• Acta Photonica Sinica
  • Vol. 50, Issue 7, 275 (2021)
Jia JIANG1、2, Minming GENG1、2、3、4, Qiang LIU1、2、3, and Zhenrong ZHANG1、2、3
Author Affiliations
  • 1School of Computer, Electronics and Information, Guangxi University, Nanning530004, China
  • 2Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, Nanning530004, China
  • 3Key Laboratory of Multimedia Communications and Information Processing of Guangxi Higher Education Institutes, Guangxi University, Nanning50004, China
  • 4Guangxi Experiment Center of Information Science, GuilinGuangxi5100, China
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    DOI: 10.3788/gzxb20215007.0713002 Cite this Article
    Jia JIANG, Minming GENG, Qiang LIU, Zhenrong ZHANG. Design of a Reconfigurable Optical Filter Based on Triple-ring-assisted Mach-Zenhnder Interferometer with Large Bandwidth Tuning Capability[J]. Acta Photonica Sinica, 2021, 50(7): 275 Copy Citation Text show less

    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.

    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 on1-4. Many devices and circuits based on silicon photonics have been proposed and demonstrated5-6, which can be widely used in optical fiber communications7, optical interconnect8, microwave photonics9, optical sensing10, optical neural network11, quantum communication12, 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 applications13. 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 AWG1415 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-grating1617 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 structures18-28 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 proposed20-28. 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 networks29. 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.

    SchemeBWmax / FSRTunable BW / nmRef.
    MRRs in an MZI0.88 nm / 9 nm0.46~0.8821
    MRRs in an MZI1.44 nm / 1.6 nm0.16~1.4422
    MRRs in an MZI1.12 nm / 8.5 nm0.37~1.1223
    MRRs in an MZI0.113 nm / 0.256 nm0.033~0.11324
    Cascaded rings1 nm / 7.2 nm0.0928 ~125
    Cascaded rings1.2 nm / 70.8 nm0.3~1.226
    Cascaded rings0.16 nm / 16 nm0.12~0.1627
    Cascaded rings0.64 nm / 1.8nm0.056~0.6428

    Table 1. The summarization of performance of different schemes

    To meet the requirements of optical fiber communication systems30, 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 k1 and k2, respectively. The three MRRs are the key phase control units in the filter. The MRR called RA is coupled with the upper arm of the MZI, and RB as well as RC is 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 θAθB and θC, respectively, to tune the center wavelength of the optical filter by thermo-optic or electro-optic effect of silicon1. The electro-optic effect usually induces extra loss caused by the absorption of the free carriers31 whereas the thermo-optic effect does not induce any extra loss. Thus, the thermo-optic effect is selected in this paper.

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

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

    According to the transfer-matrix method31-32, the relationship between the inputs and outputs of the filter meets the following equation.

    Y1Y2=c2-js2-js2c2H1z00H2zc1-js1-js1c1X1X2        =c1c2H1z-s1s2H2z -jc1s2H1z+s1c2H2z    -js1c2H1z+c1s2H2z-s1s2H1z+c1c2H2zX1X2

    In Eq. (1), the parameters of cl and sll = 1 and 2) satisfy the following equations.

    cl=1-kl, sl=-jkl, 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 kc 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.

    HY1z=Y1zX1z=c2H1z-s2H2z

    HY2z=Y2zX1z=csH1z+scH2z

    Here, H1z) is the transfer function of the upper arm coupled with RA, and H2z) is the transfer function of the lower arm coupled with RB and RC. Both H1z) and H2z) can be obtained by transfer-matrix method and shown below.

    H1z=ρA-z-1e-jθA1-ρAz-1e-jθA

    H2z=ρBρC-ρBe-jθC+ρCe-jθBz-1+e-jθB+θCz-21-ρBe-jθB+ρCe-jθCz-1+ρBρCe-jθB+θCz-2

    Here, the power coupling ratios and transmission coefficients between the resonators and straight waveguides are denoted by ki and ρii=A, B and C), respectively. The relationship between ki and ρi is shown below.

    ρi=1-ki, i=A, B and C

    In order to get the system transfer functions, take Eqs. (5) and (6) into Eqs. (3) and (4). To simplify the results, let ρB = ρC, and θB = -θC, and the system transfer functions are obtained as follows.

    HY1(z)=0.5(M1-M2z-1+M3z-2+M1e-jθAz-3)1-(2ρBcosθB+ρAe-jθA)z-1+(ρB2+2ρAρBcosθBe-jθA)z-2-ρB2ρAe-jθAz-3

    Here,M1=ρA-ρB2M2=2ρAρBcosθB+e-jθA-2ρBcosθB-ρAρB2e-jθAand M3=2ρBcosθBe-jθA+ρAρB2-2ρAρBcosθBe-jθA-1.

