WO2019204667A1

WO2019204667A1 - Polarization-dependent metasurfaces for 2d/3d switchable displays

Info

Publication number: WO2019204667A1
Application number: PCT/US2019/028209
Authority: WO
Inventors: Zhujun Shi; Federico Capasso
Original assignee: President And Fellows Of Harvard College
Priority date: 2018-04-20
Filing date: 2019-04-18
Publication date: 2019-10-24

Abstract

A 2D/3D switchable display is based on one or more polarization-dependent metasurfaces. By imparting a concave lens phase profile for LCP, and a blazed grating phase profile for RCP, the metasurfaces can generate a high resolution 2D image and multiview 3D images. The two modes can be electrically switched using, for example, an active polarization rotator.

Description

POLARIZATION-DEPENDENT METASURFACES FOR 2D/3D

SWITCHABLE DISPLAYS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of and priority to U.S. Provisional Patent Application 62/660,806, filed April 20, 2018, which is incorporated herein by reference in its entirety

STATEMENT OF FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under FA9550-14-1-0389 and FA9550-16-1-0156, awarded by Air Force Office of Scientific Research. The Government has certain rights in the invention.

BACKGROUND

[0003] Three-dimensional (3D) display has attracted great attention lately. Compared to comparative two-dimensional (2D) displays, 3D displays provide not only depth information and spatial relationships, which is usually ambiguous when projected to 2D, but also an immersive viewing experience and more intuitive user interaction.

[0004] Several approaches have been proposed to realize autostereos copic 3D displays, including holographic 3D, volumetric 3D and multiview 3D. Compared to the first two approaches, which specify redesign of the display units, multiview 3D can be readily adapted from the current 2D display technology and has been considered as a promising candidate for future 3D displays. Multiview 3D displays create 3D images by projecting multiple 2D views corresponding to different observation angles. In practice, the pixels corresponding to different perspective angles are multiplexed spatially on a display panel. For a fixed pixel density, this leads to a reduced 3D image resolution (which is inversely proportional to the number of views). In addition, the available 3D content is in shortage compared with the abundant 2D content. These challenges limit the application of 3D-only displays. To address those issues, it is desirable to have a 2D/3D switchable display, which can be switched electrically between two working modes, including a high resolution 2D display mode and a low resolution 3D display mode. In this way, one can incorporate the benefits of 3D displays without degrading the resolution of 2D images.

SUMMARY

[0005] At least some embodiments of the present disclosure relate to a 2D/3D switchable display design based on polarization-dependent metasurfaces. Metasurfaces are ultrathin planar optical devices patterned with sub wavelength nanostructures. The metasurfaces are specified such that the metasurfaces can simultaneously deflect right-hand circularly polarized (RCP) light to an angle and transmit left-hand circularly polarized (LCP) light to the normal direction. Combined with an active polarization rotator, the device can be switched between a high resolution 2D display mode and a multiview 3D display mode. In some embodiments, the nanostructures include at least one of an oxide (e.g., titanium oxide), a nitride (e.g., silicon nitride), a sulfide, a pure element, or a combination thereof. In some embodiments, a cross-section of at least one of the nanostructures has a two-fold symmetry. In some embodiments, the cross-section is rectangular. In some embodiments, the cross- section is elliptical or circular.

[0006] Certain far field radiation patterns in the 2D and 3D mode are disclosed. The effects of spectral bandwidth and beam directionality are also disclosed. Compared with liquid crystal lenses included in comparative 2D/3D switchable displays, the disclosed metasurfaces can deliver more precise phase profile control, thus less aberrations and higher image quality. Furthermore, the disclosed metasurfaces offer additional degrees of freedom in polarization manipulation, which can be integrated with back reflection removal component (including, e.g., a linear polarizer and a quarter waveplate). Moreover, the disclosed metasurfaces can be adapted to much smaller sizes, which is desirable for future high resolution 3D displays.

