Monolithic mirror and its design method

Abstract

The present invention relates to a mirror comprising a plurality of one-dimensional photonic crystals that has very high reflectivity over a very wide range of wavelengths, a wide range of directions, even hemispherical, and for all polarizations of incident photons. The present invention also relates to methods for designing such mirrors and photovoltaic cells that include such mirrors.

Description

Technical Field

[0001] The present invention relates to a mirror including a plurality of one-dimensional photonic crystals, which has a very high reflectivity in a very wide range of wavelengths, a wide range of directions, and even hemispherical, and for all polarizations of incident photons. The present invention also relates to a method for designing and manufacturing the above mirror and a photovoltaic cell including such a mirror.

Background Art

[0002] A photonic crystal is a structure in which a unit cell formed of one or several materials with variable refractive indices is periodically and indefinitely repeated in space. A photonic crystal may include a forbidden band or an energy band gap where photons cannot exist. Photons having energy within the above band gap incident on the photonic crystal cannot enter the photonic crystal and are thus totally reflected, that is, the reflectivity of the photonic crystal at the above energy is equal to 1. The introduction of photonic crystals can be found in Joannopoulos, J.D., Meade, R.D.: “Photonic Crystals: Molding the Flow of Light”, Princeton University Press, (2005).

[0003] In a one-dimensional (1D) photonic crystal, the refractive index variation occurs only in one dimension, called z, and the unit cell is usually formed by two dielectric layers with different refractive indices, called high (H) and low (L). 1D-photonic crystals also have bandgaps, but their energy positions vary with the angle of incidence (θ) of the photons with respect to the z-axis and their polarization. In practice, the photonic crystal has a finite number of unit cells, which somewhat reduces the reflectivity within the bandgap, but usually the reflectivity value remains very close to 1. In contrast, in a three-dimensional (3D) photonic crystal that forms a periodic structure where the refractive index varies in three axes of space, the bandgap, if it exists, does not depend on the angle of incidence. However, there are few existing spatial structures that can generate an appropriate bandgap and are hardly suitable for large-scale commercialization.

[0004] In 1D photonic crystals, a reference plane is formed along the z-axis and the direction of the photons incident on the crystal, i.e., according to the wave number vector k of the electromagnetic plane wave representing it. This plane can be called the yz plane. Any plane wave is a linear combination of a transverse electric (TE or s-polarized) plane wave with the electric field vector perpendicular to the yz plane and a transverse magnetic (TM or p-polarized) plane wave with the magnetic field perpendicular to the yz plane. As already mentioned, the bandgap position varies with the angle of incidence (θ) and TE or TM polarization.

[0005] The energy range of these bandgaps can be represented by the range of the photon wavelength (λ0) in vacuum, and the relationship between wavelength and energy is given by the well-known formula

Equation

[0006] Under normal incidence (θ = 0), the z-axis and the direction of the photon coincide, and any plane containing the z-axis can be regarded as a TE or TM plane, so there is no difference seen for TE polarization and TM polarization. For oblique incidence at a non-zero angle (θ), the total reflection band is blue-shifted, i.e., shifted towards lower wavelengths, and its width increases for TE polarization and decreases for TM polarization. The trailing edge also blue-shifts for both TE and TM polarizations, but the most shifted is for TM polarization. These changes are stronger for larger angles and strongest for horizontal (θ = π / 2 rad) incidence.

[0007] Despite the shift of the total reflection band of the 1D photonic crystal, there exists a wavelength range with total reflection common to the bands obtained for normal incidence, TE horizontal incidence, and TM horizontal incidence. It is the band of hemispherical (or omnidirectional) total reflection, which is referred to as the "hemispherical total reflection band" in this specification. Generally, since the hemispherical total reflection band is relatively narrow, the leading edge of this hemispherical total reflection band is the leading edge of the total reflection band under normal incidence (θ = 0 rad), and the trailing edge of this hemispherical total reflection band is the trailing edge of the total reflection band under horizontal TM polarization (θ = π / 2 rad). However, with a slight deformation of the periodic structure of the photonic crystal (which is now a pseudo-crystal), the hemispherical total reflection band can be somewhat expanded (Abdelaziz, K.B., 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-Pure and Applied Optics 7(10), 544-549 (2005). doi:10.1088 / 1464-4258 / 7 / 10 / 005).

[0008] The transmittance (T) is, in the absence of absorption (which is the case in the present invention), 1 minus the reflectance (T = 1 - R), and thus is 0 in the region of total reflection and outside thereof, which means that some photons are transmitted but not all.

[0009] The 1D photonic crystal has a layered structure. The layered structure has been studied for a long time by the method of characteristic matrices, and a classical book is the book by Born and Wolf (Born, M., Wolf, E.: “Principles of Optics”. Pergamon Press, Oxford (1975)). According to this method, each photonic crystal is described by two Chebyshev polynomials of the second kind U N-1 (α) and UN-2 It has a characteristic matrix in which (α) appears, and N is the number of unit cells in the photonic crystal. The argument α TE|TM (λ0, θ, n a n b h a h b ) is a function that depends on the vacuum wavelength (λ0) of the incident photon, the angle of incidence (θ), the high and low refractive indices (n a n b ) of the unit cell material, and the thickness (h a h b ) of the unit cell layer. The argument (α) also depends on the TE or TM polarization of the incident photon. At normal incidence (θ = 0), the argument (α) is the same for physically indistinguishable TE and TM as pointed out before, and the subscript (TE|TM) of the argument (α) may be omitted. Note that the number of unit cells forming the photonic crystal does not appear in the Chebyshev argument.

[0010] Multi-photonic crystals are sometimes proposed in the academic literature. By using several photonic crystals, the width of the total reflection band can be widened. Carniglia C K.: “Perfect mirrors - from a coating designer’s point of view”. Laser-Induced Damage in Optical Materials: 68 - 84 1999, Proc. of SPIE Vol. 3902 (2000) represents this concept and presents several unit cell structures. According to the present disclosure, a stack of four photonic crystals having “wavelength pass” (LWP) filter unit cells results in a calculated total reflection band of about 0.382 μm to 0.721 μm, and its efficiency is not calculated, but the unit cell aims for a reflectivity of at least 0.95, which is surely exceeded by the stack. The unit cell is designed to have a low (L) layer thickness equal to one quarter of the wave (also called a quarter wave in the above-mentioned paper) at the designed “center” value of the vacuum wavelength of each photonic crystal. However, such a configuration results in a narrow total reflection band.

[0011] Qiang, H., Jiang, L., Li, X.: “Design of broad omnidirectional total reflectors based on one-dimensional dielectric and magnetic Photonic Crystals”. Optics and Laser Technology 42(1), 105 - 109 (2010). doi:10.1016 / j.optlastec.2009.05.006) provides another example of the use of multi - photonic crystals for the purpose of expanding the span of the hemispherical total reflection band. However, the procedure for achieving this expansion is entirely theoretical and is based on the deposition of layers of magnetic materials of undefined properties (thus having different permeabilities one by one), and the combined values of their permittivity and permeability are probably impossible to achieve.

[0012] U.S. Patent Application Publication No. 2012 / 125429 discloses a solar cell having different layers and a 3D photonic crystal attached to its back surface, the purpose of which is to enhance its efficiency by reflecting unused light back to the cell body. As already mentioned, 3D photonic crystals can present a total reflection band that is essentially hemispherical (or omnidirectional). The width of the total reflection band extends from the visible to the near - infrared and is sufficient to enhance solar cell efficiency, but is orders of magnitude narrower compared to the span required for other applications such as thermophotovoltaic power generation that require high reflectivity in the mid - infrared.

[0013] U.S. Patent Application Publication No. 2013 / 104983 describes a procedure for improving the efficiency of any solar cell by applying optimized management of light. This management uses various methods including the use of a single photonic crystal.

[0014] Chinese Patent Application Publication No. 104076530 describes a procedure for improving the efficiency of a solar cell by means of a stack of layers doped with a luminescent material that emits strongly at a specific wavelength considered to be optimal. Furthermore, these layers may form a single photonic crystal.

