Device for concentrating a spectral distribution of quantum waves around a target wavelength and associated solar generator

Abstract

The device can have an emitter layer having an emitter thickness demi and a refractive index nemi satisfying the relationship Formula (I), where k is an integer greater than or equal to zero, a resonator layer disposed adjacent the second face of the emitter layer, the resonator layer having a thickness dres and a refractive index nres satisfying the relationship Formula (II), where I is an integer greater than or equal to zero, a reflector layer disposed against the resonator, a first zone adjacent the first face of the emitter layer, opposite the second face, and a second zone disposed adjacent the second face of the emitter layer, opposite the first face, the first zone and the second zone being asymmetric relative the emitter layer.

Description

DEVICE FOR CONCENTRATING A SPECTRAL DISTRIBUTION OF QUANTUM WAVES AROUND A TARGET WAVELENGTH AND ASSOCIATED SOLAR GENERATORBACKGROUND

[0001] Some devices could benefit form concentrating the energy of electromagnetic waves around a given wavelength. For instance, one of the greatest challenges of using the sun as a source of energy is that the sun radiates energy in the form of electromagnetic waves spectrally distributed in a “black body curve”, minus some atmospheric absorption effects, leading to a curve, when experienced at sea level, having a peak around 500 nm (wavelength), in the middle of the range of visible light, with intensity decreasing progressively from there for lower (extending into ultraviolet) and higher (extending significantly into infrared) wavelengths. On the other hand, solar cells may have an efficiency which is highest at a specific wavelength, and decreases rapidly for wavelengths below and above that specific wavelength. Such solar cells may only be efficient in absorbing energy from a very narrow band of the sun radiation’s overall spectral distribution. Solar cells are an example of a device which would benefit from coupling with a device which would concentrate the energy of electromagnetic waves around a given, target wavelength, which could be selected in this case to match the narrow absorption band of the solar cell.SUMMARY

[0002] It was found that quantum properties of structures constituted good candidates for devices which could concentrate the energy of electromagnetic waves around a target wavelength, namely quantum properties of structures associated to the formation of polaritons. More specifically, parity time (PT) symmetry is a configuration for which a non-Hermitian Hamiltonian can exhibit real eigenvalues and thus constitute a quantum mechanical observable. Promising candidates of systems described by PT-symmetric Hamiltonians are photonic systems having engineered refractive indices, for instance. The design of photonic structures leading to the degeneracy of upper and lower polariton states and to the emergence of “exceptional points” can be exploited for the realization of a device capable of concentrating a spectral distribution of electromagnetic waves around a target wavelength At. For instance, exceptional points can be achieved by breaking the mirror symmetry or adjusting theasymmetry factor of the device, thus inducing a “bound state in the continuum” (BIC), which can form a resonance with an exceptionally high quality factor, to obtain light emission possessing high directionality and tunability. This concept of spectral conversion can also be applied to other types of quantum waves, such as phonons (atomic or molecular vibrations) or magnons (spin waves).

[0003] More specifically, it was found likely that a device having the following structure could be embodied in a manner to be operable to concentrate a spectral distribution of quantum waves around a target wavelength. More specifically, the device can have a layered (e.g. laminar) structure including in sequence an emitter layer, a resonator and one or more reflector layer. A first zone may be defined adjacent a first face of the emitter layer, opposite the resonator layer, and a second zone may be defined adjacent the second face of the emitter layer, including the resonator layer. The first zone and the second zone are asymmetric relative to the emitter layer, from the perspective of propagation of the quantum waves (e.g., define asymmetrical optical paths). Typically, the device would be supported by a substrate, and it may be more convenient for the substrate to be disposed against the one or more reflector layer. A first way to achieve asymmetry, breaking the out-of-plane mirror symmetry, is to leave the first face of the emitter layer exposed. The device may further include one or more layers in the first zone, such as another resonator and one or more additional reflector layers, while still forming asymmetrical wave propagation paths on opposite sides of the emitter layer, but this is optional.

