Dynamically reconfigurable holograms for generating color holographic images

Various embodiments of the present invention are directed to negative refractive index-based holograms that can be electronically controlled and dynamically reconfigured to generate one or more color three-dimensional holographic images. In one aspect, a hologram comprises a phase-control layer having a plurality of phase modulation elements. The phase-modulation elements are configured with a negative effective refractive index and selectively transmit wavelengths associated with one of three primary color wavelength. The hologram also includes an intensity-control layer including a plurality of intensity-control elements. One or more color three-dimensional images can be produced by electronically addressing the phase-modulation elements and intensity-control elements in order to phase shift and control the intensity of light transmitted through the hologram. A method for generating a color holographic image using the hologram is also provided, as is a system for generating a color holographic image.

TECHNICAL FIELD

Embodiments of the present invention relate to holograms, and, in particular, to dynamically reconfigurable metamaterial-based holograms for generating three-dimensional color holographic images.

BACKGROUND

Photographs compress images of three-dimensional objects into flat, two-dimensional images displayed by a piece of paper, and television and motion pictures also compress images of moving three-dimensional objects into flat, moving, two-dimensional images displayed on a screen. Photographs, television, and motion pictures are examples of media that display three-dimensional objects as simply intensity mappings. In other words, when an image of a scene is ordinarily reproduced in a photograph or motion picture, a viewer does not see an accurate reproduction of the light scattered from the object, but instead a viewer sees a point-by-point record of just the square of the electromagnetic radiation amplitude reflected from the object (i.e., the irradiance). For example, the light reflected off a photograph carries with it information about the irradiance of the object displayed by the photograph but nothing about the electromagnetic wavefronts that were once scattered from the object during the taking of the photograph. As a result, a viewer only perceives a two-dimensional image of the object. Ideally, when the electromagnetic wavefronts scattered from an object can be reconstructed for a viewer, the viewer sees wavefronts that are indistinguishable from the wavefronts scattered from the original object. Thus, the viewer is able to perceives a reformed three-dimensional image of the object, as if the object was actually before the viewer.

Holography is a method of recording and showing a still three-dimensional holographic image of an object using a hologram and monochromatic light of a particular wavelength from a laser. A conventional hologram is a record of irradiance and wavefronts scattered from an object with respect to incident reference light. The hologram contains point-by-point information for reproducing a three-dimensional holographic image of the object, but is not an image of the object.FIG. 1Ashows a conventional method for generating a hologram of an object100. A laser102generates a coherent beam of light that is split by a beam splitter104to form an object beam and a reference beam. The object beam is reflected onto the object100by a mirror106and light scattered from the illuminated object100and the reference beam form an interference pattern on a photographic plate108. The resulting interference pattern recorded on the photographic plate108is a hologram which contains the information used to reproduce the wavefronts of the object100.

The hologram is used to reconstruct a three-dimensional holographic image of the object in approximately the same position that the object was in when it was recorded.FIG. 1Bshows viewing a holographic image of the object100. As shown inFIG. 1B, the laser102is positioned to illuminate a hologram110with monochromatic light stricking the hologram110at approximately the same angle as the reference beam. A viewer112looking through the hologram110sees a virtual holographic image of the object100suspended in space behind the hologram110in approximately the same position the original object100was in with respect to the photographic plate108. The holographic image changes as the position and orientation of the viewer112changes. Thus the holographic image of the object100appears three dimensional to the viewer112.

However, a hologram can only be used to produce a single still three-dimensional holographic image of an object. The systems used to generate holograms and holographic images are bulky, and the time and number of steps performed to produce a single hologram make current holographic methods and systems impractical for producing three-dimensional motion pictures of objects. In addition, the three-dimensional holographic images are typically monochromatic because light of a single wavelength is often used to generate the holographic image. Thus, it is desirable to have holographic methods and compact holographic systems that enable the production of three-dimensional color holographic images and color holographic motion pictures.

DETAILED DESCRIPTION

Various embodiments of the present invention are directed to negative index materials that can be electronically controlled and dynamically reconfigured to generate wavefronts associated with one or more color holographic images. The negative index materials are crossbar arrays enabling electronic addressing of individual primary color phase-modulation elements. The phase-modulation elements are operated to produce transmission phase changes in incident primary color wavelengths that combine to reproduce the color wavefronts reflected from objects. Thus, holograms comprising an intensity-control layer that reproduces a reflected intensity mapping of objects and a crossbar array that reproduces reflected wavefronts of the objects can be operated in combination to generate color holographic images of the objects.

Negative Index Materials

Negative index materials (“NIMs”), also called metamaterials, are materials with optical properties resulting from the structure of the material rather than from the chemical composition of the material. Natural materials have positive permeability, μ, and may have positive or negative dielectric permittivity ∈, depending on the type of conductivity of the material and frequency ranges. In contrast, NIMs have simultaneously negative ∈ and μ for certain portions of the electromagnetic spectrum, which results in optical properties that are different from those of ordinary composite materials. The optical properties of NIMs can be appreciated by comparing and contrasting the optical properties of NIMs with the optical properties of ordinary composite materials, as described inElectrodynamics of Metamaterials, by A. K. Sarychev and V. M. Shalaev (World Scientific, New York, 2007). For example, consider Maxwell's first-order differential equations for an electromagnetic wave propagating in an ordinary composite material with a time harmonic field as follows:
∇×{right arrow over (E)}=−jωμ{right arrow over (H)}
∇×{right arrow over (H)}=jω∈{right arrow over (E)}
where {right arrow over (E)} is the electric field component, {right arrow over (H)} is the magnetic field component, j=√{square root over (−1)}, and ω is the angular frequency. The solutions of these equations are the plane-wave fields:
{right arrow over (E)}={right arrow over (E)}0exp(=j{right arrow over (k)}o□{right arrow over (r)})
{right arrow over (H)}={right arrow over (H)}0exp(−j{right arrow over (k)}o□{right arrow over (r)})
Substituting the Plane-Wave Equations into Maxwell's First Order Differential Equations gives the relations:
{right arrow over (k)}o×{right arrow over (E)}=ωμ{right arrow over (H)}
{right arrow over (k)}o×{right arrow over (H)}=−ω∈{right arrow over (E)}
where {right arrow over (k)}ois a wavevector indicating the direction an electromagnetic wave propagates within a composite material.FIG. 2Ashows the spatial relationship and relative orientation of the vectors {right arrow over (E)}, {right arrow over (H)}, and {right arrow over (k)}oand reveals that for an ordinary composite material with positive ∈ and μ, the vectors {right arrow over (E)}, {right arrow over (H)}, and {right arrow over (k)}oform an orthogonal, right-handed system of vectors. In addition, the direction of the time-averaged energy flux of the electromagnetic wave is given by the real component of the Poynting vector:

S⇀o=12⁢Re⁡(E⇀×H⇀*)
which, as shown inFIG. 2B, reveals that the vectors {right arrow over (E)}, {right arrow over (H)}, and {right arrow over (S)}oalso form an orthogonal, right-handed vector system. In other words,FIGS. 2A and 2B, show that for an electromagnetic wave propagating through a ordinary composite material, the propagation direction identified by the wavevector {right arrow over (k)}oand the direction of the energy carried by the electromagnetic wave identified by the Poynting vector {right arrow over (S)}oare the same.

