A method for constructing a one-dimensional transformation photonic crystal omnidirectional mirror

Abstract

This invention discloses a method for constructing a one-dimensional transforming photonic crystal omnidirectional mirror. This method uses a thinner medium to construct a one-dimensional transforming photonic crystal omnidirectional mirror with the same omnidirectional reflection coefficient. The method includes the following steps: constructing an original one-dimensional photonic crystal omnidirectional mirror using medium A and medium B; calculating the omnidirectional reflection coefficient of the original one-dimensional photonic crystal omnidirectional mirror using the transfer matrix method; determining the compression coefficient 'a'; calculating the characteristic parameters of mediums A' and B' required to construct the one-dimensional transforming photonic crystal omnidirectional mirror; determining the materials of mediums A' and B'; and constructing the one-dimensional transforming photonic crystal omnidirectional mirror using mediums A' and B'. The one-dimensional transforming photonic crystal omnidirectional mirror constructed by this invention can achieve the same omnidirectional reflection coefficient as the original one-dimensional photonic crystal omnidirectional mirror with a thinner thickness, providing a new method for the integration and miniaturization of electronic devices.

Description

Technical Field

[0001] This invention belongs to the field of optical technology, and specifically relates to a method for constructing a one-dimensional transforming photonic crystal omnidirectional reflecting mirror. Background Technology

[0002] Photonic crystals are a novel type of artificial structural material. A photonic crystal, composed of materials with different refractive indices arranged periodically, generates a photonic bandgap. Due to their numerous potential applications in filters, optical switches, waveguides, cavities, and omnidirectional reflectors, photonic crystals have attracted considerable attention from researchers. Mirrors are commonly used optical components, with metal and dielectric mirrors being the two main types. While metal mirrors can achieve near-omnidirectional reflection, their high absorption limits their reflectivity in the infrared band. Dielectric mirrors, while providing high reflectivity, struggle to achieve omnidirectional reflection due to their limited reflection bandwidth and sensitivity to the angle of incidence. Furthermore, due to the skin effect of metals, the absorption of light waves in metal mirrors occurs only within a very thin surface depth. Under strong light, the surface temperature of a metal mirror can rise significantly, causing surface deformation and severely degrading its quality.

[0003] A Bragg reflector (also known as a distributed Bragg reflector) is a reflector structure that comprises an adjustable multilayer structure of two optical materials. The most common type is the quarter-wave reflector, where the thickness of each layer corresponds to a quarter of the wavelength. The latter condition applies to normal incidence; if the reflector is used for larger angles of incidence, a relatively thicker layer is required. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a one-dimensional transforming photonic crystal omnidirectional reflector. By reducing the thickness of the photonic crystal, the propagation space of electromagnetic waves is equivalently altered, making the propagation effect of electromagnetic waves in physical space exactly the same as the propagation effect in the constructed virtual space.

[0005] To achieve the above objectives, the solution of the present invention is:

[0006] A method for constructing a one-dimensional transform photonic crystal omnidirectional reflecting mirror includes the following steps:

[0007] Step 1: Construct a primitive one-dimensional photonic crystal omnidirectional mirror using medium A and medium B, wherein the dielectric constant of medium A is different from that of medium B;

[0008] Step 2, determine the compression factor a;

[0009] Step 3: Based on the characteristic parameters of medium A and medium B and the compression coefficient a obtained in step 2, calculate the characteristic parameters of medium A' and medium B' required to construct a one-dimensional transform photonic crystal omnidirectional mirror.

[0010] Step 4: Based on the characteristic parameters calculated in Step 3, determine the materials of medium A' and medium B', and construct a one-dimensional transform photonic crystal omnidirectional mirror using medium A' and medium B'.

[0011] The specific content of step 1 above is as follows: The original one-dimensional photonic crystal omnidirectional mirror is formed by the overlapping growth of medium A and medium B, and the arrangement structure is represented as (AB). N N represents the number of times medium A and medium B overlap.

[0012] The number of times that media A and media B overlap is N≥5.

