Light manipulating apparatus

Abstract

An apparatus (10) for manipulating incident light (3), which comprises a mirror (17); and a lens (15) having a first face (14), and a second, opposing, face (16). At least one of the first and second faces (14, 16) comprises a surface structure (21) configured to converge incident light having a first circular polarisation state passing 10 through the lens (15) from the first face (14) to the second face (16); diverge light having the first circular polarisation state passing through the lens (15) from the second face (16) to the first face (14); and reverse the circular polarisation state of light passing through the lens (15). The mirror (17) and lens (15) are arranged such that incoming light (3) passes through the lens (15) a first time, is reflected from the 15 mirror (17), and then passes through the lens (15) a second time.

Description

[0001] Light Manipulating Apparatus

[0002] Technical Field

[0003] The present invention relates to an apparatus for manipulating incident light.

[0004] Background

[0005] One of the most common ways to manipulate light in almost any optical system is with a lens to cause a beam of light either to converge or diverge. Conventional lenses are typically made from optically transparent material which is curved so that its thickness changes across the width of the beam to give the desired optical properties.

[0006] Moreover the ability to tune the focusing ability of a lens (i.e. its focal length and / or optical power) is highly desirable in many optical systems, as this allows for projecting at various distances, imaging at different depths or modulating the power incident on an area. The most common way to create a tunable lens is to use multiple fixed lenses and change the distances between them (e.g. in varifocal lens doublets).

[0007] As well as the inherent bulkiness of the lenses, such arrangements typically require bulky mechanical actuators which add to the size and cost of the system, and result in slow adjustment and actuation of the system.

[0008] Summary of Invention

[0009] According to a first aspect of the invention, there is provided an apparatus for manipulating incident light, the apparatus comprising: a mirror; and a lens having a first face, and a second, opposing, face, wherein at least one of the first and second faces comprises a surface structure configured to: converge incident light having a first circular polarisation state passing through the lens from the first face to the second face; diverge light having the first circular polarisation state passing through the lens from the second face to the first face; and reverse the circular polarisation state of light passing through the lens, wherein the mirror and lens are arranged such that incoming light passes through the lens a first time, is reflected from the mirror, and then passes through the lens a second time.

[0010] Thus it will be seen by those skilled in the art that in accordance with the invention, since the lens acts as a converging lens upon a first transmission through the lens, and as a diverging lens upon a second transmission through the lens (after having been reflected by the mirror) (or vice versa), an apparatus for manipulating (e.g. focussing, diverging, and / or collimating) incident light can be realised with a very small lens-mirror separation which may ease the prospects of fabrication using wafer level processes.

[0011] The inventors have appreciated in the arrangement of elements set out above that, from the perspective of light incident on the first and second faces, the appearance of the surface structure when the light is incident on the second face will be reflection transformed with respect to the appearance of the surface structure when the light is incident on the first face because the light is traveling the opposite way through the lens as a result of reflection by the mirror. In accordance with the invention this perceived reflection transformation means that the surface structure converges light that passes through the lens in one direction, but diverges light passing through the lens in the opposite direction. In embodiments where one or both of the first and second faces are curved (e.g. non-planar), it will be understood that it is the 2D projection (e.g. onto a plane) of the surface structure which appears as a reflection transform to light incident on the opposite face.

[0012] It will be understood that a mirror is a component having an optically reflective surface. It will be understood that one of the first face and the second face is facing the mirror, and the other of the first face and second face is facing away from the mirror.

[0013] In a set of embodiments, the apparatus is arranged such that incident light is first incident on the first face, and passes through the lens from the first face to the second face. The light is then reflected from the mirror, and passes through the lens from the second face to the first face (i.e. the second face is facing the mirror, and the first face is facing away from the mirror).

[0014] The first circular polarisation state could be right circular polarisation or left circular polarisation.

[0015] It will be understood that the apparatus is suitable for manipulating linearly polarised light as well as circularly polarised light since linearly polarised light contains right and left circular polarised light in equal amounts.

[0016] In a set of embodiments, the surface structure comprises a plurality of substructures. The sub-structures may comprise a plurality of (e.g. dielectric) pillars. The sub-structures may comprise a plurality of optical grating components.

[0017] In a set of embodiments, the apparatus comprises means to adjust the optical distance between the lens and the mirror. In embodiments, the means is an actuating device arranged to move the mirror and / or the lens. In a set of embodiments, the lens and mirror are stationary, and a spacer is provided between the mirror and lens. In a set of embodiments, the spacer is configured to have an adjustable refractive index such that the optical distance between the lens and the mirror can be adjusted by adjusting the refractive index of the spacer.

[0018] In a set of embodiments, the spacer comprises a metal oxide which is configured to change its refractive index in the presence of a selected gas. In embodiments, the spacer is provided separately from the lens and the surface structure. In embodiments, the surface structure may be embedded into the spacer. In a set of embodiments, the apparatus comprises an actuating device arranged to move the mirror and / or the lens. Moving the mirror and / or the lens may allow the optical power and / or focal length, and / or focal point location of the apparatus to be tuneable (e.g. adjustable). Such arrangements are particularly advantageous over conventional arrangements as a further reduction in size may be achieved.

[0019] In a set of embodiments, the actuating device is arranged to move the mirror and / or the lens relative to one another to alter a separation between the mirror and the lens such that the manipulation effect (e.g. focal length) of the apparatus is adjustable.

[0020] In a set of embodiments, the actuating device is arranged to move the mirror with at least two (e.g. two or three) degrees of freedom.

[0021] In a set of embodiments, the actuating device is a Micro-Electro-Mechanical Systems (MEMS) actuation device.

[0022] In a set of embodiments, the actuating device comprises at least one actuator element comprising a piezoelectric layer having a width at least five times a thickness thereof; wherein the mirror is connected to the actuator element, such that actuation of the actuator element causes movement of the mirror.

[0023] In a set of embodiments, the actuating device comprises: a first actuator element and a second actuator element each comprising a piezoelectric layer on a first side of the actuating device, wherein each of the first and second actuator elements has a respective width at least five times a respective thickness thereof; and a reinforcing ring, on a second side of the actuating device opposite to the first side, opposite a location on the first side between the first actuator element and the second actuator element; wherein the mirror is connected to at least the first actuator element, such that actuation of the first actuator element causes movement of the mirror. The reinforcing ring may alleviate mechanical stress on the actuating device so that the risk of buckling is reduced, and may also increase the range of motion of the actuating device.

[0024] Making the first actuator element in the form of a thin membrane, i.e. having a width at least five times its thickness, may allow for a large movement, e.g. deflection, of the mirror. In a set of embodiments, the actuator elements each comprise a ring shape. The first and second actuator elements may be concentric.

[0025] In a set of embodiments, the or each actuator element comprises a plurality of actuator portions.

[0026] In a set of embodiments, at least some of the actuator portions are independently addressable with respective voltages (e.g. each actuator portion is independently addressable with a respective voltage). The actuating device may be actuated by selectively applying voltages to one or more independently addressable piezoelectric elements.