On the other hand, consider NIMs, where ∈<0 and μ<0. Maxwell's first order differential equations give the relations:
{right arrow over (k)}m×{right arrow over (E)}=−ω|μ|{right arrow over (H)}
{right arrow over (k)}m×{right arrow over (H)}=ω|∈|{right arrow over (E)}
where {right arrow over (k)}mis a wavevector indicating the direction the phase the electromagnetic wave propagates in a NIM. As shown inFIG. 3A, and in contrast to the composite materials shown inFIG. 2A, for NIMs, the vectors {right arrow over (E)}, {right arrow over (H)}, and {right arrow over (k)}mform an orthogonal, left-handed system of vectors. In other words, comparing the directions of the wavefronts represented by the wavevectors {right arrow over (k)}cand {right arrow over (k)}mshown inFIGS. 2A and 3A, respectively, reveals that electromagnetic waves propagate backwards in NIMs for the same orientation of the vectors {right arrow over (E)} and {right arrow over (H)}. Thus, NIMs are also referred to as “left-handed media” or “backward media.” However, as shown inFIG. 3B, the Poynting vector {right arrow over (S)}min a metamaterial is unaffected by the change of sign of ∈ and μ, and the vectors {right arrow over (E)}, {right arrow over (H)}, and {right arrow over (S)}mstill form an orthogonal, right-handed system of vectors in a left-handed medium. Therefore, in NIMs, energy and wavefronts travel in opposite directions.

Now consider the refraction of an incident ray at the interface between ordinary and left-handed media. Based on the properties of electromagnetic waves travelling in NIMs described above, it follows that, unlike refraction observed in ordinary media, the angles-of-incidence and refraction have opposite signs. Snell's law in NIMs becomes:

sin⁢⁢θ1sin⁢⁢θ2=-k2k1≡n2n1<0,
where the subscripts1and2identify ordinary and left-handed media, respectively. Assuming n1>0, from Snell's law it follows that n2<0. That is, the sign of the square root in the definition of the refractive index is chosen to be negative:
n2=−√{square root over (∈μ)}<0
Hence the term “negative index material” is used to refer to materials having both negatives ∈ and μ.

FIG. 4shows refraction of rays of electromagnetic radiation in an ordinary right-handed medium and a negative index metamaterial. Dashed line404represents a surface normal extending perpendicular to the surface of a medium402. As shown inFIG. 4, angle θ1and wavevector {right arrow over (k)}1406represent the angle-of-incidence and direction of a ray of electromagnetic radiation propagating through an ordinary medium with index of refraction n1>0 and is incident on the medium402. Angle −θ2and wavevector {right arrow over (k)}3408represent the angle-of-refraction and direction of a refracted ray of electromagnetic radiation propagating within the medium402with refractive index n2<0, while angle θ2and wavevector {right arrow over (k)}2410represent the angle-of-refraction and direction of a refracted ray of electromagnetic radiation propagating within the medium402with refractive index n2>0, where |n2|>n1. Thus, for the medium402with a refractive index of n2<0, the incident ray406and the refracted ray408lie on the same side of the surface normal404, and for the medium402with a refractive index of n2>0, the incident ray406and the refracted ray410lie on opposite sides of the surface normal404.

Tracing the paths of optical rays through conventional concave and convex lens made of left-handed media reveals that concave lenses become convergent and convex lens become divergent, thus reversing the behavior of lenses comprising ordinary media.FIG. 5shows focusing properties of a slab502composed of a NIM for electromagnetic radiation emanating from a point source. For incident rays paraxial to an optical axis504, Snell's law gives:

n=n2n1=sin⁢⁢θ1sin⁢⁢θ2⁢•⁢tan⁢⁢θ1tan⁢⁢θ2=a′a=b′b
where n is the refractive index n2of the slab502relative to refractive index of the surrounding medium n1. As shown inFIG. 5, rays emanating from the point source are focused at two points P1and P2. Point P1lies inside the slab502and point P2lies on the side of the slab502opposite the point source. The distance from the point source to the second focusing point P2is given by:

x=a+a′+b′+b=d+dn
where d is the width of the slab. When n equals −1, the focusing effect is not restricted to paraxial rays, because in this case |θ1| equals |θ2| for any angle-of-incidence. In fact, when n equals −1, all rays emanating from the point source are focused at two points, the latter point P2being at a distance2dfrom the point source. Thus, unlike slabs comprising ordinary composite materials, slabs composed of NIMs can be configured to focus electromagnetic radiation.

Negative Index Material Crossbars

FIG. 6shows an isometric view of a NIM crossbar600configured in accordance with embodiments of the present invention. The NIM crossbar600comprises a first layer of approximately parallel nanowires602that are overlain by a second layer of approximately parallel nanowires604. The nanowires of the first layer602run substantially parallel to the x-axis and are approximately perpendicular, in orientation, to the nanowires of the second layer604, which run substantially parallel to the y-axis, although the orientation angle between the nanowires of the layers602and604may vary. The two layers of nanowires form a lattice, or crossbar, with each nanowire of the second layer604overlying all of the nanowires of the first layer602and coming into close contact with each nanowire of the first layer602at nanowire intersections called “resonant elements” that represent the closest contact between two nanowires.

FIG. 7shows an exploded isometric view of the NIM crossbar600configured in accordance with embodiments of the present invention.FIG. 7reveals an intermediate layer702sandwiched between the first layer of nanowires602and the second layer of nanowires604. The intermediate layer702is a continuous layer including an array of regularly spaced holes, such as hole704. In certain embodiments, as shown inFIG. 7, the holes can be rectangular, and in other embodiments, the holes can be square. The nanowires in the first layer602have relatively larger cross-sectional dimensions than the nanowires comprising the second layer604.FIG. 7also reveals that the nanowires in both the first and second layers602and604are configured with substantially regularly spaced protuberances called “fingers” that are separated by notches. For example, nanowire706includes fingers708and710separated by a notch712. The fingers of nanowires of one layer are approximately parallel to the length of the nanowires in the other layer, and the fingers of adjacent nanowires within the same layer are also substantially aligned within the first and second layers602and604, and the holes in the intermediate layer702are substantially aligned with the notches between fingers in the first and second layers602and604. For example, line714passes through notches of adjacent nanowires in the first layer602passes through the hole704in the intermediate layer702and passes through notches in adjacent nanowires in the second layer604.

