DEVICE FOR FORMING AN OUTGOING ELECTROMAGNETIC WAVE FROM AN INCIDENT ELECTROMAGNETIC WAVE

Abstract

An optical device forming an outgoing electromagnetic wave from an incident electromagnetic wave is disclosed. Such a device comprises at least one unit cell comprising: —at least two optical elements, an optical element being characterized by a type of optical response to said incident electromagnetic wave; —selection means enabling selective excitation of at least one optical element among the at least two optical elements, in response to said incident electromagnetic wave as a function of a wavelength of said incident electromagnetic wave, wherein said selection means comprise at one nanojet-based dielectric deflector compound of at least two dielectric material having different refractive indexes, and wherein said optical elements are placed at a distance from said nanojet-based dielectric deflector.

Claims

1. An optical device for forming an outgoing electromagnetic wave from an incident electromagnetic wave, wherein the optical device comprises at least one unit cell, the unit cell comprising: at least two optical elements; and a nanojet-based dielectric deflector configured to enable selective excitation of at least one optical element among the at least two optical elements, in response to the incident electromagnetic wave, the excitation being a function of a wavelength of the incident electromagnetic wave, wherein the nanojet-based dielectric deflector comprises at least one nanojet-based dielectric deflector compound of at least two dielectric materials having different refractive indexes, and wherein the optical elements are placed at a distance from the nanojet-based dielectric deflector.

2. The optical device of claim 1, wherein the nanojet-based dielectric deflector comprising a compound of at least two dielectric materials having different refractive indexes comprises at least a first part of dielectric material having a first refractive index n.sub.2, and a second part of dielectric material having a second refractive index n.sub.3, wherein the first part and the second part are embedded in a dielectric host medium having a refractive index n.sub.1, and wherein n.sub.1<n.sub.3<n.sub.2.

3. The optical device of claim 2, wherein the optical device is associated with a three-dimensional cartesian coordinate system defined by axis x, y and z with the z-axis being normal to the optical device, the first part and the second part of the nanojet-based dielectric deflector being positioned side by side along the x-axis, and wherein nanojet-based dielectric deflectors of the optical device are separated along the x-axis by a layer of the host medium.

4. The optical device of claim 3, wherein according to a cross section with a plane xz: the first part having a first width W.sub.1 along the x-axis, the second part having a second width W.sub.2 along the x-axis, wherein the width W.sub.1 and W.sub.2 respectively equals to or is higher than half of the wavelength of the incident electromagnetic wave propagating respectively in the first part and in the second part, the first part and the second part have a same height H along the z-axis, with $H\approx \frac{W_1+W_2}{\tan {\theta }_{B1}+\tan {\theta }_{B3}},$ θ.sub.B1 being the radiation angle of a first nanojet beam generated by a first edge along the z-axis of the nanojet-based dielectric deflector given by ${\theta }_{B1}\approx \frac{90°-{\sin }^{-1}\left(\frac{n_1}{n_2}\right)}{2},$ the first edge being between the first part and the host medium and θB.sub.3 being the radiation angle of a second nanojet beam generated by a second edge along the z-axis of the nanojet-based dielectric deflector given by ${\theta }_{B3}\approx \frac{90°-{\sin }^{-1}\left(\frac{n_1}{n_3}\right)}{2},$ the second edge being between the second part and the host medium.

5. The optical device of claim 4, wherein the distance is lower than or equals to H.sub.C−H.sub.B, and wherein H.sub.C and H.sub.B-are the distances between a bottom of the nanojet-based dielectric deflector and intersection points of nanojet beams associated with edges of the first and second parts of the nanojet-based dielectric deflector with $H_B\approx \frac{W_1+W_2}{\tan {\theta }_{B1}+\tan {\theta }_{B3}},\mathrm{and}{H}_C\approx \frac{W_2}{\tan {\theta }_{B3}-\tan {\theta }_{B2}}$ with θB.sub.2 being the radiation angle of a third nanojet beam generated by an edge along the z-axis of the nanojet-based dielectric deflector, the edge being between the first part and the second part of the nanojet-based dielectric deflector and ${\theta }_{B2}\approx \frac{90°-{\sin }^{-1}\left(\frac{n_3}{n_2}\right)}{2}.$

6. The optical device of claim 3, wherein a distance W.sub.3 between two nanojet-based dielectric deflectors along the x-axis in the optical device is higher than or equals half of a wavelength corresponding to a wavelength for the blue color.

