Patent Description:
Waveplates are key components in many instruments and optical systems for polarization control. A waveplate controls the polarization by retarding (or delaying) a component of polarization (or a polarization component) with respect to an orthogonal component. To enhance the performance of an optical system, broadband or achromatic waveplates covering wavelengths in a visible ("VIS") region, from the VIS region to near infrared ("NIR") region, are desirable.

<CIT> discloses an optical element includes at least two stacked birefringent layers having respective local optical axes that are rotated by respective twist angles over respective thicknesses of the at least two layers, and are aligned along respective interfaces between the at least two layers. The respective twist angles and/or the respective thicknesses are different. The at least two stacked birefringent layers may be liquid crystal polymer optical retarder layers. Related devices and fabrication methods are also discussed.

<CIT> discloses an achromatic converter of spatial distribution of polarization from a first to a second pre-defined distribution of polarization. The converter comprises a plurality of photo-aligned quarter-wave or half-wave liquid crystal polymer layers, wherein the patterns of alignment of the layers are correlated with each other so as to make polarization conversion achromatic. Achromatic polarization vortices can be formed. The polarization conversion efficiencies over <NUM>% have been demonstrated over most of the visible spectrum of light. The polarization converters can be used in imaging, photolithography, optical tweezers, micromachining, and other applications.

<CIT> discloses an optical element includes a plurality of stacked birefringent sublayers, such as liquid crystal sublayers, configured to alter a direction of propagation of light passing therethrough according to the Bragg condition. The stacked birefringent sublayers respectively include local optical axes that vary along respective interfaces between adjacent ones of the stacked birefringent sublayers to define respective grating periods. The respective thicknesses of the stacked birefringent sublayers may be less than a wavelength of the light. Related apparatus and methods of operation are also discussed.

<NPL>, discloses a novel and simple configuration with the combination of two twisted nematic liquid-crystal cells for the design of a true zero-order achromatic quarter-wave plate. The optimization method considers the material dispersion. Simulation computations show a good achromatic behavior of the optimized waveplate. Compared with other types of broadband quarter-wave plates, the present device is compatible with classical liquid-crystal displays and can be expected to be used in precision polarimeters with low cost and enhanced light efficiency.

<CIT> discloses an HMD which includes an electronic display and a pancake lens block. The pancake lens block includes a back curved optical element and a front curved optical element. Light propagating through the pancake lens block undergoes multiple reflections and to mitigate parasitic reflections, there are no air gaps between optical elements of the pancake lens block. A hybrid film that operates as a waveplate surface and a mirrored surface can be placed between the front curved optical element and the back curved optical element. A wide FOV can be obtained by making the coupling surfaces of the front optical element and the back optical element to be based on a convex cylindrical surface profile and a concave cylindrical surface profile, with the axis of the cylinder surface in a vertical direction for a user wearing the HMD.

One aspect of the present disclosure provides an optical waveplate. The optical waveplate includes a first birefringent film including optically anisotropic molecules arranged to form a first twist structure. The optical waveplate also includes a second birefringent film stacked with the first birefringent film and including optically anisotropic molecules arranged to form a second twist structure. The optical waveplate also includes a third birefringent film stacked with the first birefringent film and the second birefringent film, the third birefringent film including optically anisotropic molecules arranged to form a third twist structure. The optically anisotropic molecules at a first portion of the first birefringent film adjacent an interface between the first birefringent film and the second birefringent film are configured with a first azimuthal angle. The optically anisotropic molecules at a second portion of the second birefringent film adjacent the interface are configured with a second azimuthal angle. The first azimuthal angle is substantially the same as the second azimuthal angle. The optical waveplate is configured to provide a substantially constant retardance over a design wavelength range, and the substantially constant retardance over the design wavelength range is a quarter-wave retardance or a half-wave retardance for a substantially normally incident light of a design wavelength in the design wavelength range, and at least one of the first birefringent film, the second birefringent film or the third birefringent film is configured to provide a retardance other than the quarter-wave retardance or the half-wave retardance for the substantially normally incident light of the design wavelength of the design wavelength range; and wherein for a substantially normally incident light having a design wavelength that is a center wavelength of the design wavelength range.

Another aspect of the present disclosure provides an optical lens assembly. The optical lens assembly includes a first optical element. The optical lens assembly also includes a second optical element optically coupled to the first optical element and configured to reflect a light of a first polarization received from the first optical element back to the first optical element, and transmit a light of a second polarization received from the first optical element. At least one of the first optical element or the second optical element is provided with a waveplate in accordance with another aspect of the invention.

The foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the claims.

The following drawings are provided for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present disclosure. In the drawings:.

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 a 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 <NUM> 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.).

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 range, as well as other wavelength ranges, such as an ultraviolet ("UV") wavelength range, an infrared wavelength range, or a combination thereof.

The term "optical device" as used herein should be broadly interpreted to encompass all types of optical element, optical film, optical coating, optical layer, optical apparatus, optical system, optical assembly, waveplate, optical reflector, optical deflector, optical polarizer, etc..

The term "a design wavelength" refers to a wavelength for which an optical element is designed or configured to perform an optical function. The term "a design wavelength range" refers to a range of wavelengths for which the optical element is designed or configured to perform the optical function. The design wavelength is within the design wavelength range. The term "center wavelength of a design wavelength range" refers to a wavelength at the center value of the design wavelength range. The design wavelength may be at the center wavelength or may be a wavelength that is within a predetermined small range of the center wavelength range, such as -<NUM>% to +<NUM>%, -<NUM>% to +<NUM>%, -<NUM>% to +<NUM>%,-<NUM>% to +<NUM>%, or -<NUM>% to +<NUM>%, etc., which may be defined based on specific application. In some embodiments, the design wavelength may be any suitable wavelength within the design wavelength range, which may not be at or adjacent the center wavelength. In some embodiments, the design wavelength range may be a visible wavelength range (e.g., about <NUM> to about <NUM>), a near infrared wavelength range (e.g., about <NUM> to about <NUM>), or a visible-to-near infrared wavelength range (e.g., about <NUM> to about <NUM>), or some combination thereof. For example, when the design wavelength range is a visible wavelength range from <NUM> to <NUM>, the center wavelength may be <NUM>. In some embodiments, the center wavelength may be a wavelength within a predetermined small range around the center value <NUM>, such as <NUM> to <NUM> (including <NUM> and <NUM>) when the predetermined range is -<NUM>% to +<NUM>%.

Conventional achromatic waveplates are typically realized by physically laminating several retardation films and controlling a relative orientation of the retardation films. For example, a conventional achromatic quarter-wave plate typically includes a half-wave plate and a quarter-wave plate laminated together. The fabrication process for such an achromatic quarter-wave plate is complex and the fabrication cost is high. Further, attaching such an achromatic quarter-wave plate to an optical element of a high curvature is difficult due to challenges associated with laminating a flat film on a curved surface. The disclosed optical device having liquid crystal polymer coatings is directed to solve one or more disadvantages of the conventional optics technology.

The present disclosure provides an optical waveplate configured to provide a substantially constant retardance over a predetermined wavelength range, thereby achieving a broadband optical waveplate over the predetermined wavelength range. The optical waveplate may include a stack of multiple birefringent layers or films having twisted structures. In some embodiments, each birefringent layer or film may be configured with a non-zero twist angle. The twist angle represents a total amount of change (or rotation) in an in-plane orientation of an optic axis of the birefringent layer from a first side of the birefringent layer to an opposite side of the birefringent layer in the thickness direction. For discussion purposes, when the orientation of the optic axis is substantially spatially constant (e.g., the twist angle is zero) within the birefringent layer, the orientation of the optic axis may correspond to an azimuthal angle of optically anisotropic molecules included in the birefringent layer. An azimuthal angle of an optically anisotropic molecule may refer to an angle between a projection of a long axis of the optically anisotropic molecule onto a plane (e.g., an x-y plane) parallel to a substrate where the birefringent layer is disposed and a predetermined reference direction (e.g., an x-axis direction) within the plane. When the orientation of the optic axis is substantially spatially constant in a birefringent layer, the azimuthal angles of the optically anisotropic molecules are substantially the same, and can be represented by a single azimuthal angle. When the orientation of the optic axis of a birefringent layer is nonconstant (e.g., the twist angle is non-zero), i.e., spatially varying, the orientation of the optic axis varies (or changes) in space, for example, in the thickness direction of the birefringent layer. When the orientation of the optic axis varies (or changes) in space within the birefringent layer, the azimuthal angles of the optically anisotropic molecules change from the first side of the birefringent layer to the second side of the birefringent layer along the thickness direction.

In some embodiments, the optical waveplate may include at least three birefringent layers. Each of the at least three birefringent layers may be configured with an optic axis having a spatially constant orientation (e.g., twist angle is zero). Thus, there may be at least three spatially constant orientations, e.g., a first spatially constant orientation, a second spatially constant orientation, and a third spatially constant orientation. The first spatially constant orientation, a second spatially constant orientation, and a third spatially constant orientation may be different from one another. In some embodiments, the spatially constant orientation of the optic axis may correspond to an azimuthal angle of the uniformly oriented optically anisotropic molecules included in each birefringent layer. Thus, there may be at least three azimuthal angles corresponding to the optic axes of the at least three birefringent layers, e.g., a first azimuthal angle, a second azimuthal angle, and a third azimuthal angle. The first azimuthal angle, the second azimuthal angle, and the third azimuthal angle may be different from one another. The optical waveplate including at least three birefringent layers configured with optic axes having different spatially constant orientations may provide a substantially constant retardance over a design wavelength range (e.g., a broadband retardation effect). For embodiments where more than three birefringent layers are included, at least three spatially constant orientations of at least three optic axes of at least three birefringent layers may be different from one another. In some embodiments, all of the spatially constant orientations of the optic axes of the birefringent layers may be different from one another.

The present disclosure further provides an optical lens assembly including one or more of the disclosed optical waveplates. The optical lens assembly may include a first optical element. The optical lens assembly may include a second optical element optically coupled to the first optical element. The second optical element may be configured to reflect a light of a first polarization received from the first optical element back to the first optical element, and transmit a light of a second polarization received from the first optical element. One of the first optical element and the second optical element may be provided with a waveplate surface that is any one of the disclosed optical waveplates. The optical lens assembly may be implemented in an optical system, for example, a near-eye display ("NED") for virtual-reality ("VR"), augmented-reality ("AR"), and/or mixed-reality ("MR") applications.