[0013] The optical thickness of both medium A and medium B is 0.25λ0, where λ0 is the center operating wavelength of the original one-dimensional photonic crystal omnidirectional mirror.

[0014] In step 2 above, the compression coefficient 'a' is determined by calculation or by setting. If it is determined by calculation, the formula is:

[0015]

[0016] Where L is the thickness of the original one-dimensional photonic crystal omnidirectional mirror, and L' is the desired thickness for constructing a one-dimensional transformed photonic crystal omnidirectional mirror.

[0017] The specific content of step 3 above is as follows: Based on the principle of transformation optics, establish the correspondence between spatial coordinate transformation and changes in medium parameters, transforming the electromagnetic calculation problem into a spatial coordinate transformation problem. The coordinate transformation formula from the physical propagation space (x,y,z) of the electromagnetic wave to the virtual propagation space (x',y',z') is defined as follows:

[0018]

[0019] Where a is the compression coefficient and b is a constant;

[0020] The Jacobi transformation matrix is ​​expressed as:

[0021]

[0022] After transformation, the characteristic parameters of medium A' and medium B' are expressed as follows:

[0023]

[0024]

[0025] in, and Let A and B be the permittivity and permeability of dielectric A', respectively. and These are the permittivity and permeability of dielectric B', respectively, ε A and μ A These are the permittivity and permeability of medium A, ε and ε', respectively. B and μ B , respectively, are the dielectric constant and magnetic permeability of medium B.

[0026] The specific content of step 4 above is as follows: a one-dimensional transform photonic crystal omnidirectional mirror is constructed by overlapping growth of media A' and media B', and the arrangement structure is represented as (A'B'). N N represents the number of times medium A' and medium B' overlap.

[0027] The number of times that media A' and media B' overlap is N≥5.

[0028] According to optical principles, the omnidirectional reflection coefficient of the aforementioned one-dimensional transformed photonic crystal omnidirectional mirror is the same as that of the original one-dimensional photonic crystal omnidirectional mirror.

[0029] Based on the omnidirectional reflection coefficient and required compressibility coefficient of the original one-dimensional photonic crystal omnidirectional mirror, this invention calculates the dielectric constant and magnetic permeability of the required medium and constructs a one-dimensional transformed photonic crystal omnidirectional mirror. Compared with the original one-dimensional photonic crystal omnidirectional mirror, a thinner structure is achieved without affecting the omnidirectional reflection coefficient, providing a new method for the integration and miniaturization of electronic devices and providing important theoretical basis for the design and fabrication of novel omnidirectional mirrors. Attached Figure Description

[0030] Figure 1 This is a structural diagram of the original one-dimensional photonic crystal omnidirectional reflecting mirror of the present invention.

[0031] Figure 2 This is a structural diagram of the one-dimensional transforming photonic crystal omnidirectional reflecting mirror of the present invention.

[0032] Figure 3 This is the reflection spectrum of the original one-dimensional photonic crystal omnidirectional mirror of the present invention.

[0033] Figure 4 This is the bandgap diagram of the original one-dimensional photonic crystal omnidirectional reflecting mirror of the present invention.

[0034] Figure 5 These are bandgap diagrams of one-dimensional transform photonic crystal omnidirectional reflectors with different transform coefficients according to the present invention; wherein (a) is the bandgap diagram with a transform coefficient of 1, (b) is the bandgap diagram with a transform coefficient of 0.8, (c) is the bandgap diagram with a transform coefficient of 0.5, and (d) is the bandgap diagram with a transform coefficient of 0.1. Detailed Implementation

[0035] The technical solution and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings.

[0036] The most significant characteristic of photonic crystals is that they have a photonic bandgap structure, which can achieve total internal reflection in a certain frequency band by suppressing the propagation of electromagnetic waves. This property of photonic crystals can be used to make omnidirectional mirrors.

