METHOD FOR THE DESIGN OF A CORRECTABLE EXPANDED COMPOUND PARABOL CONCENTRATOR (EPC) FOR NEAR-FIELD LIGHT COLLECTION

Description

[0001] The Expanded Compound Parabolic Concentrator is intended to be integrated into an optical signal receiving device used to implement wireless optical communication. The invention relates to the field of wireless optical communication. BACKGROUND OF THE INVENTION

[0002] An optical wireless communication (or OWC, for Optical Wireless Communication ), for example a LiFi communication system (for Light Fidelity ), generally includes two main pieces of equipment: an access point; a user terminal.

[0003] The access point plays a role similar to that of a WiFi gateway.

[0004] The terminal is for example a computer, a smartphone or a tablet. Terminal compatibility can be ensured using a dongle which plugs into a USB port on the terminal, for example.

[0005] In LiFi, a user can access a network (e.g., the Internet) via their terminal as long as the terminal is connected to a nearby access point. Once this connection is established, the access point can transmit the network's downstream data to the terminal and therefore to the user, while the terminal can send the upstream data back to the network via the access point.

[0006] The quality of this two-way communication (throughput, latency, coverage, etc.) depends largely on the quality of the optical signals received, by the terminal on the one hand and by the access point on the other. This signal quality is generally evaluated by the signal-to-noise ratio (or SNR for Signal-to-Noise Ratio ), which is the ratio of the received signal power to the received noise power. The greater the received signal power and the lower the noise, the higher the SNR, and therefore the higher the communication quality. Optimizing the SNR is therefore critical to improve the performance of a wireless optical communication system, such as a LiFi system. Document US5357101 discloses a parabolic concentrator known from the prior art. SUBJECT OF THE INVENTION

[0007] The invention aims to improve the signal-to-noise ratio of wireless optical communication equipment. SUMMARY OF THE INVENTION

[0008] To achieve this aim, a compound parabolic concentrator is provided for integration into an optical signal receiving device used to implement wireless optical communication, the compound parabolic concentrator having a coupling surface for positioning on a sensitive surface of a photodetector of the receiving device, a collecting surface for receiving the optical signals, and a lateral surface located between the coupling surface and the collecting surface, the lateral surface comprising two inclined and symmetrical parabolic portions when viewed in a section plane passing through a reference axis of the compound parabolic concentrator, the lateral surface being defined by an equation using input parameters comprising a dimension of the sensitive surface of the photodetector, an acceptance angle,a first refractive index of a medium in which the compound parabolic concentrator is intended to be immersed, a second refractive index of a material used to manufacture the compound parabolic concentrator, and a diametrical expansion factor of the compound parabolic concentrator making it possible to increase an overall diameter of the compound parabolic concentrator without increasing its height or modifying the shape of the inclined and symmetrical parabolic portions.,

[0009] The lateral surface of the compound parabolic concentrator according to the invention is therefore defined from input parameters comprising the dimension of the sensitive surface of the photodetector, the acceptance angle, the first refractive index, the second refractive index, and the diametrical expansion factor.

[0010] This way of designing a concentrator is particularly innovative, and the parabolic concentrator composed according to the invention has an optimal size allowing to concentrate a maximum radiant flux in the photodetector.

[0011] Further, a compound parabolic concentrator as previously described is proposed, wherein the lateral surface area is defined by the following equation: z l = d o 1 2 + n β n α sin α − r − sign r Δ d 2 2 n β 2 − n α 2 sin 2 α n α sin α − n β d o n β + n α sin α n β d o − 2 n α sin α r − sign r Δ d 2 2 n α sin α 2 , Or d o is a diameter of the sensitive surface of the detector, α is the acceptance angle, n α is the first refractive index, n β is the second refractive index, and Δ d is such that: Δ d = d o ( f e - 1), where f e is the diametric expansion factor.

[0012] Further provided is a compound parabolic concentrator as previously described, the compound parabolic concentrator being a dielectric concentrator, the first refractive index n α and the second refractive index n β being such that: 1 < n α < n β .

[0013] Further provided is a compound parabolic concentrator as previously described, the compound parabolic concentrator being formed by an assembly of a hollow concentrator and a collecting lens comprising the collecting surface.

[0014] Further provided is a compound parabolic concentrator as previously described, in which the collection surface is curved.

[0015] Further, a compound parabolic concentrator as previously described is proposed, in which the collection surface is defined by the following equation: z a = z l d i / 2 − cd i 2 4 + 2 4 − K + 1 c 2 d i 2 − 1 4 ∑ j = 2 N C 2 j d i 2 j + cr 2 1 + 1 − K + 1 c 2 r 2 + ∑ j = 2 N C 2 j r 2 j + t e Or : c is a curvature at the top of the collecting surface; K is a conical constant; the C 2j are aspherical deformation coefficients; d i is a diameter of the collection surface.

[0016] We further propose a compound parabolic concentrator as previously described, in which we have: c = − 1 n β n α − 1 t a , t a being a distance between the top of the collecting surface and a light source with which the optical signal receiving device is arranged to communicate.

[0017] We further propose a compound parabolic concentrator as previously described, in which we have: K = − n β n α 2 .

[0018] We further propose a compound parabolic concentrator as previously described, in which we have: t e = 0 .

[0019] Further provided is a compound parabolic concentrator as previously described, wherein t e is a thickness at the edge of the collecting lens.

[0020] Further provided is a compound parabolic concentrator as previously described, wherein a back surface of the collecting lens is defined by the following equation: z b = z l d i / 2 − c ′ d i 2 4 + 2 4 − K ′ + 1 c ′ 2 d i 2 − 1 4 ∑ j = 2 N C ′ 2 j d i 2 j + c ′ r 2 1 + 1 − K ′ + 1 c ′ 2 r 2 + ∑ j = 2 N C ′ 2 j r 2 j Or : c ' is a curvature at the top; K ' is a conic constant; the C' 2j are aspherical deformation coefficients; z l ( d i / 2) = h is a height of the compound parabolic concentrator without the collection surface; d i is a diameter of the collection surface.

[0021] Further provided is a compound parabolic concentrator as previously described, further comprising one or more anti-reflective or reflective layers applied to the side surface.

[0022] A device for receiving optical signals is further proposed, comprising at least one optical assembly comprising a photodetector and a parabolic concentrator composed as previously described, the coupling surface of which is positioned on the sensitive surface of the photodetector.

[0023] Further provided is a wireless optical communication equipment comprising an optical signal receiving device as previously described.

[0024] Further provided is a wireless optical communication equipment as previously described, the wireless optical communication equipment being an access point.

[0025] Further provided is a wireless optical communication equipment as previously described, the wireless optical communication equipment being a user terminal.

[0026] Further, a method of designing a compound parabolic concentrator as previously described is proposed, comprising the following successive phases: a first phase comprising the step of defining the input parameters; a second phase comprising the step of determining, from the input parameters, output parameters comprising an optimal diameter of the collection surface, an optimal height of the compound parabolic concentrator, an equation for defining the lateral surface which uses the input parameters, and a gain of the compound parabolic concentrator, the output parameters giving the compound parabolic concentrator an optimal size making it possible to concentrate a maximum radiant flux on the photodetector and to optimize its acceptance angle; a third phase comprising the steps of verifying that the optimal size of the compound parabolic concentrator is acceptable with respect to integration constraints in the receiving device, and of validating the output parameters for manufacturing the compound parabolic concentrator if this is the case.