    HY2(z)=0.5(N1-N2z-1+N3z-2-N1e-jθAz-3)1-(2ρBcosθB+ρAe-jθA)z-1+(ρB2+2ρAρBcosθBe-jθA)z-2-ρB2ρAe-jθAz-3

    Here,N1=ρA+ρB2N2=2ρBcosθB+ρB2ρAe-jθA+2ρAρBcosθB+e-jθAand N3=2ρBcosθBe-jθA+ρAρB2+2ρAρBcosθBe-jθA+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 θB and θC while keeping θA equal to 0, θB equal to -θC and ρi constant. According to the system transfer functions, ρi and θiare the key parameters affecting the performance of the filter. Here, the impact of ρiis analyzed first and the results are shown in Figs.2 (a)~(e), respectively. First, the relationship between ρAρB 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 SERmin, should be larger than 20 dB to meets the requirement of optical fiber communication systems30. 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.

    The influence of ρA and ρB on the performance of the optical filter

    Figure 2.The influence of ρA and ρB on the performance of the optical filter

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

    The relationship between ρAρB 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 (ρAρB) 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 Y2 is 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.

    HY2(z)=0.5N1-N2z-1e-jθ+N3z-2e-j2θ-N1e-jθAz-3e-j3θ1-(2ρBcosθB+ρAe-jθA)z-1e-jθ+(ρB2+2ρAρBcosθBe-jθA)z-2e-j2θ-ρB2ρAe-jθAz-3e-j3θ

    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.

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

    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 Ri shown in Fig.4 is consisted of four arcs with radius of ri, two vertical straight waveguides with length of Lmi and two horizontal straight waveguides with length of Lnii=A, B and C).

    The structure of the race-track microring resonator

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

    As the discussion on the Fig. 2 (e), the smaller the ρA, the larger the BTR. In Fig. 4WidthGap and LnA are the key structural parameters that affect ρA. To find out the minimum value of ρA named ρAmin, FDTD method is used to calculate the value of ρAmin 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 ρAmin will be 0.008 when Width is 0.4 μm, Gap is 130 nm and LnA is 5.85 μm. A black line where ρA 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 ρB as well as ρC is 0.43, and LnB and LnC are calculated to be 3.69 μm, while keeping Width equal to 0.4 μm and Gap equal to 130 nm.

    The value of ρAmin with different Width, Gap and LnA

    Figure 5.The value of ρAmin with different Width Gap and LnA

    The transmission coefficient ρr 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, LmA is calculated to be 0.37 μm, LmB as well as LmC to be 2.75 μm and ri to be about 5 μm (i=ABandC).

    The relationship between the FSR and the minimum SER of the two outputs

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

    During the analysis in Section 2, the phase θC or θB is negative (θC = -θB), 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.

    dndT=9.48×10-5+3.47×10-7×T-1.49×10-10×T2K-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, RB can be heated and RC can be cooled, or vice versa, to keep θC equal to 2π-θB, which is the same as θC equal to -θB from the perspective of phase.

    The relationship between the initial phase and Δn

    Figure 7.The relationship between the initial phase and Δn

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

    The structure of the phase shifter

    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 θBand θC. The SER is better than 20 dB and the PL is 0.4 dB to 0.7 dB.

    ItemValue
    Waveguide typeChannel
    Waveguide height0.25 μm
    rArB and rC5 μm
    Width0.4 μm
    Gap130 nm
    Refractive index of silicon3.507
    Refractive index of silica1.447
    PolarizationTE
    LnA / LnB and LnC5.85 μm/3.69 μm
    LmA / LmB and LmC0.37 μm/2.75 μm

    Table 2. The simulation settings of the filter

    The performance of the optical filter with different θB and θC

    Figure 9.The performance of the optical filter with different θB and θC

    Both the bandwidth and wavelength can be reconstructed at the same time by tuning the phase of the resonators. The bandwidth is controlled by θB and θC, 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 θB changed between 0 to π with step of π/2 while keeping θC equal to 2π-θB. 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°.

    The reconfigurations of the wavelength and the bandwidth of the filter

    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 θB and θC, 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 θB changed between 0 to π with step of π/2 while keeping θC equal to 2π-θB. 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.

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    Jia JIANG, Minming GENG, Qiang LIU, Zhenrong ZHANG. Design of a Reconfigurable Optical Filter Based on Triple-ring-assisted Mach-Zenhnder Interferometer with Large Bandwidth Tuning Capability[J]. Acta Photonica Sinica, 2021, 50(7): 275
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