Lens element

Abstract

The invention concerns a lens element (200) intended to be placed in front of an eye of a viewer, the lens element comprising a transmissive metalens (100) having an array of nanostructures (161, 162, 163...), the transmissive metalens forming a phase gradient lens, the transmissive metalens having a first optical power in a first wavelength range, a second optical power in a second wavelength range, the first wavelength range and the second wavelength range being in a visible range and being distinct from each other, the array of nanostructures of the metalens being arranged and configured to induce a determined longitudinal chromatic aberration between the first wavelength range and the second wavelength range, a difference between the first optical power and the second optical power being comprised between 0,5 and 6 diopters in absolute value.

Description

[0001] LENS ELEMENT

[0002] TECHNICAL FIELD OF THE INVENTION

[0003] The invention relates to an optical article for reducing myopia progression. It also relates to vision compensation spectacles comprising a frame, a first optical lens intended to be worn in front of a first eye of a wearer and a second optical lens intended to be worn in front of a second eye of the wearer, in which at least one of the first and second lenses comprises such an optical article for slowing myopia progression.

[0004] More precisely the invention relates to a lens element based on a metamaterial lens, also named metasurface lens or metalens in short, configured to slow myopia progression.

[0005] BACKGROUND INFORMATION AND PRIOR ART

[0006] Myopia of an eye is characterized by the fact that the eye focuses light coming from far distance in front of the retina. In other words, a myopic eye presents a length that is not suitable for clear vision. Myopia has both genetic and environmental origins. In the latter case, it develops due for instance to the increase in near vision tasks, but also to less outdoor activities.

[0007] Many solutions exist that aim at slowing myopia progression.

[0008] Some solutions are based on optical systems for generating a difference in optical power for vision in the central foveal area and in peripheral areas of the eye. For example, it is known to use lenses having an array of refractive or diffractive micro-optical elements configured to induce blur in peripheral vision areas while enabling sharp vision in the foveal area of the eye.

[0009] Other solutions are based on the use of chromatic optical systems for creating different signals at different wavelengths in order to induce a chromatically stimulated myopic blur for controlling myopia progression. For example, it is also known to use diffusive, refractive or diffractive micro-optical elements to induce a chromatically simulated myopic blur. However, chromatism induced by a conventional optical lens is due to the lens material itself and cannot be adjusted.

[0010] SUMMARY OF THE INVENTION

[0011] The above objects are achieved according to the invention by providing a lens element intended to be placed in front of an eye of a viewer, the lens element comprising a transmissive metalens having an array of nanostructures, the transmissive metalens having a first optical power in a first wavelength range, a second optical power in a second wavelength range, the first wavelength range and the second wavelength range being in an optical range and being distinct from each other, the array of nanostructures of the metalens being arranged and configured to induce a determined longitudinal chromatic aberration between the first wavelength range and the second wavelength range, a difference between the first optical power and the second optical power being comprised between 0,5 and 6 diopters in absolute value.

[0012] Thus, some of the wavelengths transmitted by the metalens are defocused, or out of focus, on the retina.

[0013] The transmissive metalens is a phase gradient lens, or, in other words, a surface with a determined phase gradient.

[0014] The optical range comprises preferably a visible range, and / or an infrared range of wavelengths.

[0015] The difference, or spectral separation, between the first wavelength range and the second wavelength range is at least 50 nm, for example 100 nm or 200 nm.

[0016] The metalens thus configured is a compact, ultra-thin and light-weight surface providing on-demand chromatic blur for controlling abnormal refractions of the eye, in particular myopia or myopia evolution. The metalens enables to obtain performances comparable or even superior to a stack of multiple diffractive and / or refractive lenses.

[0017] According to a particular and advantageous aspect, the first wavelength range and the second wavelength range are selected among a red wavelength range, a blue wavelength range and a green wavelength range.

[0018] Indeed, these wavelength ranges are particularly relevant to decrease the myopia of the wearer.

[0019] Preferably, the first wavelength range and the second wavelength range are distinct from each other by at least 50nm, 100nm, 200nm.

[0020] According to other particular and advantageous aspects, the array of nanostructures is placed on a surface of a substrate, the substrate having an optical power or not, and the arrangement of the nanostructures varies across the surface of the substrate by at least one of the following features:

[0021] - dimension of the nanostructures parallel to the surface of the substrate; - shape of the nanostructures;

[0022] - position of the nanostructures in the array of nanostructures;

[0023] - orientation of the nanostructures ;

[0024] - material of the nanostructures ;

[0025] - material surrounding the nanostructures;

[0026] - density of the nanostructures in the array;

[0027] - height of the nanostructures transverse to the surface of the substrate. According to an embodiment, the array of nanostructures comprises a first subset of nanostructures and a second subset of nanostructures, wherein all the nanostructures of each one of the first subset and the second subset have the same features (shape, dimensions, orientation and composition...), and wherein the nanostructures of the second subset differ from the nanostructures of the first subset by at least one of the following features: shape, dimensions, orientation and / or composition.

[0028] According to another particular and advantageous aspect, the metalens comprises a single layer of nanostructures arranged on a surface of the lens element or inside the lens element or on a surface of the lens element inside a layer.

[0029] Advantageously, each nanostructure of the array has a height in a direction transverse to said surface and each nanostructure of the array has at least one submicrometric dimension parallel to said surface.