[0007] In one aspect of the present disclosure, a metasurface includes a plurality of nanostructures that define a phase profile of the metasurface and are configured to receive an incident light including a first input light component of a first circular polarization and a second input light component of a second circular polarization. The phase profile defined by the plurality of nanostructures transmits the first input light component of the first circular polarization substantially towards a normal direction of the metasurface and deflects the second input light component of the second circular polarization by a deflection angle. [0008] In some embodiments, the phase profile defined by the plurality of nanostructures further converts the first input light component of the first circular polarization into a first output light of the second circular polarization and converts the second input light component of the second circular polarization into a second output light of the first circular polarization.

[0009] In some embodiments, the phase profile of the metasurface serves as a diverging lens for the second input light component of the second circular polarization.

[0010] In some embodiments, the phase profile of the metasurface deflects the second input light component of the second circular polarization into the deflection angle by a first diffraction order.

[0011] In some embodiments, the phase profile for the second circular polarization is specified by:

wherein b is the deflection angle, and X is a location coordinate at an X-axis on the metasurface.

[0012] In some embodiments, the phase profile of the metasurface serves as a blazed grating for the first input light component of the first circular polarization.

[0013] In some embodiments, the phase profile of the metasurface converts the first input light component of the first circular polarization into a diffracted beam having a divergence angle and centered at the normal direction of the metasurface.

[0014] In some embodiments, the phase profile for the first circular polarization is specified by:

where / = V ² + Y²/ tan a, a is a half divergence angle, and (X, Y) are location coordinates on the metasurface.

[0015] In some embodiments, the first circular polarization is a left-handed circular polarization and the second circular polarization is a right-handed circular polarization. [0016] In some embodiments, the second input light component of the second circular polarization is deflected by the deflection angle into a direction different from the normal direction of the metasurface.

[0017] In one aspect of the present disclosure, a two-dimensional (2D)/three-dimensional (3D) switchable display device includes at least one light emitter configured to emit an incident light including a first input light component of a first circular polarization and a second input light component of a second circular polarization. The two-dimensional (2D)/three-dimensional (3D) switchable display device further includes a metasurface disposed on the at least one light emitter, the metasurface including a plurality of nanostructures defining a phase profile, the plurality of nanostructures of the metasurface configured to transmit the first input light component substantially towards a first normal direction of the metasurface and configured to deflect the second input light component to a second direction different from the first normal direction. The two-dimensional (2D)/three- dimensional (3D) switchable display device further includes a polarization rotator, and in an OFF state, the polarization rotator is configured to rotate the polarization of light passing through the metasurface by 90°.

[0018] In some embodiments, in an ON state, the polarization rotator does not change the polarization of the light passing through the metasurface.

[0019] In some embodiments, the plurality of nanostructures of the metasurface are further configured to convert the first input light component of the first circular polarization into a first output light of the second circular polarization and configured to convert the second input light component of the second circular polarization into a second output light of the first circular polarization.

[0020] In some embodiments, the two-dimensional (2D)/three-dimensional (3D) switchable display device further includes a quarter waveplate disposed between the metasurface and the polarization rotator, and a passive linear polarizer disposed on the polarization rotator.

[0021] In some embodiments, the quarter waveplate is configured to transform the first output light of the second circular polarization into the first output light of a first linear polarization direction, and is configured to transform the second output light of the first circular polarization into the second output light of a second linear polarization direction.

[0022] In some embodiments, the passive linear polarizer is configured to block light of the first linear polarization direction and transmit light of the second linear polarization direction.

[0023] In some embodiments, the first circular polarization is a left-handed circular polarization and the second circular polarization is a right-handed circular polarization.

[0024] In some embodiments, the second input light component of the second circular polarization emitted by the at least one light emitter corresponds to a 2D mode of the 2D/3D switchable display device.

[0025] In some embodiments, the first input light component of the first circular polarization emitted by the at least one light emitter corresponds to a plurality of views of a 3D mode of the 2D/3D switchable display device.

