WO2019217365A1

WO2019217365A1 - Modified optical microstructures for improved light extraction

Info

Publication number: WO2019217365A1
Application number: PCT/US2019/031037
Authority: WO
Inventors: Byung Yun Joo; Steven S Rosenblum; James Andrew West
Original assignee: Corning Inc
Current assignee: Corning Inc
Priority date: 2018-05-07
Filing date: 2019-05-07
Publication date: 2019-11-14
Anticipated expiration: 2020-11-07
Also published as: TW202001150A

Abstract

Disclosed is an optical assembly including a transparent lightguide plate, a low-index optical layer, and an optical lenticular layer, where the optical lenticular layer includes an array of lenticular lens whose cross-section is substantially rectangular with a sidewall angle approaching 90°.

Description

MODIFIED OPTICAL MICROSTRUCTURES FOR

IMPROVED LIGHT EXTRACTION

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims priority under 35 U.S.C. § 119(e) to United States Provisional Application No. 62/667,854, filed May 7, 2018, the entire contents of which are incorporated herein by reference.

FIELD OF THE DISCLOSURE

[0002] The present disclosure relates to backlighting for LCD panels.

BACKGROUND

[0003] Conventional backlight configurations comprise a flat glass lightguide plate (LGP) between 0.5 and 3 mm in thickness with a row of white light-emitting diodes (LEDs) along one or both long edges of the respective display or monitor. Light is uniformly extracted from the display using a pattern various scattering or refractive light extraction features that are incorporated into the LGP using screen printing, inkjet printing, laser patterning, etching or various other processes. This light extraction pattern is generally selected so that output light has a spatial luminance output that is typically peaked in the middle of the display and decreases to 60-90% of the peak luminance at the edges. To improve the angular characteristics of the backlight unit (BLU), a back reflector (diffusive or specular) is typically placed behind the LGP and various optical films are placed between the LGP and the liquid-crystal module (LCM). These optical films consist of diffusers, brightness enhancement films (BEFs) and reflective polarizers (DBEFs). The combination of reflector, LGP and optical films is known as the BLU. The optical films and the back reflector form an optical cavity that recycles and scatters light that has the wrong polarization or angular direction. Eventually the light will escape from this optical cavity when it has the correct polarization and when its angular direction falls within a desired cone of angular emission.

[0004] Recent BLUs designs also include local-dimming functionality. In an LGP without local dimming, the LED light fans out at approximately ±42° from the input LED location, thereby lighting a significant portion of the width of the LGP. In an LGP with local dimming, optical microstructures having lenticular surfaces (i.e., curved surfaces) can be added to the major surface of the LGP that is facing the LCD panel to contain the spread of LED light to redirect the light, producing a quasi-collimation. Local dimming enables spatial control of contrast enhancement by modulating the intensity of individual LEDs or groups of LEDs. Local dimming also has the effect of increasing brightness by more efficiently extracting light from the LGP.

[0005] Even more recently, BLUs can employ blue LEDs and quantum dots (QD) to improve the color gamut of the TV. Typically, QDs are encapsulated in a film placed within the BLU, above the LGP. After the blue light has been extracted from the LGP, recycling of the light within the optical cavity allows for repeated interactions of the blue light with the red and green QDs thereby enhancing wavelength conversion.

[0006] As discussed, the BLU has many optical components. Typically, these are independent and stand-alone components, but there can be advantages in integrating some of these components into a BLU with fewer independent layers. The advantages include reduced cost, fewer SKUs (stock keeping units), improved reliability, improved optical performance, ease of assembly, and increased stiffness.

[0007] Thus, there is an increasing desire to consolidate or integrate some of the optical functionality of a BLU into the LGP by laminating, depositing, or otherwise making optical contact between additional optical layers and the LGP. While the integrated LGP may offer increased mechanical rigidity, lower cost, and/or a reduced number of components for the BLU, it is typically accompanied by significantly compromised optical performance. Lor the purposes of the present disclosure, the phrase optical contact means that the adjacent surfaces of two optical elements are conformal and are in physical contact with no separation by intervening materials (such as air). Lor the structures disclosed herein, optical contact can be achieved by using a liquid or film adhesive or resin as one of the layers. This class of material will wet the surface of the second element forming a complete physical contact. If the material is a liquid- based resin, it will be cured to a solid state by optical and/or thermal curing. This is the lamination that is described in the following paragraph

[0008] Conventionally, an approach to such integration involves laminating the optical components as optical films to the LGP. However, laminating optical films to the LGP, while providing the integration advantages mentioned above, results in some undesirable effects. The LGPs rely on total internal reflection at the air interfaces on the top and bottom main surfaces of the LGPs. But, because most optical materials have refractive indices near 1.5 across the visible wavelength range, which is similar to the refractive index of the typical glass or plastic materials used in LGPs, if such materials are used in lamination, the light in the LGPs quickly escape into these added layers and light extraction can no longer be controlled to deliver uniform luminance in the BLU. A manifestation of this problem in conventional displays and monitors is a bright band of light near the LED input edge.

[0009] To avoid excess light extraction due to lamination, designs have been introduced that employ a low refractive index of material (n=l .20-1.40) layer in the laminated optical films to control the light extraction. The inventors have discovered, however, that too much light is still extracted near the LEDs due to lamination of the optical films to the LGP. Furthermore, inventors have discovered that the bright band is worse when the lenticular surface structures are added to the LGP. Thus, further improvements are desired that maintains the local dimming functionality and further reduce the excessive light extraction near the LEDs that result in bright band.

SUMMARY

[0010] Disclosed are embodiments of laminated monolithic BLUs having improved lenticular lens structures that reduce the excess light extraction near the LEDs (bright band) due to lamination while maintaining the local dimming feature.

[0011] Advantages of exemplary embodiments include an improvement to LCD performance by eliminating image degradation caused by the presence of the bright band and production of a brighter image by increasing the overall luminance of the display. Further advantages of exemplary embodiments eliminate the need for a large bezel to cover the bright band.

[0012] Some embodiments of the present disclosure relate to an optical assembly comprising a transparent LGP, a low-index optical layer, and an optical lenticular layer. In some

embodiments, the optical lenticular layer includes an array of elongated lenticular lens structures whose cross-sections are trapezoidal or substantially rectangular with a side-wall angle approaching 90°. In some embodiments, the elongated lenticular lens structures comprise a height that tapers to zero as they near the light input edge of the LGP. In some embodiments, the optical lenticular layer can be offset near the light input edge of the LGP so the lenticular lens structures do not exist within the offset distance along the light input edge of the LGP. In further embodiments, the lenticular structures can comprise a fixed height over their elongated length without tapering, thus having a rectangular profile over their length. The rectangular profile lenticular structures can also be offset from the light input edge of the LGP.

[0013] Additional features and advantages will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments as described herein, including the detailed description which follows, the claims, as well as the appended drawings.

