Topological rainbow photonic waveguide and topological rainbow photonic device
By setting specific non-mediocrity and mediocrity single cell layers in the photonic crystal to form topological gradient waveguides, the existing rainbow capture structure is solved, and an efficient and economical rainbow capture effect is achieved.
Patent Information
- Application Number
- CN202510470116.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-15
- Publication Date
- 2025-06-13
AI Technical Summary
The existing rainbow capture structure has high prices and complex structures, making it difficult to achieve efficient and economical rainbow capture effects.
By sequentially setting the first non-mediocrity single cell layer, the mediocrity single cell layer and the second non-mediocrity single cell layer along the first direction, the dielectric column extends outward or contracts inward along the center of the lattice to form a two-dimensional topological gradient waveguide to achieve the rainbow capture effect.
The spatial separation of topological photonic states at different frequencies is achieved, the local effect of the mode is enhanced, the structural complexity and cost are reduced, and the efficient rainbow capture effect is achieved.
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Figure CN120143353A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of optical information technology, and particularly to a topological rainbow photonic waveguide and a topological rainbow photonic device. Background Art
[0002] Topological photonics is a newly emerging branch of photonics research in recent years. Derived from condensed matter, it can robustly manipulate the propagation and localization of light. With the development of nanofabrication technology and new materials, topological photonics has been widely applied in many fields such as directional waveguides, power splitters, filters, lasers, etc.
[0003] Rainbow trapping is an interesting phenomenon in optics, involving the slow light effect. By manipulating the dispersion characteristics of a specific structure, lights of different wavelengths can be trapped at different spatial positions, thus forming a rainbow-like dispersion effect. Currently, the structures for realizing rainbow trapping include metamaterials, plasmonic metal gratings, chirped photonic crystals, etc. These materials have problems such as high cost and complex structures. Summary of the Invention
[0004] This application provides a topological rainbow photonic waveguide to provide a new rainbow-trapping photonic waveguide.
[0005] In a first aspect, this application provides a topological rainbow photonic waveguide, including, arranged in sequence along a first direction:
[0006] A first non-trivial unit cell layer, on the primitive lattice of the photonic crystal of the first non-trivial unit cell layer, a plurality of dielectric columns with C6 rotational symmetry are opened. The dielectric columns extend outward along the lattice center, and the degree of outward extension in a second direction is set to increase or decrease;
[0007] A trivial unit cell layer, on the primitive lattice of the photonic crystal of the trivial unit cell layer, a plurality of dielectric columns with C6 rotational symmetry are opened. The dielectric columns contract inward along the lattice center, and the degree of inward contraction in the second direction is the same; and,
[0008] A second non-trivial unit cell layer, on the primitive lattice of the photonic crystal of the second non-trivial unit cell layer, a plurality of dielectric columns with C6 rotational symmetry are opened. The dielectric columns extend outward along the lattice center, and the degree of outward extension in the second direction is the same;
[0009] Wherein, the second direction is set at an angle to the first direction.
[0010] In this application, a first non-trivial unit cell layer, a trivial unit cell layer, and a second non-trivial unit cell layer are sequentially arranged along a first direction. The dielectric columns on the photonic crystal primitive cell lattice of the first non-trivial unit cell layer extend outward along the lattice center, and the degree of outward extension increases or decreases in a second direction; the dielectric columns on the photonic crystal primitive cell lattice of the trivial unit cell layer contract inward along the lattice center, and the degree of inward contraction is the same in the second direction; the dielectric columns on the photonic crystal primitive cell lattice of the second non-trivial unit cell layer extend outward along the lattice center, and the degree of outward extension is the same in the second direction, such that a series of supercells form a two-dimensional topologically graded waveguide. Since the degree of outward extension of the first non-trivial unit cell layer increases or decreases in the second direction, while the degree of inward contraction of the trivial unit cell layer is the same, and the degree of outward extension of the second non-trivial unit cell layer is the same, when two photonic crystal unit cells with different topological properties are in contact in the second direction, there will be a topologically protected topological boundary state at their interface. By changing the degree of outward extension of the first non-trivial unit cell layer in the second direction, the frequency distribution position of the flat band of the topological boundary state is adjusted. As the degree of fusion along the waveguide direction gradually changes, a series of resonant microcavities are generated by the misalignment of the flat bands of the boundary states in adjacent supercells. When the frequency of the incident wave exactly matches a flat band, the light wave will be coupled into the cavity and trapped in a specific spatial region, realizing the rainbow trapping effect.