FIG. 8shows an isometric view of an enlargement800of a four adjacent resonant elements801-804of the NIM crossbar600configured in accordance with embodiments of the present invention. The resonant elements801-804are formed by nanowires806and808extending in the y-direction overlaying portions of nanowires810and812extending in the x-direction. The nanowires806and808are separated from the nanowires810and812by a portion814of intermediate layer702. The width wxof the nanowires810and812in the first layer602is larger than the width wyof the nanowires806and808in the second layer604. The nanowires806and808include fingers protruding in the x-direction, such as fingers816-819of nanowire806, and nanowires810and812include fingers protruding in the y-direction, such as fingers821-824of nanowire810. The fingers of adjacent nanowires lying in the same layer are separated by gaps. As shown inFIG. 8, each of the resonant elements801-804includes two fingers of a nanowire in the first layer602and two fingers of a nanowire in the second layer604. For example, resonant element801includes fingers816and817of nanowire806and fingers821and822of nanowire810.

In other embodiments, the intermediate layer702may be composed of discrete portions of a material lying within each resonant element.FIG. 9shows an isometric view of an enlargement900of four adjacent resonant elements901-904of a NIM crossbar configured in accordance with embodiments of the present invention. The resonant elements901-904include intermediate plus-shaped layers906-909, respectively, disposed within the region between the fingers of nanowires806and808overlaying nanowires810and812. As shown inFIG. 9, adjacent plus-shaped layers906-909are separated by gaps, and each plus-shaped layer fills the space between the nanowire of one layer and the fingers of a nanowire in another layer. For example, plus-shaped layer906is configured to fill the space between fingers821and822and nanowire806and fill the space between fingers816and817and nanowire810.

Although individual nanowires shown inFIG. 6-9have rectangular cross sections, nanowires can also have square, circular, elliptical, or more complex cross sections dictated by design of supporting a magneto-plasmon resonance and related NIM behavior over a particular wavelength or frequency range of interest of the electromagnetic spectrum. The nanowires may be configured to have many different widths or diameters and aspect ratios or eccentricities ranging from approximately ⅕ to approximately 1/20 of the wavelength of incident electromagnetic radiation or ranging from approximately 20 nm to approximately 200 nm. Although the fingers shown inFIGS. 6-9have clearly defined edges, in other embodiments, the fingers may have rounded edges. The term “resonant element” may refer to crossbars having one or more layers of sub-microscale wires, microscale wires, or wires with larger cross-sectional dimensions, in addition to nanowires. The nanowires can be comprised of silver (“Ag”), gold (“Au”), copper (“Cu”), aluminum (“Al”), platinum (“Pt”), or another suitable electronically conducting metal, or the nanowires can be composed of heavily doped semiconductors depending on the frequency of incident electromagnetic radiation.

The crossbar layers can be fabricated by mechanical nanoimprinting techniques. Alternatively, nanowires can be chemically synthesized and can be deposited as layers of approximately parallel nanowires in one or more processing steps, including Langmuir-Blodgett processes with subsequent patterning. Other alternative techniques for fabricating nanowires may also be employed. Thus, a two-layer nanowire crossbar comprising first and second layers of nanowires, as shown inFIGS. 6-9, can be manufactured by any of numerous relatively straightforward processes. Many different types of conductive and semi-conductive nanowires can be chemically synthesized from metallic and semiconductor substances, from combinations of these types of substances, and from other types of substances. A nanowire crossbar may be connected to microscale address-wire leads or other electronic leads, through a variety of different methods in order to electronically couple the nanowires to electronic devices.

The resonant elements can be configured with dimensions that are smaller than the wavelength λ, of electromagnetic radiation incident on the crossbar600enabling the crossbar600to be operated as a NIM over particular wavelength ranges of interest. In particular, the size and shape of the fingers can be selected to have an appropriate inductance, resistance, and capacitance response to a wavelength of interest. In addition, because each resonant element can be separately addressed by biasing the pair of nanowires crossing at the selected resonant element, the refractive index of the intermediate layer of each resonant element can be adjusted by applying appropriate electronic signals, such as voltages or currents, to the nanowires. The size and shape of the fingers and control over the refractive index of the intermediate layer of the resonant elements enables the crossbar600to be configured and operated as a NIM over particular wavelength ranges of interest and shift the transmission phase of electromagnetic radiation transmitted through the crossbar600.

FIG. 10shows a plot of the refractive index1002and phase changes1004for an exemplary NIM crossbar configured and operated in accordance with embodiments of the present invention. Plots1002and1004were obtained using the well-known finite-difference time-domain method (“FDTD”) described inComputational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition, by Allen Taflove and Susan C. Hagness, Artech House Publishers (Jun. 30, 2005).FIG. 10also includes a crossbar1006representing four adjacent resonant elements with parameters identifying the dimensions of the nanowires, fingers, and spacing between resonant elements used to obtain the results displayed in plots1002and1004. The dimensions of the parameters are provided in Table I as follows:

TABLE IParameterDimensionw1225 nmw290 nmw3450 nmw4450 nmg145 nmg245 nm
The nanowires are composed of Ag, and the plus-shaped intermediate layers1007-1010are composed of TiO2with a thickness of 60 nm.

For electromagnetic radiation polarized in the y-direction and incident on the crossbar1006in the z-direction, curves1012and1014of plot1002represent the real and imaginary refractive index components, respectively, over a range of wavelengths with no electronic signal applied to resonant elements of the crossbar1006. A portion1015of the real component1012indicates that the crossbar1006exhibits a negative refractive index for incident electromagnetic radiation with wavelengths ranging from approximately 1.42 μm to approximately 1.55 μm with the largest negative refractive index occurring for incident electromagnetic radiation with wavelengths of approximately 1.5 μm. Curves1016and1018of plot1002represent the real and imaginary refractive index components with a 6% change in the refractive index when appropriate electronic signals are applied to the nanowires of the crossbar1006. Curve1016exhibits a real negative refractive index shift for incident electromagnetic radiation with wavelengths ranging from approximately 1.32 μm to approximately 1.46 μm with the largest negative refractive index occurring for incident electromagnetic radiation with wavelengths of approximately 1.4 μm. In other words, the crossbar1006can be operated to change the refractive index that incident electromagnetic radiation encounters over particular wavelength ranges. For example, incident electromagnetic radiation with a wavelength of interest, such as a wavelength of approximately 1.5 μm, encounters the strongest real negative refractive index component when no electronic signal is applied to the crossbar1006. However, when appropriate electronic signals are applied to the nanowires, the refractive index encountered by the wavelength of interest is shifted to a positive relatively smaller in magnitude refractive index, as indicated by directional arrow1020.

A change in the refractive index encountered by the wavelength of interest shifts the transmission phase of the wavelength of interest. Curves1022-1024of plot1004represent the transmission phase of electromagnetic radiation over a range of wavelengths passing through the crossbar1006for three different refractive indices. Curve1022represents the transmission phase acquired by electromagnetic radiation over a range of wavelengths passing through the crossbar1006when no electronic signal is applied to the crossbar1006. Curve1024represents the transmission phase acquired by electromagnetic radiation over a range of wavelengths passing through the crossbar1006when electronic signals applied to the nanowires of the crossbar1006increase the refractive index of the intermediate layers1007-1010by 3%. Curve1026represents the transmission phase acquired by electromagnetic radiation over a range of wavelengths passing through the crossbar1006when electronic signals applied to the nanowires of the crossbar1006decrease the refractive index of the intermediate layers1007-1010by 3%. The crossbar1006can be operated to shift the phase acquired by a wavelength of interest. The transmission phase is the phase acquired by electromagnetic radiation transmitted through the crossbar1006. For example, when no electronic signal is applied to the crossbar1006, point1028indicates that electromagnetic radiation with the wavelength interest, approximately 1.58 μm, transmitted through the crossbar1006acquires a transmission phase of approximately −0.7 radians. On the other hand, when electronic signals corresponding to the curve1026are applied to the crossbar1006, the wavelength of interest acquires a transmission phase of approximately −1.78 radians, which is a transmission phase shift of approximately −1.2 radians from the point1028to the point1030, as indicated by directional arrow1032.