[0030] In an embodiment, each nanostructure of the array is defined by an axis and a cross-section of each nanostructure of the array is chosen among a plurality of shapes: disk, elliptical, polygonal, square, rectangle, cross, T-shape and / or a non-geometric shape and / or a composite shape, for example the composite shape is a combination of an elliptical shape and a square shape.

[0031] In a particular embodiment, each nanostructure of the array is a cylinder defined by a cylindrical cross-section and a cylindrical axis.

[0032] Advantageously in this embodiment, the cylindrical axis of each nanostructure of the array is perpendicular to the surface of the lens element.

[0033] According to an embodiment, the array comprises a subset of nanostructures having the same height, and the arrangement of the subset of nanostructures varies across the surface of the lens element by the shape of their cross-section.

[0034] Alternatively, or complementarily, the array comprises a subset of nanostructures having a cross-section of the same shape, said shape presenting an asymmetry around their axis and the arrangement of the subset of nanostructures varies across the surface of the lens element by the orientation of the nanostructures of the subset.

[0035] Still alternatively or complementarily, the array comprises a subset of nanostructures having a cross-section of the same shape and the arrangement of the subset of nanostructures varies across the surface of the lens element by the dimension of the cross-section of the nanostructures of the subset.

[0036] According to another particular aspect, each nanostructure of the array is made of a first material surrounded by void or encapsulated by a second material, each nanostructure being filled by any one of a void, the first material, the second material or a third material or each nanostructure of the array is made of a cavity in a surrounding material, the cavity being filled by void or by an inner material.

[0037] According to an embodiment, the nanostructures of the array have a crosssection with the same shape and the dimensions of the nanostructures and / or a distance between adjacent nanostructures vary across the surface of the lens element so as to form a gradient phase lens which results in a focused field in a focal plane for the first wavelength range and in a different focal plane for the second wavelength range.

[0038] For example, the nanostructures of the array are made of silicon nitride cylinders of the same height surrounded by a silicon dioxide layer, the nanostructures of the array having a cross-section with a disk shape and wherein the diameter of the nanostructures and / or a distance between adjacent nanostructures varies across the surface of the lens element so as to form a gradient phase lens having a phase response with an Airy-like field distribution in a focal plane for the first wavelength range and in a different focal plane for the second wavelength range.

[0039] Advantageously, the lens element further comprises a coating layer on the array of nanostructures.

[0040] According to a particular aspect, the lens element further comprises a second material encapsulating the array of nanostructures.

[0041] According to an example, the lens element comprises a base lens, the metalens being arranged on a surface of the base lens.

[0042] A further object of the invention is to provide a computer program for designing a transmissive metalens, the computer program comprising the following steps:

[0043] a) numerically generating a library of unit cells;

[0044] b) Selecting as an optimization target for the transmissive metalens to have a given response at least in a first wavelength range and in a second wavelength range, the first wavelength range and the second wavelength range being in an optical range and being distinct from each other;

[0045] c) adjusting the arrangement and configuration of the unit-cells on the metalens so that the transmissive metalens has a first optical power in the first wavelength range a second optical power in the second wavelength range, wherein a difference between the first optical power and the second optical power is comprised between 0.5 and 6 diopters in absolute value.

[0046] DETAILED DESCRIPTION OF EXAMPLE(S)

[0047] The following description with reference to the accompanying drawings will make it clear what the invention consists of and how it can be achieved. The invention is not limited to the embodiment / s illustrated in the drawings. Accordingly, it should be understood that where features mentioned in the claims are followed by reference signs, such signs are included solely for the purpose of enhancing the intelligibility of the claims and are in no way limiting on the scope of the claims.

[0048] In the accompanying drawings:

[0049] - Figure 1 represents in cross-section a lens element comprising refractive lens with a plurality of transmissive metalenses arranged in some areas on the surface of the refractive lens according to an embodiment of the present disclosure

[0050] - Figures 2A-2E show in perspective different examples of nanostructures suitable for being used in a metalens ;

[0051] - Figure 3 shows in cross-section an example of a nanostructure forming a cavity inside a substrate and suitable for being used in a metalens according to the present disclosure ;

[0052] - Figure 4 shows in cross-section an example of a nanostructure with a core and a coating layer made of different materials ;

[0053] - Figure 5 shows in cross-section an example of an array of nanostructures suitable for forming a metalens;

[0054] - Figure 6 shows examples of graphs of the phase distribution of a metalens for different wavelengths in the visible range, respectively at a wavelength of 450 nm for the black line and 650 nm for the dashed line ;

[0055] - Figure 7 shows in perspective an example of a metalens based on nanostructrures having a structure and geometry as disclosed in fig. 4 arranged to form a focusing field distribution;

[0056] - Figure 8 shows a cross-section view of an eye equipped with a metalens and shows the focusing of an incident light beam at a first wavelength and respectively a second wavelength ;

[0057] - Figure 9 shows an example of focal planes design targets for a metalens, at a first wavelength of 450 nm (fig. 9(A)) and respectively at a second wavelength of 650 nm (fig. 9(B)), and the optimization results at the first wavelength of 450 nm (fig. 9(C)) and respectively at the second wavelength of 650 nm (fig. 9(D)); Instead of defining target phase profiles explicitly as shown in figure 6, in this example we define focal planes from which we further reconstruct transmission phase and amplitude of metalens elements;

[0058] - Figure 10 shows graphs simulating the intensity of the electromagnetic fields in a longitudinal plane of the metalens, respectively at the first wavelength of 450 nm (fig. 10(A)), at the second wavelength of 650 nm (fig. 10(C)) and at a third wavelength of 550 nm (fig. 10(B));

[0059] - Figure 11 shows a schematic graph of a computer program for designing a transmissive metalens adjusted for inducing chromatically stimulated myopic blur according to the present disclosure.