[0027] In a set of embodiments, the or each actuator element comprises an inner actuator portion and an outer actuator portion or set of portions. Thus, the or each actuator element may comprise a plurality of actuator portions. Both the inner actuator portion(s) and outer actuator portion(s) may comprise respective distinct piezoelectric areas. Alternatively, in a set of embodiments the or each actuator element is divided azimuthally into a plurality of portions, which may be independently addressable so that a voltage can be applied to each one selectively

[0028] In a set of embodiments, the mirror is deformable, and the actuating device is arranged to bend (e.g. deflect, e.g. curve) the mirror.

[0029] In a set of embodiments, the actuating device comprises a plurality of individually addressable piezoelectric sections of the mirror, and the mirror can change shape (e.g. bend) on actuation of one or more of the piezoelectric sections. Upon actuation there may be minimal (e.g. zero) lift at the centre of the deformable mirror and maximal lift (e.g. of several hundred micrometres) around the perimeter of the deformable mirror (or vice versa), thus giving a curved profile. In a set of embodiments the surface structure comprises an inversion symmetry. It will be understood therefore that in such embodiments, each sub-structure will itself be reflection symmetric. Further, in such embodiments, the arrangement of the surface structure is such that, for each sub-structure, when the surface structure is flipped, a sub-structure of identical geometry is flipped to the same position.

[0030] In a set of embodiments, the surface structure comprises a nano-structure. Such embodiments may be advantageous for manipulating incident light in the visible and near infra-red light range.

[0031] In a set of embodiments, the surface structure comprises a micro-structure, e.g. conductive antenna elements such as split-ring resonators. Such embodiments may be advantageous for incident light in the mid-infrared, terahertz, and radio frequency ranges.

[0032] In a set of embodiments, the surface structure of the lens is configured to impose a phase shift to light passing through (e.g. being transmitted through) the lens according to the geometric phase principle (e.g. Pancharatnam-Berry phase principle).

[0033] In a set of embodiments, the surface structure comprises a free-form pattern of (e.g. dielectric elements).

[0034] In a set of embodiments, the surface structure (e.g. the plurality of sub-structures) comprises a plurality of (e.g. dielectric) pillars.

[0035] In a set of embodiments, the pillars are rectangular.

[0036] In a set of embodiments, each pillar has a rotation angle, and the rotation angle of each pillar varies across the face (e.g. different pillars have different rotation angles which may be dependent on the location of the pillars on the face). In a set of such embodiments where the surface structure has an inversion symmetry, the reflection transformation thereof effectively comprises the same pattern but with the pillars having a rotation angle which is the negative of the respective value. In a set of embodiments, the surface structure (e.g. the plurality of sub-structures) comprises an optical grating.

[0037] In a set of embodiments the optical grating comprises a plurality of grating components.

[0038] In a set of such embodiments, each grating component has a grating pattern direction, and the grating pattern direction of each grating component varies across the face (e.g. different grating component have different grating pattern directions which may be dependent on the location of the grating component on the face). These embodiments may be considered analogous to the embodiments discussed above where the surface structure comprises a plurality of pillars having different rotation angles.

[0039] In a set of embodiments, the surface structure comprises a meta-structure such that the lens comprises an optical metasurface (OMS).

[0040] In a set of embodiments, the lens comprises an array (e.g. a plurality) of sublenses. Two or more of the sub-lenses may have different focal lengths. In embodiments, the surface structure comprises a plurality of sections, wherein the surface-structure sections have different arrangements, and each section defines a sub-lens. Such embodiments may result in an apparatus having a plurality of different focal points.

[0041] In a set of embodiments, the face of the lens closer to the mirror (e.g. the first or second face) is configured to reflect at least a portion of the light reflected from the mirror to achieve multiple internal reflections (e.g. between the mirror and the lens). In such embodiments, the apparatus may have a plurality of different focal points depending on the number of times which light was internally reflected between the mirror and lens.

[0042] In a set of embodiments, one or both of the first and second surface comprises an anti-reflective coating. In a set of embodiments, the face of the lens adjacent the mirror comprises an anti-reflective coating configured to reduce total internal reflection. Anti-reflection coatings may be advantageous in situations where only one focal point is desired.

[0043] In a set of embodiments, the lens comprises an optically transparent substrate on which the surface structure is defined.

[0044] In a set of embodiments, the substrate comprises a curved refractive surface. When the substrate comprises a curved refractive surface, the focal length magnitude of the lens is different depending on the direction in which light passes through the lens (i.e. from the first face to the second face, or from the second face to the first face) because, unlike the surface structure, the curved refractive surface does not change its sign depending on the direction of transmission (e.g. it always converges, or always diverges). The use of a curved refractive surface may allow tuning of the relative focusing strength of the apparatus. Implementing the curved refractive surface on the substrate (as opposed to implementing the curved refractive surface as a separate lens, which could be implemented in accordance with the invention in broad terms) may allow the advantages of a curved refractive surface discussed above to be realised in a more compact arrangement.

[0045] The curved refractive surface may be concave or convex. The face of the substrate on which the surface structure is defined may be a curved refractive surface. The face of the substrate on which the surface structure is not defined may be a curved refractive surface. Where it is desired for only one face to be curved it may be advantageous for it to be the face of the substrate on which the surface structure is not defined since it may be easier to fabricate the surface structure on a flat surface.

[0046] In a set of embodiments, the face of the substrate which is furthest from the mirror is a curved refractive surface, and the face of the substrate which is closest to the mirror is flat (except for the surface structure thereon). Such embodiments may be advantageous since a curved surface on the face of the substrate which is closest to the mirror could impose a greater lens-mirror separation than would otherwise be desired due to the curvature. The features described above in relation to different aspects and embodiments of the present invention may be combined in various combinations. It will be understood that the combination of features in the following description and drawings are intended to be illustrative, and are non-limiting.

[0047] Brief Description of The Drawings

[0048] Certain preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0049] Figure 1 shows a schematic diagram of an apparatus for manipulating incoming light using a convention lens;

[0050] Figure 2 shows a schematic diagram of an apparatus for manipulating incoming light embodying the invention;

[0051] Figures 3a and 3b schematically show part of the lens of Figure. 2 when viewed from opposing sides;

[0052] Figure 4 schematically shows an example metastructure;

[0053] Figures 5a-b show electron microscope images of an example metastructure;

[0054] Figure 6 illustrates a ray tracing diagram showing the apparatus of Figure 2 in use;

[0055] Figure 7 is a plot of the normalized effective focal point S2 / |f | against the normalized lens-mirror separation L / |f|;

[0056] Figure 8 is a schematic diagram of a use-case of the apparatus of Figure 2;

[0057] Figure 9 is a schematic diagram of an actuating device which may be used with the apparatus of Figure 2;

[0058] Figure 10 is a second view of the actuating device of Figure 9;

[0059] Figure 11 is a cross-section of the actuating device of Figure 9;

[0060] Figure 12 is a perspective view of the cross-section shown in Figure 11 ;

[0061] Figure 13 illustrates some dimensions of a cross section of the actuating device;

[0062] Figure 14 shows a close-up view of a CAD drawing of a reinforcing ring of an actuating device;

[0063] Figure 15 shows a first actuation mode of the actuating device;

