Abstract:
Gradient Refractive Index (GRIN) optical materials [ 100 ] composed of a polymer matrix doped with functionalized nanocrystals realize high values for Vgrin, and hence nearly uniform focal lengths regardless of the wavelength of light. GRIN optical materials having low Vgrin magnitudes less than 10 are also provided.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates generally to gradient refractive index (GRIN) lenses and optical structures. More specifically, it relates to GRIN optical structures having low dispersion. 
       BACKGROUND OF THE INVENTION 
       [0002]    Gradient refractive index (GRIN) optical structures are composed of an optical material whose index of refraction, n, varies along a spatial gradient in the axial and/or radial directions of the lens. They have many useful applications such as making compact lenses with flat surfaces. However, for various reasons it has proven difficult and expensive to make GRIN lenses that overcome problems due to optical dispersion. 
         [0003]    There are several known techniques for fabricating GRIN lenses. One approach is to press films of widely varying refractive indices together into a lens using a mold. Proposals exist for making low dispersion GRIN lenses in this manner, e.g., as taught in U.S. Pat. No. 5,689,374. This process, however, is expensive to develop. 
         [0004]    A second approach for fabricating GRIN lenses is to infuse glass with ions at varying density. This approach has reached commercial production, but is effectively limited to small radially symmetric lenses by the depth to which ions will diffuse into glass, and has also failed to solve the optical dispersion problem. 
         [0005]    A third approach for fabricating GRIN lenses is to use 3D printing technology with inks composed of appropriately matched polymer and nanoparticle technology. Each droplet can deliver a distinct refractive index depending on the mix of nanoparticles and polymer material in the droplet. Therefore this technology allows 3D creation of GRIN optical elements of arbitrary shape. Producing low dispersion lenses using this approach, however, remains a challenge. 
         [0006]    As with conventional lenses, a challenge in the design of GRIN optical lenses is correcting for chromatic aberration resulting from dispersion, i.e., the variability of the index of refraction with respect to wavelength. In a conventional glass lens, for example, the dispersion of the glass causes red and blue light to be focused at different points. 
         [0007]    The amount of dispersion of a homogenous lens material is often quantified by the Abbe number, 
         [0000]        V   d =( n   yellow −1)/( n   blue   −n   red )
 
         [0008]    where n yellow  is the index of refraction of the lens material at a 587.56 nm wavelength, n blue  is the index of refraction of the lens material at a 486.13 nm wavelength, and n red  is the index of refraction of the lens material at a 656.27 nm wavelength. Red, yellow, and blue are used here for convenience and convention. In the near infrared (NIR) portion of the electromagnetic spectrum a different set of low, high, and mid value wavelengths would be chosen. 
         [0009]    When n red  and n blue  are nearly equal, the Abbe number V d  becomes large, an indication that the optical dispersion is small. Since the two numbers are equivalent (and because the transition from one to the other is usually smooth, meaning the n yellow  will be in between) the lens will bend the colors of the spectrum the same amount, leading to a small dispersion. V d  above 100 is considered quite good, and above 500 adequate for high quality optics. 
         [0010]    GRIN lenses also suffer from chromatic aberration for the same reasons as conventional homogeneous lenses. Correcting for dispersion effects in a GRIN lens, however, is far more complicated due to the spatial gradient of the index of refraction. Specifically, because of the wavelength dependence of the index of refraction, the total change in the index of refraction along the spatial gradient may be wavelength dependent as well. In other words, the difference in index of refraction between the higher index material and the lower index material may vary across the spectrum in a GRIN lens, resulting in more complicated chromatic aberration effects than in a homogeneous lens. 