[0060] Device

[0061] Figure 1 shows a lens element 200 intended to be placed in front of an eye of a viewer. The lens element 200 may be mounted to form the left or right lens of an eyewear for vision correction. An orthonormal reference system is displayed on figure 1. Figure 1 is taken in the YZ plane, the Z axis being parallel to a longitudinal propagation axis of an incoming light beam.

[0062] More precisely, the lens element 200 comprises one transmissive metalens 100 or a plurality of transmissive metalenses 100, 101, 102, 103, ..., 109 arranged in some area(s) on a surface 22 of a base lens 20, for example here a refractive lens for an ophthalmic eyewear. Each metalens 100, 101, 102, 103, ..., 109 comprises an array of nanostructures. The different metalenses 100, 101, 102, 103, ..., 109 may be identical to each other and provide a similar optical phase response, or may have different features and each metalens provides a distinct optical phase response.

[0063] As illustrated for example in the enlarged portion of figure 1, the array of nanostructures of the metalens 100 is formed on a substrate 10 having a first surface 11 and a second surface 12. The array of nanostructures of the metalens 100 is formed on the second surface 12 of the substrate. In the example illustrated in figure 1, the first surface 11 and the second surface 12 are generally plane and parallel surfaces. The substrate 10 is for example made of a glass, a mineral or organic glass, or a resist layer. Alternatively, the array of nanostructures of the transmissive metalens 100 is formed on a plane surface, convex surface 22 or concave surface 21 of the refractive lens 20.

[0064] In the present disclosure, a nanostructure forms either a protrusion or a cavity, the nanostructure having an average in-plane size or diameter, measured in the plane of the second surface 12, that is less than or of the same order of magnitude as the wavelength of the input light for which it is designed. The average in-plane size or diameter is greater than a few tens of nanometers, for example greater than 50 nm, 75 nm, 100 nm, 150 nm, 200 nm, 250 nm, 300 nm or 350 nm. Preferably, the lens element is designed to be used in daylight, at wavelengths extending between a blue range (from 400 nm to 495 nm), for example at 450 nm, and a red range (from 620 nm to about 780 nm), for example at 650 nm. The optical range includes optionally a green wavelength range from about 495 nm to about 570 nm. For application in the visible range, the average in-plane size is sub-micrometric and generally lower than 700 nm. For application in the infrared range (i.e. at wavelengths higher than 780nm and preferably lower than 2pm), the average in-plane size is sub-wavelength and generally lower than 2pm.

[0065] According to the present disclosure, an array of nanostructures refers to a set of nanostructures arranged on the same surface wherein each nanostructure of the set is at a sub-micrometric distance from the nearest neighboring nanostructure for application in the visible optical range, and respectively at a distance lower than 2 micrometers from the nearest neighboring nanostructure for application in the infrared range. The array may be arranged in a regular, periodic pattern along one or two directions. For example, the array is arranged with a square / rectangular or hexagonal grid or in a pattern with a rotational symmetry such as along concentric circles about a longitudinal optical axis transverse to the plane of the array. The array of nanostructures may cover the full surface 12 of the substrate 10 or cover only a part or separate parts thereof, for example a central part and / or one or several peripheral parts. Other patterns for the array are also considered.

[0066] The nanostructures of the array may all have the same structure, composition, dimensions, and orientation, or may vary by one or several of these parameters throughout the array. Generally, all the nanostructures of an array have the same height H in the direction transverse to the average plane of the array of nanostructures. The number of nanostructures in the array depends on the dimension of the area of the array of nanostructures, on the size and density of the nanostructures. For example, a metasurface lens on a surface area of 1mm2may include between 1 million and 10 millions unit-cells, each unit-cell containing one or several nanostructures. Each unit-cell corresponds to an element in a numerical library used to calculate separately its phase response or its focusing field distribution, with periodic boundary conditions, as detailed hereinafter.

[0067] The metasurface lens or metalens 100, 101, ...109, is a metamaterial extremely thin along the longitudinal propagation direction of light. The metalens 100, 101, ...109 operates as a phase gradient surface designed in transmission. When the metalens 100, 101 , ...109 receives an incident light field, for example from a collimated input light beam 40, the metalens 100, 101, ...109 generates an output light field having a phase gradient depending on the arrangement of the array of nanostructures. More precisely, the phase gradient is created by spatial variations of the nanostructures geometric properties in the array, such as their size, shape and / or orientation. In contrast, a conventional lens operates to create a phase gradient, in general spatially continuous, by changing locally the thickness of the lens as a function of the position of each incident light beam, which turns into an optical power.