[0064] Figure 16 shows a second actuation mode of the actuating device; Figures 17A and 17B show how the first and second actuation modes achieve piston motion in both directions;

[0065] Figures 18A and 18B show how the von Mises stress varies across the device in the first and second actuation modes;

[0066] Figure 19 is a photograph showing a second embodiment of the actuating device;

[0067] Figure 20 is a schematic diagram which shows how the actuating device according to the second embodiment can be actuated;

[0068] Figure 21 illustrates, by means of a schematic flow diagram, manufacturing steps A to F for fabricating an actuating device according to embodiments;

[0069] Figure 22 is a perspective view of a deformable mirror;

[0070] Figure 23 is a perspective view of a deformable mirror;

[0071] Figure 24 is a profile view of a deformable mirror;

[0072] Figure 25a-c show how the curvature of a deformable mirror changes how light is deflected;

[0073] Figure 26 shows a schematic diagram of a variant of the apparatus of Figure 2;

[0074] Figure 27 shows a schematic diagram of a variant of the apparatus of Figure 2;

[0075] Figure 28 shows a schematic diagram of a variant of the apparatus of Figure 2;

[0076] Figure 29 shows a schematic diagram of a variant of the apparatus of Figure 2;

[0077] Figure 30 is a plot of the effective focal point S2 against the lens-mirror separation L for the variants of Figures 26-29;

[0078] Figure 31 is a schematic diagram of a section of an example diffraction grating.

[0079] Detailed

[0080] Where the Figures contain ray diagrams, it will be understood that the diagrams have a positive and a negative direction, and that the positive direction runs from left to right, and the negative direction runs from right to left. Figure 1 shows a schematic diagram of an apparatus 1 for manipulating incoming collimated light 3. The apparatus comprises a conventional refractive converging lens 5 which has a focal length f, and a mirror 7. The lens 5 comprises a first face 4, and a second (e.g. opposite) face 6. The mirror 7 and lens 5 are arranged such that the first face 4 of the lens 5 faces the the incoming light 3, and the second face 6 of the lens faces the mirror 7. Incoming light 3 passes through the lens 5 a first time (entering the lens 5 through the first face 4 and exiting the lens 5 through the second face 6), is reflected by the mirror 7, and then passes through the lens 5 for a second time (entering the lens 5 through the second face 6, and exiting the lens 5 through the first face 4). The lens 5, and mirror 7 are arranged in parallel, and the separation between the mirror 7, and lens 5 (hereinafter referred to as the mirrorlens separation) is given by L. As shown by the ray diagram of Figure 1 , the incoming light 3 is focussed by the lens 5 when it first passes through the lens 5, the light is then reflected from the mirror 7, before being focussed again when passing through the lens 5 a second time, resulting in a focal length ftotfor the apparatus 1 as a whole. Depending on the mirror lens separation L, the effect of the apparatus 1 on the incoming light 3 can be adapted. As such, the mirror 7 may be arranged to be moveable with respect to the lens 5 such that ftotis adjustable.

[0081] In Figure 1 , a corresponding virtual arrangement 9 is also shown (using dashed lines) to illustrate that the mirror and lens arrangement of apparatus 1 is equivalent to a transmissive arrangement using two identical lenses 5, with a separation which is equal to twice the mirror lens separation L (e.g. 2L).

[0082] As explained above, by varying the mirror-lens separation L, the effect of the apparatus 1 on the incoming light 3 can be adapted. Collimation occurs when L = f, i.e. when the incoming collimated light is focused to and reflected from the focal point of the lens. Hence, this is the separation at which the largest changes in focal length occur, and hence a mirror lens separation on this order is preferred for a tunable apparatus 1 which can offer large changes in the focal length of the apparatus 1.

[0083] As such, when using a conventional refractive lens 3, the mirror-lens separation L must correspond to roughly the focal length of the lens 3 (L ~ f) in order to attain large focal length changes upon displacing the mirror. However, this can cause issues when it is desired to implement a tunable apparatus at wafer level. For example, if focal lengths are desired in the f ~ 300 pm range, then the necessary mirror lens separation L ~ 300pm is already on the length scale of a silicon wafer, and hence too large.

[0084] The applicant has recognised this problem, and thus proposes the improved apparatus discussed below.

[0085] Figure 2 shows a schematic diagram of an apparatus 10 for manipulating incoming collimated light 3. The apparatus 10 works using a similar principle to the apparatus 1 , and also comprises a mirror 17 and lens 15. The apparatus 10 comprises a geometric phase transmissive lens 15 comprising a substrate 18 having a geometric nano-structure (surface structure) 21 on one face 16, and a focal length f. In the below described embodiment, the lens 15 is a metasurface lens (i.e. metalens) which comprises a metastructure 21. The metastructure 21 is illustrated schematically in Figure 2, and is discussed in more detail with respect to Figures 3a, 3b, and 4.

[0086] In embodiments, the geometric phase transmissive lens could take other forms. For example, the geometric phase transmissive lens could be a grating-based lens. This possibility is discussed in more detail below with respect to Figure 31. Alternatively antenna elements could be used for terahetz and RF applications.

[0087] The lens 15 comprises a first face 14, and a second (e.g. opposite) face 16. The mirror 17 and lens 15 are arranged such that the first face 14 of the lens 15 faces the the incoming light 3, and the second face 16 of the lens faces the mirror 17. In the illustrated embodiment, the surface structure 21 is defined on the second face 16. It will be understood that the surface structure 21 may be defined on the first face 14, or a surface structure may be defined on both the first face 14 and the second face 16.

[0088] Incoming light 3 passes through the lens 15 a first time (entering the lens 15 through the first face 14 and exiting the lens 15 through the second face 16), is reflected by the mirror 17, and then passes through the lens 15 for a second time (entering the lens 15 through the second face 16, and exiting the lens 15 through the first face 14). The lens 15, and mirror 17 are arranged in parallel, and the separation between the mirror 17, and lens 15 (hereinafter referred to as the mirrorlens separation) is given by L. Depending on this separation, the effect of the apparatus 10 on the incoming light 3 can be adapted. The mirror 17 is moveable with respect to the lens 15. In other embodiments, the lens 15 is moveable with respect to the mirror 17.

[0089] In the illustrated embodiment, the mirror 17 is a Micro-Electro-Mechanical Systems (MEMS) mirror which is translatable upon application of a suitable voltage. The mirror 17 may comprise a feedback mechanism, e.g. a capacitive, optical or piezoelectric feedback mechanism to regulate its separation from the lens 15 and / or its degree of planarity. The mirror 17 may be constructed from any suitable materials, however, in embodiments, the mirror 17 is constructed from gold. The construction of the mirror 17, and its actuation, is discussed in detail below with reference to Figures 9 to 21.

[0090] The geometric phase principle (i.e. Pancharatnam-Berry phase principle) is used for pointwise implementation of a lens phase function, working on circular polarisation states of light. The incoming light 3 may be both collimated, and circularly polarised. The illustrated apparatus 10 comprises a polariser 19 configured to circularly polarise incoming light such that the light 3 incident on the lens 15 is circularly polarised.

