Patent ID: 12259616

DETAILED DESCRIPTION

Embodiments consistent with the present disclosure will be described with reference to the accompanying drawings, which are merely examples for illustrative purposes and are not intended to limit the scope of the present disclosure. Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or similar parts, and a detailed description thereof may be omitted.

Further, in the present disclosure, the disclosed embodiments and the features of the disclosed embodiments may be combined. The described embodiments are some but not all of the embodiments of the present disclosure. Based on the disclosed embodiments, persons of ordinary skill in the art may derive other embodiments consistent with the present disclosure. For example, modifications, adaptations, substitutions, additions, or other variations may be made based on the disclosed embodiments. Such variations of the disclosed embodiments are still within the scope of the present disclosure. Accordingly, the present disclosure is not limited to the disclosed embodiments. Instead, the scope of the present disclosure is defined by the appended claims.

As used herein, the terms “couple,” “coupled,” “coupling,” or the like may encompass an optical coupling, a mechanical coupling, an electrical coupling, an electromagnetic coupling, or any combination thereof. An “optical coupling” between two optical elements refers to a configuration in which the two optical elements are arranged in an optical series, and a light output from one optical element may be directly or indirectly received by the other optical element. An optical series refers to optical positioning of a plurality of optical elements in a light path, such that a light output from one optical element may be transmitted, reflected, diffracted, converted, modified, or otherwise processed or manipulated by one or more of other optical elements. In some embodiments, the sequence in which the plurality of optical elements are arranged may or may not affect an overall output of the plurality of optical elements. A coupling may be a direct coupling or an indirect coupling (e.g., coupling through an intermediate element).

The phrase “at least one of A or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “at least one of A, B, or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C. The phrase “A and/or B” may be interpreted in a manner similar to that of the phrase “at least one of A or B.” For example, the phrase “A and/or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “A, B, and/or C” has a meaning similar to that of the phrase “at least one of A, B, or C.” For example, the phrase “A, B, and/or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C.

When a first element is described as “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in a second element, the first element may be “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in the second element using any suitable mechanical or non-mechanical manner, such as depositing, coating, etching, bonding, gluing, screwing, press-fitting, snap-fitting, clamping, etc. In addition, the first element may be in direct contact with the second element, or there may be an intermediate element between the first element and the second element. The first element may be disposed at any suitable side of the second element, such as left, right, front, back, top, or bottom.

When the first element is shown or described as being disposed or arranged “on” the second element, term “on” is merely used to indicate an example relative orientation between the first element and the second element. The description may be based on a reference coordinate system shown in a figure, or may be based on a current view or example configuration shown in a figure. For example, when a view shown in a figure is described, the first element may be described as being disposed “on” the second element. It is understood that the term “on” may not necessarily imply that the first element is over the second element in the vertical, gravitational direction. For example, when the assembly of the first element and the second element is turned 180 degrees, the first element may be “under” the second element (or the second element may be “on” the first element). Thus, it is understood that when a figure shows that the first element is “on” the second element, the configuration is merely an illustrative example. The first element may be disposed or arranged at any suitable orientation relative to the second element (e.g., over or above the second element, below or under the second element, left to the second element, right to the second element, behind the second element, in front of the second element, etc.).

When the first element is described as being disposed “on” the second element, the first element may be directly or indirectly disposed on the second element. The first element being directly disposed on the second element indicates that no additional element is disposed between the first element and the second element. The first element being indirectly disposed on the second element indicates that one or more additional elements are disposed between the first element and the second element.

The term “processor” used herein may encompass any suitable processor, such as a central processing unit (“CPU”), a graphics processing unit (“GPU”), an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or any combination thereof. Other processors not listed above may also be used. A processor may be implemented as software, hardware, firmware, or any combination thereof.

The term “controller” may encompass any suitable electrical circuit, software, or processor configured to generate a control signal for controlling a device, a circuit, an optical element, etc. A “controller” may be implemented as software, hardware, firmware, or any combination thereof. For example, a controller may include a processor, or may be included as a part of a processor.

The term “non-transitory computer-readable medium” may encompass any suitable medium for storing, transferring, communicating, broadcasting, or transmitting data, signal, or information. For example, the non-transitory computer-readable medium may include a memory, a hard disk, a magnetic disk, an optical disk, a tape, etc. The memory may include a read-only memory (“ROM”), a random-access memory (“RAM”), a flash memory, etc.

The term “film,” “layer,” “coating,” or “plate” may include rigid or flexible, self-supporting or free-standing film, layer, coating, or plate, which may be disposed on a supporting substrate or between substrates. The terms “film,” “layer,” “coating,” and “plate” may be interchangeable. The term “film plane” refers to a plane in the film, layer, coating, or plate that is perpendicular to the thickness direction or a normal of a surface of the film, layer, coating, or plate. The film plane may be a plane in the volume of the film, layer, coating, or plate, or may be a surface plane of the film, layer, coating, or plate. The term “in-plane” as in, e.g., “in-plane orientation,” “in-plane direction,” “in-plane pitch,” etc., means that the orientation, direction, or pitch is within the film plane. The term “out-of-plane” as in, e.g., “out-of-plane direction,” “out-of-plane orientation,” or “out-of-plane pitch” etc., means that the orientation, direction, or pitch is not within a film plane (i.e., non-parallel with a film plane). For example, the direction, orientation, or pitch may be along a line that is perpendicular to a film plane, or that forms an acute or obtuse angle with respect to the film plane. For example, an “in-plane” direction or orientation may refer to a direction or orientation within a surface plane, an “out-of-plane” direction or orientation may refer to a thickness direction or orientation non-parallel with (e.g., perpendicular to) the surface plane. In some embodiments, an “out-of-plane” direction or orientation may form an acute or right angle with respect to the film plane.

The term “orthogonal” as in “orthogonal polarizations” or the term “orthogonally” as in “orthogonally polarized” means that an inner product of two vectors representing the two polarizations is substantially zero. For example, two lights or beams with orthogonal polarizations (or two orthogonally polarized lights or beams) may be two linearly polarized lights (or beams) with two orthogonal polarization directions (e.g., an x-axis direction and a y-axis direction in a Cartesian coordinate system) or two circularly polarized lights with opposite handednesses (e.g., a left-handed circularly polarized light and a right-handed circularly polarized light).

The wavelength ranges, spectra, or bands mentioned in the present disclosure are for illustrative purposes. The disclosed optical device, system, element, assembly, and method may be applied to a visible wavelength band, as well as other wavelength bands, such as an ultraviolet (“UV”) wavelength band, an infrared (“IR”) wavelength band, or a combination thereof. The term “substantially” or “primarily” used to modify an optical response action, such as transmit, reflect, diffract, deflect, block or the like that describes processing of a light means that a major portion, including all, of a light is transmitted, reflected, diffracted, deflected, or blocked, etc. The major portion may be a predetermined percentage (greater than 50%) of the entire light, such as 100%, 98%, 90%, 85%, 80%, etc., which may be determined based on specific application needs. It is understood that when a light is transmitted, the propagation direction of the light is not affected. When a light is deflected (e.g., reflected, diffracted), the propagation direction is usually changed.

The term “optic axis” may refer to a direction in a crystal. A light propagating in the optic axis direction may not experience birefringence (or double refraction). An optic axis may be a direction rather than a single line: lights that are parallel to that direction may experience no birefringence.

FIG.1Aillustrates an x-z sectional view of a conventional CLC element100including helicoidal twist structures. As shown inFIG.1A, the CLC element100may include a layer105of cholesteric liquid crystals (“CLCs”), which is an LC mixture including a nematic LC material (that is a host LC material) and a chiral dopant (that is doped into the host LC material). The nematic LC material may include uniaxial LCs (e.g., LCs in uniaxial nematic phase). The layer105of CLCs may also be referred to as a CLC layer105. LC molecules112located in close proximity to a surface115of the CLC layer105may have a uniform in-plane orientation pattern. For example, the LC molecules112may be uniformly aligned in an x-axis direction shown inFIG.1A.

Within the volume of the CLC layer105, uniaxial LC molecules112may form a plurality of helical twist structures117with a plurality of helical axes118, and a plurality of series of Bragg planes114. The helical axis118may be perpendicular to a surface115of the CLC layer105, extending in a thickness direction of the CLC layer105, and the Bragg planes114may be parallel to the surface115.FIG.1Ashows that the Bragg planes114are within an x-y plane, the helical axis118extends in a z-axis direction, and the Bragg planes114are perpendicular to the helical axis118. A distance between two adjacent Bragg planes114is defined as a Bragg period PB. A helical pitch Phof the helical twist structure117may be defined as a distance along the helical axis118over which the azimuthal angles of the LC molecules112change by3600or the directors of the LC molecules112rotate by 360°.

The helical twist structures117may be helicoidal twist structures, where the LC molecules112are located within a plane substantially perpendicular to the helical axis118. That is, the directors of the LC molecules112may be substantially perpendicular to the helical axis118. The CLCs included in the CLC layer105may be referred to as helicoidal CLCs, and the CLC layer105may be referred to as a helicoidal CLC layer. The helicoidal CLCs has a bend elastic constant (K33) and a twist elastic constant (K22), where a ratio between the bend elastic constant (K33) and the twist elastic constant (K22) is often greater than 0.5.

The CLC element100may function as a circular reflective polarizer, with a reflection bandwidth ΔλR=Δn*Ph, and a peak reflection wavelength λR=n*Ph, where Phis the helical pitch, Δn is the birefringence of the host LC material, and n is the average refractive index of the host LC material. The helical pitch Phand the Bragg period PBmay be determined by a weight concentration and a helical twist power of the chiral dopant doped into the host LC material. That is, the helical pitch Phand the Bragg period PBof the CLC element100having the helicoidal twist structures may be determined by the material properties of LC mixture. For a circularly polarized light having a wavelength range within the reflection band of the CLC element100, the CLC element100may primarily or substantially reflect the circularly polarized light when the circularly polarized light has a handedness that is the same as the handedness of the helical twist structures117, and primarily or substantially transmit the circularly polarized light when the circularly polarized light has a handedness that is opposite to the handedness of the helical twist structures117.

Referring toFIG.1A, a linearly polarized light121(having a wavelength within the reflection band of the CLC element100) incident onto the CLC element100may include a right-handed circularly polarized component and a left-handed circularly polarized component. When the helical twist structure117has a right handedness, it may be desirable to have the CLC element100substantially reflect the right-handed circularly polarized component of the input light121as a reflected light123that is a right-handed circularly polarized light, and substantially transmit the left-handed circularly polarized component of the input light121as a transmitted light124that is a left-handed circularly polarized light. However, in practical applications, due to the waveplate effect (e.g., negative C-plate effect) of the CLC element100, the polarization state of the reflected light123and/or the transmitted light124may be changed to an elliptical polarization. That is, the reflected light123and/or the transmitted light124may be an elliptically polarized light, rather than a circularly polarized light. This phenomenon is referred to as depolarization. The depolarization of the reflected light123and/or the transmitted light124may result in a light leakage of the CLC element100, which may reduce a signal efficiency (e.g., the reflection efficiency or the transmission efficiency for the incident light121, depending on different applications), and degrade the extinction ratio of the CLC element100. Further, the light leakage of the CLC element100may increase as the incidence angle increases.

The CLC element100inFIG.1Ais shown to have the constant (or single) helical pitch Ph(or Bragg period PB), and the CLC layer105is referred to as a single-pitch CLC layer. A single-pitch CLC layer often has a relatively narrow reflection band, e.g., a reflection band corresponding to a single-color spectrum range of about 20 nm˜100 nm. Thus, the conventional CLC element100may merely provide a high reflectance in a relatively narrow reflection band and a narrow angle of incidence (“AOI”) range, which limits the applications. In conventional technologies, a stack of multiple single-pitch CLC layers with different helical pitches or a CLC layer with a gradient pitch may be used to provide a high reflectance in a relatively broad reflection band and/or a wide AOI range.FIG.1Billustrates a reflection band of a conventional CLC element including a stack of single-pitch CLC layers with different helical pitches. As shown inFIG.1B, the horizontal axis represents the wavelength (unit: nanometer (“nm”)), and the vertical axis represents the normalized reflectance. The stack of single-pitch CLC layers may include three single-pitch CLC layers with different helical pitches corresponding to a red wavelength range, a green wavelength range and a blue wavelength range, respectively. Each single-pitch CLC layer may have a reflection band with a 100-nm-bandwidth. The overall reflection band of the stack of three single-pitch CLC layers may substantially cover the visible wavelength range. However, the stacking method may not solve the issue of the efficiency loss due to the depolarization of the reflected light and/or the transmitted light of each CLC layer.

FIG.1Cillustrates transitions in the CLCs with a positive dielectric anisotropy in the CLC layer105shown inFIG.1A. As shown inFIG.1C, when the electric field within the CLC layer105is zero (or lower than a first threshold voltage of the CLC layer105), the CLCs may be in a planar state, where the helical axes118of the respective helicoidal twist structures117are perpendicular to the surface115of the CLC layer105, and the directors of the LC molecules112are substantially perpendicular to the helical axis118. The CLC element100may function as a circular reflective polarizer, which reflects the right-handed circularly polarized component of the input light121as the reflected light123and transmits the left-handed circularly polarized component of the input light121as the transmitted light124, as shown inFIG.1A. The propagation directions of the reflected light123and the transmitted light124may be parallel to the propagation direction of the input light121.

When a vertical electric field Elow(that is greater than the first threshold voltage and lower than a second threshold voltage of the CLC layer105) is generated within the CLC layer105, the CLCs may transform to a focal conic state where the helicoidal twist structures117are preserved whereas the helical axes118of the respective helicoidal twist structures117are oriented in different directions. In this case, the CLC element100may function as a scattering element that scatters the right-handed circularly polarized component of the input light121as multiple reflected lights having different propagation directions. When the vertical electric field Elowis removed, the CLCs may remain in the focal conic state. When a vertical electric field Ehigh(that is greater than the second threshold voltage of the CLC layer105) is generated within the CLC layer105, the CLCs may transform to a homeotropic state where the helicoidal twist structures117are unwound, and the directors of the LC molecules112are substantially oriented along the electric field direction. In this case, the CLC element100may substantially transmit both the right-handed circularly polarized component and the left-handed circularly polarized component of the input light121. When the vertical electric field Ehighis removed, the CLCs may restore to the planar state.

In view of the limitations in the conventional technologies, the present disclosure provides a liquid crystal polarization hologram (“LCPH”) element that may operate at a heliconical state, where optically anisotropic molecules are aligned via a suitable electric field to form heliconical twist structures in the volume of a birefringent medium layer. For discussion purposes, the LCPH element that may operate at the heliconical state may be referred to as a heliconical LCPH element. A helical pitch, a Bragg period, and/or an in-plane pitch of the heliconical LCPH element may be tunable via adjusting an applied electric field. Thus, the reflection wavelength, the reflection efficiency, and/or the reflection angle of the heliconical LCPH element may be tunable via adjusting the applied electric field. In addition, the heliconical LCPH element may also be configured to reduce a light leakage, increase a signal efficiency, and enhance an extinction ratio over a wide AOI range.

The heliconical LCPH elements may include a polarization volume hologram (“PVH”) element and a cholesteric liquid crystal (“CLC”) element. A reflective PVH element may be based on self-organized CLCs, and may also be referred to as a slanted or patterned CLC element. The heliconical LCPH elements described herein may be fabricated based on various methods, such as holographic interference, laser direct writing, ink-jet printing, and various other forms of lithography. Thus, a “hologram” described herein is not limited to fabrication by holographic interference, or “holography.”

FIG.2Aillustrates an x-z sectional view of a heliconical LCPH element200(referred to as LCPH element200for simplicity), according to an embodiment of the present disclosure. As shown inFIG.2A, the LCPH element200may include a first substrate205aand a second substrate205b, and a birefringent medium layer215disposed between the first and second substrates205aand205b. The LCPH element200may include a first alignment structure210aand a second alignment structure210b, which may be disposed at two inner surfaces of the first and second substrates205aand205bthat face each other, respectively. The birefringent medium layer215may be in contact with both of the first and second alignment structures210aand210b. The LCPH element200may also include a first electrode layer207aand a second electrode layer207b(collectively referred to as electrode layer207). The first electrode layer207amay be disposed between the first substrate205aand the first alignment structure210a, and the second electrode layer207bmay be disposed between the second substrate205band the second alignment structure210b.

