Patent Publication Number: US-10788608-B2

Title: Non-color shifting multilayer structures

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The instant application is a continuation-in-part (CIP) of U.S. patent application Ser. No. 14/138,499 filed on Dec. 23, 2013, which in turn is a CIP of U.S. patent application Ser. No. 13/913,402 filed on Jun. 8, 2013, which in turn is a CIP of U.S. Patent application Ser. No. 13/760,699 filed on Feb. 6, 2013, which in turn is a CIP of Ser. No. 13/572,071 filed on Aug. 10, 2012, which in turn is a CIP of U.S. patent application Ser. No. 13/021,730 filed on Feb. 5, 2011, which in turn is a CIP of Ser. No. 12/793,772 filed on Jun. 4, 2010, which in turn is a CIP of U.S. patent application Ser. No. 12/388,395 filed on Feb. 18, 2009, which in turn is a CIP of U.S. patent application Ser. No. 11/837,529 filed Aug. 12, 2007 (U.S. Pat. No. 7,903,339). U.S. patent application Ser. No. 13/913,402 filed on Jun. 8, 2013 is a CIP of Ser. No. 13/014,398 filed Jan. 26, 2011, which is a CIP of Ser. No. 12/793,772 filed Jun. 4, 2010. U.S. patent application Ser. No. 13/014,398 filed Jan. 26, 2011 is a CIP of Ser. No. 12/686,861 filed Jan. 13, 2010 (U.S. Pat. No. 8,593,728), which is a CIP of Ser. No. 12/389,256 filed Feb. 19, 2009 (U.S. Pat. No. 8,329,247), all of which are incorporated in their entirety by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention is related to multilayer thin film structures, and in particular to multilayer thin film structures that exhibit a minimum or non-noticeable color shift when exposed to broadband electromagnetic radiation and viewed from different angles. 
     BACKGROUND OF THE INVENTION 
     Pigments made from multilayer structures are known. In addition, pigments that exhibit or provide a high-chroma omnidirectional structural color are also known. However, such prior art pigments have required as many as 39 thin film layers in order to obtain desired color properties. 
     It is appreciated that cost associated with the production of thin film multilayer pigments is proportional to the number of layers required. As such, the cost associated with the production of high-chroma omnidirectional structural colors using multilayer stacks of dielectric materials can be prohibitive. Therefore, a high-chroma omnidirectional structural color that requires a minimum number of thin film layers would be desirable. 
     SUMMARY OF THE INVENTION 
     An omnidirectional multilayer thin film is provided. The multilayer thin film includes a multilayer stack having a first layer of a first material and a second layer of a second material, the second layer extending across the first layer. The multilayer stack reflects a narrow band of electromagnetic radiation having a full width at half maximum (FWHM) of less than 300 nanometers (nm) and in some instances has a FWHM of less than 200 nm. The multilayer stack also has a color shift in the form of a center wavelength shift of less than 50 nm, preferably less than 40 nm and more preferably less than 30 nm, when the multilayer stack is exposed to broadband electromagnetic radiation and viewed from angles between 0 and 45 degrees. In the alternative, the color shift can be in the form of a hue shift of less than 30°, preferably less than 25° and more preferably less than 20°. In addition, the multilayer stack may or may not reflect a band of electromagnetic radiation in the ultraviolet (UV) range and/or reflect a band of electromagnetic radiation in the infrared (IR) range. 
     In some instances, the multilayer stack has a total thickness of less than 2 microns (μm). Preferably, the multilayer thin film has a total thickness of less than 1.5 μm and more preferably less than 1.0 μm. 
     The multilayer stack can be made from dielectric layers, i.e. the first layer and the second layer can be made from dielectric materials. In the alternative, the first layer can be a dielectric material and the second layer can be an absorbing material. The first layer has a thickness between 30-300 nm. The absorbing material can be a selective absorbing material, or in the alternative, a non-selective absorbing material. The selective absorbing material absorbs only a desired portion of the visible electromagnetic radiation spectrum and can be made from materials such as copper (Cu), gold (Au), zinc (Zn), tin (Sn), alloys thereof, and the like. In the alternative, the selective absorbing material can be made from a colorful dielectric material such as Fe 2 O 3 , Cu 2 O, and combinations thereof. Such a second layer made from a selective absorbing material can have a thickness between 20-80 nm. 
     The non-selective absorbing material/layer generally absorbs all of the visible electromagnetic radiation spectrum and can be made from materials such as chromium (Cr), tantalum (Ta), tungsten (W), molybdenum (Mo), titanium (Ti), titanium nitride, niobium (Nb), cobalt (Co), silicon (Si), germanium (Ge), nickel (Ni), palladium (Pd), vanadium (V), ferric oxide, and combinations or alloys thereof. Such a non-selective absorbing layer has a thickness between 5-20 nm. 
     The multilayer stack can further include a reflector layer with the first and second layers extending across the reflector layer. The reflector layer can be made from a metal such as aluminum (Al), silver (Ag), Au, platinum (Pt), Cr, Cu, Zn, Sn, and alloys thereof. Also, the reflector has a thickness between 50-200 nm. 
     The reflected narrow band of electromagnetic radiation characteristic of the multilayer thin film can have a generally symmetrical peak. In the alternative, the reflected narrow band of electromagnetic radiation does not have a symmetrical peak. In some instances, the multilayer thin film provides a narrow band of reflected electromagnetic radiation in the visible range by taking advantage of the non-visible UV range and/or IR range. Stated differently, the multilayer thin film can reflect a generally broad band of electromagnetic radiation; however, only a narrow band is visible. In addition, the narrow band of visible electromagnetic radiation has a very low color shift, e.g. a center wavelength shift of less than 50 nm, when the multilayer thin film is viewed from angles between 0 and 45 degrees. 
     The multilayer thin film can also have a low hue shift when viewed from 0 and 45 degrees. For example, the multilayer thin film can have a hue shift of less than 30 degrees when the thin film is viewed between angles of 0 and 45 degrees. In the alternative, the multilayer thin film can have a hue shift of less than 25 degrees, preferably less than 20 degrees, when the thin film is viewed between angles of 0 and 45 degrees. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1A  is a schematic illustration of a dielectric layer (DL) reflecting and transmitting incident electromagnetic radiation; 
         FIG. 1B  is a schematic illustration of a reflector layer (RL) reflecting incident electromagnetic radiation; 
         FIG. 1C  is a schematic illustration of an absorbing layer (AL) absorbing incident electromagnetic radiation; 
         FIG. 1D  is a schematic illustration of a selective absorbing layer (SAL) reflecting, absorbing and transmitting incident electromagnetic radiation; 
         FIG. 2  is a schematic illustration of reflectance and transmission of incident electromagnetic radiation by a 1 st  generation omnidirectional structural color multilayer thin film made from a plurality of dielectric layers; 
         FIG. 3  is a schematic illustration of a 1 st  generation omnidirectional structural color multilayer thin film made from a plurality of dielectric layers; 
         FIG. 4  is a graphical representation showing a comparison of the range to mid-range ratio of 0.2% for the transverse magnetic mode and transverse electric mode of electromagnetic radiation; 
         FIG. 5  is a graphical representation of reflectance as a function of wavelength for Case III shown in  FIG. 4 ; 
         FIG. 6  is a graphical representation of the dispersion of the center wavelength in Case I, II and III shown in  FIG. 4 ; 
         FIG. 7  is a schematic illustration of reflectance and absorption of incident electromagnetic radiation by a 2 nd  generation omnidirectional structural color multilayer thin film made from a plurality of dielectric layers and an absorbing layer; 
         FIG. 8  is a schematic illustration of a 2 nd  generation omnidirectional structural color multilayer thin film made from a plurality of dielectric layers and an absorbing layer and/or reflecting layer; 
         FIG. 9A  is schematic illustration of a 2 nd  generation 5-layer omnidirectional structural color multilayer thin film made from a plurality of dielectric layers and an absorbing/reflecting layer having a chroma (C*) of 100 and a reflectance (Max R) of 60%; 
         FIG. 9B  is a graphical representation of reflectance versus wavelength for the 2 nd  generation 5-layer multilayer stack thin film shown in  FIG. 9A  compared to a 1 st  generation 13-layer multilayer thin film and for viewing angles of 0 and 45 degrees; 
         FIG. 10  is a schematic illustration of a 3 rd  generation omnidirectional structural color multilayer thin film made from a dielectric layer, a selective absorbing layer (SAL) and a reflector layer; 
         FIG. 11A  is a schematic illustration of a zero or near-zero electric field point within a ZnS dielectric layer exposed to electromagnetic radiation (EMR) having a wavelength of 500 nm; 
         FIG. 11B  is a graphical illustration of the absolute value of electric field squared (|E| 2 ) versus thickness of the ZnS dielectric layer shown in Figure lA when exposed to EMR having wavelengths of 300, 400, 500, 600 and 700 nm; 
         FIG. 12  is a schematic illustration of a dielectric layer extending over a substrate or reflector layer and exposed to electromagnetic radiation at an angle θ relative to a normal direction to the outer surface of the dielectric layer; 
         FIG. 13  is a schematic illustration of a ZnS dielectric layer with a Cr absorber layer located at the zero or near-zero electric field point within the ZnS dielectric layer for incident EMR having a wavelength of 434 nm; 
         FIG. 14  is a graphical representation of percent reflectance versus reflected EMR wavelength for a multilayer stack without a Cr absorber layer (e.g.,  FIG. 1A ) and a multilayer stack with a Cr absorber layer (e.g.,  FIG. 3A ) exposed to white light; 
         FIG. 15A  is a graphical illustration of first harmonics and second harmonics exhibited by a ZnS dielectric layer extending over an Al reflector layer (e.g.,  FIG. 4A ); 
