Monolithic mirror and method of designing the same

Abstract

The invention relates to a mirror comprising a plurality of one-dimensional photonic crystals, which mirror has a very high reflectivity over a very wide wavelength range of the incident photons, a wide directional range, even over a hemisphere, and in all polarizations. The invention also relates to a method for designing said mirror and to a photovoltaic cell comprising such a mirror.

Description

Technical Field

[0001] This invention relates to a mirror comprising multiple one-dimensional photonic crystals, which exhibits very high reflectivity over a very wide wavelength range, a wide directional range, even on a hemisphere, and in all polarizations of incident photons. The invention also relates to a method for designing and manufacturing said mirror, and a photovoltaic cell comprising such a mirror. Background Technology

[0002] A photonic crystal is a structure formed by the periodic, infinitely repeating of unit cells in space from one or more materials with variable refractive indices. Photonic crystals may contain band gaps or band barriers where no photons are present. Photons with energy within these band gaps incident on a photonic crystal cannot penetrate the crystal and are therefore totally internally reflected; that is, the reflectivity of the photonic crystal at these energies is equal to 1. An introduction to photonic crystals can be found in Joannopoulos, JD, Meade, RD: " Photonic Crystals: Molding the Flow of Light It can be found in Princeton University Press (2005).

[0003] In a one-dimensional (1D) photonic crystal, the refractive index change occurs only in one dimension (called z), and the unit cell is typically formed by two layers of dielectric with different refractive indices (commonly referred to as high (H) and low (L)). Although the energy position of a one-dimensional photonic crystal varies with the incident angle of the photon relative to the z-axis (… θ The reflectivity varies with the angle of incidence and its polarization, but they also have band gaps. In practice, photonic crystals have a finite number of unit cells, which reduces the reflectivity within the band gap to some extent, but the reflectivity value is usually still very close to one. In contrast, in three-dimensional (3D) photonic crystals (whose refractive index is formed in a periodic structure varying along three axes in space), the band gap (if present) is independent of the angle of incidence. However, few existing spatial structures can produce a suitable band gap, and they are hardly suitable for large-scale commercialization.

[0004] In a one-dimensional photonic crystal, a reference plane is formed that includes the z-axis and the direction in which the photon is incident on the crystal, i.e., according to the wave vector of the electromagnetic plane wave representing it. k This plane can be called yz Plane. Any plane wave is a transversely polarized (TE or s-polarized) plane wave (whose electric field vector is perpendicular to the plane). yz Plane waves (and transverse magnetic (TM or p-polarized) plane waves whose magnetic fields are perpendicular to the plane) and transverse magnetic (TM or p-polarized) plane waves (whose magnetic fields are perpendicular to the plane) yz A linear combination of planes. As mentioned earlier, the band gap position varies with the incident angle ( θThe polarization varies with TE or TM.

[0005] The energy range of these band gaps can be represented by the wavelength range of photons in a vacuum. λ 0 This indicates that the relationship between wavelength and energy is expressed by the well-known formula. λ 0 = hc / eE Given, among which, h Let be Planck's constant. c The speed of light in a vacuum. e denoted as electron charge (all in SI units). E Energy is expressed in electron volts. In this specification, the energy span of the band gap will be expressed in terms of wavelength in vacuum (electron volts). λ 0 This is represented by the wavelength of a photon in a vacuum. λ 0 The reflectivity of a photonic crystal varies. R The bandgap is approximated by a rectangle of unit height and width equal to the bandgap span. Although the rectangle's height is 1, it exhibits some rounding at the corners, which becomes more pronounced as the number of unit cells in the photonic crystal decreases. The base of the rectangle is called the total internal reflection band. The edges of the rectangle are called the leading edge and trailing edge (the trailing edge is the right-hand edge with a higher wavelength). Outside this rectangle, beyond the edges, wavy reflectance regions appear, where the reflectance is below 1 everywhere.

[0006] At vertical incidence ( θ At a tilt angle of 0, no difference in polarization between TE and TM was found because the z-axis is aligned with the direction of the photon, and any plane containing the z-axis can be considered either the TE or TM plane. For tilt angles of non-zero ( θ When incident at a wavelength of , the total internal reflection band undergoes a blue shift, i.e., a shift to a lower wavelength; and its width increases with TE polarization but decreases with TM polarization. A blue shift also occurs at the trailing edge for both TE and TM polarizations, but the shift is greatest for TM polarization. These modifications are stronger at larger angles, and for horizontal ( θ = π The leveling incidence is strongest at 2 rad.

[0007] Although the total internal reflection band in a one-dimensional photonic crystal shifts, a series of wavelengths still exhibit total internal reflection, identical to those obtained with vertical, TE, and TM horizontal incidence. This is the hemispherical (or omnidirectional) total internal reflection band, referred to herein as the "hemispheric total reflection band." Generally, the hemispherical total internal reflection band is relatively narrow; therefore, its leading edge is perpendicular to the direction of incidence (vertical incidence). θ = 0 The leading edge of the total internal reflection zone (TIR) ​​is horizontally TM polarized ( rad). The trailing edge of the hemispherical TIR zone is horizontally TM polarized ( rad). θ = π The trailing edge of the total internal reflection zone is at 2 rad. However, by slightly deforming the periodic structure of the photonic crystal (now becoming a pseudo crystal), the hemispherical total internal reflection zone can be slightly enlarged (Abdelaziz, KB, Zaghdoudi, J., Kanzari, M., Rezig, B.: " A broad omnidirectional reflection band obtained from deformed Fibonacci quasi-periodic one-dimensional Photonic Crystals ". Journal of Optics a-Pureand Applied Optics 7(10), 544-549 (2005). doi:10.1088 / 1464-4258 / 7 / 10 / 005).

[0008] In the absence of absorption (which is the case in this invention), the transmittance ( T ) is 1 minus reflectance ( T = 1- R Therefore, it is zero in the total reflection region and wave-like outside of it, which means that some photons are transmitted, but not all of them.

[0009] One-dimensional photonic crystals are hierarchical structures. Hierarchical structures have long been studied using the characteristic matrix method, with the classic work being that of Born and Wolf (Born, M., Wolf, E.: " Principles of Optics "Pergamon Press, Oxford (1975)." According to this method, each photonic crystal has a characteristic matrix in which two Chebyshev polynomials of the second kind appear. U N-1 (α) and U N-2 (α) ,in α The independent variable and N-1 SubsequentN-2 Let be the degree of the polynomial. N The number of unit cells in the photonic crystal. Independent variable. α TE|TM ( λ 0 ,θ,n a , n b ,h a ,h b ) is a vacuum wavelength that depends on the incident photon ( λ 0 ), angle of incidence ( θ ), high refractive index and low refractive index of cell material ( n a , n b ) and the layer thickness of the unit cell ( h a , h b A function of ). The independent variable ( α It also depends on the polarization of the incident photon, either TE or TM. For perpendicular incident ( θ =0), the independent variables of TE and TM ( α They are the same, physically indistinguishable (as mentioned above), and the independent variable ( α The subindex (TE|TM) can be ignored. It is important to note that the number of unit cells forming the photonic crystal is not included in the Chebyshev independent variables.

[0010] Multiple photonic crystals are occasionally mentioned in academic literature. Using multiple photonic crystals can widen the total internal reflection band. (Carniglia C K.: “) Perfect mirrors - from a coating designer's point of viewThe concept was expressed and several cell structures were proposed in *Laser-Induced Damage in Optical Materials: 68-84 1999, Proc. of SPIEVol. 3902 (2000)*. According to this disclosure, a stack of four photonic crystals with “wavepass” (LWP) filter cells results in a calculated total internal reflection band of approximately 0.382 μm to 0.721 μm, where efficiency was not calculated, but these cells are designed to have a reflectivity of at least 0.95, which would certainly be exceeded by this stack. The cells are designed to have a low (L) layer thickness equal to a quarter wavelength (also referred to as quarterwave in the aforementioned article) at the “center” value of the vacuum wavelength design for each photonic crystal. However, this construction provides a narrow total internal reflection band.

[0011] In Qiang, H., Jiang, L., Li, X.: “ Design of broad omnidirectional total reflectors based on one-dimensional dielectric and magnetic Photonic Crystals In Optics and Laser Technology 42(1), 105-109 (2010). doi:10.1016 / j.optlastec.2009.05.006, another example of using multiple photonic crystals is provided to extend the span of the hemispherical total internal reflection band. However, the process of achieving this extension is entirely theoretical and based on the deposition of magnetic material layers (and therefore, with different permeabilities than one), which has indeterminate properties, and the combined values ​​of its dielectric constant and permeability may not be achievable.

[0012] Patent application US2012125429A1 discloses a solar cell with different layers and a 3D photonic crystal attached to its back, designed to reflect unused light back into the cell body, thereby improving its efficiency. As previously mentioned, the 3D photonic crystal can exhibit a total internal reflection band that is essentially hemispherical (or omnidirectional). The width of the total internal reflection band—extending from visible light to near-infrared light—is sufficient to improve the efficiency of the solar cell, but much narrower than the span required for other applications (e.g., thermophotovoltaics, which require high reflectivity in the mid-infrared range).