7. The optical device of claim 3, wherein the refractive index n.sub.3 of the second part of the nanojet-based dielectric deflector is such that n.sub.3>√{square root over (n.sub.1×n.sub.2)}.

8. The optical device of claim 3, wherein the first part and the second part of the nanojet-based dielectric deflector have a shape of cuboids, or wherein the nanojet-based dielectric deflector has a shape of a half cylinder having an axis along the z-axis, with the second part being a half cylinder of radius R.sub.2 surrounding the first part being a half cylinder of radius R.sub.1.

9. The optical device of claim 8, wherein if the nanojet-based dielectric deflector has a shape of a half cylinder, the radius R.sub.1 and R.sub.2 of the first part and the second part are such that R.sub.2−R.sub.1<R.sub.1 and n.sub.3<√{square root over (n.sub.1×n.sub.2)}.

10. The optical device of claim 3, wherein all optical elements are located at a same distance along the z-axis from a top surface of the nanojet-based dielectric deflector.

11. The optical device of claim 3, wherein each optical element of the unit cell belong to a different set of optical elements, a set of optical elements being characterized by a type of optical response to the incident electromagnetic wave, and wherein the nanojet-based dielectric deflector is configured to selectively excite all optical elements belonging to a given set.

12. The optical device of claim 11, wherein optical elements of a same set are located at a same distance along the z-axis from a top surface of the nanojet-based dielectric deflector, and wherein the sets of optical elements are positioned at different distances along the z-axis from the top surface of the nanojet-based dielectric deflector.

13. The optical device of claim 11, wherein heights along the z-axis of optical elements of a first set are different from heights of optical elements of a second set.

14. The optical device of claim 1, wherein the optical elements belong to the group comprising: metallic particles; dielectric particles; semiconductor particles; optical resonators; and optical antennas.

15. The optical device of claim 1, wherein the optical elements are assembled on or inside a dielectric substrate.

16. The optical device of claim 15, wherein the nanojet-based dielectric deflector is placed at a distance below a surface of the dielectric substrate on which the optical elements are assembled.

17. The optical device of claim 1, wherein the nanojet-based dielectric deflector is a nanojet microlens embedded in the host medium or placed on a dielectric substrate acting as a support layer.

18. The optical device of claim 1, wherein the optical device belongs to an eyewear optical device or to a display device.

Description

4. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The present disclosure can be better understood with reference to the following description and drawings, given by way of example and not limiting the scope of protection, and in which:

[0071] FIG. 1 provides examples of metasurfaces devices according to the prior art;

[0072] FIG. 2 illustrates a side view (a) of a metasurface according to the prior art, FIG. 2 (b) shows a simulated far field intensity representation, FIG. 2(c) illustrates a far-field transmission measurement;

[0073] FIG. 3 (a) illustrates an artist view of a three-layer lens and FIG. 3 (b) shows a schematic illustration of a layered structure;

[0074] FIG. 4 (a) illustrates a schematic view of an exemplary apochromatic device according to an embodiment of the disclosure; Figures (b) and (c) are schematic drawings of an optical device according to embodiments of the present disclosure;

[0075] FIG. 5(a) illustrates an exemplary topology of an NJ-based dielectric color splitter with a normal incidence of the electromagnetic wave; FIGS. 5(b) and (c) illustrate cross-section views of a double-material dielectric microlens with n.sub.3>√{square root over (n.sub.1×n.sub.2)} and n.sub.3<√{square root over (n.sub.1×n.sub.2)} respectively; FIG. 5(d) illustrates an exemplary topology of an NJ-based dielectric color splitter with an oblique incidence of the electromagnetic wave having an angle θ.sub.i.

[0076] FIG. 6A illustrates power density distribution in (a) xz plane (Y=0) and (b) xy-plane (Z=1700 nm) for an exemplary optical device according to an embodiment of the present disclosure;

[0077] FIG. 6B illustrates power density distribution in (c) xz plane (Y=0) and (d) xy-plane (Z=1500 nm) for an exemplary optical device according to another embodiment of the present disclosure;

[0078] FIG. 7 illustrates a cross-section view of two unit cells of an exemplary optical device according to an embodiment of the present disclosure;

[0079] FIG. 8 illustrates power density distribution in the near zone for an exemplary optical device according to different embodiments (a, b, c) of the present disclosure;

[0080] FIG. 9 illustrates power density distribution in the near zone (xz plane, (Y=0) for a 1D periodic array (5 unit cells) for an exemplary optical device according to different other embodiments (a, b, c) of the present disclosure;

[0081] FIG. 10 illustrates an exemplary geometry (a) of a NJ-based microlens to be used in the optical device according to an embodiment of the present disclosure and its corresponding power density distribution in the xz-plane (b) and power density distribution in the xy-plane (c) for an exemplary optical device according to an embodiment of the present disclosure,

[0082] FIG. 11 illustrates an exemplary geometry (a) of an NJ-based microlens to be used in the optical device according to an embodiment of the present disclosure and its corresponding power density distribution in the xz-plane (b) and power density distribution in the xy-plane (c) for an exemplary optical device according to an embodiment of the present disclosure.