[0068] In a metalens, the physical mechanisms for creating a gradient of phase can be different depending on the size and materials used for the nanostructures. The nanostructures can be sorted in different types depending on the type of interaction with the input light. The nanostructures can be isotropic non-resonant nanostructures, anisotropic non-resonant nanostructures or resonant nanostructures. In each case, phase gradient doesn’t require variation of nanoparticles height along the propagation direction of light, which simplifies the manufacturing of the metalens. Nevertheless, if the manufacturing technology allows varying the height of the nanostructures, this variable height can be an additional degree of freedom in the design of the metalens.

[0069] In the case of isotropic non-resonant nanostructures, the combination of the array of nanostructures and the surrounding medium in the different proportions creates a gradient of effective refractive index.

[0070] In the case of anisotropic non-resonant nanostructures, a so-called Pancharatnam-Berry phase metalens is based on an array of anisotropic nanostructures which creates an effective birefringence and leads to geometric phase accumulation for circularly polarized light.

[0071] In the case of resonant nanostructures, phase accumulates due to the resonant interaction of light with nanoparticles having the size of the order of the wavelength of the input light. In the case of a metalens based on resonant nanostructures, light is only focused in a narrow range of wavelength (of the order of 10-50 nm around the target wavelength or larger, depending of the resonance quality factor), all other wavelengths being unaffected by the resonant nanostructures. Advantageously, such a metalens has a smaller thickness, around 100-300 nm.

[0072] In the examples below, the metalens is based on non-resonant nanostructures, which can be isotropic or anisotropic depending on their geometry. However, the scope of the present application also includes resonant nanostructures.

[0073] The metalens 100 enables providing a phase gradient corresponding for example to an optical power, while being extremely thin, light weight and having a high transmission.

[0074] According to the present disclosure, the metalens 100 is conceived and manufactured to provide a specific, on-demand wavelength-dependent or chromatic optical field distribution. More precisely, the transmissive metalens 100 presents a first optical power in a first wavelength range and a second optical power in a second wavelength range, the first wavelength range and the second wavelength range being distinct from each other. Advantageously, the first wavelength range and the second wavelength range are in the visible range. Alternatively, the first wavelength range and / or the second wavelength range is / are in the near-infrared range. Moreover, the array of nanostructures of the metalens is arranged and configured to induce a determined longitudinal chromatic aberration between the first wavelength range and the second wavelength range. The difference between the first optical power and the second optical power is comprised between 0,5 and 6 diopters in absolute value and the difference between the first wavelength range and the second wavelength range is at least 50 nm, for example 100 nm or 200 nm. In other words, the difference between the focal planes between the first wavelength range and the second wavelength range is comprised between (and including) 0.2 mm and 2 mm along the direction of the longitudinal axis of propagation of the light beam.

[0075] In particular, the metalens 100 with such a specific chromatism finds application in control of the evolution of myopia and / or in prevention of myopia. The longitudinal chromatism induced by the metalens is not intended to compensate the intrinsic chromatism of the eye. In contrast, the focusing of different wavelengths in different planes at different distances from the retina may be a cue for the eye to inhibit further growth of the eye, and thus to reduce or even stop the evolution of myopia. In some cases, a reduction of the length of the eye may occur due to this induced myopic blur.

[0076] In further examples, we use the case of isotropic non-resonant nanostructures, but the scope of the present disclosure also includes the use of anisotropic or resonant nanostructures to obtain a similar effect.

[0077] As detailed in relation with figures 2A-2E, 3-4 and 6-7, the nanostructures are not only defined by their geometry but also by the materials used, the distance between adjacent nanostructures and / or the presence of a coating layer and / or of an embedding medium.

[0078] In particular, the metalens of the present disclosure is based on the use of an array of nanostructures, wherein the nanostructures present different geometries and / or in-plane dimensions to create a specific chromatism.

[0079] Figures 2A-2E show different examples of nanostructures based on various cylindrical geometries protruding out of the surface 12 of the substrate 10. Each nanostructure has a generatrix line, for example perpendicular to the surface 12 of the underlying substrate 10, 18. Alternatively, the generatrix lines of the nanostructures of an array are tilted relatively to the normal to the underlying substrate 10, 18.

[0080] Figure 2A shows a nanostructure 161 having a square cross-section of width W and height H. Figure 2B shows a nanostructure 162 of height H and having an X-shaped cross-section, each branch of the X having a thickness T and a length W.

[0081] Figure 2C shows a nanostructure 163 having a circular cross-section of diameter W and height H.

[0082] Figure 2D shows a nanostructure 164 having a non-geometric crosssection of larger width W and height H.

[0083] Figure 2E shows a nanostructure 165 having a T-shaped cross-section of height H, the leg of the T having a length L1 and a width W1 and the top of the T having a length L2 and a width W2.

[0084] The shapes illustrated in figures 2A, 2B, 2D and 3E are anisotropic and the shape illustrated in figure 2C is isotropic.

[0085] Of course, other geometric or non-geometric shapes for cylindrical crosssection are available such as rectangular or elliptical shapes.

[0086] Figure 3 illustrates another type of nanostructure 168 made of a cavity in a surrounding material 13. The cavity is filled by void or by an inner material different from the surrounding material 13. The cross section of the cavity in the XY plane is for example a non-geometric shape or a geometric shape such as a circle, a square, a rectangle, a cross, a T-shape. The cavity has an in-plane width W and a depth D in the direction Z parallel to the longitudinal propagation axis of the incoming light beam. The dimensions of the width W and depth D are less than the wavelength of the incoming light beam.

