Tunable topological valley photonic crystal filter with multi-wavelength notch

Abstract

The application discloses a multi-wavelength notch-adjustable topological valley topological photonic crystal filter, which comprises a waveguide interface, a first topological valley topological photonic crystal and a second topological valley topological photonic crystal. The first topological valley topological photonic crystal comprises a plurality of first regular hexagonal cells, a sector-shaped dielectric column is arranged at three interphase vertices of a single first regular hexagonal cell, and the first regular hexagonal cells are arranged in a honeycomb array to obtain N circular dielectric columns with a radius R. The second topological valley topological photonic crystal comprises a plurality of second regular hexagonal cells. A sector-shaped dielectric column is arranged at three interphase vertices of a single second regular hexagonal cell, and the sign of the valley Chern number of the second regular hexagonal cell is opposite to that of the first regular hexagonal cell. The second regular hexagonal cells are arranged in a honeycomb array to obtain M circular dielectric columns, the radius of M1 circular dielectric columns is R, the radius of M2 circular dielectric columns is greater than R, and M1+M2=M. The application can realize a multi-wavelength interval notch function.

Description

Technical Field

[0001] This invention belongs to the field of photonic crystal technology, specifically relating to a multi-wavelength notch tunable topological valley topological photonic crystal filter. Background Technology

[0002] Topological photonics enables robust manipulation of electromagnetic waves by introducing topological states. Valley photonic crystals, in particular, have attracted significant attention due to their ability to be realized without an external magnetic field, using all dielectric materials, and being compatible with CMOS processes. Devices based on valley topological boundary states have been used in waveguides, couplers, and other applications.

[0003] However, existing related technologies have the following main drawbacks:

[0004] 1. Error Sensitivity: Traditional waveguide structures are highly sensitive to manufacturing errors. Even minor process defects can cause a sharp decline in device performance, resulting in low yield rates.

[0005] 2. Difficulty in adjusting the operating frequency: The operating frequency of most topological photonic devices (such as topological waveguides) is determined by the geometric parameters. Once the fabrication is completed, the frequency is fixed, which limits their application in controllable spectral modulation.

[0006] 3. Existing tuning mechanisms have significant limitations: Existing tunable filters typically rely on thermal tuning, mechanical tuning, or complex multi-cavity coupling structures, which suffer from low tuning efficiency, high power consumption, or insufficient device integration.

[0007] 4. Limitations on free spectral range: When filtering multiple wavelengths, the wave response exhibits strict periodicity, making it difficult to meet the requirements of next-generation optical networks for non-uniform, arbitrary wavelength spacing channel allocation. Summary of the Invention

[0008] To address the aforementioned problems, this invention proposes a multi-wavelength notch tunable topological valley topological photonic crystal filter that can achieve multi-wavelength interval notch functionality.

[0009] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0010] A multi-wavelength notch tunable topological valley topological photonic crystal filter includes: a waveguide interface, and a first valley topological photonic crystal and a second valley topological photonic crystal distributed on both sides of the waveguide interface.

[0011] The first valley topological photonic crystal includes several first regular hexagonal units. At the three alternating vertices of a single first regular hexagonal unit, a fan-shaped dielectric pillar is set. Each first regular hexagonal unit is arranged in a honeycomb array with a period length of lattice constant a, resulting in N circular dielectric pillars. The radius of the N circular dielectric pillars is R.

[0012] The second valley topological photonic crystal comprises several second regular hexagonal units; fan-shaped dielectric pillars are respectively set at the three alternating vertices of a single second regular hexagonal unit, and the sign of their valley Chern number is opposite to that of the first regular hexagonal unit; each second regular hexagonal unit is arranged in a honeycomb array with a period length of lattice constant a, resulting in M ​​circular dielectric pillars, wherein the radius of M1 circular dielectric pillars is R, the radius of M2 circular dielectric pillars is greater than R, and the circular dielectric pillars with a radius greater than R are defined as defect pillars, M1+M2=M and M1>M2.

[0013] Optionally, the radius of the defective column can be in the range of 0.480a–0.485a.

[0014] Optionally, when the number of defective pillars is greater than 1, each defective pillar is independent of the others and is set sequentially along the extension direction of the waveguide interface.

[0015] Optionally, when the number of defective pillars is greater than 1, the defective pillars are located in the same row or different rows and are arranged sequentially along the extension direction of the waveguide interface.