[0083] The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Throughout the description, the same reference numerals are used to designate the same elements.

5. DESCRIPTION OF EMBODIMENTS

[0084] A general principle of the present disclosure relies on a wavelength-selective metasurface device capable of providing at least two different optical functions for at least two different illumination conditions. According to an embodiment of the present disclosure, the optical device is adapted for color splitting, such as R, G, B separation.

[0085] As an introduction to the description of embodiments of the present disclosure, FIG. 1 gives examples of different solutions proposed to address wavefront control with metasurface devices from the prior art. In the top panel of FIG. 1, from (a) to (c), the optical response of the nanostructures is tailored by changing the geometry of each individual resonator forming the metasurface. In the middle panel of FIG. 1, from (d) to (g), metasurfaces based on the Pancharatnam-Berry (PB) phase present very high scattering efficiencies, both in reflection and in transmission. The bottom panel of FIG. 1, from (h) to (k) shows hybrid metasurfaces, that work by using both resonant tuning and PB phase tuning.

[0086] In these examples, the subwavelength optical elements may consist in metallic strips having different shapes and orientations (see FIGS. 1 (a), (d) and (h)), or in sub-wavelength dielectric cylinders with a circular or rectangular cross-section having variable size and/or orientation (see FIGS. 1 (b), (e) to (g)), or take the form of strips creating a 1D array (see FIGS. 1 (c), (k)).

[0087] The basic units of transmitarrays (TA) and metasurfaces (MSs) are nanoresonators whose responses (amplitude and phase) are wavelength-dependent. The optical response of such optical devices is tuned by varying the size, shape, orientation and materials of individual nanoparticles. For any wavelength of an incident wave, an optical response of prior art optical devices is defined by a cumulative response of all nanoparticles. Such devices suffer from strong chromatic aberrations resulting from the intrinsic dispersive behavior of the resonators, thus compromising their performance. Even for resonators with small quality factors and corresponding broadband phase and amplitude responses, their operation still remains wavelength dependent.

[0088] An example of optical device that overcomes this limitation and preserving its functionality for three wavelengths is thus proposed. Such an optical device is based on a NJ-microlens based compound TA/MS design as illustrated in FIG. 4 (a) showing schematically an apochromatic optical device which is designed to function as a lens that focuses three different wavelengths into the same point.

[0089] An optical device which is achromatic and apochromatic is proposed. To this end, a compound optical device is built which comprises at least two types of elements corresponding to at least two TA/MS (element 1, 2 or 3), each TA/MS producing an optical response different from the other TA/MS, with a selection means enabling selective excitation for red, green and blue (RGB) colors of the elements which belong to these at least two TAs/MSs.

[0090] A unit cell UC of the optical device according to embodiments of the present disclosure comprises at least two optical elements OE, which size and spacing are smaller than the wavelength of an incident electromagnetic wave. These optical elements belong to different sets of optical elements. All optical elements of a same set contribute to the optical response of the device to an incident wave corresponding to the red, green and blue (RGB) colors in the visible spectrum.

[0091] FIG. 4(a) is a schematic view of an exemplary apochromatic optical device. The optical device is designed to function as a lens that focuses three different wavelengths into the same point. FIGS. 4(b) and 4(c) illustrate schematic drawings of an optical device according to embodiments of the present disclosure. In the figures, each unit cell UC comprises three optical elements 1,2,3, where optical elements with a same number belong to a same set of optical elements.

[0092] Moreover, the unit cell UC comprises selection means SEL for selectively exciting the optical elements of a given set as a function of the wavelength of the incident electromagnetic wave. The selection means thus enable at least two different optical responses of the optical device for different wavelengths of incoming light. For example, for the incoming electromagnetic wave corresponding to the red color, it is the optical elements of a first set, indexed 1, which are excited and thus produce the optical response of the optical device focusing the red color in some point; for a blue color, it is the optical elements of a second set, indexed 3, which are excited and thus produce a different optical response of the optical device which can focus the incident light into the same point.

