An asymmetric photonic crystal with a dirac point in the energy band and a construction method thereof

Abstract

The application discloses a method for constructing a Dirac point in an energy band of a photonic crystal. The method is based on energy band regulation of the photonic crystal, and a dielectric column is inserted into the photonic crystal structure to control the relative distance between energy bands, so that the Dirac point is constructed at a fixed position of the photonic crystal. The photonic crystal containing the Dirac point in the energy band has almost no spatial symmetry, and the application scenarios and application range of the photonic crystal Dirac point are greatly expanded.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of photonic crystals, and particularly relates to a non-symmetry photonic crystal containing a Dirac point in an energy band and a construction method thereof. BACKGROUND

[0002] The photonic crystal Dirac point is concerned due to its linear dispersion relation, which brings many strange characteristics, from the basic fixed-angle transmission and other-angle full-reflection characteristics, to pseudo-diffusion transmission and trembling, and transmission characteristics of the Dirac point topology and boundary state.

[0003] The existing photonic crystal Dirac point is closely related to the spatial symmetry of the photonic crystal structure, and the generation of the Dirac point is the result of the joint action of the spatial inversion symmetry and the time inversion symmetry of the photonic crystal, and the realization of the Dirac point through symmetry protection means that the corresponding photonic crystal structure needs to have strict spatial symmetry, which greatly limits the application range and development of the photonic crystal Dirac point. At the same time, since these Dirac points are mostly present at the high-symmetry line positions of the photonic crystal Brillouin zone, such as the K point of the triangular lattice photonic crystal and the symmetry line position of the square lattice photonic crystal, the positions of these Dirac points determined by symmetry also limit the application conditions of the Dirac point, for example, in the basic fixed-angle transmission and other-angle full-reflection application function, the position of the Dirac point determines the transmission angle that can be selected, and the high correlation between the Dirac point and the symmetry also leads to the limitation of the application scene and effect.

[0004] In summary, the main shortcomings of the prior art are: 1) the characteristics of the close connection between the Dirac point and the spatial symmetry of the photonic crystal structure limit the existence of the Dirac point to a specific photonic crystal structure, which limits the application range of the photonic crystal Dirac point; 2) the Dirac point can only be located at a few specific positions in the photonic crystal Brillouin zone, which greatly limits the implementation effect of the application function of the photonic crystal Dirac point. For the fixed-angle light wave transmission at the Dirac point frequency, the similar optical switch function of the full-reflection at other angles is limited by the fixed position of the Dirac point. SUMMARY

[0005] To solve the above technical problems, the present application proposes a method for constructing a Dirac point in a photonic crystal and a non-symmetry photonic crystal constructed based on the method, which breaks the strong dependence between the generation of the existing photonic crystal Dirac point and the spatial symmetry of the photonic crystal structure, and constructs a variety of non-symmetry photonic crystal systems containing Dirac points in the energy band, and can also realize the artificial selection and control of the position of the Dirac point.

[0006] The application discloses a method for constructing a Dirac point in a band of a photonic crystal.

[0007] S1, providing a photonic crystal;

[0008] S2, selecting two adjacent upper and lower bands and a position for pre-constructing a Dirac point in the photonic crystal;

[0009] S3, comparing spatial distribution diagrams of intrinsic field intensity of the two bands at the position for pre-constructing the Dirac point, and determining a geometric position of the photonic crystal with the largest difference in the modulus of the field intensity in the two diagrams;

[0010] S4, inserting a dielectric column at the geometric position of the photonic crystal, so that the whole band moves upward or downward, and the two bands move closer to each other in the process of moving;

[0011] S5, repeating steps S3-S4, so that the two bands continuously move closer to each other at the position for pre-constructing the Dirac point until degeneration occurs at the position, thereby constructing the Dirac point in the band of the photonic crystal.

[0012] Optionally, the structure of the photonic crystal does not require spatial symmetry.

[0013] Optionally, in step S2, the position for pre-constructing the Dirac point is linearly selected for the two adjacent upper and lower bands. The distance between the two adjacent upper and lower bands at the position for pre-constructing the Dirac point is not more than a preset value, or the distance between the two adjacent upper and lower bands at the position for pre-constructing the Dirac point is the shortest.

[0014] Optionally, in step S2, the positions of the two adjacent bands are selected according to the frequency range of the pre-constructed Dirac point.