[0015] US Patent Application Publication No. 2011203663 discloses a solar cell having various optical structures intended to capture light within the cell and enhance its efficiency. This includes an antireflection coating, a 3D photonic crystal on the front surface of the solar cell, a metallic diffraction grating on the back surface, and a 1D photonic crystal on and incorporated within the grating.

[0016] In all of the last three of the above-mentioned documents, the wavelength span on which they focus their interest refers to the visible and near-IR (less than 2 μm), while the present invention provides a hemispherical mirror having a total reflectance over a span that can include from the visible to the mid-infrared (greater than 20 μm). Furthermore, the last three of the above-mentioned documents include only a single photonic crystal and are not at all capable of obtaining the span achieved by the multi-photonic crystal mirror according to the present invention. This broad span is necessary for many applications, including, inter alia, energy storage in molten metals.

Summary of the Invention

[0017] The present invention provides a method for designing and / or manufacturing a mirror having the broadest span of hemispherical total reflection band. The method described in the claims is more effective and practical than other methods proposed heretofore.

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

[0019] In a first aspect of the invention, the present invention provides a method for designing a mirror having a predetermined maximum angle of incidence (θ max)A method for designing a mirror having a maximum reflectance in a predetermined vacuum wavelength range ([λ A , λ B ) for incident radiation having the following incident angles is defined. The mirror includes a plurality of one-dimensional photonic crystals forming layers, each photonic crystal includes a plurality of unit cells that are identically repeated a predetermined number of times, each unit cell includes a layer of a first dielectric material and a layer of a second dielectric material, and the first dielectric material and the second dielectric material have different refractive indices. The reflectance of each photonic crystal as a function of the vacuum wavelength (λ0) is the leading edge wavelength value

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[0020] Therefore, the layer of the first dielectric material and the layer of the second dielectric material form the unit cell of the photonic crystal. The unit cell is repeated N i times, and a photonic crystal of 2N i layers of dielectric material, that is, N i layers of the first dielectric material and N i layers of the second dielectric material is formed. The subscript i in the number of unit cells reflects the fact that the photonic crystals constituting the mirror may have different numbers of unit cells.

[0021] When two unit cells are bonded to each other, there is no coincidence of layers of the same dielectric material. In contrast, in the layer arrangement in a photonic crystal, even in the bonding of adjacent unit cells, the first and second dielectric materials always alternate, and the layer arrangement is always a correlated distribution of layers of two different materials.

[0022] In the context of the present 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 normal of the layer of the photonic crystal.

[0023] It should be understood that the notations "first dielectric material" and "second dielectric material" are only for distinguishing two materials within a unit cell of a photonic crystal. However, this notation is not intended to imply a specific order of the two dielectric materials within a unit cell of a photonic crystal. Thus, when layers of dielectric materials are deposited on a substrate, either the first dielectric material or the second dielectric material may be deposited on the substrate first. Dielectric materials are also referred to herein as high refractive index materials and low refractive index materials, and a high refractive index material is a dielectric material having a higher refractive index compared to other dielectric materials within a unit cell of a photonic crystal. Each refractive index is given by the material, and thus the value of the refractive index is a predetermined parameter corresponding to the previous selection of the photonic crystal unit cell layer material for the design of a multilayer mirror implemented by the method of the first aspect of the invention. Further, different pairs of materials may be used for different photonic crystals among a plurality of photonic crystals in the mirror, and a subscript i is used to distinguish them.

[0024] In a first embodiment, the method according to an aspect of the first invention is as follows for i = 1,... m (a) The leading wavelength value of the total reflection band of the i-th photonic crystal when θ = 0

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[0025] In the second embodiment, the method according to the aspect of the first invention is as follows for i = 1,... m (a) Set θ = θ max and the trailing-edge wavelength value of the total reflection band of the i-th photonic crystal for TM polarization [Number] and select the first dielectric material and the second dielectric material to form the unit cell of the i-th photonic crystal; (b) Determine the first thickness (h at,i ) of the layer of the first dielectric material and the second thickness (h bt,i ) of the layer of the second dielectric material of the i-th photonic crystal as follows: [Number] where n at,i and n bt,i are the refractive indices of the first dielectric material and the second dielectric material selected for the i-th photonic crystal, respectively, where [Number] and this is the step of (c) The first thickness (h) calculated in step (b)at,i ) and the value of the second thickness (h bt,i ), to determine the leading-edge wavelength value of the total reflection band of the i-th photonic crystal

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[0026] Therefore, the method according to the first embodiment of the first aspect of the first invention sets the leading-edge wavelength value of the photonic crystal and calculates the layer thickness to obtain the trailing-edge wavelength value, thereby from λ A to λ Bincluding the step of designing a photonic crystal up to, the method according to the second embodiment of the first aspect of the invention sets the trailing edge wavelength value of the photonic crystal and calculates the layer thickness to obtain the leading edge wavelength value, thereby λ B from λ A to including the step of designing a photonic crystal up to.

[0027] Throughout this document, the following notations are used: α TM represents the argument of the second kind Chebyshev polynomial of the characteristic matrix of the photonic crystal, and is referred to as the "Chebyshev argument" in this specification;

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[0028] According to the first embodiment, the leading edge of the total reflection band of the first photonic crystal for normal incidence

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[0029] The first thickness (h al,1 ) of the first dielectric material layer and the second thickness (h bl,1 ) of the second dielectric material layer of the first photonic crystal are determined by applying the following formula:

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[0030] The first thickness (h al,1 ) of the layer of the first dielectric material and the second thickness (h bl,1 ) of the layer of the second dielectric material are calculated, and the trailing-edge wavelength value of the total reflection band of the first photonic crystal [Equation] is determined by applying the following formula: [Equation] wherein the parameter X is obtained by solving the equation α max +1 = 0 for a predetermined maximum incident angle (θ TM ) and transverse magnetic (TM) polarization, and the above equation is solved by an iterative method with an initial value of X = 1, where [Equation] is as follows.

[0031] In the case of TE-polarized incident radiation, using TE polarization in the equation instead of TM polarization gives a wider photonic total reflection band, but this is ineffective for TM photons and thus unpolarized radiation containing an equal amount of TE photons and TM photons.

[0032] As a result of the steps described, the thickness of the layer of the first photonic crystal and the trailing-edge wavelength value of the total reflection band are determined.

[0033] 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 [Equation] of the total reflection band of the second photonic crystal for normal incidence max and the calculated trailing-edge wavelength value of the total reflection band of the first photonic crystal for θ = θ

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[0034] The set leading-edge wavelength value

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[0035] Using the values of the first thickness (h al,2 ) and the second thickness (h bl,2 ) calculated in the previous step, and using the parameters corresponding to the second photonic crystal, the trailing-edge wavelength value of the total reflection band of the second photonic crystal is determined as described in relation to the first photonic crystal.

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[0036] As a result of these steps, the thickness of the unit cell layer of the second photonic crystal and the trailing-edge wavelength value of the total reflection band are determined.

[0037] To design all the photonic crystals that will be part of the mirror, for the m-th photonic crystal, for θ = θ max and the trailing-edge wavelength value of the total reflection band for TM polarization

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[0038] In the method according to the second embodiment, an iterative process similar to the disclosed process is performed with the difference that the trailing edge wavelength values max of the total reflection bands of each photonic crystal for θ = θ

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[0039] According to the second embodiment, in order to design all the photonic crystals that form part of the mirror, for the m-th photonic crystal, until the leading wavelength value of the total reflection band of the m-th photonic crystal for θ = 0

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[0040] The number of unit cells of the photonic crystal is not included in the Chebyshev argument. Although theoretical total reflection can be obtained with an infinite number of layers, in a multi-photonic crystal mirror, 7 unit cells can provide total reflection with a reflectivity of about 0.9999, and with 10 unit cells, the reflectivity can even reach 0.999999.