[0093] In FIG. 4(b), all optical elements of a unit cell are placed at a same distance from the selecting means SEL. In FIG. 4(c), the optical elements of a same set are placed at a same distance from the selecting means SEL, while each optical element of a unit cell is placed at a different distance from the selecting means SEL than the other optical elements of the unit cell.

[0094] A numerical analysis disclosed in the following reveals that diffraction of a plane wave on a microlens based on the combination of different dielectric materials, can result in the spectral-dependent NJ beam deviation. It is demonstrated that for some particular parameters, the NJ-based double-material microlens can split colors.

[0095] The operational principle of an exemplary NJ-based dielectric deflector is schematically shown in FIG. 5a. The position of focal spot, the angle of deviation, the intensity and the shape of an output NJ beam can be controlled by the variation of the refractive indexes and sizes of the constitutive parts/blocks of the NJ microlens SEL. FIG. 5(a) illustrates an exemplary topology of a NJ microlens SEL, which can also be called an NJ-based dielectric color splitter, with an electromagnetic wave having a normal incidence. The NJ-based dielectric color splitter comprises two parts: a first part (P1) of dielectric material with refractive index n.sub.2 and a second part (P2) of dielectric material with refractive index n.sub.3. In the example disclosed on FIG. 5(a), the NJ-based dielectric color splitter is placed in a dielectric host medium with refractive index n.sub.1, and refractive indexes of the materials are such that n.sub.2>n.sub.3>n.sub.1.

[0096] FIGS. 5(b) and 5(c) illustrate cross-section views of the double-material dielectric microlens presented in FIG. 5(a) with n.sub.3>√{square root over (n.sub.1n.sub.2)} (FIG. 5(b)) and n.sub.3<√{square root over (n.sub.1n.sub.2)} (FIG. 5(c)) respectively.

5.1. Topology

[0097] The general topology of the double-material microlens is illustrated in FIG. 5(b). This cross-section view may correspond to a combination of 2 different materials (each part may have a shape of cuboid as in FIG. 10(a), for example) with refractive indexes n.sub.2 and n.sub.3 (n.sub.2>n.sub.3) embedded in a homogeneous dielectric host media with a refractive index n.sub.1<n.sub.3. By changing the parameters of the microlens, the direction of deviation and intensity of generated NJ beam can be controlled. Hereafter, it is assumed that the materials and size of the constitutive parts can be optimized in order to manage the spectral-dependent NJ beam deflection. The effect of the size and refractive indexes of the constitutive blocks on the dispersion of the generated NJs is investigated in Section 5.2 below.

[0098] Hereafter, it is considered that the structures have vertical edges parallel to z-axis and top/bottom surfaces parallel to the xy-plane, which corresponds to the base angle α=90°.

[0099] However, according to an embodiment, some prismatic structures (with arbitrary base angles) can also be used. According to this embodiment, variation of the base angle value provides an additional degree of freedom in the control of the NJ beam radiation.

5.2. Design Principles & Main Performance Characteristics

[0100] In this Section, the selecting means of the optical device disclosed herein is further described. A set of equations is presented to estimate the optimal combinations of materials and dimensions of the blocks for spectral-dependent NJ beam deflection. It is demonstrated that the hot spot position and direction of beam deviation is sensitive to the sizes of constitutive parts. For the microlenses with some particular dimensions, the side of the NJ beam deflection will depend on the wavelength of incident wave.

5.2.1 Main Characteristics of Generated NJ Beams

[0101] The beam-forming phenomenon is associated with the edge of the system and the NJ beam radiation angle is defined by the Snell's low and can be determined using the approximate formula:

[00004]$\begin{array}{cc}{\Theta }_{B1}\approx \frac{90°-{\Theta }_{\mathrm{TIR}1}}{2},\mathrm{where}{\Theta }_{\mathrm{TIR}1}={\sin }^{-1}\left(\frac{n_1}{n_2}\right)& \left(1\right)\end{array}$

is the critical angle of refraction, n.sub.1 is the refractive index of host medium, and n.sub.2 is the refractive index of microlens material.

[0102] The point of intersection of two equal NJ beams radiated from the opposite sides of the NJ microlens determines the focal length of the NJ microlens. In a first approximation, in the case of a single material element the focal length of the NJ microlens can be characterized as a function of the size (width) and index ratio of the media inside and outside the microlens. The total radiated NJ beam will be directed along the axis of the symmetry of the microlens.

