On-chip dense wavelength division multiplexing system based on cascaded fabry-perot optical filters
By using an on-chip dense wavelength division multiplexing (DWDM) system with cascaded Fabry-Perot optical filters, combined with multimode waveguide gratings and mode multiplexers/demultiplexers, the problems of high cost, large size, and poor robustness of DWDM systems are solved, achieving low insertion loss and low crosstalk DWDM effects, which is suitable for the field of optical communication.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2023-06-20
- Publication Date
- 2026-06-19
AI Technical Summary
Existing DWDM systems suffer from high costs, difficulty in packaging, and large size. FP optical cavity filters have low FSR, low extinction ratio, and high loss, while micro-ring optical filters are difficult to meet the requirements of international communication protocols and mass production due to their large size and poor robustness.
An on-chip dense wavelength division multiplexing (DWDM) system based on cascaded Fabry-Perot optical filters is adopted. By using a cascaded FP cavity structure, combined with a multimode waveguide grating and a mode multiplexer/demultiplexer, the TE0 mode of the signal is reverse-coupled to the TE1 mode, reducing the influence of higher-order modes. Furthermore, the center wavelength of different channels can be adjusted by controlling the center wavelength through the straight waveguide in the cascaded FP cavity.
It realizes a dense wavelength division multiplexing system with low insertion loss and low crosstalk, and features flexible wavelength selectivity, adjustable 3dB bandwidth, good stability, small size, low additional loss and ultra-wide free spectrum range. It is easy to process and produce at low cost, and is suitable for various optical communication applications.
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Figure CN116990903B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to an on-chip dense wavelength division multiplexing system in the field of optical communication, specifically an on-chip dense wavelength division multiplexing system based on a cascaded Fabry-Perot optical filter. Background Technology
[0002] With the gradual development and convergence of broadcast television networks and the Internet, the demand for bandwidth in data services is increasing daily. The relationship between communication transmission networks and services has become increasingly complex under the circumstances of a significant increase in service volume. The existing TDM (Time Division Multiplexing) technology cannot meet the demands of new technologies. The highest commercial rate for fiber optic single-wavelength transmission is 40 Gbits / s, and it is very expensive. TDM technology struggles to adapt to the complex network and service relationships. However, fiber optic multi-wavelength transmission technology, which uses pure optical devices for long-wavelength scheduling, breaks through the limits of electronic device processing speed. Based on SDH (Synchronous Digital Hierarchy) technology, the transmission capacity of optical fibers is significantly improved. Thus, DWDM (Dense Wavelength Division Multiplexing) systems have emerged. Its main function is to combine a group of optical wavelengths for transmission using a single optical fiber. This is a laser technology used to increase bandwidth on existing optical fiber backbones. It can also refer to the close spectral spacing of a single optical fiber carrier multiplexing within a specific optical fiber to achieve the required performance during transmission.
[0003] Currently, practical DWDM systems are composed of discrete coupled components, which suffer from drawbacks such as high cost, difficulty in packaging, and large size, far from meeting the needs of future optical device development. On-chip dense wavelength division multiplexing (DWDM) systems based on Fabry-Perot optical filters and micro-ring optical filters have attracted considerable attention due to their ease of fabrication, small size, and low cost. The biggest challenge in designing DWDM systems is meeting the requirements of international communication protocols such as IP, ATM, SONET / SDH, and Ethernet. Simultaneously, it is necessary to ensure low insertion loss and low crosstalk of the overall device while meeting bandwidth requirements. However, current FP (fiber optic) cavity filters on various platforms suffer from low FSR, low extinction ratio, and high loss, making them unsuitable for DWDM systems. Micro-rings, on the other hand, are difficult to fabricate due to their large size and poor robustness, hindering the mass production of DWDM systems. Summary of the Invention
[0004] To address the problems existing in the background technology, this invention proposes an on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters.
[0005] The technical solution adopted in this invention is:
[0006] This invention includes an input waveguide, an output waveguide, and N filter structures, which are connected sequentially. The input waveguide is connected to the input end of the first filter structure, and the output waveguide is connected to the output end of the last filter structure.