The birefringent medium layer215may have a first surface215-1and an opposing second surface215-2. In some embodiments, the first surface215-1and the second surface215-2may be substantially parallel surfaces. In some embodiments, the first surface215-1may function as an interface between the birefringent medium layer215and the first alignment structure210a, and the second surface215-2may function as an interface between the birefringent medium layer215and the second alignment structure210b. Although the body of the birefringent medium layer215is shown as flat for illustrative purposes, the body of the birefringent medium layer215may have a curved shape. For example, at least one (e.g., each) of the first surface215-1and the second surface215-2may be curved.

The substrates205aand205bmay be configured to provide support and/or protection to various layers, films, and/or structures disposed at (e.g., on or between) the substrate205aand205b. In some embodiments, at least one of the first substrate205aor the second substrate205bmay be optically transparent (e.g., having a light transmittance of about 90% or more) in at least a visible spectrum (e.g., wavelength ranging from about 380 nm to about 700 nm). In some embodiments, the substrates205aand205bmay include a suitable material that is substantially transparent to lights of the above-listed wavelength ranges, such as, a glass, a plastic, a sapphire, a polymer, a semiconductor, or a combination thereof, etc. The substrates205aand205bmay be rigid, semi-rigid, flexible, or semi-flexible. In some embodiments, the substrates205aand205bmay have one or more surfaces in a flat, convex, concave, asphere, or freeform shape. In some embodiments, at least one of the first substrate205aor the second substrate205bmay be a part of another optical element or device, or a part of another opto-electrical element or device. For example, at least one of the first substrate205aor the second substrate205bmay be a solid optical lens or a part of a solid optical lens, a part of a waveguide (or light guide), or a part of a functional device (e.g., a display screen).

The first electrode layer207aand the second electrode layer207bmay be configured to apply a driving voltage provided by a power source230to the birefringent medium layer215, and generate an out-of-plane electric field within the birefringent medium layer215, thereby controlling an operation state of the LCPH element200. One of the first electrode layer207aand the second electrode layer207bmay be a transmissive electrode layer, and the other one of the first electrode layer207aand the second electrode layer207bmay be a transmissive electrode layer or a reflective electrode layer. The electrode layer207may include a suitable conductive material, such as a transparent conductive oxide material (e.g., indium tin oxide (“ITO”), aluminum zinc oxide (“AZO”), etc.), a metal material, structured metal grids, a conducting polymer, a dielectric-metal-dielectric (“DMD”) structure, carbon nanotubes, silver nanowires, or a combination thereof. In some embodiments, the electrode layer207may include a flexible transparent conductive layer, such as ITO disposed on a plastic film. In some embodiments, the plastic film may include polyethylene terephthalate (“PET”). In some embodiments, the plastic film may include cellulose triacetate (“TAC”), which is a type of flexible plastic with a substantially low birefringence.

The electrode layer207may be a continuous planar electrode layer, a patterned planar electrode layer, a protrusion electrode layer, or any other suitable type of electrode layer. In some embodiments, both of the first electrode layer207aand the second electrode layer207bmay be continuous electrode layers. In some embodiments, one of the first electrode layer207aand the second electrode layer207bmay be a continuous electrode layer, and the other one of the first electrode layer207aand the second electrode layer207bmay be a patterned electrode layer.

FIGS.3A-3Eillustrate x-y sectional views of the electrode layer207, according to various embodiments of the present disclosure. As shown inFIGS.3A-3E, the electrode layer207may be a patterned planar electrode layer including a plurality of patterned electrodes252spaced apart from one another with gaps256. In some embodiments, the patterned electrodes252may include stripe-shaped electrodes (e.g., as shown inFIGS.3A and3B), pixelated electrodes (e.g., as shown inFIG.3C), zig-zag electrodes, interdigitated electrodes, or annular (ring-shaped) electrodes (which may include a circular electrode at the center, e.g., as shown inFIG.3D), etc.

In some embodiments, as shown inFIG.3A, the stripe-shaped electrodes may have the same width. In some embodiments, as shown inFIG.3B, the stripe-shaped electrodes may have different widths, e.g., the width of the stripe-shaped electrode may gradually decrease from a center of the electrode layer207to a periphery of the electrode layer207. In some embodiments, as shown inFIG.3D, the patterned electrodes252may include a plurality of electrodes including a central, circular electrode and a plurality of annular electrodes that are concentric with the central electrode. In some embodiments, the central, circular electrode and the annular electrodes that are concentric with the central electrode may have different surface areas. In some embodiments, the voltages applied to the patterned electrodes252may be individually controllable, via a controller (not shown). In some embodiments, the patterned electrodes252may be applied with a same voltage.

In some embodiments, both of the first electrode layer207aand the second electrode layer207bmay be patterned electrode layers, which may generate an out-of-plane electric field having a direction perpendicular to or slanted with respect to the surface215-1or215-2of the birefringent medium layer215. In some embodiments, as shown inFIG.3E, the patterned electrodes of the first electrode layer207amay be aligned with the corresponding patterned electrodes of the second electrode layer207b. In some embodiments, as shown inFIG.3F, the patterned electrodes of the first electrode layer207amay be partially offset from the patterned electrodes of the second electrode layer207b.

In some embodiments, the electrode layer207including the stripe-shaped electrodes shown inFIG.3Amay be implemented into the LCPH element200functioning as a grating. In some embodiments, the electrode layer207including the stripe-shaped electrodes shown inFIG.3Bmay be implemented into the LCPH element200functioning as a cylindrical lens. In some embodiments, the electrode layer207including the stripe-shaped electrodes shown inFIG.3Cmay be implemented into the LCPH element200functioning as a freeform phase plate. In some embodiments, the electrode layer207including the stripe-shaped electrodes shown inFIG.3Dmay be implemented into the LCPH element200functioning as a spherical lens. In some embodiments, the electrode layer207including the stripe-shaped electrodes shown inFIG.3EorFIG.3Fmay be implemented into the LCPH element200functioning as a circular reflective polarizer or a grating. In some embodiments, the electrode layer207including a continuous electrode layer may be implemented into the LCPH element200functioning as a circular reflective polarizer.

Referring back toFIG.2A, the first and second alignment structures210aand210bmay be any suitable alignment structures. For example, at least one (e.g., each) of the first alignment structure210aor the second alignment structure210bmay include a polyimide layer, a photo-alignment material (“PAM”) layer, a plurality of nanostructures or microstructures, an alignment network, or any combination thereof. The first alignment structure210aor the second alignment structure210bmay be configured to provide a surface alignment to optically anisotropic molecules located in close proximity to the surface215-1or215-2of birefringent medium layer215. In some embodiments, the first alignment structure210aor the second alignment structure210bmay be configured to provide a homogeneous surface alignment with substantially small pretilt angles (e.g., 0° to 10°, 0° to 5°, or 0° to 3°, etc.) to the optically anisotropic molecules that are in contact with the alignment structure. In some embodiments, the first alignment structure210aand the second alignment structure210bmay be configured to provide anti-parallel surface alignments, or hybrid surface alignments (e.g., one providing a homogeneous surface alignment and the other providing a homeotropic surface alignment) to the optically anisotropic molecules that are in contact with the alignment structures.

Further, at least one (e.g., each) of the first alignment structure210aor the second alignment structure210bmay be configured to provide a predetermined, suitable surface alignment pattern. The surface alignment pattern may be a uniform surface alignment pattern, or a non-uniform surface alignment pattern. The uniform surface alignment pattern may provide a substantially uniform alignment direction, whereas the non-uniform surface alignment pattern may provide alignment directions that vary in one or more in-plane directions of the alignment structure.

The birefringent medium layer215may include a birefringent medium having a chirality. In some embodiments, the birefringent medium may have an induced chirality, e.g., the birefringent medium may include a chiral dopant. In some embodiments, the birefringent medium may have an intrinsic molecular chirality, e.g., the birefringent medium may include chiral LC molecules, or molecules having one or more chiral functional groups. In some embodiments, the birefringent medium may include nematic LCs, twist-bend LCs, smectic LCs, ferroelectric LCs, or any combination thereof.

The birefringent medium may exhibit a nematic phase called twist-bend nematic phase, for example, in some embodiments, the birefringent medium may include nematic LCs that exhibit the twist-bend nematic phase. The nematic LCs that exhibit the twist-bend nematic phase may be configured with a ratio between the bend elastic constant (K33) and the twist elastic constant (K22) that is less than 0.5, i.e., K33/K22<0.5. In some embodiments, the nematic LCs having K33/K22<0.5 may include a cyanobiphenyl-based LC material. In some embodiments, the cyanobiphenyl-based LC material may include a member of 1,ω-bis(4-cyanobiphenyl-4′-yl) alkane homologous series having the following chemical structure:

where two mesogenic units (i.e., cyanobiphenyl groups) are connected using a flexible linkage consisting of an alkyl chain. 1,ω-bis(4-cyanobiphenyl-4′-yl) alkane homologous series is referred to using an acronym CBnCB, where CB denotes cyanobiphenyl and n denotes a number of methylene units in the flexible linkage. An odd-numbered member of CBnCB may have a molecular structure, where the two cyanobiphenyl groups at the two ends are connected via the alkyl chain with an odd number of carbons and are inclined at some angle with respect to each other. That is, an odd-numbered member of CBnCB may have a bent molecular shape, and such a conformation facilitates a large bend flexoelectric coefficient. An even-numbered member of CBnCB may have a molecular structure where the long axes of the two cyanobiphenyl groups at the two ends are parallel to each other. That is, an even-numbered member of CBnCB may have a linear molecular shape, and the bend flexoelectric coefficient of the even-numbered members of CBnCB may be suppressed as compared to the that of the odd-numbered members of CBnCB.

CB7CB and CB11CB are examples of odd-membered member of CBnCB. CB7CB has the following molecular structure:

where the two cyanobiphenyl groups at the two ends are connected via the alkyl chain with seven carbons and are inclined at some angle with respect to each other. CB11CB has the following molecular structure:

which is similar to that of CB11CB except that the alkyl chain consists of eleven carbons. In some embodiments, one or more oxygen atoms may substitute for one or more carbon atoms of the alkyl chain of the odd-numbered member of CBnCB, e.g., CB6OCB has the following molecular structure:

where the two cyanobiphenyl groups at the two ends are connected via the alkyl chain with seven carbons and are inclined at some angle with respect to each other, and an oxygen atom substitutes for one of the seven carbon atom of the alkyl chain.

In some embodiments, the birefringent medium may also include a chiral dopant doped into the nematic LCs having K33/K22<0.5, thereby introducing the chirality of the birefringent medium. In some embodiments, the birefringent medium may also include nematic LCs configured with the bend elastic constant (K33) greater than the twist elastic constant (K22) i.e., K33>K22, such as 5CB. The nematic LCs having K33>K22may not exhibit a twist-bend nematic phase. In some embodiments, the nematic LCs having K33/K22<0.5, the chiral dopant, and the nematic LCs having K33>K22may be mixed to form an LC mixture exhibiting the twist-bend nematic phase. In some embodiments, the nematic LCs having K33>K22may have a relatively large weight percentage in the LC mixture, whereas the nematic LCs having K33/K22<0.5 may have a relatively small weight percentage in the LC mixture. For discussion purposes, the nematic LCs having K33>K22may be referred to as an LC host, while the nematic LCs having K33/K22<0.5 may be referred to as an LC dimer. The LC mixture may be prepared in a manner known in the art, for example, heating a mixture of the host LC and the LC dimer to a temperature approximately above the clearing point, then cooling the mixture to the room temperature.

FIGS.2B and2Cillustrate x-z sectional views of the birefringent medium layer215, showing out-of-plane orientations of LC molecules212in the birefringent medium layer215shown inFIG.2A, according to various embodiments of the present disclosure. For discussion purposes, rod-like LC molecules212are used as examples of the LC molecules212of the birefringent medium layer215. The rod-like LC molecule212may have a longitudinal direction (or a length direction) and a lateral direction (or a width direction). The longitudinal direction of the LC molecule212may be referred to as a director of the LC molecule212or an LC director. An orientation of the LC director may determine a local optic axis orientation or an orientation of the optic axis at a local point of the birefringent medium layer215.

In the embodiments shown inFIGS.2B and2C, the LC molecules212within a volume of the birefringent medium layer215may be arranged in a plurality of helical twist structures217with a plurality of helical axes218, and a plurality of series of Bragg planes214. In each helical twist structure217, the directors of the LC molecules212may continuously rotate around the helical axis218in a predetermined rotation direction, e.g., clockwise direction or counter-clockwise direction. Accordingly, the helical twist structure217may exhibit a handedness, e.g., right handedness or left handedness. A helical pitch Phof the helical twist structure217may be defined as a distance along the helical axis218over which the directors of the LC molecule212rotate by 360°. The birefringent medium layer215may be a single-pitch layer having a constant helical pitch Ph, or a varying-pitch layer having a varying helical pitch Ph. In some embodiments, the birefringent medium layer215may include a stack of multiple single-pitch layers having different helical pitches Ph.

The helical twist structures217may be configured to be heliconical twist structures217, where the LC molecules212are tilted towards the helical axis218. That is, the LC molecules212may not be located in a plane perpendicular to the helical axis218, and the directors of the LC molecules212may not be perpendicular to the helical axis218. The LC molecules212forming the heliconical twist structures217may be configured with a cone angle θ, which is greater than 0° and equal to or less than a first predetermined angle (e.g., 35°, 33°, 30°, etc.). The cone angle θ of the LC molecule212is defined as an angle of the director of the LC molecule212with respect to the helical axis218. A tilt angle φ of the LC molecule212forming the heliconical twist structures217may be defined as an angle of the director of the LC molecule212with respect to a plane (e.g., Bragg plane214) that is perpendicular to the helical axis218. The cone angle θ and the tilt angle φ may be complementary angles. In some embodiments, the tilt angle φ may be configured to be equal to or greater than a second predetermined angle (e.g., 55°, 57°, 60°, etc.) and less than 90°. In some embodiments, the LC molecules212forming the heliconical twist structures217may have substantially the same cone angle θ and the same tilt angle (p.

The heliconical twist structures217where the LC molecules212are slanted with respect to the helical axis218may be introduced via an out-of-plane electric field generated within the birefringent medium layer215. An intensity of the out-of-plane electric field may be configured, such that the LC molecules212may trend to be oriented parallel with a direction of the out-of-plane electric field E to form the heliconical twist structures217. The direction of the out-of-plane electric field generated within the birefringent medium layer215may be perpendicular to a surface (e.g., at least one of the first surface215-1or the second surface215-2) of the birefringent medium layer215, or slanted with respect to the surface (e.g., at least one of the first surface215-1or the second surface215-2) of the birefringent medium layer215. The heliconical twist structures217may not be introduced via the alignment structures210aand210b, as the first alignment structure210aor the second alignment structure210bmay provide a homogeneous surface alignment with substantially small pretilt angles (e.g., 0° to 10°, 0° to 5°, or 0° to 3°, etc.) to the LC molecules212that are in contact with the alignment structures.