[0103] Assume that W.sub.1 is the width of the first element P1 (FIG. 5(b)). A second element P2 with the refractive index n.sub.3 and width W.sub.2 is attached to the first element P1 (FIG. 5(b)). Then, the angle of the NJ beam radiation from the boundary between P1 and P2 does not remain equal to Θ.sub.B1. The output NJ beam is refracted at the angle Θ.sub.B2 into the medium with higher refractive index. If n.sub.2>n.sub.3 then the angle Θ.sub.B2 can be determined as

[00005]$\begin{array}{cc}{\Theta }_{B2}\approx \frac{90°-{\Theta }_{\mathrm{TIR}2}}{2},\mathrm{where}{\Theta }_{\mathrm{TIR}2}={\sin }^{-1}\left(\frac{n_3}{n_2}\right).& \left(2\right)\end{array}$

[0104] The NJ beam radiation angle at the third edge (between the second element P2 and the host medium) corresponds to

[00006]$\begin{array}{cc}{\Theta }_{B3}\approx \frac{90°-{\Theta }_{\mathrm{TIR}3}}{2}.\mathrm{where}{\Theta }_{\mathrm{TIR}3}={\sin }^{-1}\left(\frac{n_1}{n_3}\right).& \left(3\right)\end{array}$

[0105] It shall be noteds that the length, intensity and angle of deviations of the NJs NJ1, NJ2 and NJ3 are different. The maximal intensity and minimal length correspond to the NJ beam with highest ratio between the refractive indexes; i.e; the NJ beam refracted at the angle Θ.sub.B1(NJ1).

[0106] The points of intersection of the NJs associated with the edges of the NJ microlens and radiated at the angles Θ.sub.B1, Θ.sub.B2 and Θ.sub.B3 are determined as follows. The point A of first and second Nis' (NJ1 and NJ2) intersection has the coordinates (W.sub.A, H.sub.A), where

[00007]$\begin{array}{cc}{W}_A\approx \tan {\Theta }_{B2}.Math.H_A,H_A\approx \frac{W_1}{\tan {\Theta }_{B1}+\tan {\Theta }_{B2}}.& \left(4\right)\end{array}$

[0107] First and third NJs (NJ1 and NJ3) intersect at a point B with the coordinates (W.sub.B, H.sub.B), where

[00008]$\begin{array}{cc}{W}_B\approx \tan {\Theta }_{B3}.Math.H_B-W_2,H_B\approx \frac{W_1+W_2}{\tan {\Theta }_{B1}+\tan {\Theta }_{B3}}.& \left(5\right)\end{array}$

[0108] NJ2 and NJ3 intersect only if n.sub.3>√{square root over (n.sub.1×n.sub.2)} (FIG. 5(b)). In this case the coordinates of the intersection point C is determined as

[00009]$\begin{array}{cc}{W}_C\approx \tan {\Theta }_{B3}.Math.H_C-W_2,H_C\approx \frac{W_2}{\tan {\Theta }_{B3}-\tan {\Theta }_{B2}}.& \left(6\right)\end{array}$

[0109] For NJ microlenses with equal sizes of constitutive parts and total width W≤λ (W=W.sub.1+W.sub.2, W.sub.1=W.sub.2) the output NJ beam shifts towards the part with lower refractive index n.sub.3. By varying the refractive index n.sub.3, it is possible to tune the position of the hot spot of the total NJ outside the elements. The total response of the NJ microlens is almost independent on the wavelength of incident electromagnetic wave.

[0110] For the systems with equal sizes of constitutive parts and W>λ, two cases should be distinguished: [0111] for n.sub.3<√{square root over (n.sub.1n.sub.2)} (FIG. 5 (c)), the behaviour of the NJ beam is the same as in the previous case. Also, a similar behavior is observed for a double-material microlens with n.sub.3>√{square root over (n.sub.1n.sub.2)} and H<H.sub.A. [0112] for n.sub.3>√{square root over (n.sub.1n.sub.2)} and H≥H.sub.A (FIG. 5(b)), there is a deviation of the NJ beam towards the part with higher refractive index n.sub.2. The hot spot position of the generated NJ beam depends on the wavelength of incident wave.