[0014] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understanding the nature and character of the claims. The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the description serve to explain principles and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] These figures are provided for the purposes of illustration, it being understood that the embodiments disclosed and discussed herein are not limited to the arrangements and

instrumentalities shown. All of the figures showing structures are schematic and are not intended to show the actual dimensions or proportions.

[0016] FIG. 1 A is a cross-sectional view of an exemplary display device comprising a BLU.

[0017] FIG. 1B is an illustration of an exemplary FGP showing some of the basic structures.

[0018] FIG. 2A is an illustration of the exemplary FGP viewed from the light input surface of the FGP showing the azimuthal angle f notation for the input light rays in the FGP system.

[0019] FIG. 2B is an illustration of the exemplary FGP system of FIG. 2 A viewed from the side showing the relationship between the light input cone angle 0air and

[0020] FIG. 3 is an illustration of the exemplary FGP system of FIGS. 2A and 2B viewed from an oblique angle showing the azimuthal angle ()>LGP and the light cone angle 0air for the input light rays in the FGP system.

[0021] FIG. 4 is a graph where the solid line illustrates the variation of the critical angle in a glass with refractive index of n_giass=l .5 as a function of the refractive index of a coating on the non-input glass surface. The dashed line illustrates the limiting angle of the rays of light from a Lambertian LED coupled into the input surface. The angles above the dashed line and below the solid line represent light leakage due to the loss of total internal reflection.

[0022] FIG. 5 is a graph illustrating that for an LGP with refractive index of n_LGP=L50, the new angle 0’LGP with respect to the surface normal of the non-input surface (air/LGP interface) is calculated for 3 cones of light rays that have angles of0_LGP=42°, 20°, and 5° with respect to the normal of the input face. The new angle will depend on the azimuthal angle around the input cone. In this example, no angles 0’LGP drop below the critical angle of the air/glass interface (shaded region < 42°) where the ray will no longer be subject to total internal reflection and some light will be lost. The extreme high -angle rays from the light source (i.e. 0LGP~42°) will be most at risk.

[0023] FIG. 6 is a graph similar to FIG. 5 but the non-input interface now has a low-index coating (n_¥atmg=L25).

[0024] FIG. 7 is a depiction of some exemplary prism lenticular features.

[0025] FIG. 8 is a graphical illustration of a comparison of modeled bright band illuminance versus prism side-wall angle, A.

[0026] FIG. 9 is a plot of the normalized illuminance of the bright band near the FEDs as a function of the position along the FGP away from the light input surface.

[0027] FIG. 10 is a depiction of the definition of local dimming index (EDI). EDI is local dimming index defined in S. Jung, M. Kim, D. Kim, J. Fee, "Focal dimming design and optimization for edge-type FED backlight unit," SID Symp. Dig. Tech. Papers (2011) pp. 1430- 1432. S. Jung, M. Kim, D. Kim, J. Fee, "Focal dimming design and optimization for edge-type FED backlight unit," SID Symp. Dig. Tech. Papers (2011) pp. 1430-1432.

[0028] FIG. 1 1 is a depiction of positive relief and negative relief lenticular arrays showing tapering.

[0029] FIG. 12A shows a cross-sectional view of the mathematical taper function g(z) for an embodiment of the tapered lenticular structure of the present disclosure.

[0030] FIG. 12B shows a cross-sectional view of the mathematical taper function g(z) for another embodiment of the tapered lenticular structure of the present disclosure.

[0031] FIG. 12C shows a cross-sectional view of the mathematical taper function g(z) for another embodiment of the tapered lenticular structure of the present disclosure. [0032] FIG. 13A shows a cross-sectional view of circular lenticular structures according to some embodiments viewed from the light input surface of the LGP.

[0033] FIG. 13B shows a cross-sectional view of triangular lenticular structures according to some embodiments viewed from the light input surface of the LGP.

[0034] FIG. 13C shows a cross-sectional view of trapezoidal lenticular structures with angle A<90° according to some embodiments viewed from the light input surface of the LGP.

[0035] FIG. 13D shows a cross-sectional view of rectangular lenticular structures with angle A=90° according to some embodiments viewed from the light input surface of the LGP.

[0036] While this description can include specifics, these should not be construed as limitations on the scope, but rather as descriptions of features that can be specific to particular embodiments.

DETAILED DESCRIPTION

[0037] Reference will now be made in detail to embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts.

However, this disclosure may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.

[0038] Ranges can be expressed herein as from“about” one particular value, and/or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent“about,” it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0039] Directional terms as used herein - for example up, down, right, left, front, back, top, bottom, vertical, horizontal - are made only with reference to the figures as drawn and are not intended to imply absolute orientation.

[0040] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus, specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components; plain meaning derived from grammatical organization or punctuation, and; the number or type of embodiments described in the specification.

[0041] As used herein, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. Thus, for example, reference to“a” component includes aspects having two or more such components, unless the context clearly indicates otherwise.

[0042] Similarly, whenever a group is described as consisting of at least one of a group of elements or combinations thereof, the group can consist of any number of those elements recited, either individually or in combination with each other. Unless otherwise specified, a range of values, when recited, includes both the upper and lower limits of the range.

[0043] It also is understood that, unless otherwise specified, terms such as "top," "bottom," "outward," "inward," and the like are words of convenience and are not to be construed as limiting terms.

[0044] Some embodiments include a display having an edge-lit LCD BLU with an LGP. Light from an array of LEDs is coupled into the bottom edge of the transparent LGP and then this light is extracted from the LGP at a uniform rate as it is guided towards the top of the LGP. For the LGP to function correctly it should be highly transparent to minimize light absorption, have smooth edges and sufficient thickness to enable efficient coupling of the light from the LED array, enable total internal reflection (TIR) at all of the non-extraction surface locations in order to maintain light guiding, and have a variable light extraction pattern on the back surface that can extract light at an approximately uniform rate.

[0045] Referring to FIGS. 1 A - 2A, some embodiments are directed to an optical assembly which is an LCD display device 10 comprising an LCD display panel 12 and a BLU 24 arranged to illuminate the LCD panel 12 from behind, i.e., from the backplane side of the LCD panel, using an array of LED light source 50 positioned along one edge of the BLU 24. The LCD display panel 12 comprises a first substance 14 and a second substrate 16 joined by an adhesive material 18 positioned between and around a peripheral edge portion of the first and second substrates. The first and second substrates 14, 16 and adhesive material 18 form a gap 20 therebetween containing liquid crystal material. Spacers (not shown) may also be used at various locations within the gap to maintain consistent spacing of the gap. The first substrate 14 may include color filter material. On the other hand, second substrate 16 includes thin film transistors (TFTs) for controlling the polarization state of the liquid crystal material, and may be referred to as the backplane. LCD panel 12 further includes two polarizing filters 22 disposed on opposite sides of the gap 20 containing the liquid crystal material.

[0046] In some embodiments, the BLU 24 may be spaced apart from the LCD panel 12, although in further embodiments, the BLU may be in contact with or coupled to the LCD panel, such as with a transparent adhesive. Additional optical films (not shown in FIG. 1 A) such as diffusers, BEFs, and DBEFs are commonly placed between the LCD panel 12 and the BLU 24. BLU 24 comprises a glass light guide plate LGP 26 formed with a glass sheet 28 as the light guide, glass sheet 28 including a first major surface 30, a second major surface 32, and a plurality of edge surfaces extending between the first and second major surfaces.