[0007] For the nth filter structure among the N filter structures, the nth filter structure includes a mode demultiplexer, a filter unit, and a through waveguide. The mode demultiplexer is connected to the through waveguide through the filter unit. The input end of the mode demultiplexer is connected to the input waveguide or the output end of the previous filter structure as the input end of the filter structure. The output end of the mode demultiplexer is connected to the output waveguide or the output end of the next filter structure as the output end of the filter structure.
[0008] In the nth filtering structure, the mode demultiplexer includes an input connecting waveguide, an output waveguide, a mode multiplexing working area, and an output connecting waveguide. Both the input connecting waveguide and the output waveguide are connected to one end of the mode multiplexing working area. The input connecting waveguide serves as the input end of the mode demultiplexer, and the output waveguide serves as the output end of the mode demultiplexer. The other end of the mode multiplexing working area is connected to the output connecting waveguide, and the output connecting waveguide is connected to one end of the filtering unit.
[0009] In the nth filtering structure, the filtering unit includes multiple multimode waveguide gratings and connecting waveguides. The multiple multimode waveguide gratings are arranged sequentially at intervals along the optical axis. The two multimode waveguide gratings at both ends of the filtering unit are connected to the mode demultiplexer and the through waveguide, respectively. Adjacent multimode waveguide gratings are connected through connecting waveguides.
[0010] In different filtering structures, the number of multimode waveguide gratings in the filtering unit may be different or the same.
[0011] In the nth filter structure, the filter unit is a structure that is symmetrical about the center.
[0012] The waveguide width of the connecting waveguide is the same as the waveguide width of the multimode waveguide grating.
[0013] In the filtering unit, the connecting waveguide is a straight waveguide.
[0014] In the nth filter structure, the through waveguide is composed of a third connecting waveguide and a download waveguide connected together. The third connecting waveguide is connected to the filter unit, and the download waveguide serves as the download end of the system.
[0015] In the nth filter structure, the third connecting waveguide is a tapered waveguide.
[0016] In the filtering unit, multiple multimode waveguide gratings are reverse-coupled from the TE0 mode of the signal to the TE1 mode, satisfying the following phase matching condition:
[0017] (n eff0+n eff1 ) / 2=λ / Λ
[0018] Where, n eff0 n is the effective refractive index of the TE0 mode. eff1 λ is the effective refractive index of TE1 mode, λ is the filter wavelength, and Λ is the grating sawtooth period.
[0019] This invention is based on a cascaded FP cavity, which has a large tolerance, ultra-high FSR, and adjustable 3dB bandwidth, and can realize filters with different bandwidth and channel number requirements.
[0020] The cascaded FP cavity of the present invention is mainly composed of three sets of multimode waveguide gratings and straight waveguides connected in sequence. The multimode waveguide gratings and straight waveguides on both sides have the same structure, making the filtering unit symmetrical about the center.
[0021] In this invention, a mode multiplexer is used to connect the two filtering units, so that no higher-order modes pass through, which can reduce crosstalk between channels and obtain a dense wavelength division multiplexing system with low insertion loss and low crosstalk.
[0022] This invention achieves different center wavelengths for different channels by controlling the center wavelength through the straight waveguide in the cascaded FP cavity.
[0023] The beneficial effects of this invention are as follows:
[0024] This invention multiplexes multi-channel signals into a waveguide through cascaded FP cavities, realizing an on-chip dense wavelength division multiplexing system.
[0025] This invention introduces a multimode waveguide grating and a mode multiplexer / demultiplexer, and uses mode conversion to achieve upload and download functions. It can filter out the influence of higher-order modes and does not require a dedicated mode filter.
[0026] This invention significantly reduces the overall device size by using a cascaded FP cavity structure.
[0027] The present invention reduces crosstalk between channels by using a specially designed waveguide structure that combines a mode multiplexer / demultiplexer and an FP cavity.
[0028] This invention employs a special cascaded FP cavity structure, which can reduce crosstalk between channels and has advantages such as flexible wavelength selectivity, adjustable 3dB bandwidth, good stability, small size, low additional loss and ultra-wide free spectral range, making it easy to meet the needs of various optical communication applications.
[0029] This invention controls the center wavelength by using a straight waveguide in a cascaded FP cavity, which provides high fault tolerance and greatly improves the robustness of the device.