[0027] Further provided is a design method as previously described, further comprising an intermediate phase, carried out after the second phase and before the third phase, and comprising the step of giving the collection surface a curved shape.

[0028] Further provided is a design method as previously described, wherein a hollow concentrator is obtained at the end of the first phase and the second phase, and wherein the third phase comprises the step of defining a collection lens comprising the collection surface and which is intended to be assembled with the hollow concentrator to form the compound parabolic concentrator.

[0029] A design method as previously described is further proposed, further comprising a fourth phase, implemented following the third phase in the case where the optimal size is not acceptable, and comprising a first correction step consisting of modifying the optimal diameter of the collection surface and a diameter of the coupling surface of the compound parabolic concentrator but without modifying the optimal height of the compound parabolic concentrator or the shape of the inclined and symmetrical parabolic portions, and / or a second correction step consisting of giving the hollow concentrator an effective height lower than the optimal height so as to obtain an acceptable size of the compound parabolic concentrator, and a third step consisting of repeating the second phase and the intermediate phase if these are implemented, then the third phase,until an acceptable effective footprint of the compound parabolic concentrator is obtained.,

[0030] Further, a design method as previously described is provided, in which a dielectric concentrator is obtained at the end of the first phase and the second phase.

[0031] A design method as previously described is further proposed, further comprising a fourth phase, implemented following the third phase in the case where the optimal size is not acceptable, and comprising a first correction step consisting of modifying a diameter of the collection surface and the optimal diameter of the coupling surface of the compound parabolic concentrator but without modifying the optimal height of the compound parabolic concentrator or the shape of the inclined and symmetrical parabolic portions, and / or a second correction step consisting of giving the dielectric concentrator an effective height lower than the optimal height so as to obtain an acceptable size of the compound parabolic concentrator and / or a third correction step consisting of increasing the second refractive index and repeating the second phase and the intermediate phase if the latter is implemented, then the third phase,until an acceptable size of the compound parabolic concentrator is obtained.,

[0032] The invention will be better understood in light of the following description of a particular non-limiting embodiment of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Reference will be made to the attached drawings, including: [ Fig. 1 ] there figure 1 is an exploded view of an access point in which the invention is implemented; [ Fig. 2 ] there figure 2 is a perspective view of an expanded compound parabolic concentrator according to the invention; [ Fig. 3 ] there figure 3 represents, in a cylindrical coordinate system (r,z), a portion of the parabolic southern section generating the lateral surface of the optical concentrator; [ Fig. 4 ] there figure 4 represents an offset portion of the parabolic meridional section generating the lateral surface, as well as the coupling surface of the optical concentrator; [ Fig. 5 ] there figure 5 represents a hollow CPC without a collecting lens; [ Fig. 6 ] there figure 6 represents different curves, according to different acceptance angles, of a normalized maximum gain ( d o = 1) depending on the height of the hollow CPC; [ Fig. 7 ] there figure 7 represents a hollow CPCE without an additional lens as a collecting surface; [ Fig. 8 ] there figure 8 represents light rays in a dielectric concentrator; [ Fig. 9 ] there figure 9 represents a dielectric CPC with a planar collecting surface; [ Fig. 10 ] there figure 10 represents the variation, as a function of the refractive index, of the optimal southern section of a standardized dielectric CPC ( d o = 1), that is to say of the southern section allowing to concentrate the light with a maximum gain; [ Fig. 11 ] there figure 11 represents a dielectric CPCE with a flat collecting surface; [ Fig. 12 ] there figure 12 represents in front view a CPCE with a curved collection surface; [ Fig. 13 ] there figure 13 represents the lateral surface of the concentrator before and after its extension by an enlargement. DETAILED DESCRIPTION OF THE INVENTION

[0034] The invention is implemented in a wireless optical communication equipment belonging to a wireless optical communication system.

[0035] In reference to the figure 1 , the equipment here is an access point 1. Wireless optical communication is for example LiFi communication.

[0036] The access point 1 comprises a housing 2 inside which is integrated an electrical card 3 which rests on a support 4 positioned at the bottom of the housing 2. A cover 5 makes it possible to close the housing 2.

[0037] The electrical board 3 includes a number of electrical and optoelectronic components.

[0038] Some of these components enable the implementation of an optical signal receiving device. The received optical signals are emitted by a user's terminal and carry uplink data.

[0039] Some of these components enable the implementation of an optical signal transmission device. The transmitted optical signals are received by the user's terminal and carry downstream data.

[0040] The receiving device comprises a plurality of photodetectors, which are here photodiodes 7. The photodetectors could be of different types, and comprise for example one or more phototransistors (PT), one or more photoresistors (PR), one or more PIN photodiodes, one or more avalanche photodiodes, one or more SPADs (for Single Photon Avalanche Diode ), one or more CMOS sensors (for Complementary Metal Oxide Semiconductor ), etc.

[0041] Each photodiode 7 is associated with a compound parabolic concentrator (CPC) according to the invention 8, which is positioned on said photodiode 7.

[0042] The CPC 8 is a new type of CPC, which we will call here CPCE, for “Expanded Compound Parabolic Concentrator”.

[0043] It is known that light inherently carries energy, but it can also be modulated to transmit a signal. An optical element capable of collecting light is called a concentrator. We begin by assuming that a radiating source is located at infinity so that its light can be thought of as parallel light rays. These light rays enter through the concentrator's input surface and are directed toward the output surface, which may be in contact with an energy transducer or a photoelectric detector. Here, as we have just seen, the output surface is in contact with a photodiode 7. This assumption of parallel incident rays is the physical principle underlying the usual methods of designing CPCs. However, the light incident on the CPC actually comes from a nearby object, so the incident light rays are not parallel.We therefore consider here that a CPC must have as a fundamental characteristic an entry surface whose shape allows the incident rays which pass through it to become as parallel as possible. This particular entry surface is an optional difference between a usual CPC and a CPCE according to the invention.

[0044] Here we speak of collection surface for the input surface and coupling surface for the output surface.

[0045] The optical concentrator in question here is a compound parabolic concentrator that has an external parabolic generator defined to collect light onto the photodiode. Here, the word "compound" refers to the fact that the concentrator performs several optical functions implemented in parallel.

[0046] In reference to the figure 2 , the CPCE 8 therefore has a coupling surface 9, a collection surface 10 for the light rays, and a lateral surface 11 located between the collection surface 10 and the coupling surface 9. The coupling surface 9 is a flat surface with a circular outline (but could be a surface with a different outline, for example square, rectangular, etc.) while the collection surface 10 is here a spherical or aspherical surface, continuous or lenticular (Fresnel type) which transforms a CPCE into a near-field corrected optical concentrator, without spherical aberration. This form of collection surface makes it possible to capture light more efficiently when it comes from a nearby emitter.