[0004] In accordance with one aspect, there is provided a device for concentrating a spectral distribution of quantum waves around a target wavelength At, the device comprising : an emitter layer having an emitter thickness demiand a refractive index nemisatisfying the relationship demi* nemi= ( / c + l) y , where k is an integer greater than or equal to zero, the emitter thickness demidefined between a first face and a second face and defining an emitter propagation path for the quantum waves from the first face to the second face, across the emitter thickness, the emitter layer operable to interact with the quantum waves by absorbing at the spectral distribution and emitting at the target wavelength At; a resonator layer disposed adjacent the second face of the emitter layer, the resonator layer having a thickness dresand a refractive index nressatisfying the relationship dres* nres= ^(l + , where I is an integergreater than or equal to zero; a reflector layer disposed against the resonator; a first zone adjacent the first face of the emitter layer, opposite the second face, and a second zone disposed adjacent the second face of the emitter layer, opposite the first face, the first zone and the second zone being asymmetric relative the emitter layer from the perspective of propagation of the quantum waves. It may be preferable for the resonator layer to be disposed directly against the second face of the emitter layer, as this may maximize efficiency, but in some embodiments, it may nonetheless be preferred to provide another layer between the resonator layer and the emitter layer for one reason or another.

[0005] In accordance with another aspect, there is provided a solar generator comprising : a photovoltaic cell having a maximum conversion efficiency at a target wavelength At, a device operable to concentrate the spectral distribution of sunlight around the target wavelength At, the device having : an emitter layer optically coupled to both a source of sunlight and to the photovoltaic cell, the emitter layer having an emitter thickness demiand a refractive index nemiA satisfying the relationship demi* nemi= ( / c + 1) y , where k is an integer greater than or equal to zero; a resonator layer disposed against the emitter layer, the resonator layer having a thickness dresand a refractive index nressatisfying the relationship dreswhere I is an integer greater than or equal to zero; a reflector layer disposed against the resonator; a first zone adjacent the first face of the emitter layer, opposite the second face, and a second zone disposed adjacent the second face of the emitter layer, opposite the first face, the first zone and the second zone being asymmetric relative the emitter layer from the perspective of propagation of the sunlight.

[0006] In accordance with another aspect, there is provided a device having an emitter layer having an emitter thickness demiand a refractive index nemisatisfying the relationship demi*nemi = (k + l) y , where k is an integer greater than or equal to zero, a resonator layer disposed against the second face of the emitter layer, the resonator layer having a thickness dresand a refractive index nressatisfying the relationship dreswhere I is aninteger greater than or equal to zero, a reflector layer disposed against the resonator, a first zone adjacent the first face of the emitter layer, opposite the second face, and a second zonedisposed adjacent the second face of the emitter layer, opposite the first face, the first zone and the second zone being asymmetric relative the emitter layer.

[0007] Many further features and combinations thereof concerning the present improvements will appear to those skilled in the art following a reading of the instant disclosure.DESCRIPTION OF THE FIGURES

[0008] In the figures,

[0009] Fig. 1 is a view of an example of a device for concentrating a spectral distribution of quantum waves around a target wavelength;

[0010] Fig. 2 is a view of an example solar generator;

[0011] Figs 3A to 3C are graphs showing dispersion relations for positive, zero and negative detuning, respectively;

[0012] Figs 4A to 4C are graphs showing dispersion relations for different coupling coefficient values for a given detuning;

[0013] Fig. 5 is a schematic view illustrating an example photonic structure;

[0014] Fig. 6A and 6B are graphs showing reflectance and angle-resolved reflectance (ARR) at normal incidence with and without quantum dots, respectively; and

[0015] Fig 7 includes 6 graphs showing angle-resolved photoluminescence for quantum dot layer thicknesses of 92nm, 96nm, 100nm, 104nm, 108nm, 112nm.DETAILED DESCRIPTION