[0016] Optionally, when the number of defect pillars is greater than 1, the radius of each defect pillar is different, and the interval between the resonant wavelengths corresponding to each defect pillar is different.

[0017] Optionally, the waveguide interface is sawtooth-shaped. The sawtooth waveguide interface is formed by the fan-shaped dielectric pillars at the upper left and upper right vertices of the first regular hexagonal cell distributed on one side of the waveguide interface, and the fan-shaped dielectric pillars at the lower left and lower right vertices of the second regular hexagonal cell distributed on the other side of the waveguide interface, which are arranged in a staggered and interlocking manner along the waveguide extension direction.

[0018] Optionally, when the lattice constant a is 560 nm and R is 0.3a, the operating frequency band of the topological boundary states supported by the sawtooth waveguide interface is from 172.588 THz to 199.417 THz.

[0019] Optionally, the sector-shaped dielectric column is made of an electro-optically tunable material.

[0020] Optionally, the sector-shaped dielectric column is made of barium titanate.

[0021] Optionally, when the number of defect pillars is 1, the radius Rs of the defect pillar is 0.480a, the lattice constant a is 560 nm, R is 0.3a, the defect pillar is located at a lattice point at a distance from the third layer cell of the waveguide interface, and the refractive index of the defect pillar is adjustable in the range of 2.39–2.42, the operating frequency band of the filter is 192.33 THz to 193.78 THz.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] This invention only requires the introduction of a single defect pillar to obtain a highly selective narrowband concave peak, without the need for a complex multi-cavity coupling structure. The structure is simple and compact, and easy to integrate on a chip.

[0024] This invention uses barium titanate to prepare a fan-shaped dielectric column. By utilizing the electro-optic effect of barium titanate, a small change in refractive index can cause a significant shift in the resonant wavelength, resulting in highly sensitive tunability.

[0025] This invention enables multi-wavelength filtering by cascading defect pillars of different radii. Unlike traditional devices limited by FSR, the channel spacing of this invention is fully controllable, allowing for the design of non-uniform spectrum channels according to requirements, greatly improving the flexibility of spectrum resource utilization. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0027] Figure 1 The diagram shows the structure and performance of VPC1 and VPC2; where, Figure 1 (a) is a schematic diagram of the structure of VPC1 and VPC2; Figure 1 (b) shows the phase and poynting vector distributions of VPC1 and VPC2 at point K, where the red and blue arrows represent the directions of phase changes, respectively. Figure 1 (c) is a band structure diagram of a single unit cell with a photonic band gap; Figure 1 (d) illustrates the relationship between the photonic bandgap and the radius of the sector-shaped dielectric pillar;

[0028] Figure 2 This diagram illustrates the dispersion relation, field distribution, and transmission characteristics of a Z-shaped sawtooth waveguide for the topological boundary states; among which, Figure 2 (a) is the projection of the supercell band of VPC1 and VPC2 along the kx direction and the electric field modulus of VPC1 above and VPC2 below along the z direction. The red line marks the topological boundary mode and the gray line marks the volume mode. Figure 2 (b) is a diagram of the Z-shaped sawtooth waveguide structure spliced ​​together from VPC1 and VPC2, where the blue part is VPC1 and the red part is VPC2; Figure 2 (c) shows the electric field modulus distribution in a Z-shaped waveguide with a center frequency of 192 THz; Figure 2(d) shows the transmission curve of the Z-shaped waveguide near the photonic bandgap;

[0029] Figure 3 The diagram shows the topological waveguide structure containing a single-defect cavity and its intrinsic mode field distribution characteristics. Figure 3 (a) is a schematic diagram of a straight waveguide-type topological boundary structure and its central defect cavity, with the radius of the defect column set as... ; Figure 3 (b) shows the results of the filter's intrinsic frequency solution. The horizontal axis represents the intrinsic solution number, and the vertical axis represents the intrinsic frequency. Gray dots represent bulk modes, red dots represent topological boundary states located at the interface, blue dots represent defect modes localized in the defect cavity, and green dots represent boundary states localized in the straight waveguide sections on the left and right sides of the defect. Figure 3 (c)- Figure 3 (e) shows the electric field distribution at 192.48, 193.29, and 194.77 THz for the green dot (left), blue dot (middle), and green dot (right), respectively.