         FIG. 15B  is a graphical illustration of percent reflectance versus reflected EMR wavelength for a multilayer stack with a ZnS dielectric layer extending across an Al reflector layer, plus a Cr absorber layer located within the ZnS dielectric layer such that the second harmonics shown in  FIG. 8A  are absorbed; 
         FIG. 15C  is a graphical illustration of percent reflectance versus reflected EMR wavelength for a multilayer stack with a ZnS dielectric layer extending across an Al reflector layer, plus a Cr absorber layer located within the ZnS dielectric layer such that the first harmonics shown in  FIG. 8A  are absorbed; 
         FIG. 16A  is a graphical illustration of electric field squared versus dielectric layer thickness showing the electric field angular dependence of a Cr absorber layer for exposure to incident light at 0 and 45 degrees; 
         FIG. 16B  is a graphical illustration of percent absorbance by a Cr absorber layer versus reflected EMR wavelength when exposed to white light at 0 and 45° angles relative to normal of the outer surface (0° being normal to surface); 
         FIG. 17A  is a schematic illustration of a red omnidirectional structural color multilayer stack according to an embodiment of the present invention; 
         FIG. 17B  is a graphical illustration of percent absorbance of the Cu absorber layer shown in  FIG. 10A  versus reflected EMR wavelength for white light exposure to the multilayer stack shown in  FIG. 10A  at incident angles of 0 and 45°; 
         FIG. 18  is a graphical comparison between calculation/simulation data and experimental data for percent reflectance versus reflected EMR wavelength for a proof of concept red omnidirectional structural color multilayer stack exposed to white light at an incident angle of 0°; 
         FIG. 19  is a graphical illustration of percent reflectance versus wave length for an omnidirectional structural color multilayer stack according to an embodiment of the present invention; 
         FIG. 20  is a graphical illustration of percent reflectance versus wave length for an omnidirectional structural color multilayer stack according to an embodiment of the present invention; 
         FIG. 21  is a graphical illustration of percent reflectance versus wave length for an omnidirectional structural color multilayer stack according to an embodiment of the present invention; 
         FIG. 22  is a graphical illustration of percent reflectance versus wave length for an omnidirectional structural color multilayer stack according to an embodiment of the present invention; 
         FIG. 23  is a graphical representation of a portion of an a*b* color map using the CIELAB color space in which the chroma and hue shift are compared between a conventional paint and a paint made from pigments according to an embodiment of the present invention (Sample (b)); 
         FIG. 24  is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention; 
         FIG. 25  is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention; and 
         FIG. 26  is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An omnidirectional structural color is provided. The omnidirectional structural color has the form of a multilayer thin film (also referred to as a multilayer stack herein) that reflects a narrow band of electromagnetic radiation in the visible spectrum and has a small or non-noticeable color shift when the multilayer thin film is viewed from angles between 0 to 45 degrees. The multilayer thin film can be used as pigment in a paint composition, a continuous thin film on a structure and the like. 
     The multilayer thin film includes a multilayer stack that has a first layer and a second layer extending across the first layer. In some instances, the multilayer stack reflects a narrow band of electromagnetic radiation that has a FWHM of less than 300 nm, preferably less than 200 nm and in some instances less than 150 nm. The multilayer thin film also has a color shift of less than 50 nm, preferably less than 40 nm and more preferably less than 30 nm, when the multilayer stack is exposed to broadband electromagnetic radiation, e.g. white light, and viewed from angles between 0 and 45 degrees. Also, the multilayer stack may or may not have a separate reflected band of electromagnetic radiation in the UV range and/or the IR range. 
     The overall thickness of the multilayer stack is less than 2 μm, preferably less than 1.5 μm, and still more preferably less than 1.0 μm. As such, the multilayer stack can be used as paint pigment in thin film paint coatings. 
     The first and second layers can be made from dielectric material, or in the alternative, the first and/or second layer can be made from an absorbing material. Absorbing materials include selective absorbing materials such as Cu, Au, Zn, Sn, alloys thereof, and the like, or in the alternative colorful dielectric materials such as Fe 2 O 3 , Cu 2 O, combinations thereof, and the like. The absorbing material can also be a non-selective absorbing material such as Cr, Ta, W, Mo, Ti, Ti-nitride, Nb, Co, Si, Ge, Ni, Pd, V, ferric oxides, combinations or alloys thereof, and the like. The thickness of an absorbing layer made from selective absorbing material is between 20-80 nm whereas the thickness of an absorbing layer made from non-selective absorbing material is between 5-30 nm. 
     The multilayer stack can also include a reflector layer which the first layer and the second layer extend across, the reflector layer made from metals such as Al, Ag, Pt, Cr, Cu, Zn, Au, Sn, alloys thereof, and the like. The reflector layer typically has a thickness between 30-200 nm. 
     The multilayer stack can have a reflected narrow band of electromagnetic radiation that has the form of a symmetrical peak within the visible spectrum. In the alternative, the reflected narrow band of electromagnetic radiation in the visible spectrum can be adjacent to the UV range such that a portion of the reflected band of electromagnetic radiation, i.e. the UV portion, is not visible to the human eye. In the alternative, the reflected band of electromagnetic radiation can have a portion in the IR range such that the IR portion is likewise not visible to the human eye. 
     Whether the reflected band of electromagnetic radiation that is in the visible spectrum borders the UV range, the IR range, or has a symmetrical peak within the visible spectrum, multilayer thin films disclosed herein have a reflected narrow band of electromagnetic radiation in the visible spectrum that has a low, small or non-noticeable color shift. The low or non-noticeable color shift can be in the form of a small shift of a center wavelength for a reflected narrow band of electromagnetic radiation. In the alternative, the low or non-noticeable color shift can be in the form of a small shift of a UV-sided edge or IR-sided edge of a reflected band of electromagnetic radiation that borders the IR range or UV range, respectively. Such a small shift of a center wavelength, UV-sided edge and/or IR-sided edge is typically less than 50 nm, in some instances less than 40 nm, and in other instances less than 30 nm when the multilayer thin film is viewed from angles between 0 and 45 degrees. 
     Turning now to  FIG. 1 ,  FIGS. 1A-1D  illustrate the basic components of an omnidirectional structural color design. In particular,  FIG. 1A  illustrates a dielectric layer exposed to incident electromagnetic radiation. In addition, the dielectric layer (DL) reflects a portion of the incident electromagnetic radiation and transmits a portion thereof. In addition, the incident electromagnetic radiation is equal to the transmitted portion and the reflected portion and typically the transmitted portion is much greater than the reflected portion. Dielectric layers are made from dielectric materials such as SiO 2 , TiO 2 , ZnS, MgF 2 , and the like. 
     In sharp contrast,  FIG. 1B  illustrates a reflective layer (RL) in which all of the incident electromagnetic radiation is reflected and essentially has zero transmittance. Reflector layers are typically made from materials such as aluminum, gold, and the like. 
       FIG. 1C  illustrates an absorbing layer (AL) in which incident electromagnetic radiation is absorbed by the layer and not reflected or transmitted. Such an absorbing layer can be made from, for example, graphite. Also, the total incident electromagnetic radiation is absorbed and transmission and reflectance is approximately zero. 
       FIG. 1D  illustrates a partial or selective absorbing layer (SAL) in which a portion of the incident electromagnetic radiation is absorbed by the layer, a portion is transmitted, and a portion is reflected. As such, the amount of electromagnetic radiation transmitted, absorbed, and reflected equals the amount of incident electromagnetic radiation. In addition, such selective absorbing layers can be made from material such as a thin layer of chromium, layers of copper, brass, bronze, and the like. 
     With respect to the present invention, three generations of design and manufacture of omnidirectional structural color thin films are disclosed. 
     First Generation 
     Referring now to  FIG. 2 , a schematic illustration of a multilayer thin film having a plurality of dielectric layers is shown. In addition, the reflectance and transmittance of an incident electromagnetic radiation is schematically shown. As stated above, typically transmission of the incident electromagnetic radiation is much greater than reflectance thereof and thus many layers are required. 
       FIG. 3  shows part of a multilayer thin film made from dielectric layers having a first index of refraction (DL 1 ) and a second index of refraction (DL 2 ). It should be appreciated that the double lines between the layers simply represent an interface between the different layers. 
     Not being bound by theory, one method or approach for designing and manufacturing a desired multilayer stack is the following. 
     When electromagnetic radiation impacts a material surface, waves of the radiation can be reflected from or transmitted through the material. Furthermore, when electromagnetic radiation impacts the first end  12  of the multilayer structure  10  at the angle θ 0 , the reflected angles the electromagnetic waves make with the surface of the high and low refractive index layers are θ H  and θ L , respectively. Using Snell&#39;s law:
 
 n   0  Sin θ 0   =n   L  Sin θ L   =n   H  Sin θ H    (1)
 
the angles θ H  and θ L  can be determined if the refractive indices n H  and n L  are known.
 