[0013] Patent application US2013104983A1 describes a process for improving the efficiency of any solar cell by applying optimized light management. Various methods are used in this management, including the use of a single photonic crystal.

[0014] Document CN104076530A describes a process for improving the efficiency of solar cells by stacking layers doped with luminescent materials to emit strongly at a specific wavelength considered optimal. Furthermore, these layers can form a single photonic crystal.

[0015] US patent application US2011203663A1 discloses a solar cell with multiple optical structures designed to capture light into the cell and thus improve its efficiency. The solar cell includes an anti-reflective coating, a three-dimensional photonic crystal on the front side of the solar cell, a metal diffraction grating on the back side, and a one-dimensional photonic crystal located on and integrated therein of the grating.

[0016] In the last three documents mentioned above, they focused on the wavelength span of visible and near-infrared light (less than 2 μm), while this invention provides a hemispherical mirror that exhibits total internal reflection across a span that can include visible to mid-infrared light (more than 20 μm). Furthermore, the last three documents only involve single photonic crystals, which absolutely cannot produce the span achieved with the multiphotonic crystal mirror according to the present invention. This wide span is necessary for many applications, including energy storage in molten metal. Summary of the Invention

[0017] This invention provides a method for designing and / or manufacturing a reflector with the widest possible hemispherical total reflection band. The claimed method is more efficient and feasible than any other method proposed to date.

[0018] This invention defines a method for designing a reflector according to claims 1 and 2, a method for manufacturing a reflector according to claim 4, a reflector according to claim 11, a photovoltaic cell according to claim 12, and a thermal insulation according to claim 14. The dependent claims define preferred embodiments of the invention.

[0019] In a first aspect of the invention, the present invention defines an incident radiation design within a predefined vacuum wavelength range ([ λ A ,λ B A method using a mirror with maximum reflectivity, wherein the incident angle of the incident radiation is less than or equal to a predefined maximum incident angle. θ maxThe mirror comprises multiple one-dimensional photonic crystal forming layers, wherein each photonic crystal comprises multiple unit cells that are repeated identically a predetermined number of times, and each unit cell comprises a first dielectric material layer and a second dielectric material layer, the first and second dielectric materials having different refractive indices. The reflectivity of each photonic crystal varies according to the vacuum wavelength (λ0), as shown at the leading-edge wavelength value (λ0). ) and trailing edge wavelength ( The interval between ) , The shape of the rectangular pulses in the interval is defined as the total internal reflection zone of the photonic crystal. The leading-edge and trailing-edge wavelength values ​​depend on the incident angle of the incident radiation. θ ) and polarization, which is transverse electric (TE) or transverse magnetic (TM).

[0020] Therefore, the first dielectric material layer and the second dielectric material layer form the unit cell of the photonic crystal. The unit cell repeats... N i This forms 2. N i Photonic crystals of layered dielectric materials, i.e. N i First dielectric material and N i Second dielectric material. Subscript in cell number. i This reflects the fact that the photonic crystals that make up the mirror can have different numbers of unit cells.

[0021] When two unit cells are attached to each other, layers of the same dielectric material do not overlap. Instead, the arrangement of layers in a photonic crystal is always an alternation of the first and second dielectric materials, and even in the coupling of adjacent unit cells, the arrangement of layers is always a related distribution of two different materials.

[0022] In the context of this invention, transverse magnetic polarization (TM) is a polarization in which the magnetic field of the electromagnetic wave of a photon is perpendicular to the plane formed by the direction of the incident photon and the normals of the layers of the photonic crystal.

[0023] It should be understood that the terms "first dielectric material" and "second dielectric material" are used only to distinguish the two materials within the unit cell of a photonic crystal. However, this designation is not intended to imply a specific order of these two dielectric materials within the unit cell of a photonic crystal. Therefore, when a dielectric material layer is deposited on a substrate, either the first or second dielectric material can be deposited first on the substrate. In this document, dielectric materials are also referred to as high-refractive-index materials and low-refractive-index materials, where a high-refractive-index material is a dielectric material with a higher refractive index compared to the other dielectric material within the unit cell of the photonic crystal. Each refractive index is given by the material and is therefore a value of a predefined parameter corresponding to the value of the material of the unit layer of the photonic crystal previously selected for the design of a multilayer mirror using the method of the first aspect of the invention. Furthermore, different material pairs can be used for different photonic crystals in multiple photonic crystals within a mirror, and subscripts are used. i To distinguish them.

[0024] According to the method of the first aspect of the invention, in the first embodiment, for i = 1、......m,The method includes the following steps:

[0025] (a) Settings θ = 0 of i The leading edge wavelength of the total internal reflection band of a photonic crystal ( ), and select a first dielectric material and a second dielectric material to form the first i The unit cell of a photonic crystal;

[0026] (b) Determine the first i The first thickness of the first dielectric material layer of the photonic crystal ( ) and the i The second thickness of the second dielectric material layer of the photonic crystal ( ), as detailed below:

[0027]

[0028] in, and They are respectively the first i The refractive indices of the first and second dielectric materials chosen for the photonic crystal; and

[0029] (c) Using the first thickness calculated in step (b) ) and second thickness ( The value of ) determines the first i Trailing edge wavelength of the total internal reflection zone of a photonic crystal ( ), as detailed below:

[0030]

[0031] Among them, parameters X By using a predefined maximum angle of incidence ( Equations for transverse magnetic (TM) polarization Solve X The resulting equation is solved using an iterative method, with an initial value of X = 1.

[0032] in,

[0033]

[0034] In step (a), the leading edge wavelength value ( Set to:

[0035] - For i = 1, equal to The value; and

[0036] - For i >1, equals And the first polarization of TM i -1 Trailing edge wavelength of the total internal reflection zone of a photonic crystal ( The value of );

[0037] in, m To meet And the first polarization of TM m Trailing edge wavelength of the total internal reflection zone of a photonic crystal ( ) equal to or greater than The number of photonic crystals.

[0038] According to the method of the first aspect of the invention, in the second embodiment, for i = 1、...... m The method includes the following steps:

[0039] (a) Settings And the first polarization of TM i Trailing edge wavelength of the total internal reflection zone of a photonic crystal ( ), and select a first dielectric material and a second dielectric material to form the first i The unit cell of a photonic crystal;

[0040] (b) Determine the first i The first thickness of the first dielectric material layer of the photonic crystal ( ) and the i The second thickness of the second dielectric material layer of the photonic crystal ( ), as detailed below:

[0041]

[0042] in, and They are respectively the first i The refractive indices of the first and second dielectric materials chosen for the photonic crystal are, where...

[0043]

[0044] and

[0045] (c) Using the first thickness calculated in step (b) ) and second thickness ( The value of ) determines the first i The leading edge wavelength of the total internal reflection band of a photonic crystal ( ), as detailed below:

[0046]

[0047] Among them, parameters X Through the equation Solve X The obtained equation is solved using an iterative method, and its initial value is... X =3,

[0048] in,

[0049]

[0050]

[0051] In step (a), the trailing edge wavelength value ( Set to:

[0052] - For i = 1, equal to The value; and

[0053] - For i >1, equals The i -1 The leading edge wavelength of the total internal reflection zone of a photonic crystal ( The value of );

[0054] Where m is satisfied The m The leading edge wavelength of the total internal reflection band of a photonic crystal ( ) equal to or less than The number of photonic crystals.

[0055] Therefore, the method according to the first embodiment of the first aspect of the invention includes obtaining the trailing edge wavelength value from the photonic crystal by setting the leading edge wavelength value, calculating the layer thickness, and obtaining the trailing edge wavelength value. arrive Designing a photonic crystal, and, according to a second embodiment of the first aspect of the invention, the method includes setting the trailing edge wavelength value of the photonic crystal, calculating the layer thickness, and obtaining the leading edge wavelength value to obtain... arrive Design photonic crystals.

[0056] The following symbols will be used throughout this article:

[0057] - α TM The independent variable representing the second kind of Chebyshev polynomial of the characteristic matrix of a photonic crystal is referred to as the "Chebyshev independent variable" in this paper;

[0058] - Indicates from The initial series of calculations yielded the leading-edge wavelength values ​​of the total internal reflection band of the j-th photonic crystal;

[0059] - Indicates from The initial series of calculations yielded the trailing edge wavelength values ​​of the total internal reflection zone of the j-th photonic crystal;

[0060] - and They represent from The initial series of calculations determine the thickness of the first and second material layers of the j-th photonic crystal cell;

[0061] - and They represent from The refractive indices of the first and second materials of the unit cell of the j-th photonic crystal are calculated to begin;

[0062] - Indicates from The initial series of calculations yielded the leading-edge wavelength values ​​of the total internal reflection band of the j-th photonic crystal;

[0063] - Indicates from The initial series of calculations yielded the trailing edge wavelength values ​​of the total internal reflection zone of the j-th photonic crystal;

[0064] - and They represent from The initial series of calculations determine the thickness of the first and second material layers of the j-th photonic crystal cell;

[0065] - and They represent from The refractive indices of the first and second materials of the unit cell of the j-th photonic crystal are calculated.