[0047] Note that a flat collecting surface is a limiting case of an aspherical surface.

[0048] The coupling surface 9 is intended to be positioned on a sensitive surface of the photodiode 7, which here has a rectangular shape (but which could have a different shape, for example square or circular). The lateral surface 11 is here a surface of revolution with a parabolic generator.

[0049] The purpose of the CPCE 8 is to focus all the light rays incident on the collection surface 10 up to a certain angle, which is the acceptance angle, towards the coupling surface 9 so that these light rays are captured by the photodiode 7. For this, the CPCE 8 uses the principle of total internal reflection according to which light rays incident with an angle too high to be focused directly towards the coupling surface 9 will be reflected by the lateral surface 11 one or more times in order to end up on the coupling surface 9.

[0050] Optical concentrators are classified as non-imaging (or anidolic) optical elements. Optical concentrators facilitate the transfer of light radiation between a light source and a target detector. Unlike imaging optical systems, optical concentrators are not designed to form images but to produce optimal radiation transfer.

[0051] CPCs were first designed for sunlight concentration applications. Their interest is therefore not based on object imaging but on energy transfer. Therefore, it is not the individual points of the object that are of interest, but rather its limitations. In other words, in imaging optics, each individual point belonging to an object must be rendered in the image plane. However, in non-imaging optics, rays from delimited object points may arrive scrambled in the conjugate plane. Non-imaging optics has been redefined in terms of the thermal behavior inherent to the object source. Non-imaging concentrators are used for energy transfer from a radiating source to a target. The target can be a photovoltaic element or a photodetector (here, the target is a photodiode).From a thermodynamic point of view, it has been proposed in the prior art to examine concentration at geometric and probabilistic scales.

[0052] From a geometric optical point of view, it is crucial to establish the maximum concentration ratio of a concentrator whose aperture or absorption surface is predefined.

[0053] The design process is a completely new and particularly innovative method for designing and determining the geometry of a CPC.

[0054] Here, the CPCE 8 is reinterpreted not as a radiative element - even if it remains a radiative source - but as a signal transmitter.

[0055] The CPCE may comprise a hollow concentrator, which is a hollow CPC, assembled with a collection lens on which the collection surface is defined, which is a flat or curved surface.

[0056] The CPCE can also be a dielectric and monobloc concentrator, the collection surface 10 of which is a flat or curved surface.

[0057] The dimensioning of the coupling surface 9, the collection surface 10 and the lateral surface 11 is critical and must respect several constraints.

[0058] The coupling surface 9 must be adapted to the sensitive surface of the photodiode 7. The collection surface 10 must be as large as possible to optimize the number of incident light rays likely to be focused towards the coupling surface 9. However, for a fixed coupling surface 9, the larger the collection surface 10, the higher the optical concentrator 8 will be. Furthermore, a large collection surface 10 does not facilitate integration in a restricted space. The lateral surface 11 must be designed so as to connect the collection surface 10 and the coupling surface 9 while maximizing the light reaching the photodetector.

[0059] The design method for producing the CPCE differs fundamentally from prior art methods, in which the CPC is designed by pre-fixing the diameter of the collecting surface, trying to achieve maximum gain for a pre-established refractive index, and expanding the diameter to achieve maximum radiant flux.

[0060] The design method used here comprises a plurality of distinct phases, implemented one after the other and in this order: a first phase, a second phase, an intermediate phase, a third phase and a fourth phase. As will be seen, the intermediate phase is optional.

[0061] The aim of these phases is to size the CPCE 8 prior to its manufacture.

[0062] The first phase consists of defining input parameters from which all the most critical dimensions and characteristics of the CPCE 8 will be defined.

[0063] The input parameters include an acceptance angle of the concentrator 8, as well as a diameter of the coupling surface 9 and a diametrical expansion factor. The diametrical expansion factor of the compound parabolic concentrator allows an overall diameter of the CPCE to be increased without increasing its height or changing the shape of the inclined and symmetrical parabolic portions that define its lateral surface. By "overall diameter" is meant the diameter of the CPCE over its entire height.

[0064] The input parameters also include a first refractive index of a medium in which the CPCE is intended to be immersed, and a second refractive index of a material used to manufacture the CPCE. The second refractive index must be set to the highest possible value, according to the constraints of availability, price and transmissibility of the materials.

[0065] The initial diameter of the coupling surface 9 is defined from at least one dimension of the sensitive surface of the photodiode 7. This point is fundamental: the input data is not the dimensioning of the collection surface 10, but the dimensioning of the coupling surface 9, which is obtained from the dimensions of the sensitive surface of the photodiode 7 which will actually be used in the access point 1.

[0066] The dimension of the sensitive surface of the photodiode 7 is here the length of its diagonal: the diameter of the coupling surface 9 of the CPCE 8 is equal to the length of the diagonal of the sensitive surface of the photodiode 7.

[0067] So we have d 0 = a 2 + b 2 , Or d 0 is the diameter of the coupling surface 9, a is the length and b is the width of the sensitive surface of the photodiode 7.

[0068] It is noted that if the sensitive surface of the photodiode had the shape of a square, the diameter of the coupling surface 9 of the CPCE 8 could also be equal to the length of the diagonal of the square. If the sensitive surface of the photodiode had a circular (or elliptical) shape, the diameter of the coupling surface 9 of the CPCE 8 could be equal to the maximum diameter of the sensitive surface.

[0069] The acceptance angle here is an angle α .

[0070] As seen, the CPCE 8 may comprise a hollow (or reflective) concentrator, or it may be a dielectric (or refractive) and monobloc concentrator. The hollow concentrator consists only of a lateral surface 11. Its collection surface 10 and its coupling surface 9 are in fact openings. A dielectric concentrator is solid and therefore comprises a lateral surface 11, a collection surface 10 and a coupling surface 9.

[0071] Then, the second phase comprises the step of determining, from the input parameters, output parameters comprising in a first step an optimal diameter of the collection surface 10, an optimal height of the CPCE 8, an equation of the lateral surface 11 of the CPCE 8, and a maximum gain of the CPCE 8. At the end of this first step, the collection surface is a flat surface.

[0072] The second phase then includes a second step which aims to increase the maximum communication angle of the optical concentrator 8. It is in this second step that the CPC is converted into a CPCE, i.e. into a CPC with an expanded overall diameter. The acceptance angle is a design angle which corresponds to the maximum angle at which rays can be inserted into the optical concentrator. The acceptance angle is different from the maximum communication angle, which is the maximum angle which allows wireless optical communication (here LiFi communication). The maximum communication angle is actually lower than the acceptance angle. This is explained by the fact that, for an incidence angle greater than the maximum communication angle, the optical power focused on the optical concentrator will be too low, and therefore the SNR too low for the wireless optical communication link to be functional. The received optical power is insufficient.The maximum communication angle increases as the concentrator diameter is expanded, which increases the diameter of the capture surface without changing the height and parabolic geometry of the southern section. The maximum value of focused radiant flux is reached when the diametrical expansion is equal to . d o ( f e = 2) .