         [0011]    For GRIN materials, research at facilities such as the labs of Dr. Duncan T. Moore at the University of Rochester, in papers such as the doctoral thesis “Integration of the Design and Manufacture of Gradient-Index Optical Systems” by Julie Lynn Bentley in 1995, has shown that it convenient to define a gradient-index Abbe number, V grin , in terms of the total change in the refractive index across the spatial gradient of the lens at the yellow, blue, and red wavelengths as 
         [0000]        V   grin (Δ n   yellow )/(Δ n   blue   −Δn   red )
 
         [0012]    where Δn yellow  is the total change in index of refraction across the spatial gradient of the lens at a 587.56 nm wavelength, Δn blue  is the total change in index of refraction across the spatial gradient of the lens at a 486.13 nm wavelength, and Δn red  is the total change in index of refraction across the spatial gradient of the lens at a 656.27 nm wavelength. When Δn red  and Δn blue  are nearly equal, the magnitude of this GRIN Abbe number V grin  becomes large, which indicates that the spatial gradient of the GRIN lens has small wavelength dependence (see D T Moore, et al, “Model for the chromatic properties of gradient-index glass”,  Applied Optics , Vol. 24, No. 24, 15 December 1985). As with V d , V grin  magnitudes above 100 are considered quite good, and above 500 adequate for high quality optics. However, it remains an outstanding challenge to design and inexpensively manufacture a GRIN lens that has materials of different refractive indices arranged in the proper geometry to focus light without focal length variations (aberrations) over the light spectra of interest. 
       SUMMARY OF THE INVENTION 
       [0013]    In one aspect, the present invention provides GRIN optical structures composed of nanocrystals as a dopant to a polymer matrix to realize magnitudes for V grin  larger than 100 for a predetermined wavelength range, and hence nearly uniform focal lengths in lenses using GRIN materials regardless of the wavelength of light in the range. By careful selection of such materials, V grin  magnitudes higher than 500 or even 1000 can be obtained. GRIN structures can also be intentionally designed with very low V grin  magnitudes, e.g., below 10. The nanocrystal dopants may be of a single type or a mixture of two types of nanocrystals. This latter method can be used for any host polymer in which nanocrystals can be chemically dispersed. The host polymer may also be a mixture of polymers. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  shows a simple GRIN lens, called a wood lens, according to an embodiment of the invention. 
           [0015]      FIGS. 2A ,  2 B,  2 C show a wood lens, according to another embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]    When designing a GRIN lens, chromatic aberration (i.e., different focal lengths at different wavelengths) is smaller when the total change in index of refraction Δn red  is closer to the total change in index of refraction Δn blue . Embodiments of the present invention provide for the use of nanocrystals as a dopant to a polymer matrix to satisfy this desired constraint. The nanocrystal-doped polymer material is also suitable for inexpensive GRIN lens fabrication using 3D printing technology. 
         [0017]    Doping of a polymer matrix with a nanocrystal will alter the index of refraction of the polymer matrix. The nanocrystal dopant particles, however, preferably do not create scattering at the wavelengths of interest. Thus, each nanocrystal itself is preferably sufficiently small (i.e., less than 50 nm for visible spectrum GRIN optics, or less than 100 nm for IR spectrum GRIN optics) that it does not induce Mie or Rayleigh scattering, essentially rendering the nanomaterial “invisible” at the wavelengths of interest. Examples of suitable materials for the nanocrystals are ZnS, ZrO 2 , ZnO, BeO, AlN, TiO 2 , SiO 2 , SiO 2  hollow nanospheres, and combinations of these materials with shells of ZrO 2  and ZnO. The coefficient of extinction, combining the absorbance and reflection, of the nanocrystal material is low enough (preferably below 10%, more preferably below 1%) for the application and spectrum in which the optical device is to be employed. 
         [0018]    The nanocrystals are first coated with a ligand material (such as acrylic acid, phosphonic acid, or silane) which provides chemical compatibility with the optical polymer and chemical dispersion of the nanoparticles for optical clarity. The ligands are selected to covalently bind to the surface of the nanocrystal with an “anchor”, repel each other with a “buoy” for good dispersion (preventing aggregation and light scattering), and bond covalently to the monomer so that good dispersion is maintained during polymerization. 