     Regarding omnidirectional reflectivity, a necessary but not sufficient condition for the TE mode and the TM mode of electromagnetic radiation requires the maximum angle of refraction (θ H,MAX ) inside the first layer to be less than the Brewster angle (θ B ) of the interface between the first layer and the second layer. If this condition is not satisfied, the TM mode of the electromagnetic waves will not be reflected at the second and all subsequent interfaces and thus will transmit through the structure. Using this consideration: 
                       Sin   ⁢           ⁢     θ     H   ,   Max         =       n   0       n   H         ⁢     
     ⁢   and           (   2   )                 Tan   ⁢           ⁢     θ   B       =       n   L       n   H               (   3   )               
Thereby requiring:
 
     
       
         
           
             
               
                 
                   
                     n 
                     0 
                   
                   &lt; 
                   
                     
                       
                         n 
                         H 
                       
                       ⁢ 
                       
                         n 
                         L 
                       
                     
                     
                       
                         
                           n 
                           H 
                           2 
                         
                         + 
                         
                           n 
                           L 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In addition to the necessary condition represented by Equation 4, if electromagnetic radiation of wavelength λ falls on a multilayer structure with an angle θ 0 , and the individual bi-layers of the multilayer structure have thicknesses d H  and d L  with respective refractive indices n H  and n L , the characteristic translation matrix (F T ) can be expressed as: 
                     F   T     =       1     1   +     ρ   T         ⁢                e     i   ⁢           ⁢     δ   L                 ρ   T     ⁢     e       -   i     ⁢           ⁢     δ   L                       ρ   T     ⁢     e     i   ⁢           ⁢     δ   L                 e       -   i     ⁢           ⁢     δ   L                    ×     1     1   -     ρ   T         ⁢                e     i   ⁢           ⁢     δ   H                 ρ   T     ⁢     e       -   i     ⁢           ⁢     δ   H                       ρ   T     ⁢     e     i   ⁢           ⁢     δ   H                 e       -   i     ⁢           ⁢     δ   H                              (   5   )               
which can also be expressed as:
 
                     F   T     =       1     1   +     ρ   T   2         ⁢                  e     i   ⁡     (       δ   L     +     δ   H       )         -       ρ   T   2     ⁢     e     -     i   ⁡     (       δ   H     -     δ   L       )                       -   2     ⁢   i   ⁢           ⁢     ρ   T     ⁢     e       -   i     ⁢           ⁢     δ   H         ⁢   Sin   ⁢           ⁢     δ   L                 2   ⁢   i   ⁢           ⁢     ρ   T     ⁢     e     i   ⁢           ⁢     δ   H         ⁢   Sin   ⁢           ⁢     δ   L               e     -     i   ⁡     (       δ   L     +     δ   H       )           -       ρ   T   2     ⁢     e     -     i   ⁡     (       δ   H     -     δ   L       )                                    (   6   )               
and where:
 
                     δ   H     =         2   ⁢           ⁢   π     λ     ⁢     n   H     ⁢     d   H     ⁢   Cos   ⁢           ⁢     θ   H               (   7   )                 δ   L     =         2   ⁢           ⁢   π     λ     ⁢     n   L     ⁢     d   L     ⁢   Cos   ⁢           ⁢     θ   L               (   8   )                   Cos   ⁢           ⁢     θ   H       =       1   -         n   o   2     ⁢     Sin   2     ⁢     θ   0         n   H   2             ⁢     
     ⁢   and           (   9   )                 Cos   ⁢           ⁢     θ   L       =       1   -         n   o   2     ⁢     Sin   2     ⁢     θ   0         n   L   2                   (   10   )               
In addition,
 
                       ρ   T     =         n   HT     -     n   LT           n   HT     +     n   LT           ⁢     
     ⁢   where           (   11   )                 n   HT     =     {               n   H       Cos   ⁢           ⁢     θ   H                     n   H     ⁢   Cos   ⁢           ⁢     θ   H             ⁢     
     ⁢     (     for   ⁢           ⁢   TM   ⁢           ⁢   and   ⁢           ⁢   TE   ⁢           ⁢   polarization   ⁢           ⁢   respectively     )     ⁢     
     ⁢   and               (   12   )                 n   LT     =     {               n   L       Cos   ⁢           ⁢     θ   L                     n   L     ⁢   Cos   ⁢           ⁢     θ   L             ⁢     
     ⁢     (     for   ⁢           ⁢   TM   ⁢           ⁢   and   ⁢           ⁢   TE   ⁢           ⁢   polarization   ⁢           ⁢   respectively     )                 (   13   )               
Solving ρ T  explicitly for TE and TM:
 
     
       
         
           
             
               
                 
                   
                     
                       ρ 
                       TM 
                     
                     = 
                     
                       
                         
                           
                             n 
                             H 
                           
                           ⁢ 
                           Cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             L 
                           
                         
                         - 
                         
                           
                             n 
                             L 
                           
                           ⁢ 
                           Cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             H 
                           
                         
                       
                       
                         
                           
                             n 
                             H 
                           
                           ⁢ 
                           Cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             L 
                           
                         
                         + 
                         
                           
                             n 
                             L 
                           
                           ⁢ 
                           Cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             H 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   and 
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     ρ 
                     TE 
                   
                   = 
                   
                     
                       
                         
                           n 
                           H 
                         
                         ⁢ 
                         Cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           H 
                         
                       
                       - 
                       
                         
                           n 
                           L 
                         
                         ⁢ 
                         Cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           L 
                         
                       
                     
                     
                       
                         
                           n 
                           H 
                         
                         ⁢ 
                         Cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           H 
                         
                       
                       + 
                       
                         
                           n 
                           L 
                         
                         ⁢ 
                         Cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           L 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     A viewing angle dependant band structure can be obtained from a boundary condition for the edge, also known as the bandedge, of the total reflection zone. For the purposes of the present invention, bandedge is defined as the equation for the line that separates the total reflection zone from the transmission zone for the given band structure. 
     A boundary condition that determines the bandedge frequencies of the high reflectance band can be given by:
 
Trace | F   T |=−1   (16)
 
Thus, from equation 3:
 
                         Cos   ⁡     (       δ   H     +     δ   H       )       -       ρ   T   2     ⁢     Cos   ⁡     (       δ   H     -     δ   L       )             1   -     ρ   T   2         =     -   1             (   17   )               
or expressed differently:
 
                       Cos   2     ⁡     (         δ   H     +     δ   L       2     )       =       ρ   T   2     ⁢       Cos   2     ⁡     (         δ   H     -     δ   L       2     )                 (   18   )               
Combining equations 15 and 7, the following bandedge equation is obtained:
 
                     Cos   ⁡     (       π   ⁢           ⁢     L   +       λ     )       =       ±          ρ   T            ⁢     Cos   ⁡     (       π   ⁢           ⁢     L   -       λ     )                 (   19   )               
Where:
 
                       L   +     =         n   H     ⁢     d   H     ⁢   Cos   ⁢           ⁢     θ   H       +       n   L     ⁢     d   L     ⁢   Cos   ⁢           ⁢     θ   L           ⁢     
     ⁢     and   ⁢     :               (   20   )                 L   -     =         n   H     ⁢     d   H     ⁢   Cos   ⁢           ⁢     θ   H       +       n   L     ⁢     d   L     ⁢   Cos   ⁢           ⁢     θ   L                 (   21   )               
The + sign in the bandedge equation shown above represents the bandedge for the long wavelength (λ long ) and the − sign represents the bandedge for the short wavelength (λ short ). Recompiling equations 20 and 21:
 
                       Cos   ⁡     (       π   ⁢           ⁢     L   +         λ   long       )       =       +          ρ   TE            ⁢     Cos   ⁡     (       π   ⁢           ⁢     L   -         λ   long       )       ⁢           ⁢   and       ⁢     
     ⁢       Cos   ⁡     (       π   ⁢           ⁢     L   +         λ   Short       )       =       -          ρ   TE            ⁢     Cos   ⁡     (       π   ⁢           ⁢     L   -         λ   Short       )                   (   22   )               
for the TE mode, and:
 
                       Cos   ⁡     (       π   ⁢           ⁢     L   +         λ   long       )       =       +          ρ   TM            ⁢     Cos   ⁡     (       π   ⁢           ⁢     L   -         λ   long       )       ⁢           ⁢   and       ⁢     
     ⁢       Cos   ⁡     (       π   ⁢           ⁢     L   +         λ   Short       )       =       -          ρ   TM            ⁢     Cos   ⁡     (       π   ⁢           ⁢     L   -         λ   Short       )                   (   23   )               
for the TM mode.
 