[0073] The intermediate phase (which is optional) comprises the step of transforming the flat collecting surface 10 into a curved surface. In the case where the CPCE according to the invention comprises a hollow concentrator, which has an opening at the collecting surface 10, this surface transformation is not directly possible. A collecting lens, the surface of which follows the equation obtained during this intermediate phase, is then assembled with the hollow concentrator to close it and add a curved collecting surface 10. In the case where the optical concentrator according to the invention is a dielectric concentrator, the initially flat collecting surface 10 at the end of the second phase is transformed into a curved collecting surface 10 according to the equation obtained during this first intermediate phase.

[0074] In this optimal configuration, the CPCE 8 presents maximum gain and its optical performance is optimized.

[0075] The second phase and the intermediate phase are now described in more detail.

[0076] During the second phase, the output parameters are defined in a first step as follows.

[0077] To design the lateral surface 11 of the CPCE 8, we first consider, with reference to the figures 3 et 4 , a parabolic mirror whose vertex is located at the origin of coordinates in a cylindrical coordinate system (r,z).

[0078] The parabolic mirror has the equation: z = r 2 4 f , Or f > 0 is the focal length and where the focal point F has coordinates (0, f ). The parabolic mirror 11 requires an inclination in its southern section ( r , z ).

[0079] The meridional section of a solid is the section of the solid that passes through its reference axis. On the figures 3 et 4 , this reference axis is the axis z, which is the axis of rotation of the CPCE 8.

[0080] We speak of a "parabolic" meridional section, because the lateral surface 11 is defined by a portion of a parabola, which is the generator of the revolution. When a meridional section is made, two parabolic portions are obtained, symmetrical with respect to the axis z .

[0081] We transform equation (1) into polar coordinates ( R , θ ) using the following variable changes: r → R cos θ , z → R sin θ .

[0082] We obtain the following second-degree implicit equation: R sin θ = R cos θ 2 4 f , whose explicit solution is: R = 4 f sec θ tan θ .

[0083] The tilting process requires the addition or subtraction of an angle that corresponds to the acceptance angle α of the optical concentrator. By rotating the dish around its vertex at an angle α , the corresponding polar radius is: R = 4 f sec θ − α tan θ − α .

[0084] On the figure 3 , the focal point after rotation F can be observed.

[0085] It is noted that the figure 3 was constructed using a parabola with a focal length of f = 3.194 mm, with a rotation angle α = 16.1 degrees.

[0086] The coordinates of the focal point after rotation F are : r f z f = − f sin α , f cos α .

[0087] An inverse coordinate transformation allows us to find the equation of the inclined parabola in cylindrical coordinates. We use the following change of variables and functions: R → r 2 + z 2 , cos θ → r r 2 + z 2 , sin θ → z r 2 + z 2 .

[0088] By substituting this change in the root R = 4 f dry( θ - α ) tan( θ - α ) and by simplifying, we obtain the implicit representation of the inclined parabola in cylindrical coordinates: 1 = 4 f z cos α − r sin α r cos α + r sin α 2 .

[0089] By solving this equation according to the variablez , we obtain two real solutions. These solutions describe a piecewise function for the southern section of the inclined parabola.

[0090] The following equation represents the desired curve 12: z = − cot α r − 2 f csc α − 2 csc 2 α f f + f cos 2 α − 2 r sin α .

[0091] We determine the vertex 15 represented on the figure 3 . Cartesian coordinates ( r c , z c ) of the critical point 16 where the discontinuity appears are found when the kernel of the root in equation (7) disappears. The discriminant of this equation: f f + f cos 2 α − 2 r c sin α = 0 , allows us to find the radius of the critical cylinder, which corresponds to the upper abscissa of the section located in the first quadrant { r c → f cos α cot α}.

[0092] Using this expression for the critical cylinder radius in equation (4), we obtain the coordinates of the critical point 16: r c z c = f cos α cot α , f cos α + csc α cot α .

[0093] It should be noted that at the critical point 16, the tangent line to the meridional curve has an infinite slope. A straight line 17 is constructed which passes through the focus F and which is parallel to the axis r of the southern section, as shown in the figure 3 . By equating equation (11) to z f in equation (6), it is possible to obtain the abscissa of the intersection point 18 ( r s , z s ) of the straight line 17 and the lateral surface 11: − cot α r s − 2 f csc α − 2 csc 2 α f f + f cos 2 α − 2 r s sin α = f cos α , by having a positive solution for r s : r s → 2 f sec 2 α − f sin α + 2 sec α tan α .

[0094] The coordinates of the intersection point 18 are thus reduced to: r s z s = 2 f sec 2 α − f sin α + 2 sec α tan α , f cos α .

[0095] So we can calculate the diameter d 0 of the optical concentrator output aperture, which corresponds to the distance between the focal point F and the intersection point 18.

[0096] We have: d 0 = r s − r f , with r s → 2 f sec 2 α − f sin α + 2 sec α tan α , r f → − f sin α , which once evaluated and simplified, becomes: d 0 = 2 f sec α sec α − tan α .

[0097] It is now possible to determine the coordinates ( r m , z m ) from the midpoint 20 of the outlet opening according to: r m z m = r f + d o / 2 , z f , which, after evaluation with: { r f → - f sin α , d o → 2 f (dry α - tan α ) dry α} And { z f → f cos α} , then simplification, reduces to: r m z m = f sec 2 α − sin α − sec α tan α , f cos α .

[0098] The coordinates of the midpoint 20 allow us to define the parabola after rotation using {{ r → r + r m } , { z → z + z m }} and equation (9). In this way, the midpoint 20 ( r m ,z m ) and the origin point 21 of the coordinates of the optical concentrator 8 coincide, as can be seen in the figure 4 . We therefore obtain the following equation for the parabola: z = − cot α r + r m − 2 f csc α − 2 f f + f cos 2 α − 2 r + r m sin α sin 2 α − z m .

[0099] The lateral profile 22 of the first quadrant is obtained after evaluation and simplification of equation (20): z = − r − 2 f csc α cot α + f 1 − csc α sec α − 2 f f 1 + sin α − r sin α sin 2 α .

[0100] However, to construct a lateral surface of revolution, the odd function in equation (21) must be transformed into an even function by making the following change of variables r → r 2 z → z l , which gives: z l = − r 2 − 2 f csc α cot α + f 1 − csc α sec α − 2 f f 1 + sin α − r 2 sin α sin 2 α .

[0101] It is now possible to find the new coordinates of all the essential points described in the demonstration and visible on the figure 3 : a) The critical point 16 of the maximum slope: r c z c = f csc α 1 + sin α , f csc α cot α ; b) The focal point F : r f z f = − f sin α − r m , f cos α − z m = f sec α tan α − sec α , 0 ; c) The intersection point 18: r s z s = f sec α − tan α sec α , 0 .

[0102] We therefore check that the focal point F and the intersection point 18 are symmetrical points.

[0103] It is important to mention that the maximum height of the concentrator corresponds to the ordinate of point 16, that is to say: h max = f cot α csc α .

[0104] We first consider the case where the CPCE includes a hollow concentrator.

[0105] There figure 5 shows a hollow concentrator of revolution 19. It consists of a concave mirror having an entrance opening 23 of diameter d i which collects the light emitted by a radiant source located at infinity. The entrance opening 23 corresponds to the collection surface.