[0015] Optionally, in step S4, the dielectric constant of the dielectric column is kept between 1 and 20.

[0016] Optionally, step S4 specifically comprises: when the modulus of the field intensity of the upper band at the geometric position of the photonic crystal is greater than the modulus of the field intensity of the lower band, inserting a dielectric column at the geometric position of the photonic crystal, the dielectric constant of the dielectric column is higher than the dielectric constant of the original material at the geometric position of the photonic crystal, so that the whole band moves downward, the moving amount of the upper band is greater than that of the lower band, and the two bands move closer to each other.

[0017] Optionally, the step S4 specifically comprises: when the modulus of the electric field intensity of the upper energy band at the geometric position is less than the modulus of the electric field intensity of the lower energy band, inserting a dielectric column at the geometric position of the photonic crystal, the dielectric constant of the dielectric column being lower than the dielectric constant of the original material at the geometric position of the photonic crystal, so that the energy band as a whole moves upward, the moving amount of the upper energy band being less than the moving amount of the lower energy band, and the two energy bands approach each other.

[0018] The application further discloses a non-symmetry photonic crystal with a Dirac point in an energy band, which is constructed by any of the above methods.

[0019] The method for constructing a Dirac point in an energy band of a photonic crystal proposed by the application is different from the common interaction of spatial symmetry and time symmetry, and is based on the energy band regulation of the photonic crystal, the relative distance between energy bands is controlled by inserting dielectric columns (referred to as "columns") with various dielectric constants into the photonic crystal structure, and then the Dirac point is constructed at a fixed position of the photonic crystal, at this time, the photonic crystal with the Dirac point in the energy band has almost no spatial symmetry, and the application scenarios and application range of the photonic crystal Dirac point are expanded. The operation of inserting the dielectric column into the photonic crystal structure essentially changes the material parameters of the photonic crystal structure at this position, and then changes the energy band distribution and various properties of the photonic crystal.

[0020] The application has the following beneficial effects:

[0021] 1) The existing photonic crystal Dirac point is closely related to the spatial symmetry of the photonic crystal, which means that the Dirac point usually only exists in several common high spatial symmetry photonic crystals, which greatly limits the application form and range of the photonic crystal Dirac point. The method for constructing a Dirac point in an energy band of a photonic crystal proposed by the application has no special requirement for the spatial symmetry of the photonic crystal, can construct a Dirac point in the energy band of a non-symmetry photonic crystal, and then realizes various applications of the Dirac point, such as single-angle transmission, other-angle total reflection, etc.

[0022] 2) The method for constructing a Dirac point in an energy band of a photonic crystal proposed by the application has wide applicability, has been verified in multiple two-dimensional photonic crystal systems including square lattices, triangular lattices, and oblique lattices with a top angle of 45° (including the inside of the Brillouin zone and the symmetry line position), greatly expands the photonic crystal system with a Dirac point in the energy band, and enables the various properties of the Dirac point to better play an application.

[0023] 3) The asymmetric photonic crystal obtained by this method not only contains Dirac points in the energy band and possesses the various properties brought by Dirac points, but also maintains the material parameters of the asymmetric photonic crystal structure between 1 and 20, so that the corresponding properties and functions can be effectively applied in experiments and real life. Attached Figure Description

[0024] Figure 1 In the diagram: (a) is a schematic diagram of the triangular lattice photonic crystal structure; (b) is a band structure diagram of the triangular lattice photonic crystal; (c) is a spatial distribution diagram of the eigenstate electric field intensity of the first band at point K; (d) is a spatial distribution diagram of the eigenstate electric field intensity of the second band at point K; (e) is a schematic diagram of the photonic crystal structure after the first pillar is inserted; and (f) is a diagram showing how the distance between the two bands at point K changes with the dielectric constant of the inserted pillar.

[0025] Figure 2 In the diagram: (a) is the spatial distribution of the eigenstate electric field intensity of the first energy band at point K; (b) is the distribution of the eigenstate electric field intensity of the second energy band at point K; (c) is a schematic diagram of the photonic crystal structure after the second pillar is inserted; and (d) is a diagram showing how the distance between the two energy bands at point K changes with the dielectric constant of the inserted pillar.