[0030] This invention can be fabricated using planar integrated optical waveguide technology, requiring only one etching operation. The process is simple, low-cost, high-performance, low-loss, small-sized, and has good stability, making it highly promising for mass production.
[0031] This invention can be fabricated using planar integrated optical waveguide technology, which is simple, low-cost, high-performance, and low-loss, and is compatible with traditional CMOS technology, thus having great potential for mass production.
[0032] In summary, this invention achieves a dense wavelength division multiplexing (DWDM) system with high process tolerance, ease of fabrication, simple structure, low loss, small size, high extinction ratio, good stability, and low crosstalk between communication channels on various material platforms (e.g., silicon-on-insulator, silicon nitride, lithium niobate platforms). DWDM systems with different numbers of channels and different channel bands can be implemented according to specific communication protocol requirements. Attached Figure Description
[0033] Figure 1 This is a schematic diagram of the overall structure of an on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters.
[0034] Figure 2 This is a schematic diagram of the cascaded FP cavity optical filter in the filtering unit.
[0035] Figure 3 This is a schematic diagram illustrating the working principle of an on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters.
[0036] Figure 4 This is a schematic diagram of the simulation effect of the on-chip dense wavelength division multiplexing system using multi-cascaded Fabry-Perot optical filters on SOI in Embodiment 1 of the present invention.
[0037] Figure 5 This is a schematic diagram of the simulation effect of the on-chip dense wavelength division multiplexing system using multi-cascaded Fabry-Perot optical filters on LNOI, according to Embodiment 1 of the present invention.
[0038] In the diagram: Mode demultiplexer a n1 Filter unit a n2 Straight-through waveguide a n3 Input connection waveguide n01, mode multiplexer n02, first connection waveguide n03, transmission waveguide n04, first multimode waveguide grating n05, first multimode waveguide n06, second multimode waveguide grating n07, second connection waveguide n08, third multimode waveguide grating n09, third connection waveguide n10, download waveguide n11. Detailed Implementation
[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0040] like Figure 1 As shown, the present invention is mounted on various material platforms (e.g., silicon-on-insulator, silicon nitride, lithium niobate platforms). The present invention includes an input waveguide 1, an output waveguide 2, and N filter structures, which are connected sequentially. The input waveguide 1 is connected to the input end of the first filter structure, and the output waveguide 2 is connected to the output end of the last filter structure.
[0041] Figure 2 As shown, for the nth filter structure out of N filter structures, n = 1, 2, ..., N-1, N. The nth filter structure includes a mode demultiplexer a. n1 Filtering unit a n2 and through waveguide a n3 Mode demultiplexer a n1 Through filter unit a n2 With through waveguide a n3 Connected, mode demultiplexer a n1 The input terminal of the mode demultiplexer is connected to the input waveguide 1 or the output terminal of the previous filter structure, serving as the input terminal of the filter structure. n1 The output terminal is connected to the output waveguide 2 or the output terminal of the next filter structure as the output terminal of the filter structure.
[0042] Pattern demultiplexer a n1 It includes an input connection waveguide n01, an output waveguide n04, a mode multiplexing working area n02, and an output connection waveguide n03. Both the input connection waveguide n01 and the output waveguide n04 are connected to one end of the mode multiplexing working area n02. The input connection waveguide n01 serves as the mode demultiplexer a. n1 The input terminal and the output waveguide n04 serve as the mode demultiplexer a. n1 The output terminal of the mode multiplexing working area n02 is connected to the other end of the output connection waveguide n03, and the output connection waveguide n03 is connected to the filter unit a. n2 One end is connected to the first multimode waveguide grating n05. The mode multiplexing working area n02 is used to realize the mode conversion from TE1 mode to TE0 mode, and may be composed of, but is not limited to, asymmetric directional coupling waveguide, adiabatic evolution waveguide, and grating-assisted coupling waveguide.