[0047] In some embodiments, glass sheet 28 may be a parallelogram, for example a square or a rectangle comprising four edge surfaces 34a, 34b, 34c, and 34d as shown in FIGS. 1 A and 1B extending between the first and second major surfaces defining an X-Y plane of the glass sheet 28, as shown by the X-Y-Z coordinates. For example, edge surface 34a may be opposite edge surface 34c, and edge surface 34b may be positioned opposite edge surface 34d. Edge surface 34a may be parallel with opposing edge surface 34c, and edge surface 34b may be parallel with opposing edge surface 34d. Edge surfaces 34a and 34c may be orthogonal to edge surfaces 34b and 34d. The edge surfaces 34a-34d may be planar and orthogonal to, or substantially orthogonal (e.g., 90 +/- 1 degree, for example 90 +/- 0.1 degree) to major surfaces 30, 32, although in further embodiments, the edge surfaces may include chamfers, for example a planar center portion orthogonal to, or substantially orthogonal to major surfaces 30, 32 and joined to the first and second major surfaces by two adjacent angled surface portions.

[0048] The BLU 24 comprises the transparent substrate 28 having an index of refraction n0>l, the transparent substrate 28 having a thickness tO separating an upper planar surface 30 and a lower planar surface 32 parallel to the upper planar surface. The transparent substrate 28 comprises an optical input surface 34a perpendicular to the upper and lower planar surfaces. The transparent substrate 28 also comprises an optical output surface 34c parallel to the optical input surface 34a. An axis z is defined perpendicular to the optical input surface 34a and intersecting with the optical input surface 34a at z=0, with the axis z having an intersection with the optical output surface 34c at z=L0. The optical assembly also comprises a first transparent coating layer 36 having an index of refraction nl where l<nl<n0, and has a thickness tl separating an upper planar surface and a lower planar surface of the first transparent coating layer 36. The upper planar surface of the first transparent coating layer 36 is in optical contact with the lower planar surface of the transparent substrate 28. The first transparent coating layer 36 has a first edge (near the optical input surface 34a) at z=zl>0 and has a length L1<L0 with a second edge (near the optical output surface 34c) at z=zl+Ll. LI and zl are chosen to minimize the variance in output intensity and color from the optical assembly. The optical assembly further comprises a second transparent layer 40 having an index of refraction n2 where |n2-n0|<0.05, the second transparent layer 40 having a thickness t2 separating an upper planar surface and a lower planar surface of the second transparent layer 40. The lower planar surface of the second transparent layer 40 is in optical contact with the upper planar surface of the transparent substrate 28. The second transparent layer 40 comprises a first edge at z=z2>0, and a length L2<L0 with a second edge at z=z2+L2. L2 and z2 are chosen to minimize the variance in output intensity and color from the optical assembly.

[0049] According to the embodiments of the present disclosure, an array of elongated optical structures 42, also referred to as lenticular structures, (see FIG. 1B) are disposed on the upper surface of the second transparent layer 40. The array of the lenticular structures 42 have an index of refraction n3 substantially equal to index of refraction n2. The lenticular structures 42 are disposed in an array of substantially parallel rows where the elongation direction is in an alignment direction along the axis z. The array of lenticular structures 42 are substantially periodic, in the direction x that is perpendicular to the axis z, with a period of P (see FIG. 13C, for example). The lenticular structures 42 have a length L3<L0 along axis z, a first edge at z=z3>0, and a second edge at z=z3+L3. The first edge at z3 represents where the lenticular structures 42 begins near the light input surface 34a. L3 and z3 are chosen to minimize the variance in output intensity and color from the optical assembly. z3 > z2 and in some

embodiments, z3 = z2. In other words, the lenticular structures 42 can start at the first edge of the second transparent layer 40 or offset some distance from the first edge of the second transparent layer 40.

[0050] In some embodiments, the individual lenticular structure 42 preferably comprises a trapezoidal cross-sectional shape with a side-wall angle A, where 80° < A < 90°, a width W along a direction x perpendicular to the axis z and parallel to the plane of the lower surface of the second transparent layer 40. The width W is < P, and the lenticular structures 42 have a constant height H3 in a direction y perpendicular to the plane of the upper and lower surfaces of the second transparent layer 40 (i.e., perpendicular to both the z axis and x axis).

[0051] In some embodiments, z3>0, which means that the lenticular structures 42 are offset from the edge of the optical input surface 34a of the LGP. The choice of LI, L2, L3, and zl, z2, z3 depend on the details of the illumination source incident on the light input surface 34a, bezel thickness, and any optical reflectors on surfaces 34b, 34c, or 34d.

[0052] In some other embodiments of the optical assembly, the width W of the individual lenticular structure 42 is < P and the individual lenticular structures 42 comprise a height H3 that can vary along a direction parallel to axis z. The height H3 tapers up or increases gradually starting from the first edge at position z3 and moving away from the light input surface 34a (i.e., the z=0 position) and reaches a maximum height H3max at z=z3+L3’. L3’ can be < L3

meaning that the lenticular structures 42 can reach the H3max anywhere along their full length L3. In some embodiments, the height H3 can start from no height. In some other embodiments, the height H3 can start from a fixed value as a step. In some embodiments, the tapering profile over the length L3’ is such that the height H3 reaches the maximum value H3max by increasing monotonically over the length L3’, meaning that it will not decrease at any point over the length L3’. In some embodiments, the height H3 reaches the maximum value H3max by increasing with a constant slope over the length L3’, i.e., in a straight line as shown in FIG. 12A.

[0053] Referring to FIGS. 12B and 12C, in some embodiments, the tapering profile over the length L3’ can be determined according to a mathematical taper function g(z). The taper function g(z) is equal to a constant g(z3)=g0 where 0<g0<l, the taper function g(z3+L3’) is equal to 1 , the taper function g(z) monotonically increases from z=z3 to z=z3+L3’, wherein the variable height H3 at a given distance from the first edge of the lenticular structure at z3 is defined by a product of the taper function g(z) and the maximum height H3max such that

H3(z)=H3max*g(z). FIGS. 12A-12C show examples of mathematical taper functions g(z). The taper function g(z) should be continuous and monotonically increasing but it need not be smooth in its derivative dg(z)/dz.

[0054] Further embodiments can include where the width W is substantially equal to the period P. Some embodiments include a ratio 0.l<W/P<l . Some embodiments include a slope of the mathematical function being monotonically increasing and continuous as show in FIGS. 12A-12C.

[0055] In some embodiments, the elongated lenticular structures have a circular or elliptical segment, a triangular, a trapezoidal, or a rectangular cross-sectional profile when sectioned along the direction x, as show in FIGS. 13A-13D, respectively. Some embodiments include a glass transparent substrate.