[0113] The numerical simulations presented below demonstrate that maximal spectral-dependent NJ beam deflection for 3 different wavelengths (λ.sub.1<λ.sub.2<λ.sub.3)_is observed for microlenses with W≅λ.sub.2 and H≅H.sub.B, In this case, the side of NJ deviation depends on the wavelength of incident wave. Particularly, for n.sub.3>√{square root over (n.sub.1n.sub.2)} (FIG. 5(b)) at λ=λ.sub.1, a long intensive NJ beam deviated towards the part with lower refractive index n.sub.3 is obtained. In this case, the main part of the total response of the microlens will be provided by the short but most intensive NJ beam associated with the right edge of the microlens (Nil in in FIG. 5(b)).

[0114] For the case of longer wavelengths (λ=λ.sub.2,3), the maximal total response is determined by the NJ2 and NJ3 beams which are longer but less intensive. As a result, the long intensive NJ beams are deviated towards the part with higher refractive index n.sub.2.

[0115] With n.sub.3<√{square root over (n.sub.1n.sub.2)} (FIG. 5(c)), the opposite situation is observed. At λ=λ.sub.1, the main part of the total response of the microlens is provided by the NJ beam NJ3. For the chosen parameters, the NJ beam NJ3 is less intensive than the NJ beams NJ1 and NJ2) and a resulting NJ beam is deviated towards the part with higher refractive index n.sub.2. The most intensive NJ beam NJ1 determines the response of the microlens at λ=λ.sub.2. For both discussed cases, the response of the system at λ=λ.sub.3 is related to the input of the NJ beams of medium intensity.

[0116] The angle of plane wave incidence (Θ.sub.i, FIG. 5d) has also an influence on the characteristics of proposed double-material NJ microlens. This, it shall be taken into account that for an oblique incidence, the approximate formula for NJ beam radiation angles is modified and is presented in the form:

[00010]$\begin{array}{cc}{\Theta }_{B1}\approx .Math.-\frac{90°-{\theta }_{\mathrm{TIR}1}}{2}+\frac{{\Theta }_i}{2}.Math.,{\Theta }_{B2}\approx \frac{90°-{\theta }_{\mathrm{TIR}2}}{2}+\frac{{\Theta }_i}{2},{\Theta }_{B3}\approx \frac{90°-{\theta }_{\mathrm{TIR}3}}{2}+\frac{{\Theta }_i}{2}.& \left(7\right)\end{array}$

[0117] The height H.sub.B=may then be obtained by substituting these angles into equation (5).

5.2.2 Parametric Study

[0118] data for 3D double-material microlens computed using CST MICROWAVE STUDIO software is considered to illustrate the features of the generated NJ beam when the system is illuminated by TM (Transverse Magnetic) wave. The power density distribution is simulated for the different heights values of the NJ microlens.

[0119] FIG. 6A illustrates power density distribution in (a)—xz-plane (Y=0) and (b)—xy-plane (Z=1700 nm) for the systems of FIG. 5(b) where: n.sub.1=1, n.sub.2=1.8, n.sub.3=1.6, W.sub.1=W.sub.2=600 nm, H=1200 nm, at 3 different wavelengths corresponding to the Red, Green and Blue wavelengths (620 nm, 530 nm and 450 nm respectively); FIG. 6B illustrates power density distribution in (c)—xz-plane (Y=0) and (d)—xy-plane (Z=1500 nm) for the systems of FIG. 5(c) with n.sub.1=1, n.sub.2=2, n.sub.3=1.2, W.sub.1=W.sub.2=W.sub.3=600 nm, H=1300 nm, at 3 different wavelengths corresponding to the Red Green and Blue wavelengths (620 nm, 530 nm and 450 nm respectively).

[0120] It appears that the spectral-dependent NJ beam deflection takes place if H≅H.sub.B and that the focal point B for the NJ beams related to the external boundaries of the system (NJ1 and NJ3) is close to the surface of microlens or within the microlens (FIGS. 5(b) and (c)). As a result, for the system with n.sub.3>√{square root over (n.sub.1n.sub.2)} (FIG. 5(b)) at some distance from the top surface of the element, the spot for a blue color (λ=450 nm) is situated above the part with lower refractive index, i.e. part P2, and the spots for green and red colors are above the part with higher refractive index, i.e. part P1 (FIG. 6A).

[0121] it shall be noted that for a double-material dielectric microlens with n.sub.3>√{square root over (n.sub.1n.sub.2)}, the spots corresponding to the green and red colors are quite close. By changing the materials of the layers, the positions of the spots can be controlled.