[0087] Figure 4 shows a cross-section view of another nanostructure 166 comprising pillars made of a first material 17 having a height H1 and a width W1 and further comprising a conformal coating layer 18 made of a second material. The resulting nanostructure 166 has a height H2 greater than H1 and a width W2 larger than a width W1. The thickness of the layer 18 depends on the chosen lamination or coating technique, which partially depend on the nanostructures final dimensions. The thickness of the layer 18 can vary from 1 micrometer to several tens of micrometers, for example 50 pm or 100 pm. The coating layer 18 performs its function as soon as the nanostructures are completely covered. The thickness of the coating layer 18 more than this minimum thickness doesn't change metalens properties.

[0088] In an embodiment, the metalens 100 comprises an array of nanostructures based on various geometries enabling to adjust the phase gradient induced by the metalens 100.

[0089] The array of nanostructures forming the metalens is advantageously based on a plurality of nanostructures geometry as illustrated in figures 2A-2E, which enables adjusting more than one optical parameter.

[0090] Figure 5 shows a cross-section view of a metalens 100 comprising an array of nanostructures having all the same geometry, for example a cylindrical pillar with a disk cross section of variable diameter W across the array of nanostructures. The nanostructures 16, 161, 162, 163..., respectively 168, have the same height H, respectively the same depth D. Optionally, the array of nanostructures is encapsulated by a second material 19. The encapsulating material 19 protects the array of nanostructures from dust or scratch. The encapsulating material 19 has a plane outer surface. The encapsulating material and its thickness depend on the fabrication technology. For example, the encapsulating layer is obtained by covering the nanostructures with a resist layer (such as PMMA or SU8) using spin-coating and ultraviolet or thermal polymerization. Alternatively, the encapsulating layer is obtained by lamination of a pressure sensitive adhesive, for example, Pro 22 resist, arranged on the nanostructures. Other known encapsulating materials and coating techniques can be used as well. The thickness of the encapsulating layer doesn't matter for the optical properties of the metasurface lens provided that the nanostructures are completely covered with the encapsulating material. The minimum thickness is in the range of 1 to 10 micrometers. The encapsulating material 19 used in the simulation below is a layer of silicon dioxide.

[0091] Alternatively, or complementarily, the metalens 100 is encapsulated by a sealed window 1 attached to the substrate 10 by an opto-mechanical mount 2. The voids between and / or inside the nanostructures are filled by air or another material.

[0092] A numerical library or database stores the different shapes and composition of nanostructures 161, 162, 163, 164, 165, 166, 168... The variable parameters of the nanostructures include the geometrical dimensions and the optical refractive index of the materials. The range of variation of the variable parameters is also stored in this library of nanostructures. More precisely, the database stores unit-cells, each unit-cell containing one or several nanostructures.

[0093] The optical response and in particular the phase gradient of an array of nanostructures can be simulated numerically. As mentioned above, the metalens is conceived to generate a specific chromatism between wavelengths in at least two separate wavelength ranges. Adjusting the geometrical parameters and / or the material(s) of the nanostructures of the array enables achieving a different phase gradient for at least two distinct wavelengths.

[0094] The target objectives to design a metalens comprise for example a first focal length fi at a first wavelength i and a second focal distance f2 at a second wavelength 2. As known, a focal distance or focal length, denoted f, is equal to the inverse of the optical power, denoted D, expressed in diopters: f=1 ZD. The target objectives for the metalens also comprise a transmission amplitude as high as possible, depending on each embodiment regarding the wavelengths, the patterns, the use of the wearer, the application, for example a transmission amplitude higher than 80%. Optionally, the target objectives to design a metalens comprise a third focal distance fs at a third wavelength fa, or equivalently a third optical power.

[0095] Preferably, the first wavelength range is in the blue range of visible light and the second wavelength range is in the red range of visible light. Alternatively, the first wavelength range is in the blue range of visible light and the second wavelength range is in the green range of visible light. Still alternatively, the first wavelength range is in the green range of visible light and the second wavelength range is in the red range of visible light. In a specific example, the first wavelength range is in the blue range of visible light, the second wavelength range is in the red range of visible light and the third wavelength is in the green range of visible light.

[0096] The relation between the phase profile cp(x, y) and the focal length f can be expressed by the following equation:

[0097]

[0098] where x and y stand for the coordinates in an XY plane, orthogonal to the longitudinal direction of a light beam, and X stand for the wavelength of the light beam. Using this expression enables to calculate the phase profile targets for the distinct wavelengths fa, fa and optionally fa. The relation between phase profile and focal distance can be expressed by another function.

[0099] The target objectives can thus be defined by absolute phase profiles cp(x, y) for distinct wavelengths. If the phase profile presents a rotational symmetry about the longitudinal axis of the light beam it is simplified in absolute phase profiles cp(x). Of course, non-symmetrical phase profiles are also considered without departing from the scope of the present application.

[0100] In some cases, the relation between phase profile and focal distance cannot be expressed by any analytical function at all. In this case, the phase value at each spatial point (x, y) is calculated numerically based on the position of a focal plane and desired electromagnetic field distribution in the focal plane. In this case, the target objectives are defined by a certain field distribution in the desired focal plane, without using any analytical function to define the target phase profile.