[0026] In some embodiments, the at least one light emitter includes a plurality of subpixels, and each of the plurality of subpixels corresponds to one of a plurality of views of a 3D mode of the 2D/3D switchable display device.

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] For a better understanding of the nature and objects of some embodiments of this disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.

[0028] FIG. 1(a), FIG. 1(b), and FIG. 1(c) illustrate a schematic of a metasurface-based multiview pixel.

[0029] FIG. 2(a) illustrates a metasurface-based 2D/3D switchable display in a 2D mode.

[0030] FIG. 2(b) illustrates the metasurface-based 2D/3D switchable display in a 3D mode.

[0031] FIG. 3(a) illustrates a ray tracing diagram of a metasurface in a 2D mode.

[0032] FIG. 3(b) illustrates a ray tracing diagram of the metasurface in a 3D mode.

[0033] FIG. 4(a) illustrates a normalized intensity distribution in the far field for LCP incident light. [0034] FIG. 4(b) illustrates a normalized intensity distribution in the far field for RCP incident light.

[0035] FIG. 4(c) illustrates a normalized intensity distribution in the far field for collimated RCP incident light. DESCRIPTION

[0036] Most comparative 2D/3D switchable display designs fall into three categories: parallax barrier-based design, active liquid crystal lens (LC lens) based design, and passive liquid crystal lens based design. Despite their various implementations, those 2D/3D switchable displays rely on the liquid crystal modules (e.g., LC parallax barriers, or active/passive LC lenses) to generate multiple views. The liquid crystal technology, e.g., the LC lenses, has several drawbacks and limitations in applications.

[0037] First, it is challenging to control precisely the phase retardation profile of LC lenses. In general, LC lenses suffer from poor focusing ability, undesired optical aberrations and serious crosstalk, even with sophisticated electrode patterning. For active LC lenses, the large driving electric voltage specified can be a concern as well. Second, the size of LC lenses limits the 3D image resolution. With the advances in display manufacturing, it is expected that the pixel size decreases over years. Smaller size of individual pixels leads to increased 2D image resolution. However, the 3D image resolution is still dictated by the‘multiview pixel’ size, which corresponds to the LC lens diameter and is usually on the order of hundreds of micrometers. Third, the 2D and 3D modes merely operate at linear polarizations. In many situations, however, it is advantageous to remove the ambient light reflected from the display panel. This is usually done by inserting a linear polarizer and a quarter waveplate rotated by 45° in front. In this case, only half of the light, in both the 2D and 3D modes, can pass through the final polarizer, introducing an additional 50% loss of light efficiency. The loss is not circumvented by introducing another waveplate or polarization rotator in between to transform the linearly polarized light to circularly polarized light, since the inserted component fails to block the back reflected ambient light.

[0038] At least some embodiments of the present disclosure relate to a 2D/3D switchable display design based on metasurfaces, which are ultrathin planar optical devices patterned with subwavelength nanostructures. With engineering of the nanostructures, metasurfaces can offer precise and complete control over the phase, transmittance and the polarization of the transmitted light, beyond the scope of comparative refractive and diffractive optics. The metasurfaces can implement distinct phase profiles for an arbitrary pair of orthogonal polarizations. Such metasurfaces are referred to as polarization-dependent metasurfaces. The metasurfaces are specified such that the metasurfaces can simultaneously deflect right-hand circularly polarized (RCP) light to a non-zero angle relative to a normal direction (e.g., at least about 5°, at least about 10°, at least about 20°, or at least about 30°, as shown in FIG. 1(a)) and transmit left-hand circularly polarized (LCP) light substantially parallel to the normal direction (FIG. 1(b)). When combined with an active polarization rotator, such as TN (twisted nematic) cells, the device can switch between the high resolution 2D display mode and the multiview 3D display mode.