[0091] Figure 3a schematically illustrates part of the metalens 15 showing part of the metastructure 21 as viewed from the perspective of light incident on the first face 14 of the lens 15. In the illustrated embodiment, the metastructure comprises a plurality of rectangular pillars 23. Each of the rectangular pillars 23 are offset from a given reference axis (e.g. a vertical direction) by a rotation angle a. Although not immediately apparent from Figures 3a and 3b, different rectangular pillars 23 have different rotation angles a.

[0092] Figure 3b schematically illustrates the same section of the metalens 15 as shown in Figure 3a, but as viewed from the perspective of light incident on the second face 16 of the lens 15. It can be seen that, when viewed from the opposite side of the lens, the metastructure 21 appears as a reflection transformation. It is furthermore observed that each of the rectangular pillars have rotation angle -a. In this case the reflection transformation is equivalent to changing the sign of the rotation angles as the structure has some symmetry (e.g. inversion-symmetry). Such symmetry arises in this case which implements circular-symmetric lens functions by use of a surface structure comprising a square lattice of rectangular (i.e. non-circular) pillars.

[0093] The rotation angle a of the rectangular pillars is varied pointwise over the radius r of the metalens 15 (and so may be considered a(r)) in order to impose the desired phase of a lens. An example metalens 15, with an inversion-symmetric metastructure 21 comprises a plurality of rectangular pillars 23 each having a rotation angle a(r) is shown schematically in Figure 4. In an embodiment, each pillar has dimensions 230nm x 354 nm x 1200nm, with the periodicity between pillars equal to 835nm.

[0094] The metastructure 21 is formed or otherwise provided on a silicon substrate. The silicon substrate defines the first face 14 of the lens 15 such that when light enters the lens 15 through the first face 14, it passes through the silicon substrate before reaching the metastructure 21. The substrate provides mechanical protection of the apparatus 10 from the environment. Use of silicon is not essential - other optically transmissive materials could be used depending on the wavelengths of light being used. For example in other embodiments a glass substrate could be used

[0095] Figure 5a is a scanning electron microscope image of the metastructure 21 in perspective view. Figure 5b is a scanning electron microscope image of the metastructure 21 in plan view.

[0096] In the illustrated embodiment, the substrate is a flat surface. In other embodiments, the substrate may be curved and / or may be deformable. Such embodiments are discussed below with reference to Figures 26-30.

[0097] The operation of the apparatus 10 shown in Figure 2, having the metastructure of which a very small part is shown in Figure 4, will now be explained. The operation T of the metalens 15 on right (|R)) and left (|L)) circular polarised light, places the transmitted light in a superposition of circular polarisation states according to:

[0098] T|R) = B exp(i2a)|L) + A|R) (1)

[0099] T|L> = A|L) + B exp(— i2a)|R) (2)

[0100] For a suitable design of the metastructure 21 , full cross-polarisation (e.g. full reversal of the circular polarisation state) (|A|2— > 0 and |B|2— > 1) can be achieved such that right circular polarised light is completely cross polarised to left circular polarised light upon transmission through the metalens 15 (or vice versa) i.e. 100% cross-polarisation efficiency. After transmission through the lens 15, the resulting cross-polarised field has attained a phase 2a, where a is equal to the rotation angle of the rectangular pillars. The rotation angle of the rectangular pillars a(r) is varied pointwise over the radius r of the metalens 15 in order to impose the desired phase of a lens. The metalens structure of rectangular pillars have inversion symmetry.

[0101] It will be understood that full cross-polarisation may not always be optimal, and in situations, it may be desirable for the metalens 15 to transmit some non-cross- polarised light. The metastructure 21 can be configured to have a desired amount of cross-polarisation efficiency.

[0102] In the discussed example the incoming collimated light 3 is right circular polarised |R) and the rotations of the metasurface a(r) are designed to focus the incoming light 3 upon first transmission through (entering the lens 15 through the first face 14 and exiting the lens 15 through the second face 16) the metalens 15 at the focal distance f. The light attains the desired phase pointwise over the surface and is cross-polarised to left circular light |L) according to equation (1). Upon reflection at the mirror 17 the light is restored to the original circular polarisation state |R) (since a mirror flips the circular polarisation state of light). After reflection from the mirror 17 the light rays become incident on the metalens a second time, but this time the light rays are incident on the second face 16 of the metalens 15, and hence encounter the metastructure 21 as a reflection transformation compared to when the light rays encountered the metastructure 21 upon the first transmission. Due to the symmetry of the metalens structure, the reflection transform is equivalent to changing the sign of the rotation angles. Therefore, from the perspective of the light rays, the rotation angles of the metastructures have been flipped, and the rotation angles have been given a sign change a — > -a. As explained above, in the illustrated embodiment, the rotation angles a(r) are configured such that when light is transmitted through the lens 15 from the first face 14 to the second face 16, the metastructure 21 defines a positive (converging) lens. Therefore, when light is transmitted through the lens 15 from the second face 16 to the first face 14 the same metastructure 21 is effectively reflection transformed so that a phase function of opposite sign is applied, i.e. it defines a negative (diverging) lens. As such, the geometric metalens 15 acts as a converging lens for the first transmission but as a diverging lens for the second transmission.

[0103] The apparatus 10 shown in Figure 2 is therefore analogous to a lens doublet in transmission comprising a combination of a positive and negative lens, for which the set-point spacing (around which large focal changes occur upon mirror displacement) is the difference of the absolute focal lengths. For lenses of equal focal length (which is the situation presented by the apparatus 10) this difference is zero, and so the mirror-lens separation L can tend towards zero. In embodiments, a curved refractive surface may be used to change the mirror-lens separation at which the set-point spacing is achieved. Such embodiments are discussed below with respect to Figures 26-30.

[0104] Figure 6 illustrates a ray tracing diagram showing the apparatus 10 of Figure 2 in use. The label 5 is shown in Figure 6, and is the base length of the triangle drawn between the reflection point 25 at the mirror 17, the focal point 27 of the lens 15 and the mirror intersection with the optical axis 29. The lens-mirror separation is thus given by L = 6 — |f | when the origin is placed at the lens intersection with the optical axis (i.e. assuming L = - |L|).

[0105] The effective focal point S2 of the apparatus 10 can be calculated in terms of the lens mirror separation L using the thin lens approximation. The thin lens equation can be used to calculate the focal length after the second transmission through the lens S2in terms of the (virtual or real) position of the focal point after first transmission Si according to:

[0106] Following from the diagram of Figure 6, it is observed that Si = \f | - 28. Straightforward derivation gives the result:

[0107] 2L

[0108] In the above discussed example, the metalens 15 is configured such that the apparatus 10 acts as a converging apparatus for incoming right circular polarised light. It will be understood that if left circular polarised light is incident on the apparatus 10, the metalens 15 will have the opposite effect. If left circular polarised incoming light is applied to the metalens 15, Eq. (2) shows that the cross-polarised light attains a negative phase -2a; i.e. the metalens 15 will act as a negative lens upon first transmission for left circular polarised (|L)) light, and as a positive lens upon second transmission after being reflected by the mirror 17. For left circular incoming light |L) the apparatus 10 is therefore equivalent to a doublet consisting of consecutive negative and positive lenses with equal focal length magnitudes. Performing the equivalent derivations as shown in equation (3) for this scenario gives an effective focal length of the reflective lens according to:

[0109] ,IL> lfl(2t + lfl) ,4)

[0110] If linearly polarised light were to be incident on the apparatus 10, two focal points will be present as linearly polarised light consists of equal amounts of right circular polarised light |R) and left circular polarised light |L).