[0041] The materials within the unit cell of the photonic crystal may be different for each photonic crystal. For example, the first dielectric material of photonic crystal "i" may be the same as or different from the first material of photonic crystal "j". Also, the number of unit cells may be different for each photonic crystal.

[0042] Advantageously, the present invention enables the design and manufacture of a mirror based on the deposition of a plurality of dielectric layers that exhibit a reflectivity substantially equal to 1 for a very wide range of electromagnetic radiation extending from visible to mid-infrared (beyond 20 μm). Furthermore, the designed mirror exhibits this reflectivity of 1 for radiation and hemispherical incidence of both polarizations. For this purpose, the dielectric layers are deposited monolithically on the same substrate and grouped in several photonic crystals designed by the method of the present invention. The method of the present invention enables the generation of the widest band of hemispherical total reflection. Also, it is more effective and practical than other methods proposed so far.

[0043] Today, mirrors having a single photonic crystal deposited on a substrate are frequently used in optics and communications. These mirrors are required to have a very high reflectivity at a single wavelength as well as in a single direction and polarization, i.e., in a single radiation mode or the approximate mode of a beam.

[0044] In the background art section, it is explained that the characteristic matrix of a photonic crystal includes several Chebyshev polynomials of the second kind of different orders and the same argument α. Herein, it is disclosed that a total reflection band is generated when the argument of the Chebyshev polynomial of the second kind is outside the interval of α = ±1. More specifically, the Chebyshev argument α generally has an asymptote of +1 for λ0 → ∞ (photon energy 0 eV). As λ0 decreases, the Chebyshev argument reaches the value α = -1 and decreases until it exits the interval, reaching the trailing edge of the total reflection band. As λ0 further decreases, the Chebyshev argument reaches a minimum and then reaches the value α = -1 again at a specific value of λ0, entering the interval of α = ±1 again and generating the leading edge of the total reflection band. This makes it possible to calculate the total reflection band and the positions of its leading and trailing edges. When λ0 further decreases, the Chebyshev argument describes a partially wavy curve outside the interval of α = ±1, generating additional total reflection bands (photonic band gaps), but these are not of interest for the present invention.

[0045] The positions of the leading and trailing edges of the total reflection band of any photonic crystal are θ, n a , n b , h a , h b and polarization are known, it can be calculated by solving the equation α TE|TM (λ0, θ, n a , n b , h a , h b ) + 1 = 0. The present invention selects the leading edge or alternatively the trailing edge of the total reflection band of a photonic crystal to obtain, for a given value of θ, n a、 n b for the first thickness (h of the unit cell of the photonic crystala ) and the second thickness (h b ) is based on the variation of a variable that enables the description of Chebyshev arguments so that they can be analytically determined.

[0046] Also, when the equation α + 1 = 0 is solved for the wavelength using the first thickness (h a ) and the second thickness (h b ) of the determined photonic crystal unit cell, the maximum root is the trailing-edge wavelength value of the total reflection band, and the second-largest root is the leading-edge wavelength value.

[0047] What has been described so far is valid for any angle of incidence and polarization, and the total reflection bands have different positions and widths. Considering a single photonic crystal, among the different positions and widths of the bands of this photonic crystal, the leading edge (λ L ) located at the lowest wavelength corresponds to normal incidence. The trailing edge (λ T ) located at the highest wavelength corresponds to the highest angle (θ max ) of TM polarization and a selected angular span (preferably horizontal incidence, i.e., θ max = π / 2 rad). The total reflection band for any incidence extends from λ L to λ T . For θ max = π / 2 rad, this total reflection band can be called a hemispherical or omnidirectional total reflection band. In the case of radiation coming from the outside (from air), λ L < λ T is always satisfied, and a hemispherical total reflection band exists.

[0048] When several photonic crystals are deposited on the same substrate (they are monolithic), the reflectivity curve is altered compared to the reflectivity curves of the separate photonic crystals, but the total reflection band is positioned as determined by their Chebyshev parameters as described herein. In fact, the alteration of the reflectivity affects the region of λ0 where the Chebyshev parameter is within the interval α = ±1 and does not affect the total reflection band. This makes it possible to place different total reflection bands at desired positions by appropriately selecting the materials of the layers forming the unit cell of each photonic crystal and calculating their thicknesses.

[0049] A very wide hemispherical total reflection band can be formed by monolithically depositing several photonic crystals on a single substrate.

[0050] When photons represented by a plane wave travel through a stack of dielectric layers, their angles in layers j, k, etc. follow Snell's law, so sinθ = n j sinθ j =n k sinθ k ... (where n is the refractive index of the layer and θ is the angle inside them). The wavelength within the layer is λ = λ0 / ncosθ, and h / λ (where h is the layer thickness) is a fraction of the internal wavelength. Note that the wavelength within the layer is different from the wavelength in vacuum. h a n a cosθ a =h b n b cosθ b so that the ratio h a / h bBy selecting <>, the span of the total reflection band of a particular photonic crystal is maximized (subscripts a and b, or vice versa, for the high and low refractive index layers). In other words, the maximum span occurs when the thicknesses of the high and low refractive index layers are the same fraction of their internal wavelengths. This relationship imposes a relationship between the thicknesses of the high and low refractive index layers. Since this condition can only be met for a single angle of incidence, the minimum number of photonic crystals in a monolithic array to obtain a given span of hemispherical total reflectance occurs when the above condition is met for TM polarized horizontal light (this maximizes the small TM span of the individual photonic crystals for horizontal incidence).

[0051] In one embodiment, the first and second dielectric materials selected to form the unit cell of the i-th photonic crystal are

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[0052] In one embodiment, θ max = π / 2.

[0053] In one embodiment, λ A is included in the visible range (400 - 700 nm) or the near infrared range (700 - 2500 nm).

[0054] In one embodiment, λ Bis included in the infrared range, preferably the mid-infrared range (2.5 - 50 μm).

[0055] In a preferred embodiment, λ A is included in the visible or near-infrared range and / or λ B is included in the mid-infrared range.

[0056] In one embodiment, at least one first dielectric material and / or second dielectric material of the photonic crystal is selected from MgF2, CaF2, ZnS, TiO2, Si, and Ge. Preferably, one of the at least one first and second dielectric materials of the photonic crystal is selected from MgF2, CaF2, and the other of the first and second dielectric materials of the photonic crystal is selected from ZnS, TiO2, Si, and Ge.

[0057] In a second aspect of the present invention, the present invention is a method for manufacturing a mirror including m one-dimensional photonic crystals with m > 1, including the following steps: designing a mirror according to any method of the embodiments of the first aspect of the invention; forming m stacked one-dimensional photonic crystals; each i-th photonic crystal is formed by stacking a plurality of alternating layers of a first dielectric material and a second dielectric material, the first dielectric material having a refractive index (n bl,i , n bt,i ) different from the refractive index (n al,i , n at,i ) of the second dielectric material; for i = 1,... m, for each i-th photonic crystal, the first thickness (h al,i , h at,i ) of all layers of the first dielectric material and the second thickness (h bl,i , h bt,i ) of all layers of the second dielectric material have the values determined in step (b) of any method of the embodiments of the first aspect of the invention, defining the method.

[0058] A mirror including such a plurality of stacked photonic crystals is referred to herein as a monolithic mirror of multi - photonic crystals.

[0059] In one embodiment, the layers of the photonic crystal are deposited on either an opaque or a transparent substrate. In the case of an opaque substrate, it may have a high reflectivity. One layer of the photonic crystal is first deposited on the substrate, and subsequent photonic crystals are deposited on the previously deposited photonic crystal.