[0011] In some embodiments, the rate of change of the degree of outward extension of the dielectric columns in the first non-trivial unit cell layer along the lattice center is n, where 0.1 nm / lattice ≤ |n| ≤ 2 nm / lattice. The energy field distribution of light wave trapping is affected by the flatness of the boundary state energy band. Better flatness helps to reduce the group velocity of the light wave and make the frequency shift between adjacent supercell units larger, both of which can result in a more compact modal profile. Therefore, when the rate of change of the degree of outward extension of the dielectric columns in the first non-trivial unit cell layer along the lattice center is within this range, topological photonic states can be spatially separated at different frequencies, and the topological rainbow trapping effect along the topologically graded waveguide structure can be realized.
[0012] In some embodiments, the degree of outward extension of the dielectric columns on the photonic crystal primitive cell lattice in the first non-trivial unit cell layer along the lattice center is S 1 , satisfying:
[0013]
[0014] where: x 1 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction when the dielectric columns on the photonic crystal primitive cell lattice of the first non-trivial unit cell layer extend outward to the lattice center, and 150 nm ≤ x 1 ≤ 210 nm;
[0015] l 1is the vertical distance from the dielectric column that is farthest from the lattice center in the vertical direction when the dielectric columns on the primitive cell lattice of the photonic crystal of the first non-trivial monolayer extend outward, 370 nm ≤ l 1 ≤ 430 nm.
[0016] x 1 and l 1 affect the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value ranges of x 1 and l 1 within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.
[0017] In some embodiments, the degree of inward contraction of the dielectric columns on the primitive cell lattice of the photonic crystal in the trivial monolayer is S 2 , satisfying:
[0018]
[0019] where: x 2 is the horizontal distance from the dielectric column that is farthest from the lattice center in the vertical direction when the dielectric columns on the primitive cell lattice of the photonic crystal in the trivial monolayer contract inward, 50 nm ≤ x 2 ≤ 70 nm;
[0020] l 2 is the vertical distance from the dielectric column that is farthest from the lattice center in the vertical direction when the dielectric columns on the primitive cell lattice of the photonic crystal in the trivial monolayer contract inward, 190 nm ≤ l 2 ≤ 210 nm.
[0021] x 2 and l 2 affect the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value ranges of x 2 and l 2 within this range can ensure the trivial characteristics of the unit cell structure and avoid topological phase transitions.
[0022] In some embodiments, the degree of outward extension of the dielectric columns on the primitive cell lattice of the photonic crystal in the second non-trivial monolayer is S 3 , satisfying:
[0023]
[0024] where: x 3 is the horizontal distance from the dielectric column that is farthest from the lattice center in the vertical direction when the dielectric columns on the primitive cell lattice of the photonic crystal in the second non-trivial monolayer extend outward, 16 nm ≤ x3 ≤200 nm;
[0025] l 3 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction when the dielectric column on the primitive cell lattice of the photonic crystal of the second non-trivial unit cell layer extends outward, 380 nm ≤ l 3 ≤ 420 nm.
[0026] x 3 and l 3 affect the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different energy band characteristics. The value ranges of x 3 and l 3 within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.
[0027] In some embodiments, the number of primitive cell lattices of the photonic crystal in the first direction of the trivial unit cell layer is 1 to 5. The number of primitive cell lattices of the photonic crystal in the first direction of the trivial unit cell layer affects the coupling strength of the topological boundary state modes. Within this range, a high coupling efficiency can be ensured.
[0028] In some embodiments, the number of primitive cell lattices of the photonic crystal in the second direction of the first non-trivial unit cell layer is 20 to 100; and / or,
[0029] the number of primitive cell lattices of the photonic crystal in the second direction of the trivial unit cell layer is 20 to 100; and / or,
[0030] the number of primitive cell lattices of the photonic crystal in the second direction of the second non-trivial unit cell layer is 20 to 100.
[0031] The primitive cell lattices of the photonic crystal in the second direction affect the working frequency range of the rainbow trapping device. At the same rate of change of the outward extension degree, the more the number of lattices, the wider the working frequency range. Generally, the number of primitive cell lattices of the photonic crystal in the second direction of the first non-trivial unit cell layer, the trivial unit cell layer, and the second non-trivial unit cell layer is the same. Within this range of the number of primitive cell lattices of the photonic crystal in the second direction, a good trapping effect on the mode can be ensured.