[0016] Fig. 1 shows an example of a device 10 to concentrate a spectral distribution of quantum waves around a target wavelength. More specifically, the device 10 can have a layered (e.g. laminar) structure including in sequence an emitter layer 12, a resonator layer 14 and one or more reflector layer 16. A first zone 18 may be defined adjacent a first face of the emitter layer 12, opposite the resonator layer 14, and a second zone 20 may be defined adjacent the second face of the emitter layer 12, including the resonator layer 14. The firstzone and the second zone are asymmetric relative the emitter layer 12, from the perspective of propagation of the quantum waves (e.g., the first and second zones 18, 20 define asymmetrical optical paths). Typically, the device would be supported by a substrate 22, and it may be more convenient for the substrate 20 to be disposed against the one or more reflector layer 16. A first way to achieve asymmetry is to leave the first face of the emitter layer exposed. Alternately, the device 20 may further include one or more layers in the first zone, such as another resonator and one or more additional reflector layers, while still forming asymmetrical wave propagation paths on opposite sides of the emitter layer, but this is optional.

[0017] The emitter layer 12 can be configured for absorbing the quantum waves more broadly within the spectral distribution, and re-emitting the energy more narrowly around the target wavelength. There are several types of materials which can perform the function desired in the emitter layer 12. One category of such materials are quantum dots. For instance, CsPbBra and CdSe / ZnS coreshell quantum dots may be used in some embodiments. Quantum dots based on CsPbBra structure, but where the Br atoms are replaced by one or more other halogen, and / or where the Pb is replaced by artificial chemical groups to obtain lead-free perovskites, may be suitable as well in some embodiments. Otherwise, photophores or crystalline defects, such as a diamond structure having n-v defects may be used instead of quantum dots. The example materials presented above may be suitable for embodiments where the target wavelength lies within the visible spectrum. Yet other materials may be used in embodiments where the target wavelength lies outside the visible spectrum, for instance.

[0018] It was also found in some embodiments that the desired effect was more likely if the emitter layer 12 forms a wave propagation path having a multiple of one half of the targeted wavelength At, across its thickness (between the first face and the second face). In some embodiments, a relatively high degree of precision may be needed to reach the desired results, such as a tolerance of ± At / 50 or a tolerance of ± At / 100. The wave propagation path can be referred alternately as an optical path herein for simplicity, whether or not the waves are photons or photons in the visible spectrum.

[0019] It will also be noted here that the effective dimension of the optical path may be affected both by thickness d and by effective refractive index n (which may be referred to as refractive index for short herein). Indeed, both porosity and the nature of the material mayaffect the effective refractive index. The refractive index of empty space, and to a close approximation, air, is 1 , and the refractive index of many materials adapted to quantum wave propagation are often significantly higher than 1 , often around 1.5. Accordingly, the effective refractive index can be affected by the proportion of empty space or air, which can correlate with porosity.

[0020] For convenience, a notion of optical path difference (OPD) can be defined. The OPD can be defined as OPD = d * n . For the emitter layer having a thickness demiand a refractive index nemi, an OPDemisatisfying the relationship demi* nemi= ( / c + l) y may be sought, where k is an integer greater than or equal to zero. A relatively high degree of precision may be desired to achieve a satisfactory degree of performance in some embodiments, such asnemi), f°rinstance. While k can be greater than zero in some embodiments, it can be preferred to limit k to zero, or to as close as possible to zero in some embodiments, within the limits of feasibility, as this may minimize losses and / or maximize coupling with the remainder of the wave propagation structure.

[0021] The resonator layer 14 can be selected in a manner to provide a spacing between the second face of the emitter layer 12 and the reflector layer 16 which has the effect of imparting a phase shift of TT / 2 in the time domain. This can be achieved by selecting a resonator which has a thickness dresand an refractive index nreswhich satisfy the relationship 2dresnres + TT / 2 = 2TT in the time domain. Referring back to the concept of OPD, for the resonator, it can be desired for 0PDres= dresis an integer greater than or equal to3A A 1 zero, and where — - are possible solutions. In some embodiments, desired resultsmay be achieved with a lower degree of precision for the value of OPDresthan for the value of OPDetT1i. For instance, in some embodiments it can be desired fornres ±2 / 5 (dres* nres), or = dres* nres± 2 / 25 (dres* nres). The material of the resonatorlayer 14 can be selected in a manner to minimize absorption losses (i.e., to be as transparent as feasible to the spectral distribution of quantum waves). For the latter reason, a high porositymay be preferred in some embodiments, though on the other hand, when porosity is too high the layer may become brittle and be found to have insufficient structure, so a balance between porosity and structure may be sought in some embodiments. While I can be greater than zero in some embodiments, it can be preferred to limit I to zero, or to as close as possible to zero in some embodiments, within the limits of feasibility, as this may minimize losses and / or maximize coupling with the remainder of the wave propagation structure.