<FIG> is a schematic diagram of an optical device <NUM>. The optical device <NUM> may include a stack of a plurality of birefringent material layers (or birefringent layers or birefringent films). For illustrative purposes, three birefringent layers, a first birefringent layer <NUM>, a second birefringent layer <NUM>, and a third birefringent layer <NUM>, are shown in the optical device <NUM>. The number of birefringent layers is not limited to three. In some embodiments, the number of birefringent layers may be <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, etc. In some embodiments, each of the birefringent layers <NUM>, <NUM>, and <NUM> may be a thin film including one or more birefringent materials. The birefringent materials in the birefringent layers <NUM>, <NUM>, and <NUM> may include optically anisotropic molecules <NUM>, <NUM>, <NUM>, respectively. For illustrative purposes, an optically anisotropic molecule is represented by a small rod in <FIG>, where each rod is depicted as having a longitudinal axis (or a length direction axis) and a lateral axis (or a width direction axis). Each of the birefringent layers <NUM>, <NUM>, and <NUM> may have an optic axis, which is a direction in which a ray of transmitted light experiences no birefringence. The optic axis of a birefringent layer may also be referred to an optic axis of a birefringent material included in the birefringent layer. The optic axis of each of the birefringent layers <NUM>, <NUM>, and <NUM> may have a spatially constant orientation within the corresponding birefringent layer. The optic axes of the birefringent layers <NUM>, <NUM>, and <NUM> may be configured or arranged with different spatially constant orientations, such that the optical device <NUM> may provide a substantially constant retardance over a design wavelength range.

For example, as shown in <FIG>, each of the birefringent layers <NUM>, <NUM>, and <NUM> may be presumed to include three sub-layers/portions (e.g., a bottom layer/portion, a middle layer/portion, and a top layer/portion) of optically anisotropic molecules, such as LC molecules. Take the first birefringent layer <NUM> as an example. The optic axis of the first birefringent layer <NUM> in the bottom layer/portion, the optic axis of the first birefringent layer <NUM> in the middle layer/portion, and the optic axis of the first birefringent layer <NUM> in the top layer/portion may be oriented in a same direction, e.g., a same in-plane direction. That is, the orientations of the optic axes of the first birefringent layer <NUM> in the bottom layer/portion, the middle layer/portion, and the top layer/portion may be substantially the same. In other words, the optic axis of the first birefringent layer <NUM> may have a first spatially constant orientation within the first birefringent layer <NUM>, e.g., along a first direction forming a first angle with respect to the y-axis direction, as shown in <FIG>. The first angle may correspond to a first azimuthal angle of the optically anisotropic molecules included in the first birefringent layer <NUM>. The optic axis of the second birefringent layer <NUM> may have a second spatially constant orientation within the second birefringent layer <NUM>, e.g., along a second direction forming a second angle with respect to the y-axis direction. The second angle may correspond to the second azimuthal angle of the optically anisotropic molecules in the second birefringent layer <NUM>. The optic axis of the third birefringent layer <NUM> may have a third spatially constant orientation within the third birefringent layer <NUM>, e.g., along a third direction forming a third angle with respect to the y-axis direction. The third angle may correspond to the third azimuthal angle of the optically anisotropic molecules in the third birefringent layer <NUM>. The first, second, third directions may be different. In other words, the first angle (or the corresponding first azimuthal angle), the second angle (or the corresponding second azimuthal angle), and the third angle (or the corresponding third azimuthal angle) may be different. In some embodiments, each of the optic axes of the birefringent layers <NUM>, <NUM>, and <NUM> may be oriented in a plane (e.g., the x-y plane) substantially parallel to the substrate <NUM> or perpendicular to the thickness direction of the birefringent layers (e.g., the z-axis direction).

In some embodiments, the spatially constant orientation of the optic axis of each of the birefringent layers <NUM>, <NUM>, and <NUM> may be achieved through configuring the optically anisotropic molecules included in the birefringent layer to have a substantially same azimuthal angle. The azimuthal angles of the optically anisotropic molecules included in the respective birefringent layers <NUM>, <NUM>, and <NUM> may be configured to have different values, such that the optical device <NUM> may provide a substantially constant retardance for lights in a design wavelength range. An azimuthal angle of the optically anisotropic molecule may refer to an angle between a projection of the longitudinal axis onto a plane (e.g., an x-y plane) parallel to the substrate <NUM> (or perpendicular to the thickness direction of the layer) and a predetermined reference direction (e.g., the y-axis direction or the x-axis direction) within the plane. For discussion purposes, the predetermined reference direction within the plane is the y-axis direction in <FIG>.

In addition, the optically anisotropic molecules included in each of the birefringent layers <NUM>, <NUM>, and <NUM> may have a substantially same tilt angle. The tilt angle may be defined as an angle between the longitudinal axis and an axis of the layer in the thickness direction (e.g., the z-axis). In some embodiments, the tilt angle may be relatively small, e.g., in a range of <NUM>° to <NUM>° or a range of <NUM>° to -<NUM>°. In some embodiments, the optically anisotropic molecules of the three birefringent layers <NUM>, <NUM>, and <NUM> may have a substantially same tilt angle. That is, the optically anisotropic molecules included in each of the birefringent layers <NUM>, <NUM>, and <NUM> may have a substantially same orientation (e.g., substantially same azimuthal angle and same tilt angle). In some embodiments, the optically anisotropic molecules of the three birefringent layers <NUM>, <NUM>, and <NUM> may have different tilt angles. For example, the optically anisotropic molecules included in the first birefringent layer <NUM> may have a first tilt angle, the optically anisotropic molecules included in the second birefringent layer <NUM> may have a second tilt angle, and the optically anisotropic molecules included in the third birefringent layer <NUM> may have a third tilt angle. In some embodiments, at least two of the first tilt angle, the second tilt angle, and the third tilt angle may be different. In some embodiments, all of the first tilt angle, the second tilt angle, and the third tilt angle may be different from one another.

In some embodiments, all of the birefringent layers <NUM>, <NUM>, and <NUM> may include the same birefringent material. In some embodiments, at least one of the birefringent layers <NUM>, <NUM>, and <NUM> may include a birefringent material that is different from the materials of the other layers. In some embodiments, at least one of the birefringent layers <NUM>, <NUM>, and <NUM> may be a thin film including two or more birefringent materials. The birefringent layer may be a coating (or a layer, a film, etc.) formed by, for example, spin coating a film of polymerizable birefringent material precursors on a substrate and polymerizing the birefringent material precursors. Examples of polymerizable birefringent material precursors may include mixed liquid crystal ("LC") materials and polymerizable monomers, reactive mesogens, etc. In some embodiments, the LC materials may include nematic LCs, twist-bend LCs, or chiral nematic LCs (or LCs with chiral dopant), etc. The chiral nematic LCs (or LCs with chiral dopant) may enable a dual-twist or multiple-twist structure of the birefringent layer. The LC materials may have positive or negative dielectric anisotropy. For the purpose of discussion, a liquid crystal polymer ("LCP") layer is used as an example of a birefringent layer. Hence, the first birefringent layer <NUM>, the second birefringent layer <NUM>, and the third birefringent layer <NUM> may be referred to as the first LCP layer <NUM>, the second LCP layer <NUM>, and the third LCP layer <NUM>.

The optical device <NUM> may include a substrate <NUM>. The substrate <NUM> may be any suitable substrate. In some embodiments, the substrate <NUM> may be silicon, silicon dioxide, sapphire, plastic, polymer or some other semiconductor that is substantially transparent in a visible ("VIS") band (e.g., about <NUM> nanometer (nm) to <NUM> or a portion thereof). In some embodiments, the substrate <NUM> may also be transparent in an infrared ("IR") band (e.g., about <NUM> to <NUM>, or a portion thereof). In some embodiments, the substrate <NUM> may be a flexible substrate, such as polyethylene terephthalate ("PET"), polyethylene naphthalate ("PEN") or any suitable flexible substrates. In some embodiments, the substrate <NUM> may be an optical element, for example, a convex lens, a concave lens, a plano-convex, a plano-concave lens, etc. In some embodiments, the substrate <NUM> may be a part of an optical element or an optical device, for example, an electronic display. In some embodiments, the optical device <NUM> may not include the substrate <NUM> because the substrate <NUM> may be removed after the LCP coatings are formed on the substrate <NUM>.

In some embodiments, the optical device <NUM> may include two or more LCP layers. In the embodiment shown in <FIG>, the optical device <NUM> includes the first LCP layer <NUM>, the second LCP layer <NUM>, and the third LCP layer <NUM> stacked together, which have a thickness of d1, d2, and d3, respectively. Each LCP layer may be configured with an optic axis that has a spatially constant orientation within the LCP layer. That is, the orientation of the optic axis of the LCP layer may be substantially spatially constant within the LCP layer. In other words the optic axis of the LCP layer may not change the orientation or direction (e.g., may not rotate) across the thickness of the LCP layer. The rotation of the optic axis may be substantially zero across the thickness of the LCP layer. For example, when the first LCP layer <NUM>, the second LCP layer <NUM>, and the third LCP layer <NUM> include LC materials or LC molecules <NUM>, <NUM>, and <NUM>, respectively, the azimuthal angles of the LC molecules <NUM>, <NUM>, and <NUM> may be Φ1, Φ2, and Φ3 (e.g., with respect to the y-axis direction), respectively. Accordingly, the orientations of the optic axes of the first LCP layer <NUM>, the second LCP layer <NUM>, and the third LCP layer <NUM> may be presented by Φ1, Φ2, and Φ3, respectively. The polymer network is not shown in the figures. The azimuthal angles Φ1, Φ2, and Φ3 may be different from one another. In some embodiments, when more than three LCP layers are included, at least three of azimuthal angles of at least three LCP layers may be different from one another.

