Arbitrary optical elliptical retarder and apparatus for generating optical skyrmionic topological quasiparticles

Abstract

A composite optical modulator 100 comprising a cascade of optical elements aligned along an optical axis is disclosed. An optical retarder 110 comprises first polarisation controlling birefringent spa

Description

[0001] TECHNICAL FIELD

[0002] The present disclosure relates to a universal optical modulator and its uses. In particular, the disclosure relates to an arbitrary optical elliptical retarder and apparatus for generating optical skyrmionic topological quasiparticles. BACKGROUND

[0003] The interaction between light and matter has been a fundamental question for centuries and continues to be an active area of research. This has gained renewed importance in the context of structured matter and structured light. Unprecedented control over structured matter involves the creation of artificial atoms using metasurfaces and metamaterials, which find diverse applications in enhancing light properties through linear, nonlinear, and quantum effects. The concept of topologically structured matter has transitioned from condensed matter physics to influence the realm of photonics, giving rise to topologically structured light fields. These light fields exhibit textures in polarization and phase for vectorial light, optical skyrmions, and beyond.

[0004] Light-matter interactions have also led to the use of light as a probe, where structured light plays a crucial role in deciphering intricate systems. This is evident in applications such as rotational and vectorial metrology, chirality, and clinical diagnosis. Topological protection and invariance, in particular, present exciting avenues to explore within the framework of light-matter interactions. They hold the promise of ensuring stable information transport and storage by introducing and detecting structure in both light and matter. The transportation of structured light through complex media is currently a highly relevant and topical subject, especially in the fields of communication and biomedical imaging. In this context, the development of invariant light forms and the extension of adaptive correction to various forms of light are essential aspects to consider.

[0005] While there is a concerted effort towards developing rewritable forms of structured matter, topologically structured matter currently faces limitations in terms of its static nature, preset functionality, and limited tunability. These limitations hinder its application in dynamic photonic systems that require complex, rewritable topologies. Dynamic control based on spatial light modulation technology has so far been limited to the paradigm of complex amplitude modulation using the optical axis to impart phase changes, limiting its functionality to that of a simple linear birefringent plate which cannot simultaneously modify the retardance value as well as axis shape and orientation in a user-defined pixelated manner. Indeed, the high flexible, complex forms of topologically structured matter for manipulating structured light require enhanced control not presently possible with such devices.

[0006] It is in this context the present disclosure has been devised. BRIEF SUMMARY

[0007] Viewed from one aspect, the present invention provides a phase insensitive arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation, the arbitrary optical elliptical retarder may include a cascade of optical elements aligned along an optical axis including a first polarisation controlling birefringent spatial light modulator, SLMp a, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis (or slow axis as equivalent, we use fast axis as example in later description) of the pixels of SLMp a arranged at a first angle to the optical axis, a second polarisation controlling birefringent spatial light modulator, SLMp b, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis of the pixels of SLMp b arranged at a second angle to the optical axis at a diagonal to the first angle, a third polarisation controlling birefringent spatial light modulator, SLMp c, having a plurality of pixels each individually controllable to adjust the phase retardance applied to light transmitted through the pixel, the fast axis of the pixels of the third SLMp c arranged at a third angle to the optical axis parallel to the first angle, wherein SLMp a, SLMp b and SLMp c together provide synthetic pixels controllable to adjust input light to pixels of SLMp a having a first, arbitrary polarisation to provide output light from corresponding pixels of SLMp c having a second, arbitrary polarisation. Viewed from another aspect, the present invention provides a universal optical modulator. The (phase insensitive) arbitrary optical elliptical retarder may form part of the universal optical modulator.

[0008] In accordance with these aspects of the disclosure, there is provided a universal light modulator that can provide topologically tuneable structured matter synthetically as virtual pixels, which can be used to generate structured light, with unprecedented functionality even though they are derived from a cascade of “low functionality” devices, altering the paradigm of phase and amplitude control to encompass arbitrary spatially varying structured matter. A cascade of these optical elements with judicious encoding can mimic a pixel-controllable phase insensitive arbitrary retarder of any axis shape and orientation, retardance value. In this way, the Stokes vector field representing the polarisation of light passing through the cascade can be controlled arbitrarily to obtain a desired change in polarisation, or a desired polarisation, in the light field across the synthetic pixels of the optical elements. This allows never-before achieved precise, new paradigm based dynamic control of polarisation textures, enabling a number of applications. In particular, as will be shown below, the alignment of the fast axes of the three SLM retarders allows any arbitrary input light polarisation to be changed to any arbitrary output light polarisation. The SLMs allow arbitrary polarisation textures to be imparted into wavefronts of light beams passing through the arbitrary optical elliptical retarder, in a way that is controllable and changeable at a pixel level.

[0009] As will be described in mode detail below, the universal optical modulator, and in particular the arbitrary optical elliptical retarder is a powerful reconfigurable device usable to form novel liquid crystal based synthetic compound skyrmions, harnessing the anisotropic axis shape and orientation that the light sees, as an object-wise analogy to a Stokes vector field optical skyrmion. The universal optical modulator is also capable of generating different tuneable complex topologies such as skyrmion lattices and skyrmion bags. The universal optical modulator can then be used as a beam generator to create complex structured light, including optical skyrmions in high-order skyrmionic or bimeroniumic formats. As will be seen, these dynamical states of light demonstrate topological protection through both isotropic and anisotropic media.

[0010] The universal optical modulator has other novel applications, for example finding utility in a polarimeter, wherein the arbitrary optical elliptical retarder is used to provide a Full Poincare Beam generator array reconfigurable to provide a tuned sensing pattern optimised for the sample being analysed. In this way, in a beam analyser, the Full Poincare Beam generator unit is usable to analyse all polarisation states simultaneously through providing complete analysing channels, giving high sensitivity by exploiting its tuneability for enhancement in the flexibility and measurement precision of the detection through novel polar and cartesian optimization, both highly sample dependent.

[0011] Further, the universal optical modulator may also be used in an adaptive optics apparatus, wherein the arbitrary optical elliptical retarder is used to correct the polarisation state (and phase) of input light. In this way, in an adaptive optics apparatus, the arbitrary optical elliptical retarder enables the dynamic correction of spatially varying arbitrary retardance aberration in both sensor-based and sensorless forms through a new object-wise adaptive optics regime, harnessing the ability to construct object-wise rather than light-wise retardance aberration modes.

[0012] In embodiments, each pixel of the SLMs of the arbitrary optical elliptical retarder may be individually controllable to adjust the phase retardance value applied to the light passing through such that its polarisation can be rotated around the Poincare sphere by an angle within the full 2k radian range. In embodiments, the fast axis of pixels of the SLMp a and SLMp c for the arbitrary optical elliptical retarder represent a horizontal axis for the arbitrary optical elliptical retarder, each causing rotation of the polarisation of light input thereto around the axis of the Poincare sphere defined by the first Stokes parameter SI, and wherein the pixels of the SLMp b each cause rotation of the polarisation of light input thereto around the axis of the Poincare sphere defined by the second Stokes parameter S2. In embodiments, the phase retardances applied by the sequential pixels of SLMp a, SLMp b and SLMp c of the arbitrary optical elliptical retarder may be controllable to achieve an arbitrary desired total rotation of the polarisation of the input light around the Poincare sphere, by a first rotation around the SI axis by SLMp a, a second rotation around the S2 axis by SLMp b, and a third rotation around the SI axis by SLMp c. In this way, any desired change in polarisation from an arbitrary input light polarisation to an arbitrary output light polarisation, can be achieved.

[0013] In embodiments, the SLMps of the arbitrary optical elliptical retarder may be each liquid crystal SLMs having individually addressable electrodes for each pixel to apply a voltage across the liquid crystal to adjust the retardance value applied to light passing through the liquid crystal at that pixel. In embodiments, each pixel of the SLMps of the arbitrary optical elliptical retarder may be rewritable such that the retardance value applied can be changed by applying a different voltage, the arbitrary optical elliptical retarder thereby representing structured matter usable to encode and store data. In embodiments, the arbitrary optical elliptical retarder may further include a polarisation controller coupled to the SLMps of the arbitrary optical elliptical retarder to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the voltages applied to each pixel of the SLMPs being determined by the polarisation controller to achieve a desired change in polarisation between the input light to pixels of SLMp a and the light output from corresponding pixels of SLMp c. In this way, the arbitrary optical elliptical retarder may form structured matter that may be dynamically configured, and useable to generate structured light.

[0014] In embodiments, the universal optical modulator may further include a phase modulator aligned in the cascade of optical elements. In embodiments, the phase modulator may include a deformable mirror or micromirror array controllable to move along the optical axis at the locations of different pixels to adjust a phase of the light output by the cascade. In other embodiments, the phase modulator may include a phase controlling birefringent spatial light modulator, SLMph having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis of the pixels of SLMph arranged at a fourth angle to the optical axis orthogonal to the first angle. In this way, the universal optical modulator may provide, an arbitrary optical elliptical retarder that also allows correction for phase (i.e. so that the arbitrary optical elliptical retarder is not phase insensitive). Where the phase modulator includes a deformable mirror or micromirror, this may be located at any position within the cascade of SLMps providing the arbitrary optical elliptical retarder.

[0015] In embodiments, the universal optical modulator may further include an intensity modulator aligned in the cascade of optical elements, the intensity modulator may include a pair of linear polarisers, and an intensity controlling birefringent spatial light modulator, SLMi, arranged between the pair of linear polarisers, the SLMi having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, thereby adjusting the pupil intensity value of the light transmitted through the pixel and out of the second linear polariser relative to the input light incident on the first linear polariser. In this way, the universal optical modulator may also arbitrarily control the intensity of the output light in a structured manner across the pixels of the SLMs.

[0016] In embodiments, the universal optical modulator may further include a degree of polarisation modulator aligned in the cascade of optical elements, the degree of polarisation modulator may include a sequence of two or more degree of polarisation controlling birefringent spatial light modulators, SLMdop a .dop n, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, a controller configured to control a degree of polarisation of light transmitted through pixels of the cascade by controlling the voltage of the pixels of two or more of the SLMdops in the degree of polarisation modulator to consecutively apply phase variation patterns with different retardance values to adjust the phase retardation of the light passing through the pixel. In this way, the universal optical modulator may also arbitrarily control the degree of polarisation of the output light in a structured manner across the pixels of the SLMs.

[0017] In embodiments, the universal optical modulator may further include a diattenuation modulator aligned in the cascade of optical elements, the diattenuation modulator may include a first arbitrary optical elliptical retarder may include three SLMs as recited in claim 1, a fixed polariser, a second arbitrary optical elliptical retarder may include three SLMs as recited in claim 1, and a controller coupled to the SLMs of the first and second arbitrary optical elliptical retarders of the diattenuation modulator to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the voltages applied to each pixel of the SLMs being determined by the diattenuation modulator to achieve a desired change in diattenuation between the input light to pixels of SLMp a and the light output from corresponding pixels of SLMp c. In this way, the universal optical modulator may also arbitrarily control the diattenuation of the output light in a structured manner across the pixels of the SLMs. Here, the diattenuation modulator allows the independent control of the intensity of light in orthogonal polarisations.