[0060] In one embodiment, the outermost layer of the mirror is covered with a transparent layer or a reflective metal (when the substrate is transparent), preferably silver or gold. The outermost layer of the mirror is understood to be the layer located farthest from the substrate. Advantageously, by covering the outermost layer with a reflective metal, the reflectivity of the wavelength of incident radiation outside a predetermined vacuum wavelength range ([λ A , λ B ) (i.e., outside the total reflection band of the mirror) is significantly increased, while for the wavelength of incident radiation within the predetermined vacuum wavelength range, the reflectivity remains unchanged. This may be of practical interest in certain applications. Alternatively, the monolithic mirror of multi - photonic crystals may be deposited on a substrate, which may or may not be covered with a protective thick transparent layer, and is covered with a reflective metal coating (preferably silver or gold) having the same effect and disposed on the outermost layer. When the mirror includes a reflective metal coating, during use, the mirror is preferably arranged such that the layer facing the incident radiation is the layer farthest from the reflective metal coating.

[0061] In order for the mirror to have a maximum reflectivity in a predetermined vacuum wavelength range, a plurality of one - dimensional photonic crystals having a total reflection band extending over the desired range are stacked to form the mirror.

[0062] In one embodiment, the photonic crystal has a lower limit (λ A ) of a predetermined vacuum wavelength range to an upper limit (λ BThey are arranged in the mirror in an order defined by the positions of their total reflection bands up to (λ B ). According to this embodiment, a photonic crystal having a total reflection band close to the upper limit (λ A ) is arranged downstream of a photonic crystal having a total reflection band close to the lower limit (λ A ) in the incident radiation direction in the situation where the mirror is used. In other words, the radiation first reaches a photonic crystal having a total reflection band close to the lower limit (λ B ), and then reaches a photonic crystal having a total reflection band close to the upper limit (λ A ). This applies to both the embodiment in which the photonic crystal is designed from λ B to λ B , that is, the embodiment in which the leading edge wavelength value is set, and the embodiment in which the photonic crystal is designed from λ A to λ

[0063] A ), from the lower limit (λ B ) of a predetermined vacuum wavelength range to the upper limit (λ

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[0064] ​​In one embodiment, the photonic crystal is arranged in the mirror in an order defined by the transparency of the first dielectric material and the second dielectric material of the photonic crystal, and a photonic crystal made of a material that is not transparent to radiation in a wavelength range included in the total reflection band of another photonic crystal is arranged downstream of the above-mentioned another photonic crystal in the intended direction of the incident radiation. In other words, the photonic crystal is arranged such that the material of the photonic crystal intended to first receive the incident radiation is transparent to radiation in a wavelength range included in the total reflection band of the photonic crystal arranged to subsequently receive the incident radiation.

[0065] In one embodiment, the number of unit cells in each photonic crystal is 5 or more, preferably 7 or more, more preferably 10 or more.

[0066] In a third aspect of the invention, the invention is a mirror including m one-dimensional photonic crystals where m > 1, each photonic crystal includes a plurality of stacked alternating layers of a first dielectric material and a second dielectric material, and for i = 1,... m, the first dielectric material has a refractive index (n bl,i , n bt,i ) different from the refractive index (n al,i , n at,i ) of the second dielectric material, for i = 1,... m, for each i-th photonic crystal, the first thickness (h al,i , h at,i ) of all layers of the first dielectric material and the second thickness (h bl,i , h bt,i ) of all layers of the second dielectric material have values determined by the steps of any of the methods of the embodiments of the first aspect of the invention, defining a mirror.

[0067] Such a mirror according to a third aspect of the invention corresponds to a mirror that can be obtained by the method according to the first aspect of the invention. When implementing a part of the attached mirror, considering that electron microscopy and photography methods can distinguish the alternating layers of the first and second dielectric materials of each photonic crystal together with their thicknesses and chemical compositions, such a mirror is recognizable.

[0068] The above values, together with the total reflection area and the area without total reflection of the manufactured mirror, make it possible to distinguish the configuration of the mirror corresponding to the performance of the method according to the first aspect of the invention. Therefore, such a completed mirror can be characterized as a mirror designed by the above method by its parameters.

[0069] In one embodiment, a mirror according to a third aspect of the invention is manufactured using the method according to the second aspect of the invention.

[0070] The present invention further defines a photovoltaic cell comprising a mirror according to a third aspect of the invention deposited on a transparent substrate and coated with a metal layer, wherein the photovoltaic cell is a photovoltaic cell or a thermophotovoltaic cell.

[0071] The present invention further defines a photovoltaic cell comprising a mirror according to a third aspect of the invention and a semiconductor substrate, wherein the mirror is disposed on the back surface of the semiconductor substrate and coated with a metal layer, and the photovoltaic cell is a photovoltaic cell or a thermophotovoltaic cell. The semiconductor substrate behaves as a transparent substrate for photons with energy less than the semiconductor electron bandgap.

[0072] The present invention also further defines insulation for an incandescent body, the insulation comprising at least one mirror according to a third aspect of the invention. Advantageously, the insulation effectively reflects the received photons. In one embodiment, the insulation includes at least one photovoltaic cell, at least one thermophotovoltaic cell, at least one radiated power collection device and / or at least one cooling device.

[0073] All features described in this specification (including the claims, the specification, and the drawings) and / or all steps of the described methods can be combined in any combination, except for combinations of features and / or steps that are mutually exclusive.

[0074] These and other features and advantages of the present invention will become clearly understood by considering the detailed description of the preferred embodiments of the present invention, which are given by way of example only and not limitation, with reference to the drawings.

Brief Description of the Drawings

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Figure 8

DETAILED DESCRIPTION OF THE INVENTION

[0076] FIG. 1 shows a schematic view of a monolithic mirror including several one-dimensional photonic crystals (1, 2, 3) according to an embodiment of the present invention, and all the photonic crystals are deposited on a single substrate (not shown). In this figure, the first photonic crystal (1), the second photonic crystal (2), and the third photonic crystal (3) are shown, but the blank in the center of the figure means that more photonic crystals can be present in the mirror. Each photonic crystal includes a plurality of unit cells (U1, U2, U3), and each unit cell (U1, U2, U3) includes two dielectric layers (1.1, 1.2; 2.1, 2.2; 3.1, 3.2) of high and low refractive indices, which are repeated a plurality of times with different thicknesses. In FIG. 1, only a part of the unit cell is identified. The photonic crystals included in the mirror can have different characteristics, that is, the dielectrics forming the unit cells of each photonic crystal can be different in each photonic crystal, and thus can have different refractive indices and different thicknesses, and the thickness of the layer is defined according to the method of the present invention. The mirror thus formed has a very high reflectivity in a very wide range of wavelengths, a wide range of directions (even hemispherical), and different polarizations of incident photons.

[0077] Figure 2 shows the reflectivity (R) as a function of the vacuum wavelength (λ0, in meters) of the one-dimensional photonic crystal. The reflectivity (R) is plotted for normal incidence (solid line), π / 4 rad incidence and TE polarization (dashed line), and π / 4 rad incidence and TM polarization (dotted line) of the incident photons. As can be seen in the figure, the total reflection band of the photonic crystal extends between point 7 and point 8 for normally incident photons, between point 9 and point 10 for π / 4 incident TE photons, and between point 11 and point 12 for π / 4 incident TM photons. In Figure 2, it is possible to understand how the total reflection band is shifted for different angles of incidence and polarizations.

[0078] The forbidden band or band gap of the photonic crystal occurs when the argument α of the second kind Chebyshev polynomial of the characteristic matrix of the photonic crystal goes out of the range -1 < α < +1. The absolute value of the Chebyshev argument is represented for the photonic crystal in Figure 2 for normal incidence (solid line, shown as "17" in the figure), π / 4 rad incidence and TE polarization (dashed line, shown as "18" in the figure), and π / 4 rad incidence and TM polarization (dotted line, shown as "19" in the figure).

[0079] It can be seen that when the absolute value of the Chebyshev argument exceeds the value 1, the total reflection band appears. The edges of the total reflection band are the abscissas of the ends of the segment extending from point 7 to point 8 for normal incidence, the abscissas of the segment extending from point 9 to point 10 for π / 4 rad incidence and TE polarization, and the abscissas of the segment extending from point 11 to point 12 for π / 4 rad incidence and TM polarization. According to the present invention, the wavelengths corresponding to the edges of the total reflection band are calculated using the analysis of the Chebyshev argument, which can be completely analytical. This is much faster and easier than calculating the reflectivity curve.