[0056] As mentioned, TIR at all of the non-extraction surface locations is required to maintain light guiding. To understand the requirements for enabling TIR, we first consider the LED light source. The angular output of the light from LEDs is substantially described as a Lambertian distribution which according to Lambert’s law means that the radiant intensity observed from the LED is directly proportional to the cosine of the angle Q between the direction of the incident light and the surface normal of the LED. This means that the LED emits light into the entire half sphere away from its emission surface. As a ray of light traveling with angle 0_air enters the LGP (with index of refraction IILGP), refraction bends light such that the angle in the LGP is now given using Snell’s law as 0_LGP ⁼sm ¹(sin(0_air)/n_LGp)· When 0air=9O°, the angle in the LGP is referred to as the critical angle. For glass with IILGP =1.5, the cone of rays in air (O_ai^iqO⁰) is now bounded by a much narrower cone of rays in the glass (0LGP⁼±4L8°). The Lambertian-cosine distribution is not uniform as a function of angle, so most of the rays will still be concentrated near the surface normal.

[0057] FIG. 1B is an illustration of an exemplary LGP 28 showing the basic structures. An LGP 28 with a first transparent coating layer 36, a low refractive index layer, is deposed on a bottom surface and a second transparent layer, an array of lenticular structures 40 disposed on a top surface.

[0058] FIG. 2A is an illustration of the exemplary LGP viewed from the light input surface of the LGP showing the azimuthal angle f notation for the input light rays in the LGP system.

[0059] FIG. 2B is an illustration of the exemplary LGP system of FIG. 2A viewed from the side showing the relationship between the light input cone angle 0air and [0060] FIG. 2C is an illustration of the exemplary LGP system of FIIGs. 2A and 2B viewed from an oblique angle showing the azimuthal angle f and the input light cone angle 0_air for the input light rays in an input light cone in the context of the LGP system.

[0061] FIG. 3 is an illustration of the exemplary LGP system of FIIGs. 2A and 2B viewed from an oblique angle showing the azimuthal angle f and the light cone angle 0_air for the input light rays in the LGP system.

[0062] FIG. 4 is a graph where the solid line 100 illustrates the variation of the critical angle in a glass with refractive index of n_giass=l .5 as a function of the refractive index of a coating on the non-input glass surface. The dashed line illustrates the limiting angle of the rays of light from a Lambertian LED coupled into the input surface. The angles above the dashed line and below the solid line represent light leakage due to the loss of total internal reflection.

[0063] Now that we have the distribution of rays in the LGP, we can examine the reflection of these rays as they reflect from the non-input faces. For a flat LGP with no lenticular structures, these faces are all rotated at by 90° with respect to the input faces, so the input-ray angles GLGP must be referenced to these new surface normals. In general, this new angle must be calculated using a somewhat complex geometrical relation, but from the limiting cases in which the rays are closest to the critical angle, the new angles are found when the ray is in a plane perpendicular to the non-input face. In this case, we can use 0’LGP = 90°- 0LGP· FIG. 5 is a graph illustrating that for an LGP with refractive index of IILGP =1.50, the new angle 0’LGP with respect to the surface normal of the non-input surface (air/LGP interface) is calculated for 3 cones of light rays that have angles of 0LGP =42°, 20°, and 5° with respect to the normal of the input face. The new angle after each reflection will depend on the azimuthal angle ()>LGP around the input cone. In this example, no angles 0’LGP drop below the critical angle of the air/glass interface (shaded region < 42°) where the ray will no longer be subject to total internal reflection and some light will be lost. The extreme high-angle rays from the light source (i.e. 0LGP~42°) will be most at risk. With reference to FIG. 5 and in our glass example, |0_LGp|<4l .8°, we find that

48.2°<|0^,LGP|^<9O° as shown in FIG. 5. Because the values of 0’LGP are greater than the critical angle of 41.8°, all of the rays will remain guided when they hit an air/glass interface.

[0064] When all of the interfaces are planar and there are no sources of scattering, the light rays remain on the input cone defined by their angle 0LGP with respect to the input normal. Moreover, the light rays maintain their azimuthal angle ()>LGP around the input cone, except for a symmetric flip each time they reflect on one of the planar sides.

[0065] Some embodiments provide a solution to problems that are encountered when the design of the BLU comprises two conditions where two of our basic assumptions for an ideal LGP are simultaneously broken, the two conditions being: (1) that at least one of the non-input faces of the LGP is no longer an air/LGP interface because a coating material other than air is present, and (2) at least one of the non-input faces of the LGP (not necessarily the same interface) is non-planar.

[0066] The impact of the first broken assumption is that the critical angle at this coating/glass interface is now given by

As mentioned above, FIG. 4 shows a plot of the variation of the critical angle in a glass with refractive index of n_giass=l .5 as a function of the refractive index of a coating on the glass surface. For a coating with refractive index above n_COatmg ⁼l .12, some light will escape into the coating material because of the loss of total internal reflection. Some embodiments do not prevent this light leakage and FIG. 6 shows the impact of adding a coating with n_coatmg ⁼L25 to one of the non-input faces of the LGP. Some of the rays (in the range 34° < GLGP < 42°) will hit the non-input surface too steeply and will be extracted into the low-index coating region. This raises the shaded region in the plot causing some light (in the range 34° < GLGP < 42°) to escape TIR causing light to be lost from the LGP into the low-index coating. Rays that do not exceed the critical angle will remain trapped in the LGP. If the optical scattering and attenuation properties of the low-index coating are comparable to the LGP material and the low-index material is bounded by air, no excess light will be extracted from the LGP. However, if the low-index region scatters or absorbs the light, or the low-index layer is in optical contact with another scattering (for example, the back reflector of the BLU) or absorbing material, light will be lost from the LGP. In this case, as the coating index increases, more light will be lost near the input edge of the LGP causing a bright band. All currently available optical coating materials have scattering and absorption that are greater than that of the commonly used glass and polymer LGP materials.

[0067] The impact of the second broken assumption occurs when lenticulars or other non- planar optical features are placed on one of the non-input faces. The lenticulars are aligned perpendicular to the input face and may contain light extraction features. If all of the interfaces are air/glass, there is no extraction of light by the smooth lenticulars. However, these non-planar interfaces cause the internal ray angles to be constantly redirected. The rays will remain on the same input cone (i.e., GLGP will stay constant), but their azimuthal angle about the input cone will be constantly changing as they encounter the curved lenticular surfaces. Although individual rays are being redirected, the average angular distribution of rays within the LGP will remain unchanged and will be indistinguishable from the non-lenticular case.