[0018] Viewed from another aspect, the present disclosure provides a method of transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation using the universal optical modulator may also include may include for an arbitrary desired change to the polarisation of light passing through a pixel at (x, y) in the SLMps of the arbitrary optical elliptical retarder, determining a set of voltages to be applied to each pixel of the SLMps to achieve the desired change in polarisation between the input light to pixels of the SLMp a and the light output from corresponding pixels of SLMp c, wherein the phase retardances applied by the sequential pixels of SLMp a, SLMp b and SLMp c of the arbitrary optical elliptical retarder may be controlled to achieve the desired total rotation of the polarisation of the input light around the Poincare sphere, by a first rotation around the SI axis by SLMp a, a second rotation around the S2 axis by SLMp b, and a third rotation around the SI axis by SLMp c, and controlling the SLMps to apply the determined respective voltages to the pixels at (x, y).

[0019] Viewed from another aspect, the present disclosure provides a use of the universal optical modulator may also include in a polarimeter, wherein the arbitrary optical elliptical retarder may be used to provide a Full Poincare Beam generator reconfigurable to provide a tuned sensing pattern optimised for the sample being analysed.

[0020] Viewed from another aspect, the present disclosure provides a use of the universal optical modulator may also include in an adaptive optics apparatus, wherein the arbitrary optical elliptical retarder may be used to correct the polarisation state and phase of input light.

[0021] Viewed from another aspect, the present invention provides apparatus for generating optical skyrmionic topological quasiparticles, may include an arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation, the arbitrary optical elliptical retarder including one or more spatial light modulators, SLMs, having pixels at locations (x, y) individually controllable by an applied voltage to adjust the phase retardance value applied to light transmitted through the pixel. The apparatus also includes a quasiparticle encoding controller coupled to the SLMs of the arbitrary optical elliptical retarder to apply pixel wise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the voltages applied to each pixel of the SLMs being determined by the quasiparticle encoding controller to achieve, for a pixel at a location (x, y), a desired change in polarisation between the input light to pixels of the first SLM and the light output from corresponding pixels of the last SLM so that the output light field has a topologically stable skyrmionic Stokes vector texture across the surface (x, y) having a skyrmion number N of a desired skyrmion defined by the relation where o is the boundary in (x, y) of the region within which the skyrmion is confined, and wherein S isbe the Stokes vector applied by the arbitrary retarder at a pixel at (x, y), such that the polarisation texture in S wraps around the Poincare sphere TV times within the boundary.

[0022] In embodiments, the apparatus for generating optical skyrmionic topological quasiparticles as claimed in claim 18, may include the universal optical modulator of any one of claims 1 to 12, wherein the universal optical modulator provides the arbitrary optical elliptical retarder.

[0023] The apparatus for generating optical skyrmionic topological quasiparticles may also include further may include a light source for illuminating the arbitrary optical elliptical retarder to generate in the light output from the retarder skyrmions based on the skyrmionic Stokes vector texture encoded in the SLMs of the arbitrary optical elliptical retarder.

[0024] The apparatus for generating optical skyrmionic topological quasiparticles may also include further may include one or more optical elements for guiding or storing the optical skyrmionic topological quasiparticles.

[0025] The apparatus for generating optical skyrmionic topological quasiparticles may also include further may include means for determining the skyrmionic Stokes vector texture encoded in the arbitrary optical elliptical retarder, the means for detecting the skyrmionic Stokes vector texture including an imaging device for optically detecting the generated skyrmions, and / or a Mueller matrix polarimeter.

[0026] The apparatus for generating optical skyrmionic topological quasiparticles may also include wherein the quasiparticle encoding controller may be configured to encode in the arbitrary optical elliptical retarder a skyrmionic Stokes vector texture including one or more skyrmions, skyrmioniums, meron, bimerons or bimeroniums where c may be unbound, a skyrmion, skyrmionium, meron, bimeron or bimeronium lattice where o may be bound, a skyrmion, skyrmionium, meron, bimeron or bimeronium bag.

[0027] Viewed from one aspect, the present invention provides a method of generating optical skyrmionic topological quasiparticles using an arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation, the arbitrary optical elliptical retarder including one or more spatial light modulators, SLMs, having pixels at locations (x, y) individually controllable by an applied voltage to adjust the phase retardance value applied to light transmitted through the pixel, the method may include determining pixelwise voltages to be applied to the SLMs of the arbitrary optical elliptical retarder to adjust the retardance value applied to light passing through the liquid crystal at that pixel to achieve, for a pixel at a location (x, y), a desired change in polarisation between the input light to pixels of the first SLM and the light output from corresponding pixels of the last SLM so that the output light field has a topologically stable skyrmionic Stokes vector texture across the surface (x, y) having a skyrmion number N of a desired skyrmion defined by the relation 1 ff e / \ A = -— / / b • x J dxav 4tf JJa \dx Oy ) y where g is the boundary in (x, y) of the region within which the skyrmion is confined, and wherein S is the Stokes vector applied by the arbitrary retarder at a pixel at (x, y), such that the polarisation texture in S wraps around the Poincare sphere N times within the boundary, applying the determined pixelwise voltages to the SLMs of the arbitrary optical elliptical retarder to adjust the retardance value applied to light passing through the liquid crystal at that pixel.

[0028] In embodiments, once the optical skyrmionic topological quasiparticles are encoded in the arbitrary optical elliptical retarder as structured matter, the method may further include illuminating the arbitrary optical elliptical retarder with light from a light source to generate the light output from the retarder skyrmions based on the skyrmionic Stokes vector texture encoded in the SLMs of the arbitrary optical elliptical retarder.

[0029] In embodiments, computer program product may include instructions, which when run on a processor, cause the processor to carry out the method claim 24.

[0030] It will be appreciated from the foregoing disclosure and the following detailed description of the examples that certain features and implementations described as being optional in relation to any given aspect of the disclosure set out above should be understood by the reader as being disclosed also in combination with the other aspects of the present disclosure, where applicable. Similarly, it will be appreciated that any attendant advantages described in relation to any given aspect of the disclosure set out above should be understood by the reader as being disclosed as advantages of the other aspects of the present disclosure, where applicable. That is, the description of optional features and advantages in relation to a specific aspect of the disclosure above is not limiting, and it should be understood that the disclosures of these optional features and advantages are intended to relate to all aspects of the disclosure in combination, where such combination is applicable. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Certain examples of the present disclosure will now be described, with reference to the accompanying drawings, in which:

[0032] FIG. 1 shows a schematic illustration of a universal optical modulator in accordance with aspects of the invention;

[0033] FIG. 2 shows a more detailed schematic illustration of the arbitrary optical elliptical retarder of the universal optical modulator shown in FIG. 1, the arbitrary optical elliptical retarder being usable in an apparatus for generating optical skyrmionic topological quasiparticles in accordance with aspects of the invention;

[0034] FIG. 3 shows a method of transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation using the arbitrary optical elliptical retarder of FIG. 2, in accordance with aspects of the invention;

[0035] FIG. 4 shows a schematic illustration in relation to a Poincare sphere of a series of rotations of the Stokes vector achieved by a suitably configured synthetic pixel of the arbitrary optical elliptical retarder of FIG. 2 to achieve a desired change in polarisation;

[0036] FIG. 5 shows a schematic illustration in relation to a Poincare sphere of a second series of rotations of the Stokes vector achieved by a suitably configured synthetic pixel of the arbitrary optical elliptical retarder of FIG. 2 to achieve a desired change in polarisation;

[0037] FIG. 6 illustrates the changes to the polarisation ellipse and phase of the light passing through a synthetic pixel of the arbitrary optical elliptical retarder and the phase modulator of the universal optical modulator shown in FIG. 1;

[0038] FIG. 7 illustrates the control of the Stokes vector and phase achievable using different numbers of spatial light modulators and a phase modulator;

[0039] FIG. 8 shows a method of generating optical skyrmionic topological quasiparticles using the arbitrary optical elliptical retarder of FIG. 2, in accordance with aspects of the invention;

[0040] FIG. 9 illustrates an example configuration of the arbitrary optical elliptical retarder of FIG. 2 to provide structured matter usable to generate an optical skyrmion;

[0041] FIG. 10 illustrates the mapping of the skyrmionic polarisation texture of the optical skyrmion of FIG. 9 onto the Poincare sphere;

[0042] FIG. 11 illustrates the use of different configurations of the structured matter of the synthetic pixels of the arbitrary optical elliptical retarder to generate higher order and more exotic optical skyrmionic topological quasiparticles;

[0043] FIG. 12 illustrates the generation of bound skyrmions lattice and skyrmion bags by the structured matter of the synthetic pixels of the arbitrary optical elliptical retarder;

[0044] FIG. 13 shows a more detailed schematic illustration of the intensity modulator of the universal optical modulator shown in FIG. 1;

[0045] FIG. 14 shows a more detailed schematic illustration of the degree of polarisation modulator of the universal optical modulator shown in FIG. 1;

[0046] FIG. 15 shows a more detailed schematic illustration of the diattenuation modulator of the universal optical modulator shown in FIG. 1; and

[0047] FIG. 16 shows a schematic illustration of an example controller which may be used to provide any of one or more controllers for controlling functional units of the universal optical modulator in accordance with aspects of the disclosure. DETAILED DESCRIPTION

[0048] Hereinafter, examples of the disclosure are described with reference to the accompanying drawings. However, it should be appreciated that the disclosure is not limited to the described examples, and all changes and / or equivalents or replacements thereto also belong to the scope of the disclosure. The same or similar reference denotations may be used to refer to the same or similar elements throughout the specification and the drawings.

[0049] As used herein, the terms “have,” “may have,” “include,” or “may include” a feature (e.g., a number, function, operation, or a component such as a part) indicate the existence of the feature and do not exclude the existence of other features. Throughout the description and claims of this specification, the words “comprise” and “contain” and variations of them mean “including but not limited to”, and they are not intended to (and do not) exclude other components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[0050] As used herein, the terms “A or B,” “at least one of A and / or B,” or “one or more of A and / or B” may include all possible combinations of A and B. For example, “A or B,” “at least one of A and B,” “at least one of A or B” may indicate all of (1) including at least one A, (2) including at least one B, or (3) including at least one A and at least one B.

[0051] As used herein, the terms “first” and “second” may modify various components regardless of importance and do not limit the components. These terms are only used to distinguish one component from another. For example, reference to a first component and a second component may indicate different components from each other regardless of the order or importance of the components.

[0052] It will be understood that when an element (e.g., a first element) is referred to as being (physically, operatively or communicatively) “coupled with / to,” or “connected with / to” another element (e.g., a second element), it can be coupled or connected with / to the other element directly or via a third element. In contrast, it will be understood that when an element (e.g., a first element) is referred to as being “directly coupled with / to” or “directly connected with / to” another element (e.g., a second element), no other element (e.g., a third element) intervenes between the element and the other element.