[0030] Figure 4 This is a schematic diagram illustrating the effect of changes in the radius of the defect pillar on the resonant frequency and mode field of the filter. Figure 4 (a) shows how the transmission spectrum of the filter changes by adjusting the radius of the defect column, with the horizontal axis representing frequency and the vertical axis representing transmittance; Figure 4 (b) shows the relationship between defect pillars of different radii and resonant frequencies; Figure 4 (c)- Figure 4 (f) shows the resonant frequencies respectively. , Electric field modulus plot and time-averaged power flow plot at the location;

[0031] Figure 5 This is a schematic diagram illustrating the multi-wavelength filtering characteristics at arbitrary channel intervals based on multiple independent defect pillars. Figure 5 (a) is an arbitrary channel spacing filter consisting of multiple defective pillars and a straight waveguide interface; Figure 5 (b) The transmission spectrum of the filter when R1=0.480a, R2=0.485a, and R3=0.481a; Figure 5 (c) The transmission spectrum of the filter when R1=0.480a, R2=0.485a, and R3=0.482a; Figure 5 (d) shows the transmission spectrum of the time-division filter with R1=0.480a, R2=0.485a, and R3=0.483a. The horizontal axis represents frequency, and the vertical axis represents transmittance.

[0032] Figure 6 This is a schematic diagram illustrating the effect of the refractive index variation of the defect pillar on the resonant frequency and mode field of the filter. Figure 6(a) shows how the transmission spectrum of the filter changes by adjusting the refractive index of the defect pillar. The horizontal axis represents frequency and the vertical axis represents transmittance. Figure 6 (b) shows the relationship between the defect column and the resonant frequency under different refractive indices; Figure 6 (c)- Figure 6 (f) shows the resonant frequencies respectively. , Electric field modulus plot and time-averaged power flow plot at the location;

[0033] Figure 7 This is a schematic diagram of the robustness test results of the filter for different structural disorder configurations (missing, bent, disordered); Figure 7 (a) is a schematic diagram of a perfect waveguide interface and a schematic diagram of three disordered configurations ("missing", "bent", "disordered") at the waveguide interface, used to test the robustness of the topology filter performance. Figure 7 (b) is Figure 7 (a) shows a schematic diagram of the transmission spectrum for the four scenarios. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may include different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0036] In the description of this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0037] In the description of this invention, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0038] The application principle of the present invention will be described in detail below with reference to the accompanying drawings.

[0039] This invention provides a multi-wavelength notch tunable topological valley topological photonic crystal filter, such as... Figure 5 As shown, it includes: a waveguide interface, and a first valley topological photonic crystal and a second valley topological photonic crystal distributed on both sides of the waveguide interface;

[0040] The first valley topological photonic crystal comprises several first regular hexagonal units. Sector-shaped dielectric pillars are respectively set at the three alternating vertices of each first regular hexagonal unit. Each first regular hexagonal unit is arranged in a honeycomb array with a period length of lattice constant a, resulting in N circular dielectric pillars, all with a radius of R. In a specific implementation, sector-shaped dielectric pillars are respectively set at the top vertex, lower left vertex, and lower right vertex of the first valley topological photonic crystal.

[0041] The second valley topological photonic crystal comprises several second regular hexagonal units; a sector-shaped dielectric pillar is set at each of the three alternating vertices of a single second regular hexagonal unit, and its valley Chern number sign is opposite to that of the first regular hexagonal unit; each second regular hexagonal unit is arranged in a honeycomb array with a period length of lattice constant a, resulting in M ​​circular dielectric pillars, each circular dielectric pillar being composed of three contacting sector-shaped dielectric pillars, wherein the radius of M1 circular dielectric pillars is R, the radius of M2 circular dielectric pillars is greater than R, and the circular dielectric pillars with a radius greater than R are defined as defect pillars, M1+M2=M, and M1>M2; in specific implementation, sector-shaped dielectric pillars are set at the lower vertex, upper left vertex, and upper right vertex of the second valley topological photonic crystal.

[0042] The above scheme only requires the introduction of a single defect pillar to obtain a highly selective narrowband concave peak, without the need for a complex multi-cavity coupling structure. The structure is simple and compact, and easy to integrate on-chip.

[0043] In one specific embodiment of the present invention, the radius of the defective column ranges from 0.480a to 0.485a.

[0044] In the above scheme, the radius of the defect pillar is specifically limited to ensure that the resonant frequency of the defect mode falls precisely in the central region of the topological bandgap of the photonic crystal (approximately 192 THz - 194 THz). At this point, the photonic crystal has the strongest localization ability of the light field, and the defect pillar (i.e., the defect cavity) has the highest quality factor (Q value), thus achieving an extremely narrow filtering bandwidth. If the radius is too small or too large, the defect mode may be integrated into the bulk or boundary state continuous spectrum, causing the filtering function to fail. Simultaneously, the radius variation within this range exhibits a good linear relationship with the resonant frequency, facilitating precise pre-setting of the center wavelength through geometric parameters.