Further, the LC molecule212having a first same orientation (e.g., same first tilt angle and same first azimuthal angle) may form a first series of slanted and parallel refractive index planes (i.e., a first series of Bragg planes)214periodically distributed within the volume of the birefringent medium layer215. Although not labeled, the LC molecules212with a second same orientation (e.g., same second tilt angle and same second azimuthal angle) different from the first same orientation may form a second series of slanted and parallel refractive index planes (i.e., a second series of Bragg planes)214periodically distributed within the volume of the birefringent medium layer215. Different series of Bragg planes may be formed by the LC molecules212having different orientations. In the same series of Bragg planes, the LC molecules212may have the same orientation, and the refractive index may be the same. Different series of Bragg planes may correspond to different refractive indices. When the number of the Bragg planes (or the thickness of the birefringent medium layer215) increases to a sufficient value, Bragg reflection may be established. The distance between adjacent Bragg planes214of the same series may be referred to as a Bragg period PB. In the embodiment shown inFIGS.2B and2C, the Bragg period PBis half of the helical pitch Ph. The Bragg period PBand the helical pitch Phof the LCPH element200may be tunable via tuning the intensity of the out-of-plane electric field and/or the direction of the out-of-plane electric field generated within the birefringent medium layer215.

In the embodiment shown inFIG.2B, the birefringent medium layer215may be a non-slanted CLC layer, where the helical axis218is perpendicular to a surface (e.g., at least one of the first surface215-1or the second surface215-2) of the birefringent medium layer215, extending in a thickness direction of the birefringent medium layer215. The Bragg planes214may be parallel to the surface215-1or215-2of the birefringent medium layer215.FIG.2Bshows that the Bragg planes214are within an x-y plane, the helical axis218extends in a z-axis direction, and the Bragg planes214are perpendicular to the helical axis218. The out-of-plane electric field generated within the birefringent medium layer215may be along the thickness direction (e.g. a z-axis direction) of the birefringent medium layer215, and the helical axis218may be parallel to the direction of the out-of-plane electric field.

As shown inFIG.2B, a linearly polarized incident light221of the LCPH element200may have a wavelength within the reflection band of the LCPH element200. The linearly polarized light221may include a right-handed circularly polarized component and a left-handed circularly polarized component. For discussion purposes, the helical twist structures217may have a right handedness. The first electrode layer207amay be a transmissive electrode layer, and the second electrode layer207bmay be a transmissive electrode layer or a reflective electrode layer. In some embodiments, the LCPH element200may substantially reflect the right-handed circularly polarized component of the linearly polarized light221as a reflected light223that is substantially close to a right-handed circularly polarized light, and substantially transmit the left-handed circularly polarized component of the linearly polarized light221as a transmitted light224that is substantially close to a left-handed circularly polarized light.FIG.2Bshows that when the linearly polarized light221is normally incident onto the LCPH element200, the propagation directions of the reflected light223and the transmitted light224are substantially parallel with the propagation directions of the incident light221. When the second electrode layer207bis a reflective electrode layer, the transmitted light224may be reflected at the second electrode layer207b, and output from the same side (e.g., a first side) of the LCPH element200as the reflected light223. When the second electrode layer207bis a transmissive electrode layer, the transmitted light224may be transmitted through the second electrode layer207b, and output from a second side of the LCPH element200.

In the embodiment shown inFIG.2C, the birefringent medium layer215may be a slanted CLC layer, where the helical axis218is slanted with respect to the surface (e.g., the first surface215-1or the second surface215-2) of the birefringent medium layer215, and the LCPH element200may be reflective PVH element. In some embodiments, an angle of the helical axis218with respect to a normal of the surface (e.g., the first surface215-1or the second surface215-2) of the birefringent medium layer215may be less than 45°. The Bragg planes214may form an angle (e.g., an acute angle) with the surface of the birefringent medium layer215. The x-y-z coordinate system shown inFIG.2Crefers to a global coordinate system for the birefringent medium layer215, whereas an x′-y′-z′ coordinate system shown inFIG.2Crefers to a local coordinate system for the helical twist structure217.FIG.2Cshows that the Bragg planes214are within an x′-y′ plane, the helical axis218extends in a z′-axis direction, and the Bragg planes214are perpendicular to the helical axis218. In the birefringent medium layer215(or the non-slanted CLC layer) shown inFIG.2B, the x′-y′-z′ coordinate system may coincide with the x-y-z coordinate system. The direction of the out-of-plane electric field generated within the birefringent medium layer215may be slanted with respect to the surface (e.g., the first surface215-1or the second surface215-2) of the birefringent medium layer215, and the helical axis218may be parallel to the direction of the out-of-plane electric field.

As shown inFIG.2C, the birefringent medium layer215(or the LCPH element200) may substantially diffract, via backward reflection, the right-handed circularly polarized component of the linearly polarized light221as a reflected (or diffracted) light233that is substantially close to a right-handed circularly polarized light, and substantially transmit the left-handed circularly polarized component of the linearly polarized light221as a transmitted light224that is substantially close to a left-handed circularly polarized light. When the linearly polarized light221is normally incident onto the LCPH element200, the propagation direction of the transmitted light224may be parallel with the propagation direction of the incident light221, and the propagation direction of the diffracted light233may not be parallel with the propagation direction of the linearly polarized light221. When the second electrode layer207bis a reflective electrode layer, the transmitted light224may be reflected at the second electrode layer207b, and output from the same side (e.g., a first side) of the LCPH element200as the reflected light233. When the second electrode layer207bis a transmissive electrode layer, the transmitted light234may be transmitted through the second electrode layer207b, and output from a second side of the LCPH element200.

Referring toFIGS.2B and2C, the heliconical twist structures217in the LCPH element200may be maintained via maintaining the applied electric field, or via polymerizing the heliconical twist structures217under the applied electric field and removing the applied electric field after the polymerization. Because the LC molecules212tilt towards the helical axis218, the birefringence experienced by a circularly polarized light (e.g., the right-handed a circularly polarized component of the input light221) may be lower than the birefringence (Δn=ne-no) of the birefringent medium in the birefringent medium layer215, which may narrow the reflection band of the LCPH element200.FIG.2Fillustrates a reflection band of the LCPH element200shown inFIG.2A, according to an embodiment of the present disclosure. As shown inFIG.2F, the horizontal axis represents the wavelength (unit: nanometer (“nm”)), and the vertical axis represents the normalized reflectance. For discussion purposes,FIG.2Fshows that the LCPH element200provides an ultra-narrow reflection band in the red wavelength range. In some embodiments, the LCPH element200may be configured to provide an ultra-narrow reflection band in another suitable wavelength range.

In some embodiments, the bandwidth Δλ of the LCPH element200may be within a range of about 5 nm to 10 nm, a range of about 10 nm to 20 nm, a range of about 20 nm to 30 nm, or a range of about 30 nm to 40 nm, etc. In some embodiments, the LCPH element200may be optically coupled with a corresponding narrowband light source (e.g., a light emitting diode (“LED”), a superluminescent diode (“SLED” or “SLD”), a laser diode, etc.), and the reflection band of the LCPH element200may substantially match with the emission band of the narrowband light source. The LCPH element200may substantially reflect the light received from the narrowband light source when the light is a circularly polarized light having a handedness that is the same as the handedness of the helical twist structures217. The LCPH element200may substantially transmit a light having a wavelength range outside of the ultranarrow reflection band.

Conventional narrowband (A)=20˜40 nm) CLC element or PVH element are often fabricated based on a low-birefringence LC material (e.g., no=1.4˜1.6, Δn<0.08). The stability of the low-birefringence LC material may be poor, and the material options of the low-birefringence LC materials may be rather limited. As the LC molecules212tilt towards the helical axis218, the disclosed LCPH element200may be fabricated based on a moderate-to-high birefringence LC mater (e.g., no>1.6, Δn>0.1) to provide a narrowband reflection band that is comparable to the conventional narrowband CLC element or PVH element. When the disclosed LCPH element200is fabricated based on the same low-birefringence LC material, the disclosed LCPH element200may provide a narrower reflection band than the conventional narrowband CLC element or PVH element.

FIG.2Dillustrates various operation states of the LCPH element200shown inFIG.2B, according to an embodiment of the present disclosure, andFIG.2Eillustrates various operation states of the LCPH element200shown inFIG.2C, according to an embodiment of the present disclosure. As shown inFIGS.2D and2E, the LCPH element200may operate at a helicoidal state (or planar state), a heliconical state, or a homeotropic state, depending on the intensity of the applied electric field. For discussion purposes,FIG.2Dshows that the direction of the out-of-plane electric field generated within the birefringent medium layer215is perpendicular to the surface215-1or215-2of the birefringent medium layer215, andFIG.2Eshows that the direction of the out-of-plane electric field generated within the birefringent medium layer215is slanted with respect to surface215-1or215-2of the birefringent medium layer215. For discussion purposes,FIGS.2D and2Eshow that the birefringent medium in the birefringent medium layer215has a positive dielectric anisotropy.

When the intensity of the applied electric field is greater than 0 and less than or equal to a first threshold electric field intensity E1(i.e., 0<E≤E1), the LC molecules212may not be reoriented by the applied electric field. The LCPH element200may operate at the helicoidal state, and the helical twist structures217may be helicoidal twist structures, where the LC molecules212may be located within a plane substantially perpendicular to the helical axis218, and the directors of the LC molecules212may be substantially perpendicular to the helical axis218(e.g., the tilt angle φ of the LC molecules212may be about zero degree).

The LC molecules212located in close proximity to the surface215-1or215-2of the birefringent medium layer215may be aligned in a predetermined in-plane orientation pattern according to the predetermined surface alignment pattern of the first alignment structure210aand the second alignment structure210b. The predetermined in-plane orientation pattern may be a uniform in-plane orientation pattern or a non-uniform in-plane orientation pattern. The uniform in-plane orientation pattern means that the orientations of the optical anisotropic molecules may be substantially the same. The non-uniform in-plane orientation pattern means that the orientations of the optical anisotropic distributed along one or more in-plane directions may change in the one or more in-plane directions. Depending on the in-plane orientation pattern, the LCPH element200may function as a circular reflective polarizer, a grating, a lens, a freeform phase plate, etc. Exemplary orientations of the LC molecules212located in close proximity to the surface215-1or215-2of the birefringent medium layer215are shown inFIGS.4A-4E. The orientations of the LC molecules212within the volume of the birefringent medium layer215may be determined by the material properties of the birefringent medium in the birefringent medium layer215. Thus, the Bragg period and the helical pitch of the LCPH element200operating at the helicoidal state may be determined by the material properties of the birefringent medium in the birefringent medium layer215.

When the intensity of the applied electric field is greater than the first threshold electric field intensity E1and less than or equal to a second threshold electric field intensity E2(i.e., E1<E≤E2), the LC molecules212may be reoriented by the applied electric field, whereas the helical twist structures217may be preserved. The directors of the LC molecules212may trend to be reoriented to be parallel with the direction of the applied electric field. The LCPH element200may operate at a heliconical state, and the helical twist structures217may be heliconical twist structures, where the LC molecules212may be tilted with respect to the helical axis218. In some embodiments, the cone angle θ of the LC molecules212may be greater than 0° and equal to or less than the first predetermined angle (e.g., 35°, 33°, 30°, etc.), and the tilt angle (p may be equal to or greater than the second predetermined angle (e.g., 55°, 57°, 60°, etc.) and less than 90°.

When the LCPH element200operates at the heliconical state, the direction of the helical axis may be parallel with the direction of the out-of-plane electric field generated within the birefringent medium layer215. When the LCPH element200operates at the heliconical state, the Bragg period and the helical pitch of the LCPH element200may be determined by the material properties of the birefringent medium in the birefringent medium layer215, and the intensity and the direction of the out-of-plane electric field generated within the birefringent medium layer215. For example, as shown inFIGS.2D and2E, when the intensity of the applied electric field gradually increases from the first threshold electric field intensity E1to the second threshold electric field intensity E2, the directors of the LC molecules212may be gradually reoriented to be parallel with the direction of the applied electric field. The Bragg period PB(and the helical pitch) of the LCPH element200may gradually decrease and, accordingly, the reflection band of the LCPH element200may be blue shifted (e.g., shifted toward a shorter wavelength) whereas the ultranarrow reflection band may be maintained.

When the intensity of the applied electric field is greater than the second threshold electric field intensity E2(i.e., E>E2), the LCPH element200may operate at a homeotropic state, where the heliconical twist structures217may be unwound, and the directors of the LC molecules212may be substantially oriented along the direction of the out-of-plane electric field. When the out-of-plane electric field is removed, the LCPH element200may return to the helicoidal state (or planar state).

In some embodiments, the second threshold electric field intensity E2may be determined according to the following equation:

E2=2⁢πP0⁢K22ε0⁢εa⁢K33,
where K33and K22are the bend elastic constant and the twist elastic constant of the LC material, Ea is the dielectric anisotropy of the LC material, ε0is the vacuum permittivity, P0is the helical pitch of the helical twist structures217when the helical twist structures217are helicoidal twist structures (e.g., the tilt angle φ of the LC molecules212is about zero degree). In some embodiments, the second threshold electric field intensity E2may be the threshold electric field intensity for the helical twist structures217to transform from the heliconical twist structures to the unwounded state.

In some embodiments, the first threshold electric field intensity E1may be determined according to the following equation:

E1≈E2⁢k⁡(2+2⁢(1-k))1+k,
where k is a ratio between the bend elastic constant (K33) and the twist elastic constant (K22) of the LC material, i.e., k=K33/K22, and E2is the second threshold electric field intensity. In some embodiments, the first threshold electric field intensity E1may be the threshold electric field intensity for the helical twist structures217to transform from the helicoidal twist structures where the tilt angle φ of the LC molecules212is about zero degree to the heliconical twist structures where the tilt angle φ of the LC molecules212changes to be greater than the second predetermined angle (e.g., 55°, 57°, 60°, etc.) and less than 90°.

In some embodiments, the cone angle θ of the heliconical twist structures217may be determined according to the following equation:

θ=arcsin⁡(k1-k⁢(E2E-1)),
where E is the intensity of the applied electric field within the birefringent medium layer215, k is the ratio between the bend elastic constant (K33) and the twist elastic constant (K22) of the LC material, i.e., k=K33/K22, and E2is the second threshold electric field intensity.

In some embodiments, the helical pitch Phof the heliconical twist structures217may be determined according to the following equation:

Ph=2⁢πE⁢K3⁢3ε0⁢εa=k⁢E2⁢P0E,
where E is the intensity of the applied electric field within the birefringent medium layer215, εais the dielectric anisotropy of the LC material, ε0is the vacuum permittivity, K33is the bend elastic constant of the LC material, E2is the second threshold electric field intensity, and P0is the helical pitch of the helical twist structures217when the helical twist structures217are helicoidal twist structures (e.g., the tilt angle φ of the LC molecules212is about zero degree). As the equation of the helical pitch Phof the heliconical twist structures217shows, when the intensity E of the applied electric field within the birefringent medium layer increases, the helical pitch Phof the heliconical twist structures217may decrease. Accordingly, the Bragg period PBof the LCPH element200may decrease, and the reflection band of the LCPH element200may be blued shifted.

FIGS.4A-4Eillustrate x-y sectional views of a portion of the birefringent medium layer215shown inFIG.2A, showing exemplary in-plane orientation patterns of the LC directors of the LC molecules212located in close proximity to the surface (e.g.,215-1and/or215-2) of the birefringent medium layer215, when the LCPH element200operates at the helicoidal state according to various embodiments of the present disclosure. In some embodiments, the LC molecules212located in close proximity to the surface215-1and/or215-2of the birefringent medium layer215may have other suitable surface alignment patterns different from those shown inFIGS.4A-4E.

In the embodiment shown inFIG.4A, at least one (e.g., each) of the first alignment structure210aor the second alignment structure210bmay be configured to provide spatially uniform alignments to the LC molecules212that are located in close proximity to the surface of the birefringent medium layer215. That is, the LC directors of the LC molecules212that are located in close proximity to the surface of the birefringent medium layer215may be substantially uniformly aligned (e.g., along an x-axis direction shown inFIG.4A). Accordingly, the orientations of the LC directors of the LC molecules212located in close proximity to the surface of the birefringent medium layer215may exhibit a uniform in-plane orientation pattern. In some embodiments, the LCPH element200including the birefringent medium layer215having the in-plane orientation pattern shown inFIG.4Aand the out-of-plane orientation pattern shown inFIG.2Bmay function as a circular reflective polarizer.