[0111] Figure 7 is a plot of the normalized effective focal point S2 / |f | against the normalized lens-mirror spacing L / |f|, showing S2 / |f| for both right circular polarised incoming light, and left circular polarised incoming light. Both from this plot and from equations (3) and (4) it can be seen that for both S2 and S2|L> collimation (focus at infinity) occurs for L = 0. Furthermore, most of the change in focal length is achieved as L approaches - 0.2|f| . As such if focal lengths are desired in the f ~ 200 pm range, then the necessary mirror lens separation should be between 0 and 0.2 x 200 pm, i.e. between 0 and 40 pm. This is considerably smaller than (on the order of 10% of) the separation that is required for the apparatus 1 of Figure 1 using a refractive lens. As such, by using the combination of a geometric phase transmissive metasurface lens 15 and a mirror 17, a tuneable apparatus 10 can be made which has a small enough mirror lens separation to be used in wafer level assembly between micromirror and metalens chips.

[0112] The ray diagram shown in Figure 6 illustrates the situation where the incident light is only reflected by the mirror 17 once, and is then immediately transmitted back through the lens 15. However, in embodiments, light may be subjected to multiple internal reflections between the mirror 17 and lens 15, as such the apparatus 10 may have different focal points depending on how many internal reflections the light is subjected to. In embodiments, the mirror may be tilted (e.g. non-parallel) with respect to the lens in order to configure the locations of the different focal points.

[0113] Figure 8 is a schematic diagram of a use-case of the apparatus 10. In Figure 8, the apparatus 10 is used in combination with a 50:50 beam-splitter 40. The incoming collimated and circularly polarised light is focussed by the apparatus 10, before being reflected by 90° by the beam-splitter 40 such that the light is focussed outside of the channel of incoming light 3.

[0114] The above discussion has been related to the focal length tunability of the apparatus, which may be relevant to e.g. focusing laser beams or projecting images along a wide range of distances. For other applications such as microscopic imaging, the optical power measured in diopters (ability to focus strongly, or equivalently create large angles) of the apparatus 10 is of importance. The diopter change as the mirror lens separation is increased from L = 0 to L = AL may be expressed by:

[0115] Equation 5 demonstrates that the diopter change increases with mirror-lens separation from AL = 0 and diverges at AL = — |f | / 2. Hence if a mirror actuating device is capable of adjusting the mirror-lens separation over this range, the apparatus may be arranged to function both for large focal length tunability and for large optical power tunability. Such an actuating device is discussed below with reference to Figures 9 to 21.

[0116] In embodiments, the mirror 17 may be actuated using an actuating device as disclosed in WO2022172012A1, the subject matter of which is herein incorporated by reference.

[0117] Figure 9 shows an actuating device 91 which may, in a first embodiment, be used to actuate the mirror 17. Figure 10 shows another perspective view of the actuating device 91 shown in Figure 10. The actuating device 91 has a first side 92a and a second, opposite, side 92b. While Figure 9 shows a perspective view from the second side 92b, i.e. the underside, Figure 10 shows a perspective view of the actuating device 91 from the first side 92a of the actuating device 91.

[0118] The actuating device 91 has four annular, concentric, actuator elements 97a-97d. In the centre of the actuating device 91 is the mirror 17, connected to the innermost actuator element 97a. The actuator elements 97a-d and mirror 17 are arranged such that actuation of the actuator elements 97a-d causes movement of the mirror 17. In embodiments, the mirror 17 has a mass-per-unit-area greater than the actuator elements 97a-d, thus allowing it to remain stiff and flat when the actuating device 91 is actuated.

[0119] On the underside 92b of the actuating device 91 are three concentric reinforcing rings 98a-c. The reinforcing rings 98a-c are positioned on the underside 92b at locations between neighbouring actuator elements 97a-d. The reinforcing rings 98a- c extend from the underside of the actuating device 91 in a direction normal to the x-y plane (i.e. the plane of the piezoelectric layer) in the form of concentric walls. The dimensions of these reinforcing rings 98a-c are described below with reference to Figures 11-13.

[0120] Each actuator element 97a-d is annulus-shaped having a width (the difference between the inner circle and outer circle radii) at least five times its thickness (the dimension normal to the width). In embodiments shown in Figures 9 and 10, each actuator element 97a-d has two portions, an inner portion 95a-d and an outer portion 96a-d (shown in Figure 11). The inner and outer portions 95a-d, 96a-d are annulus-shaped, like the actuator elements 97a-d themselves. These portions 95a- d, 96a-d each comprise a piezoelectric layer, e.g. made from Lead Zirconate Titanate (PZT). Each piezoelectric portion 95a-d, 96a-d can be independently addressed to apply a voltage thereto by a voltage supply module (not shown) to contract or expand the piezoelectric material.

[0121] Turning to Figure 11, a cross-sectional view of the actuating device 91 can be seen. In this view, the structure of both sides 92a, 92b of the actuating device 91 can be seen. Figure 12 provides another perspective view of the cross-section shown in Figure 11.

[0122] Figures 11 and 12 show that each reinforcing ring 98a-c is positioned between neighbouring actuator elements 97a-d.

[0123] Toward the centre of the actuating device 91 , the innermost reinforcing ring 98a is on the underside 92b at a location opposite the region between the innermost actuator element 97a and its neighbouring actuator element 97b. The inner portion 95a of the innermost actuator element 97a is next to the mirror 17 and the outer portion 96a of the innermost actuator element 97a is next to the innermost reinforcing ring 98a.

[0124] At the periphery of the actuating device 91, the outermost actuator element 97d is anchored to a substrate (not shown) at its edge. The inner portion 95d of the outermost actuator element 97d is next to the outermost reinforcing ring 98c and the outer portion 96d of the outermost actuator element 97d is next to the substrate. The actuator elements 97b, 97c between the innermost and outermost actuator elements 97a, 97d are bounded by corresponding reinforcing rings 98a-c. As can be seen in Figures 11-12, the actuating device 91 has an overall width of less than 1 cm. The mirror 17 has a width of between 2-4 mm and a thickness of approximately 400 pm. Each reinforcing ring 98a-c has a width of approximately 40 pm and a thickness of approximately 400 pm. Each actuator element 97a-d, has a width of approximately 600 pm, each portion of the actuator elements 95a-d, 96a-d having a width of approximately 300 pm. These dimensions are illustrated more clearly in Figure 13.

[0125] The above-described structure; in particular, the arrangement of the inner and outer portions 95a-d, 96a-d relative to the reinforcing rings 98a-c; helps to allow long- stroke piston motion of the actuating device 91 without buckling. With this structure, the Applicant has measured total stroke lengths of up to 70 pm.

[0126] The way in which this particular arrangement helps to achieve this long-stroke piston motion of the mirror 17 will be described below.