[0043] Filtering unit a n2 It has a structure that is about-center symmetric. Filter unit a n2 It includes multiple multimode waveguide gratings with transverse amplitude apodization and connecting waveguides. The multiple multimode waveguide gratings are arranged sequentially at intervals along the optical axis and are located in filter unit a. n2 The two multimode waveguide gratings at both ends are respectively connected to the mode demultiplexer a n1 The output connects waveguide n03 and through waveguide a. n3The third connecting waveguide n10 is connected, and adjacent multimode waveguide gratings are connected through connecting waveguides. Filtering unit a n2 In this configuration, the number of multimode waveguide gratings is one more than the number of connecting waveguides. The waveguide width of the connecting waveguides is the same as the waveguide width of the multimode waveguide gratings. The connecting waveguides are straight waveguides. When there are three multimode waveguide gratings, the filtering unit a... n2 It is composed of a first multimode waveguide grating n05, a first multimode waveguide n06, a second multimode waveguide grating n07, a second connecting waveguide n08, and a third multimode waveguide grating n09 connected in sequence.
[0044] Straight waveguide a n3 It consists of a third connecting waveguide n10 and a download waveguide n11 connected together. The third connecting waveguide n10 is connected to the third multimode waveguide grating n09 of the filter unit an2, and the download waveguide n11 serves as the download end of the system. The third connecting waveguide n10 is a tapered waveguide.
[0045] In different filter structures, filter unit a n2 The number of multimode waveguide gratings may be different or the same.
[0046] Filtering unit a n2 In this design, multiple multimode waveguide gratings are reverse-coupled from the TE0 mode of the signal to the TE1 mode. The input TE0 mode can be reverse-coupled into the TE1 mode near the Bragg resonance condition. By selecting the overall grating width, grating tooth depth, and grating period, the required center wavelength and bandwidth can be obtained. By employing an apodized grating structure, crosstalk between the various signal channels is reduced. The following phase matching conditions are met:
[0047] (n eff0 +n eff1 ) / 2=λ / Λ
[0048] Where, n eff0 n is the effective refractive index of the TE0 mode. eff1 λ is the effective refractive index of TE1 mode, λ is the filter wavelength, and Λ is the grating sawtooth period.
[0049] The following describes the operation of this invention as an ultra-low crosstalk cascaded grating type multichannel on-chip filter:
[0050] The working principle of this invention is as follows: Figure 3As shown, optical signals of various wavelengths (λ1…λN) carrying information are input from the Input terminal and pass through the cascaded FP cavity of the first channel. The light of wavelength λ1 satisfies the phase matching condition and resonates in the cascaded FP cavity, then outputs from the download waveguide. The light of other wavelengths (λ2…λN) is output from the mode demultiplexer and enters the cascaded FP cavity of the next channel. Finally, optical signals of the same wavelength are downloaded sequentially through multiple cascaded FP cavities. This results in a multi-channel on-chip dense wavelength division multiplexing system with ultra-low crosstalk between adjacent channels, ultra-high side-mode rejection ratio, and ultra-high channel roll-off.
[0051] The specific embodiment 1 of the present invention is as follows:
[0052] Filtering unit a n2 It consists of three multimode waveguide gratings and two straight waveguides connected in sequence. The multimode waveguide gratings on both sides have the same structure, making the filter unit a n2 Regarding central symmetry. In specific implementation, the three multimode waveguide gratings are denoted as n05, n07, and n09. The sawtooth distribution of the three multimode waveguide gratings always maintains an antisymmetric distribution, so that the incident TE0 / TE1 mode is converted into TE1 / TE0 mode after reflection.
[0053] A silicon nanowire optical waveguide based on silicon insulator (silicon on insulator) material was selected: its core layer is silicon material with a thickness of 220 nm and a refractive index of 3.4744; its lower cladding material is SiO2 with a thickness of 2 μm and a refractive index of 1.4404; and its upper cladding material is SU-8 with a thickness of 1.2 μm and a refractive index of 1.57.
[0054] For the mode demultiplexer, the widths of the two sides of the wide tapered waveguide in the evolution region are selected as 0.45μm and 0.55μm, respectively, and the widths of the two sides of the narrow tapered waveguide in the evolution region are selected as 0.25μm and 0.12μm, respectively. The lengths of the three segments are 20μm, 50μm and 15μm, respectively. The spacing between the wide and narrow tapered waveguides remains unchanged at 0.2μm. The maximum spacing between the front S-shaped waveguide and the optical waveguide is 0.7μm, and the maximum spacing between the rear S-shaped waveguide and the optical waveguide is 1.2μm.