[0022] The one or more reflector layer 16 can be disposed in a manner to interact with the quantum waves by reflecting them in a manner to impart a phase shift of TT / 2 in the time domain. Depending on the embodiment, the value of TT / 2 may be targeted more or less precisely. For the first, or only reflector layer 16, the value may be achieved based on the characteristics of the resonator layer 16. It is believed more likely that the desired results can be achieved by targeting TT / 2 with a tolerance of ±TT / 4, with a tolerance of ±TT / 8, or with a tolerance of ±TT / 16. There may be a single reflector layer 16, which can be a metallic layer for instance, or a semiconductor layer such as a silicon layer. There can be more than one reflector layer 16, such as a sequence of semiconductor layers forming a laminar structure and having corresponding thickness and corresponding refractive indices, where the refractive indices of individual ones of the reflector layers 16 can be different than the refractive indices of adjacent ones of the reflector layers (or other layers). When there are more than one reflector layer 16, the laminar structure of reflector layers may be terminated by a metallic layer acting as a mirror for instance, or not. Any intermediary layer between the resonator layer 14 and the last reflector layer 16 can take into consideration the other reflector layers 16 in the laminar structure and the reflecting surface of the additional reflector layers 16 can be spaced apart from the resonator layer 14 by multiples of At / 4.

[0023] For instance, reintroducing the notion of OPD for the one or more intermediary reflector layers 16 can have a thickness dref and a refractive index nref satisfying the relationship 0PDref = dref *nref =+ ~) where m is an integer greater than or equal to zero. In some embodiments, desired results may be achieved with a lower degree of precision for the value of OPDref than for the value of OPDemi. For instance, in some embodiments it can be desired25(<irey * nre ). The material of the one or more reflector layers can be selected in a mannerto minimize absorption losses (i.e. , to be as transparent as feasible to the spectral distribution of quantum waves). For the latter reason, a high porosity may be preferred in some embodiments, though on the other hand, when porosity is too high the layer may become brittle and be found to have insufficient structure, so a balance between porosity and structure may be sought in some embodiments. Moreover, it can be preferred to maximize contrast between the refractive indices of adjacent layers, such as by varying porosity, within the limits of feasibility. While m can be greater than zero in some embodiments, it can be preferred to limit m to zero, or to as close as possible to zero in some embodiments, within the limits of feasibility, as this may minimize losses and / or maximize coupling with the remainder of the wave propagation structure.

[0024] In some examples, for instance, alternating layers of silicon having different porosities can be used to form the resonator layer 14 and multiple reflector layers 16, where reflector layers 16 have alternating values of a first, less porous layer, and a second, more porous layer, and where the resonator layer 14 can have the second porosity for instance. The porosity of the second, porous layer can be the same as the porosity of the resonator layer 14 for instance. In such embodiments, it can be desired to increase contrast between the two different porosities to maximize reflection, while using higher porosities so as to minimize loss and avoiding porosities which are so high as to impart mechanical weakness in the structure or generate light emission. Porosities around 85% and 50%, such as 51 ± 2 % and 87 ± 3 % for example, can be suitable in some embodiments. Other semiconductors than silicon may be used in some embodiments.

[0025] In the case of silicon-based reflector layers 16 in the visible spectrum, it was found that using more than three layers, or more than 5 layers, could be preferred. In such embodiments, while using more than 10 reflector layers may not impede efficiency, layers above 10 may not significantly increase efficiency either, and therefore it may be found more suitable to use between about 5 and 10 layers for instance. These details are provided for the sake of illustration only, and it will be understood that such specifications may be adapted significantly to different embodiments, such as embodiments based on reflector layers made of other semiconductors than silicon or to applications outside the visible spectrum for instance. Alternatives to silicon reflector layers can include other semiconductors and their alloys, suchas Ga, As, In, P, Ge, etc, or other dielectric materials such as glass, to the extent that such materials may be handled satisfactorily in the given context.