[0039] Compared with comparative designs, the disclosed metasurface based approach has several advantages, including: 1) Metasurfaces offer precise control over the phase profile simultaneously at two polarization modes, reducing aberrations and crosstalk. This improves the overall image quality. 2) Metasurfaces can be adapted to arbitrary sizes, e.g., as small as about 10 micrometers or as large as hundreds of micrometers. This allows potential high resolution 3D displays. 3) Metasurfaces can be designed for an arbitrary pair of orthogonal polarizations, in particular, circular polarizations. Therefore, they are compatible with back- reflection removal components, and other polarization control components. 4) Metasurfaces are ultrathin, and lightweight.

[0040] Metasurface-Based Multiview Pixel

[0041] FIG. 1 illustrates a schematic of a metasurface-based multiview pixel. A 2D/3D switchable multiview display can include a plurality of such multiview pixels. Each patch of metasurface corresponds to one subpixel that projects light to a specific viewing angle in a 3D mode. To incorporate multiple views, multiple subpixels form a multiview pixel. The number of subpixels may equal the number of views in the 3D mode.

[0042] FIG. 1(a) illustrates a 3D mode of the multiview pixel. For RCP incident light, the metasurfaces diffract light to the designed viewing angle corresponding to the first order. FIG.

1(b) illustrates a 2D mode of the multiview pixel. For LCP incident light, the metasurfaces transmit light to the normal direction. FIG. 1(c) illustrates a side view of the multiview pixel. As shown in FIG. 1(c), for each multiple pixel, a metasurface layer can be patterned on a transparent spacer (e.g., glass substrate) above LED (light emitting diode) pixels. In other words, the transparent spacer is placed between the metasurface layer and the underlying LED pixel. V_t ... V_n refer to different subpixels.

[0043] A back-reflection removal component including a linear polarizer and a quarter waveplate can be used to remove back reflection from ambient light. The active polarization rotator (e.g., TN cell) can be placed between the passive linear polarizer and the quarter waveplate. By turning on and off the active polarization rotator, the device can be switched between the 2D and 3D operating modes. The active polarization rotator rotates the linear polarization by 90° in an OFF state, and maintains the polarization in an ON state. The active polarization rotator, such as LC TN cells, can modulate the final polarization without affecting the multiple views. The active polarization rotator can be uniformly turned on and off, without a need of active or passive spatially varying modulation of refractive index. Therefore, although the active polarization rotator may include a liquid crystal component, the active polarization rotator does not suffer from the drawbacks of comparative LC lens- based 2D/3D switchable displays.

[0044] The design of the metasurfaces may consider the bandwidth and directionality of the emitted light. Since in the 3D mode the metasurfaces may be interpreted as blazed gratings (for RCP light), the final diffracted angle can be a function of both the incident angle and the wavelength. Finite bandwidth and divergence lead to broadening of the diffracted beam in the far field. The divergence angle (DQ) of the diffracted beam may be large enough to allow for smooth transition between neighboring views, but not too large to prevent excessive overlapping and crosstalk. Therefore, the angular separation between neighboring views (Df) can be comparable to DQ.

[0045] For a given field of view (FOV) and diffracted beam divergence angle (DQ), the

. To accommodate more number of views in the 3D mode, it is desirable to design the light emitting elements to have higher directionality. This can be achieved by, e.g., adding additional optical cavities or engineering existing optical cavities in the LEDs. In the 2D mode, however, high directionality is usually undesired, as it may limit the viewing zone of the 2D images. To address the contradiction, the metasurfaces may be designed to function as a concave (diverging) lens, rather than a uniform transparent layer, in the 2D mode. In this way, relatively high directionality (required for more number of views) in the 3D mode and low directionality (required for broader viewing zone) in the 2D mode can be achieved at the same time.