In some embodiments, the optical device <NUM> may further include a plurality of alignment structures, such as photo-alignment material ("PAM") layers configured to have an internal structure aligned according to a polarized light irradiation. In some embodiments, each LCP layer may be provided on a PAM layer. The PAM layer may at least partially align the LC molecules in each LCP layer in a predetermined azimuthal angle. For example, the LC molecules in contact with the PAM layer may be aligned by the PAM layer to have the predetermined azimuthal angle, and the remaining LC molecules in the LCP layer may be aligned according to neighboring LC molecules that have been aligned. In the embodiment shown in <FIG>, three PAM layers may be provided. For example, a first PAM layer <NUM> may be provided at a lower side of the first LCP layer <NUM>, a second PAM layer <NUM> may be provided at a lower side of the second LCP layer <NUM>, and a third PAM layer <NUM> may be provided at a lower side of the third LCP layer <NUM>. The PAM layer may be made of photosensitive materials capable of being aligned under a polarized light irradiation. For example, after being exposed to a spatially uniform, linearly polarized light with a wavelength in an absorption band of the photosensitive materials, photosensitive material molecules in the PAM layer may be spatially uniformly aligned along a polarization direction of the spatially uniform, linearly polarized light. Due to anisotropic interfacial interaction, the PAM layer that has been uniformly aligned may align the LC molecules in the birefringent layer to have a substantially same alignment within the birefringent layer. That is, the LC molecules in the birefringent layer may be aligned to have a substantially same azimuthal angle within the birefringent layer. Accordingly, the optic axis of the birefringent layer may have a substantially spatially constant orientation within the birefringent layer. For example, the first PAM layer <NUM> may be configured to align the LC molecules <NUM> to have an azimuthal angle of Φ1 (e.g., with respect to the y-axis direction), and the orientation of the optic axis of the first LCP layer <NUM> may be represented by Φ1. The second PAM layer <NUM> may be configured to align the LC molecules <NUM> to have an azimuthal angle of Φ2 (e.g., with respect to the y-axis direction), and the orientation of the optic axis of the second LCP layer <NUM> may be represented by Φ2. The third PAM layer <NUM> may be configured to align the LC molecules <NUM> to have an azimuthal angle of Φ3 (e.g., with respect to the y-axis direction), and the orientation of the optic axis of the third LCP layer <NUM> may be Φ3.

Within each LCP layer, the orientation of the optic axis of the LCP layer may be substantially spatially constant (e.g., in a substantially same direction) across the LCP layer. Across different LCP layers in the stack, there may be a clocking angle between the neighboring LCP layers. The clocking angle may be defined as the difference between the orientations of the optic axes of two adjacent LCP layers. For example, the clocking angle between the first LCP layer <NUM> and the second LCP layer <NUM> may be the difference between Φ1 and Φ2, and the clocking angle between the second LCP layer <NUM> and the third LCP layer <NUM> may be the difference between Φ2 and Φ3. Two adjacent LCP layers may be configured to have a non-zero clocking angle, which means the orientations of the optic axes of two adjacent LCP layers may change or be different. In other words, the optic axes may rotate relative to one another around the z-axis (e.g., thickness direction) between two adjacent LCP layers.

In the embodiment shown in <FIG>, the thicknesses of the LCP layers d1, d2, and d3 may or may not be the same. The thicknesses of the LCP layers may be determined by various factors, such as the birefringence of the LC materials in the LCP layers, a specified optical function, and a specified optical property of the optical device, etc. For example, when the optical device is designed to be an achromatic waveplate over a design (or predetermined) wavelength range, each LCP layer may be configured with a predetermined retardance and an optic axis orientation, such that the optical device may be provided with a predetermined retardance over the design wavelength range. For example, the design wavelength range of an achromatic quarter-wave plate may be from about <NUM> to about <NUM>, which means the achromatic quarter-wave plate may provide a substantially constant quarter-wave retardance for a substantially normally incident light having a wavelength from about <NUM> to about <NUM>.

The retardance provide by an LCP layer can be calculated as d*Δn, where d is the thickness of the LCP layer, Δn is the birefringence of the LC material in the LCP layer. The retardance may be specified in units of degrees, waves, or nanometers. One full wave of retardance is equivalent to <NUM>°, or the number of nanometers at the wavelength of interest. Commonly used retardances include λ/<NUM> retardance, λ/<NUM> retardance, and 1λ retardance, but other values can be used in various applications. In the disclosed embodiments, each LCP layer having a specific retardance may be associated with a parameter referred to as "a number of wavelengths", or "a number of waves," which is expressed as d*Δn/λ, where λ is a center wavelength of a design wavelength range. The center wavelength of a design wavelength range may be referred to as a design wavelength in the following description. In some embodiments, the design wavelength may not be the center wavelength. For example, the design wavelength may be a wavelength within a predetermined range of the center wavelength, such as ±<NUM>%, ±<NUM>%, ±<NUM>%, ±<NUM>%, ±<NUM>%, ±<NUM>%, ±<NUM>%, etc..

For example, the number of waves of an LCP layer having a half-wave retardance for a design wavelength (e.g., when the design wavelength range is about <NUM> to about <NUM>, the center wavelength of the design wavelength range may be <NUM>) is about <NUM>, and the number of waves of an LCP layer having a quarter-wave retardance for a design wavelength (e.g., <NUM>) is about <NUM>. In conventional technologies, in some cases, the thickness d of the film may be determined based on the design wavelength λ, the number of waves, and the birefringence Δn of the LC material. For example, when green light is used as a reference light, the design wavelength λ may be selected as <NUM> for determining the thickness d of an LCP layer.

In some embodiments, an optimization algorithm may be used to compute design parameters of the optical device <NUM> including a plurality of LCP layers, such as three LC films in <FIG>. In one embodiment, the optical device <NUM> may be designed to be an achromatic quarter-wave plate. The design parameters may be: Φ1=<NUM>°, Φ2=<NUM>°, Φ3=<NUM>°, the number of waves for the LCP layer <NUM> may be <NUM> at λ=<NUM>, the number of waves for the LCP layer <NUM> may be <NUM> at λ=<NUM>, the number of waves for the LCP layer <NUM> may be <NUM> at λ=<NUM>. As shown in the design parameters, at least one of the numbers of waves for the LCP layers does not correspond to a quarter wave (<NUM>) or a half wave (<NUM>) for the design wavelength (e.g., <NUM>). In other words, at least one of the LCP layers is configured to provide a retardance other than a quarter-wave retardance or a half-wave retardance. In the above example, all of the three numbers of waves do not correspond to a quarter wave (<NUM>) or a half wave (<NUM>) for the design wavelength (e.g., <NUM>). In other words, all of the LCP layers are configured to provide a respective retardance other than a quarter-wave retardance or a half-wave retardance. As a comparison, an existing achromatic quarter-wave plate made by laminating technologies often includes a half-wave plate that provides a retardance of half wave (the number of waves is <NUM> for a design wavelength (e.g., <NUM>)) and a quarter-wave plate that provides a retardance of quarter wave (the number of waves is <NUM> for a design wavelength (e.g., <NUM>)) laminated together. Although the above example shows that all of the three numbers of waves do not correspond to a quarter wave (<NUM>) or a half wave (<NUM>) for a design wavelength, in some embodiments, it is possible that one, or more than one layer in the optical device <NUM> may correspond to either a quarter-wave plate or a half-wave plate for a design wavelength. For example, one, more than one, or all of the numbers of waves may correspond to either a quarter wave (<NUM>) or a half wave (<NUM>) for a substantially normally incident light at a design wavelength.

In some embodiments, the optical device <NUM> may be fabricated in the following processes: the first PAM layer <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at a surface (e.g., an upper surface) of the substrate <NUM>. Then a thin film of polymerizable liquid crystal precursors including the LC material <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at an upper surface of the PAM layer <NUM>, and polymerized to form the first LCP layer <NUM>. The second PAM layer <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at an upper surface of the first LCP layer <NUM>. A thin film of polymerizable liquid crystal precursors including the LC material <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at an upper surface of the second PAM layer <NUM>, and polymerized to form the second LCP layer <NUM>. The third PAM layer <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at an upper surface of the second LCP layer <NUM>. A thin film of polymerizable liquid crystal precursors including the LC material <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at an upper surface of the second PAM layer <NUM> and polymerized to form the third LCP layer <NUM>. In some embodiments, after the third LCP layer <NUM> is formed, the substrate <NUM> may be removed. In some embodiments, the substrate <NUM> may be retained, i.e., included in the optical device <NUM>. In some embodiments, at least one of the three PAM layers (e.g., PAM layer <NUM>) may be removed.

<FIG> is a schematic diagram of an optical device <NUM>. The optical device <NUM> may include at least two LCP layers, and at least one of the LCP layers may have an in-plane twist structure that is associated with a non-zero twist angle. In some embodiments, a ratio between the twist angle of each LCP layer and a thickness of each LCP layer (e.g., a twist angle per unit thickness) may be different from layer to layer (e.g., across the plurality of LCP layers). Further, the orientations of the optic axes of the LCP layers may change continuously, from film to film. For example, within an LCP layer, the orientation of the optic axis of the layer may not be spatially constant. That is, the orientation of the optic axis of the LCP layer may spatially vary across the thickness of the layer. Between two adjacent layers, the orientation of the optic axis of the first LCP layer at an interface between the first LCP layer and the second LCP layer may be substantially the same as the orientation of the optic axis of the second LCP layer at the interface. In other words, between two adjacent layers, the orientations of the optic axes of the LCP layers may be continuous. Thus, clocking angles may not be configured between two adjacent LCP layers (or may be substantially zero). In some embodiments, the optical device <NUM> may not include an additional alignment film disposed between two adjacent LCP layers.

As shown in <FIG>, the optical device <NUM> may include a substrate <NUM>, a first LCP layer <NUM>, and a second LCP layer <NUM>. The first LCP layer <NUM> may have a first thickness d1, and the second LCP layer <NUM> may have a second thickness d2. Although LCPs are used for both layers, in some embodiments, different birefringent materials may be used in different layers. In some embodiments, the tilt angles of the optically anisotropic molecules of the two LCP layers <NUM> and <NUM> may be relatively small, e.g., in a range of <NUM>° to <NUM>° or a range of <NUM>° to - <NUM>°. In some embodiments, the optically anisotropic molecules of the two LCP layers <NUM> and <NUM> may have a substantially same tilt angle (e.g., <NUM>°). In some embodiments, the optically anisotropic molecules of the two LCP layers <NUM> and <NUM> may have different tilt angles (e.g., <NUM>° and <NUM>°).

At least one of the LCP layers may have an in-plane twist structure that is associated with a non-zero twist angle, where the LC molecules may rotate along an axis (e.g., along a z-axis direction) of the twist structure, and the LC director of the LC molecules may be substantially perpendicular to the axis of the twist structure. That is, rather than having a spatially constant optic axis as shown in <FIG>, the optic axis of the LCP layer shown in <FIG> may rotate around the z-axis in the thickness direction. In other words, the orientation of the optic axis of the LCP layer may be spatially varying (e.g., may change continuously) by a predetermined degree from the bottom portion to the top portion of the LCP layer in the thickness direction (e.g., the z-axis direction shown in <FIG>). The change in the orientation of the optic axis between at the top portion and at the bottom portion of an LCP layer may be referred to as the twist angle. The spatially varying optic axis may be introduced by the in-plane twist of the LCs. Rather than being aligned in the same direction within a layer, the LC molecules may be oriented in different directions having different azimuthal angles, resulting in a twist structure having a non-zero twist angle within a layer. The in-plane twist of the LCs across the thickness direction within the LCP layer may be realized by adding chiral dopants into the polymerizable LC material precursors. Further, when the optical device includes two or more LCP layers each having an in-plane twist structure, the two or more LCP layers may have two or more different twist angles per unit thickness, which may be realized by adding different concentrations of chiral dopants and/or adding chiral dopants with different helical twisting powers ("HTP") into the polymerizable LC material precursors. Although two LCP layers are shown for illustrative purposes, the optical device <NUM> may include any other suitable number of layers, such as three, four, five, etc. In some embodiments, when more than two LCP layers are included, each may include a twist structure, and the twist angles of the more than two LCP layers may be different from one another. In some embodiments, at least two twist angles of the more than two twist angles may be different from one another.