[0032] In some embodiments, the ratio of the diameter size D1 of the dielectric column on the primitive cell lattice of the photonic crystal in the first non-trivial unit cell layer and the trivial unit cell layer, and the diameter size D2 of the dielectric column on the primitive cell lattice of the photonic crystal in the second non-trivial unit cell layer to the lattice constant a of the photonic crystal satisfies:
[0033] 0.1 ≤ D1 / a ≤ 0.25;
[0034] 0.08 ≤ D2 / a ≤ 0.18;
[0035] Among them, a is the lattice constant of the photonic crystal;
[0036] The ratio of the diameter of the dielectric pillar on the lattice of the primitive cell of the photonic crystal to the lattice constant of the photonic crystal is the lattice filling ratio, which affects the effective refractive index of the lattice. When the ratio of the diameter of the dielectric pillar on the lattice of the primitive cell of the photonic crystal to the lattice constant of the photonic crystal is within this range, it helps to enhance the topological protected edge states and at the same time avoids excessive influence on the photonic band gap.
[0037] In some embodiments, 90nm ≤ D1 ≤ 275nm, 72nm ≤ D2 ≤ 198nm. When the diameters of the dielectric pillars in the first non-trivial unit cell layer and the second non-trivial unit cell layer are within this range, good energy band distribution characteristics and good waveguide coupling strength can be ensured, and the mode localization effect can be enhanced; and / or,
[0038] 900nm ≤ a ≤ 1100nm. When the lattice constant of the photonic crystal is within this range, a better optical band gap can be achieved while taking into account the manufacturability of the structure.
[0039] In a second aspect, the present application provides a topological rainbow photonic device, including the topological rainbow photonic waveguide of the first aspect. BRIEF DESCRIPTION OF THE DRAWINGS
[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.
[0041] Figure 1 It is a schematic diagram of the typical topological photonic crystal unit cell structure and energy band of the topological rainbow photonic waveguide in an embodiment of the present application.
[0042] Figure 2 It is a schematic diagram of the supercell geometric structure, energy band structure, and upper boundary state energy band group velocity calculation diagram of the topological rainbow photonic waveguide composed of the first non-trivial region and the trivial region unit cells in an embodiment of the present application.
[0043] Figure 3 It is a schematic diagram of the geometric structure, eigenmode electric field intensity diagram, mode electric field intensity distribution excited by the lower waveguide, relationship diagram between frequency and spatial position, and transmission efficiency diagram of the topological rainbow photonic waveguide in an embodiment of the present application.
[0044] Figure 4Schematic diagram of the structure of a topological rainbow photonic waveguide excited by an upper broadband light source according to an embodiment of the present application, and a relationship diagram between the electric field intensity distribution, frequency, and spatial position of the excited mode. Detailed implementation manners
[0045] To make the objectives, technical solutions, and advantages of the present application clearer, the technical solutions of the present application will be clearly and completely described below in conjunction with the embodiments of the present application. Apparently, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.
[0046] Topological photonics is a newly emerging branch of photonics research in recent years. Derived from condensed matter, it can robustly manipulate the propagation and localization of light. With the development of nanofabrication technology and new materials, topological photonics has been widely applied in many fields such as directional waveguides, power splitters, filters, lasers, etc.
[0047] Rainbow trapping is an interesting phenomenon in optics, involving the slow light effect. By manipulating the dispersion characteristics of a specific structure, lights of different wavelengths can be trapped at different spatial positions, thus forming a rainbow-like dispersion effect. Currently, the structures for realizing rainbow trapping include metamaterials, plasmonic metal gratings, chirped photonic crystals, etc. These materials have problems such as high cost and complex structures.
[0048] In view of this, the present application provides a topological rainbow photonic waveguide to provide a new rainbow-trapping photonic waveguide.
[0049] In a first aspect, the present application provides a topological rainbow photonic waveguide, including, arranged in sequence along a first direction:
[0050] A first non-trivial unit cell layer, on the primitive lattice of the photonic crystal of the first non-trivial unit cell layer, a plurality of dielectric columns with C6 rotational symmetry are opened. The dielectric columns extend outward from the lattice center and are arranged such that the degree of outward extension increases or decreases in a second direction;
[0051] A trivial unit cell layer, on the primitive lattice of the photonic crystal of the trivial unit cell layer, a plurality of dielectric columns with C6 rotational symmetry are opened. The dielectric columns contract inward from the lattice center and the degree of inward contraction is the same in the second direction; and,
[0052] A second non-trivial unit cell layer, on the primitive lattice of the photonic crystal of the second non-trivial unit cell layer, a plurality of dielectric columns with C6 rotational symmetry are opened. The dielectric columns extend outward from the lattice center and the degree of outward extension is the same in the second direction;
[0053] Wherein, the second direction is set at an angle to the first direction.