[0080] For a given 1D photonic crystal, it is clear from Figure 2 that the total reflection band varies in position and width depending on the incident angle of the photons and their polarization. It can also be observed that in the band extending from point 7 to point 12, total reflection is generated for any incident angle up to π / 4 rad and any polarization. The same result occurs for a maximum incident angle of π / 2 rad (horizontal incidence), but in such a case, the band of hemispherical total reflection is narrower. Outside the total reflection band represented by the above segment, the reflectivity curve exhibits a wavy behavior as already described herein.

[0081] The photonic crystal shown in Figure 2 is formed from a pair of a dielectric layer of zinc sulfide having a refractive index of 2.3 and a thickness of 98 nanometers (nm) and a dielectric layer of magnesium fluoride having a refractive index of 1.35 and a thickness of 261 nm, and includes 30 unit cells. All layers are deposited on a glass substrate having a refractive index of 1.52. This material of the substrate does not affect the forbidden band (band gap), but affects the reflection generated outside them. A slight rounding is generated at the corners of the total reflection band. This is due to the finite number (60 in this case) of layers within the photonic crystal. This rounding increases when the number of layers is reduced.

[0082] This method is based on the study of Chebyshev arguments. For a given incident angle (θ) of the radiation, the reflectivity is wavy and less than 1 when |α TE|TM | < 1, and is 1 (total reflectivity) when |α TE|TM | > 1. For a given incident angle, the edges of the total reflection band occur when |α TE|TM | = 1. For the maximum incident angle (θ max ) including θ max = π / 2 corresponding to hemispherical radiation, the leading edge corresponds to vertical radiation and the trailing edge corresponds to TM polarized θ max incidence (horizontal with respect to hemispherical radiation).

[0083] The present invention proposes the use of a plurality of photonic crystals that add individual total reflection bands over a predetermined angular span (in some cases hemispherical) until the desired wavelength span is covered.

[0084] The present invention is based on a variation of variables that enables the description of Chebyshev arguments so that the first thickness (h a ) and the second thickness (h b ) of the unit cell of the photonic crystal can be determined analytically. Based on the calculated thicknesses, the other edge of the total reflection band specific to each 1D-photonic crystal is obtained.

[0085] Advantageously, the method provides highly efficient mirrors with a calculated efficiency of up to 0.999999 and having a wide span of total reflectance bands, for example, from 1.77 to 20 μm.

[0086] In contrast, configurations based on multilayer filters used for monochromatic mirrors (such as the Carniglia reference cited in the background section) do not allow for total reflection bands that include tens of micrometers and thus wavelengths from visible to mid-infrared, nor do they provide the leading and trailing edges of the photonic crystal.

[0087] Although hemispherical or omnidirectional reflectance is referred to herein, the present invention can also be applied when the total reflectance is guaranteed within a maximum incident angle θ max < π / 2.

[0088] For this purpose, the formula for the Chebyshev argument α TE|TM (λ0, θ, n a , n b , h a , h b ) can be written as follows after some mathematical manipulation from the formula in the cited book by Born and Wolf:

Equation

[0089] By making the following variable changes,

Number

Number

[0090] This change of variables provides great insight into the Chebyshev argument properties. α TE|TM (X, Y, Z TE|TM ) function is noted to vary for different radiation angles of incidence. In FIGS. 3 and 4, two plots of α TE|TM (X, Y, Z TE|TM ) versus X are presented.

[0091] The plot in FIG. 3 corresponds to the case of Y = 0. When this occurs, α TE|TM (X, Y, Z TE|TM ) is periodic on the variable X with period 4. In FIG. 3, the case of Z = 3 is plotted with a thick continuous line, and the case of Z = 0.35 (approximately the reciprocal of 3) is plotted with a thin continuous line. This is to emphasize that the values of Z and its reciprocal give the same curve. The cases of Z = 2 and Z = 0.55 (approximately 1 / 2) are plotted with a thick dotted line and a thin dotted line, respectively. The total reflection band occurs when α falls below the -1 gray line. For Z > 1, the total reflection band is wider when Z is larger. For Z < 1, the total reflection band is wider when 1 / Z is larger. When Y = 0, equal fractions of wavelength in the high refractive index layer and the low refractive index layer are achieved.

[0092] In FIG. 4, the cases of Z = 3 and three values of Y are shown. Y = 0 (thick solid line) repeats one of the curves in FIG. 3. In this case, it is the case with the largest total reflection band span. In the other cases shown in the figure, namely Y = 0.5 (dashed line) and Y = -0.45 (dotted line), the curves are approximately the same. This is to emphasize that opposite values of Y give the same α. When Y ≠ 0, α is no longer periodic. Here, the fractions of the wavelength in the high refractive index layer and the low refractive index layer are different.

[0093] Many of the graphics in this specification are expressed as a function of λ0. X and Y are inversely proportional to λ0, but their ratio Y / X = r TE|TM is independent of it, and the same is true for Z. This ratio is as follows

Equation

[0094] Furthermore, the first photonic band gap closest to X = Y = 0 that occurs for λ0 → ∞ is the most interesting. This band (as seen in FIG. 3) is generated when α TE|TM = -1, and thus the two first roots (corresponding to the trailing edge and the leading edge of the first total reflection band respectively) that enclose the first photonic band gap are of interest.

[0095] Among the characteristics that can be extracted from this analysis, it can be seen that the first photonic band gap is the largest when Y = 0, that is, when the fractions of the wavelength inside the high refractive index material and the low refractive index material are the same. The use of conventional waveform equalizers, which are very widely used in monochromatic optics, satisfies this condition. Also, it can be seen that the band gap becomes larger when the ratio n a / n b or n b / n a becomes larger.

[0096] When Y = 0, Equation (3) becomes a periodic function dominated by cos(πX / 2) (having a period of 4 in X), and the solution of α TE / TM + 1 = 0 is analytical. According to this, for a specific trailing-edge wavelength

Number

Number

Number

[0097] The arccos function has an infinite number of solutions {γ, 2π - γ, 2π + γ, 4π - γ, 4π + γ...}. The solution γ corresponds to the trailing edge of the total reflection band, and the solution 2π - γ corresponds to the leading edge of the total reflection band.

[0098] By setting either the trailing-edge wavelength or the leading-edge wavelength, when the thickness of the layer of the unit cell is determined, the photonic crystal is completely and uniquely defined by default by the number N of unit cells forming the crystal and is not included in the Chebyshev arguments as described above. The more unit cells there are, the more square the total reflection band of the photonic crystal becomes.

[0099] According to this method, an unknown band edge opposite to the band edge set at the start of the method is obtained. For the above purpose, Equation (1) is used, and the λ0 root of α + 1 = 0 is obtained by numerical iterative decomposition. Since there are several roots, the initial λ0 set to start the iteration determines the root found.

[0100] In this case, solve α(X,rX,Z)+1 = 0 at X by numerical iterative decomposition that uses the normalized equation (3), starts from the initial value 1 to obtain the trailing edge, and finds the leading edge starting from the initial value 3. Subscripts are removed as they are not necessary. These initial values are found from the scrutiny of FIG. 3. When X is extracted, using equation (2) makes it possible to write the following. [Number]

[0101] θ a and θ b (r TM (also present in) with respect to them, for the leading edge they can be set to 0, and their values can be derived from the Snell's law relationship starting from the vacuum (or air) incident angle θ max and for hemispherical illumination is π / 2: θ a = ArcSin(θ) / n a θ b = ArcSin(θ) / n b .

[0102] Refractive index / n a and n b with respect to them, their values are defined by the material used and to a lesser extent by the preparation of the material. In one embodiment, the material used for the layers of the unit cell is an insulator transparent to light. For the low refractive index layers, MgF2 or CaF2 having refractive indices 1.37397 and 1.4328, and electron band gaps 12.2 and 10 eV respectively are preferred. For the high refractive index layers, ZnS, CdS and TiO2 having refractive indices 2.3677, 2.614 and 2.609, and electron band gaps 2.54, 2.42 and 3.05 eV respectively are preferred. However, other materials including polymers and organic materials may be used.