[0066] According to the first embodiment, the leading edge of the total internal reflection zone of the vertically incident first photonic crystal ( ) is set to be equal to the predefined vacuum wavelength range ( The lower limit of ) The value of the vacuum wavelength. This predefined vacuum wavelength range will be understood as the band of total internal reflection required for the specific application or intended use of the reflector. Similarly, the predefined maximum angle of incidence ( This will be understood as the highest angle of total internal reflection of the incident photon required for the specific application or intended use of the reflector. If Then the reflecting mirror is from arrive The entire band will exhibit hemispheric total reflection or omnidirectional total reflection.

[0067] The first thickness of the first dielectric material layer of the first photonic crystal ( ) and the second thickness of the second dielectric material layer ( This is determined by applying the following expression:

[0068]

[0069] in, and It is the refractive index of the first and second dielectric materials selected to form the unit cell of the first photonic crystal.

[0070] Once the first thickness of the first dielectric layer is calculated ( ) and the second thickness of the second dielectric material layer ( The trailing edge wavelength of the total internal reflection zone of the first photonic crystal can then be determined using the following expression. ):

[0071]

[0072] Among them, parameters X By using a predefined maximum angle of incidence ( Equations for transverse magnetic (TM) polarization Solve X The obtained equation is solved using an iterative method, and its initial value is... X = 1, and where:

[0073]

[0074] For TE-polarized incident radiation, using TE polarization instead of TM polarization in the equation will produce a wider total internal reflection band for photons, but it is ineffective for TM photons, and therefore ineffective for unpolarized radiation containing equal amounts of TE and TM photons.

[0075] As a result of the above steps, the layer thickness of the first photonic crystal and the trailing edge wavelength of the total reflection zone were determined.

[0076] The calculated trailing edge wavelength value of the first photonic crystal is used to design subsequent photonic crystals. For this purpose, the first and second dielectric materials for forming the unit cell of the second photonic crystal are selected, and the leading edge wavelength value of the total internal reflection band for the vertically incident second photonic crystal is determined. Set to equal to the calculated And the trailing edge wavelength of the total internal reflection band of the first photonic crystal with TM polarization ( As a result of the aforementioned setting of the leading-edge wavelength value (or the trailing-edge wavelength value in another embodiment), the first and second photonic crystals are adapted to form a wider total internal reflection band.

[0077] Using the set leading edge wavelength value ( Using parameters corresponding to the second photonic crystal, the first thickness of the first dielectric material layer is determined as described for the first photonic crystal. ) and the second thickness of the second dielectric material layer ( ).

[0078] Using the first thickness calculated in the previous step ( ) and second thickness ( The trailing edge wavelength of the total internal reflection band of the second photonic crystal is determined using the parameters corresponding to the second photonic crystal as described in conjunction with the first photonic crystal. ).

[0079] As a result of these steps, the thickness of the unit cell layer of the second photonic crystal and the trailing edge wavelength of the total reflection band were determined.

[0080] Repeat this process to design all photonic crystals that will become part of the mirror, up to the [number missing]. m Photonic crystals satisfy And the trailing edge wavelength of the total internal reflection zone of TM polarization ( ) equal to or greater than In this iteration, the total internal reflection bands of multiple photonic crystals span the entire width of a predefined vacuum wavelength range, i.e., the range requiring total internal reflection (…). ).

[0081] For the method according to the second implementation scheme, an iterative process similar to the disclosed iterative process is performed, the difference being that... And the trailing edge wavelength value of the total internal reflection zone of each photonic crystal with TM polarization ( Instead of the leading edge wavelength value, and based on the calculated first thickness ( ) and second thickness ( The leading edge wavelength value was obtained. ), of which the first thickness ( ) and second thickness ( The value of ) is obtained using the following expression:

[0082]

[0083] Furthermore, the first i The leading edge wavelength of the total internal reflection band of a photonic crystal ( The calculation is as follows:

[0084]

[0085] Among them, parameters X Through the Equation (i.e., perpendicular incidence) Solve X The obtained equation is solved using an iterative method, and its initial value is... X =3, where:

[0086]

[0087] According to the second implementation scheme, this process is repeated to design all photonic crystals that will become part of the reflector, until the... m Photonic crystals satisfy The first m The leading edge wavelength of the total internal reflection band of a photonic crystal ( ) equal to or less than .

[0088] Chebyshev's independent variables do not include the number of unit cells in the photonic crystal. Theoretically, true total internal reflection can be obtained using an infinite number of layers, but in a multiphotonic crystal mirror, 7 unit cells can give a total internal reflection reflectivity of about 0.9999, and for 10 unit cells, the reflectivity can even reach 0.999999.

[0089] The material within the unit cell of a photonic crystal can vary depending on the specific photonic crystal. For example, a photonic crystal… i The first dielectric material can be compared with photonic crystals. j The first material may be the same or different. In addition, the number of unit cells may be different for different photonic crystals.

[0090] Advantageously, this invention allows for the design and production of mirrors based on the deposition of multiple dielectric layers, which exhibit a reflectivity of nearly 1 for a very wide range of electromagnetic radiation extending from the visible to the mid-infrared (over 20 μm). Furthermore, the designed mirror exhibits this 1 reflectivity for hemispherical radiation incident and both polarizations. For this purpose, the dielectric layers are divided into several monolithic deposits on the same substrate and designed using the method of this invention. The method of this invention allows for the production of the widest hemispherical total internal reflection band. Moreover, it is more efficient and feasible than any other method proposed to date.

[0091] Today, mirrors with a single photonic crystal deposited on a substrate are frequently used in optics and communications. These mirrors are required to have very high reflectivity in a single wavelength, a single direction, and polarization (i.e., in a single radiation mode or a close mode).

[0092] The background section describes a second-kind Chebyshev polynomial containing several different degrees and the same independent variable α in the characteristic matrix of a photonic crystal. This section discloses how the independent variable α of the second-kind Chebyshev polynomial... Outside the interval, total internal reflection bands will occur. More specifically, the Chebyshev independent variable α for... (Photon energy 0 eV) has a general asymptote of +1. When As the value decreases, the Chebyshev independent variable decreases until it reaches its value. α = -1, therefore exiting the interval; reaching the trailing edge of the total internal reflection zone. If If the value is further reduced, the Chebyshev independent variable will reach its minimum value, and then... A certain value reaches the value again. α = -1, therefore re-enter The interval leads to the leading edge of the total reflection zone. This allows for the calculation of the positions of the total reflection zone and its leading and trailing edges. If If we reduce it further, the Chebyshev independent variable will describe part of the... The waveform curves outside the range, and the additional total reflection band (photonic bandgap), are not of interest to this invention.

[0093] The positions of the leading and trailing edges of the total internal reflection zone of any photonic crystal can be determined by solving the equations. To calculate (if) (Assuming polarization is known). This invention is based on the variation of variables, which allows Chebyshev independent variables to be written in such a way that, by choosing the leading or trailing edge of the total internal reflection band of the photonic crystal, for The predefined value is used to determine the first thickness of the photonic crystal cell through analysis. ) and second thickness ( ).

[0094] Furthermore, when using the determined first thickness of the photonic crystal cell ( ) and second thickness ( Solve the equation When the wavelength is such that the highest root is the trailing edge wavelength of the total reflection zone, and the second highest root is the leading edge wavelength.

[0095] The above applies to any incident angle and polarization, and the total internal reflection band has different positions and widths. Consider a single photonic crystal; among the different positions and widths of the total internal reflection band of this photonic crystal, the leading edge located at the lowest wavelength ( This corresponds to perpendicular incidence. The trailing edge located at the highest wavelength ( ) corresponds to the selected angular span (preferably horizontal incidence, i.e., θ max = π TM polarization and maximum angle ( / 2 rad) The span of any incident total internal reflection zone is from... arrive .for θ max = π / 2 rad, this total reflection zone can be called the hemispherical total reflection zone or the omnidirectional total reflection zone. For radiation from the outside (from air), it always satisfies < Furthermore, a hemispherical total reflection zone exists.

[0096] When several photonic crystals are deposited on the same substrate (they are monolithic), the reflectivity curves will change compared to those of individual photonic crystals, but the positions of the total internal reflection bands are determined by their Chebyshev independent variables, as described in this specification. In fact, changes in reflectivity affect the Chebyshev independent variables in... α = within the ±1 interval This allows for the placement of different total reflection zones in desired locations by appropriately selecting the materials of the layers forming the unit cell of each photonic crystal and by calculating their thicknesses.