[0068] One motivation for certain embodiments is to recognize that excess light extraction occurs when a low-index coating is combined with a lenticular array. In the previous discussion of the coating with planar interfaces, we noted that some light would be extracted because some rays would exceed the critical angle condition. However, the remaining rays would remain trapped. With non-planar interfaces, the remaining rays will continue to be redirected on each reflection from the lenticular structures. This will cause the rays to move around their input cone. FIG. 6 is a graph similar to FIG. 5 but the non-input interface now has a low-index coating (n_Coatin_g=l .25). This raises the shaded region causing some light (in the range 34° < GLGP < 42°) to escape total internal reflection causing light to be lost from the LGP. As the coating’s refractive index increases, more light will be lost near the input edge of the LGP causing a bright band. The impact is that the light rays that are above the shaded region in FIG. 6 may move into the shaded region after one or more reflections. This constant mixing of the rays will cycle all of the rays on an input cone angle GLGP through the shaded region of FIG. 6, greatly increasing the amount of excess light. Eventually, all rays on this input angle will be extracted into the low- index coating. This mixing time determines the width of the excess bright band along the z axis, so the ideal lenticulars either mix the light quickly to produce a narrow but intense bright band, or the lenticulars do not mix the light at all and produce a much weaker and narrow bright band.

[0069] In the case of lenticulars with protruding circular cross-sections, the top of the circular curvature and the steep side walls in the valleys act like planar interfaces with interface angles at right angles to the input face of the LGP. These portions of the lenticulars do not mix the light around the azimuthal input cone and will not cause excess light extraction. However, the angled sides near 45°, will have the greatest impact in terms of mixing of the light rays around the azimuthal cone angle <|>LGP· It is these side-wall angles that should be limited.

[0070] Preferred lenticulars should be those with substantially vertical side walls and flat tops. This should behave identically to the planar LPG and have the expect light extraction due to the failure of TIR as shown in FIG. 6. Deviations from vertical side walls can be tolerated and the side-wall angle A is preferably >80°. In some embodiments, the side-wall angle A is 80°. In some embodiments, the side-wall angle A is 85°. In some embodiments, the side- wall angle A is preferably 87°. In some embodiments, the side-wall angle A is more preferably 89°. Some corner rounding can be tolerated.

[0071] To test the idea of rectangular lenticulars, inventors performed a simulation of prismatic lenticulars disposed on an LGP with n_COatmg=l .30, and IILGP⁼L50. The prism design is shown in FIG. 7 and the modeling results are plotted and shown in FIGS. 8 and 9. FIG. 7 shows a schematic illustration of a cross-section of an exemplary prism lenticular feature. A is the side- wall angle of the prismatic lenticular structure, P is the period of the prism lenticular features, W is the width of the prism structures, and H3 is the height of the prism structures. For FIGS. 8 and 9 the LED light coupled out of the LGP was normalized by the amount of LED light coupled in. FIG. 8 is a graphical illustration of a comparison of a modeled bright band illuminance versus prism side-wall angle A. A prism side-wall angle A of 0° represents a flat LGP without any lenticular structures. The model was an LGP with a low-index coating having a refractive index n_Coating=l .30 on the major surface opposite the major surface with the lenticular structures. All prisms had P = 25 um, W = 10 um and H3 = 5 um (for A > 45°) or H3 = 5tan(A) um (for A<45°). As predicted, the rectangular design (A = 90°) performs best with the lowest bright band. The poorest performing lenticular is just less than A = 45° with a surprisingly good design right at 45°. The rectangular prism has the same light loss as flat LGP (A = 0°). In that scenario, the benefit of the lenticular structures would be the local dimming function provided by the lenticular structures.

[0072] Inventors compared the illumination of the bright band near the LEDs among the following cases: reference LGP without any lenticular structures; LGP with circular cross- section lenticular structures; LGP with A = 90° prismatic lenticular structures; and LGP with A = 80° prismatic lenticular structures. A represents the side-wall angle of the prismatic lenticular structure as defined in the cross-sectional view shown in FIG. 7. FIG. 9 is a graphical illustration of modeled luminance of the bright bands seen near the LED light sources. In this illumination plot, the X-axis represents the distance (in mm) from the optical input surface 34a (i.e., near the LEDs) and the Y-axis representing the normalized illuminance. A luminance curve for a theoretically ideal case where there is a uniform illuminance throughout the LGP without any bright band effect would be a straight line representing a constant illuminance over the distance. In the BLU designs where conventional lenticular structures 42 are provided on the top surface of the LGP 28 to enhance light extraction, however, undesired bright bands near the optical input surface 34a is observed. This bright band effect is illustrated by the dashed line plot in FIG. 9 which is the illuminance for the standard circular cross-section lenticular structure case. The peak illuminance is very nearly the same for all four cases but the width of the bright band is very different. The circular lenticular case exhibits a wide bright band, which is not desired. The A = 90° prism lenticular structure, however, exhibits a very narrow bright band similar to the no lenticular (i.e. flat LGP) reference case. The A = 80° prism lenticular structure also exhibit similarly narrow bright band. The Y-axis in the plot in FIG. 8 is the integrated signal under the curves in FIG. 9. The two lowest points in FIG. 8 represent the no lenticular case 0° side-wall angle and 90° side-wall angle prism lenticular structure. Thus, modifying the elongated lenticular structures by shaping them to have a prismatic cross-sectional shape having a straight side-wall with a side-wall angle A that is 90° or close to 90°, such as > 80° will reduce the bright band effect. Examples of such prismatic lenticular structures are illustrated in FIGS. 7, 13B, 13C, and 13D.

[0073] The improved lenticular structures of the present disclosure will not affect the local dimming functionality provided by the conventional lenticular structures already known by those skilled in the BLU art. The local dimming effects can be measured in local dimming index (LDI) defined in S. Jung, M. Kim, I). Kim, J. Lee, "Local dimming design and optimization for edge- type LED backlight unit," SID Symp. Dig. Tech. Papers (2011) pp. 1430-1432. FIG. 10 is a graphical illustration of LDI.

[0074] FIG. 1 1 shows generic schematic illustrations of two types of tapered lenticular structures that are within the scope of the present disclosure.“Type A: Flat-positive lenti” illustrates an array of protruding lenticular lens structure whose variable height tapers to 0 at or near the light input surface 34a of the LGP. “Type B: Flat-Negative lenti” illustrates what is essentially a negative relief of the lenticular structure“Type A: Flat-positive lenti.” The illustrations in FIG. 11 show the lenticular structures as having circular cross-sectional shape but those are just simplified generic illustrations. The lenticular structure according to the present disclosure have a cross-section like the one exemplified in FIG. 7 with straight side-walls with the side-wall angle A. [0075] Some embodiments described and depicted herein comprise lenticular features that have smooth or angular cross sections. Some embodiments include a lenticular array having flat sections between individual lenticular optical elements. Some embodiments include a lenticular array that can be offset from the edge of the LGP. Some embodiments include a lenticular array having integrated light extraction features. The dimensions (height, width and cross-sectional shape) of the lenticular array elements can vary along the length of the lenticular element in some embodiments. Asymmetry in the lenticular shape in some embodiments can increase the excess bright band by causing more mixing; however, exemplary embodiments reduce the total flux extracted into the bright band and reduce the width of the bright band.