[0045] In one specific embodiment of the present invention, the refractive index of the defect pillar is 2.39–2.42.

[0046] The above scheme specifically limits the range of refractive index values ​​for the defect pillars, ensuring that the resonant frequency undergoes a linear and continuous redshift (or blueshift) during electro-optic tuning, while maintaining high tuning sensitivity (approximately 391.5 nm / RIU). Simultaneously, within this perturbation range, the overall band structure and topological properties of the photonic crystal remain unchanged, ensuring no mode jumps during tuning and maintaining the stability of the filtering performance.

[0047] In one specific embodiment of the present invention, the sector-shaped dielectric column is made of an electro-optically tunable material.

[0048] In the above scheme, an electro-optic tunable material is used to prepare a sector-shaped dielectric column. The refractive index of the sector-shaped dielectric column can be continuously varied by an applied electric field. While keeping the geometric dimensions unchanged, more flexible dynamic tuning can be achieved by changing the refractive index of the defect column.

[0049] In one specific embodiment of the present invention, the sector-shaped dielectric column is made of barium titanate.

[0050] In the above scheme, barium titanate material is used to prepare a sector-shaped dielectric column. The refractive index of the sector-shaped dielectric column can be continuously varied by an applied electric field. A small change in the refractive index of the sector-shaped dielectric column can cause a significant shift in the resonant wavelength. While keeping the geometric dimensions unchanged, more flexible dynamic tuning can be achieved by changing the refractive index of the defect column.

[0051] When the number of defect pillars is 1, the radius Rs of the defect pillar is 0.480a, the lattice constant a is 560 nm, R is 0.3a, the defect pillar is located at a lattice point at a distance from the third layer cell of the waveguide interface, and the refractive index of the defect pillar is adjustable in the range of 2.39–2.42, the operating frequency band of the filter is 192.33THz to 193.78THz.

[0052] In one specific embodiment of the present invention, when the number of defective pillars is greater than 1, each defective pillar is independent of the others and is arranged sequentially along the extension direction of the waveguide interface.

[0053] In the above scheme, each defective column is independent of the others, generating a corresponding independent resonance peak in the transmission spectrum, thereby realizing customized filtering for arbitrary channel spacing.

[0054] In one specific embodiment of the present invention, when the number of defective pillars is greater than 1, the defective pillars are located in the same row or different rows and are arranged sequentially along the extension direction of the waveguide interface.

[0055] In the above scheme, the specific locations of each defect pillar are defined. Multiple defect pillars are sequentially arranged along the waveguide interface extension direction, maintaining a certain spacing (decoupling distance). This ensures that near-field coupling (Evanescent Coupling, EC) does not occur between the local mode fields of each defect pillar. In this way, each defect pillar operates as an independent resonant unit, and its resonant wavelength is determined only by its own geometric parameters (radius), unaffected by adjacent defect pillars. This "mutually independent" arrangement is key to breaking the limitations of the free spectral range (FSR) of traditional resonant cavities and realizing multi-wavelength spacing (Arbitrary Channel Spacing, ACS) filtering.

[0056] In one specific embodiment of the present invention, when the number of defective columns is greater than 1, the radii of each defective column are different.

[0057] In the above scheme, customized filtering for arbitrary channel intervals can be achieved when the radii of each defective pillar are different.

[0058] In one specific embodiment of the present invention, when the number of defect pillars is greater than 1, the resonant wavelength intervals corresponding to each defect pillar are different.

[0059] In the above scheme, when the resonant wavelength intervals corresponding to each defect pillar are different, customized filtering for arbitrary channel intervals can be achieved.

[0060] In one specific embodiment of the present invention, the waveguide interface is sawtooth-shaped. The sawtooth-shaped waveguide interface is formed by fan-shaped dielectric pillars located at the upper left and upper right vertices of the first regular hexagonal cell on one side of the waveguide interface (which is the lower side when the waveguide interface is horizontal), and fan-shaped dielectric pillars located at the lower left and lower right vertices of the second regular hexagonal cell on the other side of the waveguide interface (which is the upper side when the waveguide interface is horizontal), arranged in a staggered and interlocking pattern along the waveguide extension direction.