In some embodiments, at least one (e.g., each) of the first alignment structure210aor the second alignment structure210bmay be configured to provide spatially non-uniform surface alignments. Thus, the orientations of the LC directors of the LC molecules212located in close proximity to the surface of the birefringent medium layer215may exhibit a non-uniform in-plane orientation pattern. For example, orientations of the LC directors of the LC molecules located in close proximity to the surface of the birefringent medium layer215may periodically or non-periodically vary in at least one in-plane direction within the surface, such as in a linear direction, in a radial direction, in a circumferential (e.g., azimuthal) direction, or a combination thereof. Accordingly, the birefringent medium layer215may provide different optical functions. For example, the LCPH element200may function as a grating, a prism, a lens, a segmented waveplate or a segmented phase retarder, a lens array, a prism array, etc. Exemplary non-uniform alignment patterns of the LC molecules that are located in close proximity to the surface of the birefringent medium layer215are shown inFIGS.4B-4E.

In the embodiment shown inFIG.4B, the directors of the LC molecules212located in close proximity to the surface of the birefringent medium layer215may exhibit a periodic, continuous rotation in a predetermined in-plane direction within the surface, e.g., the x-axis direction. The continuous rotation of the LC directors may form a periodic rotation pattern with a uniform (e.g., same) in-plane pitch Pin. It is noted that the predetermined in-plane direction may be any other suitable direction within the surface, such as the y-axis direction, the radial direction, or the circumferential direction within the x-y plane. The in-plane pitch (or horizontal pitch) Pinmay be defined as a distance along the predetermined in-plane direction (e.g., the x-axis) over which the orientations of the LC directors exhibit a rotation by a predetermined angle (e.g., 180°). The periodically varying in-plane orientations of the LC directors shown inFIG.4Bmay be referred to as a grating pattern, and the LCPH element200including the birefringent medium layer215configured with the in-plane orientation pattern shown inFIG.4Band the out-of-plane orientation pattern shown inFIG.2Cmay function as a reflective PVH grating.

In addition, within the surface of the birefringent medium layer215, the orientations of the directors of the LC molecules212may rotate along the predetermined in-plane direction (e.g., the x-axis) in a predetermined rotation direction, e.g., a clockwise direction or a counter-clockwise direction. Accordingly, the rotation of the orientations of the directors of the LC molecules212along the predetermined in-plane direction (e.g., the x-axis) may exhibit a handedness, e.g., right handedness or left handedness. For discussion purposes,FIG.2Cshows that the orientations of the directors of the LC molecules212may rotate along the predetermined in-plane direction (e.g., the x-axis) in a clockwise direction, exhibiting a left handedness.

Although not shown inFIG.4B, in some embodiments, the orientations of the directors of the LC molecules212located in close proximity to the surface of the birefringent medium layer215may exhibit a rotation in a counter-clockwise direction. Accordingly, the rotation of the orientations of the directors of the LC molecules212may exhibit a right handedness. Although not shown, in some embodiments, within the surface of the birefringent medium layer215, domains in which the orientations of the directors of the LC molecules212exhibit a rotation in a clockwise direction (referred to as domains DL) and domains in which the orientations of the directors of the LC molecules212exhibit a rotation in a counter-clockwise direction (referred to as domains DR) may be alternatingly arranged in two in-plane directions, e.g., in x-axis and y-axis directions.

The in-plane orientation pattern of the LC directors shown inFIG.4Cmay be referred to as a lens pattern (e.g., a spherical lens pattern). The LCPH element200including the birefringent medium layer215configured with the in-plane orientation pattern shown inFIG.4Cand the out-of-plane orientation pattern shown inFIG.2Cmay function as a reflective PVH lens (e.g., spherical lens). In the embodiment shown inFIG.4C, the orientations of the LC directors of LC molecules212located in close proximity to the surface of the birefringent medium layer215may exhibit a continuous rotation in at least two opposite in-plane directions from a lens pattern center450to opposite lens pattern peripheries455with a varying pitch. The orientations of the LC directors may exhibit a rotation in the same rotation direction (e.g., clockwise, or counter-clockwise) from the lens pattern center450to the opposite lens pattern peripheries455.

The in-plane pitch Λ of the in-plane orientation pattern may be defined as a distance in the in-plane direction (e.g., a radial direction) over which the orientations of the LC directors (or azimuthal angles ϕ of the LC molecules212) change by a predetermined angle (e.g., 180°) from a predetermined initial state.FIG.4Dillustrates a section of the in-plane orientation pattern taken along an x-axis in the birefringent medium layer215shown inFIG.4C, according to an embodiment of the present disclosure. As shown inFIG.4D, according to the LC director field along the x-axis direction, the pitch Λ may be a function of the distance from the lens pattern center450. The pitch Λ may monotonically decrease from the lens pattern center450to the lens pattern peripheries455in the at least two opposite in-plane directions (e.g., two opposite radial directions) in the x-y plane, e.g., Λ0>Λ1> . . . >Λr. Λ0is the pitch at a central region of the lens pattern, which may be the largest. The pitch Λris the pitch at a periphery region (e.g., lens pattern periphery455) of the lens pattern, which may be the smallest. In some embodiments, the azimuthal angle φ of the LC molecule212may change in proportional to the distance from the lens pattern center450to a local point of the birefringent medium layer215at which the LC molecule212is located.

In the embodiment shown inFIG.4E, the LCPH element200is shown as having a rectangular shape (or a rectangular lens aperture). A width direction of LCPH element200may be referred to as a lateral direction (e.g., an x-axis direction inFIG.4E), and a length direction of the LCPH element200may be referred to as a longitudinal direction (e.g., a y-axis direction inFIG.4E). In the embodiment shown inFIG.4E, the orientations of the LC molecules212located in close proximity to the surface of the birefringent medium layer215may be configured with an in-plane orientation pattern having a varying pitch in at least two opposite lateral directions, from the lens pattern center (“OL”)450to the opposite lens pattern peripheries455. The orientations of the LC directors of the LC molecules212located on the same side of an in-plane lens pattern center axis463and at a same distance from the in-plane lens pattern center axis463may be substantially the same. The rotations of the orientations of the LC directors from the lens pattern center450to the opposite lens pattern peripheries455in the two opposite lateral directions may exhibit a same handedness (e.g., right, or left handedness).

In the embodiment shown inFIG.4E, the directors of the LC molecules212may be configured with a continuous in-plane rotation pattern with a varying pitch (Λ0, Λ1, . . . , Λr) from the lens pattern center450to opposite lens pattern peripheries455in the two opposite lateral directions. As shown inFIG.4E, the pitch of the lens pattern may vary with the distance to the in-plane lens pattern center axis463in the lateral direction. In some embodiments, the pitch of the lens pattern may monotonically decrease as the distance to the in-plane lens pattern center axis463in the lateral direction increases, i.e., Λ0>Λ1> . . . >Λr, where Λ0is the pitch at a central portion of the lens pattern, which may be the largest. The pitch Λris the pitch at an edge or periphery region of the lens pattern, which may be the smallest.

The LCPH element200including the birefringent medium layer215configured with the in-plane orientation pattern shown inFIG.4Eand the out-of-plane orientation pattern shown inFIG.2Cmay function as a reflective PVH lens, e.g., an on-axis focusing cylindrical lens that may focus a beam into a line (e.g., a line of focal points or a line focus). The cylindrical lens with the in-plane orientation pattern shown inFIG.4Emay be considered as a 1D example of the spherical lens with the in-plane orientation pattern shown inFIGS.4C and4D, and the at least two opposite in-plane directions in the LCPH element200may include at least two opposite lateral directions (e.g., the +x-axis and −x-axis directions).

Referring toFIGS.2A,2C, and4B-4E, the in-plane pitch Pin(or Λ) of the LCPH element200may determine the diffraction angle of a diffracted light. The diffraction angle of a first order diffracted light may be calculated by the following grating equation:
θdef≈arcsin(λ0/(n*Pin)),
where θdefis the diffraction angle of the first order diffracted light, λ0is the wavelength of an input light of the LCPH element200, n is the refractive index of the birefringent medium in the LCPH element200, and Pinis the in-plane pitch of the LCPH element200. According to the grating equation, the diffraction angle of the first order diffracted light may increase as the in-plane pitch Pindecreases. Thus, through changing the in-plane pitch Pinof the LCPH element200, the diffraction angle of the first order diffracted light may be tunable. Accordingly, the LCPH element200may provide a beam steering function. In some embodiments, the LCPH element200may provide a continuous beam steering through changing the in-plane pitch Pinin a continuous manner. In some embodiments, the LCPH element200may provide a discrete beam steering through changing the in-plane pitch Pinof the LCPH element200in a discrete manner. In some embodiments, the beam steering range may be further increased by stacking two or more LCPH elements200with independently tunable in-plane pitches Pin. In each of the two or more LCPH elements200, the in-plane pitches Pinmay be tuned in the same or different manners or profiles. In some embodiments, a two-dimensional (“2D”) beam steering may be provided by stacking two LCPH elements200that steer a light in two different axes, respectively.

The Bragg period PB, and/or the in-plane pitch Pinof the LCPH element200operating at the heliconical state may be tunable via adjusting the intensity and/or the direction of the applied electric field. In some embodiments, as discussed inFIGS.2D and2E, the Bragg period PBof the LCPH element200may be tunable via varying the intensity of the applied electric field and, accordingly, the reflection band of the LCPH element200may be tunable. In some embodiments, the in-plane pitch Pinof the LCPH element200may be tunable via varying the direction of the applied electric field and, accordingly, the diffraction angle of a diffract light of the LCPH element200may be tunable.

In some embodiments, through varying the intensity of the applied electric field and maintaining the direction of the applied electric field, the reflection band of the LCPH element200may be tunable, while the diffraction angle of a diffract light of the LCPH element200may be maintained. In some embodiments, through varying the direction of the applied electric field and maintaining the intensity of the applied electric field, the diffraction angle of a diffract light of the LCPH element200may be tunable, while the reflection band of the LCPH element200may be maintained. In some embodiment, through varying both the intensity and the direction of the applied electric field, both the diffraction angle of a diffract light of the LCPH element200and the reflection band of the LCPH element200may be adjustable.

FIGS.5A and5Billustrate electrical tuning of a diffraction angle of a diffract light of the LCPH element200operating at the heliconical state, according to an embodiment of the present disclosure.FIG.5Cillustrates an applied electric field within the LCPH element200shown inFIG.5A, according to an embodiment of the present disclosure.FIG.5Dillustrates an applied electric field within the LCPH element200shown inFIG.5B, according to an embodiment of the present disclosure. For discussion purposes, the LCPH element200shown inFIGS.5A and5Bfunctions as a reflective PVH element, and the applied electric fields within the LCPH element200shown inFIG.5CandFIG.5Dmay have different directions and the same intensity.

As shownFIG.5C, the direction of the applied electric field within the LCPH element200may be configured to be along a first direction551, which may render the LCPH element200to have a first in-plane pitch Pin-1. The first direction551may be tilted with respect to a normal550of the surface215-1or215-2of the birefringent medium layer215by a first angle θ1. As shownFIG.5A, a circularly polarized input light502may have a wavelength range within a reflection band of the LCPH element200, and a handedness that is the same as the handedness of the heliconical twist structures of the LCPH element200. The LCPH element200may substantially reflect (e.g., via backward diffraction) the circularly polarized input light502as a substantially circularly polarized output light504, which may form a first deflection (or diffraction) angle α1with respect to the surface normal550of the LCPH element200.

As shown inFIG.5D, the direction of the applied electric field within the LCPH element200may be configured to be along a second direction552, which may render the LCPH element200to have a second in-plane pitch Pin-2. The second direction552may be tilted with respect to the surface normal550of the birefringent medium layer215by a second angle β2. Referring toFIGS.5C and5D, the second angle β2may be greater than the first angle β1shown inFIG.5C, and the second in-plane pitch Pin-2may be greater than the first in-plane pitch Pin-1shown inFIG.5C. As shown inFIG.5B, the LCPH element200may substantially reflect (e.g., via backward diffraction) the circularly polarized input light502as a substantially circularly polarized output light534, which may form a second deflection (or diffraction) angle α2with respect to the surface normal550of the LCPH element200. The second deflection (or diffraction) angle α2may be less than the first deflection (or diffraction) angle α1shown in FIG.5A.

For discussion purposes,FIGS.5A-5Dshow that as the tilting of the applied electric field with respect to the surface normal550increases, the in-plane pitch Pinthe LCPH element200may increase and, accordingly, the deflection (or diffraction) angle of the diffracted light of the LCPH element200may decrease. Thus, through varying the direction of the applied electric field within the LCPH element200, the LCPH element200may function as or may be implemented in a beam steering device.

FIG.6Aillustrates an x-z sectional view of an LCPH device600, according to an embodiment of the present disclosure. The LCPH device600may include elements that are similar to or the same as those included in the LCPH element200shown inFIGS.2A-5D. Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection withFIGS.2A-5D. As shown inFIG.6A, the LCPH device600may include a plurality of LCPH elements601,602, and603, each of which may be an embodiment of the LCPH element disclosed herein, such as the LCPH element200shown inFIGS.2A-5D. The LCPH elements601,602, and603may include heliconical twist structures having the same handedness, e.g., a first handedness. Each of the LCPH elements601,602, and603may include a single pitch layer having a constant helical pitch, whereas the helical pitches of the LCPH elements601,602, and603may vary from one to another. Thus, the reflection bands of the LCPH elements601,602, and603may vary from one to another. Each reflection band may have an ultranarrow bandwidth within a range of about 5 nm to 10 nm, a range of about 10 nm to 20 nm, a range of about 20 nm to 30 nm, or a range of about 30 nm to 40 nm, etc.

In some embodiments, the helical pitches of the LCPH elements601,602, and603may be configured to be of the same order as the wavelengths of visible lights and, accordingly, the LCPH device600may have a reflection band in the visible spectrum.FIG.6Billustrates a reflection band of the LCPH device600shown inFIG.6A, according to an embodiment of the present disclosure. As shown inFIG.6B, the horizontal axis represents the wavelength (unit: nanometer (“nm”)), and the vertical axis represents the normalized reflectance. Reflection bands621,622, and623of the LCPH elements601,602, and603may respectively correspond to a red wavelength range, a green wavelength range, and a blue wavelength range, each of which has an ultranarrow bandwidth of about 20 nm. The reflection bands of the LCPH elements601,602, and603may not overlap with one another. In some embodiments, the LCPH element601,602, or603may be optically coupled with a corresponding narrowband (e.g., 20-nm bandwidth) light source, and the reflection band of the LCPH element601,602, or603may substantially match with the emission band of the corresponding narrowband light source.

Referring back toFIG.6A, the LCPH element601,602, or603may substantially reflect a circularly polarized light having a wavelength range within the corresponding reflection band and the first handedness. The LCPH element601,602, or603may substantially transmit a light having a wavelength range outside of the corresponding reflection band, independent of the polarization state thereof. In some embodiments, the directions of the applied electric fields within the LCPH elements601,602, and603may be individually or independently adjustable and, thus, the in-plane pitches of the LCPH elements601,602, and603may be individually or independently adjustable. In some embodiments, through configuring the in-plane pitches of the LCPH elements601,602, and603, the LCPH elements601,602, and603may be configured to backwardly diffract lights of the three wavelength ranges by a common diffraction angle. Thus, the LCPH device600may be configured to function as an apochromatic device, e.g., an apochromatic grating that diffracts a polychromatic input light by a common diffraction angle, or an apochromatic grating that focuses a polychromatic input light to a common focal point, etc. For example, in some embodiments, the LCPH elements601,602, and603may function as reflective polarization volume hologram (“R-PVH”) gratings, where the LCPH element601having the red reflection band may have the greatest in-plane pitch, the LCPH element603having the blue reflection band may have the smallest in-plane pitch, and the LCPH element602having the green reflection band may have a medium in-plane pitch that is between the smallest in-plane pitch and the greatest in-plane pitch.