[0076] [Glass compositions for GLGPs]

[0077] Exemplary glass compositions in a LGP comprise between about 65.79 mol % to about 78.17 mol% SiCh, between about 2.94 mol% to about 12.12 mol% AI2O3, between about 0 mol% to about 11.16 mol% B2O3, between about 0 mol% to about 2.06 mol% LEO, between about 3.52 mol% to about 13.25 mol% Na₂0, between about 0 mol% to about 4.83 mol% K2O, between about 0 mol% to about 3.01 mol% ZnO, between about 0 mol% to about 8.72 mol% MgO, between about 0 mol% to about 4.24 mol% CaO, between about 0 mol% to about 6.17 mol% SrO, between about 0 mol% to about 4.3 mol% BaO, and between about 0.07 mol% to about 0.11 mol% SnCh.

[0078] In further embodiments, exemplary glass compositions comprise between about 66 mol % to about 78 mol% S1O2, between about 4 mol% to about 11 mol% AI2O3, between about 4 mol% to about 11 mol% B2O3, between about 0 mol% to about 2 mol% LEO, between about 4 mol% to about 12 mol% Na₂0, between about 0 mol% to about 2 mol% K2O, between about 0 mol% to about 2 mol% ZnO, between about 0 mol% to about 5 mol% MgO, between about 0 mol% to about 2 mol% CaO, between about 0 mol% to about 5 mol% SrO, between about 0 mol% to about 2 mol% BaO, and between about 0 mol% to about 2 mol% Sn0₂. In some embodiments, a respective glass article comprises a color shift < 0.008 or < 0.005. Color shift as described herein can be characterized by measuring the variation in y chromaticity coordinate of the extracted light along a length L using the CIE 1931 standard for color measurements. Lor glass LGPs the dimensionless value of color shift can be reported as Dy=|y(Lf)-y(Li)| where Lf and Li are the positions along the z axis of the panel or substrate direction away from the light source launch at the optical input surface 34a and where Lf-Li = 0.5 meters. Exemplary light- guide plates have Dy < 0.01, and preferably Dy < 0.005, Dy < 0.003, or Dy < 0.001.

[0079] In additional embodiments, exemplary glass compositions comprise between about 72 mol % to about 80 mol% SiCh, between about 3 mol% to about 7 mol% AI2O3, between about 0 mol% to about 2 mol% B2O3, between about 0 mol% to about 2 mol% LEO, between about 6 mol% to about 15 mol% Na₂0, between about 0 mol% to about 2 mol% K2O, between about 0 mol% to about 2 mol% ZnO, between about 2 mol% to about 10 mol% MgO, between about 0 mol% to about 2 mol% CaO, between about 0 mol% to about 2 mol% SrO, between about 0 mol% to about 2 mol% BaO, and between about 0 mol% to about 2 mol% Sn0₂.

[0080] In additional embodiments, exemplary glass compositions comprise between about 60 mol % to about 80 mol% S1O2, between about 0 mol% to about 15 mol% AI2O3, between about 0 mol% to about 15 mol% B2O3, and about 2 mol% to about 50 mol% R_xO, wherein R is any one or more of Li, Na, K, Rb, Cs and x is 2, or Zn, Mg, Ca, Sr or Ba and x is 1 , and wherein Le + 30Cr + 35Ni < about 60 ppm.

[0081] In yet further embodiments, exemplary glass compositions comprise between about 0 mol% to about 15 mol% AI2O3, between about 0 mol% to about 15 mol% B2O3, and about 2 mol% to about 50 mol% R_xO, wherein R is any one or more of Li, Na, K, Rb, Cs and x is 2, or Zn, Mg, Ca, Sr or Ba and x is 1, and wherein the glass has a color shift < 0.008.

[0082] In other embodiments, exemplary glass compositions comprise between about 65.79 mol % to about 78.17 mol% S1O2, between about 2.94 mol% to about 12.12 mol% AI2O3, between about 0 mol% to about 11.16 mol% B2O3, and about 3.52 mol% to about 42.39 mol% R_xO, wherein R is any one or more of Li, Na, K, Rb, Cs and x is 2, or Zn, Mg, Ca, Sr or Ba and x is 1, and wherein the glass has a color shift < 0.008.

[0083] In further embodiments, exemplary glass compositions comprise between about 60 mol % to about 81 mol% S1O2, between about 0 mol% to about 2 mol% AI2O3, between about 0 mol% to about 15 mol% MgO, between about 0 mol% to about 2 mol% LEO, between about 9 mol% to about 15 mol% Na₂0, between about 0 mol% to about 1.5 mol% K2O, between about 7 mol% to about 14 mol% CaO, between about 0 mol% to about 2 mol% SrO, and wherein Le + 30Cr + 35Ni < about 60 ppm.

[0084] In additional embodiments, exemplary glass compositions comprise between about 60 mol % to about 81 mol% S1O2, between about 0 mol% to about 2 mol% AI2O3, between about 0 mol% to about 15 mol% MgO, between about 0 mol% to about 2 mol% Li₂0, between about 9 mol% to about 15 mol% Na₂0, between about 0 mol% to about 1.5 mol% K₂0, between about 7 mol% to about 14 mol% CaO, and between about 0 mol% to about 2 mol% SrO, wherein the glass has a color shift < 0.008.

[0085] In some embodiments, a respective glass article comprises a color shift < 0.008 or < 0.005. In some embodiments, the glass comprises an R_x0/Al₂0₃ between 0.95 and 3.23, wherein R is any one or more of Li, Na, K, Rb, Cs and x is 2. In some embodiments, the glass comprises an R_x0/Al₂0₃ between 1.18 and 5.68, wherein R is any one or more of Li, Na, K, Rb, Cs and x is 2, or Zn, Mg, Ca, Sr or Ba and x is 1. In some embodiments, the glass article comprises an R_xO - Al₂C>_{3 -} MgO between -4.25 and 4.0, wherein R is any one or more of Li, Na, K, Rb, Cs and x is 2. In some embodiments, the glass comprises less than 1 ppm each of Co, Ni, and Cr. In some embodiments, the concentration of Fe is < about 50 ppm, < about 20 ppm, or < about 10 ppm.

In some embodiments, Fe + 30Cr + 35Ni < about 60 ppm, < about 40 ppm, < about 20 ppm, or < about 10 ppm. In some embodiments, the transmittance at 450 nm with at least 500 mm in length is greater than or equal to 85%, the transmittance at 550 nm with at least 500 mm in length is greater than or equal to 90%, or the transmittance at 630 nm with at least 500 mm in length is greater than or equal to 85%, and combinations thereof. In some embodiments, the glass sheet is chemically strengthened. In further embodiments, the glass comprises from about 0.1 mol % to about 3.0 mol % ZnO, from about 0.1 mol % to about 1.0 mol % Ti0_2, from about 0.1 mol % to about 1.0 mol % V₂0_3, from about 0.1 mol % to about 1.0 mol % Nb₂Os_, from about 0.1 mol % to about 1.0 mol % MnO, from about 0.1 mol % to about 1.0 mol % Zr0_2, from about 0.1 mol % to about 1.0 mol % As₂C>₃, from about 0.1 mol % to about 1.0 mol % Sn0₂, from about 0.1 mol % to about 1.0 mol % M0O3, from about 0.1 mol % to about 1.0 mol % Sb₂C>₃, or from about 0.1 mol % to about 1.0 mol % Ce0₂. In additional embodiments, the glass comprises between 0.1 mol% to no more than about 3.0 mol% of one or combination of any of ZnO, Ti0₂, V₂0₃, Nb₂0₅, MnO, Zr0₂, As₂03, Sn0₂, M0O3, Sb₂03, and Ce0₂

[0086] In additional embodiments, exemplary glass compositions comprise between about 50-80 mol% Si0₂, between 0-20 mol% Al₂0_3, and between 0-25 mol% B₂0₃, and less than 50 ppm iron (Fe) concentration.