Resonant Elements

The refractive index of the materials selected for the intermediate layer of the resonant elements can vary according to the particular molecular configuration or electronic states of the material. The materials selected for the resonant elements exhibit an appreciable refractive index change in response to externally applied electric fields, which can be used to control the resonant behavior of the phase shift, as described above with reference toFIG. 10. In certain embodiments, the material may transition reversibly from one state to another and back, so that the resonant elements may be reconfigured, or programmed, by application of differential current levels or voltages, called electronic signals, to selected resonant elements. The molecules comprising the intermediate layers of the resonant elements may have various different states in which the molecules exhibit resistive, semiconductor-like, or conductive electrical properties. The states and relative energies of the states of the intermediate layer materials may be controlled by applying differential current levels or voltages to the overlapping nanowires forming the resonant element. For example, in certain embodiments, certain states of the intermediate layer materials can be set by applying electronic signals to nanowires of a resonant element. In certain embodiments, the applied electronic signals can change the oxidation or redox state of the intermediate layer material which induces a change in the refractive index of the resonant element. Additional circuit elements such as diodes, transistors, memristors, capacitors, and resistors for optimal performance can be formed at resonant elements or a part of the nanowire crossbar. A nanowire crossbar can also be integrated with CMOS circuits.

In certain embodiments, the refractive index of the resonant elements can be configured and operated as p-n junctions in order to change the refractive index of the resonant elements by carrier injection.FIG. 11shows an isometric view a resonant element1100configured with a p-n junction intermediate layer1102in accordance with embodiments of the present invention. The p-n junction1102can be composed of a wide variety of semiconductor materials including various combinations of elemental and compound semiconductors. Indirect elemental semiconductors include silicon (Si) and germanium (Ge), and compound semiconductors include III-V materials, where Roman numerals III and V represent elements in the Ma and Va columns of the Periodic Table of the Elements. Compound semiconductors can be composed of column Ma elements, such as aluminum (Al), gallium (Ga), and indium (In), in combination with column Va elements, such as nitrogen (N), phosphorus (P), arsenic (As), and antimony (Sb). Compound semiconductors can also be further classified according to the relative quantities of III and V elements. For example, binary semiconductor compounds include semiconductors with empirical formulas GaAs, InP, InAs, and GaP; ternary compound semiconductors include semiconductors with empirical formula GaAsyP1-y, where y ranges from greater than 0 to less than 1; and quaternary compound semiconductors include semiconductors with empirical formula InxGa1-xAsyP1-y, where both x and y independently range from greater than 0 to less than 1. Other types of suitable compound semiconductors include II-VI materials, where II and VI represent elements in the IIb and VIa columns of the periodic table. For example, CdSe, ZnSe, ZnS, and ZnO are empirical formulas of exemplary binary II-VI compound semiconductors.

As shown inFIG. 11, p-n junction1102includes a p-type layer and an n-type layer, where the p-type layer is doped with electron accepting impurities and the n-type layer is doped with electron donating impurities. The impurities also called dopants can be atoms. The dopants can be p-type impurities, which are atoms that introduce vacant electronic energy levels called “holes” to the electronic band gaps of the p-n junction1102. These impurities are also called “electron acceptors.” The dopants can be n-type impurities, which are atoms that introduce filled electronic energy levels to the electronic band gap of the p-n junction1102. These impurities are called “electron donors.” For example, boron (B), Al, and Ga are p-type impurities that introduce vacant electronic energy levels near the valence band of Si; and P, As, and Sb are n-type impurities that introduce filled electronic energy levels near the conduction band of Si. In III-V compound semiconductors, column VI impurities substitute for column V sites in the III-V lattice and serve as n-type impurities, and column II impurities substitute for column III atoms in the III-V lattice to form p-type impurities. Moderate doping of the p-type and n-type layers can have impurity concentrations in excess of about 1015impurities/cm3while heavier doping can have impurity concentrations in excess of about 1019impurities/cm3.

The refractive index of the p-n junction1102can be adjusted by varying the magnitude and type of bias applied to p-n junction1102. For example, a forward bias injects electrons into the n-type layer and vacant electronic states called “holes” are injected into the p-type layer. Under a reverse bias, electrons are injected into the p-type layer and holes are injecting into the n-type layer. However, once the bias is removed, the electrons and holes are swept out of the layers and the p-n junction1102returns to an unbiased electronic state. The refractive index of the p-n junction1102is different under the forward, reverse, and no bias.

In other embodiments, the resonant elements can be configured as memristors that can change and retain their resistance state even after the bias has been removed. Each resistance state corresponds to a different refractive index.FIG. 12shows an isometric view a resonant element1200configured with an intermediate memristors layer1202in accordance with embodiments of the present invention. The memristor layer1202includes a primary active region, or layer, and a secondary active region, or layer. The primary active region comprises a thin film of a material that is electronically semiconducting or nominally electronically insulating and can also be a weakly ionic conductor. The primary active material is capable of tranporting and hosting ions that act as dopants to control the flow of electrons through the resonantor element1200. The basic mode of operation is to apply a voltage bias of an appropriate magnitude and polarity across the memristor layers at the junctions. The electrical field, also called a “drift field,” enables the motion of the dopants in the primary material to drift into or out of the primary material via ionic transport. The ionic species are specifically chosen from those that act as electrical dopants for the primary material, and thereby change the rectifying state of the primary active material. The memristor layer1202can be placed in one of the four different types of rectifying states: a forward rectifier, a reverse rectifier, a head-to-head rectifier, and a shunted rectifier, as shown inFIG. 13. Each of the rectifying states corresponds to a different refractive index.

In addition, the primary active material and the dopants are chosen such that the drift of the dopants into or out of the primary active material is possible but not too facile in order to ensure that the memristor layer1202remains in a particular rectifying state for a reasonable period of time, perhaps for many years at room temperature. This ensures that the memristor layer1202is nonvolatile. In other words, the memristor layer1202holds its rectifying state (i.e., keeps memory of its resistive state) after the drift field has been removed. Applying a drift field with a large enough magnitude causes both electron current and dopant to drift, whereas applying biases with lower relative voltage magnitudes than the drift field causes neglible dopant drift enabling the element to hold its rectifying state.

On the other hand, the secondary active region comprises a thin film that is a source of dopants for the primary active material. These dopants may be impurity atoms such as hydrogen or some other cation, such as alkali or transition metals, that act as electron donors for the primary active material. Alternatively, the dopants can be anion vacancies, which in the primary active material are charged and therefore are also electron donors for the lattice. It is also possible to drive the anions into the primary active material, which become electon acceptors or hole donors.