[0053] The terms as used herein are provided merely to describe some embodiments thereof, but not to limit the scope of other embodiments of the disclosure. It is to be understood that the singular forms “a,” “'an,” and “the” include plural references unless the context clearly dictates otherwise. All terms including technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of the disclosure belong. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0054] Referring now to the drawings, FIG. 1 shows a schematic illustration of a universal optical modulator 100 in accordance with aspects of the invention. The universal optical modulator 100 comprises an arbitrary optical elliptical retarder 110 for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation. The structure and operation of the arbitrary optical elliptical retarder 110 to arbitrarily control the polarisation of light passing through the universal optical modulator 100 will be described below in relation to FIG. 2, FIG. 3, FIG. 4, FIG. 5, FIG. 6 and FIG. 7.

[0055] Optionally, the universal optical modulator 100 may also include a phase modulator 120, an intensity modulator 130, a degree of polarisation modulator 140 and a diattenuation modulator 150. As can be seen, these are shown in FIG. 1 in broken lines indicating these features do not need to be provided in accordance with the aspects of the invention set forth herein. Indeed, these functional units may not be provided at all in the universal optical modulator 100, or they may be provided in any combination. It should be clear, however, that these features are to be considered optional.

[0056] Generally, the use of broken lines or dotted lines to outline features in the FIG. 1 or any other drawing is intended to indicate that these features are optional in the context of the apparatus shown and described in that Figure.

[0057] The universal optical modulator 100 may, optionally, also include a phase modulator 120 which may be provided together with and operated in conjunction with the arbitrary optical elliptical retarder 110 to control the phase of light passing through the universal optical modulator 100.

[0058] The arbitrary optical elliptical retarder 110 may be usable in an apparatus for generating optical skyrmionic topological quasiparticles in accordance with aspects of the invention. The operation of the arbitrary optical elliptical retarder 110 for generating optical skyrmionic topological quasiparticles will be described in FIG. 8, FIG. 9, FIG. 10, FIG. 11 and FIG. 12.

[0059] The universal optical modulator 100 may, optionally, also include an intensity modulator 130 for adjusting the pupil intensity value of the light transmitted through the universal optical modulator 100. The structure and operation of the intensity modulator 130 will be described in more detail in FIG. 13.

[0060] The universal optical modulator 100 may, optionally, also include a degree of polarisation modulator 140 to control a degree of polarisation of light transmitted through the universal optical modulator 100. The structure and operation of the degree of polarisation modulator 140 will be described in more detail in FIG. 14.

[0061] The universal optical modulator 100 may, optionally, also include a diattenuation modulator 150 to allow the independent control of the intensity of light in orthogonal polarisations. The structure and operation of the diattenuation modulator 150 will be described in more detail in FIG. 15.

[0062] Generally the universal optical modulator 100 includes a cascade of optical elements each making up the different functional units described above, the cascade of optical elements being generally arranged along an optical axis Z. The optical axis Z is to be understood to be the axis along which light propagates through the universal optical modulator 100 in use, and although shown in FIG. 1 as following a single direction, the optical axis Z may of course in practice be folded or guided by one or more mirrors or other optical elements which may be provided as part of the universal optical modulators 100, or between the functional units thereof. Nevertheless, the folding of the light path should be understood to not affect the propagation of the light through the universal optical modulator 100 along the optical axis Z.

[0063] A light source 101 may be used to generate input light. The input light 105 may be a generally paraxial beam illuminating the universal optical modulator 100. It may be of known or unknown polarisation.

[0064] In the example arrangement of the universal optical modulator 100 shown in FIG. 1, input light 105 passes through the arbitrary optical elliptical retarder 110 and has its polarisation texture modulated across its wavefront in the orthogonal surface in the (x, y) plane, resulting in the output light 115 being controlled to have an arbitrarily desired polarisation texture.

[0065] The output light 115 is input into the phase modulator 120 and has its phase modulated across its wavefront in the orthogonal surface in the (x, y) plane, resulting in the output light 125 being controlled to have an arbitrarily desired phase.

[0066] The output light 125 is input into the intensity modulator 130 and has its intensity modulated across its wavefront in the orthogonal surface in the (x, y) plane, resulting in the output light 135 being controlled to have an arbitrarily desired phase.

[0067] The output light 135 is input into the degree of polarisation modulator 140 and phase variation patterns with different retardance values applied to it by consecutive optical elements to adjust the phase retardation of the light passing through them, resulting in the output light 145 having an arbitrarily controlled the degree of polarisation.

[0068] The output light 155 is input into the diattenuation modulator 150 and the retardance value applied to light passing through the optical elements of the diattenuation modulator 150 achieve a desired change in di attenuation, which has impact to the output light 155.

[0069] A detector 103 may be used to detect the output light and measure one of more of the parameters controlled by the universal optical modulator 100. For example, the detector 103 (and after light source 105) may include an imaging Mueller matrix polarimeter usable to decompose the elliptical axis polarisation distributions in the output light, and determine, for example, a polarisation field encoded by the arbitrary optical elliptical retarder 110 acting as structured matter.

[0070] The ordering of the cascade of optical elements, or the functional elements of the universal optical modulator 100 as shown in FIG. 1 is not intended to be limiting, and the functional elements may be arranged in any suitable order.

[0071] The arbitrary optical elliptical retarder 110, phase modulator 120, intensity modulator 130, degree of polarisation modulator 140 and diattenuation modulator 150 may be such that they can modulate their respective control parameters of polarisation, phase, intensity, degree of polarisation and diattenuation in a pixel-wise manner, resulting in an high degree of arbitrary control of these parameters across the wavefront, allowing exotic structured light to be generated.

[0072] FIG. 2 shows a more detailed schematic illustration of the arbitrary optical elliptical retarder of the universal optical modulator shown in FIG. I.

[0073] The phase-insensitive arbitrary optical elliptical retarder 110 comprises a first polarisation controlling birefringent spatial light modulator SLMp a 112a, a second polarisation controlling birefringent spatial light modulator SLMp b 112b, and a third polarisation controlling birefringent spatial light modulator SLMp j 112c, arranged along an optical axis Z.

[0074] The spatial light modulators extend across the plane orthogonal to the optical axis Z defined by an x axis X and a y axis Y. Each of the spatial light modulators has a layer formed of a birefringent material, such as a nematic liquid crystal, which has different refractive indices for light polarized in two orthogonal directions (a fast axis and a slow axis). The spatial light modulators each have a series of transparent and individually addressable electrodes arranged as pixels adjacent to the birefringent material. By applying a voltage to the electrodes to apply an external electric field across the birefringent material, the relative refractive indices can be changed across the spatial light modulator in a pixelwise manner. In this way, the phase retardance or delay between light polarised along the slow axis of the birefringent material and the light polarised along the the fast axis of the birefringent material can be precisely controlled, allows for modulation of the phase of the light across the wavefront.

[0075] Thus, the first polarisation controlling birefringent spatial light modulator, SLMp a, 112a has a plurality of pixels 113a each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel. The fast axis of the pixels 113a of SLMp a 112a are arranged at a first angle to the optical axis Z. In the example, as can be seen the fast axis of the pixels 113a of SLMp112a is aligned with the ‘horizontal’, i.e. it forms an angle of 0° with the x axis X.

[0076] The second polarisation controlling birefringent spatial light modulator, SLMp b, 112b has a plurality of pixels 113b each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel. The fast axis of the pixels 113b of SLMp b 112b is arranged at a second angle to the optical axis Z at a diagonal to the first angle. In the example, as can be seen the fast axis of the pixels 113b of SLMp b 112b is at a diagonal to the ‘horizontal’, i.e. it forms an angle of 45° with the x axis X.

[0077] The third polarisation controlling birefringent spatial light modulator, SLMp c, 112c has a plurality of pixels 113c each individually controllable to adjust the phase retardance applied to light transmitted through the pixel. The fast axis of the pixels 113c of the third SLMp c 112c is arranged at a third angle to the optical axis parallel to the first angle. In practice, in the example, as can be seen the fast axis of the pixels 113c of SLMp c 112c is also aligned with the ‘horizontal’, i.e. it forms an angle of 0° with the x axis X.

[0078] The SLMp a 112a, SLMp b 112b and SLMp c 112c together provide synthetic pixels controllable to adjust input light 105 to the pixels 113a of SLMp a having a first, arbitrary polarisation to provide output light 115 from corresponding pixels of SLMp c having a second, arbitrary polarisation. By synthetic pixels it is meant that more than one pixel of the different SLMs combine and can be controlled together to provide a single ‘synthetic pixel’ giving arbitrary polarisation control. In this way, the pixelwise control of the change in polarisation provided by the SLMs allows arbitrary polarisation textures to be imparted into wavefronts of light beams passing through the arbitrary optical elliptical retarder, in a way that is controllable and changeable at a pixel level. The change in polarisation achieved by each synthetic pixel of the arbitrary optical elliptical retarder 110 may be determined by the the polarisation controller 114.

[0079] In embodiments, the universal optical modulator 100 may further include a phase modulator 120 aligned in the cascade of optical elements, although the provision of the phase modulator 120 is optional. In embodiments, the phase modulator 120 may include a phase modulating optical element 122 to adjust a phase of the output light 115 from the arbitrary optical elliptical retarder 110. The phase modulation by the phase modulating optical element 122 may be performed in a pixelwise manner, under control of a phase controller 124. The phase controller 124 may work together with the polarisation controller 114 such that the arbitrary optical elliptical retarder 110 can be operated to also provide full phase modulation across the wavefront, as well as polarisation modulation, such that the arbitrary optical elliptical retarder is not phase insensitive.

[0080] In embodiments, the phase modulating optical element 122 may be a deformable mirror or micromirror array controllable to move along the optical axis Z at the locations of different pixels to adjust a phase of the output light 115 from the arbitrary optical elliptical retarder 110. Where a deformable mirror or micromirror is used, the phase modulating optical element 122 may be provided at the end of the cascade of SLMs of the arbitrary optical elliptical retarder 110, as shown in FIG. 2, or it may be interposed between the SLMs of the arbitrary optical elliptical retarder 110.

[0081] In other embodiments, the phase modulating optical element 122 may be a phase controlling birefringent spatial light modulator, SLMph, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis of the pixels of SLMph arranged at a fourth angle to the optical axis orthogonal to the first angle. In the example shown the hast axis of the pixels of SLMph would be ‘vertical’ i.e. aligned with the y axis Y.

[0082] In this way, the universal optical modulator may provide, an arbitrary optical elliptical retarder that also allows correction for phase (i.e. so that the arbitrary optical elliptical retarder is not phase insensitive).

[0083] Referring now to FIG. 3, a method 300 of transforming the polarisation of arbitrarily polarised input light 105 to output light 115 having any arbitrary polarisation using the arbitrary optical elliptical retarder of FIG. 2 is shown. The method 300 may be performed by the polarisation controller 114 operating the SLMs.

[0084] FIG. 3 illustrates an example method 300 for summary. Although the example method 300 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of the method 300. In other examples, different components of an example device or system that implements the method 300 may perform functions at substantially the same time or in a specific sequence.