For illustrative purposes, <FIG> shows that the optical device <NUM> includes two LCP layers each having an in-plane twist structure. In the optical device <NUM> including at least one LCP layer having an in-plane twist structure, the orientations of the optic axes of the neighboring LCP layers at the interface between the neighboring LCP layers may be continuous (e.g., may have substantially the same orientations at the interface). For example, the orientation of the optic axis of the first LCP layers <NUM> at the top portion of the first LCP layer <NUM> may be substantially the same as the orientation of the optic axis of the second LCP layer <NUM> at the lower portion of the second LCP layer <NUM>.

For example, as shown in <FIG>, each of the LCP layers <NUM> and <NUM> may be presumed to include three sub-layers/portions (e.g., a bottom layer/portion, a middle layer/portion, and a top layer/portion) of optically anisotropic molecules (e.g., LC molecules). Take the first LCP layer <NUM> as an example. The optic axis of the first LCP layer <NUM> at the bottom layer/portion, the optic axis of the first LCP layer <NUM> at the middle layer/portion, and the optic axis of the first LCP layer <NUM> at the top layer/portion may be oriented in different in-plane (in the x-y plane) directions, thereby realizing an in-plane twist of the first LCP layer <NUM>. In other words, the azimuthal angels of the optically anisotropic modules <NUM> of the first LCP layer <NUM> at the bottom layer/portion, the azimuthal angels of the optically anisotropic modules <NUM> of the first LCP layer <NUM> at the middle layer/portion, and the azimuthal angels of the optically anisotropic modules <NUM> of the first LCP layer <NUM> at the top layer/portion may be different.

In some embodiments, the overall continuous orientation of the optic axes of the multiple LCP layers may be achieved through configuring optically anisotropic molecules adjacent an interface between two adjacent LCP layers to have substantially the same azimuthal angle. For example, the first LCP layer <NUM> and the second LCP layer <NUM> may have an interface <NUM>. The optically anisotropic molecules <NUM> at a first portion (e.g., the top portion) of the first LCP layer <NUM> adjacent the interface <NUM>, and the optically anisotropic molecules <NUM> at a second portion (e.g., a bottom portion) of the second LCP layer <NUM> adjacent the interface <NUM>, may be configured to have substantially the same azimuthal angle. Thus, there is a continuity between the azimuthal angles between the two LCP layers <NUM> and <NUM> at the interface <NUM>.

As shown in <FIG>, the first LCP layer <NUM> may include LCs <NUM>, and the second LCP layer <NUM> may include LCs <NUM>. Dashed lines <NUM> and <NUM> are only used to represent the interface between the films or layers that may be formed separately, or between a film and ambient air. Each of the at least two LCP layers included in the optical device <NUM> may have an in-plane twist structure associated with a non-zero twist angle. For example, the first LCP layer <NUM> may be associated with a first twist angle (δt1), and the second LCP layer <NUM> may be associated with a second twist angle (δt2). The first twist angle (δt1) may be the difference between the azimuthal angles between LC molecules at the top portion and at the bottom portion of the first LCP layer <NUM>. The second twist angle (δt2) may be the difference between the azimuthal angles between LC molecules at the top portion and at the bottom portion of the second LCP layer <NUM>. For each film, a ratio (e.g., twist angle per unit thickness) may be calculated by dividing the twist angle by the thickness. In some embodiments, the ratio may be different for different films. For example, (δt1)/d1 for the LCP layer <NUM> may be different from (δt2)/d2 for the LCP layer <NUM>. In some embodiments, the ratio may be the same for different films or layers.

The twist angle represents a total amount of change in the orientations of the optic axis across the thickness of an LCP layer. In some embodiments, the orientations of the optic axes in neighboring LCP layers having an in-plane twist structure may be continuous at the interface of the neighboring LCP layers. In other words, the orientations of the optic axes at the interface may be substantially the same. That is, the azimuthal angle of the LC molecules in the second LCP layer <NUM> at the bottom portion of the second LCP layer <NUM> adjacent the interface <NUM> may substantially equal to the sum of the azimuthal angle of the LC molecules in the first LCP layer <NUM> at the bottom portion of the first LCP layer <NUM> and the first twist angle δt1.

In some embodiments, the optical device <NUM> may include a PAM layer <NUM>, which may align the LC molecules in the first LCP layer <NUM> to have an azimuthal angle Φ1 at a bottom portion near or at a top surface of the PAM layer <NUM>. That is, the first LCP layer <NUM> may have an initial optic axis orientation (represented by Φ1) at the bottom portion near or at a top surface of the PAM layer <NUM>. The first twist angle δt1 represents a total change in angle (or the total change in the orientation of the optic axis) from the initial optic axis orientation (Φ1) at a top surface of the PAM layer <NUM> to the interface <NUM> between the first LCP layer <NUM> and the second LCP layer <NUM>. In other words, at the interface <NUM> (i.e., top portion of the first LCP layer <NUM>), the azimuthal angle of the LC molecules <NUM> may be (Φ1 + δt1). Accordingly, the orientation of the optic axis of the first LCP layer <NUM> at the interface <NUM> (i.e., top portion of the first LCP layer <NUM>) may be represented by (Φ1 + δt1). In some embodiments, across the thickness d1 within the first LCP layer <NUM>, the orientation of the optic axis may vary continuously (e.g., linearly or non-linearly) from an angle Φ1 to an angle Φ1 + δt1 (presuming that the pretilt angle is <NUM>).

The second twist angle δt2 represents a total change in angle (or a total change in the orientation of the optic axis) from the initial optic axis orientation (Φ2=Φ1+ δt1) at the interface <NUM> (e.g., at a bottom portion of the second LCP layer <NUM>) to the interface <NUM> (e.g., a top portion of the second LCP layer <NUM>). In other words, at the interface <NUM>, the azimuthal angles of the LC molecules <NUM> in the second LCP layer <NUM> may be (Φ1 + δt1) or substantially close to (Φ1 + δt1). In other words, at the interface <NUM>, the LC molecules <NUM> in the second LCP layer <NUM> may have substantially the same azimuthal angle as the LC molecules <NUM> in the first LCP layer <NUM>. The orientation of the optic axis of the second LCP layer <NUM> at the interface <NUM> may be (Φ1 + δt1 + δt2) or substantially close to (Φ1 + δt1 + δt2). Within the second LCP layer <NUM>, the orientation of the optic axis may vary continuously (e.g., linearly or non-linearly) from the bottom portion of the second LCP layer <NUM> to the top portion of the LCP layer <NUM>. For example, the orientation of the optic axis across the thickness d2 of the second LCP layer <NUM> may continuously change from (Φ1+ δt1) to (Φ1 + δt1+ δt2). The continuity in the orientations of the optic axes of the first LCP layer <NUM> and the second LCP layer <NUM> at the interface <NUM> may be maintained to be substantially the same by specially configuring the chiral dopant or the concentration of the chiral dopant, such that the azimuthal angles of the LC molecules <NUM> of the second LCP layer <NUM> near or at the interface <NUM> may be substantially the same as the azimuthal angles of the LC molecules <NUM> of the first LCP layer <NUM> near or at the interface <NUM>. Accordingly, the orientations of the optic axes of the LCP layers may vary continuously across the thickness of the optical device <NUM>, from Φ1 to (Φ1+δt1+δt2).

In some embodiments, the optical device <NUM> having two twisted LCP layers as shown in <FIG> may be configured to be an achromatic quarter-wave plate. The design parameters of the optical device having two twisted LCP layers shown in <FIG> may include: Φ1=<NUM>°, the number of waves for the first LCP layer <NUM> may be <NUM> at λ=<NUM>, the first twist angle δt1=<NUM>°, Φ2=<NUM>°, the number of waves for the second LCP layer <NUM> may be <NUM> at λ=<NUM>, the second twist angle δt2=<NUM>°. As shown in the example design parameters, at least one of the two layers does not correspond to a quarter-wave plate or a half-wave plate of a design wavelength λ (e.g., <NUM>). For example, the number of waves for the first LCP layer <NUM> is <NUM> at λ=<NUM>, and the number of waves for the second LCP layer <NUM> is <NUM> at λ=<NUM>, both of which do not correspond to a quarter wave (the number of waves is <NUM>) or a half wave (the number of waves is <NUM>) for the design wavelength λ (e.g., <NUM>). In other words, at least one (e.g., both) of the two LCP layers does not correspond to a quarter-wave plate or a half-wave plate of the design wavelength λ (e.g., <NUM>), or at least one (e.g., both) of the two LCP layers provides a retardance other than a quarter-wave retardance or a half-wave retardance. It is to be noted that although this example shows that both layers do not correspond to a quarter-wave plate or a half-wave plate, in some embodiments, one or more than one layer may correspond to either a quarter-wave plate or a half-wave plate. In other words, in some embodiments, one or more than one number of waves of the layers may correspond to a quarter wave (the number of waves is <NUM>) or a half wave (the number of waves is <NUM>) for a substantially normally incident light of a design wavelength.

The second optical device <NUM> may be fabricated in the following processes: first, the PAM layer <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at a top surface of the substrate <NUM>. A thin film of polymerizable liquid crystal precursors including the LCs <NUM> and a chiral dopant that introduces the first twist angle δt1 (if a twist angle is <NUM>°, no dopant may be added) may be disposed (e.g., coated, formed, deposited, attached, etc.) at a top surface of the PAM layer <NUM>. The polymerizable liquid crystal precursors coating including the mixed LCs <NUM> and the chiral dopant may be polymerized to form the first LCP layer <NUM>. Then, a thin film of polymerizable liquid crystal precursors including the LCs <NUM> and a chiral dopant that introduces the second twist angle δt2 (if a twist angle is <NUM>°, no dopant may be added) may be disposed (e.g., coated, formed, deposited, attached, etc.) at a top surface of the first LCP layer <NUM>. The polymerizable liquid crystal precursors coating including the mixed LCs <NUM> and the chiral dopant may be polymerized to form the second LCP layer <NUM>. After the second LCP layer <NUM> is formed, the substrate <NUM> may be removed. In some embodiments, the substrate <NUM> may be included in the optical device <NUM>. In some embodiments, the PAM <NUM> may be removed. As shown in <FIG>, an addition alignment film (e.g., an additional PAM layer) may not be provided between the first LCP layer <NUM> and the second LCP layer <NUM>, and a clocking angle may not be configured (e.g., the clocking angle may be zero) between the first LCP layer <NUM> and the second LCP layer <NUM>.