[0026] Figure 3 In the image: (a) is a schematic diagram of the structure of a triangular lattice photonic crystal; (b) is a band diagram of the triangular lattice photonic crystal; and (c) is a diagram of a three-dimensional conical dispersion surface.

[0027] Figure 4 In the diagram: (a) is a schematic diagram of an orthorhombic lattice photonic crystal with a vertex angle of 45°; (b) is a band diagram of an orthorhombic lattice photonic crystal with a vertex angle of 45°; (c) is a schematic diagram of a square lattice photonic crystal; (d) is a band diagram of a square lattice photonic crystal containing a Dirac point in the Brillouin zone; (e) is a schematic diagram of a square lattice photonic crystal; and (f) is a band diagram of a square lattice photonic crystal containing a Dirac point at the middle position of the XM region.

[0028] Figure 5 for Figure 3 (a) shows the transmittance variation of a flat plate composed of a triangular lattice photonic crystal when incident at different angles. Detailed Implementation

[0029] Generally, Dirac points exist at the K and K' points of the Brillouin zone of triangular lattice photonic crystals and other high-symmetry lines of the Brillouin zone of other lattice photonic crystals, but the positions of these Dirac points determined by symmetry greatly limit the conditions of application of Dirac points. We propose a method for constructing Dirac points in the band based on the band regulation of photonic crystals. In this method, the photonic crystal structure is changed at a suitable position by referring to the fixed position of the photonic crystal intrinsic state electric field intensity distribution and the corresponding band diagram of the photonic crystal structure. In this paper, we control the relative movement between bands by inserting medium columns with different parameters in the photonic crystal structure to construct Dirac points in the band. The specific construction method is as follows:

[0030] Referring to the formula of the band change caused by the small change of the photonic crystal structure, for TM polarization (electric field along the Z direction):

[0031]

[0032] In the formula, ω nk and ω nk are the intrinsic frequencies before and after the change of the two-dimensional photonic crystal structure, respectively, r represents the polar coordinate of the photonic crystal, and ε and ε are the dielectric constants before and after the change of the photonic crystal structure at the changed position, respectively, and E nk (r) is the electric field intensity before the change of the photonic crystal structure.

[0033] In the case of TM polarization, it can be seen from formula (1) that the sign of ω determines the direction of the band movement, and the modulus of the electric field intensity (i.e., |E 2 (r)| nk value) determines the amount of band movement, so we can artificially select the position where the spatial distribution of the intrinsic state electric field intensity of the two adjacent bands is most different to change the photonic crystal structure, thereby obtaining the maximum relative movement of the band.

[0034] In summary, the band is manipulated in two directions, and the manipulated bands are adjacent upper and lower bands. Specifically, a column with a smaller dielectric constant than the original background is inserted into the photonic crystal, and the band moves upward. The position of the inserted column is where the |E 2 (r)| nk value of the two bands is most different, and the |E 2 (r)| nk value at this position of the lower band is greater than the |E 2corresponding value; two is in the photonic crystal inserted column, the dielectric constant of the original background is greater, the overall band moves down, the position of the inserted column is the |E nk (r)| 2 value difference between the maximum, and the |E nk (r)| 2 value of the lower branch band at this position is less than the |E nk (r)| 2 corresponding value.

[0035] Thus, by the photonic crystal structure operation we can realize the adjacent two bands in the fixed position between the close, so in theory we can realize the degeneracy of the fixed position in the band by constantly inserting column, and then construct the Dirac point in the band.

[0036] The specific construction process will be described in detail below. Figure 1 (a) and (b) are two-dimensional triangular lattice photonic crystal structure schematic diagram and the corresponding band diagram, from Figure 1 (b) can be seen from the two bands at the K point there exists a band gap, but there is no Dirac point, we will be introduced in the method of band control to construct the K point position of the Dirac point.

[0037] Figure 1 (c) and (d) are the first, second band at the K point of the eigenstate electric field intensity, that is, |E nk (r)| 2 The distribution of the two figures, we choose the Figure 1 (e) shown in the position of the circular (that is, the electric field intensity difference between the maximum position, and the first branch band corresponding to the value is less than the second branch) inserted a dielectric constant of 18.92 high dielectric constant column (corresponding to the band control described in one direction), Figure 1 (f) is the distance between the two bands at the K point with the change of the dielectric constant of the inserted column, from which we can clearly see that the distance between the two bands at the K point when the dielectric constant of the original background is 7, after inserting the column with a dielectric constant of 18.92, the distance between the two bands at the K point has been significantly shortened.