[0026] Porosified silicon layers can be produced using technology known in the art. In some embodiments, a laminated structure including one or more reflector layers (which may be porous or not depending on the embodiment, and may be of a same material having different porosities or of different materials depending on the embodiment, for instance) and a resonator layer can be produced as a first step, and the emitter layer can be added by immerging the laminated structure in the material of the emitter layer in liquid phase until the liquid evaporates, leaving an emitter layer on top of the laminated structure. It is to be noted that this is but one example of how a layer, or a sequence of layers, of carefully controlled thicknesses can be applied. In other embodiments, a suitable structure may be produced via drop-casting, spin-coating, dip-coating, CVD deposition, etc.

[0027] In some embodiments, a metal layer can be used as a reflector layer 16 underneath the semiconductor layers acting as intermediary reflector layers. In some embodiments, an aperiodic structure may be used instead of a periodic structure to form a suitable reflector, such as an aperiodic photonic structure defined by a conjugated Fibonacci sequence to name one example. In still other embodiments, one or more metasurfaces may be associated to either one of the layers, namely as a reflector layer. In many cases, applying the resonator layer directly against the emitter layer will lead to better performance, however, there may be some embodiments where introducing a limited number of one or more intermediary layers, such as one or more additional reflector layer or perhaps a layer of air or vacuum, between the resonator layer and the emitter layer may be suitable. This can be the case where an aperiodic structure is used instead of a periodic structure for instance. This can be the case if the one or more additional layer otherwise meet the thickness or wave traveling distance criteria, such as by using a layer which has a thickness corresponding to one wavelength for instance.

[0028] It will be noted that in some embodiments, a resonator layer 14 and one or more reflector layers 16 may also be disposed against the first face of the emitter layer 12, while maintaining assymetrical optical paths on opposite sides of the emitter layer 12 and an overall structure based on the theory presented in greater detail below.

[0029] In some embodiments, it was found that the presence of defects or variability in terms of layer thickness affected results much more significantly when they affected the emitter layer or the resonator layer than when they effected the reflector layers.

[0030] In some embodiments, a device 10 for concentrating a spectral distribution of quantum waves around a target wavelength Atin accordance with the explanations above can be used in the context of a solar generator 24. An example of such an embodiment is presented in Fig. 2.

[0031] Referring to Fig. 2, a solar generator 24 may have one or more photovoltaic cell having a maximum conversion efficiency at the target wavelength At, optically coupled to a device for concentrating the spectral distribution of sunlight around the target wavelength At. A solar concentrator 26, such as an arrangement of concave mirrors M1 and M2 as shown in Fig. 2, may be used between the source of sunlight and the device 10, and another concentrator 28, such as the concave mirror M3, can be used between the device 10 and the photovoltaic cell 30. The photovoltaic cell 30 can more generally be referred to as an absorber and / or as a photo-current generator.

[0032] In some embodiments, the photovoltaic cell 30 can be monochromatic. In some embodiments, the photovoltaic cell 30 can be based on a Tamm structure, which can have the particularity of generating plasmons-polaritons, a quasiparticle which may be similar to the ones used in the device for concentrating the spectral distribution of the source radiation. Such a Tamm structure may be achieved with a structure similar to the structure described above in relation with Fig. 1 , but where the emitter layer 12 is replaced by a fine metallic layer, to name one possible example.

[0033] EXAMPLE

[0034] In an example, a polaritonic structure is constructed using a single Distributed Bragg Reflector plus defect scheme on top of which we add a quantum dot layer, which can be considered as part of the cavity itself as opposed to as a small perturbation inside the cavity. The structure can exhibit PT-symmetric symmetries in the cavity itself that could be observed by measuring the dispersion relations of polaritons.