[0122] FIG. 6B shows the power density distribution in the xz- and xy-planes at wavelengths corresponding to the blue, green and red colors for a double-material dielectric microlens with n.sub.3<√{square root over (n.sub.1n.sub.2)}, ((FIG. 5(c)). This figure indicates the intensity distribution at same distance from the top of the double-material NJ microlens. The spots corresponding to green color (530 nm) are close to the spots for the blue color (450 nm). For instance, when the double-material dielectric microlens is used in sensors, detectors can be placed at different points at some distance from the top of the microlens, to detect the intensity of different wavelengths.

[0123] FIG. 7 illustrates cross-section views of two unit cells UC of the optical device according to an embodiment of the present disclosure.

[0124] It can be demonstrated that for a fixed wavelength, the position of the hot spot is almost independent from the distance W.sub.3 between the double-material dielectric microlens (see FIG. 7).

[0125] At the same time, for a small distance W.sub.3 (W.sub.3<half of the blue color wavelength), it is possible to obtain a power density redistribution affecting color separation.

[0126] Increasing the angle of electromagnetic wave incidence (up to Θ.sub.i=30°), it is still possible to obtain the desirable optical function. In this case, the distance between the intensive spots corresponding to the blue and red colors is small.

[0127] The power density distribution in the xz-plane at wavelengths corresponding to the blue, green and red colors may be considered to show the selective excitation of the particles by an array of NJ-based dielectric deflectors.

[0128] A system with two layers of nanoparticles is considered. The first layer (bottom layer of FIG. 7) is a 1D array of double-material (array of NJ-based dielectric deflectors, SEL). In the example illustrated on FIG. 7, the 1D array of NJ-based dielectric deflectors comprises successively the periodic array of NJ-based dielectric deflectors comprising a part of dielectric material with refractive index n.sub.3 and a part of dielectric material with refractive index n.sub.2.

[0129] The second layer (top layer of FIG. 7) is an array of uniform dielectric nanoparticles OE.

[0130] The full system with the two layers is immersed into the host surrounding medium with refractive index n.sub.1.

[0131] For all presented simulations, it is assumed that in each set, the particles are the same. It is also assumed that each unit cell contains one NJ-based dielectric deflector (SEL) and two uniform nanoparticles (OE) in a form of 3D cuboids. Axis of the symmetry for each nanoparticle coincides with the axis of the symmetry of the constitutive part of the double-material element.

[0132] It is assumed that the elements of second layer can be elements of two different types with refractive indexes n.sub.4 and n.sub.5, heights H.sub.pj and widths W.sub.pj (here j=1,2 is the index of the set). These two types of elements can be situated at different distances H.sub.3 and H.sub.4 from the top of the double-material element. The width of each unit cell is then equal to W.sub.1+W.sub.2+W.sub.3.

[0133] The system is illuminated by a unit-amplitude TM plane wave incident from below. Then, a symmetrical excitation of both nanoparticles in each unit cell in a case of single layer system can be observed at 3 wavelengths (620 nm, 530 nm, 450 nm) on FIG. 8a for a system with refractive index as follows n.sub.1=n.sub.2=n.sub.3=1.0 which corresponds to having no selection means. A similar response of symmetrical excitation is observed on FIG. 8b for a system with refractive indexes n.sub.1=1.0 and n.sub.2=n.sub.3=1.8, which correspond to selection means composed of a single dielectric material. And nonsymmetrical and even selective excitation can be observed on FIG. 8c at 3 wavelengths (620 nm, 530 nm, 450 nm) in the case of a system with NJ-based dielectric deflectors according to an embodiment of the present disclosure, with refractive indexes n.sub.1=1.0, n.sub.2=1.8, n.sub.3=1.6, which correspond to selection means composed of double-dielectric material

[0134] FIG. 8 illustrates power density distribution in the near zone (xz-plane, Y=0) for a 1D periodic array of 5 unit cells as presented in FIG. 7, with the following parameters for the dielectric material of the first layer: W.sub.1=W.sub.2=W.sub.3=600 nm, H=1200 nm, (a) n.sub.2=n.sub.3=1.0, (b) n.sub.2=n.sub.3=1.8, (c) n.sub.2=1.8, n.sub.3=1.6, and the following parameters for the optical elements of the second layer: W.sub.p1=W.sub.p2=200 nm, H.sub.p1=H.sub.p2=200 nm, H.sub.3=H.sub.4=500 nm, n.sub.1=1, n.sub.4=n.sub.5=2.0.

[0135] Changing the parameters of the nanoparticles of the second layer can affect the phase and amplitude of incident wave.