For example, as shown inFIG.6A, an input light691of the LCPH device600may be a polychromatic light including a red portion691R, a green portion691G, and a blue portion691B. For discussion purposes,FIG.6Ashows that the LCPH device600functions as a left-handed R-PVH grating. The input light691may be a left-handed circularly polarized polychromatic light, which is substantially normally incident onto the LCPH device600. The LCPH elements601,602, and603may backwardly diffract the red portion691R, the green portion691G, and the blue portion691B of the input light691as a red light693R, a green light693G, and a blue light693B having the common diffraction angle, respectively. Thus, the red light693R, the green light693G, and the blue light693B may form a polychromatic output light693at the output side of the LCPH device600. In some embodiments, the diffraction angle of the polychromatic output light693at the output side of the LCPH device600may be adjustable via adjusting the respective directions of the applied electric fields within the LCPH elements601,602, and603.

In some embodiments, as shown inFIG.6C, the in-plane pitches of the LCPH elements601,602, and603may be configured to be the same, and the LCPH elements601,602, and603may backwardly diffract the red portion691R, the green portion691G, and the blue portion691B of the input light691as the red light693R, the green light693G, and the blue light693B having different diffraction angles.

The LCPH elements described herein may be implemented in systems or devices for imaging, sensing, communication, biomedical applications, etc. For example, the LCPH elements described herein may be implemented in various systems for augmented reality (“AR”), virtual reality (“VR”), and/or mixed reality (“MR”) applications, e.g., near-eye displays (“NEDs”), head-up displays (“HUDs”), head-mounted displays (“HMDs”), smart phones, laptops, televisions, vehicles, etc. For example, the disclosed LCPH element may be implemented as a passive or active reflective polarizer in a path-folding lens assembly (e.g., a pancake lens assembly), implemented as a light guide image combiner in a light guide display assembly, implemented as an input or output coupler (or in-coupling element or out-coupling element) in a light guide illumination assembly, or implemented as a retinal projection combiner in a retinal projection display assembly, etc. The disclosed LCPH element may also be used to provide multiple image planes, pupil steered AR, VR, and/or MR display systems (e.g., holographic near eye displays, retinal projection eyewear, and wedged waveguide displays), smart glasses for AR, VR, and/or MR applications, compact illumination optics for projectors, light-field displays, etc. In some embodiments, the disclosed LCPH element may be implemented as a passive or active reflective polarizer in an object tracking system (e.g., an eye tracking system, a face tracking system, etc.). The object tracking system including one or more disclosed LCPH elements may provide an object tracking with enhanced accuracy.

Exemplary applications of the disclosed LCPH elements in AR, VR, and/or MR systems will be explained. The various systems including one or more disclosed LCPH elements may be a part of a system for VR, AR, and/or MR applications (e.g., an NED, an HUD, an HMD, a smart phone, a laptop, or a television, etc.).FIG.7schematically illustrates an x-y sectional view of a system700, according to an embodiment of the present disclosure. As shown inFIG.7, the system700may include a display element705configured to generate an image light (or beam)722representing a virtual image, and an off-axis combiner720configured to direct the image light722toward an eyebox759of the system700. The system700may further include an eye tracking device735and a controller740. The controller740may be communicatively coupled with one or more devices in the system700, such as the display element705, the eye tracking device735, and the off-axis combiner720. The controller740may receive signals from the one or more devices, and may control the operations of the one or more devices.

In some embodiments, the display element705may include a projector (e.g., retinal projection display) configured to output the image light722. In some embodiments, the display element705may be an off-axis display element configured to provide an off-axis projection with respective to the off-axis combiner720. For example, the image light722may be an off-axis light with respective to the off-axis combiner720. In some embodiments, the display element705may include one or more narrowband light sources, e.g., outputting narrowband blue, green, and red image lights each having a bandwidth (full width at half maximum (FWHM)) within a range of about 5 nm to 10 nm, a range of about 10 nm to 20 nm, a range of about 20 nm to 30 nm, or a range of about 30 nm to 40 nm, etc. For example, the display element705may include a micro-LED display panel configured to emit blue, green, and red image lights each having a bandwidth of about 20 nm. In some embodiments, the display element705may include a laser scanning display panel configured to emit blue, green, and red image lights each having a bandwidth of several nanometers, e.g., 5 nm.

In some embodiments, the off-axis combiner720may include one or more LCPH elements disclosed herein, such as the LCPH element200shown inFIG.2A, or the LCPH device600shown inFIG.6AorFIG.6C. In some embodiments, the reflection band of the off-axis combiner720may substantially match with the emission band of the one or more narrowband light sources included in the display element705. In some embodiments, the off-axis combiner720may function as an off-axis reflective lens configured to focus the off-axis image light722to one or more spots at one or more exit pupils757within the eyebox759of the system700. An exit pupil757may be a portion of the eyebox759, where an eye pupil758of a user may be positioned to receive the image light. The size of a single exit pupil757may be larger than and comparable with the size of the eye pupil758. The exit pupils757may be sufficiently spaced apart, such that when one of the exit pupils757substantially coincides with the position of the eye pupil758, the remaining one or more exit pupils757may be located beyond the position of the eye pupil758(e.g., outside of the eye pupil758). For example, as shown inFIG.7, the off-axis combiner720may focus the off-axis image light722as an image light724propagate through one or more exit pupils757at the eyebox759.

When configured for AR or MR applications, the off-axis combiner720may also combine the image light722received from the display element705and a light (or beam)710from a real-world environment (referred to as a real-world light710), and direct both of the lights710and722toward the eyebox759. Thus, the off-axis combiner720may also be referred to as an off-axis image combiner. In some embodiments, the system700may include a compensator725coupled with (e.g., stacked with) the off-axis combiner720. The off-axis combiner720may be disposed between the compensator725and the eyebox759. The real-world light710may be incident onto the compensator725before being incident onto the off-axis combiner720. In some embodiments, the controller740may be configured to control the compensator725and the off-axis combiner720to provide opposite steering effects and lensing effects to the real-world light710. For example, when the optical powers provided by the compensator725and the off-axis combiner720have opposite signs and a substantially same absolute value, the steering provided by the compensator725and the off-axis combiner720may have opposite directions. Thus, the compensator725may compensate for the distortion of the real-world light710caused by the off-axis combiner720, such that images of real-world objects viewed through the system700may be substantially unaltered. In some embodiments, when the system700is configured for VR applications, the compensator725may be omitted.

In some embodiments, the off-axis combiner720may be a passive element that is not tunable by an external field. In some embodiments, the off-axis combiner720may be an active element that is tunable by an external field. For example, the optical power of the off-axis combiner720may be tunable by an applied voltage. In some embodiments, the birefringent medium layer included in the off-axis combiner720may include a plurality of sub-layers stacked together. The plurality of sub-layers may be configured to have high diffraction efficiencies at a plurality of wavelengths, (e.g., red, green, and blue wavelength ranges), thereby enabling a full color display. For example, the off-axis image light722may be a visible polychromatic light, and the respective sub-layers may be configured to focus the respective portions of the off-axis image light722associated with different wavelength ranges to the same exit pupil757.

In some embodiments, the birefringent medium layer included in the off-axis combiner720may include a plurality of sub-layers stacked together, and different sub-layers may be configured to reflect and focus the off-axis image light722to propagate through different exit pupils757. That is, different sub-layers may be configured to steer the off-axis image light722by different steering angles to propagate through different exit pupils757. In some embodiments, the plurality of sub-layers may function as passive elements, each of which may be configured to simultaneously reflect and focus the off-axis image light722to propagate through one of the exit pupils757with a relatively low efficiency. The plurality of sub-layers may be configured to simultaneously reflect and focus the off-axis image light722to propagate through a plurality of exit pupils757forming the eyebox759. For discussion purposes, each exit pupil757may also be referred to as a sub-eyebox, and the eyebox759formed by the plurality of exit pupils757may also be referred to as an uncompressed eyebox, which is relatively large.

In some embodiments, the plurality of sub-layers may function as active elements, each of which may be configured to operate in an active state to reflect the off-axis image light722to an exit pupil757with a relatively high efficiency, and operate in a non-active state to transmit the off-axis image light722. In some embodiments, one or more (not all) of the sub-layers may be configured to operate in the active state to focus the off-axis image light722to propagate through one or more exit pupils757(or one or more sub-eyeboxes), forming a compressed eyebox having a size smaller than a size of the uncompressed eyebox. The remaining sub-layers may operate in the non-active state to transmit the off-axis image light722. In some embodiments, the controller740may be communicatively coupled with one or more power sources (not shown) to adjust the voltages applied to the respective sub-layers included in the off-axis combiner720.

In some embodiments, the eye tracking device735may include one or more light sources (e.g., infrared light sources) and one or more optical sensors. The one or more light sources may be configured to emit infrared (“IR”) lights to illuminate one or both eyes of the user, and the optical sensors may be configured to receive the IR lights reflected from the eyes. In some embodiments, the optical sensors may be configured to generate image data of one or both eyes of the user based on the received IR lights. For example, the optical sensors may be imaging devices, such as cameras. In some embodiments, a processor included in the eye tracking device735may be configured to obtain, in real time, the eye-tracking information relating to the eye pupil758by analyzing the captured images of the eye pupil758.

The eye-tracking information may include at least one of a position (or location), a moving direction, a size, or a viewing direction of the eye pupil758. The position, moving direction, size, or viewing direction of the eye pupil758may be dynamically changing. Thus, the eye tracking device735may dynamically capture the images of the eye pupil758and dynamically obtain and/or provide the eye-tracking information in real time. In some embodiments, the eye tracking device735may measure or determine (e.g., through the processor) the position and/or movement of the eye pupil758up to six degrees of freedom (i.e., 3D position, roll, pitch, and yaw).

In some embodiments, the eye tracking device735may transmit, through a transmitter included in the eye tracking device735, the eye-tracking information to the controller740. In some embodiments, the eye tracking device735may transmit the images (i.e., image data) of the eye pupil758to the controller740, and the controller740may analyze the images to obtain the eye-tracking information in real time. In some embodiments, the controller740may determine, based on one or more types of the eye-tracking information (e.g., based on the position of the eye pupil758), the operation state of the off-axis combiner720, such as, the operation states of the active sub-layers included in the off-axis combiner720.

According to the eye-tracking information, the off-axis combiner720may provide different steering angles to the off-axis image light722to focus the off-axis image light722to propagate through different exit pupils757. In other words, the off-axis combiner720may function as a pupil steering element that provides a pupil steering function. For example, during an operation, based on the eye-tracking information, the controller740may control one or more of the sub-layers included in the off-axis combiner720to operate in the active state, and the remaining sub-layers to operate in the non-active state. For illustrative purposes,FIG.7shows two operation states of the off-axis combiner720. For example, at a first time instance, the eye tracking device735may detect that the eye pupil758of the user is located at a position P1at the eyebox759. Based on the eye-tracking information, the controller740may control a first sub-layer in the off-axis combiner720to operate in the active state while controlling the remaining sub-layers to operate in the non-active state. The first sub-layer may reflect and focus the off-axis image light722as an image light724, which propagates through to an exit pupil757(e.g., a first sub-eye box) that substantially coincides with the position P1of the eye pupil758.

At a second time instance, the eye tracking device735may detect that the eye pupil758of the user has moved to a new position P2at the eyebox759in the x-axis direction from the previous position P1. Based on new eye-tracking information relating to the new position P2, the controller740may control a second, different sub-layer in the off-axis combiner720to operate in the active state while controlling the remaining sub-layers to operate in the non-active state. The second sub-layer may reflect and focus the off-axis image light722as an image light726(represented by dashed lines), which propagates through an exit pupil757(e.g., a second sub-eye box) that substantially coincides with the position P2of the eye pupil758.

For discussion purposes,FIG.7shows that the off-axis combiner720provides a 1D pupil steering, e.g., steering the exit pupil757in the x-axis direction shown inFIG.7. In some embodiments, although not shown, the off-axis combiner720may provide a 2D pupil steering, e.g., steering the exit pupil757in two different directions (e.g., the x-axis direction and the y-axis direction shown inFIG.7). In some embodiments, although not shown, the off-axis combiner720may provide a 3D pupil steering, e.g., steering the exit pupil757in three different directions (e.g., the x-axis direction, the y-axis direction, and the z-axis direction shown inFIG.7). For example, the off-axis combiner720may include three birefringent medium layers configured to steer the exit pupil757in the x-axis direction, the y-axis direction, and the z-axis direction, respectively.

FIG.8Aschematically illustrates a diagram of a system800, according to an embodiment of the present disclosure. The system800may also be referred to as a light guide display system or assembly. As shown inFIG.8A, the system800may include a light source assembly805that includes a display element (e.g., a display panel)820and a collimating lens825, a light guide810coupled with an in-coupling element (or input coupler)835and an out-coupling element (or output coupler)845, and the controller740. The light guide810coupled with the in-coupling element835and the out-coupling element845may also be referred to as a light guide image combiner.

The display panel820may output an image light829representing a virtual image (having a predetermined image size associated with a linear size of the display panel820) toward the collimating lens825. The image light829may be a divergent image light including a bundle of rays. For illustrative purposes,FIG.8Ashows a single ray of the image light829. The collimating lens825may transmit the image light829as an image light830having a predetermined input field of view (“FOV”) (e.g., a) toward an input side of the light guide810. The collimating lens825may transform or convert a linear distribution of the pixels in the virtual image formed by the image light829into an angular distribution of the pixels in the image light830having the predetermined input FOV. Each ray in the in the image light830may represent an FOV direction of the input FOV. For illustrative purposes,FIG.8Ashows a single ray (e.g., central ray) of the image light830that is normally incident onto the in-coupling element835, and the single ray of the image light830may represent a single FOV direction (e.g., 0° FOV direction) of the input FOV.

The in-coupling element835may couple the image light830into the light guide810as an in-coupled image light831, which may propagate inside the light guide810toward the out-coupling element845via total internal reflection (“TIR”). The out-coupling element845may couple the in-coupled image light831out of the light guide810as a plurality of output image lights832at different locations along the longitudinal direction (e.g., x-axis direction) of the light guide810, each of which may have an output FOV that may be substantially the same as the input FOV (e.g., as represented by an angle α). For discussion purposes,FIG.8Ashows three output image lights832, and shows a single ray (e.g., central ray) of each output image light832. At least one of the in-coupling element835or the out-coupling element845may include one or more LCPH elements disclosed herein, such as the LCPH element200shown inFIG.2A, or the LCPH element600shown inFIG.6AorFIG.6C. In some embodiments, the LCPH element may be configured to function as a grating that couples the image light into the light guide810or out of the light guide810via diffraction. Thus, the light guide810coupled with the in-coupling element835and the out-coupling element845may replicate the image light830at the output side of the light guide810, to expand an effective pupil of the system800.

For discussion purposes,FIG.8Ashows a one-dimensional pupil expansion along the x-axis direction inFIG.8A. In some embodiments, the system800may also provide a two-dimensional pupil expansion, e.g., along both the x-axis direction and the y-axis direction inFIG.8A. For example, in some embodiments, although not shown, the system800may also include a redirecting element (or folding element) coupled to the light guide810, and configured to redirect the in-coupled image light831to the out-coupling element845. The redirecting element may be configured to expand the input image light830in a first direction, e.g., the y-axis direction, and the out-coupling element845may be configured to expand the input image light830) in a second, different direction, e.g., the x-axis direction.

In some embodiments, the redirecting element may include one or more disclosed LCPH elements functioning as a grating that redirects the in-coupled image light831to the out-coupling element845. The plurality of image lights832may propagate through the exit pupils757located in the eyebox759of the system800. The light guide810and the out-coupling element845may also transmit a light842from a real-world environment (referred to as a real-world light842), combining the real-world light842with the output image light832and delivering the combined light to the eye760. Thus, the eye760may observe the virtual scene optically combined with the real world scene.