[0035] The results presented below are based reflection and transmission calculations using the transfer matrix method. This method based on refractive indexes and thicknesses in stratified media is a tool to compute efficiently and quickly light propagation in photonic cavities and is used in a variety of research articles studying polaritons. A perovskite-type two-level emitter, CsPbBr3in particular, and porous silicon were chosen here to provide an example of materials that could be used experimentally, yet any excitonic material could be used instead of perovskites, and many other materials such as Ga,As,Ge, other dielectric materials, ... could be used for the photonic structure.

[0036] Polaritons are quasiparticles generated through a strong coupling interaction between an excitonic material and photons. To achieve strong coupling, the electromagnetic field from the photons must be confined thanks to photonic cavities to maximize the interactions between the photons and the excitons

[0037] A common way to describe excitons-polaritons is to use the Jaynes-Cummings model, corresponding to the following Hamiltonian:

[0038] H = j

[0039] This Hamiltonian has for eigenstates two polaritons called upper and lower polaritons, defined as:

[0040] \UP) = Cx\X) + CP|P)

[0041] \LP} = Cx\X} — CP\P}

[0042] Associated to the eigenvalues, or energies:

[0044] Where fl =stands for the Rabi frequency, and Exand Ecare the energies forrespectively, the excitonic state, and the coupled cavity mode. 8 = Ec- Exis often referred to as detuning. Depending on its sign, three cases can be observed as represented by Figs.3A, 3B and 3C yet, for the clarity of the discussion, only the positive detuning case (i.e. Ec> Ex) will be considered.

[0045] A Hamiltonian describing PT-symmetric properties can be as follows:

[0049] The relevance of this Hamiltonian hinges on the possibility to have a negative term inside the square root

[0050] Three different cases can then be distinguished, depending on the sign of <52(0) - 4 / t2fl2. As the energy of the cavity mode is angle dependent, it is possible to obtain all cases within a single photonic cavity, still by using simple and widely known cavities based on Distributed Bragg Reflectors, two cavities would be needed to observe a first case where the 82(6) - 4 / t2fl2is positive for any angle, and a second one where this term ends up being negative for a range of values for 6.

[0051] Hence, the dispersion relations, meaning the angle dependence of both polariton states are depicted in Figs 4A, 4B, 4C.

[0052] Fig. 4A demonstrates the case where the term in the square root remains positive among the whole dispersion relation, while Figs 4B and 4C represent the cases where the term in the square root has negative values when 8 6 < g, leading to imaginary values for the eigenvalues in what is called a broken PT-symmetry region. The profound physical meaning of these non-zero imaginary part of the energies of the polaritons, remains to be determined.

[0053] Excitons-polaritons are natural qubits where, for example, one can encode information as:

[0054] |0) = |LP) , |1) = | UP)

[0055] And in general, \ p) = a\UP) + (3\LP)

[0056] with \a\2+ | / ?|2= 1

[0057] If we assume that a system could be designed so that the phase factor could be dynamically changed within a cavity, then it would open the way to design logical operators that would mix and / or separate both states. It might be used to implement experimentally the Hadamard gate, where mixing both polaritons could ease the even weighting across both states.

[0058] Focusing on the design of an optical cavity corresponding to the Hamiltonian HPTITl described earlier, let us rewrite i as i = e~ to explicit the approach used in this study. Since in quantum mechanics an imaginary term describes a phase term, the photonic cavity will be designed in such a way that is generating phase terms O = (in the time domain).

[0059] Also, to stress out the non-hermicity of our system, the photonic cavity can be an open system. This means that, instead of confining some quantum dots in between two mirrors, only one single mirror can be used, while the quantum dots themselves can be considered to be a second mirror.

[0060] In the example, this mirror can based on a structure such as depicted in Fig. 5, where a defect layer is used as a resonator layer 114, having a thickness in terms of optical path of:

[0061] (ddefect) = nBddefect= , corresponding to a resonator.

[0062] This defect is followed by 10 periodic unit cells 116 that have thicknesses corresponding to, respectively:

[0065] At the surface of the photonic structure, is added a quantum dot layer 112 that has a thickness corresponding to:

[0066] Such that it could also be a resonator to maximize the amplitude of the electric field in this layer.