     An approximate solution of the bandedge can be determined by the following expression:
 
 L   −   =n   H   d   H  Cos θ H   −n   L   d   L  Cos θ L ˜0   (24)
 
This approximate solution is reasonable when considering a quarter wave design (described in greater detail below) and optical thicknesses of the alternating layers chosen to be equal to each other. In addition, relatively small differences in optical thicknesses of the alternating layers provide a cosine close to unity. Thus, equations 23 and 24 yield approximate bandedge equations:
 
                         λ   long     ⁡     (     θ   0     )       =         π   ⁢           ⁢       L   +     ⁡     (     θ   0     )             Cos     -   1       ⁢            ρ   TE     ⁡     (     θ   0     )                ⁢           ⁢   and       ⁢     
     ⁢         λ   Short     ⁡     (     θ   0     )       =       π   ⁢           ⁢       L   +     ⁡     (     θ   0     )             Cos     -   1       ⁡     (     -            ρ   TE     ⁡     (     θ   0     )              )                   (   25   )               
for the TE mode and:
 
                         λ   long     ⁡     (     θ   0     )       =       π   ⁢           ⁢       L   +     ⁡     (     θ   0     )             Cos     -   1       ⁢            ρ   TM     ⁡     (     θ   0     )                  ⁢     
     ⁢   and   ⁢     
     ⁢         λ   Short     ⁡     (     θ   0     )       =       π   ⁢           ⁢       L   +     ⁡     (     θ   0     )             Cos     -   1       ⁡     (     -            ρ   TM     ⁡     (     θ   0     )              )                   (   26   )               
for the TM mode.
 
     Values for L +  and ρ TM  as a function of incident angle can be obtained from equations 7, 8, 14, 15, 20 and 21, thereby allowing calculations for λ long  and λ short  in the TE and TM modes as a function of incident angle. 
     The center wavelength of an omnidirectional reflector (λ c ), can be determined from the relation:
 
λ c =2( n   H   d   H  Cos θ H   +n   L   d   L  Cos θ L )   30)
 
The center wavelength can be an important parameter since its value indicates the approximate range of electromagnetic wavelength and/or color spectrum to be reflected. Another important parameter that can provide an indication as to the width of a reflection band is defined as the ratio of range of wavelengths within the omnidirectional reflection band to the mid-range of wavelengths within the omnidirectional reflection band. This “range to mid-range ratio” (η) is mathematically expressed as:
 
                     η   TE     =     2   ⁢           λ   long   TE     ⁢     (       θ   0     =     90   ⁢   °       )       -       λ   Short   TE     ⁡     (       θ   0     =     0   0       )               λ   long   TE     ⁡     (       θ   0     =     90   0       )       +       λ   Short   TE     ⁡     (       θ   0     =     0   0       )                     (   31   )               
for the TE mode, and:
 
                     η   TM     =     2   ⁢           λ   long   TM     ⁢     (       θ   0     =     90   ⁢   °       )       -       λ   Short   TM     ⁡     (       θ   0     =     0   0       )               λ   long   TM     ⁡     (       θ   0     =     90   0       )       +       λ   Short   TM     ⁡     (       θ   0     =     0   0       )                     (   32   )               
for the TM mode. It is appreciated that the range to mid-range ratio can be expressed as a percentage and for the purposes of the present invention, the term range to mid-range ratio and range to mid-range ratio percentage are used interchangeably. It is further appreciated that a ‘range to mid-range ratio’ value provided herein having a ‘%’ sign following is a percentage value of the range to mid-range ratio. The range to mid-range ratios for the TM mode and TE mode can be numerically calculated from equations 31 and 32 and plotted as a function of high refractive index and low refractive index.
 
     It is appreciated that to obtain the narrow omnidirectional band that the dispersion of the center wavelength must be minimized. Thus, from equation 30, the dispersion of the center wavelength can be expressed as: 
                           Δλ   c     =       ⁢       λ   c     ⁢     ❘       θ   0     =     0   0         ⁢       -     λ   c       ⁢     ❘       θ   0     =     90   0                         =       ⁢     2   ⁢     (           n   H     ⁢     d   H       1     +         n   L     ⁢     d   L       1     -         n   H     ⁢     d   H           1   -       n   0   2       n   H   2             -         n   L     ⁢     d   L           1   -       n   0   2       n   L   2               )                     (   34   )               
where:
 
                     Δλ   c     =         λ   0     4     ⁢     F   c               (   35   )               
and F c , the center wavelength dispersion factor can be expressed as:
 
     
       
         
           
             
               
                 
                   
                     F 
                     c 
                   
                   = 
                   
                     ( 
                     
                       2 
                       - 
                       
                         1 
                         
                           
                             1 
                             - 
                             
                               
                                 n 
                                 0 
                                 2 
                               
                               
                                 n 
                                 H 
                                 2 
                               
                             
                           
                         
                       
                       - 
                       
                         1 
                         
                           
                             1 
                             - 
                             
                               
                                 n 
                                 0 
                                 2 
                               
                               
                                 n 
                                 L 
                                 2 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     Given the above, a multilayer stack with a desired low center wavelength shift (Δλ c ) can be designed from a low index of refraction material having an index of refraction of n L  and one or more layers having a thickness of d L  and a high index of refraction material having an index of refraction of n H  and one or more layers having a thickness of d H . 
     In particular,  FIG. 4  provides a graphical representation of a comparison of the range to midrange ratio of 0.2% for the transverse magnetic mode and transverse electric mode of electromagnetic radiation plotted as a function of high refractive index versus low refractive index. As shown in the figure, three cases are illustrated in which Case I refers to a large difference between the transverse magnetic mode and the transverse electric mode, Case II refers to a situation for a smaller difference between the transverse magnetic mode and transverse electric mode, and Case III refers to a situation for a very small difference between the transverse magnetic mode and transverse electric mode. In addition,  FIG. 5  illustrates a percent reflectance versus wavelength for reflected electromagnetic radiation for a case analogous with Case III. 
     As shown in  FIG. 5 , a small dispersion of the center wavelength for a multilayer thin film corresponding to Case III is shown. In addition, and with reference to  FIG. 6 , Case II provides a shift in the center wavelength of less than 50 nm (Case II) when a multilayer thin film structure is viewed between 0 and 45 degrees and Case III provides a center wavelength shift of less than 25 nm when the thin film structure is exposed to electromagnetic radiation between 0 and 45 degrees. 
     Second Generation 
     Referring now to  FIG. 7 , an illustrative structure/design according to a second generation is shown. The multilayer structure shown in  FIG. 7  has a plurality of dielectric layers and an underlying absorbing layer. In addition, none of the incident electromagnetic radiation is transmitted through the structure, i.e. all of the incident electromagnetic radiation is reflected or absorbed. Such a structure as shown in  FIG. 7  allows for the reduction of the number of dielectric layers that are needed in order to obtain a suitable amount of reflectance. 
     For example,  FIG. 8  provides a schematic illustration of such a structure in which a multilayer stack has a central absorbing layer made from Cr, a first dielectric material layer (DL 1 ) extending across the Cr absorbing layer, a second dielectric material layer (DL 2 ) extending across the DL 1  layer, and then another DL 1  layer extending across the DL 2  layer. In such a design, the thicknesses of the first dielectric layer and the third dielectric layer may or may not be the same. 
     In particular,  FIG. 9A  shows a graphical representation of a structure in which a central Cr layer is bounded by two TiO 2  layers, which in turn are bounded by two SiO 2  layers. As shown by the plot, the layers of TiO 2  and SiO 2  are not equal in thickness to each other. In addition,  FIG. 9B  shows a reflectance versus wavelength spectrum of the 5-layer structure shown in  FIG. 9A  and compared to a 13-layer structure made according to the first generation design. As illustrated in  FIG. 9B , a shift in the center wavelength of less than 50 nm, and preferably less than 25 nm is provided when the structures are viewed a 0 and 45 degrees. Also shown in  FIG. 9B  is the fact that a 5-layer structure according to the second generation essentially performs equivalent to a 13-layer structure of the first generation. 
     Third Generation 
     Referring to  FIG. 10 , a third generation design is shown in which an underlying reflector layer (RL) has a first dielectric material layer DL 1  extending thereacross and a selective absorbing layer SAL extending across the DL 1  layer. In addition, another DL 1  layer may or may not be provided and extend across the selective absorbing layer. Also shown in the figure is an illustration that all of the incident electromagnetic radiation is either reflected or selectively absorbed by the multilayer structure. 
     Such a design as illustrated in  FIG. 10  corresponds to a different approach that is used for designing and manufacturing a desired multilayer stack. In particular, a zero or near-zero energy point thickness for a dielectric layer is used and discussed below. 
     For example,  FIG. 11A  is a schematic illustration of a ZnS dielectric layer extending across an Al reflector layer. The ZnS dielectric layer has a total thickness of 143 nm, and for incident electromagnetic radiation with a wavelength of 500 nm, a zero or near-zero energy point is present at 77 nm Stated differently, the ZnS dielectric layer exhibits a zero or near-zero electric field at a distance of 77 nm from the Al reflector layer for incident EMR having a wavelength of 500 nm In addition,  FIG. 11B  provides a graphical illustration of the energy field across the ZnS dielectric layer for a number of different incident EMR wavelengths. As shown in the graph, the dielectric layer has a zero electric field for the 500 nm wavelength at 77 nm thickness, but a non-zero electric field at the 77 nm thickness for EMR wavelengths of 300, 400, 600 and 700 nm. 
     Regarding calculation of a zero or near-zero electric field point,  FIG. 12  illustrates a dielectric layer  4  having a total thickness ‘D’, an incremental thickness ‘d’ and an index of refraction ‘n’ on a substrate or core layer  2  having a index of refraction n s  is shown. Incident light strikes the outer surface  5  of the dielectric layer  4  at angle θ relative to line  6 , which is perpendicular to the outer surface  5 , and reflects from the outer surface  5  at the same angle. Incident light is transmitted through the outer surface  5  and into the dielectric layer  4  at an angle θ F  relative to the line  6  and strikes the surface  3  of substrate layer  2  at an angle θ s . 
     For a single dielectric layer, θ s =θ F  and the energy/electric field (E) can be expressed as E(z) when z=d. From Maxwell&#39;s equations, the electric field can be expressed for s polarization as:
 