The primary active material can be nanocrystalline, nanoporous, or amorphous. The mobility of the dopants in such nanostructured materials is much higher than in bulk crystalline material, since diffusion can occur through grain boundaries, pores or through local structural imperfections in an amorphous material. Also, because the primary active material film is thin, the amount of time needed for dopants to diffuse into or out of region of the film to substantially change the film's conductivety is relatively rapid. For example, the time needed for a diffusive process varies as the square of the distance convered, so the time to diffuse one nanometer is one-millionth the time to diffuse one micrometer.

The primary active and secondary active regions of the memristor layer1202are contacted on either side by nanowires or one of the nanowires can be composed of a semiconductor material and the other a metal. When the memristor layer1202is composed of semiconductor material, the contract between a metal electrode and the memristor layer1202depletes the memristor layer1202of free charge carriers. Thus, the memristor layer1202has a net charge that depends on the identity of the dopant which is positive in the case of electron donors and negative in the case of electron acceptors.

Switching from one rectifying state to another can be accomplished by applying an electric field of an appropriate magnitude and polarity across the memristor layer1202. The electric field forces the dopants to drift into or out of the electrode/active region interface regions thus changing the rectifying state of the memristor layer1202. For example, as shown inFIG. 13, an appropriate electric field can be used to force dopants located near the interfaces of the shunted rectifier to move to one of the interfaces thus changing the shunted rectifier into either the forward rectifier or the reverse rectifier.

The ability of the charged species to diffuse into and out of the primary active material is substantially improved if one of the interfaces connecting the memristor layer1202to a metal or semiconductor electrode is non-covalently bonded. Such an interface may be caused by a void in the material or it may be the result of an interface that contains a material that does not form covalent bonds with the electrode, the primary active material, or both. This non-covalently bonded interface lowers the activation energy of the atomic rearrangements that are needed for drift of the dopants in the primary active material. This interface is essentially an extremely thin insulator, and adds very little to the total series resistance of the element.

The primary and secondary active materials of the memristor layer1202can be oxides, sulfides, selenides, nitrides, phosphides, arsenides, chlorides, hydrides, and bromides of the transition and rare earth metals, with or without the alkaline earth metals being present. In addition, there are various alloys of these compounds with each other, which can have a wide range of compositions if they are mutually soluble in each other. In addition, the memristor layer1202can be composed of mixed compounds, in which there are two or more metal atoms combined with some number of electronegative elements. The dopants can be anion vacancies or different valence elements doped in the memristor layer1202. One combination of materials is a primary active material that is undoped and stoichiometric, and thus a good insulator, combined with a secondary source/sink of the same or related parent material that either contains a large concentration of anion vacancies or other dopants that can drift into the primary material under the application of an appropriate bias.

The memristor layer1202can be composed of oxides that contain at least one oxygen atom (O) and at least one other element. In particular, the memristor layer1202can be composed of silica (SiO2), titania (TiO2), nickel-oxide (NiO), zirconia (ZrO2), and hafnia (HfO2) with or without 3d impurities (e.g., Cr, Mn), or sp-impurities (e.g., Li, Be, Ca). These materials are compatible with silicon (Si) integrated circuit technology because they do not create doping in the Si. Other embodiments for the memristor layer1202include alloys of these oxides in pairs or with all three of the elements Ti, Zr, and Hf present. For example, the memristor layer1202can be composed of TixZryHfzO2, where x+y+z=1. Related compounds include titanates, zirconates, and hafnates. For example, titanates includes ATiO3, where A represents one of the divalent elements strontium (Sr), barium (Ba) calcium (Ca), magnesium (Mg), zinc (Zn), and cadmium (Cd). In general, the memristor layer1202can be composed of ABO3, where A represents a divalent element (e.g., Sr++, Ba++) and B represents Ti4+, Zr4+, and Hf+. The memristor layer1202can also be composed of alloys of these various compounds, such as CaaSrbBacTixZryHfzO3, where a+b+c=1 and x+y+z=1. There are also a wide variety of other oxides of the transition and rare earth metals with different valences that may be used, both individually and as more complex compounds. In each case, the mobile dopant can be an oxygen vacancy or an aliovalent element doped into the memristor layer1202. The oxygen vacancies effectively act as dopants with one shallow and one deep energy level. Because even a relatively minor nonstoichiometry of about 0.1% oxygen vacancies in TiO2, is approximately equivalent to 1020dopants/cm3, modulating oxygen vacancy profiles have strong effect on electron transport.

In other embodiments, the memristor layer1202can be a sulfide or a selenide of the transition metals with some ionic bonding character, essentially the sulfide and selenide analogues of the oxides described above.

In other embodiments, the memristor layer1202can be a semiconducting nitride or a semiconducting halide. For example, semiconducting nitrides include MN, GaN, ScN, YN, LaN, rare earth nitrides, and alloys of these compounds and more complex mixed metal nitrides, and semiconducting halides include CuCl, CuBr, and AgCl. The memristor layer1202can be a phosphide or an arsenide of various transition and rare earth metals. In all of these compounds, the mobile dopant can be an anion vacancy or an aliovalent element.

A variety of dopants can be used and are selected from a group consisting of hydrogen, alkali, and alkaline earth cations, transition metal cations, rare earth cations, oxygen anions or vacancies, nitrogen anions or vacancies, pnictide anions or vacancies, or halide anions or vacancies. Other suitable materials include metal hydrides, such as Mg2NiH4, Mg2MnH7, Mg6CO2H11, Mg2CoH5, Mg2CoH5, and Mg2FeH6, and copper oxides, such as Cu2O and CuO, exhibit large changes in refractive indices.

Dynamically Reconfigurable Color Holograms

FIG. 14shows an exploded isometric view of an electronically addressable and dynamically reconfigurable hologram1400configured in accordance with embodiments of the present invention. The hologram1400includes a phase-control layer1402and an intensity-control layer1404. As shown in the example ofFIG. 14, the surface1406of phase-control layer1402and the surface1408of intensity-control layer1404include grid lines that outline two different two-dimensional arrays of squares. Each square in of phase-control layer1402represents a “phase-modulation element” that is substantially aligned with an “intensity-control element” of intensity-control layer1204. For example, as shown inFIG. 14, directional arrow1410passes through a highlighted first phase-modulation element1412located in phase-control layer1402and passes through an associated second highlighted intensity-control element1414located in intensity-control layer1404.