[0127] To achieve the desired movement of the mirror 17, specific piezoelectric portions must receive a voltage to actuate them. These specific portions and their resulting deflection will be described below in Figures 14 to 18B. In the drawings, the portions having a voltage applied thereto are indicated by the addition of '+’ signs on those portions. For the purposes of the embodiment presented in Figures 9-18B, the polarity of the applied voltage is such that the piezoelectric layer contracts radially. However, as the skilled person would appreciate, a voltage of the opposite polarity may have the inverse effect, i.e. the layer would expand.

[0128] A close-up view of one of the reinforcing rings 98a is shown in Figure 14. As can be seen in Figure 14, the reinforcing ring 98a is located on the second side 92b of the actuating device opposite to the first side 92a, opposite a location on the first side 92a between the first actuator element 97a and the second actuator element 97b. The first actuator element 97a is shown to have two distinct piezoelectric areas providing the inner and outer actuator portions 95a, 96a having a small gap therebetween. The second actuator element 97b similarly has two distinct piezoelectric areas providing the inner and outer actuator portions 95b, 96b having a small gap therebetween. Figure 15 shows the actuating device 9T in a first mode of operation, the first mode being denoted by a single prime (‘), where a voltage is applied to the outer portion 96a’-d’ of each of the actuator elements 97a’-97d’. Turning to Figure 17A the resulting vertical deflection of the actuator elements 97a’-d’ and piston motion of the mirror 17’ can be seen.

[0129] As will be appreciated by the skilled person, the voltage applied to the outer portions 96a’-96d’ causes the piezoelectric material of the outer portions 96a’-96d’ to contract in the radial direction. The width to thickness ratio of the actuator elements 97a-d means that they have some flexibility which allows strain on the piezoelectric layer to be transferred along the width of each actuator element. Thus, the contraction of the piezoelectric layer of the outer portions 96a’-96d’ causes the actuator element to curve so that the inner edge of each of the inner portions 95a’- 95d’ of each actuator element 97a’-d’ lifts vertically, i.e. translating each reinforcing ring 98a-c in the positive z-direction. The substrate (not shown) at the periphery of the actuating device 91 and the reinforcing rings 98a-c provide a stiff anchor for the outermost portions 96a’-96d’ to deform relative to.

[0130] Figure 17A shows, with an upwards arrow, that the mirror 17’ is displaced normal to the x-y plane in the positive z-direction (i.e. the x-y plane being the plane of the mirror 17’ at rest).

[0131] Figure 16 shows the actuating device 91” in a second mode of operation, the second mode being denoted by a double prime (“), where a voltage is applied to the inner portion 95a”-95d” of each of the actuator elements 97a”-97d”. Again, alternate piezoelectric portions have a voltage applied thereto. Figure 17B shows, with a downwards arrow, the resulting vertical deflection of the actuator elements 97a”-d” and ‘piston’ motion of the mirror 17” in the second mode.

[0132] The voltage applied to the inner portions 95a”-95d” causes the piezoelectric material of these portions to contract in the radial direction. The flexibility of the actuator elements 97a”-d” allows the strain to be transferred across the width, so that the contraction of the piezoelectric layer of the outer portions 96a’-96d’ causes the actuator element to curve. The contraction causes the inner edges of each of the inner portions 95a’-95d’ of each actuator element 97a’-d’ to lower vertically, i.e. translating each reinforcing ring 98a-c in the negative z-direction. The mirror 17” and the reinforcing rings 98a-c provide stiff anchors for the innermost portions 95a”- 95d” to deform relative to. The mirror 17” is, thus, displaced normal to the x-y plane in the negative z-direction (i.e. the x-y plane being the plane of the mirror 17” at rest). The second mode thus results in the mirror 17” moving in the opposite direction to the movement associated with the first mode.

[0133] Figures 18A and 18B shows how the von Mises stress (N / m2) varies across the actuating device in the first mode and the second mode.

[0134] Figure 18A shows the von Mises stress on the actuating device 9T operating in the first mode, where the mirror 17’ is deflected in the positive z-direction. Figure 18B shows the von Mises stress on the actuating device 91” operating in the second mode, where the mirror 17’ is deflected in the negative z-direction. For both modes, the von Mises stress is between zero and 0.5 x 108N / m2at the inactive portions where a voltage is not being applied and approximately 1.5 x 108N / m2at the active portions where the voltage is applied. Thus, the von Mises stress is greatest where the piezoelectric layer is receiving a voltage. The presence of the reinforcing rings between each of the actuator elements limits the stress from becoming too high and thus reduces the risk of buckling.

[0135] Figure 19 shows an actuating device 910 which may, in a second embodiment, be used to actuate the mirror 17. The structure of this device 910 is similar to the arrangement described above as there are four actuator elements 920a-d and three reinforcing rings (not shown) and a mirror 17 in the centre of the actuating device 910. The actuating device 910 also has a substrate 921 to which the outer actuator element 920d is attached.

[0136] In this embodiment, each actuator element 920a-d has an inner ring of actuator portions and an outer ring of actuator portions, each segmented into four individual portions. Therefore, there are eight separate actuator portions, meaning that each portion has a separate piezoelectric area. For example, the innermost actuator element 920a has four inner actuator portions 912a, 913a, 914a, 915a and four outer actuator portions 916a, 917a, 918a, 919a. It can be seen from Figure 19 that the actuator portions are arranged in quadrants. Each of the piezoelectric portions 912a-919a has an annular sector shape subtending an angle of 90°. These portions 912a-919a are independently addressable which means that a voltage can be selectively applied to any one of their piezoelectric layers. By actuating a subset of the actuator portions a ‘tip-tilt’ motion can be achieved. The ‘piston’ motion described above can be achieved by applying a voltage to all inner portions, e.g. 912a-915a, of each actuator element 920a-d or all four outer portions, e.g. 916a- 919a, of each actuator element 920a-d.

[0137] Tilting motion can be achieved by applying a voltage to one or more inner portions, e.g. 912a in one quadrant or half of the actuating device, and applying a voltage to the corresponding outer portions, e.g. 919a, in a quadrant or half of the actuating device on the side of the mirror 17 diametrically opposite to the other quadrant or side.

[0138] Figure 20 shows a schematic diagram of the different piezoelectric portions that can be independently addressed by control electronics to actuate the actuating device of Figure 19. In the actuating device depicted in Figures 18 and 19 there are eight actuator portions per actuator element, e.g. 912a-919a, and there are four actuator elements in total. Thus for the actuating device 910 of Figures 18 and 19, each actuator element has a North West Inner (NW-I), North West Outer (NW-0), North East Inner (NE-I), North East Outer (NE-O), South East Inner (SE-I), South West Inner (SW-I) and South West Outer (SW-0) actuator portion. For the four actuator elements, this amounts to a total of 32 piezoelectric actuator portions that can be independently actuated which allows both piston and tilting motion to be achieved. The different portions are indicated by different shading.

[0139] When applying a voltage to actuate the device, the control electronics may provide a voltage to all the piezoelectric portions having the same label - e.g. one or more of NW-I, NW-0, NE-I, NE-O, SE-I, SW-I and SW-0 - thus actuating a specific subset of piezoelectric portions. This may help to achieve large deflection angles and deflection heights.