[0101] Figure 6 shows an example of target cross-section phase profiles, here for two different wavelengths. The modeled metalens has a diameter of 1 mm. The black line graph represents a target phase profile at a first wavelength of 450 nm, i.e. in the blue range of visible light. It corresponds to a focal distance of 50 mm. The dashed line graph represents a target phase profile at a second wavelength of 650 nm, i.e. in the red range of visible light. The phase profiles are assumed to present a rotational symmetry about the longitudinal axis of the light beam of coordinates (x, y) = (0, 0). The target phase profiles in figure 6 present the same phase for the coordinate x=0, i.e. along the longitudinal axis of the light beam, for the red and blue wavelengths. However, the phase gradient along the X axis is different for each wavelength.

[0102] Simple or composite nanostructures of defined or arbitrary shape (for example illustrated in figures 2A-2E) make a library of elements, also called unitcells, for the metalens design, also called metasurface library. The more diverse is this library, the bigger is the number of parameters that can be used in numerical simulations of the metalens properties. While preparing the library of elements, such parameters as refractive index and thickness relative to the substrate 10, the coating layer 18, the encapsulating material 19 and / or respectively to the protective window 1 are also taken into account to calculate the performance of the individual nanostructures.

[0103] An inverse design software with numerical optimization is used to optimize the design of the metalens in order to obtain the defined target objectives. The inverse design software uses the library of nanostructures and enables selecting nanostructure’s shape for each spatial position. For example, the software calculates the field distribution in the focal plane and in the cross-section of the focal plane. The optimization can be based not on a single target at a single wavelength but on multiple targets. The target is not to produce an achromatic metalens, but, in contrast, a metalens with a specific chromatism. To that end, on-demand performances of the metalens are requested simultaneously for several wavelengths. When we design a metalens with a certain chromatic response, we need to satisfy several phase objectives for several wavelengths at the same time (for example as illustrated on figure 6). For that, we need to calculate not only the metalens phase, but also its rate of change with respect to wavelength (ora spectral derivative of a phase). The more diverse is the library of elements, the more combinations of phase and its derivative are available for accurately mapping all the phase objectives at different wavelengths.

[0104] Preferably, the target objectives of the inverse design software also include a transmission efficiency at the considered wavelengths. In the present disclosure, a transmission efficiency is defined as the ratio of the transmitted power to the incident power, it is calculated for every unit-cell separately. While optimizing the focusing objectives, which are often expressed as a phase profile target, we also want to maximize the transmitted power.

[0105] The point-by-point elements selection of the nanostructures is done using numerical optimization. In case it is not possible to fulfill all the target objectives exactly, some targets have a higher priority than other targets.

[0106] The simulated metalens can be designed as a polarization-independent component. Alternatively, the simulated metalens is conceived to operate for a certain state of polarization, for example circular or linear. In some cases, the resulting metalens is conceived to be polarization-multiplexed : the metalens performs one function for one state of polarization and another function for another state of polarization.

[0107] Figure 7 shows an example of a metalens calculated to provide chromatically stimulated myopic blur. First, nanostructures are selected in the library of elements. The selected nanostructures are based on the geometry and structure illustrated in figure 4. The nanostructures 166 consist of nanocylinders made of a first material 17, here silicon nitride SisN4 placed on a substrate 10 of silicon dioxide glass, SiC>2, and wherein the nanocylinders are surrounded by a layer made of a second material 18, here silicon dioxide SiCh. The nanopillars, nanocylinders and nanostructures 166 have a circular cross-section. The medium on top of the nanostructures 166 is also glass to account for the top coating. In this example, both top and bottom media are considered infinite. Alternatively, the top coating has a finite thickness and presents an interface with air on top which becomes a propagation medium. Other materials are also available for the first and / or second materials. An important criterion is to have a sufficient refractive index contrast between the pillars made of the first material 17 and the top medium made of a second material.

[0108] In this example, the nanostructures are arranged on a square grid having a period of 500 nm. The height H2 of the nanostructures is fixed to 1100 nm. In modeling, the radius of the nanostructures 166 varies for example between 40 nm and 200 nm with a minimum step of 5 nm. In manufacturing, the radius of the nanostructures 166 varies across the surface of the metalens 100, here for example between 40 nm and 200 nm, with a minimum step depending on the spatial resolution of the manufacturing method. These parameters are selected to produce sufficiently high transmission phase variation or phase gradient (preferably from 0 to 2TT) and as high a transmission amplitude as possible.

[0109] According to the present disclosure, the metalens enables generating on-demand wavelength-dependent optical field distribution, in particular for myopia control. The difference between the first optical power and the second optical power is adjusted on-demand and comprised between 0,5 and 6 diopters in absolute value. The design and optimization of the metalens enables a high degree of chromatism control with a single layer of a nanostructured surface.

[0110] Figure 8 schematically shows a myopic eye 30 equipped with a metalens 100 placed in front of the cornea of the eyeball. A collimated light beam 40 is transmitted and focused by the metalens 100 and enters the eye through the cornea, crystalline lens 31 and aqueous humor of the eye. The metalens 100 is here designed to focus the blue light at a relatively short focal distance (for example, fi = 50 mm) and to focus the red light at a longer focal distance (for example, f2 = 100 mm). In other words, the difference between the first optical power and the second optical power is here equal to 2 diopters in absolute value. Focal plane locations can be adapted to a given eye and prescription. Myopic blur is induced by defocusing in the retina.