The phase-control layer1402is a resonant plasmonic metamaterial that can be operated to exhibit negative refraction for particular wavelengths of light. The resonant behavior translates into phase changes of refracted light. The effective refractive index of each phase-modulation element in phase-control layer1402can be independently and electronically controlled, and the transparency of each intensity-control element in intensity-control layer1404can also be independently and electronically controlled. In other words, the phase-modulation elements and the intensity-control elements are said to be “electronically addressable.” For a ray of light passing through any pair of aligned phase-modulation and intensity-control elements, a transmission phase can be applied to the ray by the phase-modulation element followed by a reduction in the intensity produced by the corresponding intensity-control element. For example, suppose directional arrow1410represents a ray of light originating from a light source (not shown) located behind phase-control layer1402. As the ray passes through the phase-modulation element1412, a first electronic signal applied to the element1412induces a change in the refractive index of the element1412. As a result, the ray1410acquires a transmission phase as it emerges from the pixel1412, and it may also experience an intensity decrease due to insertion loss. As the ray subsequently passes through intensity-control element1414, a second electronic signal applied to the element1414changes the transparency of the element1414and, thus, adjusts the intensity of the ray as it emerges from the intensity-control layer1404. In other words, the phase-control layer1402and the intensity-control layer1404can be operated in conjunction to reproduce both wavefronts and intensity variations in light transmitted through individual elements of the phase-control layer1402and the intensity-control layer1404. As a result, three-dimensional images can be produced by this collective optical effect of controlling the wavefront and the intensity of light emerging from the hologram1400. Because the effective refractive index and the intensity of each element can be separately and electronically controlled, three-dimensional motion pictures can be produced. A more detailed description of the operation of the hologram1400is described below.

Embodiments of the present invention are not limited to a one-to-one correspondence between phase-modulation elements and intensity-control elements. In other embodiments, the phase-modulation elements and intensity-control elements can be arranged and configured so that light is transmitted through one or more phase-modulation elements and subsequently transmitted through one or more intensity-control elements.

FIG. 15shows an isometric view of the phase-control layer1402configured in accordance with embodiments of the present invention. An enlarged region1502reveals that the phase-control layer1402is implemented as a NIM crossbar comprising an intermediate layer sandwiched between a first layer of substantially parallel nanowires1504and a second layer of approximately parallel nanowires1506, where the nanowires in the first layer1504are approximately perpendicular to the nanowires in the second layer1506.

FIG. 16shows an exploded isometric view of the phase-control layer1402comprising an intermediate layer1601sandwiched between two outer nanowire layers1602and1603, as described above with reference toFIG. 7. The intermediate layer1601serves as a phase-modulation layer as described below and, hereinafter, is also referred to as the phase-modulation layer1601. Each phase-modulation element is electronically addressed by applying appropriate electronic signals to substantially orthogonal overlapping nanowires defining the phase-modulation element. For example, as shown inFIG. 16, applying an appropriate electronic signal to nanowires1606of nanowire layer1602and simultaneously applying an appropriate electronic signal to nanowires1608of nanowire layer1603produces a voltage across, or current passing through, a region1610of layer1601causing the refractive index of the region1610to change. The degree to which the refractive index is changed can be varied depending on the magnitude of the electronic signal applied to the region1610.

The intermediation layer1601is composed of materials and configured so that each phase-modulation element transmits only one of three wavelengths, each wavelength associated with one of three primary colors of the color spectrum. For example, in certain embodiments, a first wavelength λrcorresponds to a wavelength in the red portion of the color spectrum, a second wavelength λgcorresponds to a wavelength in the green portion of the color spectrum, and a third wavelength λbcorresponds to a wavelength in the blue portion of the color spectrum. The three different types of phase-modulation elements are referred as red, green, and blue elements. A red element transmits only the wavelength λr, a green element transmits only the wavelength λg, and the green element transmits only the wavelength λb.

A color pixel can be formed by three proximate red, green, and blue phase-modulation elements.FIG. 17shows an isometric view of the phase-control layer1402and three different enlargements of the same region. Each enlargement displays one of three different patterns1701-1703for arranging red, green, and blue elements to form pixels in accordance with embodiment of the present invention. In each pattern, heavy shaded phase-modulation elements, such as element1704, represent red elements; lightly shaded phase-modulation elements, such as element1705, represent green elements; and cross-hatched phase-modulation elements, such as element1706, represent blue elements. Pattern1701represents an embodiment where the red, green, and blue elements run along a diagonal of the phase-control layer1402. Pattern1702represents an embodiment where odd rows comprise alternating green and blue elements and even rows comprise alternating red and green elements. A color pixel for the pattern1701can be composed of red, green, and blue elements1704-1706; and a color pixel for the pattern1702can be composed of red and blue elements1708and1709and two green elements1710. The pattern1703comprises elongated elements arranged in columns of the same color extending in the y-direction. For example, blue, red, and green elongated elements1711-1713comprise one pixel; and blue, red, and green elongate elements1714-1716comprise adjacent pixel. The blue elements1711and1714lie within a column of blue elements, the red elements1712and1715lie within a column of red elements, and the green elements1713and1716lie within a column of green elements. The red, green, and blue columns of elements extend in the y-direction along the entire length of the phase-control layer1402. The pattern of elements1701-1703represent only three of many possible ways in which primary color elements can be arranged to form pixels. In other embodiments, other suitable patterns of primary color elements can be used.

FIG. 18shows an isometric view of an enlarged region of the phase-control layer1402shown inFIG. 17in accordance with embodiments of the present invention. Four phase-modulation elements1801-1804are identified inFIG. 18by dashed-line enclosures. The phase-modulation elements1801-1804are each composed of a square array of 9 resonant elements and each phase-modulation element transmits one of the three primary color wavelengths λr, λg, and λb. As shown inFIG. 18, the phase-modulation elements1801and1803only transmit the wavelength λg, the phase-modulation element1802only transmits the wavelength λr, and the phase-modulation element1804only transmits the wavelength λb. A change in the effective refractive index of a phase-modulation element is the result of changes in the effective refractive indices of the resonant elements comprising the phase-modulation element. As described above in the subsections Negative Index Material Crossbars and Resonant Elements, an effective refractive index change of a resonant element can be the result of changes in an oxidation or redox state, resistivity, variation in ion concentration, injection of charge carriers under a forward or reverse bias, or any other source of refractive index change. A change in the effective refractive index of a resonant element depends on the chemical composition of the intermediate layer of the resonant element and on the magnitude and polarity of the current or voltage applied to the resonant element.

As shown inFIG. 18, the nanowires of the phase-modulation elements1801-1804are electronically coupled to voltage sources so that the resonant elements of each phase-modulation element can be individually and electronically addressed. The effective refractive indices of the resonant elements comprising the phase-modulation element1801are changed by applying the same voltage V3to the nanowires1806-1808and a different voltage V2to all three of the nanowires1810-1812resulting in the same voltage applied across each of the nine resonant elements of the phase-modulation element1801. As a result, the effective refractive indices of the resonant elements comprising the phase-modulation element1801are changed to approximately the same effective refractive index, and electromagnetic radiation with the wavelength λgis transmitted through the phase-modulation element1801and acquires a corresponding transmission phase shift, as described above with reference toFIG. 10. The phase-modulation elements1802-1804are separately and electronically addressed in a similar manner by applying different sets of voltages to corresponding nanowires to produce different effective refractive indices that result in transmission phase shifts in the wavelengths λb, λg, and λr, respectively.