<FIG> is a schematic diagram of an optical device <NUM>. The optical device <NUM> may have a structure that is similar to the optical device <NUM>, except that the optical device <NUM> may include at least one third LCP layer. Detailed descriptions of the same or similar elements included in the optical device <NUM> may refer to the above description rendered in connection with the optical device <NUM>. Although three layers are shown for illustrative purposes, in some embodiments, more than three films (e.g., four, five, six, etc.) may be included. Similar to the configuration of the optical device <NUM>, at least one of the LCP layers may have an in-plane twist structure associated with a non-zero twist angle. Also similar to the optical device <NUM>, the orientations of the optic axes of the LCP layers may spatially vary continuously from one film (or layer) to another. At any interface between two adjacent LCP layers, the orientation of the optic axis of a lower layer at a top portion adjacent the interface may be substantially the same as the orientation of the optic axis of an upper layer at a bottom portion adjacent the interface. In other words, presuming that the pretilt angle is substantially the same, the azimuthal angles of the LC molecules at or near the interface between two layers may be substantially the same. Accordingly, a continuity in the orientations of the optic axes in multiple LCP layers may be maintained.

As shown in <FIG>, the optical device <NUM> may include a substrate <NUM>, a first LCP layer <NUM>, a second LCP layer <NUM>, and a third LCP layer <NUM>. A PAM layer <NUM> may be provided at a top surface of the substrate <NUM>. The first LCP layer <NUM> having LC molecules <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at a top surface of the PAM layer <NUM>. The second LCP layer <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at a top surface of the first LCP layer <NUM>, and the third LCP layer <NUM> may be disposed (e.g., coated, formed, deposited, attached, etc.) at a top surface of the second LCP layer <NUM>. Each layer may have a thickness d1, d2, and d3, respectively. Each film or layer may have a twist angle δt1, δt2, and δt3, respectively.

The PAM layer <NUM> may align LC molecules <NUM> near or at the top surface of the PAM layer <NUM> in an azimuthal angel Φ1. The orientation of the optic axis of the first LCP layer <NUM> near or at the top surface of the PAM layer <NUM> may correspond to Φ1. Within the first LCP layer <NUM>, across the thickness direction (e.g., the z-axis direction shown in <FIG>), the orientation of the optic axis may spatially vary continuously (e.g., linearly continuously or non-linearly continuously). That is, the orientation of the optic axes of the three LCP layers <NUM>, <NUM>, and <NUM> spatially vary continuously (e.g., linearly continuously or non-linearly continuously) across the stack in the thickness direction (e.g., the z-axis direction shown in <FIG>). For example, at a first interface <NUM> between the first LCP layer <NUM> and the second LCP layer <NUM>, the orientation of the optic axis of the first LCP layer <NUM> may be represented by Φ2, where Φ2 = Φ1 + δt1. The orientation of the optic axis of the second LCP layer <NUM> at the first interface <NUM> may be substantially the same as the orientation of the optic axis of the first LCP layer <NUM>, i.e., Φ2 = Φ1 + δt1. Thus, the continuity in the orientations of the optic axes from the first LCP layer <NUM> to the second LCP layer <NUM> is maintained at the first interface <NUM>. At a second interface <NUM> between the second LCP layer <NUM> and third LCP layer <NUM>, the orientation of the optic axis of the second LCP layer <NUM> may be represented by Φ3, where Φ3 = Φ2+ δt2. The orientation of the optic axis of the third LCP layer <NUM> at the second interface <NUM> may be substantially the same as the orientation of the optic axis of the second LCP layer <NUM>, i.e., Φ3 = Φ2+ δt2. Thus, the continuity in the orientations of the optic axes from the second LCP layer <NUM> to the third LCP layer <NUM> is maintained at the second interface <NUM>. At the third interface <NUM>, the orientation of the optic axis of the third LCP layer <NUM> may be Φ3+ δt3. Thus, across the thickness, the orientations of the optic axes of the LCP layers <NUM>, <NUM>, and <NUM> may spatially vary continuously (e.g., linearly or non-linearly). The continuity in the orientation of the optic axis between adjacent layers is maintained.

In some embodiments, a ratio between the twist angle and the thickness of each LCP layer, i.e., a twist angle per unit thickness, may be calculated for the optical device <NUM>. The ratio may be different for different LCP layers (e.g., at least two ratios may be different from one another or all three ratios may be different). For example, δt1/d1 may be different from δt2/d2. In some embodiments, δt1/d1 may be different from δt3/d3. In some embodiments, δt2/d2 may be different from δt3/d3. In some embodiments, at least one of the three ratios may be different from the other two ratios that may be the same. In some embodiments, at least two ratios may be the same. In some embodiments, all three ratios may be the same. The fabrication process for the optical device <NUM> may be similar to that of the optical device <NUM>, which is described above in connection with the optical device <NUM>.

In some embodiments, the optical device <NUM> may be configured to be an achromatic quarter-wave plate over a design wavelength range. The design parameters for the optical device <NUM> may include: Φ1=<NUM>°, the number of waves for the first LCP layer <NUM> may be <NUM> at λ=<NUM>, the twist angle δt1 for the first LCP layer <NUM> may be <NUM>°, Φ2=<NUM>°, the number of waves for the second LCP layer <NUM> may be <NUM> at λ=<NUM>, the twist angle δt2 for the second LCP layer <NUM> may be <NUM>°, Φ3=<NUM>°, the number of waves for the third LCP layer <NUM> may be <NUM> at λ=<NUM>, and the twist angle δt3 for the third LCP layer <NUM> may be <NUM>°.

As shown in this example design, at least one of the three numbers of waves for the three LCP layers does not correspond to a quarter wave (the number of waves is <NUM>) or a half wave (the number of waves is <NUM>) of a design wavelength λ (e.g., <NUM>). In other words, at least one of the three LCP layers does not correspond to a quarter-wave plate or a half-wave plate, or at least one of the three LCP layers provides a retardance other than the quarter-wave retardance or the half-wave retardance. In this example, the number of waves for the second LCP layer <NUM> is <NUM> at λ=<NUM>, which corresponds to a half wave of the design wavelength λ (e.g., <NUM>), but the other two numbers of waves for the first LCP layer <NUM> (<NUM>) and the third LCP layer <NUM> (<NUM>) do not correspond to a quarter wave or a half wave of the design wavelength λ (e.g., <NUM>). In other words, except for the number of the waves of the second LCP layer <NUM>, which may correspond to a half-wave plate of the design wavelength λ (e.g., <NUM>), the number of the waves of the first LCP layer <NUM> and the third LCP layer <NUM> do not correspond to a quarter-wave plate or a half-wave plate of the design wavelength λ (e.g., <NUM>). In other words, the first LCP layer <NUM> and the third LCP layer <NUM> are configured to each provide a retardance other than a quarter-wave retardance or a half-wave retardance.

<FIG> shows simulation results comparing the conventional achromatic quarter-wave plate and the disclosed achromatic quarter-wave plate formed by LCP coatings or layers. <FIG> plots light leakage (measured as a percentage) versus the wavelength of a normally incident light. To calculate the light leakage, a linear polarizer, a quarter-wave plate, and a circular polarizer are arranged in optical series. The linear polarizer may be configured to receive an unpolarized incident light. The unpolarized light may become a linear polarized light after being transmitted through the linear polarizer. The linearly polarized light may have a polarization axis parallel to a polarization axis or transmission axis of the linear polarizer. A polarization axis of the quarter-wave plate may be oriented relative to a polarization axis of the linear polarizer to convert the linearly polarized light to a circularly polarized light having a left or right handedness propagating toward the circular polarizer. To measure the light leakage, when the circularly polarized light output by the quarter-wave plate has the left handedness, the circular polarizer may be configured to transmit a circularly polarized light having a right handedness, and block a circularly polarized light having a left handedness. When the circularly polarized light output by the quarter-wave plate has the right handedness, the circular polarizer may be configured to transmit a circularly polarized light having a left handedness, and block a circularly polarized light having a right handedness. The light leakage may be calculated as a ratio of the intensity of the light transmitted through the circular polarizer over the intensity of the light incident onto the linear polarizer.

The light leakage of the quarter-wave plate is calculated for a design wavelength range covering from <NUM> to <NUM>. A design wavelength, which may be the center wavelength of the design wavelength range, is <NUM>. Smaller light leakage over the design wavelength range indicates a better the broadband performance of the quarter-wave plate. The plot of <FIG> evaluates the broadband performance of the various designs (including the conventional designs). Five different designs are compared. The "single layer-LCP" (also labeled "(a)") and the "<NUM>-layer w/o twist" (also labeled "(b)") are two conventional configurations: one including a single LCP layer, and the other including two LCP layers without an in-plane twist structure for each LCP layer. The other three configurations are embodiments of the present disclosure: "<NUM>-layer w/o twist" (also labeled "(c)") represents an embodiment shown in <FIG>, "<NUM>-layer with twist" (also labeled "(d)") represents an embodiment shown in <FIG>, and "<NUM>-layer with twist" (also labeled "(e)") represents an embodiment shown in <FIG>. Except for the single LCP layer configuration, the design parameters for the other four configurations are provided in the following table. It is noted that in the example simulation results shown in <FIG>, the design wavelength λ is <NUM>, and the design wavelength range is <NUM> to <NUM>.