In the embodiment shown inFIG.8A, the light guide image combiner may generate an image of the display element820at an image plane that has an infinite depth (or image plane distance) with respect to the eye pupil758positioned at the eyebox759. In some embodiments, the light guide image combiner may generate an image of the display element820at an image plane that has a finite depth (or image distance) with respect to the eye pupil758positioned at the eyebox759.FIG.8Bschematically illustrates a diagram of a system850, according to an embodiment of the present disclosure. The system850may also be referred to as a light guide display system or assembly. The system850may include elements that are similar to or the same as those included in the system800shown inFIG.8A. Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection withFIG.8A.

As shown inFIG.8B, the system850may include the light source assembly805, and the light guide810coupled with the in-coupling element835and the output-coupling element845(also referred to as the light guide image combiner). The system800may also include a lens or lens assembly853disposed between the light guide image combiner and the eyebox759. In some embodiments, the lens assembly853may be configured to provide at least one of an adjustable optical power or an adjustable steering angle to the output image lights832.

In some embodiments, based on the eye tracking information from the eye tracking system (not shown), the controller740may be configured to control the lens assembly853to steer and focus the plurality of output image lights832to an image plane within the eyebox759, where one or more exit pupils757are located. In some embodiments, the lens assembly853may be configured to provide a 3D beam steering to the output image lights832. For example, the lens assembly853may be configured to laterally steer (or shift) the focus of the output image lights832in one or two dimensions (e.g., an x-axis direction and/or a y-axis direction). In some embodiments, the lens assembly853may also be configured to vertically shift the image plane, at which the output image lights832are focused, in a third dimension (e.g., in a z-axis direction). Thus, a continuous or discrete shift of the exit pupil757of the system850may be provided in a 3D space to cover an expanded eyebox based on the eye tracking information.

In some embodiments, the vertical distance of the image plane of the display element820with respect to the eyebox759may be adjusted for addressing the vergence accommodation conflict. Accordingly, the user experience of the system850may be improved. For example, the display element820may display a virtual image. Based on the eye tracking information provided by the eye tracking system (not shown), the controller740may determine a virtual object within the virtual image at which the eyes760are currently looking. The controller740may determine a vergence depth (dv) of the gaze of the user based on the gaze point or an estimated intersection of gaze lines determined by the eye tracking system. The gaze lines may converge or intersect at the distance dv, where the virtual object is located. The controller740may control the lens assembly853to adjust the optical power to provide an accommodation that matches the vergence depth (dv) associated with the virtual object at which the eyes760are currently looking, thereby reducing the accommodation-vergence conflict in the system850. For example, the controller740may control the lens assembly853to operate in a desirable operation state to provide an optical power corresponding to a focal plane (or an image plane) that matches the vergence depth (dv).

In some embodiments, when used for AR and/or MR applications, in addition to the lens assembly853(referred to as a first lens assembly853), the system850may further include a second lens assembly855. The first lens assembly853and the second lens assembly855may be disposed at two sides of the light guide810. The controller740may be communicatively coupled with the second lens assembly855. In some embodiments, when used for AR and/or MR applications, the controller740may be configured to control the first lens assembly853and the second lens assembly855to provide opposite steering effects and lensing effects to the real-world light842. For example, the optical powers provided by the first lens assembly853and the second lens assembly855may have opposite signs and a substantially same absolute value, the steering provided by the first lens assembly853and the second lens assembly855may have opposite directions. Thus, the second lens assembly855may be configured to compensate for the distortion of the real-world light842caused by the first lens assembly853, such that images of the real-world objects viewed through the system850may be substantially unaltered.

In some embodiments, each of the first lens assembly853and the second lens assembly855may be an active element. For example, the steering effect and lensing effect of the first lens assembly853or the second lens assembly855may be adjustable by an external field. When the birefringent medium layer included in the first lens assembly853or the second lens assembly855includes a plurality of sub-layers, the steering effect and lensing effect of each sub-layer may be adjustable by an external field. In some embodiments, each of the first lens assembly853and the second lens assembly855may be a passive element. Each of the first lens assembly853and the second lens assembly855may be coupled with a switchable halfwave plate. The switchable halfwave plate may control the polarization of a light that is to be incident onto the first lens assembly853or the second lens assembly855. Thus, the steering effect and lensing effect of the first lens assembly853or the second lens assembly855may be adjustable by controlling the switchable halfwave plate. When the birefringent medium layer included in the first lens assembly853or the second lens assembly855includes a plurality of sub-layers, each sub-layer may be coupled with a switchable halfwave plate, and the steering effect and lensing effect of each sub-layer may be individually or independently adjustable by controlling the corresponding switchable halfwave plate.

Referring toFIGS.8A and8B, in some embodiments, the display element (e.g., display panel)820may include one or more narrowband light sources, e.g., one or more LEDs, a one or more SLEDs, one or more laser diodes, or a combination thereof, etc. In some embodiments, the one or more narrowband light sources may output narrowband blue, green, and red image lights each having a bandwidth (full width at half maximum (FWHM)) within a range of about 5 nm to 10 nm, a range of about 10 nm to 20 nm, a range of about 20 nm to 30 nm, or a range of about 30 nm to 40 nm, etc. For example, the display element (e.g., display panel)820may include a micro-LED display panel configured to emit blue, green, and red image lights each having a bandwidth of about 20 nm. In some embodiments, the display element (e.g., display panel)820may include a laser scanning display panel configured to emit blue, green, and red image lights each having a bandwidth of several nanometers, e.g., 5 nm. In some embodiments, the reflection band of at least one of the in-coupling element835, the out-coupling element845, the redirecting element first lens assembly853, or the second lens assembly855may substantially match with the emission band of the one or more narrowband light sources included in the display element (e.g., display panel)820.

FIG.9Aschematically illustrates a diagram of a system900, according to an embodiment of the present disclosure. As shown inFIG.9A, the system900may include a light guide illumination assembly903, a display panel901, and a lens assembly902. The light guide illumination assembly903may include a light source assembly940, and a light guide930coupled with an in-coupling element935and an out-coupling element945. The display panel901and the lens assembly902may be disposed at opposite sides of the light guide930. The display panel901and the lens assembly902may be arranged in parallel, and may be aligned on a same axis970. The axis970may be an optical axis of the lens assembly902, or an axis of symmetry of the display panel901. The light guide930may be arranged in parallel with the display panel901and the lens assembly902, with the surface normal of the light guide930being parallel with the axis970. The light source assembly940may output a light951toward the light guide930.

The light951may be guided by the light guide930to the display panel901for illuminating the display panel901. The in-coupling element935may couple the light951into the light guide930as an in-coupled light953that prorogates along the light guide930toward the out-coupling element945via total internal reflection (“TIR”). The out-coupling element945may couple the in-coupled light953out of the light guide930as a light955propagating toward the display panel901to illuminate the display panel901. Thus, the light955may also be referred to as an illuminating light955. In some embodiments, the in-coupling element935may include a direct edge illumination, an input grating, a prism, a mirror, and/or photonic integrated circuits. In some embodiments, at least one of the in-coupling element935or the out-coupling element945may include one or more LCPH elements disclosed herein, such as the LCPH element200shown inFIG.2A, or the LCPH element600shown inFIG.6AorFIG.6C. In some embodiments, the one or more LCPH elements may be configured to function as a grating that couples the illumination light into the light guide910or out of the light guide910via diffraction.

The light955may be normally incident onto the display panel901. The display panel901may modulate and convert the light955into an image light957that represents a virtual image generated by the display panel901. The lens assembly902may focus the image light957to an exit pupil757in the eyebox759. Thus, the eye760located at the exit pupil757may perceive the image light959that represents the virtual image displayed on the display panel901. In some embodiments, the lens assembly902may be configured to provide at least one of an adjustable optical power or an adjustable steering angle to the image light959.

The display panel901may be a reflective display panel or a transmissive display panel. For illustrative purposes,FIG.9Ashows the display panel901as a reflective display panel (e.g., a reflective LCD panel) that modulates and reflects the light955into the image light957. In a system980shown inFIG.9B, a display panel982may be a transmissive display panel (e.g., a transmissive LCD panel) that modulates and transmits the light955as an image light987that represents a virtual image generated by the display panel982. The display panel982may be disposed between the lens assembly902and the light guide930, and the lens assembly902may focus the image light987to the exit pupil757in the eyebox759. In some embodiments, as shown inFIG.9B, the system980may also include a polarizer or quarter-wave plate981disposed between the display panel982and the light guide930. The polarizer or quarter-wave plate981may be configured to convert the illuminating light955into an illuminating light985having a predetermined polarization state, e.g., a linear polarization.

Referring toFIGS.9A and9B, in some embodiments, the light source assembly940may include one or more narrowband light sources, e.g., one or more LEDs, a one or more SLEDs, one or more laser diodes, or a combination thereof, etc. In some embodiments, the one or more narrowband light sources may output narrowband blue, green, and red image lights each having a bandwidth (full width at half maximum (FWHM)) within a range of about 5 nm to 10 nm, a range of about 10 nm to 20 nm, a range of about 20 nm to 30 nm, or a range of about 30 nm to 40 nm, etc. For example, the light source assembly940may include one or more LEDs configured to emit blue, green, and red image lights each having a bandwidth of about 20 nm. In some embodiments, the light source assembly940may include one or more laser diodes configured to emit blue, green, and red image lights each having a bandwidth of several nanometers, e.g., 5 nm. In some embodiments, the reflection band of at least one of the in-coupling element935or the out-coupling element945may substantially match with the emission band of the one or more narrowband light sources included in the light source assembly940.

FIG.10Aschematically illustrates a system1000, according to an embodiment of the present disclosure. The system1000may include a light source assembly (e.g., a display element)1050configured to output an image light1021(e.g., a divergent image light) representing a virtual image. The system1000may also include a path-folding lens assembly (e.g., pancake lens assembly)1001configured to fold the optical path of the image light1021, and transform the rays (forming the divergent image light1021) emitted from each light outputting unit of the display element1050into a bundle of parallel rays that substantially cover one or more exit pupils757in the eyebox759of the system1000. Due to the path folding, the lens assembly1001may increase a field of view (“FOV”) of the system1000without increasing the physical distance between the display element1050and the eyebox region759, and without compromising the image quality. The path-folding lens assembly1001may include one or more LCPH elements disclosed herein, such as the LCPH element200shown inFIG.2A, or the LCPH device600shown inFIG.6AorFIG.6C.

In some embodiments, the display element1050may be a monochromatic display that includes a narrowband monochromatic light source (e.g., a 30-nm-bandwidth light source). In some embodiments, the display element1050may be a polychromatic display (e.g., a red-green-blue (“RGB”) display) that includes a broadband polychromatic light source (e.g., 300-nm-bandwidth light source covering the visible wavelength range). In some embodiments, the display element1050may be a polychromatic display (e.g., an RGB display) including a stack of a plurality of monochromatic displays, which may include corresponding narrowband monochromatic light sources respectively.

In some embodiments, the path-folding lens assembly1001may include a first optical element (e.g., a first optical lens)1005and a second optical element (e.g., a second optical lens)1010. In some embodiments, the path-folding lens assembly1001may be configured as a monolithic pancake lens assembly without any air gaps between optical elements included in the path-folding lens assembly. In some embodiments, one or more surfaces of the first optical element1005and the second optical element1010may be shaped (e.g., curved) to compensate for field curvature. In some embodiments, one or more surfaces of the first optical element1005and/or the second optical element1010may be shaped to be spherically concave (e.g., may be a portion of a sphere), spherically convex, a rotationally symmetric asphere, a freeform shape, or some other shape that can mitigate field curvature. In some embodiments, the shape of one or more surfaces of the first optical element1005and/or the second optical element1010may be designed to additionally compensate for other forms of optical aberration. The disclosed LCPH element may be formed on one or more curved surfaces of at least one of the first optical element1005or the second optical element1010. In some embodiments, one or more of the optical elements within the path-folding lens assembly1001may have one or more coatings, such as an anti-reflective coating, to reduce ghost images and enhance contrast. In some embodiments, the first optical element1005and the second optical element1010may be coupled together by an adhesive1015. Each of the first optical element1005and the second optical element1010may include one or more optical lenses. In some embodiments, at least one of the first optical element1005or the second optical element1010may have at least one flat surface.

The first optical element1005may include a first surface1005-1facing the display element1050and an opposing second surface1005-2facing the eye760. The first optical element1005may be configured to receive an image light at the first surface1005-1from the display element1050and output an image light with an altered property at the second surface1005-2. The path-folding lens assembly1001may also include a linear polarizer1002, a waveplate1004, and a mirror1006arranged in an optical series, each of which may be an individual layer, film, or coating disposed at (e.g., bonded to or formed at) the first optical element1005. The linear polarizer1002, the waveplate1004, and the mirror1006may be disposed at (e.g., bonded to or formed at) the first surface1005-1or the second surface1005-2of the first optical element1005. For illustrative purposes,FIG.10Ashows that the linear polarizer1002and the waveplate1004are disposed at (e.g., bonded to or formed at) the first surface1005-1facing the display element1050, and the mirror1006is disposed at (e.g., bonded to or formed at) the second surface1005-2facing the second optical element1010. Other arrangements are also contemplated.

In some embodiments, the waveplate1004may be a quarter-wave plate (“QWP”). A polarization axis of the waveplate1004may be oriented relative to the polarization direction of a linearly polarized light to convert the linearly polarized light into a circularly polarized light or vice versa for a visible spectrum and/or an IR spectrum. In some embodiments, for an achromatic design, the waveplate1004may include a multilayer birefringent material (e.g., a polymer, liquid crystals, or a combination thereof) to produce quarter-wave birefringence across a wide spectral range. For example, an angle between the polarization axis (e.g., the fast axis) of the waveplate1004and the transmission axis of the linear polarizer1002may be configured to be in a range of about 35-50 degrees. In some embodiments, for a monochrome design, an angle between the polarization axis (e.g., the fast axis) of the waveplate1004and the transmission axis of the linear polarizer1002may be configured to be about 45 degrees. In some embodiments, the mirror1006may be a polarization non-selective partial reflector that is partially reflective to reflect a portion of a received light. In some embodiments, the mirror1006may be configured to transmit about 50% and reflect about 50% of a received light, and may be referred to as a “50/50 mirror.” In some embodiments, the handedness of the reflected light may be reversed, and the handedness of the transmitted light may remain unchanged.

The second optical element1010may have a first surface1010-1facing the first optical element1005and an opposing second surface1010-2facing the eye760. The path-folding lens assembly1001may also include a reflective polarizer1008, which may be an individual layer, film, or coating disposed at (e.g., bonded to or formed at) the second optical element1010. The reflective polarizer1008may be configured to primarily reflect a circularly polarized light having a first handedness and primarily transmit a circularly polarized light having a second handedness that is orthogonal to the first handedness.

In the embodiment shown inFIG.10A, the reflective polarizer1008may include one or more LCPH elements disclosed herein. Thus, the light leakage of the reflective polarizer1008for an input light having a large incident angle (e.g., greater than or equal to 60°) may be reduced. Accordingly, the ghost image caused by the light leakage may be suppressed. In some embodiments, the reflective polarizer1008may function as a passive reflective polarizer with zero optical power. In some embodiments, the reflective polarizer may function as an active reflective polarizer with an adjustable optical power, for addressing the vergence accommodation conflict in the system1001.

The reflective polarizer1008may be disposed at (e.g., bonded to or formed at) the first surface1010-1or the second surface1010-2of the second optical element1010and may receive a light output from the mirror1006. For illustrative purposes,FIG.10Ashows that the reflective polarizer1008is disposed at (e.g., bonded to or formed at) the first surface1010-1of the second optical element1010. That is, the reflective polarizer1008may be disposed between the first optical element1005and the second optical element1010. For example, the reflective polarizer1008may be disposed between the second surface1010-2of the second optical element1010and the adhesive layer1015. In some embodiments, the reflective polarizer1008may be disposed at the second surface1010-2of the second optical element1010.