[0037] like Figure 1 and Figure 2 The diagram shows the original one-dimensional photonic crystal omnidirectional reflector and the one-dimensional transformed photonic crystal omnidirectional reflector of this invention. A photonic crystal is an artificial periodic structure with the basic characteristics of a bandgap and localization. When electromagnetic waves propagate in a photonic crystal, Bragg scattering occurs, and energy forms a band structure. A photonic bandgap appears between adjacent bands, exhibiting excellent frequency selectivity. The bandgap size of a photonic crystal is related to the contrast of the dielectric constant of the overlapping medium; the greater the contrast, the easier it is to obtain a photonic crystal with a wider bandgap. Localization refers to the phenomenon where introducing a defect into a photonic crystal creates photonic localization within the bandgap, allowing microwave frequencies that were originally in the bandgap to tunnel through the photonic crystal structure, forming defect transmission peaks.

[0038] in Figure 1 This is a structural diagram of a primitive one-dimensional photonic crystal omnidirectional mirror. For photonic crystals, the greater the difference in relative permittivity between the two dielectric layers, the wider the photonic bandgap can be obtained. In this embodiment, the omnidirectional mirror is composed of Ge with a relatively high permittivity and polyethylene with a relatively low permittivity, arranged in a periodic alternation, represented by the structure (AB). N Where N = 10, and N is the number of times medium A and medium B overlap; the media used in the omnidirectional mirror in this embodiment are all non-magnetic (μ). r1 =μ r2 =1), setting the central working wavelength λ0 = 4μm, the λ0 / 4 film photonic crystal ensures that the light beams reflected from all interfaces of the film system return to the front surface with the same phase. The resulting phase length allows the entire film system to achieve a maximum reflectivity. Therefore, the optical thickness of each layer of the medium is one-quarter of the wavelength, that is: ε r1 Let μ be the relative permittivity of dielectric A. r1 Let ε be the relative permeability of medium A. r2 Let μ be the relative permittivity of dielectric B. r2 Let d1 be the relative permeability of medium B; d1 be the physical thickness of medium A; and d2 be the physical thickness of medium B. The thickness of the original one-dimensional photonic crystal omnidirectional mirror is L = N(d1 + d2) = 10(d1 + d2).

[0039] in Figure 2This is a structural diagram of a one-dimensional transforming photonic crystal omnidirectional mirror. After optical transformation, the thickness of the one-dimensional transforming photonic crystal omnidirectional mirror becomes thinner. When the transformation coefficient a = 0.5, the thickness of the one-dimensional transforming photonic crystal omnidirectional mirror is half the thickness of the original one-dimensional photonic crystal omnidirectional mirror. The thickness L' of the one-dimensional transforming photonic crystal omnidirectional mirror is L' = a·L = 5(d1 + d2).

[0040] The reflection spectrum of a photonic crystal is simulated using the transfer matrix method, as follows: Figure 2 As shown, in the original one-dimensional photonic crystal omnidirectional mirror, the transfer matrix of the l-th layer medium Y is expressed as:

[0041]

[0042] Where, θ l It is the incident angle of the l-th medium; d l Let z be the thickness of the l-th dielectric layer. l (ω) and y l (ω) represents the admittance and impedance of the l-th dielectric layer, respectively, and is expressed as z l (ω)=jωμ l and y l (ω)=jωε l μ l ε is the magnetic permeability of the medium. l U is the dielectric constant of the medium, and each layer of the medium is a non-magnetic medium, i.e., μ. l =μ0, where μ0 is the permeability of free space; Y represents medium A or medium B;

[0043] The transmission matrix of the original one-dimensional photonic crystal omnidirectional mirror is obtained by concatenating and multiplying the transmission matrices of each medium layer, as expressed by:

[0044]

[0045] Where Q represents the number of layers of the medium in the original one-dimensional photonic crystal omnidirectional mirror, and x 11 (ω), x 12 (ω), x 21 (ω), x 22 (ω) represents each element of the concatenated matrix;

[0046] The expression for the omnidirectional reflection coefficient of the original one-dimensional photonic crystal omnidirectional mirror is:

[0047]

[0048] E x (-) (0), E x (+)(0) represents the electric field strength of the electromagnetic wave reflected from the incident interface and the electric field strength of the electromagnetic wave emitted from the incident interface, respectively; k0 and k S Let θ0 and θe be the propagation constants in the incident and exit spaces, respectively. S These are the incident angle and the exit angle, μ S Let be the permeability of the ejection space.