As shown in <FIG>, the light leakage for the quarter-wave plate having a single LCP layer configuration ("labeled "Single layer-LCP"), which is a conventional technology, is small for only a relatively narrow bandwidth. For example, if light leakage of <NUM>% is used as a threshold, the quarter-wave plate having the single LCP layer configuration may provide a substantially constant retardance (i.e., may be achromatic) over a wavelength range from about <NUM> to about <NUM> (or a bandwidth of <NUM>). The quarter-wave plate having a "<NUM>-layer w/o twist" configuration, which is also a conventional configuration in which each layer corresponds to either a quarter-wave plate (d*Δn/λ =<NUM>) or a half-wave plate (d*Δn/λ= <NUM>) at the design wavelength <NUM>, may provide a substantially constant retardance over a wavelength range from about <NUM> to about <NUM> (or a bandwidth of about <NUM>). In comparison, the quarter-wave plate having the "<NUM>-layer w/o twist" configuration of the present disclosure, in which none of the three layers corresponds to a quarter-wave plate or a half-wave plate at the design wavelength <NUM>, may provide a substantially constant retardance over a wavelength range from about <NUM> to over <NUM> (or a bandwidth of greater than <NUM>). The quarter-wave plate having the "<NUM>-layer with twist" configuration according to an embodiment of the present disclosure, in which neither of the two layers corresponds to a quarter-wave plate or a half-wave plate at the design wavelength <NUM>, may provide a substantially constant retardance over a wavelength range from about <NUM> to <NUM> (or a bandwidth of about <NUM>). The quarter-wave plate having the "<NUM>-layer with twist" configuration according to an embodiment of the present disclosure, in which two of the three layers do not correspond to a quarter-wave plate or a half-wave plate at the design wavelength range <NUM>, may provide a substantially constant retardance over a wavelength range from lower than <NUM> to over <NUM> (or a bandwidth of greater than <NUM>). As shown in <FIG>, the quarter-wave plates having the configuration according to an embodiment of the present disclosure may have an improved broadband performance as compared to the quarter-wave plates having the configuration of conventional technologies.

If the light leakage of <NUM>% is used as a threshold, the quarter-wave plate having the single LCP layer configuration may provide a substantially constant retardance (i.e., may be achromatic) over a wavelength range from about <NUM> to <NUM> (or a bandwidth of about <NUM>). The quarter-wave plate having a "<NUM>-layer w/o twist" configuration, in which each layer corresponds to either a quarter-wave plate (d*Δn/λ =<NUM>) or a half-wave plate (d*Δn/λ= <NUM>) at the design wavelength <NUM>, may provide a substantially constant retardance over a wavelength range from about <NUM> to about <NUM> (or a bandwidth of about <NUM>). In comparison, the quarter-wave plate having the "<NUM>-layer w/o twist" configuration of the present disclosure, in which none of the three layers corresponds to a quarter-wave plate or a half-wave plate at the design wavelength <NUM>, may provide a substantially constant retardance over a wavelength range from <NUM> to over <NUM> (or a bandwidth of greater than <NUM>). The quarter-wave plate having the "<NUM>-layer with twist" configuration according to an embodiment of the present disclosure, in which neither of the two layers corresponds to a quarter-wave plate or a half-wave plate, may provide a substantially constant retardance over a wavelength range from about <NUM> to about <NUM> (or a bandwidth of about <NUM>). The quarter-wave plate having the "<NUM>-layer with twist" configuration according to an embodiment of the present disclosure, in which two of the three layers do not correspond to a quarter-wave plate or a half-wave plate at the design wavelength <NUM>, may provide a substantially constant retardance over a wavelength range about <NUM> to over <NUM> (or a bandwidth of greater than <NUM>). As shown in <FIG>, the quarter-wave plates having the configuration according to an embodiment of the present disclosure may have an improved broadband performance as compared to the quarter-wave plates having the configuration of conventional technologies.

The achromatic quarter-wave plates disclosed in the present disclosure may have a simplified fabrication process and a reduced cost as compared to a conventional achromatic quarter-wave plate fabricated by laminating a half-wave plate and a quarter-wave plate together. In addition to flat substrates, the disclosed optical device fabricated based on LCP coatings (or layers, films, etc.) may also be fabricated on a curved substrate surface, which may overcome the challenges of laminating a flat film on a curved surface, thereby providing more freedom to the optical device design.

The disclosed optical device fabricated based on LCP coatings may have a large variety of applications in a number of fields, which are all within the scope of the present disclosure. Some exemplary applications in augmented reality ("AR"), virtual reality ("VR"), mixed reality ("MR)" fields or some combinations thereof will be explained below. Near-eye displays ("NEDs") have been widely used in a large variety of applications, such as aviation, engineering, science, medicine, computer gaming, video, sports, training, and simulations. One application of NEDs is to realize VR, AR, MR or some combination thereof. Desirable characteristics of NEDs include compactness, light weight, high resolution, large field of view ("FOV"), and small form factor. An NED may include a display element configured to generate an image light and a lens system configured to direct the image light toward eyes of a user. The lens system may include a plurality of optical elements, such as lenses, waveplates, reflectors, etc., for focusing the image light to the eyes of the user. To achieve a compact size and light weight and to maintain satisfactory optical characteristics, an NED may adopt a pancake lens assembly in the lens system to fold the optical path, thereby reducing a back focal distance in the NED. A focus of a pancake lens assembly is often strongly chromatic. In other words, lights output from the lens system feature chromatic aberration, which reduces image quality in an imaging device that employs a lens system with the pancake lens and a light source that emits lights of multiple wavelengths or color channels. The disclosed optical films, for example, the disclosed achromatic quarter-wave plate, may be implemented in the pancake lens to reduce the chromatic aberration, thereby improving the image quality of the pancake lens.

<FIG> illustrates a schematic diagram of a pancake lens assembly or pancake lens <NUM> according to an embodiment of the disclosure. As shown in <FIG>, the pancake lens assembly <NUM> may include a first optical element <NUM> and a second optical element <NUM> arranged in optical series. In some embodiments, the first optical element <NUM> and the second optical element <NUM> may be coupled together by an adhesive <NUM>. The first optical element <NUM> may receive a light and output a light to the second optical element <NUM>. The second optical element <NUM> coupled with the first optical element <NUM> may be configured to reflect a light of a first polarization received from the first optical element back to the first optical element, and transmit a light of a second polarization received from the first optical element.

In some embodiments, at least one (e.g., each) of the first optical element <NUM> and the second optical element <NUM> may include one or more optical lenses. The pancake lens <NUM> may be configured to receive an image light <NUM> emitted by an electrical display <NUM> (or a light source <NUM>), alter one or more properties of the image light <NUM>, and provide the image light <NUM> with altered properties to an eye <NUM> of a user located at an eye box <NUM>. In some embodiments, the first optical element <NUM> may include a first surface <NUM>-<NUM> facing the electronic display <NUM> and configured to receive an image light from the electronic display <NUM>. The first optical element <NUM> may also include a second surface <NUM>-<NUM> facing the eye <NUM> and configured to output an altered image light. The first optical element <NUM> may further include a mirror <NUM> and a waveplate <NUM>, which may be separate films, layers, or coatings disposed at one or more surfaces of the first optical element <NUM>. In some embodiments, the waveplate <NUM> may be disposed (e.g., bonded, formed, deposited, attached) at the second surface <NUM>-<NUM> of the first optical element <NUM>, and the mirror <NUM> may be disposed (e.g., bonded, formed, deposited, attached) at the first surface <NUM>-<NUM> of the first optical element <NUM>.

The mirror <NUM> may include a partial reflector that is partially reflective to reflect a portion of the received light. In some embodiments, the mirror <NUM> may be configured to transmit about <NUM>% of an incident light and reflect about <NUM>% of the incident light. Such a mirror is often referred to as a <NUM>/<NUM> mirror. In some embodiments, the waveplate <NUM> may include a quarter-wave plate ("QWP") configured to alter the polarization of a received light. A quarter-wave plate includes a polarization axis, and the polarization axis of the QWP may be oriented relative to a linearly polarized incident light to convert the linearly polarized light into a circularly polarized light for a visible spectrum and/or infrared spectrum. In some embodiments, the QWP may convert a circularly polarized light into a linearly polarized light. In some embodiments, the waveplate <NUM> may include a QWP according to any one of embodiments of the disclosed achromatic quarter-wave plates, such as optical devices <NUM>, <NUM>, or <NUM>.

The second optical element <NUM> may have a first surface <NUM>-<NUM> facing the first optical element <NUM> and an opposing second surface <NUM>-<NUM> facing the eye <NUM>. The pancake lens <NUM> may include a reflective polarizer <NUM>, which may be an individual film, layer, or coating. In some embodiments, the reflective polarizer <NUM> may be disposed (e.g., bonded, formed, deposited, attached) at the first surface <NUM>-<NUM> or the second surface <NUM>-<NUM> of the second optical element <NUM>. In one embodiment, as shown in <FIG>, the reflective polarizer <NUM> may be disposed (e.g., bonded, formed, deposited, attached) at the first surface <NUM>-<NUM> of the second optical element <NUM>.

The reflective polarizer <NUM> may be a partially reflective mirror configured to reflect a received light of a first linear polarization and transmit a received light of a second linear polarization. For example, the reflective polarizer <NUM> may reflect light polarized in a blocking direction (e.g., x-axis direction), and transmit light polarized in a perpendicular direction (e.g., y-axis direction). In the disclosed embodiments, the blocking direction is referred as a direction of a blocking axis or a blocking axis direction of the reflective polarizer <NUM>, and the perpendicular direction is referred as a direction of a transmission axis or a transmission axis direction of the reflective polarizer <NUM>.

The schematic configuration of the pancake lens assembly <NUM> shown in <FIG> is for illustrative purposes. In some embodiments, one or more of the first surface <NUM>-<NUM> and the second surface <NUM>-<NUM> of the first optical element <NUM> and the first surface <NUM>-<NUM> and the second surface <NUM>-<NUM> of the second optical element <NUM> may be flat or curved. The locations where the mirror <NUM>, the waveplate <NUM>, and the reflective polarizer <NUM> are disposed are for illustrative purposes only. The mirror <NUM>, the waveplate <NUM>, and the reflective polarizer <NUM> may be disposed at other locations in the pancake lens <NUM>. In addition, the sequence in which the mirror <NUM>, the first optical element <NUM>, the waveplate <NUM>, the adhesive <NUM>, the reflective polarizer <NUM>, and the second optical element <NUM> are arranged in the optical series is for illustrative purposes only. Other sequence may be adopted. In some embodiments, the pancake lens assembly <NUM> may have one optical element or more than two optical elements. In some embodiments, the pancake lens assembly <NUM> may further include other optical elements in addition to the first and second optical elements, such as a linear polarizer, a quarter-wave plate, which is not limited by the present disclosure. In some embodiments, the quarter-wave plate may be any one of the embodiments of the disclosed achromatic quarter-wave plates. With the disclosed achromatic quarter-wave plates, the chromatic aberration may be suppressed by the pancake lens assembly, the image quality provided by the pancake lens assembly may be improved.

Further, to produce a large FOV, optical elements in the pancake lens assembly often have a high optical curvature. However, traditional waveplates are typically flat. Attaching flat waveplates on the optical elements of high curvature in the pancake lens assembly may be difficult due to challenges associated with laminating a flat film on a curved surface. Thus, the design freedom of a conventional pancake lens assembly may be limited. The disclosed optical device fabricated based on LCP coatings, for example, a disclosed achromatic quarter-wave plate, may be fabricated on a curved substrate surface, thereby providing an additional degree of freedom in pancake lens design for AR/VR/MR NEDs, through which large FOV and compact pancake lenses may be realized. Accordingly, complex imaging functions, a small form factor, a large FOV, and/or a large eye-box may be achieved in AR/VR/MR NEDs.