[0106] The hollow concentrator 19 conducts the light entering through the inlet opening 23 into the outlet opening 24 of diameter d o . The outlet opening 24 corresponds to the coupling surface.

[0107] This optical system, well known in the state of the art of the usual technique, consists of two independent optical subsystems which collect light in parallel: a first subsystem which receives the light through its exit aperture 24, and a second subsystem which reflects the incident light in the lateral internal mirror 25 onto the exit aperture 24. Therefore, this type of optical system is called a compound optical system.

[0108] Two variables are used to design the hollow concentrator 19 (which are the input parameters): the diameter d o of the output aperture 24 (i.e. the diameter of the coupling surface 9 - assuming a rotationally symmetric concentrator), and the semi-angular acceptance field noted α (this is the acceptance angle).

[0109] These input parameters allow us to find the diameter d i of the inlet opening, the height 26 of the hollow concentrator 19 with the dimension h , and the geometry of the mirror 25 including the lateral surface z l .

[0110] Previously, the basic formulation for the parabola after rotation was deduced based on only two parameters: the acceptance angle α and the focal length f. These formulations allow us to deduce in the following the expressions necessary to design the hollow CPC 19 as a function of d o and of α.

[0111] From equation (17) we can solve f depending on d o and of α : f = d o 1 + sin α 2 .

[0112] This expression of f is then used in equation (22) to express the lateral surface area as a function of d o And α , as indicated by: z l = cot α d o 2 + d o csc α − r 2 − d o 1 + sin α d o − 2 r 2 sin α sin 2 α .

[0113] The inlet opening 23 in diameter d i must meet the condition 0 < d i ≤ d imax . The upper limit of the interval is obtained with equations (23) and (27). Thus, the maximum diameter of the inlet opening 23 is: d imax = d 0 csc α .

[0114] This maximum diameter is also the optimal diameter of the collection surface.

[0115] The maximum height 26 of the hollow concentrator 19 is then calculated by substituting equation (27) for equation (26): h max = d 0 cos α 1 + sin α 2 sin 2 α .

[0116] Calculating the optimal height h of the hollow CPC with the condition {0 < h ≤ h max ] requires understanding its optical function as a function of its optical gain G. Suppose that light emerging from a radiative source located at infinity arrives collimated in a CPC and that all the radiation striking the collection surface is collected in the coupling output surface. So suppose the efficiency is 100%. Then the maximum gain is G max = E o / E i , Or E o is the irradiance of the exit opening (radiant flux density, in [Watts / m2]), and E i is the irradiance at the entrance aperture.

[0117] If the output and input powers are respectively W o And W i , and the two are equal, the gain is reduced to: G max = d i d o 2 .

[0118] The gain is the ratio between the area of ​​the collection surface A i and that of the coupling surface A o . There is a dependency between the area of ​​the collection surface A i and height h of the hollow CPC. By evaluating equation (28) with r = d i / 2, we can see that: h = − cot α d i 2 − d o 2 − d o csc α − d o 1 + sin α d o − d i sin α sin 2 α .

[0119] This equation has an analytical solution for d i > has with: d i = d o + 2 cos 2 α csc α d o sin α 1 + sin α 2 + hd o sin α 1 + sin α sin 2 α − d o 1 + sin α − h sin α cos α

[0120] By replacing d i in equation (33) by equation (31), the maximum gain as a function of acceptance, coupling surface diameter and hollow CPC height is: G max = 1 + 2 cos 2 α csc α sin α 1 + sin α 2 + h sin α 1 + sin α sin 2 α d o − 1 + sin α − h sin α cos α d o 2 ,

[0121] Assuming that d o = 1 and normalizing the hollow CPC with the ratio h / d o , we can express the normalized maximum gain of the concentrator as a function of its normalized height and the acceptance angle.

[0122] We see on the figure 6 expected normalized maximum gain curves for a normalized sparse CPC. The normalized maximum gain curves for the eight acceptance angles α The following are represented: 30, 32, 34, 36, 38, 40, 42 and 44 degrees.

[0123] It is then easy to conclude that the hollow concentrator should be designed for a height equal to the maximum height 27 in order to achieve maximum gain, which is possible if there is no height restriction in the CPC design specifications. CPCs with a height less than the maximum height 27 are called "truncated CPCs". The optimal height of the hollow CPC 19 is therefore the maximum height.

[0124] We produce the set of equations (35a)-(35d) necessary for modeling hollow CPCs: d i max = d 0 sin α , h max = d 0 cos α 1 + sin α 2 sin 2 α , z l = cot α d o 2 + d o csc α − r 2 − d o 1 + sin α d o − 2 r 2 sin α sin 2 α , G max = 1 sin 2 α .

[0125] The set of equations (35) includes the output parameters, which are therefore the optimal diameter d i max collection surface 10, the optimal height h max of the CPC, the equation of the portions of the parabola, and the maximum gain G max .

[0126] The second step of the second phase of creating a hollow CPC aims to increase the maximum communication angle and to increase the radiant flux at the photodetector. For this, the optical concentrator 19 is extended by homothety, more precisely by an enlargement ( figure 7 ), which gives our new CPCE. For this, we predefine an expansion factor f e with condition 1 < f e < 2, to diametrically expand a hollow CPC with the change of variable { r → ( r - sign ( r )Δ d / 2} , where Δ d = d o ( f e - 1), which allows us to obtain the set of equations (36a)-(36b): d i max = d 0 sin α + Δ d z l = cot α d o 2 + d o csc α − r − sign r Δ d 2 2 − d o 1 + sin α d o − 2 r − sign r Δ d 2 2 sin α sin 2 α ,

[0127] The value of the diametrical increment Δ d is determined experimentally, taking into account the excitation of the transmitter, to obtain a larger communication angle.

[0128] After expansion, the diameter of the coupling surface is also transformed into { d o → f e d o = d o +Δ d}. It is important to note that the geometry of the lateral surface 25 is nevertheless calculated with the unexpanded diameter, which is the main characteristic of the concentrator proposed here. This technique, which is not referenced in the existing literature, makes it possible to transform a hollow CPC into a hollow CPCE with internal focal points F and F' at the coupling section 24, as shown in figure 7 .

[0129] The dimensions of the hollow CPC 19 of the figure 5 are as follows: d o = 4.4 mm, α = 37.5°, h = 7.577 mm, and d i = 7.228 mm. The lateral surface has a focal length f = 3.539 mm.

[0130] The hollow CPC 19 shown on the figure 7 was then obtained from the hollow CPC 19 of the figure 5 by expansion. The dimensions of the hollow CPC 19 of the figure 7 are as follows: Δ d = 0.8 mm, d o = 4.4 + Δ d mm = 5.2 mm, α = 37.5°, h = 7.577 mm, and d i = 7.228 + Δ d = 8.028 mm. The lateral surface has a focal length f = 3.539 mm.

[0131] We are now interested in the case where the optical concentrator 8 according to the invention does not comprise a hollow CPC, but is a dielectric (or refractive) concentrator and we describe the first step of the second phase of design of such a dielectric CPC.