[0055] For the three multimode waveguide gratings constituting the FP cavity, the selected parameters are all: total grating width of 1100 nm, grating tooth depth of 600 nm, grating period of 320 nm, grating period numbers of 30, 70, and 30, and grating duty cycle of 0.5. The center wavelength of the cascaded FP cavity is adjusted by controlling the cavity length between two cascaded FP cavities, thus achieving different channel numbers. Here, the eight straight waveguide lengths selected for eight different channels are: 0.320, 0.336, 0.352, 0.368, 0.384, 0.400, 0.416, and 0.432.
[0056] For the three multimode waveguide gratings, an intensity apodization scheme was adopted, and the apodization form was Gaussian apodization.
[0057] The dense wavelength division multiplexing system composed of cascaded FP cavities was simulated and verified using a three-dimensional time-domain finite difference algorithm. Figure 4 Corresponding to the simulation results, as shown in the figure, the device of the present invention has a 3dB bandwidth of 0.8nm in the eight channels around 1550nm, achieving flat-top filtering while the insertion loss at the 1550nm peak is <0.6dB, and the crosstalk on both sides of adjacent channels is <-25dB. Therefore, the device of the present invention can achieve a DWDM system with low insertion loss and low crosstalk at a 3.2nm channel spacing.
[0058] The specific embodiment 2 of the present invention is as follows:
[0059] The filtering unit remains the same as described above.
[0060] A shallow-etched lithium niobate waveguide based on lithium niobate material was selected: its core layer is lithium niobate material with a thickness of 400 nm and a refractive index of 2.21; its lower cladding material is SiO2 with a thickness of 3 μm and a refractive index of 1.4404; and its upper cladding material is air cladding.
[0061] For the mode demultiplexer, the widths of the two sides of the wide tapered waveguide in the evolution region are selected as 1μm and 2μm, respectively, and the widths of the two sides of the narrow tapered waveguide in the evolution region are selected as 0.6μm and 0.2μm, respectively. The lengths of the three segments are 50μm, 200μm and 50μm, respectively. The spacing between the wide and narrow tapered waveguides remains unchanged at 0.25μm. The maximum spacing between the front S-shaped waveguide and the optical waveguide is 1.2μm, and the maximum spacing between the rear S-shaped waveguide and the optical waveguide is 2μm.
[0062] For the three multimode waveguide gratings constituting the cascaded FP cavity, the selected parameters are: total grating width of 1850 nm, grating tooth depth of 850 nm, grating period of 420 nm, grating period numbers of 50, 110, and 50 respectively, and grating duty cycle of 0.5. The center wavelength of the cascaded FP cavity is adjusted by controlling the cavity length between two cascaded FP cavities, thus achieving different channel numbers. Here, the eight straight waveguide lengths selected for eight different channels are: 0.420, 0.455, 0.490, 0.525, 0.560, 0.595, 0.630, and 0.665.
[0063] For the mode demultiplexer, the widths of the two sides of the wide tapered waveguide in the evolution region are selected as 0.45μm and 0.55μm, respectively, and the widths of the two sides of the narrow tapered waveguide in the evolution region are selected as 0.25μm and 0.12μm, respectively. The lengths of the three segments are 20μm, 50μm and 15μm, respectively. The spacing between the wide and narrow tapered waveguides remains unchanged at 0.2μm. The maximum spacing between the front S-shaped waveguide and the optical waveguide is 0.7μm, and the maximum spacing between the rear S-shaped waveguide and the optical waveguide is 1.2μm.
[0064] For the three multimode waveguide gratings, an intensity apodization scheme was adopted, and the apodization form was Gaussian apodization.
[0065] The dense wavelength division multiplexing system composed of cascaded FP cavities was simulated and verified using a three-dimensional time-domain finite difference algorithm. Figure 5 Corresponding to the simulation results, as shown in the figure, the device of the present invention has a 3dB bandwidth of 1.2nm in the eight channels around 1550nm, achieving flat-top filtering while the insertion loss at the 1550nm peak is <0.5dB, and the crosstalk on both sides of adjacent channels is <-25dB, with a channel spacing of 1.6nm. Therefore, the device of the present invention can achieve a DWDM system with low insertion loss, low crosstalk, and a 1.6nm channel spacing.