         [0019]    The functionalized nanocrystals are then blended with the monomeric form of an optical polymer material. Examples of suitable polymer matrix materials are di(ethylene glycol) diacrylate, neopentyl glycol diacrylate, hexanediol diacrylate, bisphenol a novolak epoxy resin (SU8), 2-Hydroxyethylmethacrylate (HEMA), polyacrylate, polymethyl methacrylate (PMMA), styrene, and poly[(2,3,4,4,5,5 -hexafluorotetrahydro furan-2,3 -diyl)(1,1,2,2-tetrafluoro ethylene)] (CYTOP)). The monomers as a class are UV crosslinkable with minimal shrink (20% or less is desirable to minimize the strain and subsequent deformation of the optical structure), clear (i.e., less than 10% haze and extinction combined), low viscosity in the monomer form (i.e., less than 20 cPoise so that it can be inkjet printed), and offer covalent (and, preferably, anionic as well) bonding sites for the ligands. 
         [0020]    The blend of the monomeric polymer and functionalized nanocrystals, once deposited into the form of an optical device by various 3D printing processes (such as digital drop on demand inkjet, continuous flow inkjet, screen printing, lithographic printing, tampo printing, etc) is then polymerized into transparent solids through UV or thermal curing, though UV is preferred due to speed and reduced or eliminated material shrinkage. Experience shows that the cured monomer, now a polymer, will have a somewhat (&lt;5%) lower index of refraction than the liquid monomer. 2D and 3D GRIN optical components designed using principles of GRIN optics well known in the art are fabricated by standard drop-on-demand inkjet printing or by other printing techniques known in the art (such as screen printing, tampo printing, aerosol jet printing, and laser cure printing). 
         [0021]    For example,  FIG. 1  shows a GRIN lens  100  according to an embodiment of the invention. The nanocrystal-doped polymer material is deposited using 3D printing such that the refractive index is at its highest (that is, the dopant nanocrystals are at their highest concentration in the host polymer matrix) in the center  102  of the lens near the optical axis, and the refractive index is at its lowest (that is, pure polymer matrix or lowest concentration of nanocrystals) at the outer edge  104  radially far from the optical axis. The difference An between the index of refraction at the center, n center , and the index of refraction at the edge, n edge , drives the optical power of the lens. By suitable selection of materials according to the principles of the present invention, this difference Δn is substantially wavelength independent over the range of wavelengths for which the lens is designed to operate, thereby effectively eliminating chromatic aberration. Consequently, all light rays  108  passing through the lens all converge at the same focal point  106  irrespective of their wavelength. 
         [0022]    Similarly,  FIG. 2A  shows a cross-sectional diagram of a wood lens  200  having a radial index of refraction gradient with largest index, n center , on the central optical axis and smallest index, n edge , at the edge far from the axis. The total change in index along the radial gradient is Δn=n center −n edge , which is substantially wavelength independent over the range of wavelengths for which the lens is designed to operate. In this design, the focal length f L  of this lens is equal to the thickness of the lens, as indicated by the convergence of the rays  202  at the focal point  204 .  FIG. 2B  is a cross-sectional diagram of the same lens viewed along the optical axis, showing high index material  206  (containing higher nanocrystal doping concentration) near the central optical axis and low index material  208  (containing lower nanocrystal doping) near the edge. Such a lens may be VIRGO-printed with a 25-mm diameter and 0.4-mm-thickness. A 6 vol % ZrO 2  in diethylene glycol diacrylate (DEGDA) may be used in 10 layers.  FIG. 2C  shows a final printed part with printed square frame. 
         [0023]    Various different nanocrystals and polymers may be used according to the principles of the present invention in order to produce GRIN optical structures whose total gradient Δn is substantially wavelength independent over the range of wavelengths for which the structure is designed to operate. Several illustrative examples are described below. 