Referring toFIG.10A, in some embodiments, the image light1021emitted from the display element1050may be an unpolarized light. The linear polarizer1002and the waveplate1004may be replaced by a circular polarizer, which may be configured to convert the unpolarized light into a circularly polarized light, and direct the circularly polarized light toward the mirror1006. In some embodiments, the image light1021emitted from the display element1050may be a linearly polarized light, and the linear polarizer1002may be omitted. A polarization axis of the waveplate1004may be oriented relative to the polarization direction of the linearly polarized light to convert the linearly polarized light into a circularly polarized light or vice versa for a visible spectrum and/or an IR spectrum. In some embodiments, the image light1021emitted from the display element1050may be a circularly polarized light, and the linear polarizer1002and the waveplate1004may be omitted.

In some embodiments, one or more of the first surface1005-1and the second surface1005-2of the first optical element1005and the first surface1010-1and the second surface1010-2of the second optical element1010may be curved surface(s) or flat surface(s). In some embodiments, the path-folding lens assembly1001may have one of the optical elements1005and1010, or may include more than two optical elements that may be similar to the optical element1005or1010. In some embodiments, the path-folding lens assembly1001may further include other optical elements in addition to the first and second optical elements1005and1010, such as one or more linear polarizers, one or more waveplate, one or more circular polarizers, etc.

FIG.10Billustrates a schematic cross-sectional view of an optical path1060of a light propagating in the path-folding lens assembly1001shown inFIG.10A, according to an embodiment of the present disclosure. In the light propagation path1060, the change of polarization of the light is shown. Thus, the first optical element1005and the second optical element1010, which are presumed to be lenses that do not affect the polarization of the light, are omitted for the simplicity of illustration. InFIG.10B, the letter “R” appended to a reference number (e.g., “1027R”) denotes a right-handed circularly polarized light, and the letter “L” appended to a reference number (e.g., “1025L”) denotes a left-handed circularly polarized light, the letter “s” appended to a reference number (e.g., “1023s”) denotes an s-polarized light.

For discussion purposes, as shown inFIG.10B, the linear polarizer1002may be configured to transmit an s-polarized light and block a p-polarized light, and the reflective polarizer1008may be a left-handed reflective polarizer configured to reflect a left-handed circularly polarized light and transmit a right-handed circularly polarized light. For illustrative purposes, the display element1050, the linear polarizer1002, the waveplate1004, the mirror1006, and the reflective polarizer1008are illustrated as having flat surfaces inFIG.10B. In some embodiments, one or more of the display element1050, the linear polarizer1002, the waveplate1004, the mirror1006, and the reflective polarizer1008may include a curved surface.

As shown inFIG.10B, the display element1050may generate the unpolarized image light1021covering a predetermined spectrum, such as a portion of the visible spectral range or substantially the entire visible spectral range. The unpolarized image light1021may be transmitted by the linear polarizer1002as an s-polarized image light1023s, which may be transmitted by the waveplate1004as a left-handed circularly polarized image light1025. A first portion of the left-handed circularly polarized image light1025may be reflected by the mirror1006as a right-handed circularly polarized image light1027toward the waveplate1004, and a second portion of the left-handed circularly polarized image light1025may be transmitted as a left-handed circularly polarized image light1028toward the reflective polarizer1008. The left-handed circularly polarized image light1028may be reflected by the reflective polarizer1008as a left-handed circularly polarized image light1029toward the mirror1006. The left-handed circularly polarized image light1029may be reflected by the mirror1006as a right-handed circularly polarized image light1031, which may be transmitted through the reflective polarizer1008as a right-handed circularly polarized image light1033toward the eyebox759.

FIG.11schematically illustrates an x-z sectional view of a system1100, according to an embodiment of the present disclosure. The system1100may include the display element1050(which is an example of a light source) configured to output an image light1121representing a virtual image, and a path-folding lens assembly1101(also referred to as a lens assembly1101) configured to fold the path of the image light1121from the display element1050to the eyebox759. The lens assembly1101may be disposed between the display element1050and the eyebox759. The lens assembly1101may transform the rays (forming a divergent image light) emitted from each light outputting unit of the display element1050into a bundle of parallel rays that substantially cover one or more exit pupils757in the eyebox759of the system1100. For illustrative purposes,FIG.11shows a single ray of the image light1121emitted from a light outputting unit (e.g., a pixel) at the upper half of the display element1050. The exit pupil757may correspond to a spatial zone where the eye pupil758of the eye760may be positioned in the eyebox759of the system1100to perceive the virtual image.

The lens assembly1101may include a first circular polarizer1103, a first polarization selective reflector1105(e.g., a first reflective PVH element configured with a first optical power (i.e., functioning as a first PVH lens)), a polarization non-selective partial reflector1107(also referred to as a partial reflector1107), a second polarization selective reflector1115(e.g., a second reflective PVH element configured with a second optical power (i.e., functioning as a second PVH lens)), and a second circular polarizer1113arranged in an optical series. For discussion purposes, the first polarization selective reflector1105and the second polarization selective reflector1115are referred to as a first PVH element1105and a second PVH element1115, respectively.

In the embodiment shown inFIG.11, at least one of the first PVH element1105or the second PVH element1115may include one or more disclosed LCPH elements, e.g., one or more disclosed passive or active LCPH elements. In some embodiments, the birefringent medium layer included in at least one of the first PVH element1105or the second PVH element1115may include a plurality of sub-layers.

The partial reflector1107may be configured to partially transmit an input light while maintaining the polarization and propagation direction, and partially reflect the input light while changing the polarization, independent of the polarization of the input light. That is, regardless of the polarization of the input light, the partial reflector1107may partially transmit the input light and partially reflect the input light. For discussion purposes, the partial reflector1107is also referred to as a mirror. In some embodiments, the mirror1107may be configured to transmit about 50% of an input light and reflect about 50% of the input light (referred to as a 50/50 mirror).

FIG.11illustrates an optical path or a propagation path of the image light1121propagating from the display element1050to the eyebox759through the lens assembly1101. In below figures, the letter “R” appended to a reference number (e.g., “1124R”) denotes a right-handed circularly polarized light, and the letter “L” appended to a reference number (e.g., “1123L”) denotes a left-handed circularly polarized light, the letter “s” appended to a reference number denotes an s-polarized light, and the letter “p” appended to a reference number denotes a p-polarized light.

In the embodiment shown inFIG.11, the first PVH element1105and the second PVH element1115may have the same optical power and different polarization selectivities (e.g., may reflect lights of orthogonal polarizations). For example, the first PVH element1105may function as a right-handed PVH lens that reflects and converges, via diffraction, a right-handed circularly polarized light, and transmits a left-handed circularly polarized light with negligible or zero diffraction. The second PVH element1115may function as a left-handed PVH lens that reflects and converges, via diffraction, a left-handed circularly polarized light, and transmits a right-handed circularly polarized light with negligible or zero diffraction. A distance (e.g., L1) between the first PVH element1105and the mirror1107may be equal to a distance (e.g., L1) between the second PVH element1115and the mirror1107. In some embodiments, the first PVH element1105and the second PVH element1115may have different optical powers, and the distance between the first PVH element1105and the mirror1107may be different from the distance the second PVH element1115and the mirror1107.

As shown inFIG.11, the first circular polarizer1103may convert the image light1121into an image light1122L. The first PVH element1105may substantially transmit the image light1122L as an image light1123L toward the mirror1107. The mirror1107may transmit a first portion of the image light1123L as an image light1125L toward the second PVH element1115, and reflect a second portion of the image light1123L back to the first PVH element1105as an image light1124R. The second PVH element1115may substantially reflect and converge, via diffraction, the image light1125L as an image light1127L toward the mirror1107. The mirror1107may transmit a first portion of the image light1127L toward the first PVH element1105as a left-handed circularly polarized image light (not shown), and reflect a second portion of the image light1127L back to the second PVH element1115as an image light1129R. The second PVH element1115may substantially transmit the image light1129R while maintaining the polarization and propagation direction. The second circular polarizer1113may transmit the image light1129R as an image light1131R toward the eyebox759.

When the image light1123L is normally incident onto the mirror1107, the image light1124R may propagate in a direction opposite to the propagation direction of the image light1123L. That is, the image light1124R and the image light1123L may substantially coincide with one another and have opposite propagation directions. To better illustrate the optical paths of the image light1124R and the image light1123L,FIG.11shows a small gap between the image light1124R and the image light1123L. The first PVH element1105may reflect and converge, via diffraction, the image light1124R as an image light1126R toward the mirror1107. The mirror1107may transmit a first portion of the image light1126R toward the second PVH element1105as an image light1128R, and reflect a second portion of the image light1126R back to the first PVH element1105as a left-handed circularly polarized image light (not shown). The second PVH element1115may substantially transmit the image light1128R, while maintaining the propagation direction and the polarization. The second circular polarizer1113may transmit the image light1128R as an image light1130R toward the eyebox759.

In the embodiment shown inFIG.11, both of the first PVH element1105and the second PVH element1115may be passive elements, or both of the first PVH element1105and the second PVH element1115may be active elements configured to operate in the active state. As the first PVH element1105and the second PVH element1115have the same optical power, and the same axial distance (e.g., L1) to the mirror1107along an optical axis1120of the system1100, the image light1130R and the image light1131R may substantially coincide or overlap with one another, forming a single image with a high image quality within the eyebox759. When the distance between the between the first PVH element1105and the mirror1107is different from the distance between the second PVH element1115and the mirror1107, the optical powers of the first PVH element1105and the second PVH element1115may be configured to be different, and additional optical elements may be included such that the image light1130R and the image light1131R may still substantially coincide or overlap with one another.

FIG.13Aillustrates an x-z sectional view of a system1300, according to an embodiment of the present disclosure. The system1300may include elements that are similar to or the same as those included in the system1100shown inFIG.11. Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection withFIG.11. As shown inFIG.13A, the system1300may include the display element1050, and a path-folding lens assembly1301(also referred to as lens assembly1301) configured to fold the path of an image light emitted from the display element1050to the eyebox759. The lens assembly1301may include the first circular polarizer1103, the first PVH lens1105(also referred to as a first lens1105), the mirror1107, the second PVH lens1115(also referred to as a second lens1115), and the second circular polarizer1113arranged in an optical series.

The system1300may also include a transmissive lens1307(also referred to as a third lens1307) disposed between the eyebox759and the second circular polarizer1113. The transmissive lens1307may include a conventional solid lens including at least one curved surface (e.g., a glass lens, a polymer lens, or a resin lens, etc.), a liquid lens, a Fresnel lens, a meta lens, a transmissive PVH lens, etc. The transmissive lens1307may be configured with a fixed optical power or a tunable optical power. For discussion purposes,FIG.13Ashows that the transmissive lens1307includes flat surfaces. In some embodiments, the transmissive lens1307may include at least one curved surface.

In the embodiment shown inFIG.13A, each of the first PVH lens1105and the second PVH lens1115may be an active element that is switchable between operating in an active state and operating in a non-active state. When operating in the active state, the first PVH lens1105or the second PVH lens1115may selectively reflect or transmit an input light depending on a polarization of the input light. When operating in the non-active state, the first PVH lens1105or the second PVH lens1115may transmit an input light independent of the polarization of the input light. Thus, the first PVH lens1105or the second PVH lens1115operating in the active state may have a polarization selective optical power (e.g., zero or non-zero optical power depending on the polarization of the input light), and the first PVH lens1105or the second PVH lens1115operating in the non-active state may have a zero optical power independent of the polarization of the input light. For example, the first PVH lens1105or the second PVH lens1115may operate in the active state when an applied voltage is less than or equal to a first threshold value (e.g., a voltage that is insufficient to reorientate the LC molecules), and may operate in the non-active state when the applied voltage is equal to or greater than a second threshold value (e.g., a voltage that is sufficiently high to reorientate the LC molecules to be substantially parallel with an electric field direction).

In some embodiments, the controller740(not shown) may be communicatively coupled with the first PVH lens1105and the second PVH lens1115to control the operation state thereof. For example, the first PVH lens1105or the second PVH lens1115may be electrically coupled with a power source (not shown). The controller740may control the output of the power source to control the electric field in the first PVH lens1105or the second PVH lens1115, thereby controlling the operation state of the first PVH lens1105or the second PVH lens1115.

The optical power of the first PVH lens1105or the second PVH lens1115may be fixed or adjustable. The first PVH lens1105and the second PVH lens1115may be configured to have at least one of different optical powers or different axial distances (e.g., L1and L2) to the mirror1107along the optical axis1120. For example, in some embodiments, the first PVH lens1105and the second PVH lens1115may be configured to have the same optical power, and different axial distances to the mirror1107. In some embodiments, the first PVH lens1105and the second PVH lens1115may be configured to have different optical powers, and the same axial distance to the mirror1107. In some embodiments, the first PVH lens1105and the second PVH lens1115may be configured to have different optical powers, and different axial distances to the mirror1107. For discussion purposes,FIG.13Ashows that the axial distance L1is greater than the axial distance L2. In some embodiments, the axial distance L1may be equal to or smaller than the axial distance L2.

FIG.13Aalso illustrates an optical path of an image light1332from the display element1050to the eyebox759, according to an embodiment of the present disclosure. InFIG.13A, the controller740(not shown) may control the first PVH lens1105to operate in the active state, and control the second PVH lens1115to operate in the non-active state.

FIG.13Billustrates an optical path of an image light1362from the display element1050to the eyebox759, according to an embodiment of the present disclosure. InFIG.13B, the controller740(not shown) may control the first PVH lens1105to operate in the non-active state, and control the second PVH lens1115to operate in the active state.

For discussion purposes, inFIGS.13A and13B, the first PVH lens1105operating in the active state may reflect and converge a right-handed circularly polarized light, and may transmit a left-handed circularly polarized light while maintaining the propagation direction of the left-handed circularly polarized light. The second PVH lens1115operating in the active state may reflect and converge a left-handed circularly polarized light, and may transmit a right-handed circularly polarized light while maintaining the propagation direction of the right-handed circularly polarized light. For discussion purposes, the transmissive lens1307may be a right-handed PBP lens configured to converge a right-handed circularly polarized light and diverge a left-handed circularly polarized light, the first circular polarizer1103may transmit a left-handed circularly polarized light and block a right-handed circularly polarized light, and the second circular polarizer1113may transmit a right-handed circularly polarized light and block a left-handed circularly polarized light.

Referring back toFIG.13A, the display element1050may output a first image light1332(e.g., representing a first virtual object). The first circular polarizer1103may convert the image light1332into an image light1333L toward the first PVH lens1105. The first PVH lens1105operating in the active state may substantially transmit the image light1333L as an image light1335L toward the mirror1107. The mirror1107may transmit a first portion of the image light1335L as an image light1336L toward the second PVH lens1115, and reflect a second portion of the image light1335L back to the first PVH lens1105as an image light1337R. The second PVH lens1115may transmit the image light1336L as an image light1338L toward the second circular polarizer1113. The second circular polarizer1113may block the image light1338L from being incident onto the transmissive lens1307, such that a ghost image may be suppressed.

The first PVH lens1105may reflect and converge, via diffraction, the image light1337R as an image light1339R toward the mirror1107. The mirror1107may transmit a first portion of the image light1339R toward the second PVH lens1115as an image light1341R, and reflect a second portion of the image light1339R back to the first PVH lens1105as a left-handed circularly polarized image light (not shown). The second PVH lens1115may substantially transmit the image light1341R as an image light1343R toward the second circular polarizer1113. The second circular polarizer1113may transmit the image light1343R as an image light1345R toward the transmissive lens1307. The transmissive lens1307may focus the image light1345R into an image light1347L. The light intensity of the image light1347L may be about 25% of the light intensity of the image light1332L output from the display element1050. The optical path of an image light from being the image light1332L to being the image light1347L may be referred to as a first optical path.

The lens assembly1301may image the display element1050to a first image plane1305having a first axial distance of da1to the eyebox759, along the optical axis1120of the lens assembly1301. Thus, the first virtual object displayed by the display element1050(e.g., displayed on the display panel) may be imaged, by the lens assembly1301, to the first image plane1305that is apart from the eyebox759by the first axial distance of da1. In other words, the lens assembly1301may form an image of the first virtual object at the first image plane1305. Accordingly, for the eye760placed at the exit pupil757within the eyebox759, the accommodation distance of the first virtual object may be substantially equal to the first axial distance da1.