FIG. 19Ashows a cross-sectional view along a line19A-19A, shown inFIG. 18, of the phase-modulation element1801and1802operated in accordance with embodiments of the present invention. Shaded resonant elements1901represent three of the nine resonant elements comprising the phase-modulation element1801, and shaded resonant elements1902represent three of the nine resonant elements comprising the phase-modulation element1802.FIG. 19Bshows a cross-sectional view along a line19B-19B, shown inFIG. 18, of the phase-modulation elements1803and1804operated in accordance with embodiments of the present invention. Shaded resonant elements1903represent three of the nine resonant elements comprising the phase-modulation element1803, and shaded resonant elements1904represent three of the nine resonant elements comprising the phase-modulation element1804.

Embodiments of the present invention are not limited to phase-modulation elements comprising a square array of nine resonant elements. Because voltages can be applied to individual crossed nanowires, the phase-modulation layer1402can be operated with phase-modulation elements ranging from as few as 4 to hundreds or even thousands of resonant elements. In addition, the individual nanowires enable phase-modulation elements to have various shapes such as square, rectangular, circular, elliptical, triangular, or any other suitable shape.

FIG. 20shows a side view of electromagnetic radiation having one of the red, green, or blue wavelengths transmitted through three corresponding red, green, or blue phase-modulation elements of the phase-modulation layer1402operated in accordance with embodiments of the present invention. Rays of electromagnetic radiation2001-2003emanating from point sources2004-2006that generate the same wavelength pass through phase-modulation elements2007-2009, respectively. In the example shown inFIG. 20, each phase-modulation element is electronically addressed, as described above with reference toFIG. 18, and has a different refractive index with phase-modulation element2007having the largest refractive index, phase-modulation element2008having the second largest refractive index, and phase-modulation element2009having the smallest refractive index. As rays2001-2003enter associated phase-modulation elements2007-2009, the electromagnetic radiation slows to a velocity v=c/n where v is the velocity of electromagnetic radiation propagating through a phase-modulation element, c is the speed of electromagnetic radiation in free space, and n is the magnitude of the effective refractive index of the phase-modulation element. Thus, the ray2004passing through the phase-modulation element2007has the slowest velocity, the ray2005passing through the phase-modulation element2008has the second slowest velocity, and the ray2006has the highest relative velocity. As shown inFIG. 20, points2010-2012represent points on electromagnetic waves that simultaneously enter the phase-modulation elements2007-2009, respectively, but due to the different refractive indices at each phase-modulation element, the points2010-2012of the electromagnetic waves emerge at different times from the phase-modulation elements2007-2009and, therefore, are located at different distances from the phase-modulation layer1402. In other words, the electromagnetic waves emerging from the phase-modulation elements2007-2009acquire transmission phase shifts. As shown inFIG. 20, the relative phase difference between the electromagnetic waves emerging from phase-modulation elements2007and2008is φ1, and the relative phase difference between electromagnetic waves emerging from phase-modulation elements2008and2009is φ2, with the greatest relative phase difference of φ1+φ2for electromagnetic waves emerging from phase-modulation elements2007and2009. The electronic signal applied to the phase-modulation elements2007-2009can be rapidly modulated, which, in turn, rapidly modulates the effective refractive indices of the phase-modulation elements2007-2009resulting in rapid changes in relative phase differences between rays emerging from the phase-modulation elements2007-2009.

The red, green, and blue elements each produce three separate red, green, and blue holographic image components, each component corresponds to a separate red, green, and blue wavefront generated as described with reference toFIG. 20. The red, green, and blue components mix or combine at the pixel level such that a viewer perceives a color holographic image.

FIGS. 21A-21Cshows a side view of separate wavefronts associated with three separate red, green, and blue beams of light entering and emerging from the phase-control layer1402, respectively, in accordance with embodiments of the present invention. Ideally monochromatic light is used for each of three primary color wavelengths. However, in practice it is recognized that a light source does not emit true monochromatic light but instead can emit light in a narrow band of wavelengths, which is called “quasimonochomatic light.”FIGS. 21A-21Cshow three separate quasimonochromatic red, green, and blue light uniform wavefronts2101-2103with wavelengths λr, λg, and λb, respectively. The uniform wavefronts2101-2103can be simultaneously generated by three separate light sources, such as three separate lasers with each laser generating a different wavelength. Each wavefront crest is identified by a solid line and each wavefront trough is identified by a dashed line. As shown inFIGS. 21A-21C, the wavefronts2101-2103enter the phase-control layer1402with substantially uniform wavefronts. The phase-modulation elements (not identified) of the phase-control layer1402are simultaneously and selectively electronically addressed to produce corresponding red, green, and blue non-uniform wavefronts2104-2106by changing the transmission phase of different portions of the uniform wavefronts2101-2103, as described above with reference toFIGS. 18-20. In particular, the non-uniform wavefronts2104-2106result from portions of the incident uniform wavefronts2101-2103passing through associated phase-modulation color elements that have been electronically configured with relatively different refractive index magnitudes. For example, the non-uniform wavefront2104is produced by the uniform wavefront2101passing through the red elements, which are electronically addressed so that a portion of the wavefront2104in region2108emerges from certain red elements of the phase-control layer1402later than portions of the wavefront2104in region2110. In other words, the phase-control layer1402is configured to introduce relatively large transmission phase differences between portions of wavefronts emerging in region2108and portions of the wavefront2104emerging in region2110. In practice, in order to produce a three-dimensional color holographic image, all three beams2101-2103are simultaneously sent into the phase-control layer1402. The wavefronts2104-2106are the red, green, and blue holographic image components. A viewer observing the phase-control layer1402perceives a color holographic image produced by the three separate wavelengths2104-2106mixing at the pixel level.

Returning toFIG. 14, in certain embodiments, the intensity-control layer1404can be a liquid crystal layer. The red, green, and blue wavelengths emerging from the phase-modulation elements of the phase-control layer1402pass through corresponding intensity-control elements of intensity-control layer1404, as described above with reference toFIG. 14. The individual intensity-control elements of the intensity-control layer1404can be operated to vary the intensity of the red, green, and blue wavelengths transmitted through corresponding phase-modulation elements in order to produce substantially full color pixels. Each intensity-control element of intensity-control layer1404comprises of a layer of liquid crystal molecules aligned between two transparent electrodes, and two polarizing filters with substantially perpendicular axes of transmission. The electrodes are composed of a transparent conductor such as Indium Tin Oxide (“ITO”). Thus, with no liquid crystal filling the pixel between the polarizing filters, light passing through the first filter is blocked by the second filter. The surfaces of the transparent electrodes contacting the liquid crystal material are treated with a thin polymer molecule that aligns the liquid crystal molecules in a particular direction.

Before applying an electric field to a pixel, the orientation of the liquid crystal molecules is determined by the alignment at the polymer deposited on surfaces of the tranparent electrode. An intensity-control element comprising twisted nematic liquid crystals, the surface alignment direction of the polymer on the first electrode is substantially perpendicular to the alignment direction of the polymer on the second electrode, and the liquid crystal molecules between the electrodes arrange themselves in a helical structure. Because the liquid crystal is birefringent, light passing through one polarizing filter is rotated by the liquid crystal helix allowing the light to pass through the second polarized filter.