[0046] FIG. 2(a) illustrates a metasurface-based 2D/3D switchable display in a 2D mode. FIG. 2(b) illustrates the metasurface-based 2D/3D switchable display in a 3D mode. The light emitted from the LEDs is unpolarized and includes LCP and RCP light. The metasurface functions as a diverging lens for LCP light, and as a blazed grating for RCP light. Note that in addition to deflect or transmit the light beam, the metasurface also converts input LCP light to output RCP light, and converts input RCP light to output LCP light.

[0047] The quarter waveplate transforms the LCP and RCP light to x-direction and y- direction linearly polarized light. In the OFF state, the TN cell rotates the linear polarization by about 90°. The passive linear polarizer is oriented such that the x-direction polarization, which corresponds to the 2D image, passes through. In the ON state, the TN cell is transparent, and does not perform any polarization rotation. In this case, the x-direction polarization corresponds to the 3D image. The passive linear polarizer is still oriented such that the x-direction polarization, which now corresponds to the 3D image, passes through.

[0048] In some embodiments, the metasurfaces can be fabricated using, e.g., single-step lithography. In some embodiments, the center of the metasurface and the center of the corresponding subpixel do not necessarily to be precisely aligned. But for optimal result, the metasurface may cover merely one subpixel and does not overlap with other subpixels.

[0049] Design and Phase Profile of Metasurface

[0050] FIG. 3(a) illustrates a ray tracing diagram of a metasurface in a 2D mode. FIG. 3(b) illustrates a ray tracing diagram of the metasurface in a 3D mode. In the 2D mode, the metasurface functions as a concave lens. The phase profile for the 2D mode is given by

where / = V² + Y² / tan a. a is the target half angle (as illustrated in FIG. 3(a)), and ( X , Y) are the location coordinates on the metasurface.

[0051] In the 3D mode, the metasurface functions as a blazed grating. The phase profile for the 3D mode is given by

where b is the target deflection angle (as illustrated in FIG. 3(b)).

[0052] In some embodiments, as demonstrative examples, four metasurfaces may be designed to deflect the beam to about b = 0°, 10°, 20°, 30° in the 3D mode respectively. In those designs, the half diverging angle in the 2D mode may be fixed to be about a = 20°. Viewing angles of about b =—10°,— 20°,—30° may be achieved by simply patterning the metasurfaces in a mirror reflection manner. In total, the design yields a FOV of about 60°. The diameter of the metasurfaces may be designed to be about 20 pm . The incident wavelength may be centered at about 530 nm, with an FWHM (full width at half maximum) spectral bandwidth of about 10 nm.

[0053] The far field radiation patterns in the 2D and 3D modes may be demonstrated. FIG. 4(a) illustrates a normalized intensity distribution in the far field for LCP incident light. The incident light has an FWHM spectral bandwidth of about 10 nm, and a divergence angle of about 5°. FIG. 4(b) illustrates a normalized intensity distribution in the far field for RCP incident light. The incident light has an FWHM spectral bandwidth of about 10 nm, and divergence angle of about 5°.

[0054] For LCP (2D mode), light is transmitted to the zeroth order. As shown in FIG. 4(b), the beam divergence angle is broadened to 35° due to the concave lens phase profile. For RCP (3D mode), light is deflected to the +lst order with an average efficiency of 83%, as shown in FIG. 4(b). In some embodiments, the 0th, -lst and higher diffraction orders may be negligible in the designs due to the precise control of phase profiles of metasurfaces. The divergence angle of the deflected beam (DQ) may be about 9°, providing a smooth transition between the neighboring views (e.g., angular separation Df = 10° by design) while avoiding excessive overlapping and crosstalk. [0055] In some embodiments, the incident light may be collimated, FIG. 4(c) illustrates a normalized intensity distribution in the far field for collimated RCP incident light. The collimated incident light has an FWHM spectral bandwidth of about 10 nm. The design of the metasurface of FIG. 4(c) may be the same as the design of the metasurface of FIGs. 4(a) and 4(b). The divergence of the deflected beam may be primarily dominated by the divergence of the incident light. If highly directional emitted light can be achieved, the number of views to enhance the 3D effect can be further increased.