[0085] In step 302, the method 300 includes determining a set of voltages to be applied to each pixel of the SLMps to achieve the desired change in polarisation between the input light to pixels of the SLMp a and the light output from corresponding pixels of SLMp c. The phase retardances applied by the sequential pixels of SLMp a, SLMp b and SLMp c of the arbitrary optical elliptical retarder may be controlled to achieve the desired total rotation of the polarisation of the input light around the Poincare sphere, by a first rotation around the SI axis by SLMp a, a second rotation around the S2 axis by SLMp b, and a third rotation around the SI axis by SLMp c, and controlling the SLMps to apply the determined respective voltages to the pixels at (X, Y).

[0086] This follows from the orientations ( ^,) of the fast axes of the SLMp a, SLMp b and SLMp c being, respectively, horizontal, diagonal, and horizontal, corresponding to the uniformed Stokes vectors:

[0087] The cascase of these three SLMs can mimic a phase-insensitive arbitrary optical elliptical retarder at the pixel level, with any desired fast (and slow) axis orientation and retardance value resulting from the synthetic pixels of the combination of the three SLMs. By introducing a deformable mirror or another phase modulating optical element 122 into the cascade, full control of the absolute phase of the light field can be achieved in the spatial domain.

[0088] The state of polarisation of the input light 105 at the pixel level is only affected by the three SLMp a, SLMp b and SLMp c retarders. Each of them rotates the Poincare sphere around its fast axis by an angle equal to its retardance value defined by the applied voltage at the pixel level.

[0089] It is then sufficient to decompose an arbitrary rotation (such as a desired change in polarisation, or a change in polarisation needed to obtain a desired output polarisation state) into a sequence of three about a fixed axis orientation, according to the rotations around the Stokes vectors of the alignment of the fast axes of the different SLMs.

[0090] To understand why it is always possible to achieve a mapping from any input state of polarisaation to any desired output state of polarisation, let us consider an arbitrary rotation &~ where SO(3) js group of all 3D rotations of the Stokes vector of the state of polarisation of the input light 105 about the origin of three-dimensional Euclidean represented by an orthogonal 3 x 3 matrix with R = 1

[0091] Let us denote the unit vectors in the x, y, z directions by x,y,z e g3 , and rotations about them by R, £ SO (3)- Suppose that J is rotated to the point $ R£

[0092] It is always possible to transform from one point on the unit-sphere to another one by carrying out a sequence of two rotations with orthogonal axes. Hence, for any R there exist $2, in the interval L'17- such that: R^2)R.x(#i)p - X [R^R^OR]X - R x = x

[0093] Where R / g SO (3) represents a rotation. However, any R' satisfying Rx = x must describe a rotation around xby an angle in the range <As A Therefore it holds that: R^^R^QR - ra» o R r^OMR^M)

[0094] This proves that any R can be expressed as a sequence of rotations about the x — y — x directions with angles between or equivalently over any interval of length 271. This can be applied by the polarisation controller 114 to deduce a decomposition of the desired rotation into a sequence of rotations around the SI, S2, and SI axes of the Poincare sphere by the SLMs of the arbitrary optical elliptical retarder 110, allowing the determination of the three voltage values to be applied to the consecutive pixels. This applies to each pixel across the field in (x, y), allowing polarisation textures to be generated.

[0095] To explicitly compute such a decomposition, (not necessarily unique), quaternions can be used to find expressions for the system’s overall axis and retardance, as well as the retardance values of the cascaded SLMs. Quaternions are mathematical structures extending complex numbers to four dimensions, and the unit quaternions, as a double cover of $0(3), are often used to represent rotations in three-dimensions. A rotation by angle 0 around the axis can be defined by the unit vector (a pure unit quaternion): u (0, ux, uy, uz) Uzi + Uyj -r uzk and can be represented by conjugation through a unit quaternion q: q = cos (uxi + Uyj -+- uzk)

[0096] Consider a series of rotations about x by 91, y by 02, and x by 93 (such transformations can be achieved by using the SLM retarders with corresponding axis orientations and retardance values). Using quaternions, the resulting rotation can be obtained from the product: qiqaqs cos --- V 2 + sin + sin

[0097] Multiplying out and equating with the unit quaternion corresponding to the rotation induced by an elliptical retarder with fast axis 8 = + $2j + S^k and retardance , we get: / 01+03 cos I .................... X 2 sin () cos (= Si sin()i sml v 1 cosl Jj “ 63 sml p smi I sml jk ” 5g sml )k where S is the normalised Stokes vector of the retarder’s eigen-axis. For 0 <02 <2,1 an(] 0-2 / I € Z (which corresponds to a horizontally oriented fast axis, retardance value of u). We then have: r a Os \ (Os = arctan 2 cos — , Si sin I — \ 2 / \ 2 +- n7r, n &Z S3 sin + m27r, m G Z

[0098] From these equations we can recover two distinct sets of solutions for 91 and 93 both in the range [0, 2k] . A closed form solution of 92 (angle of rotation about the y axis Y) is then given by: S2 sin + Sin ---:1--- + S3 sin wh$h uiyp p^e^olution in the interval [0, 2%] for each set of 01,2 (only differing in sign). For we can assign — 0S 02-O 03 =0

[0099] These expressions deduce values 01,2,3 for an arbitrary rotation of the Poincare sphere, corresponding to the action of how three SLMs should behave with respect to any phase-insensitive elliptical retarder. Thus using the above method, in step 302, the polarisation controller 114 may determine the voltages to be applied to each pixel to achieve a desired change in polarisation by three rotations of the Poincare sphere.

[0100] Once the polarisation controller 114 has determined the voltages to be applied, in step 304, the polarisation controller 114 then controls the SLMps to apply the determined respective voltages to the pixels at the locations in (X, Y) across the wavefront.

[0101] Thus the fast axis of pixels of the SLMp a 112a and SLMp c 112c for the arbitrary optical elliptical retarder 110 represent a horizontal axis (x axis X) for the arbitrary optical elliptical retarder 110, each causing rotation of the polarisation of light input thereto around the axis of the Poincare sphere defined by the first Stokes parameter SI. The pixels of the SLMp b H2b each cause rotation of the polarisation of light input thereto around the axis of the Poincare sphere defined by the second Stokes parameter S2. Each pixel of the SLMs of the arbitrary optical elliptical retarder 110 may be individually controllable to adjust the phase retardance value applied to the light passing through such that its polarisation can be rotated around the Poincare sphere by an angle within the full 2k radian range. In this way, the phase retardances applied by the sequential pixels of SLMp a 112a, SLMp b 112b and SLMp c 112c of the arbitrary optical elliptical retarder 110 may be controllable to achieve an arbitrary desired total rotation of the polarisation of the input light around the Poincare sphere, by a first rotation around the SI axis by SLMp a 112a, a second rotation around the S2 axis by SLMp b 112b, and a third rotation around the SI axis by SLMp c 112c. In this way, any desired change in polarisation from an arbitrary input light polarisation to an arbitrary output light polarisation, can be achieved.

[0102] An example of this change in polarisation achievable by a synthetic pixel of the arbitrary optical elliptical retarder 110 can be seen in FIG. 4.

[0103] FIG. 4 shows a schematic illustration in relation to a Poincare sphere of a series of rotations of the Stokes vector achieved by a suitably configured synthetic pixel of the arbitrary optical elliptical retarder of FIG. 2 to achieve a desired change in polarisation.

[0104] Input light 105 to a pixel of the first phase controlling birefringent spatial light modulator SLMp a 112a has an initial polarisation state Si indicated by the dot marking its Stokes vector. Si is close to being horizontally polarised, but it also has components diagonal and right hand circular polarisation. It is desired that the synthetic pixel rotates the polsarisation state of the pixel in the output light 115 to have an output polarisation state So indicated by the dot marking its Stokes vector, to have more right hand circular polarisation. As a result, the SLMp a 112a is configured by the polarisation controller 114 to apply a retardance causing a rotation of the polarisation state from the Si around the Si Stokes vector as indicated by the rotation RI. The SLMp b 112b is configured by the polarisation controller 114 to apply a retardance causing a further rotation of the polarisation state around the S2 Stokes vector as indicated by the rotation R2. Finally, the SLMp c 112c is configured by the polarisation controller 114 to apply a retardance causing a further rotation of the polarisation state around the Si Stokes vector as indicated by the rotation R3, causing the output light 115 at that synthetic pixel to have an output polarisation state So.

[0105] Another example of this change in polarisation achievable by a synthetic pixel of the arbitrary optical elliptical retarder 110 can be seen in FIG. 5.

[0106] FIG. 5 shows a schematic illustration in relation to a Poincare sphere of a second series of rotations of the Stokes vector achieved by a suitably configured synthetic pixel of the arbitrary optical elliptical retarder of FIG. 2 to achieve a desired change in polarisation;

[0107] Input light 105 to a pixel of the first phase controlling birefringent spatial light modulator SLMp a 112a has an initial polarisation state Si indicated by the dot marking its Stokes vector. In FIG. 5, Si is completely horizontally polarised. It is desired that the synthetic pixel rotates the polsarisation state of the pixel in the output light 115 to to have an output polarisation state So indicated by the dot marking its Stokes vector, again to have more right hand circular polarisation. As the fast axis of the SLMp a 112a is aligned horizontally, it can have no effect on the phase of the input light 105 at this pixel, because rotation of the polarisation state around the Si Stokes vector does not have any effect to rotate the input polarisation state Si around the Poincare sphere, and so no rotation RI is shown. The SLMp b 112b is configured by the polarisation controller 114 to apply a retardance causing a rotation of the input polarisation state Si around the S2 Stokes vector as indicated by the rotation R2, which causes the state of polarisation to have more diagonal polarisation. Finally, the SLMp c 112c is configured by the polarisation controller 114 to apply a retardance causing a further rotation of the polarisation state around the Si Stokes vector as indicated by the rotation R3, causing the output light 115 at that synthetic pixel to have an output polarisation state So that had higher right hand circular polarisation.

[0108] Thus this has demonstrated that the arrangement of the three SLMs of the phaseinsensitive arbitrary optical elliptical retarder 110 allows a pixelwise control of arbitrary to arbitrary states of polarisation.

[0109] FIG. 6 illustrates the changes to the polarisation ellipse and phase of the light passing through a synthetic pixel of the arbitrary optical elliptical retarder and the phase modulator of the universal optical modulator shown in FIG. 1. As can be seen, the each pixel of the first SLM 112a, second SLM 112b, and third SLM 112c of the arbitrary optical elliptical retarder 110, combines with a pixel of the phase modulating optical element 122 (which may be a pixel if the phase modulating optical element 122 is an SLM, or a micromirror or a segment of the deformable mirror) to provide a synthetic pixel 122s (one of which is shown in the detailed view in the circle). The polarisation of output light 125 from each synthetic pixel 122s can be described as shown by its axis shape a (i.e. defined by its minor and major axis ai, a?), its axis orientation p, the retardance value applied y, each controlled by the SLMs of the arbitrary optical elliptical retarder 110, and the phase 8, controlled by the phase modulating optical element 122.

[0110] FIG. 7 illustrates this control of the Stokes vector and phase achievable using different numbers of SLMs to make up the arbitrary optical elliptical retarder 110 and the phase modulator 120.