[0097] A very wide hemispherical total reflection band can be formed by monolithically depositing several photonic crystals on a single substrate.

[0098] When a photon, represented by a plane wave, travels through a dielectric layer, it... j , k The angles within the same layer follow Snell's law, therefore... ...(in, n The refractive index of the layer, θ (The angle within the layer). The wavelength within the layer is... ,and, h / ( h (where the thickness of the layer is the fraction of the internal wavelength). It should be noted that the wavelengths within the layer differ from those in a vacuum. This is achieved by selecting a ratio... Make the relationship satisfy The span of the total internal reflection band of a certain photonic crystal is maximized (subscripts of high refractive index layer and low refractive index layer). a and b (or vice versa). In other words, the maximum span occurs when the thicknesses of the high-refractive-index and low-refractive-index layers are equal to the fractions of their internal wavelengths. This relationship defines the relationship between the thicknesses of the high-refractive-index and low-refractive-index layers. Since this condition can only be satisfied at a single incident angle, the number of photonic crystals producing a given hemispherical total internal reflection span in a monolithic array is minimized when the condition is satisfied for a TM-polarized horizontal ray (which maximizes the possibility of achieving a small TM span for a single photonic crystal for horizontal incidence).

[0099] In one implementation, selected to form the first i The first and second dielectric materials of the unit cell of a photonic crystal include and Radiation within a certain wavelength range is transparent. This is because the leading-edge wavelength value of the total internal reflection zone of each photonic crystal is set according to the method of the first aspect of the invention (…). ) or trailing edge wavelength value ( Therefore, a first dielectric material and a second dielectric material can be selected for the photonic crystal such that they are transparent to radiation having wavelengths in the range including the set wavelength value.

[0100] In one implementation scheme .

[0101] In one implementation scheme This includes the visible light range (400-700 nm) or the near-infrared light range (700-2500 nm).

[0102] In one implementation scheme Includes the infrared range, preferably the mid-infrared range (2.5-50 μm).

[0103] In a preferred embodiment, Including the visible or near-infrared light range and / or Included in the mid-infrared light range.

[0104] In one embodiment, the first dielectric material and / or the second dielectric material of at least one photonic crystal are selected from MgF2, CaF2, ZnS, TiO2, Si, and Ge. Preferably, one of the first dielectric material and the second dielectric material of at least one photonic crystal is selected from MgF2 and CaF2, and the other of the first dielectric material and the second dielectric material of the photonic crystal is selected from ZnS, TiO2, Si, and Ge.

[0105] In a second aspect of the invention, the present invention defines a method for manufacturing comprising m A method for using a one-dimensional photonic crystal mirror, wherein... m >1. The method includes the following steps:

[0106] Design a reflector according to a method of any embodiment of the first aspect of the invention; and

[0107] form m A stack of one-dimensional photonic crystals;

[0108] Among them, each of the first i Photonic crystals are formed by stacking multiple alternating layers of a first dielectric material and a second dielectric material, wherein the first dielectric material has a different refractive index than the second dielectric material. , The refractive index of ) , ),and

[0109] Among them, for each of the first i Photonic crystal, the first thickness of each first dielectric material layer ( , ) and the second thickness of each second dielectric material layer ( , The value determined in step (b) of the method having any embodiment of the first aspect of the invention, wherein, i = 1、...... m .

[0110] This type of mirror, which comprises multiple stacked photonic crystals, is referred to in this specification as a monolithic mirror with multiple photonic crystals.

[0111] In one embodiment, a photonic crystal layer is deposited on an opaque or transparent substrate. In the case of an opaque substrate, it can have high reflectivity. One photonic crystal layer is deposited first on the substrate, and subsequent photonic crystals are deposited on top of the previously deposited photonic crystal.

[0112] In one embodiment, the outermost layer of the mirror is covered with a transparent layer or a reflective metal (if the substrate is transparent), preferably silver or gold. The outermost layer of the mirror should be understood as the layer furthest from the substrate. Advantageously, covering the outermost layer with a reflective metal results in a wider range of predefined vacuum wavelengths (…). The reflectivity increases significantly at incident radiation wavelengths outside the total reflection band of the mirror (i.e., outside the total reflection band of the mirror), while the reflectivity remains unchanged for incident radiation wavelengths within a predefined vacuum wavelength range. This can be practically significant in certain applications. Alternatively, a monolithic mirror of multiple photonic crystals can be deposited on a substrate covered with a reflective metallic coating (preferably silver or gold) having the same effect and with or without a protective thick transparent layer disposed on the outermost layer. In use, when the mirror includes a reflective metallic coating, the mirror is preferably arranged such that the layer facing the incident radiation is the layer furthest from the reflective metallic coating.

[0113] To maximize the reflectivity of a mirror within a predefined vacuum wavelength range, multiple one-dimensional photonic crystals with total reflection bands spanning the desired range are stacked to form the mirror.

[0114] In one implementation, photonic crystals are configured according to the lower limit of their range from a predefined vacuum wavelength range (…). ) to the upper limit of the predefined vacuum wavelength range ( The total internal reflection zones are arranged in a specific order within the reflector. According to this embodiment, when using reflectors, the total internal reflection zones are positioned closer to the upper limit ( ) in the direction of incident radiation. The photonic crystal is positioned closer to the lower limit of the total internal reflection band. Downstream of the photonic crystal. In other words, radiation first reaches its total internal reflection zone closer to the lower limit ( ). The photonic crystal then reaches the total internal reflection band closer to the upper limit ( ) ( ) photonic crystals. This applies to both from arrive The implementation scheme for designing photonic crystals (i.e., setting the leading-edge wavelength value) is also applicable to... arrive Design an implementation scheme for a photonic crystal (i.e., set the trailing edge wavelength value).

[0115] In another implementation, the photonic crystal operates at a lower limit different from that defined by its range from a predefined vacuum wavelength range (…). ) to the upper limit of the predefined vacuum wavelength range ( The total internal reflection zones are arranged in a specific order within the reflectors, defined by their positions. In this embodiment, the conditions...

[0116] , , ,... ,

[0117] The conditions are still met. However, when photonic crystals are deposited to form mirrors, they are deposited in a different order.

[0118] In one embodiment, photonic crystals are arranged in a reflector in an order defined by the transparency of a first dielectric material and a second dielectric material of the photonic crystal, such that a photonic crystal made of a material opaque to radiation within a wavelength range included in the total internal reflection band of another photonic crystal is located downstream of the other photonic crystal in the direction intended for incident radiation. In other words, the photonic crystals are arranged such that the material of the photonic crystal intended to receive incident radiation first is transparent to radiation within a wavelength range included in the total internal reflection band of the photonic crystal subsequently arranged to receive incident radiation.

[0119] In one embodiment, the number of unit cells in each photonic crystal is greater than or equal to 5, preferably greater than or equal to 7, and more preferably greater than or equal to 10.

[0120] In a third aspect of the invention, the present invention defines a reflector comprising: m A one-dimensional photonic crystal, wherein... m >1,

[0121] Each photonic crystal comprises multiple stacked alternating layers of a first dielectric material and a second dielectric material, wherein the first dielectric material has a refractive index that is different from that of the second dielectric material. , Different refractive indices , ),in, i = 1、......m,and

[0122] Among them, for each of the first i Photonic crystal, the first thickness of each first dielectric material layer ( , ) and the second thickness of each second dielectric material layer ( , ) is the value determined in step (b) of the method in any embodiment of the first invention, wherein, i =1、......m.

[0123] This reflector according to the third aspect of the invention corresponds to a reflector obtainable by the method of the first aspect of the invention. Considering that electron microscopy and photography allow for the differentiation of alternating layers of the first and second dielectric materials of each photonic crystal, as well as their thickness and chemical composition, when a portion of the reflector is installed, the reflector is identifiable.

[0124] The values, together with the total reflection region and the region in which there is no total reflection of the manufactured mirror, allow for the differentiation of the construction of a mirror corresponding to the performance of the method according to the first aspect of the invention. Thus, such a finished mirror can be characterized by its parameters as a mirror designed by the method described above.

[0125] In one embodiment, the reflector according to the third aspect of the invention is manufactured using the method according to the second aspect of the invention.

[0126] The present invention further defines a photovoltaic cell comprising a reflector according to a third aspect of the invention deposited on a transparent substrate and coated with a metal layer, the photovoltaic cell being a photovoltaic cell or a thermo-photovoltaic cell.

[0127] The present invention further defines a photovoltaic cell comprising a reflector according to a third aspect of the invention and a semiconductor substrate, the reflector being disposed on the back side of the semiconductor substrate and coated with a metal layer, the photovoltaic cell being either a photovoltaic cell or a thermophotovoltaic cell. For photons with energies below the semiconductor electronic bandgap, the semiconductor substrate is transparent.