[0056] Therefore, in at least some embodiments, a 2D/3D switchable display is disclosed based on one or more polarization-dependent metasurfaces. By imparting a concave lens phase profile for LCP, and a blazed grating phase profile for RCP, the metasurfaces can generate a high resolution 2D image or multiview 3D images. The two modes can be electrically switched using, e.g., an active polarization rotator. In some embodiments, the metasurface-based multiview pixel may have a target field of view and an angular resolution of about 60° and about 10°, respectively. The angular resolution may be further improved by engineering the directionality of the LEDs.

[0057] It is to be understood that the term“design” or“designed” (e.g., as used in“design wavelength,”“design focal length” or other similar phrases disclosed herein) refers to parameters set during a design phase; which parameters after fabrication may have an associated tolerance.

[0058] As used herein, the singular terms“a,”“an,” and“the” may include plural referents unless the context clearly dictates otherwise.

[0059] Spatial descriptions, such as“above,”“below,”“up,”“left,”“right,”“down,”“top,”

“bottom,”“vertical,”“horizontal,”“side,”“higher,”“lower,”“upper,”“over,”“under,” and so forth, are indicated with respect to the orientation shown in the figures unless otherwise specified. It should be understood that the spatial descriptions used herein are for purposes of illustration only, and that practical implementations of the structures described herein can be spatially arranged in any orientation or manner, provided that the merits of embodiments of this disclosure are not deviated by such arrangement.

[0060] As used herein, the terms“approximately,”“substantially,”“substantial” and“about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, the terms can refer to a range of variation less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%. For example, two numerical values can be deemed to be “substantially” the same if a difference between the values is less than or equal to ±10% of an average of the values, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.

[0061] For example, substantially parallel can refer to a range of angular variation relative to 0° of less than or equal to ±10°, such as less than or equal to ±5°, less than or equal to ±4°, less than or equal to ±3°, less than or equal to ±2°, less than or equal to ±1°, less than or equal to ±0.5°, less than or equal to ±0.1°, or less than or equal to ±0.05°. For example, substantially perpendicular can refer to a range of angular variation relative to 90° of less than or equal to ±10°, such as less than or equal to ±5°, less than or equal to ±4°, less than or equal to ±3°, less than or equal to ±2°, less than or equal to ±1°, less than or equal to ±0.5°, less than or equal to ±0.1°, or less than or equal to ±0.05°.

[0062] Additionally, amounts, ratios, and other numerical values are sometimes presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified.

[0063] While the present disclosure has been described and illustrated with reference to specific embodiments thereof, these descriptions and illustrations do not limit the present disclosure. It should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the true spirit and scope of the present disclosure as defined by the appended claims. The illustrations may not be necessarily drawn to scale. There may be distinctions between the artistic renditions in the present disclosure and the actual apparatus due to manufacturing processes and tolerances. There may be other embodiments of the present disclosure which are not specifically illustrated. The specification and drawings are to be regarded as illustrative rather than restrictive. Modifications may be made to adapt a particular situation, material, composition of matter, method, or process to the objective, spirit and scope of the present disclosure. All such modifications are intended to be within the scope of the claims appended hereto. While the methods disclosed herein have been described with reference to particular operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or re-ordered to form an equivalent method without departing from the teachings of the present disclosure. Accordingly, unless specifically indicated herein, the order and grouping of the operations are not limitations of the present disclosure.

Claims

CLAIMS What is claimed is:

1. A metasurface, comprising:

a plurality of nanostructures that define a phase profile of the metasurface and are configured to receive an incident light including a first input light component of a first circular polarization and a second input light component of a second circular polarization, wherein the phase profile defined by the plurality of nanostructures transmits the first input light component of the first circular polarization towards a normal direction of the metasurface and deflects the second input light component of the second circular polarization by a deflection angle.