[0111] As can be seen, in the top row of FIG. 7, where one SLM is provided, only the phase 6 and the applied phase retardance value y of the output light is arbitrarily controllable (from an arbitrary input phase to an arbitrary output phase).

[0112] In the middle row of FIG. 7, where three SLMs are provided, configured as above to provide an arbitrary optical elliptical retarder 110, the axis shape a and axis orientation p of the polarisation ellipse are fully arbitrarily controllable, as well as the phase retardance value applied y. Meaning that any arbitrary polarisation state of input light can be transformed to any arbitrary polarisation state of output light. In this way, the arbitrary optical elliptical retarder 110 may form structured matter that may be dynamically configured, and useable to generate structured light with arbitrarily desired polarisation textures. Here, the arbitrary optical elliptical retarder 110 is a phase insensitive arbitrary optical elliptical retarder. For example, as will be explained below, the arbitrary optical elliptical retarder 110 may be usable to encode structured matter that can be used to generate optical skyrmionic topological quasiparticles.

[0113] In the bottom row of FIG. 7, where four devices are provided, configured as above to provide an arbitrary optical elliptical retarder 110 and a phase modulator 120, the axis shape a and axis orientation 0 of the polarisation ellipse are fully arbitrarily controllable, as well as the phase retardance value applied y and the phase 5.

[0114] As can be seen in Fig 6, the collation of synthetic pixels 122s across the field of the cascade of optical elements provides for a form of structured matter usable for a range of applications, and usable to generate output light having arbitrary polarisation and phase textures and values.

[0115] Rewritable digital technology, in the form of the programmable optical elements such as SLMs, is thus an enabling tool for structured light. The number of devices enable different functionality of these synthetic pixels and can be seen to be a synthetic rewritable form of structured matter itself.

[0116] This synthetic structured matter can be harnessed for novel topological control of light and matter, as an information carrier, structured light generator, as well as a beam analyser (in a polarimeter, for instance), and corrector (in an adaptive optics system).

[0117] As will be described in more detail below, the universal optical modulator, and in particular the arbitrary optical elliptical retarder is a powerful reconfigurable device usable to form novel liquid crystal based synthetic compound skyrmions, harnessing the anisotropic axis shape and orientation that the light sees, as an object-wise analogy to a Stokes vector field optical skyrmion. The universal optical modulator is also capable of generating different tuneable complex topologies such as skyrmion lattices and skyrmion bags. The universal optical modulator can then be used as a beam generator to create complex structured light, including optical skyrmions in high-order skyrmionic or bimeroniumic formats. As will be seen, these dynamical states of light demonstrate topological protection through both isotropic and anisotropic media.

[0118] The universal optical modulator has other novel applications, for example finding utility in a polarimeter, wherein the arbitrary optical elliptical retarder is used to provide a Full Poincare Beam generator reconfigurable to provide a tuned sensing pattern optimised for the sample being analysed. In this way, in a beam analyser, the arbitrary optical elliptical retarder is usable to analyse all polarisation states simultaneously through providing complete analysing channels, giving high sensitivity by exploiting its tuneability for enhancement in the flexibility of the detection through novel polar and cartesian optimization, both highly sample dependent. A polarimeter in which the universal optical modulator disclosed herein can be used to provide a programmable and thus optimisable Full Poincare Beam generator is described, for example, in International Patent Application Publication no. WO2022136835.

[0119] Further, the universal optical modulator may also be used in an adaptive optics apparatus, wherein the arbitrary optical elliptical retarder is used to correct the polarisation state of input light. In this way, in an adaptive optics apparatus, the arbitrary optical elliptical retarder enables the dynamic correction of spatially varying arbitrary retardance aberration in both sensor-based and sensorless forms through a new object-wise adaptive optics regime, harnessing the ability to construct object-wise rather than light-wise retardance aberration modes. An adaptive optics system in which the universal optical modulator disclosed herein can be used to correct the polarisation state of input light in a sensor-based or sensorless mode of operation is described, for example, in “Vectorial Adaptive Optics”, Chao He, Jacopo Antonello, Martin J. Booth, 6 Oct 2021, arXiv:2110.02606, https: / / arxiv.org / ftp / arxiv / papers / 2110 / 2110.02606.pdf.

[0120] The use of the arbitrary optical elliptical retarder 110, or any arbitrary optical elliptical retarder capable of encoding arbitrary polarisation textures, in the generation of optical skyrmionic topological quasiparticles will now be described in more detail.

[0121] Referring again to FIG. 2, here the arbitrary optical elliptical retarder 110 of the universal optical modulator 100 is controlled by the polarisation controller configured to operate as a quasiparticle encoding controller 114.

[0122] Here, the quasiparticle encoding controller 114 uses the ability of the arbitrary optical elliptical retarder 110 to encode arbitrary polarisation textures to into the SLMs that are usable to generate optical skyrmionic topological quasiparticles. However, it is to be understood that the apparatus for generating optical skyrmionic topological quasiparticles, disclosed herein may include any suitable programmable arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation.

[0123] The quasiparticle encoding controller 114 coupled to the SLMs of the arbitrary optical elliptical retarder 110 is configured to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the determination and application of the voltages being in accordance with the method 800 shown in FIG. 8.

[0124] FIG. 8 shows a method of generating optical skyrmionic topological quasiparticles using the arbitrary optical elliptical retarder of FIG. 2, in accordance with aspects of the invention.

[0125] Although the example method 800 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of the method 800. In other examples, different components of an example device or system that implements the method 800 may perform functions at substantially the same time or in a specific sequence, or the steps may be performed continuously so that the polarisation texture applied is dynamically updated.

[0126] The method 800 includes, at step 802, determining pixelwise voltages to be applied to the SLMs so that the output light field has a topologically stable skyrmionic Stokes vector texture across the surface (x, y).

[0127] In more detail, the the voltages to be applied to each pixel of the SLMs of the arbitrary optical elliptical retarder 110 are determined by the quasiparticle encoding controller 114 to achieve, for a pixel at a location (X, Y), a desired change in polarisation between the input light to pixels of the first SLM and the light output from corresponding pixels of the last SLM so that the output light field has a topologically stable skyrmionic Stokes vector texture across the surface (X, Y) having a skyrmion number N of a desired skyrmion defined by the relation where o is the boundary in (X, Y) of the region within which the skyrmion is confined, and wherein S is the Stokes vector applied by the arbitrary retarder at a pixel at (X, Y), such that the polarisation texture in S wraps around the Poincare sphere N times within the boundary.

[0128] Once the voltages for encoding the optical skyrmionic topological quasiparticles in the arbitrary optical elliptical retarder have been determined, the method 800 includes in step 804 applying the determined pixelwise voltages to the SLMs. In this way the quasiparticle encoding controller 114 can configure the arbitrary optical elliptical retarder 110 to encode skyrmionic textures as structured matter. Due to their properties of topological preservation, and defined and detectable structures, the encoding of optical skyrmionic topological quasiparticles in this way can provide an effective information carrier. In arbitrary optical elliptical retarders where the configuration is maintained absent applied voltage, this would represent a novel and high density data storage. As the information can be recovered, read and transmitted using illumination by light beams, the arbitrary optical elliptical retarders encoding these optical skyrmionic topological quasiparticles can be used for information readout and high information density communication.

[0129] Thus, in some embodiments, the method 800 may further include illuminating the arbitrary optical elliptical retarder 110 with light from a light source to generate skyrmions at step 806.

[0130] In embodiments, once the optical skyrmionic topological quasiparticles are encoded in the arbitrary optical elliptical retarder as structured matter, the method may further include illuminating the arbitrary optical elliptical retarder with light from a light source to generate in the light output from the retarder skyrmions based on the skyrmionic Stokes vector texture encoded in the SLMs of the arbitrary optical elliptical retarder.

[0131] This is shown in more detail in FIG. 9, which illustrates an example configuration of the arbitrary optical elliptical retarder 110 of FIG. 2 to provide a polarisation texture encoding an optical skyrmionic topological quasiparticle as structured matter 902 (illustrating the elliptical polarisation texture encoded by the synthetic pixels of the arbitrary optical elliptical retarder 110). As can be seen, when illuminated by input light 105 generated by light source 101 (which may have any arbitrary known Stokes vector polarisation field and phase), the output light 115 includes an optical skyrmion 904. For example the input light 105 beam may have a uniform circular polarisation and a flat phase for simplicity. The desired change in polarisation in the Stokes vector field is then chosen to be a skyrmion, in the example shown in FIG. 9 is a low order skyrmion, which may be a Neel type or Bloch type depending on the phase, or an anti-skyrmion or a meron (a half skyrmion) and encoded into the structured matter of the arbitrary optical elliptical retarder 110.

[0132] The lower half of the resulting optical skyrmion 904 is shown in FIG. 9 by the elliptical axis polarisation texture corresponding to the synthetic pixels, and in the upper half, the surface of the Stokes vector polarisation field for a skyrmion is shown, showing a clear mapping and relation between the two.

[0133] To detect and decode the optical skyrmions 904, a detector 103 may be used. The detector 103 (and illumination 105) may include imaging Mueller matrix polarimeter usable to decompose the elliptical axis polarisation distributions from the obtained images. In this way, information encoded in the optical skyrmionic topological quasiparticles in the structured matter can be read and decoded. The apparatus for generating optical skyrmionic topological quasiparticles may also include further may include one or more optical elements for guiding or storing the optical skyrmionic topological quasiparticles. For example, the optical skyrmions may be stored in a holographic storage device, or another suitable storage technology. The skyrmions may also be used in data communication, such as free space optical communication, and one or more optical elements may be used to guide the skyrmions to provide a communications channel.

[0134] The elliptical retarder array resembles a cascaded linear birefringent array, hence the complex skyrmions appear from the beam’s point of view, as a synthetic structure.

[0135] Skyrmions have received considerable attention as an intriguing topologically protected information carrier. To realise the skyrmions, the arbitrary optical elliptical retarder 110 is controlled in steps 802 and 804 by voltages through a determined mathematical relationship described in more detail below. In the example, the phase modulator 120 is also used and controlled, such that y and 8 as constant values for simplicity (3a: / 2 and 0). This enables the universal optical modulator 100 to be used to write pre-determined information - e.g., complex skyrmions - into the axis field (x, y) of the matter.

[0136] The use of an arbitrary optical elliptical retarder in generating optical skyrmionic topological quasiparticles will now be explained in more detail. In paraxial beams, mapping an appropriately determined spatially varying normalised Stokes vector of the transverse electric field of light passing through the arbitrary optical elliptical retarder, onto the topologically nontrivial Poincare sphere, can form baby-Skyrmions. Skyrmions are topologically protected 2-dimensional quasiparticles. The topological number N of a Skyrme field V) is defined as: which corresponds to the degree of the map y) when extended via continuity to the sphere. Certain technical considerations arise regarding when the extension is possible, but these can be sidestepped by only considering fields that approach a constant value on their boundary, as is the case for Bloch and Neel type skyrmions. The topological protection of the field is then a result of two important facts, namely (1) the degree of a continuous function is always an integer for stable skyrmions (albeit for stable merons, a half integer may be possible) and (2) it is invariant under homotopy.