[0067] Finally, we obtain two resonators, one is the quantum dot layer 112, and the second one is the porous silicon defect layer 114, and the interaction of the two resonators is going to be our gain-loss pair usually considered for PT-symmetry, while the distributed Bragg reflector (DBR) is enhancing the total structure by confining the electric field. The control of the symmetry of the system may allow the creation of a bound state in the continuum, that is, a non-radiating state hidden within the continuum of propagating modes, which become accessible when coupled with a radiation channel as quasi-bound states (q-BICs). This is achieved by adjusting the asymmetry factor of the system, allowing the control of the spectral position and bandwidth of its emission.

[0068] The thickness of each layer 112, 114, 116 is also considered so that the reflection at each interface is generating a dephasing, as detailed below:

[0069] <p1 =^

[0072] Finally: A< > = <pk+1~ <pk= ^ V / c

[0073] Porous silicon is chosen here for its simplicity in term of experiments. It would be possible to fabricate the cavity in a single shot thanks to electro-etching. The different refractive indexes can be obtained easily by adjusting the porosity of each layer. Also, besides its affordability, it has been very well characterized thanks to its presence in integrated photonics.

[0074] The simulated reflectance spectrum at normal incidence and the angle-resolved spectrum in Fig. 6A exhibits an absence of a reflection dip while it is usually considered as the cavity mode that will be coupled with the quantum dots once they are added to the system. The absence of a dip is not surprising since we are describing a mirror and not an actual cavity.

[0075] Then, once the quantum dot layer is added, a dip can be seen in the reflectance spectrum at normal incidence as shown in Fig. 6B. This dip corresponds to the degenerated polariton states, as it can be observed while looking at the angle resolved simulation exhibiting the dispersion relation depicted in Fig. 6C.

[0076] Another way to characterize polaritons is to measure their photoluminescence, meaning their capabilities to emit photons when excited by a pump laser. As the material used here for the mirror is porous silicon and this material is not emitting light, photoluminescence is an efficient method as the only light emitted comes either from the non-coupled emitters or from the polaritons. Assuming the non-coupled emission is well-known, the polariton emission can then easily be determined.

[0077] In Fig 7, angle-resolved photoluminescence (ARPL) for different thicknesses of the quantum dot layer is represented, given that the porous silicon mirror remains unchanged. The thickness here is used as a parameter to modify the value of the coupling coefficient g while preserving the phase. Hence, it could be possible to measure experimentally different dispersion relations corresponding to different coupling values, while the other parameters remain the same, by fabricating a gradient of thicknesses of the quantum dot layer on top of the photonic. The dispersion relation observed in photoluminescence and in reflectance are both in accordance with Fig. 7 showcasing that the proposed Hamiltonian HPTdescribes a physical system and could be observed experimentally.

[0078] The condition <52(0) - 4 / i2n2< 0 is met here for thicknesses of the quantum dot layer superior to 96 nm, leading to the degeneration of both polaritons as expected.

[0079] Nevertheless, being able to choose any arbitrary value for the phase term, i.e. to replace i = e~ by a phase factor < > = ei<p, where <p could take any value could be worth ofinterest for researchers exploring topology. However, it does not seem possible in a simple way, as the photonic structure relies on interferences and electromagnetic field confinement. Still, it could potentially be achieved by designing more sophisticated cavities.

[0080] In a simulation made with the transfer matrix method, based on complex refractive indexes of porous silicon and CsPbBr3perovskites, and where the optical indexes for porous silicon are based on experimental data, layers labelled “A” and “B” are respectively corresponding to a porosity of 65.0% and of 86.5%.

[0081] The cavity modes used for dispersion relations fitting are based on the formula:

[0083] Where neffis the effective refractive index of the cavity

[0084] As can be understood, the examples described above and illustrated are intended to be exemplary only. The scope is indicated by the appended claims.