 Ē ( d )={ u ( z ), 0, 0}exp ( ikαy )| z=d    (37)
 
and for p polarization as:
 
                       E   ⇀     ⁡     (   d   )       =         {     0   ,     u   ⁡     (   z   )       ,       -     α       ɛ   ~     ⁡     (   z   )           ⁢     v   ⁡     (   z   )           }     ⁢     exp   ⁡     (     i   ⁢           ⁢   k   ⁢           ⁢   α   ⁢           ⁢   y     )         ⁢     ❘     z   =   d                 (   38   )               
where
 
             k   =       2   ⁢   π     λ           
and λ is a desired wavelength to be reflected. Also, α=n s  sin θ s  where ‘s’ corresponds to the substrate in  FIG. 5  and {tilde over (ε)}(z) is the permittivity of the layer as a function of z. As such,
 
 |E ( d )| 2   =|u ( z )| 2  exp (2 ikαy )| z=d    (39)
 
for s polarization and
 
                            E   ⁡     (   d   )            2     =         [              u   ⁡     (   z   )            2     +              α     n       ⁢     v   ⁡     (   z   )              2       ]     ⁢     exp   ⁡     (     2   ⁢   i   ⁢           ⁢   k   ⁢           ⁢   α   ⁢           ⁢   y     )         ⁢     ❘     z   =   d                 (   40   )               
for p polarization.
 
     It is appreciated that variation of the electric field along the Z direction of the dielectric layer  4  can be estimated by calculation of the unknown parameters u(z) and v(z) where it can be shown that: 
                       (         u           v         )       z   =   d       =       (           cos   ⁢           ⁢   φ             (     i   ⁢     /     ⁢   q     )     ⁢   sin   ⁢           ⁢   φ               i   ⁢           ⁢   q   ⁢           ⁢   sin   ⁢           ⁢   φ           cos   ⁢           ⁢   φ           )     ⁢       (         u           v         )         z   =   0     ,   substrate                 (   41   )               
Naturally, ‘i’ is the square root of −1. Using the boundary conditions u| z=0 =1, v| z=0 =q s , and the following relations:
 
q s =n s  cos θ s  for s-polarization   (42)
 
 q   s   =n   s /cos θ s  for  p -polarization   (43)
 
q=n cos θ F  for s-polarization   (44)
 
 q=n /cos θ F  for  p -polarization   (45)
 
φ= k·n·d  cos (θ F )   (46)
 
u(z) and v(z) can be expressed as:
 
                               u   ⁡     (   z   )       ⁢     ❘     z   =   d         =       ⁢     u   ⁢     ❘     z   =   0       ⁢         cos   ⁢           ⁢   φ     +   v     ⁢     ❘     z   =   o       ⁢     (       i   q     ⁢   sin   ⁢           ⁢   φ     )                     =       ⁢       cos   ⁢           ⁢   φ     +         i   ·     q   s       q     ⁢   sin   ⁢           ⁢   φ               ⁢     
     ⁢   and           (   47   )                         v   ⁡     (   z   )       ⁢     ❘     z   =   d         =       ⁢       i   ⁢           ⁢   q   ⁢           ⁢   u     ⁢     ❘     z   =   0       ⁢         sin   ⁢           ⁢   φ     +   v     ⁢     ❘     z   =   0       ⁢     cos   ⁢           ⁢   φ                     =       ⁢       i   ⁢           ⁢   q   ⁢           ⁢   sin   ⁢           ⁢   φ     +       q   s     ⁢   cos   ⁢           ⁢   φ                     (   48   )               
Therefore:
 
                                  E   ⁡     (   d   )            2     =       ⁢       [         cos   2     ⁢   φ     +         q   s   2       q   2       ⁢     sin   2     ⁢   φ       ]     ⁢     e     2   ⁢   i   ⁢           ⁢   k   ⁢           ⁢   αγ                     =       ⁢       [         cos   2     ⁢   φ     +         n   s   2       n   2       ⁢     sin   2     ⁢   φ       ]     ⁢     e     2   ⁢   i   ⁢           ⁢   k   ⁢           ⁢   αγ                       (   49   )               
for s polarization with φ=k·n·d cos (θ F ), and:
 
                                  E   ⁡     (   d   )            2     =       ⁢     [         cos   2     ⁢   φ     +         n   s   2       n   2       ⁢     sin   2     ⁢   φ     +         α   2     n     ⁢     (         q   s   2     ⁢     cos   2     ⁢   φ     +       q   2     ⁢     sin   2     ⁢   φ       )         ]                 =       ⁢     [         (     1   +         α   2     ⁢     q   s   2       n       )     ⁢     cos   2     ⁢   φ     +       (         n   s   2       n   2       +         α   2     ⁢     q   2       n       )     ⁢     sin   2     ⁢   φ       ]                   (   50   )               
for p polarization where:
 
     
       
         
           
             
               
                 
                   α 
                   = 
                   
                     
                       
                         n 
                         s 
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         θ 
                         s 
                       
                     
                     = 
                     
                       n 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         θ 
                         F 
                       
                     
                   
                 
               
               
                 
                   ( 
                   51 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       q 
                       s 
                     
                     = 
                     
                       
                         n 
                         s 
                       
                       
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           s 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   and 
                 
               
               
                 
                   ( 
                   52 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     s 
                   
                   = 
                   
                     n 
                     
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         θ 
                         F 
                       
                     
                   
                 
               
               
                 
                   ( 
                   53 
                   ) 
                 
               
             
           
         
       
     
     Thus for a simple situation where θ F =0 or normal incidence, φ=k·n·d, and α=0: 
                                    E   ⁡     (   d   )            2     ⁢           ⁢   for   ⁢           ⁢   s   ⁢     -     ⁢   polarization     =       ⁢              E   ⁡     (   d   )            2     ⁢           ⁢   for   ⁢           ⁢   p   ⁢     -     ⁢   polarization                 =       ⁢     [         cos   2     ⁢   φ     +         n   s   2       n   2       ⁢     sin   2     ⁢   φ       ]                 =       ⁢       [         cos   2     ⁡     (     k   ·   n   ·   d     )       +         n   s   2       n   2       ⁢       sin   2     ⁡     (     k   ·   n   ·   d     )           ]     ⁢     (   55   )                     (   54   )               
which allows for the thickness ‘d’ to be solved for, i.e. the position or location within the dielectric layer where the electric field is zero.
 