[0054] In this application, a first non-trivial unit cell layer, a trivial unit cell layer, and a second non-trivial unit cell layer are sequentially arranged along a first direction. The dielectric columns on the primitive lattice of the photonic crystal in the first non-trivial unit cell layer extend outward from the lattice center, and the degree of outward extension increases or decreases in a second direction; the dielectric columns on the primitive lattice of the photonic crystal in the trivial unit cell layer contract inward from the lattice center, and the degree of inward contraction is the same in the second direction; the dielectric columns on the primitive lattice of the photonic crystal in the second non-trivial unit cell layer extend outward from the lattice center, and the degree of outward extension is the same in the second direction, so that a series of supercells form a two-dimensional topologically graded waveguide. Since the degree of outward extension of the first non-trivial unit cell layer increases or decreases in the second direction, while the degree of inward contraction of the trivial unit cell layer is the same, and the degree of outward extension of the second non-trivial unit cell layer is the same, when two photonic crystal unit cells with different topological properties are in contact in the second direction, there will be a topologically protected topological boundary state at their interface. By changing the degree of outward extension of the first non-trivial unit cell layer in the second direction, the frequency distribution position of the flat band of the topological boundary state is adjusted. As the degree of fusion along the waveguide direction gradually changes, a series of resonant microcavities are generated by the misalignment of the flat bands of the boundary states in adjacent supercells. When the frequency of the incident wave exactly matches a flat band, the light wave will be coupled into the cavity and trapped in a specific spatial region, realizing the rainbow trapping effect.
[0055] It should be noted that a non-trivial unit cell layer refers to a unit cell structure in which the intra-cell hopping of energy is less than the inter-cell hopping, and its topological property is non-trivial, with the occurrence of band quadrupole state and dipole state inversion. A trivial unit cell layer refers to a unit cell structure in which the intra-cell hopping of energy is greater than the inter-cell hopping, and its topological property is trivial. The primitive lattice of a photonic crystal refers to the smallest repeating unit structure in the photonic crystal, which contains all the necessary geometric information to describe the periodic arrangement of the entire crystal. A dielectric column refers to a cylinder made of dielectric material. Contracting inward from the lattice center means that both x 2 and l 2 decrease simultaneously. Extending outward from the lattice center means that both x 1 and l 1 increase simultaneously. A topological boundary state refers to a special photonic mode generated by the topological phase at the boundary or surface of a photonic crystal, which is usually robust to local perturbations.
[0056] In combination with the first aspect, in some embodiments provided by the present application, the rate of change of the extent of the dielectric pillars in the first non-trivial unit cell extending outward along the lattice center is n, where 0.1 nm / lattice ≤ |n| ≤ 2 nm / lattice. The energy field distribution of light wave trapping is affected by the flatness of the edge state energy band. Better flatness helps to reduce the group velocity of the light wave and results in a larger frequency shift between adjacent supercell units, both of which can lead to a more compact mode profile. Therefore, when the rate of change of the extent of the dielectric pillars in the first non-trivial unit cell extending outward along the lattice center is within this range, topological photonic states can be spatially separated at different frequencies, and the topological rainbow trapping effect along the topological gradient waveguide structure can be achieved. Specifically, the extent of outward extension can increase by 0.1 nm / lattice or decrease by 0.1 nm / lattice, and the extent of outward extension can increase by 2 nm / lattice or decrease by 2 nm / lattice.
[0057] In combination with the first aspect, in some embodiments provided by the present application, the extent of the dielectric pillars on the primitive cell lattice of the photonic crystal in the first non-trivial unit cell extending outward along the lattice center is S 1 , satisfying:
[0058]
[0059] where: x 1 is the horizontal distance from the dielectric pillar farthest from the lattice center in the vertical direction when the dielectric pillars on the primitive cell lattice of the photonic crystal in the first non-trivial unit cell extend outward to the lattice center, 150 nm ≤ x 1 ≤ 210 nm;
[0060] l 1 is the vertical distance from the dielectric pillar farthest from the lattice center in the vertical direction when the dielectric pillars on the primitive cell lattice of the photonic crystal in the first non-trivial unit cell extend outward to the lattice center, 370 nm ≤ l 1 ≤ 430 nm.
[0061] x 1 and l 1 affect the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different energy band characteristics. The value ranges of x 1 and l 1 are within this range, which can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.
[0062] In combination with the first aspect, in some embodiments provided by the present application, the extent of the dielectric pillars on the primitive cell lattice of the photonic crystal in the trivial unit cell contracting inward along the lattice center is S 2 , satisfying:
[0063]
[0064] Wherein: x 2 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric columns on the primitive cell lattice of the photonic crystal in the trivial monolayer contract inward, 50 nm ≤ x 2 ≤ 70 nm;
[0065] l 2 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric columns on the primitive cell lattice of the photonic crystal in the trivial monolayer contract inward, 190 nm ≤ l 2 ≤ 210 nm.