[0128] The present invention also defines a thermal insulator for an incandescent body, wherein the thermal insulator includes at least one mirror according to a third aspect of the invention. Advantageously, the thermal insulator effectively reflects received photons back. In one embodiment, the thermal insulator includes at least one photovoltaic cell, at least one thermophotovoltaic cell, at least one radiant power collection device, and / or at least one cooling device.

[0129] All features and / or steps of the methods described in this specification (including the claims, description, and drawings) may be combined in any combination, except for combinations of mutually exclusive features and / or steps.

[0130] Brief description of the attached figures

[0131] These and other features and advantages of the invention will become clear from the accompanying drawings and in conjunction with the detailed description of the invention, which will become apparent from the preferred embodiments thereof, wherein the preferred embodiments are given by way of example only and are not limited thereto.

[0132] Figure 1 A schematic diagram of a monolithic mirror made of a multiphoton crystal according to one embodiment of the present invention is shown.

[0133] Figure 2The diagram shows the variation of the reflectivity of the photonic crystal with respect to the vacuum wavelength (in meters) for incident photons at normal incidence (solid line), π / 4 rad incidence with TE polarization (dashed line), and π / 4 rad incidence with TM polarization (dotted line). Furthermore, the absolute values ​​of the Chebyshev independent variables for normal incidence (solid line), π / 4 rad incidence with TE polarization (dashed line), and π / 4 rad incidence with TM polarization (dotted line) are shown.

[0134] Figure 3 It shows that for Y =0、 Z =3 (thick solid line) Z =2 (thick dashed line) Z =0.35 (thin solid line) and Z =0.55 (thin dashed line), α and X The relationship.

[0135] Figure 4 It shows that for Z = 3、 Y = 0 (solid line) Y =0.5X (dashed line) and X =-0.45 Y (Pointed line), α and X The relationship.

[0136] Figure 5 The reflectivity curves (upper part of the figure) and Chebyshev independent variables (mainly lower part of the figure) are shown, varying with the vacuum wavelength (in meters) of the two photonic crystals and incident photons at different incident angles.

[0137] Figure 6 It shows Figure 5 The first photonic crystal in China α and X The relationship. Solid lines represent perpendicular incidence (…). Y = 0); dashed lines indicate Y ≠0. The leading and trailing edges of the total internal reflection zone of the hemisphere are marked in the diagram. X value.

[0138] Figure 7 The reflectivity curves of a monolithic mirror made of multiple photonic crystals are shown to vary with vacuum wavelength (in meters) at different incident angles.

[0139] Figure 8 The spectral power of a blackbody at 1410 °C is shown in W / cm². 2 The relationship between wavelength (in meters) and vacuum wavelength (in meters). Detailed Implementation

[0140] Figure 1A schematic diagram of a monolithic mirror comprising a plurality of one-dimensional photonic crystals (1, 2, 3) according to an embodiment of the present invention is shown, wherein all photonic crystals are deposited on a single substrate (not shown). In this figure, a first photonic crystal (1), a second photonic crystal (2), and a third photonic crystal (3) are shown, but the blank area in the middle of the figure implies that more photonic crystals may exist in the mirror. Each photonic crystal comprises multiple unit cells (U1, U2, U3), and each unit cell (U1, U2, U3) comprises two dielectric layers (1.1, 1.2; 2.1, 2.2; 3.1, 3.2) with different thicknesses and having higher and lower refractive indices, repeated multiple times. Figure 1 The diagram shows only a portion of the unit cells. The photonic crystals included in the mirror can have different properties; that is, the dielectric forming each unit cell of the photonic crystal can be different in each photonic crystal, thus having different refractive indices, and can have different thicknesses, the thickness of which is defined by the method according to the invention. The mirror thus formed has high reflectivity over a wide wavelength range, over a wide range of directions (even hemispherical), and in different polarizations of the incident photons.

[0141] Figure 2 The reflectivity of a one-dimensional photonic crystal is shown. R According to the vacuum wavelength ( The reflectivity (R) varies (in meters). Reflectivity (R) is plotted for perpendicular incident (solid line), π / 4 rad incident with TE polarization (dashed line), and π / 4 rad incident with TM polarization (dotted line). The graph shows that for perpendicularly incident photons, the total internal reflection band of the photonic crystal extends between points 7 and 8; for π / 4 incident TE photons, it extends between points 9 and 10; and for π / 4 incident TM photons, it extends between points 11 and 12. Figure 2 It is understandable how the total internal reflection zone shifts with different incident angles and polarization.

[0142] When the independent variable of the second-type Chebyshev polynomial of the characteristic matrix of the photonic crystal... α Exceeding -1< α When the value is less than +1, a band gap or band barrier will appear in the photonic crystal. Figure 2 The absolute values ​​of the Chebyshev independent variables of the photonic crystal are shown for perpendicular incidence (solid line, denoted as "17" in the figure), π / 4 rad incidence with TE polarization (dashed line, denoted as "18" in the figure), and π / 4 rad incidence with TM polarization (dotted line, denoted as "19" in the figure).

[0143] It can be seen that a total internal reflection band appears when the absolute value of the Chebyshev independent variable exceeds 1. The edge of the total internal reflection band is the x-coordinate of the end of the segment extending from point 7 to point 8 for perpendicular incidence, the x-coordinate of the end of the segment extending from point 9 to point 10 for π / 4 rad incidence with TE polarization, and the x-coordinate of the end of the segment extending from point 11 to point 12 for π / 4 rad incidence with TM polarization. According to the present invention, the wavelength corresponding to the edge of the total internal reflection band is calculated by analyzing the Chebyshev independent variable (which can be fully analytical). This is faster and simpler than calculating the reflectance curve.

[0144] from Figure 2 As can be clearly seen in the figure, for a given one-dimensional photonic crystal, the position and width of the total internal reflection band vary with the incident angle of the photon and its polarization. It can also be observed from the figure that total internal reflection occurs for any incident angle up to π / 4 rad and for any polarization in the band extending from point 7 to point 12. The same result occurs for the maximum incident angle π / 2 rad (horizontal incidence), but in this case, the hemispherical total internal reflection band is narrower. Beyond the total internal reflection band represented by the above segment, the reflectivity curve exhibits wavy behavior, as described in this specification.

[0145] Figure 2 The photonic crystal represented in the image contains 30 unit cells, formed by a pair of zinc sulfide dielectric layers with a refractive index of 2.3 and a thickness of 98 nanometers (nm) and a magnesium fluoride dielectric layer with a refractive index of 1.35 and a thickness of 261 nm. All layers are deposited on a glass substrate with a refractive index of 1.52. This substrate material does not affect the band gap, but it does affect the reflection generated outside the band gap. A slight rounding occurs at the corner of the total internal reflection band. This is due to the finite number of layers in the photonic crystal (60 in this case). If the number of layers is reduced, this rounding will increase.

[0146] This method is based on the study of Chebyshev's independent variables. For a given incident angle of radiation ( θ ),when At that time, the reflectivity is wavy and less than 1; and, when At a given incident angle, the reflectivity is 1 (total internal reflection). At this time, the edge of the total internal reflection zone appears. For the maximum incident angle ( )(include The leading edge corresponds to hemispheric radiation, the trailing edge corresponds to vertical radiation, and the trailing edge corresponds to TM polarization. Incident (horizontal incident for hemispherical radiation).

[0147] The present invention proposes the use of multiple photonic crystals that add their respective total reflection bands to a specified angular span (possibly hemispherical) until the desired wavelength span is covered.

[0148] This invention is based on the variation of variables, which allows Chebyshev independent variables to be written in such a way that the first thickness of the photonic crystal cell can be analytically determined by selecting the leading or trailing edge of the total internal reflection zone of the photonic crystal. ) and second thickness ( The other edge of the total internal reflection band inherent in each one-dimensional photonic crystal is obtained based on the calculated thickness.

[0149] Advantageously, the method of the present invention provides a highly efficient reflector with a calculated efficiency of up to 0.999999 and a wide total reflection band, for example, from 1.77 μm to 20 μm.

[0150] Conversely, the construction of multilayer filters for monochromatic mirrors (as cited in the background section of Carniglia's references) neither allows for total internal reflection bands of tens of micrometers (and thus wavelengths from visible to mid-infrared) nor provides the leading and trailing edges of a photonic crystal.

[0151] Although hemispherical or omnidirectional reflectivity is referenced here, the invention can also be applied at the maximum incident angle. The case where total internal reflection is guaranteed.

[0152] Therefore, the expression for Chebyshev's independent variable... After some mathematical processing, the expression from the cited book by Born and Wolf can be written as:

[0153]

[0154]

[0155] Following Snell's Law, , ,in, θ Let be the angle of incidence in the air relative to the z-axis. , For thickness , The angle (or plane wave vector) of the photons within the layer.

[0156] By making the following changes to the variables:

[0157]

[0158]

[0159] It can be written as:

[0160]

[0161] This change in the variable provides a deeper understanding of the properties of Chebyshev's independent variable. Please note that... The function varies with different incident angles of radiation. Figure 3 and Figure 4 The middle section provides two... and X A graph showing the relationship.