     Referring now to  FIG. 13 , Equation 55 was used to calculate that the zero or near-zero electric field point in the ZnS dielectric layer shown in  FIG. 11A  when exposed to EMR having a wavelength of 434 nm is at 70 nm (instead of 77 nm for a 500 nm wavelength). In addition, a 15 nm thick Cr absorber layer was inserted at a thickness of 70 nm from the Al reflector layer to afford for a zero or near-zero electric field ZnS—Cr interface. Such an inventive structure allows light having a wavelength of 434 nm to pass through the Cr—ZnS interfaces, but absorbs light not having a wavelength of 434 nm Stated differently, the Cr—ZnS interfaces have a zero or near-zero electric field with respect to light having a wavelength of 434 nm and thus 434 nm light passes through the interfaces. However, the Cr—ZnS interfaces do not have a zero or near-zero electric field for light not having a wavelength of 434 nm and thus such light is absorbed by the Cr absorber layer and/or Cr—ZnS interfaces and not reflected by the Al reflector layer. 
     It is appreciated that some percentage of light within +/−10 nm of the desired 434 nm will pass through the Cr—ZnS interface. However, it is also appreciated that such a narrow band of reflected light, e.g. 434+/−10 nm, still provides a sharp structural color to a human eye. 
     The result of the Cr absorber layer in the multilayer stack in  FIG. 13  is illustrated in  FIG. 14  where percent reflectance versus reflected EMR wavelength is shown. As shown by the dotted line, which corresponds to the ZnS dielectric layer shown in  FIG. 13  without a Cr absorber layer, a narrow reflected peak is present at about 400 nm, but a much broader peak is present at about 550+ nm. In addition, there is still a significant amount of light reflected in the 500 nm wavelength region. As such, a double peak that prevents the multilayer stack from having or exhibiting a structural color is present. 
     In contrast, the solid line in  FIG. 14  corresponds to the structure shown in  FIG. 13  with the Cr absorber layer present. As shown in the figure, a sharp peak at approximately 434 nm is present and a sharp drop off in reflectance for wavelengths greater than 434 nm is afforded by the Cr absorber layer. It is appreciated that the sharp peak represented by the solid line visually appears as sharp/structural color. Also,  FIG. 14  illustrates where the width of a reflected peak or band is measured, i.e. the width of the band is determined at 50% reflectance of the maximum reflected wavelength, also known as full width at half maximum (FWHM). 
     Regarding omnidirectional behavior of the multilayer structure shown in  FIG. 13 , the thickness of the ZnS dielectric layer can be designed or set such that only the first harmonics of reflected light is provided. It is appreciated that this is sufficient for a “blue” color, however the production of a “red” color requires additional considerations. For example, the control of angular independence for red color is difficult since thicker dielectric layers are required, which in turn results in a high harmonic design, i.e. the presence of the second and possible third harmonics is inevitable. Also, the dark red color hue space is very narrow. As such, a red color multilayer stack has a higher angular variance. 
     In order to overcome the higher angular variance for red color, the instant application discloses a unique and novel design/structure that affords for a red color that is angular independent. For example,  FIG. 15A  illustrates a dielectric layer exhibiting first and second harmonics for incident white light when an outer surface of the dielectric layer is viewed from 0 and 45 degrees. As shown by the graphical representation, low angular dependence (small Δλ c ) is provided by the thickness of the dielectric layer, however, such a multilayer stack has a combination of blue color (1 st  harmonic) and red color (2 nd  harmonic)and thus is not suitable for a desired “red only” color. Therefore, the concept/structure of using an absorber layer to absorb an unwanted harmonic series has been developed.  FIG. 15A  also illustrates an example of the location of the reflected band center wavelength (λ c ) for a given reflection peak and the dispersion or shift of the center wavelength (Δλ c ) when the sample is viewed from 0 and 45 degrees. 
     Turning now to  FIG. 15B , the second harmonic shown in  FIG. 15A  is absorbed with a Cr absorber layer at the appropriate dielectric layer thickness (e.g. 72 nm) and a sharp blue color is provided. More importantly for the instant invention,  FIG. 15C  illustrates that by absorbing the first harmonics with the Cr absorber at a different dielectric layer thickness (e.g. 125 nm) a red color is provided. However,  FIG. 15C  also illustrates that the use of the Cr absorber layer can result in more than desired angular dependence by the multilayer stack, i.e. a larger than desired Δλ c  . It is appreciated from  FIGS. 15B and 15C  that there is an outer dielectric layer extending over the CR absorber layer. 
     It is appreciated that the relatively large shift in λ c  for the red color compared to the blue color is due to the dark red color hue space being very narrow and the fact that the Cr absorber layer absorbs wavelengths associated with a non-zero electric field, i.e. does not absorb light when the electric field is zero or near-zero. As such,  FIG. 16A  illustrates that the zero or non-zero point is different for light wavelengths at different incident angles. Such factors result in the angular dependent absorbance shown in  FIG. 16B , i.e. the difference in the 0° and 45° absorbance curves. Thus in order to further refine the multilayer stack design and angular independence performance, an absorber layer that absorbs, e.g. blue light, irrespective of whether or not the electric field is zero or not, is used. 
     In particular,  FIG. 17A  shows a multilayer stack with a Cu absorber layer instead of a Cr absorber layer extending across a dielectric ZnS layer. The results of using such a “colorful” or “selective” absorber layer is shown in  FIG. 17B  which demonstrates a much “tighter” grouping of the 0° and 45° absorbance lines for the multilayer stack shown in  FIG. 17A . As such, a comparison between  FIG. 16B  and  FIG. 16B  illustrates the significant improvement in absorbance angular independence when using a selective absorber layer rather than non-selective absorber layer. 
     Based on the above, a proof of concept multilayer stack structure was designed and manufactured. In addition, calculation/simulation results and actual experimental data for the proof of concept sample were compared. In particular, and as shown by the graphical plot in  FIG. 18 , a sharp red color was produced (wavelengths greater than 700 nm are not typically seen by the human eye) and very good agreement was obtained between the calculation/simulation and experimental light data obtained from the actual sample. Stated differently, calculations/simulations can and/or are used to simulate the results of multilayer stack designs according to one or more embodiments of the present invention and/or prior art multilayer stacks. 
     A list of simulated and/or actually produced multilayer stack samples is provided in the Table 1 below. As shown in the table, the inventive designs disclosed herein include at least 5 different layered structures. In addition, the samples were simulated and/or made from a wide range of materials. Samples that exhibited high chroma, low hue shift and excellent reflectance were provided. Also, the three and five layer samples had an overall thickness between 120-200 nm; the seven layer samples had an overall thickness between 350-600 nm; the nine layer samples had an overall thickness between 440-500 nm; and the eleven layer samples had an overall thickness between 600-660 nm 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Ave. Chroma 
                   
                 Max. 
                   
               
               
                   
                 (0-45) 
                 Δh (0-65) 
                 Reflectance 
                 Sample Name 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                  3 layer 
                 90 
                 2 
                 96 
                 3-1 
               
               
                  5 layer 
                 91 
                 3 
                 96 
                 5-1 
               
               
                  7 layer 
                 88 
                 1 
                 92 
                 7-1 
               
               
                   
                 91 
                 3 
                 92 
                 7-2 
               
               
                   
                 91 
                 3 
                 96 
                 7-3 
               
               
                   
                 90 
                 1 
                 94 
                 7-4 
               
               
                   
                 82 
                 4 
                 75 
                 7-5 
               
               
                   
                 76 
                 20 
                 84 
                 7-6 
               
               
                  9 layer 
                 71 
                 21 
                 88 
                 9-1 
               
               
                   
                 95 
                 0 
                 94 
                 9-2 
               
               
                   
                 79 
                 14 
                 86 
                 9-3 
               
               
                   
                 90 
                 4 
                 87 
                 9-4 
               
               
                   
                 94 
                 1 
                 94 
                 9-5 
               
               
                   
                 94 
                 1 
                 94 
                 9-6 
               
               
                   
                 73 
                 7 
                 87 
                 9-7 
               
               
                 11 layer 
                 88 
                 1 
                 84 
                 11-1  
               
               
                   
                 92 
                 1 
                 93 
                 11-2  
               
               
                   
                 90 
                 3 
                 92 
                 11-3  
               
               
                   
                 89 
                 9 
                 90 
                 11-4  
               
               
                   
               
            
           
         
       
     
