave-band ultra-wideband signal by using Mach Zehnder modulator. Acta Photonica Sinica, 44(2015).

[10] Jiawen LI, Jiahong ZHANG, Xiaoping XU et al. Integrated optical waveguide Mach-Zehnder interferometer power frequency intensive electric field sensor. Acta Photonica Sinica, 48(2019).

[11] C HUANG, P R PRUCNAL. Reconfigurable all-optical nonlinear activation functions for neuromorphic photonics. Optics Letters, 45, 4819-4822(2020).

[12] K WEI, W LI, H TAN et al. High-speed measurement-device-independent quantum key distribution with integrated silicon photonics. Physical Review X, 10(2020).

[13] Y XIE, Y SHI, L LIU et al. Thermally-reconfigurable silicon photonic devices and circuits. IEEE Journal of Selected Topics in Quantum Electronics, 26, 1-20(2020).

[14] S TONDINI, C CASTELLAN, M MANCINELLI et al. Methods for low crosstalk and wavelength tunability in arrayed-waveguide grating for on-silicon optical network. Journal of Lightwave Technology, 35, 5134-5141(2017).

[15] Y LIU, Z LI, D LI et al. Thermo-optic tunable silicon arrayed waveguide grating at 2-μm wavelength band. IEEE Photonics Journal, 12, 1-8(2020).

[16] J ST-YVES, H BAHRAMI, P JEAN et al. Widely bandwidth-tunable silicon filter with an unlimited free-spectral range. Optics Letters, 40, 5471-5474(2015).

[17] K IKEDA, R KONOIKE, K SUZUKI et al. 2× 2 16-ch silicon photonics wavelength-selective switch based on waveguide gratings. Optics Express, 28, 26861-26869(2020).

[18] L YANG, Y XIA, F ZHANG et al. Reconfigurable nonblocking 4-port silicon thermo-optic optical router based on Mach–Zehnder optical switches. Optics Letters, 40, 1402-1405(2015).

[19] H WANG, J DAI, H JIA et al. Polarization-independent tunable optical filter with variable bandwidth based on silicon-on-insulator waveguides. Nanophotonics, 7, 1469-1477(2018).

[20] H SHOMAN, H JAYATILLEKA, A H K PARK et al. Compact wavelength-and bandwidth-tunable microring modulator. Optics Express, 27, 26661-26675(2019).

[21] Y DING, M PU, L LIU et al. Bandwidth and wavelength-tunable optical bandpass filter based on silicon microring-MZI structure. Optics Express, 19, 6462-6470(2011).

[22] P ORLANDI, C FERRARI, M J STRAIN et al. Reconfigurable silicon filter with continuous bandwidth tunability. Optics Letters, 37, 3669-3671(2012).

[23] L SHEN, Z GUO, L LU et al. Reconfigurable silicon optical filters using a dual-ring assisted Mach-Zehnder interferometer based 16×16 switch, 1-3(2017).

[24] J LI, S YANG, H CHEN et al. Reconfigurable rectangular filter with continuously tunable bandwidth and wavelength. IEEE Photonics Journal, 12, 1-9(2020).

[25] R KUMAR, S MOOKHERJEA. Ultra-high-contrast and tunable-bandwidth filter using cascaded high-order silicon microring filters. IEEE Photonics Technology Letters, 25, 1543-1546(2013).

[26] T DAI, G WANG, J JIANG et al. Bandwidth tunable filter with large bandwidth and wavelength tuning range, 1-3(2018).

[27] H SHEN, M H KHAN, L FAN et al. Eight-channel reconfigurable microring filters with tunable frequency， extinction ratio and bandwidth. Optics Express, 18, 18067-18076(2010).

[28] G POULOPOULOS, G GIANNOULIS, N ILIADIS et al. Fully flexible filtering element on SOI with 7~80 GHz bandwidth tunability and full FSR tuning, 1-3(2018).

[29] E PINCEMIN, M SONG, Y LOUSSOUARN et al. Towards 400G/1T flexible optical transport networks, 1-13(2013).

[30] J M SIMMONS. Optical network design and planning(2014).

[31] R SOREF, B BENNETT. Electrooptical effects in silicon. IEEE journal of quantum electronics, 23, 123-129(1987).

[32] C K MADSEN, J H ZHAO. Optical filter design and analysis(1999).

[33] G COCORULLO, F G DELLA CORTE, I RENDINA. Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm. Applied physics letters, 74, 3338-3340(1999).

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