[0103] In one embodiment, when arranging a photonic crystal in a mirror, in order to avoid absorption of photons before reaching a depth where the photons must undergo interference, a layer of material having a small electron bandgap is not placed in the path of the radiation. For example, the vacuum wavelength corresponding to CdS is λ0 = hc / 2.42e = 5.12×10 -7 m, which does not make this material transparent below 512 nm and is thus opaque to blue and UV radiation. In the case of medium IR radiation, the use of semiconductors is preferred. Since Si and Ge are not transparent to radiation in the visible range, Si and Ge with refractive indices of 3.42 and 4.04 are ideal as high refractive index layers with λ0(Si) = hc / 1.12e = 1.107×10 -6 m and λ0(Ge) = hc / 0.67e = 1.85051×10 -6 m or more.

[0104] Therefore, a photonic crystal containing these semiconductors is preferably placed in a mirror downstream of a photonic crystal having a higher electron bandgap dielectric such that high-energy photons are already reflected by the above photonic crystal when the incident radiation reaches the semiconductor.

[0105] There are many possible techniques for manufacturing the layer of the photonic crystal. Sputtering techniques are interesting in terms of cost and reliability, but other techniques such as MBE (Molecular Beam Epitaxy) or MOVPE (Metal-Organic Vapor Phase Epitaxy) can be very interesting for exploring high refractive index layers.

[0106] FIG. 5 shows the reflectivity curve (upper part of the graph) and the Chebyshev parameter (mainly the lower part of the graph) as a function of the vacuum wavelength (in meters) of the incident photons for two photonic crystals. For both photonic crystals, two cases are represented, namely under normal incidence (θ = 0), as well as under horizontal incidence (θ = π / 2 rad) and TM polarization. The solid line represents the reflectivity (R) and the Chebyshev parameter (α) of the first photonic crystal under normal incidence (θ = 0). The dotted line represents the reflectivity (R) and the Chebyshev parameter (α) of the first photonic crystal under horizontal incidence (for the Chebyshev parameter, θ = π / 2 rad; for the reflectivity, θ = 0.99×π / 2 rad) and TM polarization. The dashed line represents the reflectivity (R) and the Chebyshev parameter (α) of the second photonic crystal under normal incidence (θ = 0). The dash-dotted line represents the reflectivity (R) and the Chebyshev parameter (α) of the second photonic crystal under horizontal incidence (for the Chebyshev parameter, θ = π / 2 rad; for the reflectivity, θ = 0.99×π / 2 rad) and TM polarization. For the reflectivity, an incident light that is approximately horizontal (θ = 0.99×π / 2 rad) is used. The reason for using a light ray that is "approximately" horizontal in the reflectivity is to avoid the existence of a false total reflection band formed by the light rays that do not actually enter the photonic crystal. This is not necessary for the Chebyshev parameter for which horizontal incidence (θ = π / 2 rad) is used.

[0107] In the case of the first photonic crystal, the Chebyshev argument of the first photonic crystal for normal incidence that defines its leading edge is divided at point 24 (solid line) located at the frame edge where α = -1, and the Chebyshev argument of the first photonic crystal for horizontal incidence and TM polarization that defines its trailing edge appears at point 25 (dotted line) in the frame. A hemispherical total reflection band is formed between them, which is the hemispherical total reflection band of the first photonic crystal (extending from point 24 to point 25) as explained in the discussion of FIG. 2. In the case of the second photonic crystal, a hemispherical total reflection band is formed between the point 26 (broken line) that divides the Chebyshev argument of the second photonic crystal for normal incidence that defines its leading edge and the point 27 (dash-dotted line) where the Chebyshev argument of the second photonic crystal for horizontal incidence and TM polarization that defines its trailing edge appears. This is the hemispherical total reflection band of the second photonic crystal (extending from point 26 to point 27).

[0108] The fact that the trailing edge wavelength value (25) of the first photonic crystal coincides with the leading edge wavelength value (26) of the second photonic crystal makes it possible to match the two photonic crystals when the two photonic crystals are deposited on the same substrate, forming a wider hemispherical total reflection band extending from point 24 to point 27. The reflectivity of the mirror including the two photonic crystals is not depicted in the figure and is closer to a square than that presented for the separated photonic crystals.

[0109] Once the leading edge (24) of the first photonic crystal for normal incidence is known, the thicknesses of the two layers of the unit cell are calculated using the equation (6) specialized for normal incidence (also labeled "front side" in the X coordinate of FIG. 6). Next, the trailing edge wavelengths for horizontal radiation and TM polarization are calculated, and the trailing edge of the hemispherical total reflection band of the first photonic crystal is obtained. As already explained, this is obtained by solving the equation α(X, rX, Z)+1 = 0 for X starting from X = 1 for horizontal incidence and TM polarization. Once X is obtained, the trailing edge wavelength (25) is calculated using equation (7) again for horizontal incidence and TM polarization (labeled "rear side" in FIG. 6). FIG. 6 shows a plot of the function α(X, rX, Z)X for normal incidence (solid line) as well as for horizontal incidence and TM polarization (dashed line in FIG. 6). As shown, the dashed curve is slightly aperiodic, which means that Y≠0 for this curve. In the figure, the X values of the front side band edge and the rear side band edge are marked with thick dots.

[0110] For the second photonic crystal, since the trailing edge of the first photonic crystal obtained above becomes the leading edge (26), a complete match of the two total reflection bands is brought about. The calculation method described for the first photonic crystal is repeated for the second photonic crystal. For a mirror including three or more photonic crystals, this process is repeated for every two photonic crystals until the trailing edge of the last photonic crystal is equal to or greater than the maximum vacuum wavelength (λ B ) up to which it is desirable for the hemispherical total reflection band to extend, that is, at the appearance point of the Chebyshev argument for horizontal (θ max = π / 2 rad) incidence and TM polarization of the last photonic crystal. Regarding the initial wavelength of the hemispherical total reflection band of the mirror, it is located at the leading edge (λ A ) of the hemispherical total reflection band of the first photonic crystal, that is, at the splitting point of the Chebyshev argument for normal incidence of the first photonic crystal.

[0111] In the example of FIG. 5, the high and low refractive indices of the first deposited photonic crystal are 3.43 (silicon) and 1.37 (magnesium fluoride), respectively, and the layer thicknesses are 166 nm and 413 nm, respectively. For the second deposited photonic crystal, the refractive indices are 4.04 (germanium) and 1.37 (magnesium fluoride), respectively, and the layer thicknesses are 186 nm and 557 nm, respectively. The two photonic crystals are deposited on two separate glass substrates with a refractive index of 1.52 without front protection (air). The leading edge (24) of the total reflection band of the mirror including the monolithic combination of the first and second photonic crystals is 1.77 μm, corresponding to a photovoltaic cell with an electron bandgap of 0.7 eV, and the trailing edge (27) of the total reflection band of the resulting mirror is 3.32 μm. In the case of a mirror including three or more photonic crystals that are conveniently matched, the trailing edge is much higher.

[0112] In FIG. 5, it can be understood that the total reflection bands at different incident angles and polarizations extend far beyond the total reflection band of hemispherical total reflection extending from point 24 to point 27. This means that there is redundancy in the sense that many photons can find two or more photonic crystals that can reflect them. The same thing happens with horizontal photons with TE polarization, the reflectivity of which is not depicted, but forms a wider total reflection band, and generally the same thing happens with all photons. This explains that good results were obtained even using very thin photonic crystals with few unit cells. The results in FIG. 5 correspond to 10 unit cells per photonic crystal, but often only 7 unit cells yield good results, and this number can be reduced.