[0066] x 2 and l 2 affect the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different energy band characteristics. The value ranges of x 2 and l 2 within this range can ensure the trivial characteristics of the unit cell structure and avoid topological phase transitions.
[0067] Combined with the first aspect, in some embodiments provided in this application, the degree of outward extension of the dielectric columns on the primitive cell lattice of the photonic crystal in the second non-trivial monolayer along the lattice center is S 3 , satisfying:
[0068]
[0069] Wherein: x 3 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric columns on the primitive cell lattice of the photonic crystal in the second non-trivial monolayer extend outward, 175 nm ≤ x 3 ≤ 205 nm;
[0070] l 3 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric columns on the primitive cell lattice of the photonic crystal in the second non-trivial monolayer extend outward, 395 nm ≤ l 3 ≤ 425 nm.
[0071] x 3 and l 3 affect the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different energy band characteristics. The value ranges of x 3 and l 3 within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.
[0072] In combination with the first aspect, in some embodiments provided by the present application, the number of photonic crystal primitive cell lattices of the trivial monolayer in the first direction is 1 to 5. The number of photonic crystal primitive cell lattices of the trivial monolayer in the first direction affects the coupling strength of the topological boundary state modes. Within this range, a relatively high coupling efficiency can be ensured.
[0073] In combination with the first aspect, in some embodiments provided by the present application, the number of photonic crystal primitive cell lattices of the first non-trivial monolayer in the second direction is 20 to 100.
[0074] In combination with the first aspect, in some embodiments provided by the present application, the number of photonic crystal primitive cell lattices of the trivial monolayer in the second direction is 20 to 100.
[0075] In combination with the first aspect, in some embodiments provided by the present application, the number of photonic crystal primitive cell lattices of the second non-trivial monolayer in the second direction is 20 to 100.
[0076] The photonic crystal primitive cell lattices in the second direction affect the working frequency range of the rainbow trapping device. At the same rate of change of the outward extension degree, the more the number of lattices, the wider the working frequency range. Generally, the number of photonic crystal primitive cell lattices of the first non-trivial monolayer, the trivial monolayer, and the second non-trivial monolayer in the second direction is the same. Within this range of the number of photonic crystal primitive cell lattices in the second direction, a better trapping effect on the modes can be ensured.
[0077] In combination with the first aspect, in some embodiments provided by the present application, the ratio of the diameter D1 of the dielectric pillar on the photonic crystal primitive cell lattice of the first non-trivial monolayer and the trivial monolayer, and the ratio of the diameter D2 of the dielectric pillar on the photonic crystal primitive cell lattice of the second non-trivial monolayer to the lattice constant of the photonic crystal satisfy:
[0078] 0.1 ≤ D1 / a ≤ 0.25;
[0079] 0.08 ≤ D2 / a ≤ 0.18;
[0080] where a is the lattice constant of the photonic crystal;
[0081] The ratio of the diameter of the dielectric pillar on the photonic crystal primitive cell lattice to the lattice constant of the photonic crystal, that is, the lattice filling ratio, affects the effective refractive index of the lattice. Within this range of the ratio of the diameter of the dielectric pillar on the photonic crystal primitive cell lattice to the lattice constant of the photonic crystal, it helps to enhance the topologically protected boundary states and at the same time reduces the excessive influence on the photonic bandgap.
[0082] In combination with the first aspect, in some embodiments provided by the present application, 90nm ≤ D1 ≤ 275nm, 72nm ≤ D2 ≤ 198nm. When the diameters of the dielectric columns in the first non-trivial unit cell layer and the second non-trivial unit cell layer are within this range, good energy band distribution characteristics and good waveguide coupling strength can be ensured, enhancing the mode localization effect.
[0083] In combination with the first aspect, in some embodiments provided by the present application, 900nm ≤ a ≤ 1100nm. When the lattice constant of the photonic crystal is within this range, a better optical bandgap can be achieved while taking into account the manufacturability of the structure.
[0084] Specifically, a photonic crystal unit cell structure containing 12 dielectric cylinders in an air background can be taken as an example for illustration. The polarization mode of the photonic crystal is the Transverse-Magnetic (TM) mode. In the lattice structure of the photonic crystal, the lattice constant a = 1μm, the cylinder diameter D = 180nm, and the refractive indices of the dielectric column and the air background are 3.27 and 1 respectively.