2. The metasurface of claim 1, wherein the phase profile defined by the plurality of nanostructures further converts the first input light component of the first circular polarization into a first output light of the second circular polarization and converts the second input light component of the second circular polarization into a second output light of the first circular polarization.

3. The metasurface of claim 1, wherein the phase profile of the metasurface serves as a diverging lens for the second input light component of the second circular polarization.

4. The metasurface of claim 1, wherein the phase profile of the metasurface deflects the second input light component of the second circular polarization into the deflection angle by a first diffraction order.

5. The metasurface of claim 1, wherein the phase profile for the second circular polarization is specified by:

F(C)= C sin/?,

6. The metasurface of claim 1, wherein the phase profile of the metasurface serves as a blazed grating for the first input light component of the first circular polarization.

7. The metasurface of claim 1, wherein the phase profile of the metasurface converts the first input light component of the first circular polarization into a diffracted beam having a divergence angle and centered at the normal direction of the metasurface.

8. The metasurface of claim 1, wherein the phase profile for the first circular polarization is specified by:

where / = vA² + Y² / tan a, a is a half divergence angle, and (X, Y) are location coordinates on the metasurface.

9. The metasurface of the claim 1, wherein the first circular polarization is a left-handed circular polarization and the second circular polarization is a right-handed circular polarization.

10. The metasurface of the claim 1, wherein the second input light component of the second circular polarization is deflected by the deflection angle into a direction different from the normal direction of the metasurface.

11. A two-dimensional (2D)/three-dimensional (3D) switchable display device, comprising: at least one light emitter configured to emit an incident light including a first input light component of a first circular polarization and a second input light component of a second circular polarization;

a metasurface disposed on the at least one light emitter, the metasurface including a plurality of nanostructures defining a phase profile, the plurality of nanostructures of the metasurface configured to transmit the first input light component towards a first normal direction of the metasurface and configured to deflect the second input light component to a second direction different from the first normal direction; and a polarization rotator, wherein in an OFF state, the polarization rotator is configured to rotate the polarization of light passing through the metasurface by 90°.

12. The 2D/3D switchable display device of claim 11, wherein in an ON state, the polarization rotator does not change the polarization of the light passing through the metasurface.

13. The 2D/3D switchable display device of claim 11, wherein the plurality of nanostructures of the metasurface are further configured to convert the first input light component of the first circular polarization into a first output light of the second circular polarization and configured to convert the second input light component of the second circular polarization into a second output light of the first circular polarization.

14. The 2D/3D switchable display device of claim 13, further comprising:

a quarter waveplate disposed between the metasurface and the polarization rotator; and

a passive linear polarizer disposed on the polarization rotator.

15. The 2D/3D switchable display device of claim 14, wherein the quarter waveplate is configured to transform the first output light of the second circular polarization into the first output light of a first linear polarization direction, and is configured to transform the second output light of the first circular polarization into the second output light of a second linear polarization direction.

16. The 2D/3D switchable display device of claim 15, wherein the passive linear polarizer is configured to block light of the first linear polarization direction and transmit light of the second linear polarization direction.

17. The 2D/3D switchable display device of claim 11, wherein the first circular polarization is a left-handed circular polarization and the second circular polarization is a right-handed circular polarization.

18. The 2D/3D switchable display device of claim 11, wherein the second input light component of the second circular polarization emitted by the at least one light emitter corresponds to a 2D mode of the 2D/3D switchable display device.

19. The 2D/3D switchable display device of claim 11, wherein the first input light component of the first circular polarization emitted by the at least one light emitter corresponds to a plurality of views of a 3D mode of the 2D/3D switchable display device.

20. The 2D/3D switchable display device of claim 11, wherein the at least one light emitter includes a plurality of subpixels, and each of the plurality of subpixels corresponds to one of a plurality of views of a 3D mode of the 2D/3D switchable display device.