<FIG> illustrates a schematic of a light propagation path <NUM> in the pancake lens assembly <NUM> shown in <FIG>. In <FIG>, "s" denotes s-polarized light, "p" denotes p-polarized light, "R" denotes right-handed circularly polarized light, and "L" denotes left-handed circularly polarized light. In the light propagation path <NUM>, the first optical element <NUM> and the second optical element <NUM>, which are presumed to be optical lenses that may not affect the polarization of the light, are omitted for simplicity of the illustration. In one embodiment, as shown in <FIG>, a light <NUM> emitted from the electronic display <NUM> may be left-handed circularly polarized light ("<NUM>") and transmitted to the mirror <NUM>. At the mirror <NUM>, a first portion of the left-handed circularly polarized light <NUM> ("<NUM>") may be reflected by the mirror <NUM>, and a second portion of the left-handed circularly polarized light <NUM> ("<NUM>") may be transmitted by the mirror as a light <NUM> propagating towards the waveplate <NUM>. The light <NUM> transmitted through the mirror <NUM> may remain as a left-handed circularly polarized light ("<NUM>"). The waveplate <NUM> may be a quarter-wave plate, which may convert the left-handed circularly polarized light <NUM> ("<NUM>") into an s-polarized light <NUM> ("<NUM>").

The s-polarized light <NUM> ("<NUM>") may be incident on the reflective polarizer <NUM>, which may reflect a light polarized in a blocking direction (e.g., x-axis direction), and transmit a light polarized in a perpendicular direction (e.g., y-axis direction). That is, the reflective polarizer <NUM> may transmit a p-polarized light and reflect an s-polarized light. Thus, the s-polarized light <NUM> ("<NUM>") propagating in the positive z-direction from the waveplate <NUM> may be reflected by the reflective polarizer <NUM> to be an s-polarized light <NUM> ("<NUM>") propagating in the negative z-direction. The reflected s-polarized light <NUM> ("<NUM>") may be transmitted through the waveplate <NUM> for a second time and converted into a left-handed circularly polarized light <NUM> ("<NUM>") propagating in the negative z-direction. The left-handed circularly polarized light <NUM> ("<NUM>") propagating in the negative z-direction may be reflect by the mirror <NUM> to be a right-handed circularly polarized light <NUM> ("186R"). The right-handed circularly polarized light <NUM> ("186R") may be transmitted through the waveplate <NUM> and converted into a p-polarized light <NUM> ("187p"). Because the reflective polarizer <NUM> may transmit a p-polarized light and reflect an s-polarized light, the p-polarized light <NUM> ("187p") may be transmitted through the reflective polarizer <NUM> as a p-polarized light <NUM> ("188p"), which may be focused to the eye-box.

For illustrative purposes, a left-handed circularly polarized light <NUM> emitted from the electronic display <NUM> is used as an example. In some embodiments, the light emitted from the electronic display <NUM> may be a right-handed circularly polarized light. In some embodiments, the light emitted from the electronic display <NUM> may be a linearly polarized light, and a quarter-wave plate may be arranged between the electronic display <NUM> and the mirror <NUM>, or disposed at a surface of the mirror <NUM>, to convert the linearly polarized light into a circularly polarized light, which is then incident onto the mirror <NUM>. In some embodiments, the light emitted from the electronic display <NUM> may be an unpolarized light, and a linear polarizer and a quarter-wave plate may be arranged between the electronic display <NUM> and the mirror <NUM>, or disposed at a surface of the mirror <NUM>. The linear polarizer may convert the unpolarized light emitted from the electronic display <NUM> into a linearly polarized light, and the quarter-wave plate may be orientated relative to the linear polarizer to convert the linearly polarized light received from the linear polarizer into a circularly polarized light, which is then incident onto the mirror <NUM>.

The above-mentioned applications of the optical device fabricated based on LCP coatings in the NEDs are for illustrative purposes. In addition, the disclosed optical device fabricated based on LCP coatings may be used to realize eye-tracking components, display resolution enhancement components (e.g., for increasing pixel density), and pupil steering elements, etc. The optical device fabricated based on LCP coatings may be implemented as multifunctional optical components in the NEDs to significantly improve the optical performance of the NEDs.

<FIG> shows a block diagram of a system <NUM> according to an embodiment of the disclosure. As shown in <FIG>, the system <NUM> may include an NED <NUM>, a console <NUM>, an imaging device <NUM>, and an input/output interface <NUM>. The NED <NUM>, the imaging device <NUM>, and the input/output interface <NUM> may be coupled to the console <NUM>. Although <FIG> shows that the system <NUM> includes one NED <NUM>, one imaging device <NUM>, and one input/output interface <NUM>, in some embodiments, any other suitable number of components may be included in the system <NUM>. For example, the system <NUM> may include multiple NEDs <NUM> each having an associated input/output interface <NUM> and one or more imaging devices <NUM>. In some embodiments, each NED <NUM>, input/output interface <NUM>, and imaging device <NUM> may communicate with the console <NUM>. In some embodiments, different and/or additional components may be included in the system <NUM>. The system <NUM> may operate in a VR system environment, an AR system environment, an MR system environment, or some combination thereof.

The NED <NUM> may be a head-mounted display configured to present media content to a user. Examples of media content presented by the NED <NUM> include one or more images, videos, audios, or some combination thereof. In some embodiments, audios may be presented via an external device (e.g., speakers and/or headphones) configured to receive audio information from the NED <NUM>, the console <NUM>, or both. The external device may present audio data based on the received audio information. An example of the NED <NUM> is further described below with reference to <FIG> and <FIG>.

The NED <NUM> may include one or more bodies, which may be rigidly or non-rigidly coupled to each other. A rigid coupling between rigid bodies may cause the coupled rigid bodies to act as a single rigid entity. In contrast, a non-rigid coupling between rigid bodies may allow the rigid bodies to move relative to each other. In some embodiments, the NED <NUM> may present VR, AR, MR contents, or some combination thereof to the user. In the VR, AR and/or MR environments, the NED <NUM> may augment views of a physical, real-world environment with computer-generated elements (e.g., images, video, sound, etc.).

As shown in <FIG>, the NED <NUM> may include an electronic display block <NUM>, a pancake lens assembly <NUM>, one or more locators <NUM>, one or more position sensors <NUM>, and an inertial measurement unit ("IMU") <NUM>. The electronic display block <NUM> may display images to the user in accordance with data received from the console <NUM>. In some embodiments, the electronic display block <NUM> may include an electronic display and an optics block. The electronic display may generate an image light. In some embodiments, the electronic display may include a single electronic display or multiple electronic displays (e.g., a display for each eye of a user). Examples of the electronic display may include: a liquid crystal display ("LCD"), an organic light emitting diode ("OLED") display, an active-matrix organic light-emitting diode display ("AMOLED"), a transparent organic light emitting diode display ("TOLED"), some other display, a projector, or a combination thereof.

The optics block may include combinations of different optical elements. An optical element may be an aperture, a Fresnel lens, a convex lens, a concave lens, a filter, or any other suitable optical element that may affect the image light emitted from the electronic display. In some embodiments, one or more of the optical elements in the optics block may have one or more coatings, such as anti-reflective coatings. Magnification of the image light by the optics block may allow elements of the electronic display to have reduced sizes, reduced weight, and consume less power than larger displays. Additionally, magnification may increase a field of view of the displayed media content. For example, the field of view of the displayed media content may be widened or increased, such that the displayed media content may be presented using a significant portion of the field of view of the user (e.g., <NUM> degrees diagonal). In some embodiments, the optics block may be configured to have an effective focal length larger than the spacing to the electronic display, thereby magnifying the image light projected by the electronic display. Additionally, in some embodiments, the amount of magnification may be adjusted by adding or removing optical elements.

The pancake lens assembly <NUM> may include any one of the disclosed quarter-wave plate, such as optical device <NUM>, <NUM>, or <NUM>. In some embodiments, the pancake lens assembly <NUM> may be configured as a monolithic pancake lens assembly without any air gap between optical elements of the pancake lens assembly. For example, the pancake lens assembly <NUM> may be an embodiment of the pancake lens assembly <NUM>. The pancake lens assembly <NUM> may also magnify an image light received from the electronic display, correct optical aberrations associated with the image light, such that the corrected image light may be presented to a user of the NED <NUM>.

The locators <NUM> may be objects located at various positions on the NED <NUM> relative to one another and relative to a specific reference point on the NED <NUM>. A locator <NUM> may be a light emitting diode ("LED"), a corner cube reflector, a reflective marker, a type of light source that contrasts with an environment in which the NED <NUM> operates, or a combination thereof. In some embodiments, when the locators <NUM> may be active (i.e., an LED or other type of light-emitting device) elements, the locators <NUM> may emit lights in the visible band (e.g., about <NUM> to about <NUM>), in the infrared ("IR") band (e.g., about <NUM> to about <NUM>), in the ultraviolet band (e.g., about <NUM> to about <NUM>), any other suitable portion of the electromagnetic spectrum, or a combination thereof.

In some embodiments, the locators <NUM> may be located beneath an outer surface of the NED <NUM>, which may be transparent to the light emitted from or reflected by the locators <NUM>. In some embodiments, the locators <NUM> may be sufficiently thin to not substantially attenuate the wavelengths of the light emitted from or reflected by the locators <NUM>. In some embodiments, the outer surface or other portions of the NED <NUM> may be opaque in the visible band. Thus, the locators <NUM> may emit lights in the IR band under an outer surface that may be transparent in the IR band but opaque in the visible band.

The IMU <NUM> may be an electronic device configured to generate fast calibration data based on measurement signals received from one or more of the position sensors <NUM>. A position sensor <NUM> may generate one or more measurement signals in response to the motion of the NED <NUM>. Examples of the position sensors <NUM> may include: one or more accelerometers, one or more gyroscopes, one or more magnetometers, another suitable type of sensor that detects motion, a sensor configured for error correction of the IMU <NUM>, or one or more combinations thereof. The position sensors <NUM> may be located external to the IMU <NUM>, internal to the IMU <NUM>, or a combination thereof.

