One-dimensional zero refractive index superconducting waveguide structure and design method thereof

Abstract

The disclosure provides a one-dimensional zero refractive index superconductor structure and a design method thereof. The superconductor structure comprises a plurality of structure units arranged periodically in a set direction, each structure unit comprising a first dielectric column and two second dielectric columns, the second dielectric columns being symmetrically arranged on both sides of the first dielectric column and forming a circular arc interface with the first dielectric column. The design method comprises: establishing a physical model for simulating the superconductor; initializing the geometric parameters and adjusting the width, long semi-axis and short semi-axis of each structure unit, so that the physical model appears a Dirac cone at the center of the Brillouin zone in the wave vector space, and realizes lateral radiation coherent cancellation in the plane; adjusting the height of each structure unit, so that the superconductor realizes coherent cancellation in the vertical direction; and equal proportionally enlarging or reducing the geometric parameters of the superconductor, so that the degenerate frequency is adjusted to the design value. The disclosure helps to greatly improve the flexibility of zero refractive index materials while reducing the chip area occupied by the zero refractive index materials.

Description

Technical Field

[0001] This disclosure belongs to the field of metamaterials, specifically relating to a one-dimensional zero-refractive-index metamaterial waveguide structure and its design method. Background Technology

[0002] Most metamaterials are composite materials composed of subwavelength unit structures arranged in a periodic or quasi-periodic manner. Through engineering design, metamaterials can exhibit material properties that are not found in nature or are difficult to obtain, including negative refractive index, zero refractive index, and magnetic response in the optical band. Currently, metamaterials are mainly used in fields such as stealth, sensing, imaging, beam scanning, and holographic imaging. Zero-refractive-index metamaterials possess a series of extreme optical properties, including infinite wavelength and phase velocity, and zero spatial phase change. Based on these optical properties, zero-refractive-index metamaterials can realize several potential applications, including on-chip supercoupling, wide-side continuous beam scanning, and extended superradiation. The extreme optical properties and potential applications of zero-refractive-index metamaterials make them valuable for both fundamental science and engineering applications.

[0003] In 2017, Professor Eric Mazur's research group at Harvard University extracted a row from a two-dimensional planar zero-refractive-index metamaterial and realized a zero-refractive-index waveguide with no phase change in the communication band. However, because the two electromagnetic modes (electric monopoles and magnetic dipoles) constituting the zero-refractive-index waveguide are located in the optical continuum, they do not satisfy the total internal reflection condition. Therefore, there is significant energy coupling with free space in both the in-plane and out-of-plane directions, resulting in substantial transmission loss. To suppress this transmission loss, Professor Mazur's group added photonic bandgap material to both sides of the zero-refractive-index waveguide. This material cannot support the propagation of optical modes, so it can be used as an on-chip mirror to suppress light waves radiated from the zero-refractive-index waveguide. However, the introduction of the photonic bandgap material also limits the flexibility of the zero-refractive-index waveguide, making it impossible to achieve free bending on a chip.

[0004] Furthermore, the applicant's research team has proposed a low-loss zero-refractive-index metamaterial and its design method (Patent No.: ZL201910724822.7). This design includes multiple periodically arranged two-dimensional crystal units, where the height of the dielectric pillars in each crystal unit satisfies the photon bound state condition, resulting in the highest magnetic dipole quality factor at the center of the Brillouin zone of the zero-refractive-index metamaterial, thus minimizing the loss of the zero-refractive-index metamaterial. However, the zero-refractive-index metamaterial designed using this method has an infinitely large spatial size in the plane, lacking the flexibility to form integrated optical components. Summary of the Invention

[0005] The purpose of this disclosure is to overcome the shortcomings of existing technologies and propose a low-loss one-dimensional zero-refractive-index metawaveguide structure, thereby significantly improving the flexibility of zero-refractive-index materials and enabling the integration of various optical components based on zero-refractive-index materials. This disclosure utilizes optically bound states to realize a low-loss zero-refractive-index metawaveguide. By establishing the relationship between the geometric parameters of the unit structure and the quality factor of the intrinsic modes, the loss of the zero-refractive-index metawaveguide is minimized. Simultaneously, no photonic bandgap material is required, significantly reducing the chip area occupied by the zero-refractive-index metawaveguide. Furthermore, this invention can be fabricated using silicon-insulating material and CMOS-compatible planar processing technology, offering advantages such as mature technology, low cost, and suitability for mass production.