[0085] The degree of lattice deformation is determined by x and l. Figure 1 (a) and Figure 1 (b) are the energy band distribution diagrams of the corresponding trivial and non-trivial unit cell structures of the reference photonic crystal supercell structure, and their optical bandgap sizes Δω are 0.135c / a and 0.172c / a respectively, where c is the speed of light in air. The red and blue energy bands represent the dipole state and the quadrupole state respectively. According to the bulk-edge correspondence, when two photonic crystal unit cells with different topological properties are in contact, there will be a topologically protected topological boundary state at their interface. Figure 2 (a) is a schematic diagram of the reference supercell structure, which is composed of 10 trivial unit cells and 10 non-trivial unit cells in the vertical direction. Figure 2 (b) is Figure 2 (a) The energy band distribution diagram of the structure in (a). On the premise of ensuring the topological properties remain unchanged, the present invention selects = 400nm, = 180nm (corresponding to the non-trivial unit cell), = 200nm, = 60nm (corresponding to the trivial unit cell) as a set of schematic parameters, and there is a relatively large bandgap of 0.047c / a between the two boundary state energy bands. Figure 2 (b) The upper boundary state energy band in (b) shows a flat band characteristic in the entire Brillouin zone, and its frequency range significantly deviates from the bulk mode energy band, resulting in an observable bandgap between the upper boundary state energy band and the bulk mode energy band, providing a flexible frequency modulation range. Figure 2 (c) is a schematic diagram of the group velocity distribution of the upper boundary state energy band under this set of parameters. The group velocity is in a very low range (absolute value less than 0.005) in the entire Brillouin zone, which is crucial for controlling the propagation speed of light and achieving rainbow trapping.
[0086] Based on this, a topological gradient waveguide structure is designed, and the schematic diagram is as shown in Figure 3 (a). In this application, the parameter space composed of (l 1 , x 1 , l 2 , x 2 ) can affect the topological properties of the unit cell structure, and further affect the energy band distribution characteristics and flatness of the supercell structure. The flatness of the energy band has little correlation with the structural parameters (l 1 , x 1 ) of the non-trivial unit cell on the upper side of the waveguide. Therefore, along the x-direction on both sides of the topological waveguide, (l 1 , x 1 ) is increased or decreased at the same step size. In the schematic structure of Figure 3 (a), the variation range of x 1 is 150 nm to 210 nm, and the value range of l 1 is 370 nm to 430 nm. Within this range, the flatness of the upper boundary energy band can be maintained at a good level. The parameters of the trivial unit cell on the lower side of the waveguide, that is, (l 2 , x 2 ), remain unchanged. (l 1 , x 2 ) determines the degree of fusion of the dielectric cylinders and adjusts the frequency distribution position of the flat band of the topological boundary state. As the degree of fusion gradually changes along the waveguide direction, a series of resonant microcavities are generated by the misalignment of the flat bands of the boundary states in adjacent supercells. When the frequency of the incident wave exactly matches a flat band, the light wave will be coupled into the cavity and trapped in a specific spatial region, realizing the rainbow trapping effect. The energy field distribution of the light wave trapping is affected by the flatness of the boundary state energy band. Better flatness helps to reduce the group velocity of the light wave and makes the frequency shift between adjacent supercell units larger. Both of these can lead to a more compact modal profile. Therefore, topological photonic states can be spatially separated at different frequencies, and the topological rainbow trapping effect along the topological gradient waveguide structure can be realized.
[0087] Furthermore, a topological rainbow photonic device with a bus waveguide structure is used to couple broadband boundary state light waves into the topological gradient waveguide to achieve rainbow trapping, as shown in Figure 3 (b). This device has a three-layer heterostructure, with 35 periods in the second direction and 20 periods in the first direction. The distance between the two layers of topological waveguides is three lattice periods. The (l 1 , x 1 ) parameters of the upper non-trivial lattice are linearly tuned along both sides of the x-axis with an increasing step size of 1 nm. The initial (l 1 , x 1) is (400nm, 180nm). The middle mediocre lattice and the lower non-mediocre lattice parameters remain unchanged. Specifically, (l 2 , x 2 ) is (200nm, 60nm), (l 3 , x 3 ) is (410nm, 190nm), forming a topological bus waveguide structure with ordinary boundary state dispersion characteristics (non-flat band) within the frequency requirement range, suitable for rainbow trapping. Thanks to the supercell structure with a large bandgap, the construction of the bus waveguide structure can be very convenient, and the pseudo-spin characteristics similar to those of photonic crystals based on the topological quantum Hall effect also ensure very good coupling between the bus waveguide and the microcavities in the topological gradient waveguide.