As shown inFIG.13B, the display element1050may output a second image light1362(e.g., representing a second virtual object). The first circular polarizer1103may convert the image light1362into an image light1363L propagating toward the first PVH lens1105. The first PVH lens1105may substantially transmit the image light1363L as an image light1365L toward the mirror1107. The mirror1107may transmit a first portion of the image light1365L as an image light1366L toward the second PVH lens1115, and reflect a second portion of the image light1365L back to the first PVH lens1105as an image light1367R. The first PVH lens1105may transmit the image light1367R as an image light1369R toward the first circular polarizer1103. The first circular polarizer1103may block the image light1369R from being incident onto the display element1050.

The second PVH lens1115may reflect and converge, via diffraction, the image light1366L as an image light1368L toward the mirror1107. The mirror1107may transmit a first portion of the image light1368L toward the first PVH lens1105as a left-handed circularly polarized image light (not shown), and reflect a second portion of the image light1368L back to the second PVH lens1115as an image light1370R. The second PVH lens1115may substantially transmit the image light1370R as an image light1372R toward the second circular polarizer1113. The second circular polarizer1113may transmit the image light1372R as an image light1374R toward the transmissive lens1307. The transmissive lens1307may focus the image light1374R into an image light1376L. The light intensity of the image light1376L may be about 25% of the light intensity of the image light1362L output from the display element1050. The optical path of an image light from being the image light1363L to being the image light1376L may be referred to as a second optical path.

The lens assembly1301may image the display element1050to a second image plane1310having a second axial distance of da2to the eyebox759, along the optical axis1120of the lens assembly1301. Thus, the second virtual object displayed by the display element1050(e.g., displayed on the display panel) may be imaged by the lens assembly1301to be at the second image plane1310that is spaced apart from the eyebox759by the second axial distance of da2. In other words, the lens assembly1301may form an image of the second virtual object at the second image plane1310. Accordingly, for the eye760placed at the exit pupil757within the eyebox759, the accommodation distance of the second virtual object may be substantially equal to the second axial distance da2.

Referring toFIGS.13A and13B, in some embodiments, when the axial distances L1and L2are fixed, the first axial distance da1of the first image plane1305may be determined by the respective optical powers of the first PVH lens1105and the transmissive lens1307, and the second axial distance da2of the second image plane1310may be determined by the respective optical powers of the second PVH lens1115and the transmissive lens1307. Thus, through configuring the respective optical powers of the transmissive lens1307, the first PVH lens1105, and the second PVH lens1115, the second axial distance da2may be configured to be different from the first axial distance da1. For discussion purposes,FIGS.13A and13Bshow that the first axial distance da1is greater than the second axial distance da2, and the first virtual object and the second virtual object displayed by the display element1050may be a distant virtual object and a close virtual object, respectively.

Thus, when each of the transmissive lens1307, the first PVH lens1105, and the second PVH lens1115is presumed to have a fixed optical power, the lens assembly1301may image the display element1050to two different image planes having different axial distances to the eyebox759. In other words, the lens assembly1301may form respective images of the first virtual object and the second virtual object displayed by the display element1050(e.g., displayed on the display panel) at two different image planes that are spaced apart from the eyebox759by different axial distances. Accordingly, for the eye760placed at the exit pupil757within the eyebox759, the accommodation distance of the first virtual object and the second virtual object may be different from one another.

When the display element1050displays the first virtual object and the second virtual object associated with different vergence distances (from the eye760placed at the exit pupil757within the eyebox759), the respective optical powers of the transmissive lens1307, the first PVH lens1105, and the second PVH lens1115may be configured, and the axial distances L1, and L2for the lens assembly1301may be configured, such that the first axial distance da1may be substantially equal to the vergence distance of the first virtual object, and the second axial distance da2may be substantially equal to the vergence distance of the second virtual object.

Thus, the vergence-accommodation conflict in the system1300may be reduced, and the user experience may be enhanced. In some embodiments, when at least one of the transmissive lens1307, the first PVH lens1105, or the second PVH lens1115has an adjustable optical power, the lens assembly1301may image the virtual content displayed by the display element1050to more than two different image planes having different axial distances to the eyebox759. The accommodation capability of the lens assembly1301may be further improved.

In some embodiments, during a display frame of the display element1050, a distant virtual object and a close virtual object may be displayed by the display element1050, during different sub-frames of the display frame. The display element1050may render the close virtual object to appear closer to the eyes760than the distant virtual object. Referring toFIGS.13A and13B, the distant virtual object may be the first virtual object represented by the image light1332shown inFIG.13A, and the close virtual object may be the second virtual object represented by the image light1362shown inFIG.13B.

The display element1050may be configured to display virtual objects associated with different vergence distances in a time sequential manner during the operation of the system200. For example, the display element1050may be configured to switch between displaying the distant virtual object and displaying the close virtual object at a predetermined frequency or predetermined frame rate. In some embodiments, the display frame of the display element1050may include a first sub-frame and a second sub-frame. The controller740may be configured to control the display element1050to display the distant virtual object and the close virtual object during the respective sub-frames of the display frame of the display element1050. In some embodiments, the frame rate of the display element1050may be at least 60 Hz according to the frame rate of the human vision.

In addition, during the operation of the system1300, the controller740may be configured to control each of the first PVH lens1105and the second PVH lens1115to switch between the active state and the non-active state. In some embodiments, when the display frame of the display element1050includes a first sub-frame and a second sub-frame, the controller740may be configured to control the first PVH lens1105and the second PVH lens1115to sequentially operate in the active state during the two sub-frames. The switching of the first PVH lens1105and the second PVH lens1115may be synchronized with the switching of the display element1050between displaying the distant virtual object and the close virtual object.

For example, during the first sub-frame, the controller740may be configured to control the display element1050to display only the distant virtual object, and output the image light1332representing the distant virtual object (as shown inFIG.13A). In some embodiments, based on the eye tracking information provided by the eye tracking device (not shown), the controller740may determine a vergence distance dv1of the distant virtual object. Based on the determined eye tracking information, the controller740may control the first PVH lens1105to operate in the active state and the second PVH lens1115to operate in the non-active state. Referring toFIG.13A, the lens assembly1301may image the distant virtual object to the first image plane1305having the first axial distance of da1to the eyebox759. In some embodiments, the first axial distance of da1may be configured to be substantially equal to the vergence distance dv1of the distant virtual object. Thus, the eyes760placed at the exit pupil757within the eyebox759may accommodate for the distant virtual object.

During the second sub-frame, the controller740may be configured to control the display element1050to display only the close virtual object, and output the image light1362representing the close virtual object (as shown inFIG.13B). Based on the eye tracking information provided by the eye tracking device (not shown), the controller740may determine a vergence distance dv2of the close virtual object. Based on the determined eye tracking information, the controller740may control the first PVH lens1105to operate in the non-active state and the second PVH lens1115to operate in the active state. Referring toFIG.13B, the lens assembly1301may image the close virtual object to the second image plane1310having the second axial distance of da2to the eyebox759. In some embodiments, the second axial distance of da2may be configured to be substantially equal to the vergence distance dv2of the close virtual object. Thus, the eyes760placed at the exit pupil757within the eyebox759may accommodate for the close virtual object.

Referring toFIGS.10A-11andFIGS.13A and13B, in some embodiments, the display element1050may include one or more narrowband light sources, e.g., one or more LEDs, a one or more SLEDs, one or more laser diodes, or a combination thereof, etc. In some embodiments, the one or more narrowband light sources may output narrowband blue, green, and red image lights each having a bandwidth (full width at half maximum (FWHM)) within a range of about 5 nm to 10 nm, a range of about 10 nm to 20 nm, a range of about 20 nm to 30 nm, or a range of about 30 nm to 40 nm, etc. For example, the display element1050may include a micro-LED display panel configured to emit blue, green, and red image lights each having a bandwidth of about 20 nm. In some embodiments, the display element1050may include a laser scanning display panel configured to emit blue, green, and red image lights each having a bandwidth of several nanometers, e.g., 5 nm. In some embodiments, referring toFIG.10A, the reflection band of the reflective polarizer1008may substantially match with the emission band of the one or more narrowband light sources included in the display element1050. In some embodiments, referring toFIG.11andFIGS.13A and13B, the reflection band of at least one of (e.g., each of) the first PVH element1105or the second PVH element1115may substantially match with the emission band of the one or more narrowband light sources included in the display element1050.

FIG.12Aillustrates a schematic diagram of an artificial reality device1200according to an embodiment of the present disclosure. In some embodiments, the artificial reality device1200may produce VR, AR, and/or MR content for a user, such as images, video, audio, or a combination thereof. The artificial reality device1200may include one or more disclosed LCPH elements, and may provide an enhanced performance and user experience. In some embodiments, the artificial reality device1200may be smart glasses. In one embodiment, the artificial reality device1200may be a near-eye display (“NED”). In some embodiments, the artificial reality device1200may be in the form of eyeglasses, goggles, a helmet, a visor, or some other type of eyewear. In some embodiments, the artificial reality device1200may be configured to be worn on a head of a user (e.g., by having the form of spectacles or eyeglasses, as shown inFIG.12A), or to be included as part of a helmet that is worn by the user. In some embodiments, the artificial reality device1200may be configured for placement in proximity to an eye or eyes of the user at a fixed location in front of the eye(s), without being mounted to the head of the user. In some embodiments, the artificial reality device1200may be in a form of eyeglasses which provide vision correction to a user's eyesight. In some embodiments, the artificial reality device1200may be in a form of sunglasses which protect the eyes of the user from the bright sunlight. In some embodiments, the artificial reality device1200may be in a form of safety glasses which protect the eyes of the user. In some embodiments, the artificial reality device1200may be in a form of a night vision device or infrared goggles to enhance a user's vision at night.

For discussion purposes,FIG.12Ashows that the artificial reality device1200includes a frame1205configured to mount to a head of a user, and left-eye and right-eye display systems1210L and1210R mounted to the frame1205.FIG.12Bis a cross-sectional view of half of the artificial reality device1200shown inFIG.12Aaccording to an embodiment of the present disclosure. For illustrative purposes,FIG.12Bshows the cross-sectional view associated with the left-eye display system1210L. The frame1205is merely an example structure to which various components of the artificial reality device1200may be mounted. Other suitable type of fixtures may be used in place of or in combination with the frame1205.

In some embodiments, the left-eye and right-eye display systems1210L and1210R each may include suitable image display components configured to generate virtual images, such as the display element705shown inFIG.7, the display panel901and the light guide illumination assembly903shown inFIG.9A, the display panel982and the light guide illumination assembly903shown inFIG.9B, or the display element1050shown inFIG.10A,FIG.11, andFIGS.13A and13B, etc. In some embodiments, the left-eye and right-eye display systems1210L and1210R may each include a light guide display system, e.g., the system800shown inFIG.8Aor the system850inFIG.8B. In some embodiments, the left-eye and right-eye display systems1210L and1210R may include one or more disclosed LCPH elements.

In some embodiments, the artificial reality device1200may also include a viewing optics system1224disposed between the left-eye display system1210L or right-eye display system1210R and the eyebox759. The viewing optics system1224may be configured to guide an image light (representing a computer-generated virtual image) output from the left-eye display system1210L or right-eye display system1210R to propagate through one or more exit pupils757within the eyebox759. For example, the viewing optics system1224may include the off-axis combiner720shown inFIG.7, the lens assembly853shown inFIG.8B, the lens assembly902shown inFIG.9AorFIG.9B, the path-folding lens assembly1001shown inFIG.10A, the path-folding lens assembly1101shown inFIG.11, or the path-folding lens assembly1301shown inFIGS.13A and13B, etc. In some embodiments, the viewing optics system1224may also be configured to perform a suitable optical adjustment of an image light output from the left-eye display system1210L or right-eye display system1210R, e.g., correct aberrations in the image light, adjust a position of the focal point of the image light in the eyebox759, etc. In some embodiments, the viewing optics system1224may include one or more disclosed LCPH elements. In some embodiments, the viewing optics system1224may be omitted.

In some embodiments, as shown inFIG.12B, the artificial reality device1200may also include an object tracking system1250(e.g., eye tracking system and/or face tracking system). In some embodiments, the object tracking system1250may include one or more disclosed LCPH elements. For example, the object tracking system1250may include one or more IR light sources1255configured to illuminate the eye760and/or the face, a light deflecting element1256configured to deflect the IR light reflected by the eye760toward an optical sensor1257. The optical sensor1257may receive the IR light deflected by the deflecting element1256and generate a tracking signal (e.g., an eye tracking signal).

The foregoing description of the embodiments of the present disclosure have been presented for the purpose of illustration. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Persons skilled in the relevant art can appreciate that modifications and variations are possible in beam of the above disclosure.

Any of the steps, operations, or processes described herein may be performed or implemented with one or more hardware and/or software modules, alone or in combination with other devices. In one embodiment, a software module is implemented with a computer program product including a computer-readable medium containing computer program code, which can be executed by a computer processor for performing any or all of the steps, operations, or processes described. In some embodiments, a hardware module may include hardware components such as a device, a system, an optical element, a controller, an electrical circuit, a logic gate, etc.

Embodiments of the present disclosure may also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the specific purposes, and/or it may include a general-purpose computing device selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a non-transitory, tangible computer readable storage medium, or any type of media suitable for storing electronic instructions, which may be coupled to a computer system bus. The non-transitory computer-readable storage medium can be any medium that can store program codes, for example, a magnetic disk, an optical disk, a read-only memory (“ROM”), or a random access memory (“RAM”), an Electrically Programmable read only memory (“EPROM”), an Electrically Erasable Programmable read only memory (“EEPROM”), a register, a hard disk, a solid-state disk drive, a smart media card (“SMC”), a secure digital card (“SD”), a flash card, etc. Furthermore, any computing systems described in the specification may include a single processor or may be architectures employing multiple processors for increased computing capability. The processor may be a central processing unit (“CPU”), a graphics processing unit (“GPU”), or any processing device configured to process data and/or perform computation based on data. The processor may include both software and hardware components. For example, the processor may include a hardware component, such as an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or a combination thereof. The PLD may be a complex programmable logic device (“CPLD”), a field-programmable gate array (“FPGA”), etc.

Embodiments of the present disclosure may also relate to a product that is produced by a computing process described herein. Such a product may include information resulting from a computing process, where the information is stored on a non-transitory, tangible computer readable storage medium and may include any embodiment of a computer program product or other data combination described herein.

Further, when an embodiment illustrated in a drawing shows a single element, it is understood that the embodiment or an embodiment not shown in the figures but within the scope of the present disclosure may include a plurality of such elements. Likewise, when an embodiment illustrated in a drawing shows a plurality of such elements, it is understood that the embodiment or an embodiment not shown in the figures but within the scope of the present disclosure may include only one such element. The number of elements illustrated in the drawing is for illustration purposes only, and should not be construed as limiting the scope of the embodiment. Moreover, unless otherwise noted, the embodiments shown in the drawings are not mutually exclusive, and they may be combined in any suitable manner. For example, elements shown in one figure/embodiment but not shown in another figure/embodiment may nevertheless be included in the other figure/embodiment. In any optical device disclosed herein including one or more optical layers, films, plates, or elements, the numbers of the layers, films, plates, or elements shown in the figures are for illustrative purposes only. In other embodiments not shown in the figures, which are still within the scope of the present disclosure, the same or different layers, films, plates, or elements shown in the same or different figures/embodiments may be combined or repeated in various manners to form a stack.

Various embodiments have been described to illustrate the exemplary implementations. Based on the disclosed embodiments, a person having ordinary skills in the art may make various other changes, modifications, rearrangements, and substitutions without departing from the scope of the present disclosure. Thus, while the present disclosure has been described in detail with reference to the above embodiments, the present disclosure is not limited to the above described embodiments. The present disclosure may be embodied in other equivalent forms without departing from the scope of the present disclosure. The scope of the present disclosure is defined in the appended claims.