[0137] In the use of the arbitrary optical elliptical retarder, the axis shapes a and orientations P can be harnessed across the field to form novel optical skyrmions. The cascaded devices of the SLMs can form arbitrary retarder with Jones matrices of the form: cos a — sin ae td sinaeid cos a e'v: (¢, / 2 q r cos a sjn ae 0 [_sinae^ cos a which features eigenvector v) that is equivalent to its fast axis condition, and can be described by a Jones vector: cos ct sin aert

[0138] An elliptical retarder array can therefore possess a similar topological property encoded in its spatially varying fast axes as the above-mentioned paraxial beam. Like an electric field, corresponds to the polarisation ellipse with a well-defined axis orientation and ellipticity and can be characterized using the Stokes vector s'(;r, y) QI Si cos 2a sin 2a cos 5 sin 2a sin 5 cos xcos cos x sin V' sin x

[0139] which can represent a skyrmion field in the same way as a paraxial beam. These skyrmion fields arising from the arbitrary optical elliptical retarder, which are fixed in time, differ qualitatively from the statistical nature of polarisation fields in paraxial beams. However, this difference in physical interpretation is not an obstruction to the topological protection of the field, which only depends on the topological nature of the target space.

[0140] Thus the axes and orientation of the polarisation ellipses of the synthetic pixels of arbitrary retarders act as a new basis of generating skyrmions and other optical skyrmionic topological quasiparticles.

[0141] FIG. 10 illustrates the mapping of the skyrmionic polarisation texture of the optical skyrmion of FIG. 9 onto the Poincare sphere.

[0142] In the top of FIG. 10, the demonstration of one-to-one mapping between a half skyrmionic field and a half-polarisation axes and orientation based skyrmionic field is shown. In the bottom of FIG. 10, it can be seen how these maps to fold exactly once around the Poincare sphere, meaning that the Stokes vector field generated by the arbitrary optical elliptical retarder provides a skyrmion with topological protection.

[0143] Although FIG. 9 and FIG. 10 show the use of the arbitrary optical elliptical retarder to generate a simple single skyrmion of low order, in which the Stokes vector field within the bounded region of the space for confining the skyrmion wraps around the Poincare sphere exactly once (i.e. N= 1), the arbitrary optical elliptical retarder is usable to generate higher order skyrmions, or more exotic textures, in lattices or bags. These all represent stable skyrmionic fields in accordance with the foregoing disclosure.

[0144] FIG. 11 illustrates the use of different configurations of the structured matter of the synthetic pixels of the arbitrary optical elliptical retarder to generate higher order and more exotic optical skyrmionic topological quasiparticles. That is, the arbitrary optical elliptical retarder 110 may be configured to generate an expected output field to be either a high-order skyrmionic beam (where N >1), a skyrmionium (a coupled state connecting two skyrmions with opposite polarities and resulting into skyrmion number of e.g. N = 1 - 1 =0), a bimeron (where the initial point of the unwrapping is changed away from the pole or the Poincare sphere to the equatom, the bimeron has the texture composed by two half-skyrmions (merons) with opposite polarities) or a bimeroniumic beam (similar to a skyrmionium, a bimeronium is a coupled state connecting two bimerons).

[0145] As can be seen in FIG. 11, the arbitrary optical elliptical retarder 110 is tunable to generate these arbitrary desired, more exotic, optical skyrmionic topological quasiparticles.

[0146] FIG. 12 illustrates the generation of bound skyrmions lattice and skyrmion bags by the structured matter of the synthetic pixels of the arbitrary optical elliptical retarder. In the examples shown at the top of Fig. 12, the bounded region confining the skyrmion is set to be limited, causing the arbitrary optical elliptical retarder 110 to encode Stokes vector polarisation textures that generate synthetic skyrmion lattices, or skyrmionium lattices of single confined skyrmions. In the examples shown at the bottom of FIG. 12, nested skyrmions are used to generate skyrmion bags of any topoligical degress, causing the arbitrary optical elliptical retarder 110 to encode Stokes vector polarisation textures that generate synthetic skyrmion bags, or high order skyrmion bags.

[0147] In this way, the arbitrary optical elliptical retarder 110 is able to encode a large variety of optical skyrmionic topological quasiparticles, each preserving the information they may be used to encode in a topologically stable manner. The encoded information may be recovered using imaging Mueller matrix polarimetry to detect and determine the parameters of the skyrmions generated. The experiment has shown the optical skyrmionic topological quasiparticles generated by the arbitrary optical elliptical retarder 110 to be topologically protected even when passed through isotropic (uniform water solution sandwiched between two thin glass slides) and anisotropic (unknown waveplate) random perturbations. Thus the structured matter and structured light provide a valuable mechanism for dense information storage and communication using skyrmions. The formation of virtually pixelated retarders enables beam manipulation with unprecedented precision and flexibility, and more broadly circumvent the restriction of needing to pre-determine the input SoP and phase. Note theoretically, any complex topology can be realized via the structured matter using the arbitrary optical elliptical retarder 110 through the same procedure.

[0148] Turning now to the other functional modulator units that may be included in the universal optical modulator 100, FIG. 13 shows a more detailed schematic illustration of the intensity modulator 130 of the universal optical modulator 100 shown in FIG. 1.

[0149] Where provided, the intensity modulator 130 may be aligned in the cascade of optical elements, arranged to receive output light 125. The intensity modulator 130 may include a pair of linear polarisers including a linear polariser 132a and a linear polariser 132c, and an intensity controlling birefringent spatial light modulator, SLMi, 132b, arranged between the pair of linear polarisers.

[0150] The SLMi 132b has a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, thereby adjusting the pupil intensity value of the output light 135 transmitted through the pixel and out of the second linear polariser 132c relative to the input light 125 incident on the first linear polariser 132a.

[0151] The operation of the intensity modulator 130 will now be described in more detail.

[0152] By putting a pair of linear polarisers before and after the SLMi 132b, pixelated control of the intensity value can be quantitatively achieved by controlling the SLM condition. Note theoretically other low functionality devices may also serve this purpose, such as pixelated attenuator arrays.

[0153] Suppose that the wave equation of the incident beam after the incident vertical linear polariser is written as: Ej — Ey cos (wt) y

[0154] Let An be the difference between the extraordinary (ne) and ordinary (no) refractive indices of the liquid crystal (LC) of the SLMi, and the average value of them be nm. Thus: An = ne — ng _ — 2 ne ~ nm 4-An. no = nm -

[0155] The projection of incident light along and perpendicular to the direction of the director after the LC layer is expressed as: ~ Ey cos ^x) cos ¢¢¢: / ..... E — Ey sin (x \ cos (wt — d where / is the angle between the LC director and the angle of the first linear polariser 132a.

[0156] If the angle of the second linear polariser 132c is parallel to the angle of the first linear polariser 132a, then the projection of the parallel field and perpendicular field onto second linear polariser 132c are represented as: ~ E^cos^xj cos^xj cos^wf — ^‘-dj ~ Ey cos2fx) cos(wt -- d -- d\ y / \ A Ay and E: p sin 1 x) sin[x) cos (wi — d = EySin2(x) cosl wi -- ^2&.d + d

[0157] Thus the output electric field is expressed as: Eo - (E^. + E±p)± t, r 2 / \ / , — by cos I x I cos I wt--— 7rAn A . 2 / \ / 27rnm ?rAn Al —-—d j + sm I x 1 cos I wt---—a H---—d | x

[0158] Based on the trigonometric functions, the electric field after the second linear polariser 132c can be simplified as: [ / 2imm A / irAn A ( \ ( Ey cos I wt —.......--.......d I cost —-—d I -j- cos I 2x | sml wt 27m

[0159] When the angle between the polariser and LC director % is exactly 45°, then the whole expression can be simplified to: Eo = Ey cos cos I wt \ A —-—d lx

[0160] So the transmission rate under this situation can be expressed by the ratio between the two intensities — as li — cos2 TrAnd A when x = 45° 1 / 27rAnd — COS I --------- 2 \ A when x = 45

[0161] In this way, the universal optical modulator 100, incorporating the intensity modulator 130, may also arbitrarily control the intensity of the output light in a structured manner across the pixels of the SLMs.

[0162] FIG. 14 shows a more detailed schematic illustration of the degree of polarisation modulator 140 of the universal optical modulator 100 shown in FIG. 1.

[0163] Where provided, the degree of polarisation modulator 140 may be aligned in the cascade of optical elements, arranged to receive output light 135. The degree of polarisation modulator 140 may include a sequence of two or more degree of polarisation controlling birefringent spatial light modulators, SIAIdopa^^ 142a...l42e.... That is the degree of polarisation modulator 140 may include two, three, four or more than four polarisation controlling birefringent spatial light modulators, SLMdop. The degree of polarisation controlling birefringent spatial light modulators, SLMdop a...dop n 142a...142e each have a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel.

[0164] A degree of polarisation controller 144 is coupled to each of the degree of polarisation controlling birefringent spatial light modulators, SLMdop a...dop n 142a... 142e. Th degree of polarisation controller 144 is configured to control a degree of polarisation of light transmitted through pixels of the SLMdop a...dop n cascade into output light 145 by controlling the voltage of the pixels of two or more of the SLMdops in the degree of polarisation modulator 140 to consecutively apply phase variation patterns with different retardance values to adjust the phase retardation of the light passing through the pixel.

[0165] The operation of the degree of polarisation modulator 140 will now be described in more detail.

[0166] Depolarisation represents a reduction in the degree of polarisation, DoP, in the output light 145 from the degree of polarisation modulator 140 compared to the input light. Depolarisation is achieved by the degree of polarisation modulator 140 using incoherent spatiotemporal coupling of polarised light into unpolarised light to achieve pixelated control of the depolarisation patterns by applying time dependent retardance patterns. The strategy for realizing pixelated control of DoP is to use the cascaded SLMdop a...dop n devices to generate pixelated time-varying retardance patterns, resulting in a temporally varying State of Polarisation, SoP, in each pixel. This will introduce a depolarisation effect if the temporal variation is faster than the integration time of the detector 103. A generated temporally varying SoP can be described as an incoherent superposition of n Stokes vectors that represent n fully polarised SoPs. The effective Stokes vector of the temporally varying SoP can be expressed by averaging the n SoPs within a time period 7: ~ + t2S2 + • • • + tnSn] where ^1+^2 +----'rtn~T

[0167] To achieve pixelated depolarisation modulation, w phase patterns with different retardance values are consecutively applied to the synthetic matter during the integration time of the detector. For a homogeneous input SoP, each retardance pattern can be described by a Mueller matrix Mn of the matter: Si (x5 y) = M1 (x, y)S-m(x, y) Sn(x,y) = Mn(x,y)Sm(x,y) where (x, j) represents the spatial coordinate of the matter. The device we use in this section is the cascade of SLMdops, whose Mueller matrix can be expressed as: M = M2 • • • MBMA

[0168] For a combination of 3 SLMs with their fast axis arranged in a sequence of 0°, 45° , and 0°, the corresponding retardance profile 0a, 0b, 0c will lead to the Mueller matrix being in the form of: '10 0 0 0 cos 0b 0 — sin 63 M — 0 sin(0A + 0c) sin 0b cos(0a + 0c) sin(0A + 0c) cos0b _0 cos(0a + 0c) sin 0b — sin(0A + 0c) cos(0a + 0c) cos0b_

[0169] The Mueller matrix of depolarisation modulation effects during the integration period T can be expressed as: / \ 1 {Mlx,y\} = — [hM^x^y) + t2M2(x,y) 4-----F tnMn(x, y)]

[0170] where M represents the different combinations of 0A, 0b, 0c.