[0038] Similarly, after inserting the first column in the photonic crystal, we continue to compare Figure 2 (a) and (b) shown in the two bands at the K point of the eigenstate electric field intensity distribution, we choose the Figure 2 (c) shown in the position of the circular (that is, the electric field intensity difference between the maximum position, and the first branch band corresponding to the value is greater than the second branch) inserted a dielectric constant of 1 low dielectric constant column (corresponding to the band control described in another direction),Figure 2 (d) is the distance between the two bands at K point as a function of the dielectric constant of the inserted column, from which it can be clearly seen that the distance between the two bands at K point is 7 for the dielectric constant of the original background, and the distance between the two bands at K point is further shortened after the insertion of the column with a dielectric constant of 1. It is worth noting that due to the significant effect of this band manipulation method, we can control the dielectric constant of the inserted column to be between 1 and 20, which also makes the preparation of photonic crystals in the infrared band have a reasonable material selection.

[0039] By repeating the above operation, we can continuously shorten the distance between the two bands at K point, and finally make the distance between the two bands at K point zero, and the two bands at K point degenerate, and the Dirac point is formed. As shown in Figure 3 Figure 3 (a) is a schematic diagram of a triangular lattice photonic crystal containing a Dirac point in the band, from which it can be seen that the photonic crystal almost has no spatial symmetry, but in Figure 3 (b) and (c) are band diagrams and three-dimensional conical dispersion surface diagrams that can clearly show the existence of Dirac points and Dirac cones at K points, which fully prove the correctness of the method proposed by us for constructing asymmetric photonic crystals containing Dirac points.

[0040] In addition, we have also successfully constructed a variety of different band asymmetric two-dimensional photonic crystal systems containing Dirac points by the above method of constructing photonic crystal Dirac points, and the Dirac points are located at multiple positions in the photonic crystal Brillouin zone. Of course, we can also select the positions of the adjacent two bands according to the frequency range of the Dirac point we want to construct, because different bands correspond to different frequency ranges, and the specific selection can be made according to the actual application.

[0041] As shown in Figure 4 (a) and (b) are schematic diagrams of rhombic lattice photonic crystals with a top angle of 45° and corresponding band diagrams, respectively, which can show the asymmetry of the photonic crystal structure and the Dirac point contained in the band at K point; Figure 4 (c) is a schematic diagram of a square lattice photonic crystal, which contains a Dirac point at the position marked by a vertical line in the band Figure 4 (d); Figure 4 Figure 4 ​​(e) and (f) are the schematic diagram of square lattice photonic crystal structure and the corresponding band structure containing Dirac point at the middle position of XM, respectively. Thus, we prove the correctness of the method proposed in the previous section for constructing photonic crystal Dirac point in multiple photonic crystal systems, and the successful construction of Dirac point in different Brillouin zone positions of different photonic crystal systems further proves the flexibility and applicability of the method.

[0042] We further verify the transmission characteristics of the constructed photonic crystal Dirac point. For the Dirac point, there is only one state in the band at the Dirac point position, and only when the incident angle of the electromagnetic wave exactly excites the state of the Dirac point, the electromagnetic wave can propagate in the photonic crystal. Other angles are equivalent to a band gap and cannot propagate. In this example, we use the triangular lattice photonic crystal shown in (a) to analyze the transmittance of the flat plate formed by the photonic crystal at different angles at the Dirac point frequency, as shown in (b). Figure 3 Figure 5 From the figure, it can be clearly seen that only when the angle is exactly 0°, that is, the vertical incidence directly excites the state of the K point Dirac point, a transmittance peak can be obtained, and at other angles far from the vertical incidence, the transmittance sharply decreases to 0, which cannot be transmitted in the photonic crystal.

[0043] Based on the single-angle transmission and other-angle total reflection transmission characteristics of the Dirac point, the photonic crystal containing the Dirac point in the band can be applied to single-angle gating optical switches or filters. The method proposed for constructing the asymmetric photonic crystal containing the Dirac point in the band expands the application range of the photonic crystal Dirac point, and the Dirac point is located at different positions of the Brillouin zone of multiple photonic crystal systems, which expands the transmission angle selection range and increases the application of corresponding characteristics.