[0006] To achieve the above objectives, the technical solution provided in this disclosure is as follows:

[0007] The first aspect of this disclosure provides a one-dimensional zero-refractive-index meta-waveguide structure, comprising:

[0008] A one-dimensional zero-refractive-index metawaveguide is used to transmit optical signals while maintaining the phase information of the optical signal during transmission. The one-dimensional zero-refractive-index metawaveguide includes multiple structural units arranged periodically along the optical signal transmission direction. Each structural unit includes a first dielectric pillar and two identical second dielectric pillars. The two second dielectric pillars are symmetrically arranged on both sides of the first dielectric pillar, forming an arc-shaped interface with the first dielectric pillar. The heights of all dielectric pillars are equal and must satisfy the requirement of completely confining the electromagnetic field within the height range of the corresponding structural unit. The length and width of the first dielectric pillar, as well as the major and minor semi-axes of the ellipse of the second dielectric pillars, should satisfy the requirement of completely confining the electromagnetic field within the width range of the corresponding structural unit.

[0009] A substrate is used to support the one-dimensional zero-refractive-index meta-waveguide and to generate a refractive index difference with it to form an optical mode.

[0010] In some embodiments, the structural units in the one-dimensional zero-refractive-index metawaveguide are arranged sequentially without gaps, and the first dielectric pillar and the second dielectric pillar in a single structural unit are arranged without gaps.

[0011] In some embodiments, the first dielectric pillar is made of silicon, silicon nitride, titanium oxide, lithium niobate, aluminum nitride, diamond, or a III-V compound semiconductor material.

[0012] In some embodiments, the second dielectric pillar is selected from semiconductor materials with a lower refractive index than the first dielectric pillar and capable of supporting the corresponding optical modes.

[0013] In some embodiments, the substrate is selected from semiconductor materials with a lower refractive index than the first dielectric pillar and capable of supporting the corresponding optical modes.

[0014] In some embodiments, the projection of the interface between the first dielectric pillar and the second dielectric pillars on both sides of the first dielectric pillar in all structural units onto the chip plane is fishbone shaped.

[0015] The second aspect of this disclosure provides a design method for a one-dimensional zero-refractive-index meta-waveguide structure according to any embodiment of the first aspect of this disclosure, comprising:

[0016] A physical model of the one-dimensional zero-refractive-index meta-waveguide structure was established using the finite element analysis method. The physical model consists of multiple structural units arranged periodically in the x-direction of the three-dimensional coordinate system xyz, and the structural parameters (height) of each structural unit along the z-direction are equal.

[0017] Under the conditions of the set excitation light wavelength and the set excitation light polarization direction, the period and height of each structural unit are initialized, and the width, semi-major axis and semi-minor axis of each structural unit are adjusted so that the frequencies of the electric monopole mode and the magnetic dipole mode located at the center of the Brillouin zone in the wave vector space of the physical model are degenerate together.

[0018] By adjusting the minor semi-axis of the ellipse of each structural unit, the relationship between the eigenmode Q value of the electric monopole and the minor semi-axis of the ellipse of the structural unit is obtained. Then, a minor semi-axis r of the ellipse of a selected structural unit is chosen. b * This enables the intrinsic mode Q value of the electric monopole to reach the target value;

[0019] By adjusting the width and semi-major axis of each structural unit, the relationship between the eigenmode Q value of the electric monopole and the width and semi-major axis of the ellipse of the structural unit is obtained. A set of structural units with widths b is then selected. * and the semi-major axis r of the ellipse a * This allows the intrinsic mode Q value of the electric monopole to reach its maximum value;

[0020] By adjusting the height of each structural unit, the relationship between the eigenmode Q value of the magnetic dipole and the height of the structural unit is obtained. With other geometric parameters fixed, a height h of one structural unit is selected. * This allows the eigenmode Q value of the magnetic dipole to reach the target value;

[0021] The period 'a' and width 'b' of each structural unit in the physical model are scaled up or down proportionally. * ellipse semi-axis r a * ellipse minor semi-axis r b * and height h * This makes the magnetic dipoles and electric monopoles of the physical model degenerate at the design frequency.

[0022] In some embodiments, the parameters set by the physical model also include electromagnetic boundary conditions.

[0023] In some embodiments, the target value of the intrinsic mode Q value of the electric monopole is determined by a set loss index.

[0024] In some embodiments, the eigenmode Q values ​​of the electric monopole and the magnetic dipole are both obtained by solving an eigenmode solver.