[0140] Although Figures 19 and 20 show eight piezoelectric portions per actuator element, this is just one of a number of possibilities. Figure 21 illustrates steps A to F of a process of fabricating the actuating device 91 , 910. The diagrams shown in Figure 21 depict a cross section of one half of the actuating device 910.

[0141] The process starts with step A, where a 400 pm Silicon on Insulator (SOI) wafer is provided as a starting material having a 500 nm BOX (buried oxide) layer 9201 sandwiched between an 8 pm device layer 9202 and a 400 pm bulk (e.g. Si) layer 9200.

[0142] Step B is an oxidation step where 1.6 pm SiO2 layers 9203, 9204 are formed both below the bulk layer 9200 and above the device layer 9202.

[0143] This is followed by the stack deposition step, i.e. step C. A PZT stack is deposited on the SiO2 layer 9203 that is adjacent to the device layer 9202. The PZT stack is made of a 2 pm PZT layer 9206 sandwiched between a top electrode 9207 and a bottom electrode 9205. In this case, the top electrode 9207 is a 250 nm layer of gold and the bottom electrode 9205 is a 100 nm layer of platinum.

[0144] Step D follows, where the structuring and etching of the PZT 9206 and electrodes 9205, 9207 forms the individual piezoelectric portions. Here, cavities 9208a-h are formed in the PZT stack forming distinct piezoelectric areas.

[0145] Then, in step E, a moveable surface, e.g. a mirror, is defined by etching away the top layer of SiC>2 and the device layer 9202 to form a central cavity where the moveable surface is located.

[0146] Lastly, step F involves etching away the bulk layer 9200 and bottom SiC>2 layer 9204 to form a plurality of reinforcing rings 98a, b,c between cavities 9210a-d formed by etching.

[0147] In embodiments, it may be advantageous to replace the flat mirror 17 shown in the foregoing embodiments with a deformable mirror which may be configured to further manipulate the incoming light. Figure 22 shows a perspective view of a deformable mirror 70, which is a variant of the mirror 17 shown in the foregoing embodiments. The deformable mirror 70 of Figure 22 has two independently actuable sections. The first section 72 is a central circular section and the second section 74 has the shape of an annulus arranged concentrically around the central circular section 72. Although only two sections are shown, there may be more concentrically arranged sections (e.g. further annuli) surrounding the central section.

[0148] A voltage can be applied independently to each section of the deformable mirror 70 in order to deform (e.g. curve) the mirror 70

[0149] Figure 23 is a perspective view showing the deformable mirror 70 of Figure 22 upon actuation. The shading in Figure 23 illustrates the variation in vertical displacement, i.e. lift (in the z direction), of the surface. Minimal vertical displacement is shown in black and maximal vertical displacement is shown in white. Intermediate vertical displacements are represented by shades of grey.

[0150] Figure 24 is a side view of the actuated deformable mirror 70 shown in Figure 23. The deformable mirror 70, comprises a curved surface with minimal vertical displacement around the perimeter of the element and maximal vertical displacement at the centre of the deformable element. Figure 24 shows that the vertical displacement of the deformable mirror 70 can reach 200 pm for a diameter of between 2-3 mm.

[0151] As illustrated in Figures. 23-24 the first section 72 and the second section 74 may be actuated with a different voltage to cause at least part of the surface of the deformable mirror 70 to be displaced in the z direction. Applying a voltage to just the central section 72 of the deformable mirror 70 may result in a concave deformation of the deformable mirror 70. Applying a voltage to just the outer ring section 74 of the deformable mirror 70 may result in the opposite convex deformation. Having the deformable mirror 70, segmented in this way, may allow deformation of the deformable mirror 70 in both directions, upwards and downwards (e.g. in a convex or concave manner). In this example, a voltage is applied to only one of the sections and the centre of the deformable mirror is lifted the most from its rest position. This gives the deformable mirror the curved profile shown in Figure 24.

[0152] Figures 25 (a)-(c) show how the changing curvature of a deformable mirror 70 changes the way light is deflected by the mirror 70.

[0153] A schematic version of a convex deformable mirror 70a is shown in Figure 25a. The convex optically reflective surface causes the divergence angle of the reflected light 80a to be greater than the divergence angle of the incident light and thus the incoming light is de-focussed. A schematic version of a planar deformable mirror 70b is shown in Figure 25b. The planar optically reflective surface causes the divergence angle of the reflected light 80b to be the same as the divergence angle of the incident light and so the surface provides specular reflection. A schematic version of a concave deformable mirror 70c is shown in Figure 25c. The concave optically reflective surface causes the divergence angle of the reflected light 80c to be less than the divergence angle of the incident light and so the incoming light is focussed.

[0154] In the embodiments described herein, the apparatus 10 (or the apparatus 100 discussed below) includes a deformable mirror. The effect of the curvature of the deformable mirror 70 on the overall effect of the apparatus 10, 100 will be equivalent to the effect which would be realised by adding an additional refractive lens. As such, in embodiments with a deformable mirror 70, the shape (e.g. curvature) of the mirror 70 can be controlled to provide further tunability of the focal length of the apparatus 10, 100.

[0155] Figures 26 to 29 show schematic diagrams of an apparatus 100a, 100b, 100c, 100d respectively which are variants of the apparatus 10 shown in Figure 2. Unless stated otherwise, the construction, and function of the apparatus’ 100a-d should be understood to be the same as that discussed above in relation to apparatus 10.

[0156] Each of apparatus’ 100a-d comprise metalenses 115a-d which have curved refractive surfaces 150a-d provided on the substrates 118a-d. By use of a curved refractive surface 150a-d added to the metasurface substrate 118a-d (whether on the face 16 of the lens 115a-d where the metasurface structure is defined or on the other face 14) it is possible to change the relative focal lengths of the lens 115a-d.

[0157] When the substrate 118a-d comprises a curved refractive surface 150a-d, the focal length magnitude of the lens 115a-d is different depending on the direction in which light passes through the lens - i.e. whether from the first face to the second face, or from the second face to the first face - because, unlike the surface structure 21 , the curved refractive surface 150a-d does not change its sign depending on the direction of transmission (it always converges, or always diverges). The use of a curved refractive surface may allow the tuning of the relative focusing strength of the apparatus.

[0158] The apparatus 100a-d is equivalent to a doublet consisting of a negative and positive lens of unequal focal length magnitudes. The set point at which large focal changes occur is still given by their focal length difference, but this no longer coincides with a zero lens-mirror separation. In such embodiments, it becomes possible to have a finite resulting focal length of the reflective lens at a zero lensmirror separation, and it becomes possible to achieve higher diopter changes by suitable design.

[0159] Figure 26 shows an apparatus 100a having a lens 115a which comprises a substrate 118a. The substrate 118a has a convex surface 150a on which the metastructure 21 is defined. As such, for a given mirror-lens separation L, the focal length of the apparatus 100a is shortened with respect to the focal length of the apparatus 10 (having a flat substrate).