[0132] There figure 8 represents the path of light rays in a dielectric CPC of height h , of collection surface diameter d i , of coupling surface diameter d o . This figure shows the total internal reflection (TIR for total internal reflexion ) rays on the lateral surface.

[0133] Hub 28 of the figure 9 is a dielectric revolution concentrator. This concentrator is a monolithic and transparent CPC 28 with a reflective surface. It is assumed that the CPC 28 is made of an isotropic and homogeneous refractive index material n β , and immersed in an external medium of refractive index n α weaker. By "immersed" we mean that the CPC 28 is entirely immersed in a liquid or gaseous medium. Here, the medium is air (but the medium could be different, for example water).

[0134] The refractive index n β is an input parameter of the first phase.

[0135] The material from which the CPC is made can be, for example, glass or plastic, for example, polycarbonate (PC), polymethyl methacrylate (PMMA) or silicone. Here, the CPC is made of plastic.

[0136] The collecting surface 29 of the CPC 28 is assumed to be flat. The diameter d i of the collecting surface 29 makes it possible to collect light coming from a radiation source located at infinity. The function of the CPC is to bring the light from the collecting surface 29 to the coupling surface 30. The coupling surface 30 of diameter d o is in physical contact with the sensitive surface of the photodiode.

[0137] A light ray 31 striking the collecting surface 29 with an acceptance angle α is refracted in the CPC with an internal acceptance angle β smaller, with the condition n β > n α . The Snell-Descartes law governs the relationship between these two rays, and gives β = sin -1< ( n α sin / n β ).

[0138] Considering the condition β < α, we can conclude that a dielectric concentrator is more advantageous than a hollow concentrator. A dielectric CPC allows to increase the maximum gain according to: G max = 1 + 2 cos 2 β csc β sin β 1 + sin β 2 + h / d o sin β 1 + sin β sin 2 β − 1 + sin β − h / d o sin β cos β 2 .

[0139] There figure 10 shows the variation of the optimal southern section (in terms of optical gain) for a normalized dielectric CPC, as a function of its relative refractive index n = n β / n α . Here, α = 30°.

[0140] A quick comparison of equations (34) and (38) allows us to see that the only difference is the angle. Consequently, the equations obtained for a hollow CPC remain valid for dielectric CPCs by modifying the variable { α → β}. The set of equations (35a)-(35d) necessary to design a rotationally symmetric dielectric CPC with maximum gain is thus reduced to: d i max = d 0 sin β , h max = d 0 cos β 1 + sin β 2 sin 2 β , z l = cot β d o 2 + d o csc β − r 2 − d o 1 + sin β d o − 2 r 2 sin β sin 2 β , G max = 1 sin 2 β .

[0141] By substituting {β → sin -1< ( n α sin α / n β )} in equation (27) then by simplifying, this set of equations becomes the set of equations (39a)-(39d): d i max = n β d 0 n α sin α , h max = d o n α sin α + n β n β 2 − n α 2 sin 2 α 2 n α 2 sin 2 α , z l = d o 1 2 + n β n α sin α − r 2 n β 2 − n α 2 sin 2 α n α sin α − n β d o n β + n α sin α n β d o − 2 r 2 n α sin α n α sin α 2 G max = n β 2 / n α 2 sin 2 α .

[0142] The set of equations (39a)-(39d) includes the output parameters, which are therefore the optimal diameter of the collection surface d i max, the optimal height h max of the CPC, the equation of the lateral surface of revolution, and the maximum gain G max .

[0143] The second step of the second phase of designing a dielectric CPC aims to increase the maximum communication angle and the radiant flux at the photodetector. For this, the optical concentrator 28 is extended by homothety, more precisely by an enlargement ( figure 11 ), which gives our new dielectric CPCE.

[0144] Only the diameter of the collecting surface 29 and the optimal diameter of the coupling surface 30 are increased by this homothety. The optimal height h of the optical concentrator and the parabolic generator are not modified, even if the equation of the lateral surface z l change. We see on the figure 13 the lateral surface 33 of the optical concentrator before the implementation of the second step of the second phase, and the lateral surface 34 of the optical concentrator after the implementation of the second step of the second phase. It can be seen that the radial offset is constant between the two lateral surfaces 33 and 34.

[0145] In order to implement this enlargement, an expansion factor is predefined f e with condition 1< f e < 2 , to diametrically expand the dielectric CPC with the change of variable { r → ( r - sign ( r )Δd / 2} ,where Δ d = d o ( f e - 1), which allows us to obtain the set of equations (40a)-(40b): d i max = n β d 0 n α sin α + Δ d z l = d o 1 2 + n β n α sin α − r − sign r Δ d 2 2 n β 2 − n α 2 sin 2 α n α sin   α − n β d o n β + n α sin α n β d o − 2 n α sin α r − sign r Δ d 2 2 n α sin α 2 .

[0146] These two equations are the most important because they describe the main characteristics of a dielectric CPCE. If n α = n β , the dielectric CPCE is transformed into a hollow CPCE. In other words, any CPCE can be represented with equations (40a), (39b), (40b) and (39d).

[0147] The value of the diametrical increment Δ d is determined experimentally, taking into account the excitation of the transmitter, to obtain a larger communication angle.

[0148] After expansion, the diameter of the coupling surface is also transformed into { d o → f e d o = d o +Δ d}. It is important to note that the geometry of the lateral surface 19 is nevertheless calculated with the unexpanded diameter, which is the main characteristic of the concentrator proposed here. This technique, which is not referenced in the existing literature, makes it possible to transform a dielectric CPC into a dielectric CPCE with internal focal points F and F' at the coupling section 30, as shown in figure 11 .

[0149] After enlargement, the diameter of the collecting surface and the optimal diameter of the coupling surface are each increased by a value equal to Δd.

[0150] This change in diameters, during the manufacture of the optical concentrator 8, makes it possible to increase the maximum communication angle by 5° when Δ d = 1.6 mm. The acceptance angle of α = 65° remains the same.

[0151] Advantageously, we make the Δ depend dused the communication performance of the modem of the access point receiving device, i.e. its ability to establish communication with a given SNR. The Δ d used therefore does not depend solely on optical properties.

[0152] From equation (40b) we can deduce the following equation: z = − 11,3591 + 9,258 12,5714 − 1.81311 r − 0,8 sign r 2 − 1.63826 × r − 0,8 sign r 2 . This equation is of the form: z = f ( r ) .

[0153] The function f is obtained as follows: z = f ( r ) = h max - z l , with h max And z l defined according to the set of equations (39b) and (40b).

[0154] To arrive at this equation, the following parameters were used.

[0155] The sensitive surface of the photodiode has length a and width b : a = 5.4 mm, b = 4.8 mm.

[0156] We calculate the diameter of the coupling surface d 0 = a 2 + b 2 = 7,225 mm.

[0157] The acceptance angle is: α = 65 °.

[0158] The diametric increase is Δ d = 1.8 mm.

[0159] The first refractive index n α corresponds to the refractive index of the air in which the CPCE is immersed, that is to say n α ≃ 1.000275.