[0162] Figure 3 The curve in the middle corresponds to Y The case where =0. When this happens. Regarding variables X It is periodic, with a period of 4. In Figure 3 middle, Z The case where =3 is drawn with a thick solid line, while for... Z The case of 0.35 (approximately the reciprocal of 3) is drawn with a thin solid line. This is for emphasis. Z The value of and its reciprocal give the same curve. Z =2 and Z When the value is 0.55 (approximately 1 / 2), it is drawn with both thick and thin dotted lines. When... α Below the -1 gray line, a total internal reflection band appears. If Z > 1, the larger Z is, the wider the band. If Z < 1, the larger 1 / Z is, the wider the band. Y When the wavelength fraction is 0, the wavelength fractions in the high-refractive-index layer and the low-refractive-index layer are equal.

[0163] Figure 4 It shows Z =3 and three Y The value of the case. Y =0 (thick solid line) is repeated. Figure 3 One of the curves shown. This case represents the largest span of the total internal reflection zone. For the other cases shown in the figure, i.e., for... Y = 0.5 (dashed line) and Y = -0.45 (dotted line), the curves are almost identical. This is for emphasis. Y The opposite value gives the same α .when Y ≠0 o'clock, α It is no longer periodic. Here, the wavelength fractions differ in the high-refractive-index layer and the low-refractive-index layer.

[0164] Many of the figures in this article are represented as The function. X and Y and They are inversely proportional, but their ratio is... It is irrelevant to it, because it is also Z The ratio is:

[0165]

[0166] In addition, what happened closest The first photonic bandgap is one of the most studied bandgapes. This band is generated at that time (e.g.) Figure 3 As shown), therefore, the two first roots containing the first photonic bandgap (corresponding to the trailing and leading edges of the first total reflection band, respectively) are roots of interest.

[0167] Among the properties that can be extracted from the current analysis, the first photonic bandgap was found to be... Y The value is maximized when the wavelength fraction is 0 (i.e., when the wavelength fractions within the high-refractive-index and low-refractive-index materials are the same). This condition is satisfied by the traditional use of quarter-wavelengths in monochromatic optics. It was also found that when the ratio... or The larger the value, the larger the band gap.

[0168] for Y =0, equation (3) becomes a periodic function dominated by cos(πX / 2) (period) X (4) The solution is analytical. Therefore, if a certain trailing edge wavelength is selected... We can obtain the following expression:

[0169]

[0170] The subscript for Z has been removed to indicate that the equation is valid for both polarizations. If a leading edge is chosen, the equation becomes as follows:

[0171]

[0172] The arccos function has infinitely many solutions. .untie Corresponding to the trailing edge of the total reflection zone, the solution Corresponding to the leading edge of the total reflection zone.

[0173] Once the thickness of the unit cell is determined, the photonic crystal can be completely and uniquely defined by setting the trailing or leading edge wavelength, with the number of unit cells forming the crystal by default. N (As mentioned above) It is not included in the Chebyshev independent variables. The more unit cells there are, the more square the total internal reflection band of the photonic crystal becomes.

[0174] According to the method of the present invention, an unknown band edge opposite to the band edge set at the beginning of the method is obtained. For this purpose, equation (1) is used, and the result of numerical iteration is obtained where α+1=0. There are several roots, therefore, the initial iteration begins... The settings will determine which root is found.

[0175] Therefore, the normalized equation (3) is used to solve the equation through numerical iteration. Solve X The trailing edge is obtained starting from initial value 1, and the leading edge is found starting from initial value 3. The indices have been removed as they are unnecessary. These initial values ​​are derived from... Figure 3 It was discovered during the inspection. Once... X Extracted, equation (2) can then be written as:

[0176]

[0177] about and (Also exists) (In the middle), for the leading edge, they can be 0, and their values ​​can be derived from the incident angle in vacuum (or air). It begins with the relationship derived from Snell's law, which states that for hemispheric illumination, it is π / 2: , .

[0178] Regarding refractive index and Their values ​​are defined by the materials used and, to a lesser extent, by the method of material preparation. In one embodiment, the materials used for the layers of the unit cell are light-transparent insulators. For low-refractive-index layers, MgF2 or CaF2 with refractive indices of 1.37397 and 1.4328, and electronic band gaps of 12.2 eV and 10 eV, are preferred. For high-refractive-index layers, ZnS, CdS, and TiO2 with refractive indices of 2.3677, 2.614, and 2.609, and electronic band gaps of 2.54 eV, 2.42 eV, and 3.05 eV, are preferred. However, other materials, including polymers and organic materials, can be used.

[0179] In one implementation, when a photonic crystal is arranged in a mirror, a material layer with a small electronic bandgap is not in the radiation path to avoid absorption of photons before they reach the depth where they must be disturbed. For example, the vacuum wavelength corresponding to CdS is... = hc / 2.42 e=5.12×10 -7 This makes the material opaque below 512 nm, and therefore, it is opaque to blue and ultraviolet radiation. For mid-infrared radiation, a semiconductor is preferred. Si and Ge, with refractive indices of 3.42 and 4.04 respectively, are ideal high-refractive-index layers, exceeding... (Si)= hc / 1.12 e =1.107×10 -6 m and (Ge)= hc / 0.67 e =1.85051×10 -6 m, because Si and Ge are opaque to radiation in the visible light range.

[0180] Therefore, the photonic crystal containing these semiconductors is preferably located in a downstream photonic crystal of a mirror with a high electronic bandgap dielectric, such that when incident radiation reaches the semiconductor, the high-energy photons have already been reflected by the photonic crystal.

[0181] There are many possible technologies for fabricating photonic crystal layers. Sputtering technology is of great interest in terms of cost and reliability, but other technologies such as MBE (molecular beam epitaxy) or MOVPE (metal-organic vapor phase epitaxy) may be of great interest for exploring high refractive index layers.

[0182] Figure 5 The graph shows reflectivity curves (upper half) as a function of the vacuum wavelength (in meters) of the incident photons from two photonic crystals, and Chebyshev independent variables (mainly in the lower half). For these two photonic crystals, two cases are represented: in perpendicular incidence (…). θ =0) and at horizontal incidence ( θ =π / 2 rad) and under TM polarization; the solid line represents perpendicular incidence ( θ The reflectivity of the first photonic crystal at (= 0) R ) and Chebyshev independent variables ( α The dotted line represents horizontal incidence (for Chebyshev independent variables). θ = π / 2 rad, and for reflectivity θ =0.99× π / 2 rad) and the reflectivity of the first photonic crystal under TM polarization ( R ) and Chebyshev independent variables ( α The dashed line indicates perpendicular incidence. θThe reflectivity of the second photonic crystal at (=0) R ) and Chebyshev independent variables ( α The dotted line represents horizontal incidence (for Chebyshev independent variables). θ = π / 2 rad, and for reflectivity θ = 0.99× π / 2 rad) and the reflectivity of the second photonic crystal under TM polarization ( R ) and Chebyshev independent variables ( α For reflectivity, almost horizontal () was used. θ =0.99× π The incident radiation is 2 rad. The reason for using "almost" horizontal rays in the reflection is to avoid the appearance of a false total internal reflection band formed by rays that do not actually enter the photonic crystal. This is unnecessary in the Chebyshev independent variable, hence the use of horizontal incident radiation ( ). θ = π / 2 rad).

[0183] For the first photonic crystal, a hemispherical total internal reflection band is formed between point 24 (solid line) of the Chebyshev independent variable of the first photonic crystal, which is perpendicularly incident on the frame edge (which defines its leading edge) and point 25 (dotted line) of the Chebyshev independent variable of the first photonic crystal, which is horizontally incident and TM polarized (which defines its trailing edge); this is the hemispherical total internal reflection band of the first photonic crystal (from point 24 to point 25), as follows: Figure 2 As discussed in the discussion. For the second photonic crystal, a hemispherical total internal reflection zone is formed between the dive point 26 (dashed line) of the Chebyshev independent variable of the vertically incident second photonic crystal (which defines its leading edge) and the occurrence point 27 (dashed dot line) of the Chebyshev independent variable of the horizontally incident and TM-polarized second photonic crystal (which defines its trailing edge); this is the hemispherical total internal reflection zone of the second photonic crystal (from point 26 to point 27).

[0184] The fact that the trailing edge wavelength (25) of the first photonic crystal coincides with the leading edge wavelength (26) of the second photonic crystal allows the two photonic crystals to be matched. If the two photonic crystals are deposited on the same substrate, they form a wider hemispherical total internal reflection band spanning from point 24 to point 27. The reflectivity of the mirror including the two photonic crystals is not plotted in the figure, but is more square than the reflectivity exhibited by the photonic crystals alone.