[0061] In the above scheme, the transmittance can be improved by designing the waveguide interface as a sawtooth shape.

[0062] When the lattice constant a is 560 nm and R is 0.3a, the operating frequency band of the topological boundary states supported by the sawtooth waveguide interface is from 172.588 THz to 199.417 THz.

[0063] The following is combined Figure 1 (a)- Figure 7 (b) A detailed description of the tunable topological valley topological photonic crystal filter of the present invention is provided.

[0064] To realize the tunable valley-topological photonic crystal filter proposed in this embodiment of the invention, the structure of the valley-topological photonic crystal is first designed. The valley-topological photonic crystal is designed based on a two-dimensional honeycomb lattice, arranged in a honeycomb array with a period length of lattice constant a = 560 nm. To construct the first and second valley-topological photonic crystals, as follows... Figure 1As shown in (a), this embodiment designs two different hexagonal unit cells with different topological phases, namely the first hexagonal unit cell VPC1 and the second hexagonal unit cell VPC2. Sector-shaped dielectric pillars are respectively set at the first vertices of the three phases of a single first hexagonal unit cell, and sector-shaped dielectric pillars are respectively set at the second vertices of the three phases of a single second hexagonal unit cell. The first vertices are different from the second vertices. This design breaks the spatial inversion symmetry. This symmetry breaking introduces Berry curvature and mass term m with opposite signs at the momentum space K / K' point, as shown in Figure 1(b). The phase of the first hexagonal unit cell VPC1 rotates clockwise, while the phase of the second hexagonal unit cell VPC2 rotates counterclockwise. The different phase rotation directions directly correspond to the reversal of the signs of the Berry curvature and the mass term m, causing the originally degenerated Dirac points to form a photonic bandgap with considerable spacing (170.66 THz-220.71 THz), as shown in Figure 1(b). Figure 1 As shown in (c), the first regular hexagonal unit cell VPC1 and the second regular hexagonal unit cell VPC2 coincide with each other during inversion, thus sharing the same frequency band structure. The radius of the sector-shaped dielectric pillar and the bandwidth of the photonic bandgap are inversely proportional, as shown in... Figure 1 As shown in (d), as the radius of the sector-shaped dielectric pillar increases, the photonic bandgap shifts towards decreasing frequency, while the bandwidth narrows. In specific implementations, the radius of the sector-shaped dielectric pillar can be set to R = 0.3a. The sector-shaped dielectric pillar is made of barium titanate material with a refractive index n = 2.40.

[0065] For the first regular hexagonal unit cell VPC1 ( For the second hexagonal unit cell VPC2, the Berry curvature at point K is positive, and the Berry curvature at point K′ is negative; while for the second hexagonal unit cell VPC2... Then this relationship is reversed. The valley Chern number of the first regular hexagonal unit cell VPC1 is: , The valley Chern number of the second regular hexagonal unit cell VPC2 is: , The valley number signs of the two structures are opposite, which means that when they are spliced ​​together, valley polarized boundary states will necessarily be formed according to the volume-edge correspondence.

[0066] The first regular hexagonal unit cell VPC1 and the second regular hexagonal unit cell VPC2 can be joined at the interface to form a valley topological boundary state. For example... Figure 2As shown in (a), boundary states connecting the upper and lower energy bands across the band gap appear within the common band gap region, and a continuous energy band connecting the upper and lower energy bands across the band gap appears within the common band gap region, i.e., topological valley boundary states. The boundary state mode field distribution indicates that its energy is tightly localized at the interface and decays rapidly into the crystal interior. Due to the large momentum gap between the K and K′ modes, conventional scattering is unlikely to cause inter-valley coupling, giving the boundary states a natural anti-backscattering capability. Further constructing a Z-shaped interface waveguide, despite containing two sharp 120° bends, the boundary states can still achieve low-loss propagation. The electromagnetic field smoothly deflects at each bend and continues to propagate along the interface, as shown in the figure. Figure 2 (b) and Figure 2 As shown in (c). Figure 2 The transmission spectrum results in (d) show that the transmittance is close to 0 dB within the boundary state operating frequency band, while the transmittance is as low as -80 dB outside the bandgap. This characteristic demonstrates the high robustness of the topological waveguide in this invention to structural disturbances.