[0025] This disclosure has the following characteristics and beneficial effects:

[0026] This disclosure provides a one-dimensional zero-refractive-index metamorphic waveguide structure and its design method. By adjusting the period, width, semi-major axis, semi-minor axis, and height parameters of the metamorphic waveguide unit structure, optical coherence destructiveness in the in-plane lateral and out-of-plane vertical directions is achieved, i.e., bound states in the optical continuum. This reduces the transmission loss of the metamorphic waveguide and frees it from the spatial constraints of photonic bandgap materials. This method improves the flexibility of zero-refractive-index materials while reducing the chip area occupied by them, enabling the realization of various integrated optical components on a zero-refractive-index waveguide platform. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the structure of a one-dimensional zero-refractive-index meta-waveguide provided in the first aspect of this disclosure.

[0028] Figure 2 It constitutes Figure 1 The diagram shows the model and geometric parameters of a single structural unit in the metamorphic waveguide.

[0029] Figure 3 This is an overall flowchart of the design method for a one-dimensional zero-refractive-index metawaveguide provided in the second aspect of this disclosure. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this application clearer, the application will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0031] Conversely, this application covers any alternatives, modifications, equivalent methods, and schemes made within the spirit and scope of this application as defined by the claims. Furthermore, to provide the public with a better understanding of this application, certain specific details are described in detail below. However, this application can be fully understood by those skilled in the art even without these detailed descriptions.

[0032] The specific embodiments of this disclosure will be further described below with reference to the accompanying drawings:

[0033] Example 1

[0034] See Figure 1 , Figure 2 The first aspect of this disclosure provides a one-dimensional zero-refractive-index meta-waveguide structure, comprising:

[0035] A one-dimensional zero-refractive-index silicon waveguide 1 is composed of multiple structural units arranged periodically along the x-direction (i.e., the direction of optical signal transmission). It is used to transmit optical signals and maintain the phase information of the optical signals during transmission. Each structural unit consists of a first dielectric pillar 3 and two identical second dielectric pillars 4 symmetrically arranged on both sides of the first dielectric pillar 3. The interfaces between the two second dielectric pillars 4 and the first dielectric pillar 3 are both arc surfaces. The heights of the dielectric pillars are equal, and the optical coherence destructive condition is satisfied in the out-of-plane vertical direction, that is, the electromagnetic field can be completely confined within the height range of the corresponding structural unit. The length and width of the first dielectric pillar 3 and the major and minor semi-axes of the second dielectric pillars 4 are designed to satisfy the optical coherence destructive condition in the in-plane lateral direction (i.e., perpendicular to the direction of light propagation), that is, the electromagnetic field can be completely confined within the width range of the corresponding structural unit. The projection of the interfaces between the first dielectric pillar 3 and the second dielectric pillars 4 on both sides of the first dielectric pillar 3 in the chip plane is fishbone shaped.

[0036] A silicon dioxide substrate 2 is used to support a one-dimensional zero-refractive-index silicon waveguide 1 and to generate a refractive index difference with the silicon waveguide to form an optical mode. The substrate material is not limited to silicon dioxide; any semiconductor material with a lower refractive index than the one-dimensional zero-refractive-index waveguide 1 and capable of supporting the corresponding optical mode is acceptable.

[0037] The first dielectric pillar 3, a single structural unit of the one-dimensional zero-refractive-index metawaveguide 1, is made of silicon in this embodiment (this application also applies to dielectric pillars made of other materials with mature fabrication processes in the art, such as silicon nitride (SiN), titanium dioxide (TiO), lithium niobate (LN), aluminum nitride (AlN), diamond, or group III-V compounds, etc.). The projection of the first dielectric pillar 3 onto the chip plane is a rectangle, excluding the portions shared with the second dielectric pillar 4 on both sides, forming a geometric shape characterized by the parameters of period a (corresponding to the dimension of the first dielectric pillar 3 along the x-direction), width b (corresponding to the dimension of the first dielectric pillar 3 along the y-direction), and height h (corresponding to the dimension of the first dielectric pillar 3 along the z-direction). By adjusting the height h of the first dielectric pillar 3, optical coherence cancellation can be achieved in the z-direction, thereby reducing the transmission loss of optical modes in the one-dimensional zero-refractive-index silicon waveguide 1. In this embodiment, the optimal design parameters for the period a, width b, and height h of the first dielectric pillar 3 are 588 nm, 340 nm, and 820 nm, respectively.