[0160] The second refractive index n β corresponds to the refractive index of the material with which the CPCE is made. Here we have: n β = 1.74. Note that the refractive index of the material is equal to 1.76 for yellow light but is equal to 1.74 for infrared light ( λ t = 840-940 nm).

[0161] For an angle of acceptance α predefined, and a standardized output opening d o = 1, d imax And h max are calculated from equations (40a) and (39b).

[0162] The output parameters provide the optical concentrator with an optimal footprint to concentrate maximum radiant flux onto the photodetector.

[0163] At this stage of the design, the optical concentrator obtained can be related to a CPCE (hollow or dielectric) insofar as its collection surface 10 is flat.

[0164] The intermediate phase (optional) consists of transforming this CPCE into a CPCE having a curved spherical or aspherical refractive collecting surface. This curved collecting surface makes it possible to optimize the radiant flux concentrated on the photodetector when it comes from a near-field light emitter.

[0165] There figure 12 represents, in front view, a dielectric CPCE 32 with such a curved collection surface z a .

[0166] The curved collection surface is defined by the following equation: z a = h − cd i 2 4 + 2 4 − K + 1 c 2 d i 2 − 1 4 ∑ j = 2 N C 2 j d i 2 j + cr 2 1 + 1 − K + 1 c 2 r 2 + ∑ j = 2 N C 2 j r 2 j + t e . Or : c is the curvature at the vertex. If the rays inside the lens are to be free of spherical aberration, this curvature is defined by: c = − 1 n β / n α − 1 t a , n β being the refractive index of the material used to manufacture the optical concentrator, n α being an index of a medium in which the optical concentrator is immersed, t a being a distance between a vertex of the collection surface and a light source Tx with which the optical signal receiving device communicates; K is the conic constant. It is recommended that it be hyperbolic, that is: K = − n β / n α 2 ; C 2j are the N - 1 aspherical deformation coefficients; h is the height of the optical concentrator without the collection surface; d i is the diameter of the collection surface. t e is the thickness at the edge.

[0167] The corrected total height of the optical concentrator is then: h t = z a 0 = h − cd i 2 4 + 2 4 − K + 1 c 2 d i 2 − 1 4 ∑ j = 2 N C 2 j d i 2 j + t e .

[0168] In the case of a hollow CPCE, this curved collection surface is materialized by a collection lens. This collection lens has an upper collection surface whose shape is defined by (42) and a posterior surface whose shape is defined by: z b = h − cd i max 2 4 + 2 4 − K + 1 c 2 d i 2 − 1 4 ∑ j = 2 N C 2 j d i 2 j + cr 2 1 + 1 − K + 1 c 2 r 2 + ∑ j = 2 N C 2 j r 2 j . Or c , K And C 2 j are local variables defined for this posterior surface.

[0169] It is recommended that this lens be hyperbolic-plane of refractive index n γ = n β . This hyperbolic-plane lens is then assembled with the hollow concentrator obtained at the end of the previous phases so as to replace its collection opening 23.

[0170] In the case of a dielectric concentrator, the correction of the collection surface 10 is done simply by modifying the equation of this collection surface 10 using (42).

[0171] As seen earlier, the intermediate phase is optional: the design process described here could be implemented while maintaining a flat collection surface.

[0172] It should be noted, however, that the intermediate phase, if implemented, is likely to modify the optimal height and therefore the optimal size of the optical concentrator 28.

[0173] The design method according to the invention then comprises a third phase which consists of verifying that the optimal size of the CPCE 28 is acceptable in relation to integration constraints in the receiving device. The integration constraints consist, for example, of not exceeding a height and / or a width and / or a length of a volume intended to accommodate the optical concentrator.

[0174] If so, the output parameters are validated to manufacture the CPCE 28.

[0175] If this is not the case, that is to say if the CPCE obtained 28 is too cumbersome, the design process includes a fourth phase.

[0176] If the CPCE 28 comprises a hollow concentrator, the fourth phase firstly comprises a first correction step, and / or a second correction step and then a third correction step. The first correction step consists of modifying the expansion factor of the CPCE, which modifies the diameter of the collection surface and the optimal diameter of the coupling surface of the CPCE but without modifying the optimal height of the CPCE or the shape of the parabolic generator. The second step consists of giving the CPCE 28 an effective height less than the maximum height, so as to obtain an acceptable size of the optical concentrator 28. This is then referred to as a “truncated” CPCE.The third step consists of repeating the second phase and the intermediate phase if these are implemented, that is to say updating the dimensions of the curved lens added to the hollow CPCE using the values ​​of the variables updated in equation (42), then the third phase, until obtaining an acceptable effective size of the optical concentrator 28.

[0177] If the CPCE 28 is a dielectric CPCE, the fourth phase firstly comprises a first correction step, and / or a second correction step, and / or a third correction step. The first correction step consists of modifying the expansion factor of the CPCE, which modifies the diameter of the collection surface and the optimal diameter of the coupling surface of the CPCE but without modifying the optimal height of the CPCE or the shape of the parabolic generator. The second correction step consists of giving the optical concentrator 28 an effective height less than the maximum height so as to obtain an acceptable size of the optical concentrator. The third correction step consists of increasing the second refractive index n β and to repeat the second phase and the first intermediate phase if these are implemented, and the third phase, until an acceptable effective size of the optical concentrator 28 is obtained.

[0178] We can therefore either modify the expansion of the concentrator, or truncate the CPCE 28 optical concentrator, or increase the refractive index n β then repeat the second phase, the first intermediate phase and the third phase (with the new input parameters including the new refractive index n β ) to obtain an optical concentrator with reduced effective height but which, thanks to this reduction in the refractive index, presents an acceptable gain. The three corrections can also be carried out in a combined manner.

[0179] The design method just described is therefore adapted to maximizing the light power detected by the photodiode 7, to the sensitive surface of the photodiode 7 itself and to the way in which the photodiode 7 is integrated into the access point 1.

[0180] Advantageously, an anti-reflective varnish or a thin layer is applied to the lateral surface of the optical concentrator 8, at the end of its manufacture, in order to improve the capture and total internal reflection performance of the optical concentrator 8.

[0181] Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.

Claims

1. A compound parabolic concentrator for integration into an optical signal receiving device used to implement optical wireless communication, the compound parabolic concentrator (8 ; 32) comprising a coupling surface (9, 24) for positioning on a sensitive surface of a photodetector (7) of the receiving device, a collecting surface (10, 23) for receiving optical signals, and a side surface (11) located between the coupling surface and the collecting surface, the side surface comprising two inclined and symmetrical parabolic portions when viewed in a cross-sectional plane passing through a reference axis of the compound parabolic concentrator, characterized in that the side surface is defined by the following equation: z l = d o 1 2 + n β n α sin α − r − sign r Δ d 2 2 n β 2 − n α 2 sin 2 α n α si − n β d o n β + n α sin α n β d o − 2 n α si r − sign r Δ d 2 2 n α sin α 2 , this equation using input parameters including do which is a diameter of the sensitive surface of the photodetector (7), α which is an acceptance angle, nα which is a first refractive index of a medium wherein the compound parabolic concentrator is to be immersed, nβ which is a second refractive index of a material used to manufacture the compound parabolic concentrator, and fe which is a diametrical expansion factor of the compound parabolic concentrator allowing an overall diameter of the compound parabolic concentrator to be increased without increasing its height nor changing the shape of the inclined and symmetrical parabolic portions, with Δd which is such that: Δd = do(fe - 1).