[0067] To achieve tunable narrowband filtering based on topological boundary states, localized defect pillars are introduced on the linear topological interface formed by the first regular hexagonal cell VPC1 and the second regular hexagonal cell VPC2. Figure 3(a) shows a schematic diagram of the tunable topological photonic crystal filter: the radius of the fan-shaped dielectric pillars at the vertices of three specific units above the center of the topological boundary is adjusted to... This results in the formation of localized defect modes within the bandgap. Since the defect pillar is located at the position of maximum energy of the topological boundary states, its eigenmodes can effectively couple with the boundary states, thus forming a narrow-band concave peak in the transmission spectrum. To verify whether the defect pillar introduces an independent resonant mode, the eigenfrequency of the structure was solved, and the results are shown in Figure 3(b). The gray dots represent bulk modes, distributed throughout the entire bandgap and independent of the filtering mechanism; the red dots represent topological boundary states, whose mode fields are distributed along the straight interface, representing the main path of energy propagation. Notably, an independent blue frequency point appears within the cluster of red dots, with its electric field strongly localized around the heterostructure as shown in Figure 3(d), exhibiting extremely weak leakage, indicating that this mode is a high-quality defect pillar resonant mode within the bandgap. In contrast, although the two green dots to the left and right of the blue dots have similar frequencies, their mode fields are distributed on the left and right sides of the straight waveguide, as shown in Figure 3(c). Figure 3 As shown in (e), these are normal topological boundary states and do not produce a resonance peak. The comparison of the intrinsic modes above clearly shows that the narrowband resonance of the filter originates from the localized mode of the defect pillar corresponding to the blue dot, rather than the boundary state itself. When the operating frequency approaches the eigenfrequency of this localized defect mode, energy couples from the topological channel into the defect pillar, significantly reducing the transmittance of the main channel and forming a deep and narrow resonance peak; while at non-resonant frequencies, the straight interface still maintains the high transmittance characteristic unique to the topological state.

[0068] Since the intrinsic frequency of a defect pillar is determined by both its local effective refractive index and geometric dimensions, the radius of the defect pillar... or refractive index The modulation of these parameters can induce a smooth change in the position of the resonance concave peak.

[0069] To quantify the impact of defect pillar geometry on filter resonant performance while maintaining the material's refractive index For the radius of the defective column A scan was performed in the range of 0.480a–0.485a, and the resulting transmission spectra are shown in Figure 4(a). The transmission rates of all refractive indices at the resonant frequencies are less than -20dB. It can be observed that as the radius of the defect pillar increases, the resonant concave peak in the transmission spectrum gradually shifts from high frequencies to low frequencies, indicating that the local defect mode of the defect pillar is significantly affected by the size change. The relationship between the operating frequency and the radius is plotted in Figure 4(b). The resonant frequency decreases linearly (redshift), and the fitting results show that: ,in, The radius sensitivity coefficient, , THz, Figures 4(c) and 4(e) respectively show the minimum radius and maximum radius The electric field distribution under the given conditions is shown in Figure 4(d) and Figure 4(f). It can be seen that under both radii, the electric field is highly localized within the heterostructure region; as the radius increases, the electric field distribution expands slightly outward, demonstrating stronger cavity mode confinement; the mode field shape remains consistent, indicating that no abrupt changes or mode transitions occur during tuning. Figures 4(d) and 4(f) show the time-averaged power flow distribution at the corresponding frequencies. At the resonant frequency, energy couples from the topological interface into the defect pillar and is locally captured, causing a deep and narrow concave peak in the topological interface transmission; the power flow distribution exhibits high consistency under different radii, further proving that structural tuning does not disrupt the propagation characteristics of the topological boundary states themselves. The above analysis demonstrates that adjusting the radius of the defect pillar can achieve stable and predictable resonant tuning.

[0070] To achieve multi-channel filtering and break the free spectral range (FSR) limitation of traditional devices, this invention introduces multiple independent defect pillars along the propagation direction on the topological interface (as shown in Figure 5). Multiple defect pillars (e.g., three) are placed at different locations on the waveguide interface, with each defect pillar having a dielectric pillar radius of [missing information]. The resonant frequency of each defect pillar is primarily determined by its own geometric radius or refractive index, and is independent of the spacing between defect pillars (beyond a certain decoupling distance). This can be achieved through independent design ( The value of ) can produce three corresponding independent resonance peaks in the transmission spectrum. Unlike traditional resonators, the spacing between these wavelengths ( No longer constrained by the periodicity of the cavity length, it can be designed arbitrarily. For example, by fine-tuning the radius... It can make the resonance peak Located at the resonance peak and resonance peak It can be positioned at any position between channels, thus enabling customized filtering for any channel spacing.