[0113] Figure 7 shows the reflectivity (R) curve of a monolithic mirror fabricated with a multi - photonic crystal as a function of the vacuum wavelength in meters. The monolithic mirror is intended to reflect the radiation received hemispherically in the range of 1.77 - 20 μm. In this embodiment, the mirror is formed by a monolithic stack of eight photonic crystals, each photonic crystal having ten unit cells, all of which are monolithically deposited on the back surface of a photovoltaic cell with an electronic bandgap of 0.7 eV (close to that of germanium) and covered with a thick silver layer. In total, the stack has 160 layers of different dielectrics.

[0114] In this figure, the solid line is the reflectivity under normal incidence, and the dashed and dotted lines are the reflectivity curves under θ = 0.99×π / 2 rad and TE and TM polarizations, respectively. The radiation spectrum in the range of 1.77 - 20 μm, emitted by a blackbody at 1410 °C (the melting point of metallurgical silicon), whose emission spectrum is shown in Figure 8, is unpolarized (equal number of TE photons and TM photons) and averaged by the energy spectrum at all hemispherical angles of incidence. The average reflectivity under this radiation spectrum is 0.999999. Thus, in this example, a hemispherical total - reflection band with a width of 18.24 μm is achieved with a given average energy efficiency. It should be noted that the best results obtained using theoretical magnetic materials and genetic algorithms in Qiang, H., Jiang, L., Li, X.: “Design of broad omnidirectional total reflectors based on one - dimensional dielectric and magnetic Photonic Crystals”, Optics and Laser Technology 42(1), 105 - 109 (2010), doi:10.1016 / j.optlastec.2009.05.006 result in a hemispherical total - reflection band of 6.80 μm, which is in contrast to the 18.24 μm achieved in the example of Figure 7, and no efficiency data is given.

[0115] In this embodiment, the high refractive index material of the photonic crystal is zinc sulfide, silicon, or germanium (depending on the specific photonic crystal), the low reflectivity material is magnesium fluoride, and their thicknesses vary for each photonic crystal. The layers described in relation to the embodiment of FIG. 5 are part of this mirror. As already mentioned, the use of a substantially horizontal incidence (θ = 0.99×π / 2 rad) is to avoid the apparent total reflection of photons that do not enter the mirror.

[0116] The present invention also defines insulation for an incandescent body, and the insulation comprises at least one mirror according to the present invention. Preferably, the insulation comprises a plurality of mirrors according to the present invention. The incandescent body may be part of, inter alia, a furnace or a system for energy storage.

[0117] In the above embodiment, a very high-quality mirror is designed according to the method of the present invention by repeating from a low wavelength to a high wavelength. In the present invention, it is equally possible to design a similar structure that starts from a high wavelength and then repeats towards shorter wavelengths. When the trailing-edge wavelength is known, using Equation (5), the thickness of the layers of the unit cell for horizontal incidence can be easily obtained, and the successive leading edges are calculated starting from X = 3 using the solution at X where α(X, rX, Z)+1 = 0, and this is converted to a wavelength using Equation (7).

[0118] A possible application of the present invention is the lining of a furnace for storing the energy of molten silicon at 1410°C. The silicon is held in a container heated by a resistor, microwave, or other means. This energy is ultimately extracted as electricity by means of thermophotovoltaic power.

[0119] In one embodiment of the present invention, the insulation of the incandescent container is a packaging material including monolithic mirrors of a plurality of multi-photonic crystals. These mirrors reflect photons emitted by the incandescent container with very high efficiency. The average reflectivity for blackbody radiation at 1410 °C in the range of 0.6 μm to 35 μm (the power outside this range can be ignored) for all hemispherical directions of unpolarized radiation is 0.9998, which constitutes a very good heat insulator. In fact, the connections to the resistor that heats the container and some pivots necessary to hold the container in place leak heat, but they should be reduced to the extent strictly necessary to ensure electrical input and mechanical stability.

[0120] In a preferred embodiment, the mirrors for insulating the incandescent body as described above include 15 photonic crystals each including 7 unit cells, monolithically deposited on a metal covered with a thick layer of silver or gold. Several materials are used for the high refractive index layer, namely zinc sulfide (2.614), silicon (3.42) and germanium (4.04). Magnesium fluoride (1.374) is used for the low refractive index layer in every photonic crystal. The mirror includes a total of 210 layers. The mirror is designed by the method of the present invention using the equation n a h a =n b h b (Equation 6, normal incidence). Using the above procedure, weighted by the blackbody radiation spectral power density at 1410 °C within a bandwidth of 0.6 to 20 μm, and expanding this weighted average to all hemispherical collision angles and polarizations of the incident radiation, an average efficiency of 99.9899% is calculated. According to the Stefan-Boltzmann law, the radiation power of the blackbody at 1683 K (1410 °C) is 45.5098 W / cm 2 and with the calculated average reflectivity, the reflected power in the range of 0.6 to 20 μm is 45.3341 W / cm 2 and the reflectivity outside this range is estimated by the inventors to be 70%, and in the leftmost range of 0 to 0.6 μm, the reflected power is 0.0158632 W / cm 2is brought about, and in the rightmost range of 20 to ∞ μm, the reflected power is 0.150173 W / cm 2 is brought about. The difference between the incident power and the reflected powers of the three components in total is 0.00970275 W / cm 2 which is the power absorbed and lost due to the heat insulation of the lining. This power is easily dissipated to the surroundings without substantially increasing the temperature of the mirror. The typical loss of state-of-the-art lining for fire resistance / heat insulation exceeds 1 W / cm 2 . Therefore, this calculation gives more than 100 times less heat loss by this mirror lining.

[0121] In one embodiment, part of the mirror's packaging material is replaced by a thermophotovoltaic cell. In their manufacture, a mirror incorporating a multi-photonic crystal is deposited on the back of the thermophotovoltaic cell to reflect many photons with energies too low to generate a photocurrent back into the hot container and thus be hardly absorbed. In a thermophotovoltaic cell adapted to convert the blackbody spectrum at the melting silicon temperature (1410 °C), the wasted photons are less than 0.7 eV and correspond to a wavelength of 1.77 μm. The mirror is deposited on the back of the cell during the manufacture of the semiconductor cell and is conveniently finished with a layer of silver or gold to form the back electrical contact. The reflectivity curves appear in Figure 7 and their behavior has been previously described herein. As stated here, an average hemispherical reflectivity of 0.999999 is obtained at 1.77 to 20 μm. However, the reflected power is substantially less today due to different losses in the thermophotovoltaic cell, but this result could stimulate important progress in thermophotovoltaic efficiency.

[0122] Regarding coating the monolithic mirror of the multi-photonic crystal with silver or gold, the zone of total reflection remains unchanged, but the outer zones increase its reflectivity significantly, but not as much as the zone of total reflection. This could be of practical interest in many applications.

[0123] In another use, the monolithic mirror according to the present invention can be used for a parabolic mirror of a celestial telescope deposited on a hexagonal tessera, which usually constitutes the parabolic mirror, and the small curvature of the tessera does not affect its manufacture. Instead of receiving only light perpendicular to the telescope within a medium wavelength band achievable with a single photonic crystal, this mirror can operate to receive light of a complete filament over a very wide spectrum.

[0124] For mirrors designed and / or manufactured in accordance with the present invention, many other uses can be envisioned.