When a voltage is applied across the electrodes of an intensity-control element, a torque is created that aligns the liquid crystal molecules parallel to the electric field, distorting the helical structure. This reduces the rotation of the polarization of the incident light, and the pixel appears opaque. When the applied voltage is large enough, the liquid crystal molecules are almost completely untwisted and aligned with the electric field, and the polarization of the incident light is not rotated as it passes through the liquid crystals. This light will then be mainly polarized perpendicular to the second filter, and as a result, the light is blocked by the second filter and the pixel appears black. By controlling the voltage level applied to each intensity-control element, the intensity of light passing through each intensity-control element can be varied thus constituting different intensity levels.

FIG. 22shows intensity levels associated with red, green, and blue wavelengths passing through phase-modulation elements of phase-control layer1402and corresponding intensity-control elements of intensity-control layer1404in accordance with embodiments of the present invention. The red, green, and blue wavelengths emerging from phase-modulation elements in phase-control layer1402pass through intensity-control elements2202-2204that are each configured to produce a different intensity level. As shown inFIG. 22, bars2206-2008represent red, green, and blue intensity levels associated with a single color pixel. To a viewer positioned a distance away from the hologram1400, the light emerging from the intensty-control elements2202-2204is mixed or combined and therefore, the perceives a single color pixel rather than the individual colors comprising the pixel.

FIG. 23shows a control-flow diagram of a method for viewing a color holographic image in accordance with embodiments of the present invention. In step2301, three-dimensional color holographic image data is received from memory, another electronic data storage device, or any three-dimensional color holographic image generating method or system. For example, the color holographic image data can be generated by a CAD program or any other suitable application. In step2302, the three-dimensional color holographic image data associated with each phase-modulation element and intensity-control element is converted into appropriate corresponding electronic signals that can be applied to phase-modulation elements and the intensity-control elements, as described above with reference toFIG. 14-22. In step2303, the electronic signals are applied to the phase-modulation elements of the phase-modulation layer1402and the intensity-control elements of the intensity-control layer1404, as described above with reference toFIGS. 18 and 22. In step2304, three separate primary color beams are generated and transmitted through the hologram1400. Note that in other embodiments, because the phase-modulation elements pass only a limited range of red, green, and blue wavelengths, a while light source can also be used.

The hologram1400can be operated by a computing device that allows a user to electronically address each resonant element as described above with reference toFIG. 17. In practice, the computing device can be any electronic device, including, but not limited to: a desktop computer, a laptop computer, a portable computer, a display system, a computer monitor, a navigation system, a personal digital assistant, a handheld electronic device, an embedded electronic device, or an appliance.

FIG. 24shows a schematic representation of a computing device2400configured in accordance with embodiments of the present invention. The system2400includes one or more processors2402, such as a central processing unit; one or more display devices2404, such as a monitor; a hologram1400interface2406; one or more network interfaces2408, such as a USB port, an Ethernet, or FireWire port; one or more computer-readable mediums2410. Each of these components is operatively coupled to one or more buses2412. For example, the bus2412can be an EISA, a PCI, a USB, a FireWire, a NuBus, or a PDS.

The computer readable medium2410can be any medium that participates in providing instructions to the processor2402for execution and storage of data regarding electronically addressing the layers1402and1404of the hologram1400. For example, the computer readable medium2410can be non-volatile media, such as an optical or a magnetic disk; volatile media, such as memory; and transmission media, such as coaxial cables, copper wire, and fiber optics. Transmission media can also take the form of acoustic, electromagnetic radiation, or radio frequency waves. The color holographic image data can be stored in the computer readable medium2410. The image data includes ranges for each primary color and may be quantified in several different ways and stored as a numerical value. For example, a primary color can range from “0” to “1,” with “0” corresponding to no color represented, “1” corresponding to the full primary color intensity, and any fractional value in between. This reprentation can be used in systems that use floating-point representations for primary color intensities. In computing, 256 intensities associated with each color band can be stored as an integer ranging from “0” to “255,” which is the range offered by a single 8-bit byte. For example, the red, green, and blue triplets (255,0,255) and (255,255,0) represent magenta and yellow pixels, respectively. For relatively higher-end digital imaging systems, the integer range 0 to 65,535 can be used for each color band, which is the range a single 16-bit word can represent.

The computer-readable medium2410also includes an operating system2414, such as Mac OS, Windows, Unix, and Linux; a network communications module2416; and a hologram application2418. The operating system2414can be multi-user, multiprocessing, multitasking, multithreading, real-time and the like. The operating system2414can also perform basic tasks such as recognizing input from input devices, such as a keyboard or a keypad; sending output to the display2404; keeping track of files and directories on medium2410; controlling peripheral devices, such as disk drives, printers, and the phase-control layer1402; and managing traffic on the one or more buses2412. The network applications2416includes various components for establishing and maintaining network connections, such as software for implementing communication protocols including TCP/IP, HTTP, Ethernet, USB, and FireWire. The computer readable medium2410can also store other software applications, including word processors, browsers, e-mail, Instant Messaging, and media players.

The hologram application2418provides various software components for enabling electronic addressing of resonant elements of the phase-control layer1402, as described above with reference toFIG. 18. In certain embodiments, some or all of the processes performed by the application2418can be integrated into the operating system2414. In certain embodiments, the processes can be at least partially implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in any combination thereof.

FIG. 25shows an example of a system for generating a three-dimensional color holographic image in accordance with embodiments of the present invention. The system comprises a desktop computer2502, the hologram1400, and a light source2504comprising three separate green, blue, and red lasers2506-2508. In other embodiments, the light source2504can be a white light source. The computer2502includes a processor and memory that processes and stores the data representing various images of objects and scenes. The images are stored in the memory as data files comprising three dimensional coordinates and associated intensity and color values. A three dimensional image of an object can be displayed on one side of the hologram1400as follows. The light source2504is positioned and configured to emit quasimonochromatic light that passes through the electronically addressed hologram1400, as described above with reference toFIGS. 14-23. A program stored on the computer system memory displays the image as a three-dimension object by translating the data files into electronic addresses that are applied to particular phase-modulation and intensity-control elements of the layers1402and1404. Light passing through each phase-modulation and associated intensity-control element acquires an appropriate transmission phase and intensity in order to reproduce the wavefront reflected by the object and intensty mapping over a range of viewing angles. As a result, the image stored in the computer is perceived by a viewer2505as a virtual three-dimensional color holographic image of an object suspended behind the hologram1400. For example, as shown inFIG. 25, the computer2502displays a two-dimensional image of an airplane2508on a monitor2509and displays a virtual three-dimensional color holographic image2510of the same airplane on the side of the hologram1400opposite the viewer2505. The viewer2505looking at the hologram1400perceives the airplane2510in depth by varying the position of her head or changing her perspective of the view.

In other embodiments, two or more color holographic images can be displayed. In addition, because the hologram1400is dynamically controlled and can be rapidly changed, color holographic motion pictures can also be displayed.