[0185] Once the leading edge (24) of the first photonic crystal at perpendicular incidence is known, a method specifically designed for perpendicular incidence (in) can be used. Figure 6The thickness of the two-layer unit cell is calculated using equation (6), which is also labeled as the "leading edge" on the X-axis. Then, the trailing edge wavelengths of horizontal radiation and TM polarization are calculated to produce the trailing edge of the hemispherical total internal reflection zone of the first photonic crystal. As already explained, this is done by applying equation (6). Obtained from horizontally incident and TM polarized X =1 to begin with. Once obtained X Then, use equation (7) to calculate the trailing wavelength (25), and the same applies to horizontally incident and TM polarized (in Figure 6 (The middle part is marked as "tail edge"). Figure 6 This shows vertical incidence (solid line) and horizontal incidence with TM polarization (…). Figure 6 The function (with dashed lines in the text) The graph shows that the dashed curve is slightly aperiodic, meaning that for its... Y ≠0. In this diagram, the front and rear edges are... X Values ​​are marked with bold dots.

[0186] For the second photonic crystal, the trailing edge of the first photonic crystal obtained above becomes the leading edge (26), thus resulting in a perfect fitting of the two total reflection bands. The calculation method described for the first photonic crystal is repeated for the second photonic crystal. For a mirror containing more than two photonic crystals, this process is repeated for every two photonic crystals until the trailing edge of the last photonic crystal is equal to or exceeds the highest vacuum wavelength of the desired extended hemispherical total reflection band (26). That is, at the level of the last photonic crystal ( θ max = π The point of occurrence of the Chebyshev independent variable with incident light of / 2 rad and TM polarization. As for the initial wavelength of the total internal reflection zone of the mirror hemisphere, it is located at the leading edge of the total internal reflection zone of the first photonic crystal hemisphere ( ), which is the point of dive of the Chebyshev independent variable when the first photonic crystal is incident perpendicularly.

[0187] exist Figure 5In the example, the first deposited photonic crystal has a high refractive index of 3.43 (silicon) and a low refractive index of 1.37 (magnesium fluoride), with layer thicknesses of 166 nm and 413 nm, respectively. For the second deposited photonic crystal, the refractive indices are 4.04 (germanium) and 1.37 (magnesium fluoride), with layer thicknesses of 186 nm and 557 nm, respectively. Both photonic crystals are deposited on two separate glass substrates with a refractive index of 1.52 and no frontal protection (air). The leading edge (24) of the total internal reflection band of the mirror comprising the first and second photonic crystals is 1.77 μm, corresponding to the electronic bandgap of a 0.7 eV photovoltaic cell; the trailing edge (27) of the total internal reflection band of the resulting mirror is 3.32 μm. For mirrors comprising more than two easily mounted photonic crystals, the trailing edge will be much higher.

[0188] from Figure 5 As can be seen, the total internal reflection bands at different incident angles and polarizations extend far beyond those of hemispherical total internal reflection (which extends from point 24 to point 27). This implies redundancy, as many photons are found to be reflected by more than one photonic crystal. The same occurs with TE-polarized leveling photons, whose reflectivity is not plotted but forms even wider total internal reflection bands, and generally, the same occurs with all photons. This explains why good results can be obtained even when using extremely thin photonic crystals with very few unit cells. Figure 5 The results correspond to 10 units per photonic crystal, but typically only 7 units provide good results, and this number may be reduced.

[0189] Figure 7 The reflectivity (R) curve of a monolithic mirror made of multiple photonic crystals is shown as a function of vacuum wavelength (in meters). The monolithic mirror is designed to reflect radiation received by a hemispherical surface in the range of 1.77 to 20 μm. In this embodiment, the mirror is formed by a monolithic stack of eight photonic crystals, each having 10 unit cells, all monolithically deposited on the back of a photovoltaic cell with an electron bandgap of 0.7 eV (close to germanium) and covered with a thick layer of silver. The stack has a total of 160 layers of different dielectrics.

[0190] In this figure, the solid line represents the reflectance under perpendicular incidence, while the dashed line and dotted line represent... θ = 0.99× π / 2 rad and reflectance curves under TE and TM polarization. Average reflectance of a blackbody at 1410℃ (melting point of metallurgical silicon) under the emission spectrum (its emission spectrum is shown in Figure 1). Figure 8As shown, the range is 1.77–20 μm, and the unpolarized (TE as many as TM photons and averaged by the energy spectrum) is 0.999999 at all hemispherical incident angles. Therefore, a hemispherical total internal reflection band of 18.24 µm width is achieved in this example with a given average energy efficiency. It should be noted that, using Qiang, H., Jiang, L., Li, X.: “ Design of broad omnidirectional total reflectors based on one-dimensional dielectric and magnetic Photonic Crystals The best results obtained from theoretical magnetic materials and genetic algorithms in Optics and Laser Technology 42(1), 105-109 (2010), doi:10.1016 / j.optlastec.2009.05.006 produce a hemispherical total internal reflection band of 6.80 µm. Figure 7 The example achieves 18.24 µm, but no efficiency data is given.

[0191] In this implementation, the high-refractive-index material of the photonic crystal is zinc sulfide, silicon, or germanium (depending on the specific photonic crystal), while the low-refractive-index material is magnesium fluoride, and their thicknesses vary in each photonic crystal. Figure 5 The layer described in the implementation scheme is part of the reflector. As previously mentioned, near-horizontal incidence ( θ =0.99× π / 2 rad) is to avoid the apparent total internal reflection of photons that do not enter the reflector.

[0192] The present invention also defines a thermal insulator for an incandescent body, wherein the thermal insulator includes at least one reflector according to the invention. Preferably, the thermal insulator includes multiple reflectors according to the invention. The incandescent body may, for example, be part of a furnace or an energy storage system.

[0193] In the above embodiments, the method according to the invention designs a very high-quality reflector through iterative design from low wavelength to high wavelength. Using the invention, similar structures can also be designed iteratively from high wavelength to shorter wavelengths. Knowing the trailing edge wavelength, the thickness of the horizontally incident cell layer can be easily obtained using equation (5), and by applying equation... +1=0 (Solve problem) X Calculate the continuous leading edge, where, from X =3 starts; and converts it to wavelength using equation (7).

[0194] One possible application of this invention is as a furnace lining for storing energy from molten silicon at 1410°C. The silicon is stored in a container heated by a resistor, microwave, or other means. This energy is ultimately extracted as electricity through thermo-photovoltaics.

[0195] In one embodiment of the invention, the thermal insulator of the incandescent vessel is a wrapper comprising multiple monolithic mirrors of multiple photonic crystals. These mirrors reflect photons emitted by the incandescent vessel with very high efficiency. A blackbody at 1410°C has an average reflectivity of 0.9998 for unpolarized radiation in all hemispherical directions between 0.6 μm and 35 μm (outside this range, power is negligible), constituting a very good thermal insulator. In reality, heat leakage will occur at the joints of the resistors heating the vessel and at some pivots required to hold the vessel in place, but this should be reduced to what is absolutely necessary to ensure electrical input and mechanical stability.

[0196] In a preferred embodiment, the mirror for the thermal insulator of an incandescent body, as described above, comprises 15 photonic crystals, each with 7 unit cells, monolithically deposited on a metal covered with a thick layer of silver or gold. Several materials are available for the high refractive index layer: zinc sulfide (2.614), silicon (3.42), and germanium (4.04). For the low refractive index layer, magnesium fluoride (1.374) is used for each photonic crystal. The mirror comprises a total of 210 layers. The mirror has been used with the method of the present invention using an equation for the ratio of high to low refractive index thicknesses. (Equation 6, perpendicular incidence) is used for the design. Using the above procedure, an average efficiency of 99.9899% is calculated, weighted by the power density of the radiation spectrum of a 1410℃ blackbody within a bandwidth of 0.6–20 μm, and this weighted average is extended to all hemispherical incident angles and polarizations of the incident radiation. According to Stefan-Boltzmann's law, the radiative power of a 1683K (1410℃) blackbody is 45.5098 W / cm². 2 The reflected power (using the calculated average reflectivity) in the 0.6–20 μm range is 45.3341 W / cm². 2 We estimate the reflectance outside this range to be 70%, which produces 0.0158632 W / cm² for the leftmost 0 – 0.6 μm range. 2 The reflected power, for the rightmost range of 20 - ∞ μm, produces 0.150173 W / cm². 2 The reflected power. The difference between the three components of the incident power and the reflected power is 0.00970275 W / cm².2 This is the power absorbed and lost in the thermal insulation lining. This power is readily dissipated into the environment without a significant increase in the temperature of the reflector. Typical losses in state-of-the-art fire-resistant / insulating linings exceed 1 W / cm². 2 Therefore, this calculation shows that the heat loss using this mirror liner is more than 100 times less.