[0044] In addition, considering the actual workload and the complexity of the final asymmetric photonic crystal structure, we choose the adjacent two bands to maintain a certain linear relationship and appropriate distance at the determined pre-constructed Dirac point position. For example, for the purpose of constructing a Dirac point, we can directly select the two bands with the shortest distance at the pre-constructed Dirac point position for manipulation.

[0045] ​In summary, we propose a method to construct Dirac points in photonic crystal systems, namely a method to construct asymmetric photonic crystals with Dirac points in the band structure, successfully construct Dirac points in various photonic crystal systems, and verify the properties corresponding to the Dirac points. This method breaks the dependence of ordinary Dirac points on the spatial symmetry of the photonic crystal structure, and has no special requirements for the photonic crystal structure before the band manipulation, which can have symmetry or no symmetry, expanding the application range of photonic crystal Dirac points, and almost any lattice photonic crystal can realize Dirac points at any position, for example, the models implemented include different Brillouin zone positions of square lattice, triangular lattice, orthorhombic lattice and other photonic crystal systems, expanding the angle selection range of single-angle transmission characteristics and increasing the application. Moreover, the construction method used in the present application is simple and efficient, and the dielectric constant of the asymmetric photonic crystal with Dirac points in the constructed band structure is kept between 1 and 20, making the preparation of photonic crystals have a reasonable material selection in the infrared band.

[0046] Finally, it should be noted that although the embodiments of the present application are described above in combination with the drawings, the present application is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the guidance of the present application without departing from the scope of the claims of the present application, which are all within the protection of the present application.

Claims

1. A method of constructing a Dirac point in the energy band of a photonic crystal, characterized by, The application relates to a method for constructing a Dirac point in a photonic crystal. S1, providing a photonic crystal; S2, selecting adjacent upper and lower energy bands and a position of a pre-constructed Dirac point in the photonic crystal; S3, comparing the intrinsic state electric field intensity spatial distribution maps of the two energy bands at the position of the pre-constructed Dirac point, and determining the photonic crystal geometric position with the maximum difference in electric field intensity modulus value in the two maps; S4, inserting a dielectric column at the photonic crystal geometric position, so that the energy bands as a whole move upwards or downwards, and the upper and lower energy bands approach each other in the moving process; S5, repeating steps S3-S4, so that the upper and lower energy bands continuously approach each other at the position of the pre-constructed Dirac point until degeneration occurs at the position, thereby constructing a Dirac point in the energy bands of the photonic crystal.

2. The method of claim 1, wherein, The structure of the photonic crystal does not require spatial symmetry.

3. The method of claim 1, wherein, In the step S2, the position of the adjacent upper and lower energy bands at the pre-constructed Dirac point is linear.

4. The method of claim 3, wherein, In the step S2, the distance of the adjacent upper and lower energy bands at the pre-constructed Dirac point is not more than a preset value.

5. The method of claim 3, wherein, In the step S2, the distance of the selected adjacent upper and lower energy bands at the pre-constructed Dirac point is the shortest.

6. The method of claim 1, wherein, In the step S2, the position of the adjacent two energy bands is selected according to the frequency range of the pre-constructed Dirac point.

7. The method of claim 1, wherein, In the step S4, the dielectric constant of the dielectric column is kept between 1 and 20.

8. The method of claim 1, wherein, The step S4 specifically comprises: When the electric field intensity modulus value of the upper energy band at the geometric position is greater than that of the lower energy band, a dielectric column is inserted at the photonic crystal geometric position, the dielectric constant of the dielectric column is higher than that of the original material at the photonic crystal geometric position, the energy bands as a whole move downwards, the moving amount of the upper energy band is greater than that of the lower energy band, and the two energy bands approach each other.

9. The method of claim 1, wherein, The step S4 specifically comprises: When the electric field intensity modulus value of the upper energy band at the geometric position is less than that of the lower energy band, a dielectric column is inserted at the photonic crystal geometric position, the dielectric constant of the dielectric column is lower than that of the original material at the photonic crystal geometric position, the energy bands as a whole move upwards, the moving amount of the upper energy band is less than that of the lower energy band, and the two energy bands approach each other.

10. A symmetry-broken photonic crystal with Dirac points in the band structure, characterized in that, The structure of the asymmetric photonic crystal constructed by any one of the methods in claims 1-9 does not have spatial symmetry.

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