[0111] In alternative embodiments, the metalens 100 is designed to focus the red light at a relatively short focal distance and to focus the blue light at a longer focal distance. In the example illustrated in figure 8, the red light is focused in a plane in front of the retina 32 and the blue light is also focused in front of the retina 32, the red light being focused closer than the blue light from the retina. However, depending on the prescription for controlling myopia, other configurations are also considered and achievable such as : focusing the red light on the retina and the blue light in front of the retina, or focusing the red light on the retina and the blue light behind the retina, or focusing both the blue light and the red light behind the retina.

[0112] A metalens 100 having a diameter of 1 mm is simulated based on the following requirements. The metalens 100 is here designed to focus the blue light at the first wavelength fa of 450 nm at the first focal length fi of 50 mm and to focus the red light at the second wavelength fa of 650 nm at the second focal length f2 of 100 mm.

[0113] Figure 9(A), respectively 9(B), represents the target of the intensity of the electromagnetic field distribution in the XY plane at the first focal distance for the first wavelength fa, respectively at the second focal distance the second wavelength fa. The design target for the distribution of the electromagnetic field is assumed to be diffraction-limited focal spot for the first wavelength fa of 450 nm in the focal plane fi = 50 mm, and respectively for the second wavelength fa of 650 nm in the focal plane f2 = 100 mm. In addition to focusing, the target of maximizing the possible transmission and focusing efficiency was added. The design of a metalens 100 is optimized for these target parameters using the inverse design software based on the adjoint method. The optimization results are shown in Fig. 9(C) for first wavelength fa and, respectively, Fig. 9(D) for the second wavelength fa. By comparing fig. 9(A) and 9(C), respectively 9(B) and 9(D), it is observed that the distribution of intensity in the respective focal planes resemble closely to the target diffraction-limited spots.

[0114] Figure 10 shows the longitudinal cross-section of the focused electromagnetic fields respectively for the blue light at the first wavelength fa of 450 nm (fig. 10(A)), for the green light at a third wavelength fa of 550 nm, and for the red light at the second wavelength fa of 650 nm. The maxima of intensity along the longitudinal axis Z correspond respectively to the focal length fi of 50 mm for the first wavelength fa of 450 nm (fig. 10(A)), to the focal length fs of about 45 mm for the green light at a third wavelength fa of 550 nm, and to the focal length f2 of 100 mm for the red light at the second wavelength fa of 650 nm. Both transmission amplitude and phase are modeled for each unit-cell using rigorous coupled wave analysis (RCWA), or, alternatively, using finite difference time domain method or finite element method. Transmission amplitude for the unit-cells chosen for the metalens is averaged. Average transmission for the calculated library is the example illustrated in figure 10, of 94% at 650 nm, 91% at 550 nm, and 77% at 450 nm.

[0115] The transmission efficiency of the metalens can be further improved by selecting specific dimensions, materials and coatings for the library of nanostructures. Similarly, the focusing efficiency at each wavelength can be improved by selecting in the library a plurality of nanostructures of different crosssection shapes : squares, crosses, etc. or by adding nanostructures with holes or cavities of different shapes and sizes, rectangles or more complex composite nanostructures. The use of anisotropic nanostructures also enables to adjust the orientation of each anisotropic nanostructure in the metalens.

[0116] A metalens according to the optimized design is manufactured using for example electron beam lithography, nano-imprint, 2-photon absorption or deep UV lithography.

[0117] The thickness of the metalens is mostly equal to the thickness of the substrate, for example of the order of 0.5 mm, and the total weight is about 15 g, because the size and weight of the nanostructures are negligibly small compared to the substrate on which they are deposited.

[0118] The metalens can be placed on a plane and parallel glass substrate. Alternatively, the metalens thus obtained is placed on the glass or refractive lens of an eyewear, the refractive lens being suitable for correcting refractive error of the eye. The area of the metalens covers the full surface of the glass or only a part of it. In another application, the metalens is formed on a surface of a contact lens. Preferably in this case, the metalens 100 is encapsulated with an embedding layer.

[0119] The same metalens disclosed in the present specification can be described from another point of view using the Modulation Transfer Function (MTF) as a metric. MTF is a lens’s ability to reproduce different spatial details of an object. It describes how well the lens preserves contrast at various spatial frequencies. The MTF can vary with wavelength because optical properties — such as diffraction, dispersion, and aberrations — are wavelength-dependent. However, the design described in this invention is able to control the difference between MTF at different wavelengths. In other words, this design provides the possibility to control the contrast of the image perceived by eye at different wavelengths.

[0120] Process

[0121] Figure 11 schematically shows a computer program for designing a transmissive metalens for inducing chromatically stimulated myopic blur. The computer program is connected to a library or database including values of each unit-cell response in terms of complex fields or reflection and transmission coefficients at various wavelengths. These values are calculated considering different nanostructures geometry and composition, including refractive indices of materials, a period, shapes and sizes of nanoparticles. The positions of the unitcells with respect to each other on the surface of the metalens are not included into library. The positions of the nanostructures are determined during the process of optimization.