[0087] In additional embodiments, exemplary glass compositions comprise between about 70 mol % to about 85 mol% Si0₂, between about 0 mol% to about 5 mol% AhCb, between about 0 mol% to about 5 mol% B2O3, between about 0 mol% to about 10 mol% Na₂0, between about 0 mol% to about 12 mol% K₂0, between about 0 mol% to about 4 mol% ZnO, between about 3 mol% to about 12 mol% MgO, between about 0 mol% to about 5 mol% CaO, between about 0 mol% to about 3 mol% SrO, between about 0 mol% to about 3 mol% BaO, and between about 0.01 mol% to about 0.5 mol% Sn02.

[0088] In additional embodiments, exemplary glass compositions comprise between about 80 mol % S1O2, between about 0 mol% to about 0.5 mol% AI2O3, between about 0 mol% to about 0.5 mol% B2O3, between about 0 mol% to about 0.5 mol% Na₂0, between about 8 mol% to about 11 mol% K2O, between about 0.01 mol% to about 4 mol% ZnO, between about 6 mol% to about 10 mol% MgO, between about 0 mol% to about 0.5 mol% CaO, between about 0 mol% to about 0.5 mol% SrO, between about 0 mol% to about 0.5 mol% BaO, and between about 0.01 mol% to about 0.11 mol% Sn0₂.

[0089] In additional embodiments, exemplary glass compositions are substantially free of AI2O3 and B2O3 and comprises greater than about 80 mol % S1O2, between about 0 mol% to about 0.5 mol% Na₂0, between about 8 mol% to about 11 mol% K2O, between about 0.01 mol% to about 4 mol% ZnO, between about 6 mol% to about 10 mol% MgO, and between about 0.01 mol% to about 0.11 mol% Sn0₂. In some embodiments, the glass sheet is substantially free of B2O3, Na₂0, CaO, SrO, or BaO, and combinations thereof.

[0090] In additional embodiments, exemplary glass compositions is an alumina free, potassium silicate composition comprising greater than about 80 mol % S1O2, between about 8 mol% to about 11 mol% K2O, between about 0.01 mol% to about 4 mol% ZnO, between about 6 mol% to about 10 mol% MgO, and between about 0.01 mol% to about 0.11 mol% Sn0₂. In some embodiments, the glass sheet is substantially free of B2O3, Na₂0, CaO, SrO, or BaO, and combinations thereof.

[0091] In some embodiments, exemplary glass compositions comprise between about 72.82 mol % to about 82.03 mol% S1O2, between about 0 mol% to about 4.8 mol% AI2O3, between about 0 mol% to about 2.77 mol% B2O3, between about 0 mol% to about 9.28 mol% Na₂0, between about 0.58 mol% to about 10.58 mol% K2O, between about 0 mol% to about 2.93 mol% ZnO, between about 3.1 mol% to about 10.58 mol% MgO, between about 0 mol% to about 4.82 mol% CaO, between about 0 mol% to about 1.59 mol% SrO, between about 0 mol% to about 3 mol% BaO, and between about 0.08 mol% to about 0.15 mol% Sn0₂. In further embodiments, the glass sheet is substantially free of AI₂O₃, B₂O₃, Na₂0, CaO, SrO, or BaO, and combinations thereof.

[0092] In additional embodiments, exemplary glass compositions are substantially free of AI2O3 and B2O3 and comprises greater than about 80 mol % S1O2, and wherein the glass has a color shift < 0.005. In some embodiments, the glass sheet comprises between about 8 mol% to about 11 mol% K2O, between about 0.01 mol% to about 4 mol% ZnO, between about 6 mol% to about 10 mol% MgO, and between about 0.01 mol% to about 0.11 mol% SnC .

[0093] In additional embodiments, exemplary glass compositions are substantially free of AI2O3, B2O3, Na₂0, CaO, SrO, and BaO, and wherein the glass has a color shift < 0.005. In some embodiments, the glass sheet comprises greater than about 80 mol % S1O2_. In some embodiments, the glass sheet comprises between about 8 mol% to about 11 mol% K2O, between about 0.01 mol% to about 4 mol% ZnO, between about 6 mol% to about 10 mol% MgO, and between about 0.01 mol% to about 0.11 mol% Sn0₂.

[0094] While preferred embodiments of the present disclosure have been described, it is to be understood that the embodiments described are illustrative only and that the scope of the invention is to be defined solely by the appended claims when accorded a full range of equivalence, many variations and modifications naturally occurring to those of skill in the art from a perusal hereof.

[0095] While this description can include many specifics, these should not be construed as limitations on the scope thereof, but rather as descriptions of features that can be specific to particular embodiments. Certain features that have been heretofore described in the context of separate embodiments can also be implemented in combination in a single embodiment.

Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub combination. Moreover, although features can be described above as acting in certain combinations and can even be initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination can be directed to a sub combination or variation of a sub combinations.

Claims

What is claimed is:

1. An optical assembly comprising:

a transparent substrate comprising an upper planar surface and a lower planar surface that are parallel to each other,

wherein the transparent substrate has an index of refraction n0>l .0 and a uniform thickness defined between the upper planar surface and the lower planar,

wherein the transparent substrate has a length L0, an optical input surface that is perpendicular to the upper and lower planar surfaces, and an optical output surface parallel to the optical input surface, wherein the distance between the optical input surface and the optical output surface defines the length L0 of the transparent substrate; and

an axis z perpendicular to the optical input surface having an intersection with the optical input surface at z=0, with the axis z having an intersection with the optical output surface at z=L0; and

a first transparent coating layer comprising an upper planar surface and a lower planar surface that are parallel to each other,

wherein the first transparent coating layer has an index of refraction nl and a uniform thickness defined between the upper planar surface and the lower planar surface,

wherein 1.0<nl<n0, the upper planar surface of the first transparent coating layer in optical contact with the lower planar surface of the transparent substrate,

wherein the first transparent coating layer has a first edge at z=zl, the first transparent coating layer having a length LI with a second edge at z=zl+Ll; and

a second transparent layer comprising an upper planar surface and a lower planar surface that are parallel to each other,

wherein the second transparent layer has an index of refraction n2 and a uniform thickness defined between the upper planar surface and the lower planar surface,

wherein |n2-n0|<0.05, the lower planar surface of the second transparent layer in optical contact with the upper planar surface of the transparent substrate,

wherein the second transparent layer has a first edge at z=z2, the second transparent layer having a length L2 with a second edge at z=z2+L2; and

an array of elongated optical structures disposed on the upper planar surface of the second transparent layer, wherein the array of elongated optical structures having an index of refraction n3 that is substantially equal to the index of refraction n2, the elongated optical structures disposed in an array of rows that are parallel to the axis z,

wherein the array of rows of the elongated optical structures has a periodicity of p,

wherein each individual elongated optical structure has a length L3 along axis z, the array of elongated optical structures having a first edge at z=z3, the array of elongated optical structures having a second edge at z=z3+L3,

wherein each individual elongated optical structure has a trapezoidal cross- sectional shape with a side-wall angle A, wherein 80° < A < 90°, width W along a direction x perpendicular to axis z and parallel to the plane of the lower surface of the second transparent layer, wherein W < P, and each elongated optical structure has a constant height H3 along a direction y that is perpendicular to the plane of the lower surface of the second transparent layer.