[0038] The second dielectric pillar 4 is a single structural unit of the one-dimensional zero-refractive-index metawaveguide 1. This dielectric pillar is arranged without gaps with the first dielectric pillar 3. In this embodiment, the second dielectric pillar 4 is made of air, that is, the second dielectric pillar 4 is an elliptical air-hole structure. The material of the second dielectric pillar 4 is not limited to air; any semiconductor material with a lower refractive index than the first dielectric pillar 3 and capable of supporting the corresponding optical mode is acceptable. Note that when changing the material of the second dielectric pillar 4, the air material surrounding the metawaveguide should also be replaced with the new material. The elliptical semi-axis r of the second dielectric pillar 4 is adjusted... a and the minor semi-axis r of the ellipse b The parameters can achieve optical coherence cancellation in the y-direction, thereby further reducing the transmission loss of optical modes in the one-dimensional zero-refractive-index silicon waveguide 1. In this embodiment, the semi-elliptical major axis r of the second dielectric pillar 4... a and the minor semi-axis r of the ellipse b The optimal design parameters are 307nm and 215nm, respectively.

[0039] Example 2

[0040] The second aspect of this disclosure provides a design method for the aforementioned low-loss one-dimensional zero-refractive-index metawaveguide structure. The overall process is described in [link to documentation]. Figure 3 This includes the following steps:

[0041] 1) A physical model of a one-dimensional zero-refractive-index metawaveguide structure is established using finite element method (FEM). This model consists of multiple structural units arranged periodically in the x-direction of a three-dimensional coordinate system (xyz). The structural parameters (height) of each structural unit are equal along the z-direction. The parameters set in this physical model include: the excitation wavelength and polarization direction of the metawaveguide, the initial values ​​of the geometric parameters of the structural units based on the materials of the first and second dielectric pillars, and the electromagnetic boundary conditions. In this embodiment, the optical simulation software COMSOL Multiphysics is used to establish a physical model for simulating the metawaveguide structure, including the geometric model, material settings (silicon waveguide and silicon dioxide substrate), excitation source settings (1550nm operating wavelength, TM polarization), and electromagnetic boundary condition settings (periodic boundary in the x-direction, scattering boundaries in the y and z directions).

[0042] 2) Under the conditions of the set excitation light wavelength and the set excitation light polarization direction, initialize the period a and height h of each structural unit, and adjust the width b and semi-major axis r of each structural unit. a and the minor semi-axis r of the ellipse bThis allows the physical model to exhibit a Dirac cone-like structure at the center of the Brillouin zone in wave vector space, achieving degeneracy of both the electric monopole and magnetic dipole modes, corresponding to zero refractive index for impedance matching. This degeneracy remains stable over a wide range of geometric parameter variations, thus providing a large parameter space for subsequent designs to reduce transmission loss in metaguides.

[0043] 3) By adjusting the minor semi-axis r of the ellipse of each structural unit b This allows us to obtain the intrinsic mode quality factor (Q value) and r of the electric monopole. b The relationship between them, choose an r b * This ensures that the Q value of the electric monopole constituting the Dirac cone reaches the target value, which is determined by a set loss index. The lower the set loss value, the higher the corresponding quality factor.

[0044] 4) By adjusting the width b and the semi-major axis r of each structural unit a We can obtain the Q values ​​and b, r values ​​of the electric monopole eigenmodes constituting the Dirac cone. a The relationship between them, choose a set b * and r a * This causes the Q value of the electric monopole constituting the Dirac cone to reach its maximum value.

[0045] 5) By adjusting the height h of each structural unit, the relationship between the Q-values ​​of the eigenmodes of the magnetic dipole constituting the Dirac cone and h can be obtained. When other geometric parameters are fixed, a height h is selected. * This allows the Q value of the magnetic dipole constituting the Dirac cone to reach the target value. At this point, the metawaveguide has essentially eliminated radiation losses along the in-plane lateral and out-of-plane vertical directions, thus achieving a bound state in the optical continuum, thereby reducing the waveguide's transmission loss.

[0046] 6) After obtaining the optimal geometric parameters according to the above steps, both the electric monopole and the magnetic dipole can achieve degeneracy, and the Q value can reach the target value. However, the degeneracy frequency at this time is not necessarily at the ideal frequency. Therefore, according to the scale invariance of Maxwell's equations, it is only necessary to proportionally enlarge or reduce the period a and width b of each structural unit in the physical model of the one-dimensional zero-refractive-index metamorphic waveguide structure. * ellipse semi-axis r a * ellipse minor semi-axis r b * and height h * This makes the magnetic dipoles and electric monopoles of the physical model degenerate at the design frequency without compromising other properties.

[0047] The above is merely a preferred embodiment based on silicon-on-insulator (SOI) of this disclosure. The same design method can also be applied to silicon-on-insulator (SiN), titanium oxide (TiO), lithium niobate (LN), aluminum nitride (AlN), diamond, or III-V compounds. Therefore, the scope of protection of this application is not limited thereto. Any person skilled in the art who needs to design a low-loss one-dimensional zero-refractive-index waveguide structure should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope defined in the claims.