[0071] The defect pillar in this invention uses electro-optically tunable barium titanate material, which allows the refractive index to be continuously variable through an applied electric field.

[0072] While keeping the geometric dimensions constant, more flexible dynamic tuning can be achieved by changing the refractive index of the defect pillar. Compared to adjusting the geometric parameter (radius), Figures 6(a) and 6(b) show the transmission spectrum and resonance frequency response when the refractive index varies in the range of 2.39–2.42. As the refractive index increases, the resonance peak exhibits a smooth and continuous low-frequency shift, consistent with the behavior of geometric tuning. Resonance frequency It has an approximately linear relationship with the change in refractive index: ,in, For refractive index tuning sensitivity , The electric field mode distributions in Figures 6(c) and 6(e) at THz show that the refractive index change did not alter the localization characteristics of the defect modes. The power flow distributions in Figures 6(d) and 6(f) further illustrate that the energy localization mechanism at the resonant frequency remains stable, and the background transmission at the topological interface remains unchanged throughout the entire scanning range. Since refractive index tuning does not affect the topological properties of the lattice, tuning only causes a shift in the position of the resonance peak without changing its shape and depth. These results demonstrate that refractive index tuning not only offers higher sensitivity but also possesses good reversibility and dynamic fast modulation potential, making it highly suitable for electro-optic tunable filtering applications in integrated photonic devices.

[0073] Thanks to the topological protection properties of the valley topological boundary states, this filter exhibits extremely high immunity to errors introduced in actual manufacturing processes. Even when structural perturbations are introduced near the waveguide interface (as shown in Figure 7(a) and...), the filter remains highly resistant to these errors. Figure 7 (b) shows “dielectric pillar missing”, “path bent”, and “position disorder”. The center frequency and quality factor of the filter can still remain stable, ensuring the reliability of the filter under non-ideal process conditions.

[0074] In summary, the present invention has the following beneficial effects:

[0075] 1. The sector-shaped dielectric pillars are made of electro-optically tunable materials such as barium titanate (BaTiO3). By introducing spatial inversion symmetry breaking (such as rotation or cutting of the sector) within the cell unit cell of the honeycomb lattice, a valley topological photonic crystal with non-zero Berry curvature is formed.

[0076] 2. Topology-protected waveguide interface: A topological interface (such as linear or Z-type) is formed by splicing two photonic crystals with opposite valley Chern numbers, which supports topology-protected boundary state transmission.

[0077] 3. Embedded local defect cavity: On the topological interface path, defect columns (i.e., local defect cavities) are constructed by adjusting the geometric parameters (such as radius Rs) of the fan-shaped dielectric columns at specific locations, and narrowband filtering concave peaks are generated by utilizing the critical coupling between boundary states and defect modes.

[0078] 4. Multi-wavelength filtering structure with arbitrary channel spacing (core innovation): Multiple defect pillars with different geometric parameters (such as radii R1, R2, R3...) are connected in series along the topological waveguide path. The resonant wavelength of each defect pillar is independently controllable, and the wavelength spacing is not limited by the periodicity of the free spectral range (FSR), which can realize the channel allocation of multiple wavelength spacing.

[0079] 5. Linear tuning mechanism based on refractive index control: A method to linearly and continuously adjust the filter center frequency by changing the refractive index of the defect pillar by applying an external electric field (sensitivity better than 390 nm / RIU).

[0080] 6. Highly robust filter device structure: Utilizing the backscattering suppression characteristics of valley topological boundary states, the filter maintains its center frequency offset and transmittance loss within a preset tolerance range when faced with manufacturing defects (such as missing dielectric pillars, disordered positions, or sharp bends in the waveguide).

[0081] Implementation Method 1: Construction of Valley Topological Photonic Crystal Structure

[0082] Lattice constant: set to a = 560 nm

[0083] Medium material: The refractive index of the sector-shaped medium column is set to n = 2.4, and the rest is air with n = 1;

[0084] Unit cell design: The radius R = 0.3a of the fan-shaped dielectric pillar at the apex. By fine-tuning the geometry to break the symmetry, a photonic bandgap in the frequency range of 170.66 THz - 220.71 THz is opened.

[0085] Defect design: At the topology interface, the radius of the sector-shaped dielectric column at the apex of three specific cells is adjusted to Rs = 0.48a to form a defect column.