[0171] The de minimis arrangement for modulating the DoP is to have two SLMdops and to have, so in this case the number of retardance patterns n = 2 and temporal variation ti = t2 = T / 2 . And also we first assume that only SLMdop b 142b will change its retardance in this demonstration. Hence the Mueller matrix of the depolarisation modulation effect during integration period T can be described as: {M (x, y\} = 1 [Mi (x, y) + M2(x, ^)] \ / M where Ml has the retardance combination of and M2 has the retardance combination of 0A»$B2; ^C.

[0172] For an arbitrarily illuminated fully polarised SoP __ , the effective output Stokes vector can be obtained: 2S0 («WBf T c<Wb,)S; - (sin©B +sin0B.,)S3 sin(^A + ^c)[(sha<^B] + sin + (cos^B; + + 2cos($a + ^c)^2 _cos(^a + ^c)[(sin^Bi + sin + (cos^Bi + cos ^)^31 — 2sin(^A +

[0173] Hence the DoP is expressed as: DoP If S2\'2 , 9 ( - < / b2 \ ., / < / Bj - < / b, \ V "c~ sm --”75---- ) + COS ----o---- ) y y z>0 y y 2 y \ 2 y

[0174] For a uniform input polarisation field (say S2 equals to 0 across all the pixels), any pixelated output DoP level can be achieved by manipulating the retardance patterns. Hence, arbitrary DoPs can be manipulated in a pixelated manner via synthetic matter.

[0175] In this way, the universal optical modulator 100 including the degree of polarisation modulator 140 may also arbitrarily control the degree of polarisation of the output light in a structured manner across the pixels of the SLMdops. In the example shown, the degree of polarisation modulator 140 is separate from the arbitrary optical elliptical retarder 110. However, in some embodiments, the three SLMps of the arbitrary optical elliptical retarder 110 may also be used to provide the SLMdops of the degree of polarisation modulator 140, allowing simultaneous arbitrary modulation of the polarisation and the degree of polarisation.

[0176] FIG. 15 shows a more detailed schematic illustration of the diattenuation modulator 150 of the universal optical modulator 100 shown in FIG. 1.

[0177] Where provided, the diattenuation modulator 150 may be aligned in the cascade of optical elements, arranged to receive output light 145. The diattenuation modulator 150 includes a first arbitrary optical elliptical retarder 152a (including three SLMps configured as described above in relation to FIG. 2) a fixed linear polariser 152b and a second arbitrary optical elliptical retarder 152c (also including three SLMps configured as described above in relation to FIG. 2).

[0178] The diattenuation modulator 150 also includes a diattenuation controller 154 coupled to the SLMs of the first and second arbitrary optical elliptical retarders of the diattenuation modulator 150 to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel.

[0179] The voltages applied to each pixel of the SLMs are determined by the diattenuation controller 154 to achieve a desired change in diattenuation between the output light 155 and the light input to the pixels of diattenuation modulator 150.

[0180] The operation of the diattenuation modulator 150 will now be described in more detail.

[0181] A model of the cascade of optical elements making up the diattenuation modulator 150 (assuming a perfect polariser) can be expressed as: AD a ~ ARi • P • AR, where AD a is the Mueller matrix of the arbitrary diattenuator that we want to achieve, AR5 and AR2 are the Mueller matrices of the arbitrary retarders before and after a certain diattenuator and P is the Mueller matrix of the fixed polariser with an arbitrary axis.

[0182] The Jones matrix expression of the arbitrary retarder is: •I AR = cos a sin ae*'5 sinae^' cos a J 0 cos a — sin ae^ sin ae ~ COSO

[0183] And its Mueller matrix can be expressed as: T 0 0 s| (1 -- cos ■+- cos 0 0 8183(1 - cos¢) — S3 sinci 0 8183(1 - cos ¢) + «2 sin 0 8183(1 -- cos ci) 4 S3 sin 0 82 (1 — cos 0) 4- cos 0 8283(1 - cosd) — si sin<p 0 s 1 s 3 (1 — cos 0) ■— s 2 sin 0 8383(1 — COS0) + Si sind 8|(1 - cos 0) + cos<$ ■ 1 0 1 0T mJ where 1 cos 2a sin 2a cos 8 sin 2a sin 3_ is the Stokes vector form of the eigenvector of the arbitrary retarder and mR is the orthogonal rotation matrix.

[0184] From the Jones matrix expression, a polariser with a fixed axis can be expressed as: J AD - cos a .sin ae^ — sin ae cos a cos 7 0 1 [" cos a sin 7J [—sinae^ sin ae cos a and its Mueller matrix can be expressed as: where 27-+-(1- sin 27).« | (1 — sin 27)51^2 (1 — sin 27)3333 (1 — sin 27)^1^2 sin 27 + (1 - sin 27 (1 — sin 27)5333 (1 — sin 27)5353 (1 — sin 27)5733 sin 27 + (1 — sin 27)53 — sin 2713x3 4- (1 ■■■■ sin 27)8 • S1 — cos 27S with the definition of 1 cos 2a sin 2a cos 8 sin 2a sin 8_

[0185] So the final cascaded structure for the diattenuation modulator 150 can be expressed as: AR, P AR2 i r i 2 Or ° 1 I"1 IP dti r i o mDJ |oT ms. 1 I" 1 DTmR, 2 [mR1D mR1mpmR,

[0186] To form an arbitrary diattenuator using this cascaded structure, the following equations should hold: mR,D = Da = mpA

[0187] Considering that mRl and mR2 are rotation matrices, we find that: mR, • mR, I

[0188] By expanding m7?imPmR3 “ mDA and assuming that distinction ratio y is the same for the fixed polariser and resulting arbitrary diattenuator, we obtain: mR,m / >m.R, = ms, (sin 27I3.. 3 + (1 — sin 27)8 • S?)m^ — sin27ms,Isx3¾ + (1 -- sin27)ms1S • SJms, = sin27l3x3 + -~|^mRp • DrmR, = sin 271.3x3 +(1- sin 27) SA ■ Sj = mpA

[0189] Thus the above equations do hold and this proves that an arbitrary diattenuator (with infinite extinction ratio) can be achieved by cascading several arbirary retarders and a fixed polariser.

[0190] In this way, the universal optical modulator 100 including a diattenuation modulator 150 may also arbitrarily control the diattenuation of the output light in a structured manner across the pixels of the SLMs. Here, the diattenuation modulator 150 allows the independent control of the intensity of light in orthogonal polarisations.

[0191] FIG. 16 shows an example controller 1600 for implementing any of the modulator contollers used to control the functional units of the universal optical modulator 100 in accordane with aspects of the present disclosure. That is, the controller 1600 may be used to implement the polarisation controller 114, the phase controller 124, the intensity controller 134, the degree of polarisation controller 144 and / or the diattenuation controller 154. The controller 1600 may implement one or more of these controllers. That is one controller 1600 may be used to implement all of the controllers to control all of the modulator functional units provided. In alternative implementations, more than one controller 1600 may be used, each implementing one or more different controllers to control the different modulator functional units provided. The controller 1600 is provided only by way of example, and other controller architectures may be used, wherever suitable. For example, the controllers may be implemented solely in pre-configured programmable hardware using suitably designed field programmable gate arrays, microcontrollers, or processor circuitry.

[0192] In the embodiment shown, however, the controller 1600 comprises one or more processors 1602, a memory 1604 and an input / output module 1608. A bus system (not shown) may be provided which supports communication between at the least one processor 1602, memory 1604 and input / output module 1608. The processor 1602 may be implemented, for example, as a hardware circuit comprising an integrated circuit (IC) such as a custom Very Large Scale Integrated, VLSI, circuit or an Application Specific Integrated Circuit (ASIC) or as gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. The controller 1600 may thus be a general purpose computing apparatus. The processor 1602 can include any suitable number(s) and type(s) of processors or other devices in any suitable arrangement.

[0193] The memory 1604 may be provided by any structure(s) capable of storing and facilitating retrieval of information (such as data, program code, and / or other suitable information on a temporary or permanent basis). The memory 1604 can represent a random access memory or any other suitable volatile or non-volatile storage device(s). The memory 1604 may also contain one or more components or devices supporting longer-term storage of data, such as a read only memory, hard drive, flash memory, or optical disc, which may store software code for loading into the memory 1604 at runtime. In use, the processor 1602 and memory 1604 provide a runtime environment 1606 in which instructions or code loaded into the memory 1604 can be executed by the processor to generate instances of software modules in the runtime environment 1606.

[0194] The controller 1600 also comprises input / output module 1608 providing a communications interface for receiving data from at least the universal optical modulator 100 and other sensors which may provide sensing information about the wavefront parameters to the controller 1600 for use in controlling the one or more functional modulator units of the universal optical modulator 100.

[0195] In the example shown, the memory 1604 comprises instructions which, when executed by the one or more processors 1602, cause the one or more processors 1602 to instantiate a modulator control module 1610 which generates control signals usable to control, for example, one or more of the optical elements in the cascade providing the universal optical modulator 100. These control signals may be responsive to information received through the input / output module 1608, for example, measuring the polarisation of input light 105, or receiving a desired polarisation texture to encode structured matter. In this way the modulator control module 1610 may then generate pixel control signals usable to apply voltages to the pixels of the different spatial light modulators of the arbitrary optical elliptical retarder 110 for example to generate optical skyrmionic topological quasiparticles according to desired skyrmion parameters. These may be routed to the universal optical modulator 100 via the input / output module 1608.

[0196] In embodiments, the memory 1604 may store instructions, which when run on a processor, cause the processor to carry out the method described in relation to FIG. 3 and / or the method described in relation to Fig. 8.

[0197] Features, integers, characteristics or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and / or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and / or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. In particular, any dependent claims may be combined with any of the independent claims and any of the other dependent claims.

[0198] Each feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. The claims should not be construed to cover merely the foregoing embodiments, but also any embodiments which fall within the scope of the claims.

Claims

1. A universal optical modulator comprising:an arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation, the arbitrary optical elliptical retarder comprising a cascade of optical elements aligned along an optical axis including:a first polarisation controlling birefringent spatial light modulator, SLMp a, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis of the pixels of SLMp a arranged at a first angle to the optical axis;a second polarisation controlling birefringent spatial light modulator, SLMp b, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis of the pixels of SLMp b arranged at a second angle to the optical axis at a diagonal to the first angle;a third polarisation controlling birefringent spatial light modulator, SLMp c, having a plurality of pixels each individually controllable to adjust the phase retardance applied to light transmitted through the pixel, the fast axis of the pixels of the third SLMp c arranged at a third angle to the optical axis parallel to the first angle;wherein SLMp^a, SLMp^b and SLMp r together provide synthetic pixels controllable to adjust input light to pixels of SLMp a having a first, arbitrary polarisation to provide output light from corresponding pixels of SLMp c having a second, arbitrary polarisation.