2. The compound parabolic concentrator according to claim 1, wherein the compound parabolic concentrator is a dielectric concentrator (28), the first refractive index nα and the second refractive index nβ being such that: 1 < n α < n β .

3. The compound parabolic concentrator according to claim 1, wherein the compound parabolic concentrator is formed by an assembly of a hollow concentrator (19) and a collection lens comprising the collecting surface.

4. The compound parabolic concentrator according to any of the preceding claims, wherein the collecting surface is curved and defined by the following equation: z a = z l d i / 2 − cd i 2 4 + 2 4 − K + 1 c 2 d i 2 − 1 4 ∑ j = 2 N C 2 j d i 2 j + cr 2 1 + 1 − K + 1 c 2 r 2 + ∑ j = 2 N C 2 j r 2 j + t e where: - c is a curvature at the top of the collecting surface; - K is a conic constant, for example of value K = -(nβ / nα)2; - the C2j are aspheric deformation coefficients; - di is a diameter of the collecting surface; - te = 0 if the compound parabolic concentrator is a dielectric concentrator (28), or te is a thickness at the edge of the collection lens if the compound parabolic concentrator is formed by an assembly of a hollow concentrator (19) and a collection lens comprising the collecting surface.

5. The compound parabolic concentrator according to claim 4, wherein: c = − 1 n β n α − 1 t a , ta being a distance between the top of the collecting surface and a light source with which the optical signal receiving device is arranged to communicate.

6. The compound parabolic concentrator according to claim 3, wherein a back surface of the collection lens is defined by the following equation: z b = z l d i / 2 − c ′ d i 2 4 + 2 4 − K ′ + 1 c ′ 2 d i 2 − 1 4 ∑ j = 2 N C ′ 2 j d i 2 j + c ′ r 2 1 + 1 − K ′ + 1 c ′ 2 r 2 + ∑ j = 2 N C ′ 2 j r 2 j where: - c' is a curvature at the top; - K' is a conic constant; - the C'2j are aspheric deformation coefficients; - zl(di / 2) = h is a height of the compound parabolic concentrator without the collecting surface; - di is a diameter of the collecting surface.

7. The compound parabolic concentrator according to any of the preceding claims, further comprising one or more antireflective or reflective layers applied to the side surface.

8. A device for receiving optical signals, comprising at least one optical assembly comprising a photodetector (7) and a compound parabolic concentrator (8) according to one of the preceding claims, the coupling surface (9) of which is positioned on the sensitive surface of the photodetector (7) .

9. An optical wireless communication equipment, of access point (1) or user terminal type, comprising an optical signal receiving device according to claim 8.

10. A method for manufacturing a compound parabolic concentrator (8; 32) intended to be integrated into an optical signal receiving device used to implement optical wireless communication, the compound parabolic concentrator (8 ; 32) comprising a coupling surface (9, 24) to be positioned on a sensitive surface of a photodetector (7) of the receiving device, a collecting surface (10, 23) for receiving the optical signals, and a side surface (11) located between the coupling surface and the collecting surface, the side surface comprising two inclined and symmetrical parabolic portions when viewed in a cross-sectional plane passing through a reference axis of the compound parabolic concentrator, the side surface being defined by an equation using input parameters including a diameter d0 of the sensitive surface of the photodetector, an acceptance angle α, a first refractive index nα of a medium wherein the compound parabolic concentrator is to be immersed, a second refractive index nβ of a material used to manufacture the compound parabolic concentrator, and a diametrical expansion factor fe of the compound parabolic concentrator to increase an overall diameter of the compound parabolic concentrator without increasing its height nor changing the shape of the inclined and symmetrical parabolic portions, wherein the method comprises the following successive phases: - a first phase comprising the step of defining the input parameters; and - a second phase comprising the step of determining, from the input parameters, output parameters comprising an optimal diameter (di) of the collecting surface, an optimal height (h) of the compound parabolic concentrator, an equation for defining the side surface that uses the input parameters in the following form: − z l = d o 1 2 + n β n α sin − r − sign r Δ d 2 2 n β 2 − n α 2 sin 2 α n α sin α − n β d o n β + n α sin α n β d o − 2 n α sin α r − sign r Δ d 2 2 n α sin α 2 , with Δd such that Δd = do(fe - 1), and a gain of the compound parabolic concentrator, the output parameters providing the compound parabolic concentrator with an optimal overall size for concentrating maximum radiant flux on the photodetector and optimizing its acceptance angle α, prior to the manufacture of the composite parabolic concentrator.

11. The manufacturing method according to claim 10, further comprising an intermediate phase, carried out after the second phase and before a third phase, and comprising the step of giving the collecting surface a curved shape, the third phase then comprising the steps of verifying that the optimal overall size of the compound parabolic concentrator is acceptable with respect to integration constraints into the receiving device, and validating the output parameters for manufacturing the compound parabolic concentrator if this is the case or proceeding to a fourth corrective phase prior to manufacturing if this is not the case.

12. The manufacturing method according to claim 11, wherein a hollow concentrator (19) is obtained at the end of the first phase and the second phase, and wherein the third phase comprises the step of defining a collection lens comprising the collecting surface and which is intended to be assembled with the hollow concentrator (19) to form the compound parabolic concentrator.

13. The manufacturing method according to claim 11 and 12, wherein the fourth corrective phase, implemented following the third phase in case that the optimal overall size is not acceptable, comprises a first correction step of changing the optimal diameter of the collecting surface and a diameter of the coupling surface of the compound parabolic concentrator but without changing the optimal height of the compound parabolic concentrator nor the shape of the inclined and symmetric parabolic portions, and / or a second correction step consisting of giving the hollow concentrator an effective height lower than the optimal height so as to obtain an acceptable overall size of the compound parabolic concentrator, and a third step consisting of repeating the second phase and the intermediate phase, if these are implemented, and then the third phase, until an acceptable effective overall size of the compound parabolic concentrator is obtained.

14. The manufacturing method according to any of claims 10 or 11, wherein a dielectric concentrator (28) is obtained after the first phase and the second phase.

15. The manufacturing method according to claims 11 and 14, wherein the fourth corrective step, implemented following the third step in case the optimal overall size is not acceptable, comprises a first correction step of changing a diameter of the collecting surface and the optimal diameter of the coupling surface of the compound parabolic concentrator but without changing the optimal height of the compound parabolic concentrator nor the shape of the inclined and symmetric parabolic portions, and / or a second correction step consisting of giving the dielectric concentrator an effective height lower than the optimal height so as to obtain an acceptable overall size of the compound parabolic concentrator and / or a third correction step consisting of increasing the second refractive index and reiterating the second phase and the intermediate phase, if the latter is implemented, then the third phase, until an acceptable overall size of the compound parabolic concentrator is obtained.