[0049] Based on the principles of transformation optics and the invariance of Maxwell's equations under three-dimensional coordinate transformations, the permittivity and permeability tensors of a medium in real physical space are derived through spatial coordinate transformations. By using transformation optics to establish the correspondence between spatial coordinate transformations and changes in medium parameters, complex electromagnetic calculation problems can be transformed into simple spatial coordinate transformation problems.

[0050] The coordinate transformation formula from the physical propagation space (x, y, z) to the virtual propagation space (x', y', z') of electromagnetic waves is defined as follows:

[0051]

[0052] Where a is the compression coefficient and b is a constant; Where L' is the thickness of the one-dimensional transformed photonic crystal omnidirectional mirror, and L is the thickness of the original one-dimensional photonic crystal omnidirectional mirror.

[0053] The Jacobi transformation matrix is ​​expressed as:

[0054]

[0055] After transformation, the characteristic parameters of medium A' and medium B' are expressed as follows:

[0056]

[0057]

[0058] in, and Let A and B be the permittivity and permeability of dielectric A', respectively. and These are the permittivity and permeability of dielectric B', respectively, ε A and μ A These are the permittivity and permeability of medium A, ε and ε', respectively. B and μ B , respectively, are the dielectric constant and magnetic permeability of medium B.

[0059] A one-dimensional transformation photonic crystal omnidirectional mirror is constructed by overlapping growth of media A' and B', with the arrangement structure represented as (A'B'). NOne overlap of medium A' and medium B' consists of one layer of medium A' and one layer of medium B'. N is the number of times medium A' and medium B' overlap, and the number of times medium A' and medium B' overlap N ≥ 5.

[0060] To study the reflection characteristics of photonic crystals, the bandgap width is defined as the wavelength range when R > 99.9%, such as... Figure 3 As shown, the change in incident angle has a modulation effect on the photonic bandgap bandwidth. As the incident angle increases, the bandgap of the photonic crystal gradually shifts towards shorter wavelengths. When the incident angle increases from 0° to 85°, the starting wavelength of the photonic crystal bandgap gradually decreases from 3.04μm to 2.5μm, and the cutoff wavelength of the bandgap also decreases from 5.86μm to 5.75μm. The one-dimensional transformation photonic crystal of the present invention has a total internal reflection bandgap window of 3.04μm-5.86μm. Light within this wavelength range will be completely reflected regardless of whether it is incident perpendicularly or obliquely at 85°, thus realizing the function of an all-angle reflector.

[0061] like Figure 4 As shown, the bandgap width of incident light at different angles is displayed. As the incident angle increases, the bandgap of the photonic crystal gradually widens, increasing from 2.82 μm at 0° to 3.25 μm at 85°, an increase of 0.43 μm.

[0062] To verify that the theoretically designed one-dimensional transform photonic crystal omnidirectional mirror has the same photonic bandgap as the original one-dimensional photonic crystal omnidirectional mirror, this embodiment uses the microwave studio of CST Studio Suite 3D electromagnetic simulation software to establish the same numerical structure and simulates the reflection characteristics by using a frequency domain solver.

[0063] like Figure 5 As shown, the numerically calculated reflectivity agrees well with the theoretical calculation under different transformation coefficients, verifying the correctness of the linear transformation method. Among them, (a) is the bandgap diagram with a transformation coefficient of 1, (b) is the bandgap diagram with a transformation coefficient of 0.8, (c) is the bandgap diagram with a transformation coefficient of 0.5, and (d) is the bandgap diagram with a transformation coefficient of 0.1. Since the bandgap range of the one-dimensional transformed photonic crystal omnidirectional mirror is consistent with that before the transformation, the one-dimensional transformed photonic crystal omnidirectional mirror has the same omnidirectional reflection coefficient as the original one-dimensional photonic crystal omnidirectional mirror, and the function of the omnidirectional mirror is realized in this wavelength range.