[0122] The resulting optical phase and the transmission coefficient for each nanostructure or unit-cell may be computed individually, thus forming a library of elements.

[0123] Depending on the prescription for a given eye, the target phase profiles and / or or the target positions of the focal planes are generated for at least two distinct wavelengths.

[0124] The inverse design software based for example on the adjoint method is used to select the elements from a pre-calculated library in order to optimize the resulting response and minimize the difference between the target performance and the real performance of the component.

[0125] In summary, the computer program comprises the following steps :

[0126] 17a) numerically generating a library of elements by calculating unit-cells response (complex transmitted and / or reflected fields or complex transmission and / or reflection coefficients calculated with periodic boundary conditions) as a function of unit-cell geometry for given materials selected for this library

[0127] 17b) Setting the optimization target by selecting a desired response (for example, focusing light at a first focal distance for a first wavelength and at a second focal distance at a second wavelength. We can also add a target of maximizing the component transmission (or other efficiency targets).

[0128] 17c) adjusting the arrangement and configuration of the array of nanostructures with numerical optimization using the data from the pre-calculated library so that the transmissive metalens produces a desired response defined as an optimization target (for example, has a first optical power in the first wavelength range a second optical power in the second wavelength range, wherein a difference between the first optical power and the second optical power is comprised between 0.5 and 6 diopters in absolute value).

Claims

CLAIMS1. Lens element intended to be placed in front of an eye of a viewer, the lens element comprising:a transmissive metalens having an array of nanostructures, the transmissive metalens having a first optical power in a first wavelength range, a second optical power in a second wavelength range, the first wavelength range and the second wavelength range being in an optical range and being distinct from each other, the array of nanostructures of the metalens being arranged and configured to induce a determined longitudinal chromatic aberration between the first wavelength range and the second wavelength range,a difference between the first optical power and the second optical power being comprised between 0,5 and 6 diopters in absolute value.

2. Lens element according to claim 1 wherein the first wavelength range and the second wavelength range are selected among a blue wavelength range, a green wavelength range and a red wavelength range.

3. Lens element according to any one of claims 1 to 2, wherein the array of nanostructures is placed on a surface of a substrate and wherein the arrangement of the nanostructures varies across the surface of the substrate by at least one of the following features:- dimension of the nanostructures parallel to the surface of the substrate;- shape of the nanostructures;- position of the nanostructures in the array of nanostructures;- orientation of the nanostructures ;- material of the nanostructures ;- material surrounding the nanostructures;- density of the nanostructures in the array;- height of the nanostructures transverse to the surface of the substrate.

4. Lens element according to any one of claims 1 to 3, wherein the array of nanostructures comprises a first subset of nanostructures and a second subset of nanostructures, wherein all the nanostructures of each one of the first subset and the second subset have the same features (shape, dimensions, orientation and composition...), and wherein the nanostructures of the second subset differ from the nanostructures of the first subset by at least one of the following features: shape,dimensions, orientation and / or composition.

5. Lens element according to any one of claims 1 to 4, wherein the metalens comprises a single layer of nanostructures arranged on a surface of the lens element or inside the lens element or on a surface of the lens element inside a layer.

6. Lens element according to claim 5 wherein each nanostructure of the array has a height in a direction transverse to said surface of the lens element and each nanostructure of the array has at least one submicrometric dimension parallel to said surface.

7. Lens element according to any one of claims 1 to 6, wherein each nanostructure of the array is defined by an axis and a cross-section of each nanostructure of the array is chosen among a plurality of shapes: disk, elliptical, polygonal, square, rectangle, cross, T-shape and / or a non-geometric shape and / or a composite shape.

8. Lens element according to claim 7, wherein each nanostructure of the array is a cylinder defined by a cylindrical cross-section and a cylindrical axis.

9. Lens element according to the claims 6 and 7, wherein the array comprises a subset of nanostructures having the same height, and wherein the arrangement of the subset of nanostructures varies across the surface of the lens element by the shape of their cross-section.

10. Lens element according to the claims 6 and 7, wherein the array comprises a subset of nanostructures having a cross-section of the same shape, said shape presenting an asymmetry around their axis and wherein the arrangement of the subset of nanostructures varies across the surface of the lens element by the orientation of the nanostructures of the subset.

11. Lens element according to any one of claims 7 to 10, wherein the array comprises a subset of nanostructures having a cross-section of the same shape and wherein the arrangement of the subset of nanostructures varies across the surface of the lens element by the dimension of the cross-section of the nanostructures of the subset.

12. Lens element according to any one of claims 1 to 11, wherein each nanostructure of the array is made of a first material surrounded by void or encapsulated by a second material, each nanostructure being filled by any one of a void, the first material, the second material or a third material or wherein eachnanostructure of the array is made of a cavity in a surrounding material, the cavity being filled by void or by an inner material.

13. Lens element according to the claims 7 and 12, wherein the dimensions of the nanostructures of the array and / or a distance between adjacent nanostructures varies across the surface of the lens element so as to form a gradient phase lens which results in a focused field in a focal plane for the first wavelength range and in a different focal plane for the second wavelength range.

14. Lens element according to any one of claims 1 to 13 further comprising a coating layer on the array of nanostructures.

15. Lens element comprising a base lens wherein the metalens is arranged on a surface of the base lens.

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