[0136] FIG. 9 illustrates power density distribution in the near zone (xz-plane, Y=0) for the 1D periodic array comprising 5 unit cells as presented in FIG. 7 with the following parameters for the double-material dielectric microlens: n.sub.1=1, n.sub.2=1.8, n.sub.3=1.6, W.sub.1=W.sub.2=W.sub.3=600 nm, H=1200 nm.

[0137] FIG. 9 illustrates the power density distribution in the xz-plane at wavelengths corresponding to the blue, green and red colors for the different parameters of the dielectric nanoparticles of second layer (corresponding to the optical elements OE of FIG. 7). FIG. 9(a) illustrates the responses obtained for optical elements of the second layer with the following parameters: W.sub.p1=W.sub.p2=200 nm, H.sub.p1=H.sub.p2=200 nm, H.sub.3=H.sub.4=500 nm, n.sub.4=n.sub.5=1.3. It can be seen that using the double-material dielectric microlens array as the first layer, totally different responses for RGB colors even for a second layer comprising 2 similar sets of nanoparticles as illustrated on FIG. 8(c), and FIG. 9(a) are obtained.

[0138] FIG. 9(b) illustrates the responses obtained for optical elements of the second layer which have different size, and the following parameters W.sub.p1=W.sub.p2=200 nm, H.sub.p1=200 nm, H.sub.p2=400 nm, H.sub.3=H.sub.4=500 nm, n.sub.4=n.sub.5=2.0. It can be seen that the response of the system is modified using the sets with different size of the particles.

[0139] FIG. 9(c) illustrates the responses obtained for optical elements of the second layer placed at different distances from the top of the double-material microlens, and with the following parameters: W.sub.p1=W.sub.p2=200 nm, H.sub.p1=H.sub.p2=200 nm, H.sub.3=600 nm, H.sub.4=300 nm, n.sub.4=n.sub.5=2.0.

[0140] According to an embodiment, the provided optical device is a compound metasurfaces device that allows to provide an aberration corrected optical response as desired for the next generation of eyewear optical devices.

[0141] FIGS. 10 and 11 illustrate exemplary embodiments of geometry for the selection means for the optical device. In FIG. 10(a), the double-material color-splitter has a shape of a cuboid wherein each part of material has a shape of cuboid. Results for the cuboid double material color-splitter are provided for illustration in FIGS. 10(b) and 10(c). FIG. 10(b) illustrates power density distribution in the xz-plane and FIG. 10(c) illustrates power density distribution in the xy-plane at λ=550 nm for the double-material microlenses with: n.sub.1=1, n.sub.2=1.8, n.sub.3=1.6, W.sub.1=1000 nm, W.sub.2=700 nm, W.sub.3=1000 nm, H=900 nm.

[0142] In FIG. 11(a), the double-material color-splitter has a shape of a half cylinder wherein the first part (P1) has a half cylinder shape and the second part (P2) is a half cylinder surrounding the first part P1. Results for the half cylinder double material color-splitter are provided for illustration in FIGS. 11(b) and 11(c). FIG. 11(b) illustrates power density distribution in the xz-plane and FIG. 11(c) illustrates power density distribution in the xy-plane at A=550 nm for the double-material microlenses with: n.sub.1=1, n.sub.2=1.8, n.sub.3=1.3, R.sub.1=500 nm, R.sub.2=850 nm, H=900 nm.

[0143] The color-splitters can be embedded in a host medium or placed on a dielectric substrate acting as a support layer. In the last case (FIG. 10(b)), a proper combination of the parameters of the system (R.sub.2−R.sub.1<R.sub.1 and n.sub.3<√{square root over (n.sub.1n.sub.2)}) provides an additional intensification of generated NJ beam and prevents splitting of the beam.

[0144] Two exemplary embodiments for a unit cell of TA/MS are illustrated in FIGS. 4(b) and (c). In the simplest case, a unit cell comprises only two optical elements of the second layer belonging to two sets of optical elements. Due to the nonsymmetrical and selective excitation of the elements of second layer at wavelengths corresponding to RGB colors, it is possible to get different optical responses of the optical device even in the case of two similar sets of elements. The optical element arrays of the second layer can be one-dimensional (1D) or two-dimensional (2D), thus having periodicity in one or two planes.

[0145] According to an embodiment, the optical elements belonging to the same sets are not identical in order to ensure a predefined functionality of the optical device, such as on- or off-axis focusing, for example.

[0146] The proposed microlenses can be fabricated using established nano-fabrication methods, such as UV/DUV/E-beam lithography.