       EXAMPLE 1 
     BeO in Polyacrylate 
       [0024]    For Polyacrylate, n red =1.4995, n yellow =1.4942, and n blue =1.4917. For BeO, n red =1.7239, n yellow =1.7186, and n blue =1.7162. Thus for a Polyacrylate matrix doped with BeO the maximum Δn red =0.2244, Δn yellow =0.2244, Δn blue =0.2245, and thus V grin =−2560. 
       EXAMPLE 2 
     AlN in SU8.  
       [0025]    For Bisphenol A Novolak Epoxy Resin (SU8), n red =1.5994, n yellow =1.5849, and n blue =1.5782. For AlN, n red =2.1704, n yellow =2.1543, and n blue =2.1476. Thus for an SU8 matrix doped with AlN the maximum An red =0.5710, Δn yellow =0.5694, Δn blue =0.5694, and thus V grin =375. 
       EXAMPLE 3 
     ZrO 2  in SU8 
       [0026]    For Bisphenol A Novolak Epoxy Resin (SU8), n red =1.5994, n yellow =1.5849, and n blue =1.5782. For ZrO 2 , n red =2.2272, n yellow =2.2148, and n blue =2.2034. Thus for an SU8 matrix doped with ZrO 2  the maximum Δn red =0.6278, Δn yellow =0.6299, Δn blue =0.6253, and thus V grin =248. 
       EXAMPLE 4 
     w-AlN in Polyacrylate 
       [0027]    For Polyacrylate, n red =1.4995, n yellow =1.4942, and n blue =1.4917. For wurtzite w-AlN, n red =2.1730, n yellow =2.1658, and n blue =2.1659. Thus for a Polyacrylate matrix doped with wurtzite w-AlN the maximum Δn red =0.6735, Δn yellow =0.6717, Δn blue =0.6742, and thus V grin =−962. 
         [0028]    These examples demonstrate the degree to which the dispersion can be controlled with careful material selection. 
         [0029]    Another way to accomplish a high V grin  is by combining two (or more) types of nanocrystals when doping the polymer. The nanocrystal&#39;s relative contribution to the change in refractive index will depend on the percentage of the total employed in the polymer matrix. That is, for the nanocrystals n blue =X*n blue +Y*n blue  for the percentage of nanoparticles X and Y employed, respectively. 
       EXAMPLE 5 
     Mixture of 80% ZrO2 and 20% MgO in SU8 
       [0030]    For Bisphenol A Novolak Epoxy Resin (SU8), n red =1.5994, n yellow =1.5849, and n blue =1.5782. For ZrO 2 , n red =2.2272, n yellow =2.2148, and n blue =2.2034. For MgO, n red =1.7471, n yellow =1.7375, and n blue =1.7334. For a mixture of 80% ZrO2 and 20% MgO nanocrystals n red =2.1312, n yellow =2.1194, and n blue =2.1094. Thus for an SU8 matrix doped with a mixture of 80% ZrO2 and 20% MgO nanocrystals the maximum An red =0.5318, Δn yellow =0.5345, Δn blue =0.5312, and thus V grin =992. 
       EXAMPLE 6 
     Mixture of 1 vol % SiGe (2% of the Nanocrystal Being Ge) with 10 vol % 
       [0031]    SiO 2  Hollow Nanospheres (66% air, 33% SiO 2 ) in SU8, combined with 1.8 vol % TiO 2  in SU8. 
         [0032]    For Bisphenol A Novolak Epoxy Resin (SU8), n red =1.5994, n yellow =1.5849, and n blue =1.5782. For SiGe, n red =3.8463, n yellow =3.9838, and n blue =4.3970. For SiO 2  Hollow Nanospheres, n red =1.1521, n yellow =1.1529, and n blue =1.1544. For TiO 2 , n red =2.8537, n yellow =2.9124, and n blue =3.0639. For 1 vol % SiGe with 10 vol % SiO 2  Hollow Nanospheres in SU8, n red =1.5582, n yellow =1.5657, and n blue =1.5829. For 1.8 vol % TiO 2  in SU8, n red =1.6011, n yellow =1.6088, and n blue =1.6258. Thus for a pair of inks, SU8 doped with 1 vol % SiGe and 10 vol % SiO 2  Hollow Nanospheres, and SU8 doped with 1.8 vol % TiO 2 , Δn red =−0.0429, Δn yellow =−0.0431, Δn blue =−0.0429, and thus V grin =13,213.74. 