     Turning now to  FIG. 19 , a plot of percent reflectance versus reflected EMR wavelength is shown for an omnidirectional reflector when exposed to white light at angles of 0 and 45° relative to the surface of the reflector. As shown by the plot, both the 0° and 45° curves illustrate very low reflectance, e.g. less than 20%, provided by the omnidirectional reflector for wavelengths greater than 500 nm However, the reflector, as shown by the curves, provides a sharp increase in reflectance at wavelengths between 400-500 nm and reaches a maximum of approximately 90% at 450 nm It is appreciated that the portion or region of the graph on the left hand side (UV side) of the curve represents the UV-portion of the reflection band provided by the reflector. 
     The sharp increase in reflectance provided by the omnidirectional reflector is characterized by an IR-sided edge of each curve that extends from a low reflectance portion at wavelengths greater than 500 nm up to a high reflectance portion, e.g. &gt;70%. A linear portion 200 of the IR-sided edge is inclined at an angle (β) greater than 60° relative to the x-axis, has a length L of approximately 50 on the Reflectance-axis and a slope of 1.2. In some instances, the linear portion is inclined at an angle greater than 70° relative to the x-axis, while in other instances β is greater than 75°. Also, the reflection band has a visible FWHM of less than 200 nm, and in some instances a visible FWHM of less than 150 nm, and in other instances a visible FWHM of less than 100 nm In addition, the center wavelength λ c  for the visible reflection band as illustrated in  FIG. 19  is defined as the wavelength that is equal-distance between the IR-sided edge of the reflection band and the UV edge of the UV spectrum at the visible FWHM. 
     It is appreciated that the term “visible FWHM” refers to the width of the reflection band between the IR-sided edge of the curve and the edge of the UV spectrum range, beyond which reflectance provided by the omnidirectional reflector is not visible to the human eye. In this manner, the inventive designs and multilayer stacks disclosed herein use the non-visible UV portion of the electromagnetic radiation spectrum to provide a sharp or structural color. Stated differently, the omnidirectional reflectors disclosed herein take advantage of the non-visible UV portion of the electromagnetic radiation spectrum in order to provide a narrow band of reflected visible light, despite the fact that the reflectors may reflect a much broader band of electromagnetic radiation that extends into the UV region. 
     Turning now to  FIG. 20 , a generally symmetrical reflection band provided by a multilayer stack according to an embodiment of the present invention and when viewed at 0° and 45° is shown. As illustrated in the figure, the reflection band provided by the multilayer stack when viewed at 0° has a center wavelength (λ c (0°)) shifts less than 50 nm when the multilayer stack is viewed at 45° (λ c (45°)), i.e. Δλ c (0-45°)&lt;50 nm In addition, the FWHM of both the 0° reflection band and the 45° reflection band is less than 200 nm. 
       FIG. 21  shows a plot of percent reflectance versus reflected EMR wavelength for another omnidirectional reflector design when exposed to white light at angles of 0 and 45° relative to the surface of the reflector. Similar to  FIG. 19 , and as shown by the plot, both the 0° and 45° curves illustrate very low reflectance, e.g. less than 10%, provided by the omnidirectional reflector for wavelengths less than 550 nm However, the reflector, as shown by the curves, provides a sharp increase in reflectance at wavelengths between 560-570 nm and reaches a maximum of approximately 90% at 700 nm It is appreciated that the portion or region of the graph on the right hand side (IR side) of the curve represents the IR-portion of the reflection band provided by the reflector. 
     The sharp increase in reflectance provided by the omnidirectional reflector is characterized by a UV-sided edge of each curve that extends from a low reflectance portion at wavelengths below 550 nm up to a high reflectance portion, e.g. &gt;70%. A linear portion 200 of the UV-sided edge is inclined at an angle (β) greater than 60° relative to the x-axis, has a length L of approximately 40 on the Reflectance-axis and a slope of 1.4. In some instances, the linear portion is inclined at an angle greater than 70° relative to the x-axis, while in other instances β is greater than 75°. Also, the reflection band has a visible FWHM of less than 200 nm, and in some instances a visible FWHM of less than 150 nm, and in other instances a visible FWHM of less than 100 nm In addition, the center wavelength λ c  for the visible reflection band as illustrated in  FIG. 18  is defined as the wavelength that is equal-distance between the UV-sided edge of the reflection band and the IR edge of the IR spectrum at the visible FWHM. 
     It is appreciated that the term “visible FWHM” refers to the width of the reflection band between the UV-sided edge of the curve and the edge of the IR spectrum range, beyond which reflectance provided by the omnidirectional reflector is not visible to the human eye. In this manner, the inventive designs and multilayer stacks disclosed herein use the non-visible IR portion of the electromagnetic radiation spectrum to provide a sharp or structural color. Stated differently, the omnidirectional reflectors disclosed herein take advantage of the non-visible IR portion of the electromagnetic radiation spectrum in order to provide a narrow band of reflected visible light, despite the fact that the reflectors may reflect a much broader band of electromagnetic radiation that extends into the IR region. 
     Referring now to  FIG. 22 , a plot of percent reflectance versus wavelength is shown for another seven-layer design omnidirectional reflector when exposed to white light at angles of 0 and 45° relative to the surface of the reflector. In addition, a definition or characterization of omnidirectional properties provided by omnidirectional reflectors disclosed herein is shown. In particular, and when the reflection band provided by an inventive reflector has a maximum, i.e. a peak, as shown in the figure, each curve has a center wavelength (λ c ) defined as the wavelength that exhibits or experiences maximum reflectance. The term maximum reflected wavelength can also be used for λ c . 
     As shown in  FIG. 22 , there is shift or displacement of λ c  when an outer surface of the omnidirectional reflector is observed from an angle 45°(λ c (45°)), e.g. the outer surface is tiled 45° relative to a human eye looking at the surface, compared to when the surface is observed from an angle of 0°((λ c (0°)), i.e. normal to the surface. This shift of λ c  (Δλ c ) provides a measure of the omnidirectional property of the omnidirectional reflector. Naturally a zero shift, i.e. no shift at all, would be a perfectly omnidirectional reflector. However, omnidirectional reflectors disclosed herein can provide a Δλ c  of less than 50 nm, which to the human eye can appear as though the surface of the reflector has not changed color and thus from a practical perspective the reflector is omnidirectional. In some instances, omnidirectional reflectors disclosed herein can provide a Δλ c  of less than 40 nm, in other instances a Δλ c  of less than 30 nm, and in still other instances a Δλ c  of less than 20 nm, while in still yet other instances a Δλ c  of less than 15 nm Such a shift in Δλ c  can be determined by an actual reflectance versus wavelength plot for a reflector, and/or in the alternative, by modeling of the reflector if the materials and layer thicknesses are known. 
     Another definition or characterization of a reflector&#39;s omnidirectional properties can be determined by the shift of a side edge for a given set of angle refection bands. For example, and with reference to  FIG. 19 , a shift or displacement of an IR-sided edge (ΔS IR ) for reflectance from an omnidirectional reflector observed from 0° (S IR (0°)) compared to the IR-sided edge for reflectance by the same reflector observed from 45° (S IR (45°)) provides a measure of the omnidirectional property of the omnidirectional reflector. In addition, using ΔS IR  as a measure of omnidirectionality can be preferred to the use of Δλ c  , e.g. for reflectors that provide a reflectance band similar to the one shown in  FIG. 19 , i.e. a reflection band with a peak corresponding to a maximum reflected wavelength that is not in the visible range (see  FIGS. 19 and 21 ). It is appreciated that the shift of the IR-sided edge (ΔS IR ) is and/or can be measured at the visible FWHM. 
     With reference to  FIG. 21 , a shift or displacement of a UV-sided edge (ΔS IR ) for reflectance from an omnidirectional reflector observed from 0° (S UV (0°)) compared to the IR-sided edge for reflectance by the same reflector observed from 45° (S UV (45°)) provides a measure of the omnidirectional property of the omnidirectional reflector. It is appreciated that the shift of the UV-sided edge (ΔS UV ) is and/or can be measured at the visible FWHM. 
     Naturally a zero shift, i.e. no shift at all (ΔS i =0 nm; i=IR, UV), would characterize a perfectly omnidirectional reflector. However, omnidirectional reflectors disclosed herein can provide a ΔS L  of less than 50 nm, which to the human eye can appear as though the surface of the reflector has not changed color and thus from a practical perspective the reflector is omnidirectional. In some instances, omnidirectional reflectors disclosed herein can provide a ΔS i  of less than 40 nm, in other instances a ΔS i  of less than 30 nm, and in still other instances a ΔS i  of less than 20 nm, while in still yet other instances a ΔS i  of less than 15 nm Such a shift in ΔS i  can be determined by an actual reflectance versus wavelength plot for a reflector, and/or in the alternative, by modeling of the reflector if the materials and layer thicknesses are known. 
     The shift of an omnidirectional reflection can also be measured by a low hue shift. For example, the hue shift of pigments manufactured from multilayer stacks according an embodiment of the present invention is 30° or less, as shown in  FIG. 23  (see Δθ 1 ), and in some instances the hue shift is 25° or less, preferably less than 20°, more preferably less than 15° and still more preferably less than 10°. In contrast, traditional pigments exhibit hue shift of 45° or more (see Δθ 2 ). 
     In summary, a schematic illustration of an omnidirectional multilayer thin film according to an embodiment of the present invention in which a first layer  110  has a second layer  120  extending thereacross is shown in  FIG. 24 . An optional reflector layer  100  can be included. Also, a symmetric pair of layers can be on an opposite side of the reflector layer  100 , i.e. the reflector layer  100  can have a first layer  110  oppositely disposed from the layer  110  shown in the figure such that the reflector layer  100  is sandwiched between a pair of first layers  110 . In addition, a second layer  120  can be oppositely disposed the reflector layer  100  such that a five-layer structure is provided. Therefore, it should be appreciated that the discussion of the multilayer thin films provided herein also includes the possibility of a minor structure with respect to one or more central layers. As such,  FIG. 24  can be illustrative of half of a five-layer multilayer stack. 
     The first layer  110  and second layer  120  can be dielectric layers, i.e. made from a dielectric material. In the alternative, one of the layers can be an absorbing layer, e.g. a selective absorbing layer or a non-selective absorbing layer. For example, the first layer  110  can be a dielectric layer and the second layer  120  can be an absorbing layer. 
       FIG. 25  illustrates half of a seven-layer design at reference numeral  20 . The multilayer stack  20  has an additional layer  130  extending across the second layer  120 . For example, the additional layer  130  can be a dielectric layer that extends across an absorbing layer  110 . It is appreciated from  FIG. 25  that layer  130  is an outer dielectric layer, i.e. there is not another layer extending over layer  130  and layer  130  can be the same or a different material as layer  110 . In addition, layer  130  can be added onto the multilayer stack  20  using the same or a different method that used to apply layers  100 ,  110  and/or  120  such as with a sol gel process. 
       FIG. 26  illustrates half of a nine-layer design at reference numeral  24  in which yet an additional layer  105  is located between the optional reflector layer  100  and the first layer  110 . For example, the additional layer  105  can be an absorbing layer  105  that extends between the reflector layer  100  and a dielectric layer  110 . A non-exhaustive list of materials that the various layers can be made from are shown is shown in Table 2 below. 
     