[0066] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.
Claims
1. An on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters, characterized in that, It includes an input waveguide (1), an output waveguide (2), and N filter structures. The N filter structures are connected in sequence. The input waveguide (1) is connected to the input end of the first filter structure, and the output waveguide (2) is connected to the output end of the last filter structure. For the nth filter structure among the N filter structures, the nth filter structure includes a mode demultiplexer (a n1 ), Filtering unit (a) n2 ) and through waveguide (a n3 ), mode demultiplexer (a n1 ) through the filter unit (a n2 ) and through waveguide (a n3 ) connected, mode demultiplexer (a n1 The input terminal of the mode demultiplexer (a) is connected to the input waveguide (1) or the output terminal of the previous filter structure as the input terminal of the filter structure. n1 The output of the filter structure is connected to the output waveguide (2) or the output of the next filter structure.
2. The on-chip dense wavelength division multiplexing system based on a cascaded Fabry-Perot optical filter according to claim 1, characterized in that, In the nth filtering structure, the mode demultiplexer (a n1 The circuit includes an input connection waveguide (n01), an output waveguide (n04), a mode multiplexing working area (n02), and an output connection waveguide (n03). Both the input connection waveguide (n01) and the output waveguide (n04) are connected to one end of the mode multiplexing working area (n02). The input connection waveguide (n01) serves as the mode demultiplexer (a n1 The input terminal of the waveguide (n04) is used as the output waveguide (n04) for the mode demultiplexer (a). n1 The output of the mode multiplexing working area (n02) is connected to the output connection waveguide (n03), and the output connection waveguide (n03) is connected to the filter unit (a). n2 One end is connected.
3. The on-chip dense wavelength division multiplexing system based on a cascaded Fabry-Perot optical filter according to claim 1, characterized in that, In the nth filter structure, the filter unit (a n2 It includes multiple multimode waveguide gratings and connecting waveguides. The multiple multimode waveguide gratings are arranged sequentially at intervals along the optical axis and are located in the filtering unit (a). n2 The two multimode waveguide gratings at both ends are respectively connected to the mode demultiplexer (a n1 ) and through waveguide (a n3 The two adjacent multimode waveguide gratings are connected by a connecting waveguide.
4. The on-chip dense wavelength division multiplexing system based on a cascaded Fabry-Perot optical filter according to claim 1, characterized in that, In different filter structures, the number of multi-mode waveguide gratings of the filter unit (a n2 ) is different or the same.
5. The on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters of claim 1, wherein, In the nth filter structure, the filter unit (a n2 ) is a structure that is symmetric about the center.
6. The on-chip dense wavelength division multiplexing system based on a cascaded Fabry-Perot optical filter according to claim 3, characterized in that, The waveguide width of the connecting waveguide is the same as the waveguide width of the multimode waveguide grating.
7. The on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters of claim 3, wherein, The filtering unit (a) n2 In this context, the connecting waveguide is a straight waveguide.
8. The on-chip dense wavelength division multiplexing system based on a cascaded Fabry-Perot optical filter according to claim 3, characterized in that, In the nth filtering structure, the through waveguide (a n3 It consists of a third connecting waveguide (n10) and a download waveguide (n11) connected together. The third connecting waveguide (n10) is connected to the filter unit (a). n2 Connected to the network, the download waveguide (n11) serves as the download end of the system.
9. The on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters of claim 8, wherein, In the nth filter structure, the third connecting waveguide (n10) is a tapered waveguide.
10. The on-chip dense wavelength division multiplexing system based on cascaded Fabry-Perot optical filters of claim 3, wherein, The filtering unit (a) n2 In this process, multiple multimode waveguide gratings are reverse-coupled from the TE0 mode to the TE1 mode, satisfying the following phase matching condition: (n eff0 +n eff1 ) / 2 = λ / Λ where n eff0 is the effective refractive index for TE0 mode, n eff1 is the effective refractive index for TE1 mode, λ is the filter wavelength, and Λ is the grating sawtooth period.
Citation Information
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