2. The universal optical modulator of claim 1, wherein each pixel of the SLMs of the arbitrary optical elliptical retarder is individually controllable to adjust the phase retardance value applied to the light passing through such that its polarisation can be rotated around the Poincare sphere by an angle within the full 2ti radian range.

3. The universal optical modulator of claim 1 or 2, wherein the fast axis of pixels of the SLMp a and SLMp c for the arbitrary optical elliptical retarder represent a horizontal axis for the arbitrary optical elliptical retarder, each causing rotation of the polarisation of light input thereto around the axis of the Poincare sphere defined by the first Stokes parameter Si,and wherein the pixels of the SLMp b each cause rotation of the polarisation of light input thereto around the axis of the Poincare sphere defined by the second Stokes parameter S2.

4. The universal optical modulator of any one of claims 1 to 3, wherein the phase retardances applied by the sequential pixels of SLMp a, SLMp b and SLMp c of the arbitrary optical elliptical retarder are controllable to achieve an arbitrary desired total rotation of the polarisation of the input light around the Poincare sphere, by a first rotation around the Sy axis by SLMp a, a second rotation around the S2 axis by SLMp b, and a third rotation around the Sy axis by SLMp c.

5. The universal optical modulator of any one of claims 1 to 4, wherein the SLMps of the arbitrary optical elliptical retarder are each liquid crystal SLMs having individually addressable electrodes for each pixel to apply a voltage across the liquid crystal to adjust the retardance value applied to light passing through the liquid crystal at that pixel.

6. The universal optical modulator of any one of claims 1 to 5, wherein each pixel of the SLMps of the arbitrary optical elliptical retarder is rewritable such that the retardance value applied can be changed by applying a different voltage, the arbitrary optical elliptical retarder thereby representing structured matter usable to encode and store data.

7. The universal optical modulator of any one of claims 1 to 6, the arbitrary optical elliptical retarder further comprising a polarisation controller coupled to the SLMps of the arbitrary optical elliptical retarder to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the voltages applied to each pixel of the SLMps being determined by the polarisation controller to achieve a desired change in polarisation between the input light to pixels of SLMp a and the light output from corresponding pixels of SLMp c.

8. The universal optical modulator of any one of claims 1 to 7, further comprising a phase modulator aligned in the cascade of optical elements, the phase modulator comprising:a deformable mirror or micromirror array controllable to move along the optical axis at the locations of different pixels to adjust a phase of the light output by the cascade; ora phase controlling birefringent spatial light modulator, SLMph having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, the fast axis of the pixels of SLMph arranged at a fourth angle to the optical axis orthogonal to the first angle.

9. The universal optical modulator of any one of claims 1 to 8, further comprising an intensity modulator aligned in the cascade of optical elements, the intensity modulator comprising:a pair of linear polarisers; andan intensity controlling birefringent spatial light modulator, SLMi, arranged between the pair of linear polarisers, the SLMi having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel, thereby adjusting the pupil intensity value of the light transmitted through the pixel and out of the second linear polariser relative to the input light incident on the first linear polariser.

10. The universal optical modulator of any one of claims 1 to 9, further comprising a degree of polarisation modulator aligned in the cascade of optical elements, the degree of polarisation modulator comprising:a sequence of two or more degree of polarisation controlling birefringent spatial light modulators, SLMdop .4...dop v, having a plurality of pixels each individually controllable to adjust the phase retardance value applied to light transmitted through the pixel;a controller configured to control a degree of polarisation of light transmitted through pixels of the cascade by controlling the voltage of the pixels of two or more of the SLMdops in the degree of polarisation modulator to consecutively apply phase variation patterns with different retardance values to adjust the phase retardation of the light passing through the pixel.

11. The universal optical modulator of claim 10, wherein the controller is configured to apply the phase variation patterns to all of the SLMdops within the integration time of a detector used to detect the light passing through the cascade.

12. The universal optical modulator of any one of claims 1 to 11, further comprising a diattenuation modulator aligned in the cascade of optical elements, the diattenuation controller comprising:a first arbitrary optical elliptical retarder comprising three SLMs as recited in claim 1;a fixed polariser;a second arbitrary optical elliptical retarder comprising three SLMs as recited in claim 1; anda controller coupled to the SLMs of the first and second arbitrary optical elliptical retarders of the diattenuation modulator to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the voltages applied to each pixel of the SLMs being determined by the diattenuation modulator to achieve a desired change in diattenuation between the input light to pixels of SLMp and the light output from corresponding pixels of SLMp c.

13. A method of transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation using the universal optical modulator of any one of claims 1 to 12, comprising:for an arbitrary desired change to the polarisation of light passing through a pixel at (x, y) in the SLMps of the arbitrary optical elliptical retarder, determining a set of voltages to be applied to each pixel of the SLMps to achieve the desired change in polarisation between the input light to pixels of the SLMp a and the light output from corresponding pixels of SLMp c, wherein the phase retardances applied by the sequential pixels of SLMp a, SLMp b and SLMp c of the arbitrary optical elliptical retarder are controlled to achieve the desired total rotation of the polarisation of the input light around the Poincare sphere, by a first rotation around the Sy axis by SLMp a, a second rotation around the Sy axis by SLMp b, and a third rotation around the Sy axis by SLMp c; andcontrolling the SLMps to apply the determined respective voltages to the pixels at (x, y)-14. The method of claim 13, further comprising, for an input beam having a known polarisation state at the pixel (x, y) at the SLMp a, determining the desired change in polarisation as being the rotation around the Poincare sphere needed to achieve the desired polarisation of light output from corresponding pixel (x, y) at the SLMp c;decomposing the rotation around the Poincare sphere needed to achieve the desired polarisation of output light into a first rotation around the Sy axis by SLMp a, a second rotation around the Sy axis by SLMp b, and a third rotation around the Sy axis by SLMp c; anddetermining the set of voltages to be applied to the pixel (x, y) at SLMp a, SLMp b and SLMp c as being the voltages required to deliver the decomposed rotations of the Stokes vector.

15. Computer program product comprising instructions, which when run on a processor, cause the processor to carry out the method claim 13 or 14.

16. Use of the universal optical modulator of any one of claims 1 to 12 in a polarimeter, wherein the arbitrary optical elliptical retarder is used to provide a Full Poincare Beam generator reconfigurable to provide a tuned sensing pattern optimised for the sample being analysed.

17. Use of the universal optical modulator of any one of claims 1 to 12 in an adaptive optics apparatus, wherein the arbitrary optical elliptical retarder is used to correct the polarisation state of input light.

18. Apparatus for generating optical skyrmionic topological quasiparticles, comprising:an arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation, the arbitrary optical elliptical retarder including one or more spatial light modulators, SLMs, having pixels at locations (x, y) individually controllable by an applied voltage to adjust the phase retardance value applied to light transmitted through the pixel;a quasiparticle encoding controller coupled to the SLMs of the arbitrary optical elliptical retarder to apply pixelwise voltages thereto to adjust the retardance value applied to light passing through the liquid crystal at that pixel, the voltages applied to each pixel of the SLMs being determined by the quasiparticle encoding controller to achieve, for a pixel at a location (x, y), a desired change in polarisation between the input light to pixels of the first SLM and the light output from corresponding pixels of the last SLM so that the output light field has a topologically stable skyrmionic Stokes vector texture across the surface (x, y) having a skyrmion number N of a desired skyrmion defined by the relation:1 / 7' JJ\ ~ — II q • I —-— x ~~— j axay4% J J \dx dy )where a is the boundary in (x, y) of the region within which the skyrmion is confined, and wherein S is the Stokes vector applied by the arbitrary retarder at a pixel at (x, y), such that the polarisation texture in 5 wraps around the Poincare sphere N times within the boundary.

19. The apparatus for generating optical skyrmionic topological quasiparticles as claimed in claim 18, comprising the universal optical modulator of any one of claims 1 to 12, wherein the universal optical modulator provides the arbitrary optical elliptical retarder.

20. The apparatus for generating optical skyrmionic topological quasiparticles of claim 18 or 19, further comprising:a light source for illuminating the arbitrary optical elliptical retarder to generate in the light output from the retarder skyrmions based on the skyrmionic Stokes vector texture encoded in the SLMs of the arbitrary optical elliptical retarder.

21. The apparatus for generating optical skyrmionic topological quasiparticles of any one of claims 18 to 20, further comprising one or more optical elements for guiding or storing the optical skyrmionic topological quasiparticles.

22. The apparatus for generating optical skyrmionic topological quasiparticles of any one of claims 18 to 21, further comprising:means for determining the skyrmionic Stokes vector texture encoded in the arbitrary optical elliptical retarder, the means for detecting the skyrmionic Stokes vector texture including:an imaging device for optically detecting the generated skyrmions; and / or a Mueller matrix polarimeter.

23. The apparatus for generating optical skyrmionic topological quasiparticles of any one of claims 18 to 22, wherein the quasiparticle encoding controller is configured to encode in the arbitrary optical elliptical retarder a skyrmionic Stokes vector texture including one or more:skyrmions, skyrmioniums, meron, bimerons or bimeroniums where a is unbound;a skyrmion, skyrmionium, meron, bimeron or bimeronium lattice where g is bound;a skyrmion, skyrmionium, meron, bimeron or bimeronium bag.

24. A method of generating optical skyrmionic topological quasiparticles using an arbitrary optical elliptical retarder for transforming the polarisation of arbitrarily polarised input light to output light having any arbitrary polarisation, the arbitrary optical elliptical retarder including one or more spatial light modulators, SLMs, having pixels at locations (x, y) individually controllable by an applied voltage to adjust the phase retardance value applied to light transmitted through the pixel, the method comprising:determining pixelwise voltages to be applied to the SLMs of the arbitrary optical elliptical retarder to adjust the retardance value applied to light passing through the liquid crystal at that pixel to achieve, for a pixel at a location (x, y), a desired change in polarisation between the input light to pixels of the first SLM and the light output from corresponding pixels of the last SLM so that the output light field has a topologically stable skyrmionic Stokes vector texture across the surface (x, y) having a skyrmion number A of a desired skyrmion defined by the relation:14tt0S dxwhere o is the boundary in (x, y) of the region within which the skyrmion is confined, and wherein S is the Stokes vector applied by the arbitrary retarder at a pixel at (x, y), such that the polarisation texture in V wraps around the Poincare sphere N times within the boundary;applying the determined pixelwise voltages to the SLMs of the arbitrary optical elliptical retarder to adjust the retardance value applied to light passing through the liquid crystal at that pixel; andilluminating the arbitrary optical elliptical retarder with light from a light source to generate in the light output from the retarder skyrmions based on the skyrmionic Stokes vector texture encoded in the SLMs of the arbitrary optical elliptical retarder.

25. Computer program product comprising instructions, which when run on a processor, cause the processor to carry out the method claim 24.

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