2. The optical assembly of claim 1, wherein A is 80°.

3. The optical assembly of claim 1, wherein A is 85°.

4. The optical assembly of claim 1, wherein A is 87°.

5. The optical assembly of claim 1, wherein A is 89°.

6. The optical assembly of claim 1, wherein z3 is > 0.

7. The optical assembly of claim 1, wherein each of the individual elongated optical structure has a cross-sectional profile of a trapezoid when sectioned along the direction x.

8. The optical assembly of claim 1, wherein the transparent substrate is glass.

9. An optical assembly comprising:

a transparent substrate having an index of refraction h0>1 , the transparent substrate having a thickness separating an upper planar surface and a lower planar surface parallel to the upper planar surface, the transparent substrate having a length L0, an optical input surface that is perpendicular to the upper and lower planar surfaces, the transparent substrate having an optical output surface parallel to the optical input surface, wherein the distance between the optical input surface and the optical output surface defines the length L0 of the transparent substrate;

a first transparent coating layer having an index of refraction nl where l<nl<n0, the first transparent coating layer having a thickness separating an upper planar surface of the first transparent coating layer and a lower planar surface of the first transparent coating layer, the upper planar surface of the first transparent coating layer in optical contact with the lower planar surface of the transparent substrate, the first transparent coating layer having a first edge at z=zl, the first transparent coating layer having a length LI with a second edge at z=zl+Ll;

a second transparent layer having an index of refraction n2 where |n2-n0|<0.05, the second transparent layer comprising a thickness separating an upper planar surface of the second transparent layer and a lower planar surface of the second transparent layer, the lower planar surface of the second transparent layer being in optical contact with the upper planar surface of the transparent substrate, the second transparent layer having a first edge at z=z2, the second transparent layer having a length L2 with a second edge at z=z2+L2; and

an array of elongated optical structures disposed on the upper planar surface of the second transparent layer,

wherein the array of elongated optical structures having an index of refraction n3 substantially equal to the index of refraction n2,

wherein the elongated optical structures disposed on an array of substantially parallel rows having an alignment direction along an axis z,

wherein the array of elongated optical structures being substantially periodic with a period of P,

wherein the individual elongated optical structures having a length L3 along the axis z,

wherein the array of elongated optical structures having a first edge at z=z3, the array of elongated optical structures having a second edge at z=z3+L3,

wherein the individual elongated optical structures having a width W along a direction x perpendicular to axis z and parallel to the plane of the lower surface of the second transparent layer,

wherein each of the individual elongated optical structure having a cross-sectional shape with a side-wall angle A, wherein 80° < A < 90°, the width W < P, and

wherein the individual elongated optical structures has a height H3 that varies along a direction parallel to axis z, wherein the height H3 reaches a maximum value H3max at z=z3+L3’, wherein L3’ < L3.

10. The optical assembly of claim 9, wherein the height H3 reaches the maximum value H3max by increasing monotonically.

11. The optical assembly of claim 9, wherein the height H3 reaches the maximum value H3max by increasing with a constant slope.

12. The optical assembly of claim 9, wherein L3’ = L3.

13. The optical assembly of claim 9, wherein W is substantially equal to P.

14. The optical assembly of claim 9, wherein the ratio 0.l<W/P<l.

15. The optical assembly of claim 9, wherein the slope of the mathematical taper function g(z) is monotonically increasing and continuous.

16. The optical assembly of claim 9, wherein the individual elongated optical structure has a cross-sectional profile of a trapezoid when sectioned along the direction x.

17. The optical assembly of claim 9, wherein the transparent substrate is glass.

18. The optical assembly of claim 9, wherein A is 80°.

19. The optical assembly of claim 9, wherein A is 85°.

20. The optical assembly of claim 9, wherein A is 87°.

21. The optical assembly of claim 9, wherein A is 89°.

22. The optical assembly of claim 9, wherein z3 is > 0.

23. An optical assembly comprising:

a transparent substrate having an index of refraction h0>1 , the transparent substrate having a thickness separating an upper planar surface and a lower planar surface parallel to the upper planar surface, the transparent substrate having a length L0 and having an optical input surface perpendicular to the upper and lower planar surfaces, the transparent substrate having an optical output surface parallel to the optical input surface; an axis z perpendicular to the optical input surface having an intersection with the optical input surface at z=0, with the axis z having an intersection with the optical output surface at z=L0;

a second transparent layer having an index of refraction n2 where |n2-n0|<0.05, the second transparent layer having a thickness separating an upper planar surface of the second transparent layer and a lower planar surface of the second transparent layer, the lower planar surface of the second transparent layer in optical contact with the upper planar surface of the transparent substrate, the second transparent layer having a first edge at z=z2, the second transparent layer having a length L2 with a second edge at z=z2+L2; and

wherein the array of elongated optical structures having an index of refraction n3 substantially equal to index of refraction n2, the elongated optical structures disposed on an array of substantially parallel rows having an alignment direction along an axis z,

wherein the individual elongated optical structures having a length L3 along axis z,

wherein the individual elongated optical structures having a non-trapezoidal cross-sectional shape,

wherein the individual elongated optical structures having a width W along a direction x perpendicular to axis z and parallel to the plane of the lower surface of the second transparent layer, the width W < P, and wherein the individual elongated optical structures having a height H3 that varies along a direction parallel to axis z, and wherein the height H3 reaches a maximum value H3max at z=z3+L3’, wherein L3’ < L3.

24. The optical assembly of claim 23 , wherein the height H3 reaches the maximum value H3max by increasing monotonically.

25. The optical assembly of claim 23, wherein the height H3 reaches the maximum value H3max by increasing with a constant slope.

26. The optical assembly of claim 23, wherein L3’ = L3.

27. The optical assembly of claim 23, wherein the individual elongated optical structure has a cross-sectional profile of a trapezoid, a circular segment, an elliptical segment, or a triangle when sectioned along the direction x.

28. The optical assembly of claim 23, wherein the transparent substrate is glass.

29. The optical assembly of claim 23, wherein z3 is > 0.