Claims

1. A one-dimensional zero-refractive-index metawaveguide structure, characterized in that, include: A one-dimensional zero-refractive-index meta-waveguide is used to transmit optical signals while maintaining the phase information of the optical signals during transmission. The one-dimensional zero-refractive-index meta-waveguide includes multiple structural units arranged periodically along the direction of optical signal transmission. Each structural unit includes a first dielectric pillar and two identical second dielectric pillars. The two second dielectric pillars are symmetrically arranged on both sides of the first dielectric pillar and form an arc-shaped interface with the first dielectric pillar. The height of each dielectric pillar is equal and meets the requirement of completely confining the electromagnetic field within the height range of the corresponding structural unit. The length and width of the first dielectric pillar and the major and minor axes of the ellipse of the second dielectric pillar should meet the requirement of completely confining the electromagnetic field within the width range of the corresponding structural unit. and A substrate is used to support the one-dimensional zero-refractive-index meta-waveguide and to generate a refractive index difference with it to form an optical mode.

2. The one-dimensional zero-refractive-index metawaveguide structure according to claim 1, characterized in that, In the one-dimensional zero-refractive-index meta-waveguide, each structural unit is arranged sequentially without gaps, and the first dielectric pillar and the second dielectric pillar in a single structural unit are arranged without gaps.

3. The one-dimensional zero-refractive-index metawaveguide structure according to claim 1, characterized in that, The first dielectric pillar is made of silicon, silicon nitride, titanium oxide, lithium niobate, diamond, or group III-V compound semiconductor materials.

4. The one-dimensional zero-refractive-index metawaveguide structure according to claim 1, characterized in that, The second dielectric pillar is made of a semiconductor material with a lower refractive index than the first dielectric pillar and capable of supporting the corresponding optical modes.

5. The one-dimensional zero-refractive-index metawaveguide structure according to claim 1, characterized in that, The substrate is selected from semiconductor materials with a lower refractive index than the first dielectric pillar and capable of supporting the corresponding optical modes.

6. The one-dimensional zero-refractive-index metawaveguide structure according to any one of claims 1 to 5, characterized in that, In all structural units, the interface between the first dielectric pillar and the second dielectric pillars on both sides is projected in a fishbone shape on the chip plane.

7. A design method for a one-dimensional zero-refractive-index metawaveguide structure according to any one of claims 1 to 6, characterized in that, include: A physical model of the one-dimensional zero-refractive-index metawaveguide structure is established using the finite element method. This physical model is defined in a three-dimensional coordinate system. xyz of x It consists of multiple structural units arranged periodically in a specific direction, with each structural unit along... z The structural parameters, i.e., the height, are all equal. Under the conditions of the set excitation light wavelength and the set excitation light polarization direction, the period and height of each structural unit are initialized, and the width, semi-major axis and semi-minor axis of each structural unit are adjusted so that the frequencies of the electric monopole mode and the magnetic dipole mode located at the center of the Brillouin zone in the wave vector space of the physical model are degenerate together. By adjusting the minor semi-axis of the ellipse of each structural unit, the eigenmode of the electric monopole is obtained. Q The relationship between the value and the minor semi-axis of the ellipse of the structural unit is used to select a minor semi-axis of the ellipse of the structural unit. r b * This makes the intrinsic mode of the electric monopole Q The value has reached the target value; By adjusting the width of each structural unit and the semi-major axis of the ellipse, the eigenmode of the electric monopole is obtained. Q The relationship between the value and the width of the structural unit and the major semi-axis of the ellipse is used to select a set of structural unit widths. b * and the semi-major axis of the ellipse r a * This makes the intrinsic mode of the electric monopole Q The value reached its maximum. By adjusting the height of each structural unit, the eigenmode of the magnetic dipole is obtained. Q The relationship between the value and the height of the structural unit, when other geometric parameters are fixed, involves selecting the height of a structural unit. h * This makes the eigenmodes of the magnetic dipole Q The value has reached the target value; The period of each structural unit in the physical model is scaled up or down proportionally. a ,width b * ellipse semi-major axis r a * ellipse semi-axis r b * and height h * This makes the magnetic dipoles and electric monopoles of the physical model degenerate at the design frequency.

8. The design method according to claim 7, characterized in that, The parameters set in the physical model also include electromagnetic boundary conditions.

9. The design method according to claim 7, characterized in that, The intrinsic mode of the electric monopole Q The target value is determined by the set loss index.

10. The design method according to claim 7, characterized in that, The intrinsic mode of the electric monopole Q Value and the eigenmode of the magnetic dipole Q The values ​​are all obtained by solving the intrinsic mode solver.

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