Claims

1. For an incident unpolarized radiation having an incident angle (θ) equal to or less than a predetermined maximum incident angle (θ ｍａｘ ), a method for designing a mirror having a total reflectance in a predetermined vacuum wavelength range ([λ Ａ , λ Ｂ ), comprising: The mirror includes a plurality of one-dimensional photonic crystals forming layers, each photonic crystal includes a plurality of unit cells repeatedly identical a predetermined number of times, each unit cell includes a layer of a first dielectric material and a layer of a second dielectric material, the first dielectric material and the second dielectric material have different refractive indices, Vacuum wavelength (λ ０ ) as a function of the reflectance of each photonic crystal at the leading-edge wavelength value 【Number 1】 and the trailing edge wavelength value 【Number 2】 the interval between 【Mathematics 3】 shows a rectangular pulse shape having a rounded corner of height 1, the pulse at the interval is identified as a total reflection band, the leading edge wavelength value and the trailing edge wavelength value depend on the incident angle (θ) and polarization of the incident radiation, The method is i = 1,... For m, the following (a) the leading edge wavelength value of the total reflection band of the i-th photonic crystal when θ = 0 【Number 4】 setting, and selecting the first dielectric material and the second dielectric material to form the unit cell of the i-th photonic crystal; (b) the first thickness (h ａｌ，ｉ ) of the layer of the first dielectric material of the i-th photonic crystal and the second thickness (h ｂｌ，ｉ ) of the layer of the second dielectric material of the i-th photonic crystal are determined as follows: 【Number 5】 where n ａｌ，ｉ and n ｂｌ，ｉ are respectively the refractive indices of the first dielectric material and the second dielectric material selected for the i-th photonic crystal, step (c) Using the values of the first thickness (h ａｌ，ｉ ) and the second thickness (h ｂｌ，ｉ ), the trailing edge wavelength value of the total reflection band of the i-th photonic crystal 【Number 6】 as 【Number 7】 determined as a step of wherein the parameter X is obtained by solving the equation α ｍａｘ + 1 = 0 for X with respect to a predetermined maximum incident angle (θ ＴＭ ), and the equation is solved by an iterative method with an initial value of X = 1, wherein 【Number 8】 is a step of In step (a), the leading edge wavelength value 【Number 9】 is When i = 1, λ Ａ a value equal to, and When i > 1, θ = θ ｍａｘ and the trailing edge wavelength value of the total reflection band of the (i - 1)th photonic crystal for TM polarization 【Number 10】 set to a value equal to Here, m is the trailing edge wavelength value of the total reflection band of the m-th photonic crystal for θ = θ ｍａｘ and TM polarization 【Number 11】 is λ Ｂ A method which is the number of the photonic crystals satisfying the condition of being λ or more.

2. For incident unpolarized radiation having an incident angle (θ) below a predetermined maximum incident angle (θ ｍａｘ ), a method for designing a mirror having a maximum reflectance in a predetermined vacuum wavelength range ([λ Ａ , λ Ｂ ), comprising: The mirror includes a plurality of one-dimensional photonic crystals forming layers, each photonic crystal includes a plurality of unit cells repeatedly identical a predetermined number of times, each unit cell includes a layer of a first dielectric material and a layer of a second dielectric material, the first dielectric material and the second dielectric material have different refractive indices, Vacuum wavelength (λ ０ ) as a function of the reflectance of each photonic crystal at the leading-edge wavelength value 【Number 12】 and the trailing edge wavelength value 【Number 13】 and the interval between 【Number 14】 shows a rectangular pulse shape having a rounded corner of height 1, the pulse at the interval is identified as a total reflection band, the leading edge wavelength value and the trailing edge wavelength value depend on the incident angle (θ) and polarization of the incident radiation, The method is i = 1,... For m, the following (a) θ = θ ｍａｘ and the trailing edge wavelength value of the total reflection band of the i-th photonic crystal for TM polarization 【Number 15】 setting, and selecting the first dielectric material and the second dielectric material to form the unit cell of the i-th photonic crystal; (b) the first thickness (h ａｔ，ｉ ) of the layer of the first dielectric material of the i-th photonic crystal and the second thickness (h ｂｔ，ｉ ) of the layer of the second dielectric material of the i-th photonic crystal are determined as follows: 【Number 16】 where n ａｔ，ｉ and n ｂｔ，ｉ are the refractive indices of the first dielectric material and the second dielectric material selected for the i-th photonic crystal, respectively, wherein 【Number 17】 is a step of (c) Using the values of the first thickness (h ａｔ，ｉ ) and the second thickness (h ｂｔ，ｉ ) calculated in step (b), the leading edge wavelength value of the total reflection band of the i-th photonic crystal 【Number 18】 as 【Number 19】 determined as a step of In the formula, the parameter X is obtained by solving the equation α ＴＭ + 1 = 0 for X when θ = 0, and the equation is solved by an iterative method with an initial value of X = 3, wherein 【Number 20】 is a step of In step (a), the trailing edge wavelength value [Number 21] is When i = 1, λ Ｂ a value equal to, and When i > 1, the leading edge wavelength value of the total reflection band of the (i - 1)-th photonic crystal for θ = 0 【Number 22】 set to a value equal to Here, m is the leading edge wavelength value of the total reflection band of the m-th photonic crystal when θ = 0 【Number 23】 is λ Ａ A method which is the number of the photonic crystals satisfying the condition of being λ or more.

3. λ Ａ is included in the visible or near-infrared range and / or λ Ｂ is included in the mid-infrared range, the method according to claim 1 or 2.

4. The predetermined maximum incident angle (θ ｍａｘ ) is such that θ ｍａｘ < π / 2, and the method according to any one of claims 1 to 3.

5. The predetermined maximum incident angle (θ ｍａｘ ) is 0.99π / 2, the method according to any one of claims 1 to 4.

6. A method for manufacturing a mirror including m one-dimensional photonic crystals with m > 1, comprising the following designing the mirror according to the method according to any one of claims 1 to 5; forming m stacked one-dimensional photonic crystals. Each i-th photonic crystal is formed by laminating a plurality of alternating layers of a first dielectric material and a second dielectric material, the first dielectric material having a refractive index (n ｂｌ，ｉ , n ｂｔ，ｉ ) different from the refractive index (n ａｌ，ｉ , n ａｔ，ｉ ) of the second dielectric material, For i = 1,..., m, for each i-th photonic crystal, the first thickness (h ａｌ，ｉ , h ａｔ，ｉ ) of all the layers of the first dielectric material and the second thickness (h ｂｌ，ｉ , h ｂｔ，ｉ ) of all the layers of the second dielectric material have the values determined in step (b) of any one of claims 1 to 5, a method.

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

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

9. The layer of the photonic crystal is covered with a thick protective transparent layer, preferably transparent in the range of [λ Ａ , λ Ｂ . The method according to any one of claims 6 to 8.

10. (a) the photonic crystal is arranged in the mirror in an order defined by the positions of those total reflection bands from λ Ａ to λ Ｂ or (b) the photonic crystal is arranged in the mirror in an order different from the order defined by the positions of those total reflection bands from λ Ａ to λ Ｂ ​ The method according to any one of claims 6 to 9.

11. The photonic crystal is arranged in the mirror in an order defined by the transparency of the first dielectric material and the second dielectric material of the photonic crystal, and a photonic crystal made of a material that is not transparent to radiation in a wavelength range included in the total reflection band of another photonic crystal is arranged downstream of the other photonic crystal in the intended direction of the incident radiation. The method according to any one of claims 7 to 10.

12. The method according to any one of claims 6 to 11, wherein the number of unit cells in each photonic crystal is 5 or more, preferably 7 or more, more preferably 10 or more.

13. A method for manufacturing a mirror including m one-dimensional photonic crystals where m > 1, the mirror being manufactured according to the method according to any one of claims 6 to 12, the predetermined maximum incident angle (θ ｍａｘ ) being 0.99π / 2, a method for manufacturing a mirror.

14. A method for manufacturing a photovoltaic cell, comprising a mirror manufactured by the method for manufacturing a mirror according to claim 13, deposited on a transparent substrate and coated with a metal layer, and manufacturing a photovoltaic cell that is a thermophotovoltaic cell.

15. A method for manufacturing a photovoltaic cell, comprising a mirror manufactured by the method for manufacturing a mirror according to claim 13 and a semiconductor substrate, wherein the mirror is deposited on the back surface of the semiconductor substrate and coated with a metal layer, and the photovoltaic cell is a thermophotovoltaic cell.

16. A method for manufacturing a heat insulating material, manufacturing a heat insulating material for an incandescent body, including at least one mirror manufactured by the method for manufacturing a mirror according to claim 13.

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