Claims

WHAT IS CLAIMED IS:

1. A device for concentrating a spectral distribution of quantum waves around a target wavelength At, the device comprising : an emitter layer having an emitter thickness demiand a refractive index nemiA satisfying the relationship demi* nemi= ( / c + l) y , where k is an integer greater than or equal to zero, the emitter thickness demidefined between a first face and a second face and defining an emitter propagation path for the quantum waves from the first face to the second face, across the emitter thickness, the emitter layer operable to interact with the quantum waves by absorbing at the spectral distribution and emitting at the target wavelength At; a resonator layer disposed adjacent the second face of the emitter layer, the resonator layer having a thickness dresand a refractive index nressatisfying the relationship dresis an integer greater than orequal to zero; a reflector layer disposed against the resonator layer; a first zone adjacent the first face of the emitter layer, opposite the second face, and a second zone disposed adjacent the second face of the emitter layer, opposite the first face, the first zone and the second zone being asymmetric relative the emitter layer from the perspective of propagation of the quantum waves.

2. The device of claim 1 wherein the resonator layer is disposed against the second face of the emitter layer.

3. The device of claim 1 or 2 wherein the reflector layer has a thickness dref and a refractive index nref satisfying the relationship dref* nref= where m is aninteger greater than or equal to zero, the refractive index nref being different than the refractive index nres.

4. The device of claim 3 further comprising a metal layer disposed against the reflector layer.

5. The device of claim 3 wherein m is smaller than 3, preferably smaller than 1.

6. The device of claim 3 wherein the reflector layer is a first reflector layer, the first layer forming part of a laminar structure of reflector layers stacked directly against one another and further including one or more additional reflector layer, the one or more additional reflector layer having corresponding thicknesses and corresponding refractive indices also satisfying the relationship, the corresponding refractive indices being different for each one of the reflector layers of the laminar structure than that of an adjacent one or more of the reflector layers of the laminar structure.

7. The device of claim 6 wherein the laminar structure has more than 3 reflector layers, preferably between 5 and 20.

8. The device of claim 6 or 7 wherein the reflector layers of the laminar structure have alternating values of porosity, and associated alternating values for the corresponding refractive indices.

9. The device of claim 8 wherein the reflector layers are made of silicon, the alternating values of porosity are of about 50 % and 85 %, respectively.

10. The device of claim 9 wherein the alternating values of porosity are of 51 ± 2 % and 87 ± 3 %.

11. The device of any one of claims 6 to 10 further comprising a metal layer disposed against the one or more additional reflector layer.

12. The device of claim 1 wherein the reflector layer is a metal layer.

13. The device of any one of claims 1 to 12 wherein k is smaller than 3, preferably smaller than 1.

14. The device of any one of claims 1 to 13 wherein I is smaller than 3, preferably smaller than 1.

15. The device of any one of claims 1 to 14 further comprising an other resonator layer disposed against the first face of the emitter layer, and a laminar structure of other reflector layers stacked directly against one another and against the resonator.

16. The device of any one of claims 1 to 14 wherein the first face of the emitter layer is exposed.A17. The device of any J one of claims 1 to 16 wherein ( / c + 1) — 2 = dpemfiLiL * npcmifLiL + —1 / 25 ( demi* nemi), preferably wherein18. The device of any one of claims 1 to 17, wherein y l = dres* nres±l / 25(cZres* nres), preferably wherein y (z + ) = dres* nres± l / 50(cZres* nres).

19. The device of claim 2 wherein m + nref),preferably wherein20. The device of any one of claims 1 to 19 wherein the quantum waves are photons.21 . A solar generator comprising : a photovoltaic cell having a maximum conversion efficiency at a target wavelength At ; and a device operable to concentrate the spectral distribution of sunlight around the target wavelength At, the device having :an emitter layer optically coupled to both a source of sunlight and to the photovoltaic cell, the emitter layer having an emitter thickness demiand a refractive index nemisatisfying the relationship demi* nemi=(k + 1) y , where k is an integer greater than or equal to zero; a resonator layer disposed against the emitter layer, the resonator layer having a thickness dresand a refractive index nressatisfying the relationship dresis an integer greater thanor equal to zero; a reflector layer disposed against the resonator; a first zone adjacent the first face of the emitter layer, opposite the second face, and a second zone disposed adjacent the second face of the emitter layer, opposite the first face, the first zone and the second zone being asymmetric relative the emitter layer from the perspective of propagation of the sunlight.

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