[0197] In one implementation, a portion of the reflector's packaging is replaced by a thermophotovoltaic cell. During their fabrication, an integrated reflector of multiple photonic crystals can be deposited on the back of the thermophotovoltaic cell to reflect many photons with too low energy to generate a photocurrent back to the thermal container, thus being barely absorbed. In thermophotovoltaics with a blackbody spectrum suitable for converting molten silicon (1410°C), the number of useless photons is less than 0.7 eV, corresponding to a wavelength of 1.77 μm. During cell fabrication, the reflector is deposited on the back of the semiconductor cell, which can be conveniently finished with a layer of silver or gold to form the back electrical contact. The reflectivity curve appears... Figure 7 Furthermore, their characteristics have been described previously in this specification. As mentioned above, an average hemispherical reflectance of 0.999999 was obtained between 1.77 μm and 20 μm. However, due to varying losses in thermophotovoltaic cells, the reflected power is currently much smaller, but this result could spur significant advancements in thermophotovoltaic efficiency.

[0198] Regarding monolithic mirrors that are coated with multiple photonic crystals using silver or gold, the total reflection area remains unchanged, but the reflectivity of the regions outside them increases significantly, though never as much as the total reflection area. This could have practical implications in many applications.

[0199] In various applications, the monolithic mirror according to the invention can be used as a parabolic mirror in astronomical telescopes. These mirrors are deposited within hexagonal tesserae, which typically constitute them, where the small curvature of the tesserae does not affect their fabrication. Instead of receiving only mid-band light perpendicular to the telescope (which can be achieved with a single photonic crystal), the mirror can be operated to receive light with a very broad spectrum across the entire sky.

[0200] Many other applications can be envisioned for the reflectors designed and / or manufactured according to the present invention.

Claims

1. A design for incident unpolarized radiation in a predefined vacuum wavelength range [ λ A ,λ B A method with a total internal reflection mirror, wherein the incident angle of the incident unpolarized radiation is... θ Less than or equal to the predefined maximum angle of incidence θ max , in, The mirror includes multiple one-dimensional photonic crystal forming layers, wherein each photonic crystal includes multiple unit cells that are repeated the same number of times, and each unit cell includes a first dielectric material layer and a second dielectric material layer, the first dielectric material and the second dielectric material having different refractive indices; Among them, according to the vacuum wavelength The varying reflectivity of each photonic crystal is shown at the leading-edge wavelength value. With trailing edge wavelength value The interval between ( , The region contains rectangular pulses of rounded corners and unit height, the pulses within which are defined as total internal reflection zones, and the leading-edge and trailing-edge wavelengths depend on the incident angle of the incident radiation. θ and polarization; Among them, for i = 1、...... m， The method includes the following steps: (a) Settings θ = 0 of i The leading edge wavelength of the total internal reflection band of a photonic crystal And select the first dielectric material and the second dielectric material to form the first dielectric material. i The unit cell of a photonic crystal; (b) Determine the first i First thickness of the first dielectric material layer of the photonic crystal and the first i Second thickness of the second dielectric material layer of the photonic crystal The details are as follows: in, and They are respectively the first i The photonic crystal selects the refractive indices of the first and second dielectric materials; and (c) Using the first thickness calculated in step (b) and the second thickness The value of the first i Trailing edge wavelength of the total internal reflection zone of a photonic crystal The details are as follows: Among them, parameters X By using a predefined maximum angle of incidence Equations for transverse magnetic TM polarization Solve X The obtained equation is solved using an iterative method, and its initial value is... X = 1, in, In step (a), the leading edge wavelength value is... Set to: - For i = 1, equal to The value; and - For i > 1, equals And the first polarization of TM i -1 Trailing edge wavelength of the total internal reflection zone of a photonic crystal The value; in, m It is to satisfy And the first polarization of TM m Trailing edge wavelength of the total internal reflection zone of a photonic crystal equal to or greater than The number of photonic crystals.

2. A design for incident unpolarized radiation in a predefined vacuum wavelength range [ λ A ,λ B A method for using a mirror with maximum reflectivity, wherein the incident angle of the incident unpolarized radiation is... θ Less than or equal to the predefined maximum angle of incidence θ max , in, The mirror includes multiple one-dimensional photonic crystal forming layers, wherein each photonic crystal includes multiple unit cells that are repeated the same number of times, and each unit cell includes a first dielectric material layer and a second dielectric material layer, the first dielectric material and the second dielectric material having different refractive indices; Among them, according to the vacuum wavelength The varying reflectivity of each photonic crystal is shown at the leading-edge wavelength value. With trailing edge wavelength value The interval between ( , The region contains rectangular pulses of rounded corners and unit height, the pulses within which are defined as total internal reflection zones, and the leading-edge and trailing-edge wavelengths depend on the incident angle of the incident radiation. θ and polarization; Among them, for i = 1、...... m The method includes the following steps: (a) Settings And the first polarization of TM i Trailing edge wavelength of the total internal reflection zone of a photonic crystal And select the first dielectric material and the second dielectric material to form the first dielectric material. i The unit cell of a photonic crystal; (b) Determine the first i The first thickness of the first dielectric material layer of the photonic crystal and the first i The second thickness of the second dielectric material layer of the photonic crystal The details are as follows: in, and They are respectively the first i The refractive indices of the first and second dielectric materials selected for the photonic crystal are, wherein, and (c) Using the first thickness calculated in step (b) and the second thickness The value of the first i The leading edge wavelength of the total internal reflection band of a photonic crystal The details are as follows: Among them, parameters X Through the equation Solve X The obtained equation is solved using an iterative method, and its initial value is... X =3, in, In step (a), the trailing edge wavelength value is... Set to: - For i = 1, equal to The value; and - For i > 1, equals The i -1 The leading edge wavelength of the total internal reflection zone of a photonic crystal The value; in, m It is to satisfy The m The leading edge wavelength of the total internal reflection band of a photonic crystal equal to or less than The number of photonic crystals.

3. The method according to claim 1 or 2, wherein, Including the visible or near-infrared light range and / or Included in the mid-infrared light range.

4. The method according to claim 1 or 2, wherein, The predefined maximum angle of incidence for < .

5. The method according to claim 1 or 2, wherein, The predefined maximum angle of incidence for .

6. A manufacturing process comprising... m A method for using a one-dimensional photonic crystal mirror, wherein... m >1. The method includes the following steps: The reflector is designed according to the method of any one of the preceding claims; and form m A stack of one-dimensional photonic crystals; Among them, each of the first i Photonic crystals are formed by stacking multiple alternating layers of a first dielectric material and a second dielectric material, wherein the first dielectric material has a refractive index different from that of the second dielectric material, and Among them, for each of the first i The photonic crystal has a first thickness of each first dielectric material layer and a second thickness of each second dielectric material layer having values ​​determined in step (b) of any of the preceding claims, wherein, i = 1、...… m .

7. The method according to claim 6, wherein, The photonic crystal layer is deposited on the substrate.

8. The method according to claim 7, wherein, The substrate is covered with a reflective metal layer; and the photonic crystal is deposited on the layer.

9. The method according to claim 8, wherein, The reflective metal layer is silver or gold.

10. The method according to any one of claims 6 to 9, wherein, The photonic crystal is covered with a protective, thick, transparent layer.

11. The method according to claim 10, wherein, The protective, thick, transparent layer in It is transparent within the area.

12. The method according to any one of claims 6 to 9, wherein: (a) The photonic crystals are arranged according to their... arrive The positions of the total internal reflection zones are arranged in a specific order within the mirrors, or (b) The photonic crystals are arranged differently from those derived from them. arrive The positions of the total reflection strips are arranged in a specific order within the reflector.

13. The method according to any one of claims 7 to 9, wherein, The photonic crystals are arranged in the mirror in an order defined by the transparency of the first and second dielectric materials of the photonic crystals, such that the photonic crystal made of a material opaque to radiation in the wavelength range included in the total reflection band of the other photonic crystal is located downstream of the other photonic crystal in the direction intended for incident radiation.

14. The method according to any one of claims 6 to 9, wherein, The number of unit cells in each photonic crystal is greater than or equal to 5.

15. The method according to any one of claims 6 to 9, wherein, The number of unit cells in each photonic crystal is greater than or equal to 7.

16. The method according to any one of claims 6 to 9, wherein, The number of unit cells in each photonic crystal is greater than or equal to 10.

17. A product manufactured according to any one of claims 6 to 16, comprising... m A mirror of a one-dimensional photonic crystal, wherein... m >1, where the predefined maximum incident angle for .

18. A photovoltaic cell comprising a reflector according to claim 17 deposited on a transparent substrate and coated with a metal layer, wherein the photovoltaic cell is a thermophotovoltaic cell.

19. A photovoltaic cell comprising a reflector and a semiconductor substrate according to claim 17, wherein the reflector is deposited on the back side of the semiconductor substrate and coated with a metal layer, and the photovoltaic cell is a thermophotovoltaic cell.

20. A thermal insulator for incandescent materials, wherein, The thermal insulator includes at least one reflector according to claim 17.

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