       
         
           
               
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Refractive Index Materials 
                 Refractive Index Materials 
               
               
                 (visible region) 
                 (visible region) 
               
            
           
           
               
               
               
               
            
               
                   
                 Re- 
                   
                 Re- 
               
               
                   
                 fractive 
                   
                 fractive 
               
               
                 Material 
                 Index 
                 Material 
                 Index 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Germanium (Ge) 
                 4.0-5.0 
                 Chromium (Cr) 
                 3.0 
               
               
                 Tellurium (Te) 
                 4.6 
                 Tin Sulfide (SnS) 
                 2.6 
               
               
                 Gallium Antimonite  
                 4.5-5.0 
                 Low Porous Si 
                 2.56 
               
               
                 (GaSb) 
                   
                 Chalcogenide glass 
                 2.6 
               
               
                 Indium Arsenide (InAs) 
                 4.0 
                 Cerium Oxide (CeO 2 ) 
                 2.53 
               
               
                 Silicon (Si) 
                 3.7 
                 Tungsten (W) 
                 2.5 
               
               
                 Indium Phosphate (InP) 
                 3.5 
                 Gallium Nitride (GaN) 
                 2.5 
               
               
                 Gallium Arsenate (GaAs) 
                 3.53 
                 Manganese (Mn) 
                 2.5 
               
               
                 Gallium Phosphate (GaP) 
                 3.31 
                 Niobium Oxide  
                 2.4 
               
               
                 Vanadium (V) 
                 3 
                 (Nb 2 O 3 ) 
                   
               
               
                 Arsenic Selenide  
                 2.8 
                 Zinc Telluride (ZnTe) 
                 3.0 
               
               
                 (As 2 Se 3 ) 
                   
                 Chalcogenide glass +  
                 3.0 
               
               
                 CuAlSe 2   
                 2.75 
                 Ag 
                   
               
               
                 Zinc Selenide (ZnSe) 
                 2.5-2.6 
                 Zinc Sulfate (ZnSe) 
                 2.5-3.0 
               
               
                 Titanium Dioxide  
                 2.36 
                 Titanium Dioxide  
                 2.43 
               
               
                 (TiO 2 )-solgel 
                   
                 (TiO 2 )-vacuum  
                   
               
               
                 Alumina Oxide (Al2O3) 
                 1.75 
                 deposited 
                   
               
               
                 Yttrium Oxide (Y2O3) 
                 1.75 
                 Hafnium Oxide (HfO 2 ) 
                 2.0 
               
               
                 Polystyrene 
                 1.6 
                 Sodium Aluminum  
                 1.6 
               
               
                 Magnesium Fluoride 
                 1.37 
                 Fluoride (Na3AlF6) 
                   
               
               
                 (MgF2) 
                   
                 Polyether Sulfone (PES) 
                 1.55 
               
               
                 Lead Fluoride (PbF2) 
                 1.6 
                 High Porous Si 
                 1.5 
               
               
                 Potassium Fluoride (KF) 
                 1.5 
                 Indium Tin Oxide  
                 1.46 
               
               
                 Polyethylene (PE) 
                 1.5 
                 nanorods (ITO) 
                   
               
               
                 Barium Fluoride (BaF2) 
                 1.5 
                 Lithium Fluoride (LiF4) 
                 1.45 
               
               
                 Silica (SiO2) 
                 1.5 
                 Calcium Fluoride 
                 1.43 
               
               
                 PMMA 
                 1.5 
                 Strontium Fluoride  
                 1.43 
               
               
                 Aluminum Arsenate  
                 1.56 
                 (SrF2) 
                   
               
               
                 (AlAs) 
                   
                 Lithium Fluoride (LiF) 
                 1.39 
               
               
                 Solgel Silica (SiO2) 
                 1.47 
                 PKFE 
                 1.6 
               
               
                 N,N′ bis(1naphthyl)- 
                 1.7 
                 Sodium Fluoride (NaF) 
                 1.3 
               
               
                 4,4′Diamine (NPB) 
                   
                 Nano-porous Silica  
                 1.23 
               
               
                 Polyamide-imide (PEI) 
                 1.6 
                 (SiO2) 
                   
               
               
                 Zinc Sulfide (ZnS) 
                 2.3 + 
                 Sputtered Silica (SiO2) 
                 1.47 
               
               
                   
                 i(0.015) 
                 Vacuum Deposited  
                 1.46 
               
               
                 Titanium Nitride (TiN) 
                 1.5 +  
                 Silica (SiO2) 
                   
               
               
                   
                 i(2.0)  
                 Niobium Oxide (Nb 2 O 5 ) 
                 2.1 
               
               
                 Chromium (Cr) 
                 2.5 +  
                 Aluminum (Al) 
                 2.0 +  
               
               
                   
                 i(2.5)  
                   
                 i(15) 
               
               
                 Niobium Pentoxide 
                 2.4 
                 Silicon Nitride (SiN) 
                 2.1 
               
               
                 (Nb2O5) 
                   
                 Mica 
                 1.56 
               
               
                 Zirconium Oxide (ZrO2) 
                 2.36 
                 Polyallomer 
                 1.492 
               
               
                 Hafnium Oxide (HfO2) 
                 1.9-2.0 
                 Polybutylene 
                 1.50 
               
               
                 Fluorcarbon (FEP) 
                 1.34 
                 Ionomers 
                 1.51 
               
               
                 Polytetrafluro-Ethylene 
                 1.35 
                 Polyethylene (Low 
                 1.51 
               
               
                 (TFE) 
                   
                 Density) 
                   
               
               
                 Fluorcarbon (FEP) 
                 1.34 
                 Nylons (PA) Type II 
                 1.52 
               
               
                 Polytetrafluro- 
                 1.35 
                 Acrylics Multipolymer 
                 1.52 
               
               
                 Ethylene(TFE) 
                   
                 Polyethylene 
                 1.52 
               
               
                 Chlorotrifiuoro- 
                 1.42 
                 (Medium Density) 
                   
               
               
                 Ethylene(CTFE) 
                   
                 Styrene Butadiene 
                 1.52-1.55 
               
               
                 Cellulose Propionate 
                 1.46 
                 Thermoplastic 
                   
               
               
                 Cellulose Acetate  
                 1.46-1.49 
                 PVC (Rigid) 
                 1.52-1.55 
               
               
                 Butyrate 
                   
                 Nylons (Polyamide) 
                 1.53 
               
               
                 Cellulose Acetate 
                 1.46-1.50 
                 Type 6/6 
                   
               
               
                 Methylpentene Polymer 
                 1.485 
                 Urea Formaldehyde 
                 1.54-1.58 
               
               
                 Acetal Homopolymer 
                 1.48 
                 Polyethylene 
                 1.54 
               
               
                 Acrylics 
                 1.49 
                 (High Density) 
                   
               
               
                 Cellulose Nitrate 
                 1.49-1.51 
                 Styrene Acrylonitrile 
                 1.56-1.57 
               
               
                 Ethyl Cellulose 
                 1.47 
                 Copolymer 
                   
               
               
                 Polypropylene 
                 1.49 
                 Polystyrene 
                 1.57-1.60 
               
               
                 Polysulfone 
                 1.633 
                 (Heat &amp; Chemical) 
                   
               
               
                   
                   
                 Polystyrene 
                 1.59 
               
               
                   
                   
                 (General Purpose) 
                   
               
               
                   
                   
                 Polycarbornate  
                 1.586 
               
               
                   
                   
                 (Unfilled) 
                   
               
               
                   
                   
                 SnO2 
                 2.0 
               
               
                   
               
            
           
         
       
     
     Methods for producing the multilayer stacks disclosed herein can be any method or process known to those skilled in the art or one or methods not yet known to those skilled in the art. Typical known methods include wet methods such as sol gel processing, layer-by-layer processing, spin coating and the like. Other known dry methods include chemical vapor deposition processing and physical vapor deposition processing such as sputtering, electron beam deposition and the like. 
     The multilayer stacks disclosed herein can be used for most any color application such as pigments for paints, thin films applied to surfaces and the like. 
     The above examples and embodiments are for illustrative purposes only and changes, modifications, and the like will be apparent to those skilled in the art and yet still fall within the scope of the invention. As such, the scope of the invention is defined by the claims and all equivalents thereof.