[0160] Figure 27 shows an apparatus 100b having a lens 115b which comprises a substrate 118b. The substrate 118b has a concave surface 150b on which the metastructure 21 is defined. As such, for a given mirror-lens separation L, the focal length of the apparatus 100b is lengthened with respect to the focal length of the apparatus 10 (having a flat substrate). Figure 28 shows an apparatus 100c having a lens 115c which comprises a substrate 118c. The substrate 118c has a convex surface 150c which is opposite the surface on which the metastructure 21 is defined. As such, for a given mirrorlens separation L, the focal length of the apparatus 100c is shortened with respect to the focal length of the apparatus 10 (having a flat substrate).

[0161] Figure 29 shows an apparatus 100d having a lens 115d which comprises a substrate 118d. The substrate 118d has a concave surface 150d on which the metastructure 21 is defined. As such, for a given mirror-lens separation L, the focal length of the apparatus 100d is lengthened with respect to the focal length of the apparatus 10 (having a flat substrate).

[0162] The effect of a curved refractive surface will be explained with reference to the apparatus 100d shown in Figures 29. It will be understood that the concepts and formulae discussed apply equally to the apparatus’ 100a-c shown in Figures 26-28.

[0163] The combined focal length of the lens 115d is given by the product of the focal lengths of the refractive curved surface 150d, and the surface structure 21, divided by the sum of the focal lengths of the refractive curved surface 150d, and the surface structure 21. As such, when the light is travelling in the negative direction (from the first face to the second face), the focal length of the lens 115d is given by:

[0164] Where \ f | is the focal length of the surface structure 21 , and fRis the focal length of the curved refractive surface 150d.

[0165] By contrast, when the light is travelling in the positive direction (after being reflected from the mirror) (from the second face to the first face), the focal length of the lens 115d is given by:

[0166] -\f\ - fR fnet (7)

[0167] ~\f\ + fR In embodiments where the focal length fRof the refractive curved surface 150d is long compared to the focal length \ f | of the surface structure 21, the above equations (6) and (7) may be approximated such that the effect of the curved refractive surface is to apply a fixed focal length change to the total focal length. This approximation can be demonstrated using a Taylor’s expansion of the above formulae, as follows:

[0168] = \f\ ~

[0169] = -| / | - A /

[0170] The function of the apparatus’ 100a, and 100c may be the same, and the function of the apparatus’ 100b and 100d, but the apparatus’ 100c and 100d (the embodiments shown in Figures 28 and 29) may be advantageous since it may be easier to fabricate a metastructure on a flat surface and this arrangement avoids an enforced gap between the mirror and the lens resulting from the lens being curved.

[0171] Figure 30 shows a plot of the focal length S2 against the mirror lens separation L. It can be seen from the plot that by using a refractive curved surface in addition to the surface structure, the focal length can be shifted. For example, when using a convex surface, and hence adding a positive focal length change, a finite focal length can be achieved with a zero mirror-lens separation L.

[0172] Although much of the above discussion relates to metasurfaces, it will be understood by the skilled person that the surface structure could comprise an optical grating. Figure 31 schematically illustrates a section of such an optical grating. The optical grating 200 comprises a plurality of grating components202. Each grating component 202 has a grating pattern direction, and the grating pattern direction of each grating component 202 varies across the face (i.e. different grating component have different grating pattern directions which may be dependent on the location of the grating component on the face). This embodiment may be considered analogous to the embodiment discussed above where the surface structure comprises a plurality of pillars having different rotation angles, with the grating components being equivalent to the individual pillars.

[0173] It will be appreciated by those skilled in the art that the invention has been illustrated by describing one or more specific embodiments thereof, but is not limited to these embodiments; many variations and modifications are possible, within the scope of the accompanying claims.

Claims

Claims1. An apparatus for manipulating incident light, the apparatus comprising: a mirror; and a lens having a first face, and a second, opposing, face, wherein at least one of the first and second faces comprises a surface structure configured to: converge incident light having a first circular polarisation state passing through the lens from the first face to the second face; diverge light having the first circular polarisation state passing through the lens from the second face to the first face; and reverse the circular polarisation state of light passing through the lens, wherein the mirror and lens are arranged such that incoming light passes through the lens a first time, is reflected from the mirror, and then passes through the lens a second time.

2. The apparatus of claim 1, wherein the apparatus comprises an actuating device arranged to move the mirror and / or the lens.

3. The apparatus of claim 2, wherein the actuating device is arranged to move the mirror and / or the lens relative to one another to alter a separation between the mirror and the lens such that the manipulation effect of the apparatus is adjustable.

4. The apparatus of claim 2 or claim 3, wherein the actuating device is arranged to move the mirror with at least two degrees of freedom.

5. The apparatus of any one of claims 2 to 4, wherein the actuating device is a Micro-Electro-Mechanical Systems actuation device.

6. The apparatus of claim 5, wherein the actuating device comprises: a first actuator element and a second actuator element each comprising a piezoelectric layer on a first side of the actuating device, wherein each of the first and second actuator elements has a respective width at least five times a respective thickness thereof; anda reinforcing ring, on a second side of the actuating device opposite to the first side, opposite a location on the first side between the first actuator element and the second actuator element; wherein the mirror is connected to at least the first actuator element, such that actuation of the first actuator element causes movement of the mirror.

7. The apparatus of claim 6, wherein each actuator element comprises a plurality of actuator portions.

8. The apparatus of claim 7, wherein at least some of the actuator portions are independently addressable with respective voltages.

9. The apparatus of any of claims 2 to 8, wherein the mirror is deformable, and wherein the actuating device is arranged to bend the mirror.

10. The apparatus of claim 9, wherein the actuating device comprises a plurality of individually addressable piezoelectric sections of the mirror, wherein the mirror can change shape on actuation of one or more of the piezoelectric sections.

11. The apparatus of any one of the preceding claims, wherein the surface structure of the lens is configured to impose a phase shift to light passing through the lens according to a geometric phase principle.

12. The apparatus of claim 11 , wherein the surface structure comprises a plurality of rectangular pillars.

13. The apparatus of claim 12, wherein each pillar has a rotation angle relative to a given axis, and wherein the rotation angle of each pillar varies across the lens.

14. The apparatus of any one of the preceding claims, wherein surface structure comprises a meta-structure such that the lens comprises an optical metasurface.

15. The apparatus of any one of claims 1 to 11, wherein the surface structure comprises an optical grating.

16. The apparatus of claim 15, wherein the optical grating comprises a plurality of grating components, wherein each grating component has a grating pattern direction, and the grating pattern direction of each grating component varies across the face.

17. The apparatus of any one of the preceding claims, wherein the lens comprises an array of sub-lenses, wherein two or more of the sub-lenses have different focal lengths.

18. The apparatus of any one of the preceding claims, wherein the face of the lens closest to the mirror is configured to reflect at least a portion of the light reflected from the mirror to achieve multiple internal reflections.

19. The apparatus of any one of the preceding claims, wherein one or both of the first and second surface comprises an anti-reflective coating.

20. The apparatus of any one of the preceding claims, wherein the lens comprises an optically transparent substrate on which the surface structure is defined.

21. The apparatus of claim 20, wherein the substrate comprises a curved refractive surface.

22. The apparatus of any one of the preceding claims, wherein the apparatus comprises a further lens having a face comprising a surface structure configured to converge or diverge incident light.

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