[0088] Figure 3 (c) shows the typical eigenmode electric field distribution of the gradient topological waveguide, whose frequency range is from 0.5133c / a to 0.5186c / a. The topological eigenstates of different frequencies are tightly bound and are sequentially dispersed at different spatial positions along the second direction. Due to the flat band characteristics of the proposed supercell structure, the resonance modes in each resonator have a very wide k-space, which strongly confines the optical modes in the spatial domain, thus achieving a high degree of field enhancement. The topological rainbow in the upper topological gradient waveguide is excited by the broadband point source in the lower waveguide, and the point source is marked in red in Figure 3 (b). The topological boundary states propagating along the lower bus waveguide will couple into the topological gradient waveguide structure, forming multiple resonances separated in the frequency domain and distributed along the waveguide propagation direction. Figure 3 (d) shows the relationship between the electric field distribution, frequency, and spatial position. The light waves of different resonance frequencies are trapped at different spatial positions in the second direction, presenting a typical "rainbow trapping" phenomenon. The frequency range of the rainbow trapping mode is from 0.5019c / a to 0.5288c / a. These resonance frequency ranges correspond to the topological boundary states of the flat band, and the resonances of the bulk states and other hybrid modes are not observed. Figure 3 (e) is the transmission efficiency diagram of the topological waveguide composed of the mediocre region and the second non-mediocre region for the broadband point source. Additionally, due to the tight field energy confinement brought by the ultra-wide flat band property, the topological rainbow trapping structure in this application has a smaller size compared to other solutions. Moreover, the rich adjustable parameters in the structure also enhance the flexibility of the rainbow trapping characteristics, including the frequency domain coverage, broadband topological rainbow, and compatibility with other optical devices, making the proposed novel topological rainbow photonic device a promising platform for laser source, optical storage, and optical routing applications.
[0089] In addition to exciting the topological rainbow by means of the bus waveguide, the gradient topological waveguide structure proposed in this application can also be excited by the broadband light from above, and its structural schematic diagram is as shown in Figure 4As shown in (a), the red arrow is the broadband excitation source. Figure 4 (b) shows the relationship between the electric field intensity distribution, frequency, and spatial position of the mode excited thereby. The peak frequencies at different spatial positions correspond to Figure 3 (c), Figure 3 (d) and are consistent, demonstrating the feasibility of these two excitation methods and the universality of the tapered waveguide structure proposed in the present invention for achieving topological rainbow trapping.
[0090] In a second aspect, the present application provides a topological rainbow photonic device, including the topological rainbow photonic waveguide of the first aspect.
[0091] In summary, by sequentially arranging a first non-trivial unit cell layer, a trivial unit cell layer, and a second non-trivial unit cell layer in the first direction, the dielectric pillars on the primitive cell lattice of the photonic crystal in the first non-trivial unit cell layer extend outward along the lattice center, and the degree of outward extension is set to increase or decrease in the second direction; the dielectric pillars on the primitive cell lattice of the photonic crystal in the trivial unit cell layer contract inward along the lattice center, and the degree of inward contraction is the same in the second direction; the dielectric pillars on the primitive cell lattice of the photonic crystal in the second non-trivial unit cell layer extend outward along the lattice center, and the degree of outward extension is the same in the second direction, such that a series of supercells form a two-dimensional topological tapered waveguide. Since the degree of outward extension of the first non-trivial unit cell layer is set to increase or decrease in the second direction, while the degree of inward contraction of the trivial unit cell layer is the same, and the degree of outward extension of the second non-trivial unit cell layer is the same, when two photonic crystal unit cells with different topological properties are in contact in the second direction, there will be a topologically protected topological boundary state at their interface. By changing the degree of outward extension of the first non-trivial unit cell layer in the second direction, the frequency distribution position of the flat band of the topological boundary state is adjusted. As the degree of fusion along the waveguide direction gradually changes, a series of resonant microcavities are generated by the misalignment of the flat bands of the boundary states in adjacent supercells. When the frequency of the incident wave exactly matches a flat band, the light wave will be coupled into the cavity and trapped in a specific spatial region, achieving the rainbow trapping effect.
[0092] In the description of this specification, the descriptions with reference to terms such as "one embodiment / way", "some embodiments / ways", "example", "specific example" or "some examples" etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment / way or example are included in at least one embodiment / way or example of this application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment / way or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments / ways or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments / ways or examples described in this specification and the features of different embodiments / ways or examples.
[0093] It should be noted that in this application, relational terms such as "first" and "second" etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of another identical element in the process, method, article or device comprising the said element. In this application, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.