[0064] In summary, this invention discloses a method for constructing a one-dimensional transforming photonic crystal omnidirectional mirror. This method uses a thinner medium to construct a one-dimensional transforming photonic crystal omnidirectional mirror with the same omnidirectional reflection coefficient as the original one-dimensional photonic crystal omnidirectional mirror. The method includes the following steps: constructing an original one-dimensional photonic crystal omnidirectional mirror using medium A and medium B, wherein the dielectric constant of medium A is different from that of medium B; calculating the omnidirectional reflection coefficient of the original one-dimensional photonic crystal omnidirectional mirror using the transfer matrix method; determining the compression coefficient α; calculating the characteristic parameters of mediums A' and B' required to construct the one-dimensional transforming photonic crystal omnidirectional mirror based on the characteristic parameters of mediums A and B and the obtained compression coefficient α; determining the materials of mediums A' and B' based on the calculated characteristic parameters; and constructing the one-dimensional transforming photonic crystal omnidirectional mirror using mediums A' and B'.

[0065] The one-dimensional transforming photonic crystal omnidirectional mirror constructed in this invention can achieve the same omnidirectional reflection coefficient as the original one-dimensional photonic crystal omnidirectional mirror with a thinner thickness, providing a new method for the integration and miniaturization of electronic devices and providing important theoretical basis for the design and fabrication of novel omnidirectional mirrors.

[0066] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A method for constructing a one-dimensional transform photonic crystal omnidirectional reflecting mirror, characterized in that, Includes the following steps: Step 1: Construct a primitive one-dimensional photonic crystal omnidirectional mirror using medium A and medium B, wherein the dielectric constant of medium A is different from that of medium B; Step 2, determine the compression factor 'a'; Step 3: Based on the characteristic parameters of media A and media B and the compression coefficient 'a' obtained in Step 2, calculate the media required to construct the one-dimensional transform photonic crystal omnidirectional mirror. 'and medium ''s characteristic parameters; Step 4: Determine the medium based on the characteristic parameters calculated in Step 3. 'and medium 'Materials, utilizing media and medium Construct a one-dimensional transform photonic crystal omnidirectional reflecting mirror; In step 2, the compression coefficient 'a' is determined by calculation or by setting. If it is determined by calculation, the formula is: ， in, It is the thickness of the original one-dimensional photonic crystal omnidirectional mirror. It is the desired thickness for constructing a one-dimensional transforming photonic crystal omnidirectional mirror.

2. The construction method as described in claim 1, characterized in that, The specific content of step 1 is as follows: The original one-dimensional photonic crystal omnidirectional mirror is formed by the overlapping growth of medium A and medium B, and the arrangement structure is represented as (AB). N N represents the number of times medium A and medium B overlap.

3. The construction method as described in claim 2, characterized in that, The number of times N of the overlap between medium A and medium B 5.

4. The construction method as described in claim 1, characterized in that, The optical thickness of both medium A and medium B is 0.

25. ,in, The wavelength is the center operating wavelength of the original one-dimensional photonic crystal omnidirectional mirror.

5. The construction method as described in claim 1, characterized in that, The specific content of step 3 is as follows: Based on the principle of transformation optics, establish the correspondence between spatial coordinate transformation and changes in medium parameters, transforming the electromagnetic calculation problem into a spatial coordinate transformation problem, and defining the physical propagation space of electromagnetic waves. To virtual communication space The coordinate transformation formula is defined as follows: ， in, The compression factor is 1. It is a constant; The Jacobi transformation matrix is ​​expressed as: ， After transformation, the medium 'and medium The characteristic parameters of ' are expressed as: ， ， in, and medium respectively The permittivity and permeability of ' and medium respectively The dielectric constant and permeability, and medium respectively The dielectric constant and permeability, and medium respectively The dielectric constant and permeability of .

6. The construction method as described in claim 1, characterized in that, The specific content of step 4 is: using a medium 'and medium 'Overlapping growth to construct a one-dimensional transform photonic crystal omnidirectional mirror, the arrangement structure is represented as ( ') N N is the medium 'and medium The number of times they overlap.

7. The construction method as described in claim 6, characterized in that, The medium 'and medium Number of overlaps N 5.

Images