Based on the one or more measurement signals from one or more position sensors <NUM>, the IMU <NUM> may generate fast calibration data indicating an estimated position of the NED <NUM> relative to an initial position of the NED <NUM>. For example, the position sensors <NUM> may include multiple accelerometers to measure translational motions (forward/back, up/down, left/right) and multiple gyroscopes to measure rotational motions (e.g., pitch, yaw, roll). In some embodiments, the IMU <NUM> may rapidly sample the measurement signals and calculate the estimated position of the NED <NUM> from the sampled data. For example, the IMU <NUM> may integrate the measurement signals received from the accelerometers over time to estimate a velocity vector and integrate the velocity vector over time to determine an estimated position of a reference point on the NED <NUM>. In some embodiments, the IMU <NUM> may provide the sampled measurement signals to the console <NUM>, which may determine the fast calibration data. The reference point may be a point that may be used to describe the position of the NED <NUM>. While the reference point may generally be defined as a point in space, in some embodiments, the reference point may be defined as a point within the NED <NUM> (e.g., a center of the IMU <NUM>).

The IMU <NUM> may receive one or more calibration parameters from the console <NUM>. As discussed below, the one or more calibration parameters may be used to maintain tracking of the NED <NUM>. Based on a received calibration parameter, the IMU <NUM> may adjust one or more IMU parameters (e.g., a sampling rate). In some embodiments, one or more calibration parameters may cause the IMU <NUM> to update an initial position of the reference point, the initial position corresponds to a next calibrated position of the reference point. Updating the initial position of the reference point as the next calibrated position of the reference point may help reduce accumulated errors associated with the determined estimated position. The accumulated errors, also referred to as drift errors, may cause the estimated position of the reference point to "drift" away from the actual position of the reference point over time.

The imaging device <NUM> may generate slow calibration data in accordance with calibration parameters received from the console <NUM>. Slow calibration data may include one or more images showing observed positions of the locators <NUM> that may be detectable by the imaging device <NUM>. The imaging device <NUM> may include one or more photo cameras, one or more video cameras, any other device capable of capturing images including one or more of the locators <NUM>, or some combination thereof. Additionally, the imaging device <NUM> may include one or more filters (e.g., for increasing signal to noise ratio). The imaging device <NUM> may be configured to detect lights emitted or reflected from locators <NUM> in a field of view of the imaging device <NUM>.

In some embodiments, when the locators <NUM> include passive elements (e.g., a retroreflector), the imaging device <NUM> may include a light source that illuminates some or all of the locators <NUM>, which retro-reflect the light towards the light source in the imaging device <NUM>. Slow calibration data may be communicated from the imaging device <NUM> to the console <NUM>, and the imaging device <NUM> may receive one or more calibration parameters from the console <NUM> to adjust one or more imaging parameters (e.g., focal length, focus, frame rate, ISO, sensor temperature, shutter speed, aperture, etc.).

The input/output interface <NUM> may be a device configured to receive an input from a user, such as an action request to the console <NUM>, or to output data received from the console <NUM>. An action request may be a request to perform a particular action. For example, an action request may be to start or end an application or to perform a particular action within the application. The input/output interface <NUM> may include one or more input devices and/or output devices. Example input devices may include: a keyboard, a mouse, a game controller, or any other suitable device for receiving action requests and communicating the received action requests to the console <NUM>. The output devices may include a data transfer port, a display, an video/audio player, etc. An action request received by the input/output interface <NUM> may be communicated to the console <NUM>, which may perform an action corresponding to the action request. In some embodiments, the input/output interface <NUM> may provide haptic feedback to the user in accordance with instructions received from the console <NUM>. For example, haptic feedback may be provided when an action request is received, or the console <NUM> may communicate instructions to the input/output interface <NUM> causing the input/output interface <NUM> to generate haptic feedback when the console <NUM> performs an action.

The console <NUM> may provide media content to the NED <NUM> for presenting to the user in accordance with information received from one or more of: the imaging device <NUM>, the NED <NUM>, and the input/output interface <NUM>. In some embodiments, as shown in <FIG>, the console <NUM> may include an application store <NUM>, a tracking module <NUM>, and a virtual reality ("VR") engine <NUM>. In some embodiments, the console <NUM> may include modules different from those shown in <FIG>. The functions further described below may be distributed among components of the console <NUM> in a manner different from the manner described herein.

The application store <NUM> may store one or more applications for execution by the console <NUM>. An application may be a group of instructions, which when executed by a processor, may generate content for presenting to the user. Content may be generated by an application in response to inputs received from the user via movement of the NED <NUM> or the input/output interface <NUM>. Examples of applications may include gaming applications, conferencing applications, video playback application, or other suitable applications.

The tracking module <NUM> may calibrate the system <NUM> using one or more calibration parameters and may adjust one or more calibration parameters to reduce errors in determination of the position of the NED <NUM>. For example, the tracking module <NUM> may adjust the focus of the imaging device <NUM> to obtain a more accurate position for observed locators on the NED <NUM>. Moreover, calibration performed by the tracking module <NUM> may also account for information received from the IMU <NUM>. Additionally, when tracking of the NED <NUM> is lost (e.g., when the imaging device <NUM> loses line of sight of at least a threshold number of the locators <NUM>), the tracking module <NUM> may re-calibrate portions of or the entire system <NUM>.

The tracking module <NUM> may track movements of the NED <NUM> based on slow calibration data or information from the imaging device <NUM>. The tracking module <NUM> may determine positions of a reference point of the NED <NUM> based on observed locators <NUM> from the slow calibration information and a model of the NED <NUM>. The tracking module <NUM> may also determine positions of a reference point of the NED <NUM> based on position information from the fast calibration data or information. Additionally, in some embodiments, the tracking module <NUM> may use portions of the fast calibration information, the slow calibration information, or some combination thereof, to predict a future location of the NED <NUM>. The tracking module <NUM> may provide the estimated or predicted future position of the NED <NUM> to the engine <NUM>.

The engine <NUM> may execute applications within the system <NUM> and receive position information, acceleration information, velocity information, predicted future positions, or some combination thereof of the NED <NUM> from the tracking module <NUM>. Based on the received information, the engine <NUM> may determine content to provide to the NED <NUM> for presenting to the user. For example, when the received information indicates that the user looks to the left, the engine <NUM> may generate content for the NED <NUM> that mirrors the user's movement in a virtual environment. Additionally, the engine <NUM> may perform an action within an application executing on the console <NUM> in response to an action request received from the input/output interface <NUM>, and provide feedback to the user that the action was performed. The provided feedback may be visual or audible feedback via the NED <NUM> or haptic feedback via the input/output interface <NUM>.

<FIG> illustrates a diagram of the NED <NUM> shown in <FIG>. Referring to <FIG> and <FIG>, the NED <NUM> may include a front body <NUM> and a band <NUM>. The front body <NUM> may include one or more electronic display elements of the electronic display and optics block (not shown in <FIG>), the IMU <NUM>, the one or more position sensors <NUM>, and the locators <NUM>. In the embodiment shown in <FIG>, the position sensors <NUM> may be located within the IMU <NUM>. In some embodiments, neither the IMU <NUM> nor the position sensors <NUM> may be visible to the user.

The locators <NUM> may be located at fixed positions on the front body <NUM> relative to one another and relative to a reference point <NUM>. In the embodiment shown in <FIG>, the reference point <NUM> may be located at the center of the IMU <NUM>. Each of the locators <NUM> may emit lights that may be detectable by the imaging device <NUM>. The locators <NUM>, or some of the locators <NUM>, may be located on a front side 820A, a top side 820B, a bottom side 820C, a right side 820D, and a left side 820E of the front rigid body <NUM>.

<FIG> is a cross-sectional view of the front body <NUM> of the NED <NUM> shown in <FIG>. As shown in <FIG>, the front body <NUM> may include the electronic display <NUM> and the pancake lens assembly <NUM> configured to provide an altered image light to an exit pupil <NUM>. The exit pupil <NUM> may be at a location of the front body <NUM> where an eye <NUM> of the user may be positioned. For illustrative purposes, <FIG> shows a cross-section of the front body <NUM> associated with a single eye <NUM>. Another similar electronic display, separate from the electronic display <NUM>, may provide image light altered by the optics block to another eye of the user.

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 a combination thereof. Other processors not listed above may also be used. A processor may be implemented as software, hardware, firmware, or a 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 a 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 ("ROM"), a flash memory, etc..

The term "unit," "sub-unit," or "module" may encompass a hardware component, a software component, or a combination thereof. For example, a "unit," "sub-unit," or "module" may include a housing, a device, a sensor, a processor, an algorithm, a circuit, an electrical or mechanical connector, etc..

Some portions of this description may describe the embodiments of the disclosure in terms of algorithms and symbolic representations of operations on information. These operations, while described functionally, computationally, or logically, may be implemented by computer programs or equivalent electrical circuits, microcode, or the like. Furthermore, it has also proven convenient at times, to refer to these arrangements of operations as modules, without loss of generality. The described operations and their associated modules may be embodied in software, firmware, hardware, or any combinations thereof.

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 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 performing 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 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 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 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 embodiment but not another embodiment may nevertheless be included in the other embodiment. Such combinations of different features shown in different drawings are also within the scope of the present disclosure.

Claim 1:
An optical waveplate (<NUM>), comprising:
a first birefringent film (<NUM>) including optically anisotropic molecules (<NUM>) arranged to form a first twist structure;
a second birefringent film (<NUM>) stacked with the first birefringent film (<NUM>) and including optically anisotropic molecules (<NUM>) arranged to form a second twist structure; and
a third birefringent film (<NUM>) stacked with the first birefringent film (<NUM>) and the second birefringent film (<NUM>), the third birefringent film (<NUM>) including optically anisotropic molecules (<NUM>) arranged to form a third twist structure,
wherein the optically anisotropic molecules (<NUM>) at a first portion of the first birefringent film (<NUM>) adjacent an interface (<NUM>) between the first birefringent film (<NUM>) and the second birefringent film (<NUM>) are configured with a first azimuthal angle,
wherein the optically anisotropic molecules (<NUM>) at a second portion of the second birefringent film (<NUM>) adjacent the interface (<NUM>) are configured with a second azimuthal angle,
wherein the first azimuthal angle is substantially the same as the second azimuthal angle,
wherein the optical waveplate (<NUM>) is configured to provide a substantially constant retardance over a design wavelength range, and
the substantially constant retardance over the design wavelength range is a quarter-wave retardance or a half-wave retardance for a substantially normally incident light of a design wavelength in the design wavelength range, and
at least one of the first birefringent film (<NUM>), the second birefringent film (<NUM>) or the third birefringent film (<NUM>) is configured to provide a retardance other than the quarter-wave retardance or the half-wave retardance for the substantially normally incident light of the design wavelength of the design wavelength range; and
wherein the design wavelength is a center wavelength of the design wavelength range.