[0094] The above are only specific embodiments of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features claimed herein.
Claims
1. A topological rainbow photonic waveguide, characterized in that: The method comprises the following steps arranged in sequence along a first direction: A first non-trivial unit cell layer, wherein a plurality of dielectric columns with C6 rotational symmetry are provided on the photonic crystal primitive cell lattice of the first non-trivial unit cell layer, the dielectric columns extend outwardly along the center of the lattice, and the degree of extension outwardly in a second direction is gradually increased or decreased; A mediocre single cell layer, wherein a plurality of dielectric columns with C6 rotational symmetry are provided on the photonic crystal primitive cell lattice of the mediocre single cell layer, and the dielectric columns shrink inwardly along the center of the lattice, and the degree of inward shrinkage in the second direction is the same; as well as, A second non-trivial unit cell layer, wherein a plurality of dielectric columns with C6 rotational symmetry are provided on the photonic crystal primitive cell lattice of the second non-trivial unit cell layer, the dielectric columns extend outward along the center of the lattice, and the degree of outward extension in the second direction is the same; Wherein, the second direction is arranged at an angle with the first direction.
2. The topological rainbow photonic waveguide according to claim 1, characterized in that: The rate of change of the extension degree of the dielectric column in the first non-trivial single cell layer along the center of the lattice is n, 0.1nm / lattice≤|n|≤2nm / lattice.
3. The topological rainbow photonic waveguide according to claim 1, characterized in that: The dielectric column on the photonic crystal primitive cell lattice in the first non-trivial single cell layer extends outward along the lattice center to S1, satisfying: Wherein: x1 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric column on the photonic crystal primitive cell lattice of the first non-trivial unit cell layer extends outward, 150nm≤x1≤210nm; l1 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric column on the photonic crystal primitive cell lattice of the first non-trivial single cell layer extends outward, 370nm≤l1≤430nm.
4. The topological rainbow photonic waveguide according to claim 1, characterized in that: The dielectric column on the photonic crystal primitive cell lattice in a mediocre single cell layer shrinks inward along the lattice center to a degree of S2, satisfying: Where: x2 is the horizontal distance from the dielectric column farthest from the lattice center to the lattice center in the vertical direction when the dielectric column on the photonic crystal primitive cell lattice of the mediocre single-cell layer shrinks inward, 50nm≤x2≤70nm; l2 is the vertical distance from the dielectric column farthest from the lattice center to the lattice center in the vertical direction when the dielectric column on the photonic crystal primitive cell lattice of a mediocre single-cell layer shrinks inward, 190nm≤l2≤210nm.
5. The topological rainbow photonic waveguide according to claim 1, characterized in that: The dielectric column on the photonic crystal primitive cell lattice in the second non-trivial single cell layer extends outward along the lattice center to S3, satisfying: Wherein: x3 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric column on the photonic crystal primitive cell lattice of the second non-trivial unit cell layer extends outward, 175nm≤x3≤205nm; l3 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when the dielectric column on the photonic crystal primitive cell lattice of the second non-trivial single cell layer extends outward, 395nm≤l3≤425nm.
6. The topological rainbow photonic waveguide according to claim 1, characterized in that: The number of the photonic crystal primitive cell lattices of the mediocre single cell layer in the first direction is 1 to 5.
7. The topological rainbow photonic waveguide according to claim 1, characterized in that: The number of the photonic crystal primitive cell lattices in the second direction of the first non-trivial unit cell layer is 20 to 100; and / or, The number of photonic crystal primitive cell lattices of the mediocre single cell layer in the second direction is 20 to 100; and / or the number of photonic crystal primitive cell lattices of the second non-mediocre single cell layer in the second direction is 20 to 100.
8. The topological rainbow photonic waveguide according to claim 7, characterized in that: The ratio of the diameter D1 of the dielectric column on the photonic crystal primitive cell lattice in the first non-trivial single cell layer and the ordinary single cell layer, the diameter D2 of the dielectric column on the photonic crystal primitive cell lattice in the second non-trivial single cell layer and the lattice constant of the photonic crystal satisfies: 0.1≤D1 / a≤0.25; 0.08≤D2 / a≤0.18; Where a is the lattice constant of the photonic crystal.
9. The topological rainbow photonic waveguide according to claim 8, characterized in that: 90nm≤D1≤275nm; and / or, 72nm≤D2≤198nm; and / or, 900nm≤a≤1100nm.
10. A topological rainbow photonic device, characterized in that: Comprising the topological rainbow photonic waveguide as claimed in any one of claims 1 to 9.