[0086] Performance: At the resonant frequency (around 193 THz), the transmission spectrum forms a deep and narrow concave peak, the transmittance at non-resonant frequencies is close to 0 dB, and the transmittance outside the band gap is as low as -80 dB;

[0087] Implementation Method 2: Defective Cavity Narrowband Filter

[0088] Adjust the radius of the three media columns in the center of the interface to 0.48a;

[0089] The eigenvalue solution yields the local modulus within the bandgap;

[0090] The filter concave peak was found to appear around 193 THz.

[0091] Transmittance concave peak depth ≤ −20 dB;

[0092] The pattern is highly localized;

[0093] Implementation Method 3: Dynamic Tuning of Barium Titanate Refractive Index

[0094] Set the refractive index scan to 2.39–2.42;

[0095] Linear redshift of the resonant wavelength;

[0096] Average tuning sensitivity: 391.5 nm / RIU;

[0097] The electric field pattern remains unchanged;

[0098] Background topological transmission remains at 0 dB.

[0099] Implementation Method 4: Arbitrary Adjustability of Interval

[0100] With R1=0.480a and R2=0.485a set, the interval between the two peaks is relatively large. By introducing R3=0.482a, a third peak is successfully "inserted" between the two peaks. The wavelength of the newly added peak can be adjusted by changing the radius of R3.

[0101] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only used to facilitate the description of the present invention and to simplify the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of the present invention.

[0102] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A multi-wavelength notch-filtered tunable topological valley topological photonic crystal filter, characterized in that, include: Waveguide interface, and first valley topological photonic crystal and second valley topological photonic crystal distributed on both sides of the waveguide interface; The first valley topological photonic crystal includes several first regular hexagonal units. At the three alternating vertices of a single first regular hexagonal unit, a fan-shaped dielectric pillar is set. Each first regular hexagonal unit is arranged in a honeycomb array with a period length of lattice constant a, resulting in N circular dielectric pillars. The radius of the N circular dielectric pillars is R. The second valley topological photonic crystal comprises several second regular hexagonal units; fan-shaped dielectric pillars are respectively set at the three alternating vertices of a single second regular hexagonal unit, and the sign of their valley Chern number is opposite to that of the first regular hexagonal unit; each second regular hexagonal unit is arranged in a honeycomb array with a period length of lattice constant a, resulting in M ​​circular dielectric pillars, wherein the radius of M1 circular dielectric pillars is R, the radius of M2 circular dielectric pillars is greater than R, and the circular dielectric pillars with a radius greater than R are defined as defect pillars, M1+M2=M and M1>M2; The radius of the defective column ranges from 0.480a to 0.485a; When the number of defect pillars is greater than 1, the radius of each defect pillar is different, and the interval between the resonant wavelengths corresponding to each defect pillar is different and can be set independently.

2. The tunable topological valley topological photonic crystal filter with multi-wavelength notch filtering according to claim 1, characterized in that: When the number of defective pillars is greater than 1, each defective pillar is independent of the others and is set sequentially along the extension direction of the waveguide interface.

3. The tunable topological valley topological photonic crystal filter with multi-wavelength notch filtering according to claim 1, characterized in that: When the number of defective pillars is greater than 1, the defective pillars are located in the same row or different rows, and are set sequentially along the extension direction of the waveguide interface.

4. The tunable topological valley topological photonic crystal filter with multi-wavelength notch filtering according to claim 1, characterized in that: The waveguide interface is sawtooth-shaped. The sawtooth waveguide interface is formed by the fan-shaped dielectric pillars at the upper left and upper right vertices of the first regular hexagonal cell distributed on one side of the waveguide interface, and the fan-shaped dielectric pillars at the lower left and lower right vertices of the second regular hexagonal cell distributed on the other side of the waveguide interface, which are arranged in a staggered and interlocking manner along the waveguide extension direction.

5. A multi-wavelength notch tunable topological valley topological photonic crystal filter according to claim 4, characterized in that: When the lattice constant a is 560 nm and R is 0.3a, the operating frequency band of the topological boundary states supported by the sawtooth waveguide interface is from 172.588 THz to 199.417 THz.

6. The tunable topological valley topological photonic crystal filter with multi-wavelength notch filtering according to claim 1, characterized in that: The sector-shaped dielectric column is made of an electro-optically tunable material.

7. A multi-wavelength notch-filter tunable topological valley topological photonic crystal filter according to claim 6, characterized in that: The sector-shaped media column is made of barium titanate.

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