       EXAMPLE 7 
     Mixture of 1 vol % TiO 2 /ZrO 2  (TiO 2  with a ZrO 2  Shell Representing 30% of the Nanocrystal Volume) in PMMA Combined With 10 vol % ZrO 2  in PMMA 
       [0033]    For PMMA, n red =1.4880, n yellow =1.4914, and n blue =1.4973. For TiO 2 /ZrO 2 , n red =2.6370, n yellow =2.6799, and n blue =2.7850. For ZrO 2 , n red =2.2034, n yellow =2.2148, and n blue =2.2272. For 1 vol % TiO 2 /ZrO 2  in PMMA, n red =1.4995, n yellow =1.5033, and n blue =1.5102. For 10 vol % ZrO 2  in PMMA, n red =1.5595, n yellow =1.5637, and n blue =1.5703. Thus for a pair of inks, PMMA doped with 1 vol % TiO 2 /ZrO 2  and PMMA doped with 10 vol % ZrO 2 , Δn red =−0.0601, Δn yellow =−0.0605, Δn blue =−0.0601, and thus V grin =1,091.83. 
       EXAMPLE 8 
     Mixture of 20 vol % BeO in PMMA Combined With 6 vol % SiO 2  Hollow Nanospheres (66% air, 33% SiO 2 ) in PMMA  
       [0034]    For PMMA, n red =1.4880, n yellow =1.4914, and n blue =1.4973. For BeO, n red =1.7162, n yellow =1.7186, and n blue =1.7239. For SiO 2  Hollow Nanospheres, n red =1.1521, n yellow =1.1529, and n blue =1.1544. For 20 vol % BeO in PMMA, n red =1.5336, n yellow =1.5368, and n blue =1.5426. For 6 vol % SiO 2  Hollow Nanospheres in PMMA, n red =1.4678, n yellow =1.4711, and n blue =1.4767. Thus for a pair of inks, PMMA doped with 20 vol % BeO and PMMA doped with 3 vol % SiO 2  Hollow Nanospheres, Δn red =0.0658, Δn yellow =0.0658, Δn blue =0.0659, and thus V grin =668.25. 
         [0035]    This latter method, mixing nanocrystals to tune the change in refractive index to match that of the host polymer, can be repeated for any host polymer in which nanocrystals can be chemically dispersed. 
         [0036]    If a great degree of dispersion is desired (V grin &lt;10) for a particular application, such as prismatic dispersal of spectra, diffractive optics, etc., the following technique can also be used. 
       EXAMPLE 9 
     Mixture of 5 vol % TiO 2  in PMMA, Combined With 5 vol % SiO 2  Hollow Nanospheres (66% air, 33% SiO 2 ) in PMMA 
       [0037]    For PMMA, n red =1.4880, n yellow =1.4914, and n blue =1.4973. For SiO 2  Hollow Nanospheres, n red =1.1521, n yellow =1.1529, and n blue =1.1544. For TiO 2 , n red =2.8537, n yellow =2.9124, and n blue =3.0639. For 5 vol % TiO 2  in PMMA, n red =1.5562, n yellow =1.5625, and n blue =1.5756. For 5 vol % SiO 2  Hollow Nanospheres in PMMA, n red =1.4712, n yellow =1.4745, and n blue =1.4802. Thus for a pair of inks, PMMA doped with 5 vol % SiO 2  Hollow Nanospheres, and PMMA doped with 5 vol % TiO 2 , Δn red =0.0955, Δn yellow 0.0880, Δn blue =0.0851, and thus V grin =8.46.