Patent Publication Number: US-10768341-B2

Title: Optical material, optical element and method for manufacturing same

Description:
This is a continuation of U.S. application Ser. No. 15/068,030 filed on Mar. 11, 2016, which is a Divisional of U.S. application Ser. No. 13/248,331 filed on Sep. 29, 2011 (now U.S. Pat. No. 9,310,520), which is a Continuation of International Application No. PCT/JP2010/056403 filed on Apr. 8, 2010 claiming the conventional priority of U.S. Provisional Application No. 61/202,845 filed on Apr. 10, 2009, Japanese Patent Application No. 2009-243438 filed on Oct. 22, 2009 and Japanese Patent Application No. 2009-243439 filed on Oct. 22, 2009, all of the disclosures of which are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The present teaching relates to an optical material which is used as a component (a part or a portion) of a liquid or solid to which an illumination light (illumination light beam) is irradiated, an optical liquid and an optical element which include the optical material, a method for producing the optical material and a method for producing the optical liquid and the optical element. More specifically, the present teaching relates to, for example, an optical material having relative permeability which is different from 1 (one). 
     BACKGROUND ART 
     Optical materials such as conventional optical glass all have a relative permeability that is approximately 1 and have a relative permittivity that is greater than 1, and thus have refractive index with a positive value greater than 1. In view of this situation, researches are made with respect to so-called meta-materials that are substances provided with a structure smaller than the wavelength of a light as an objective to which the meta-materials are to be applied and greater than an atom or molecule and exhibiting a relative permeability value and/or relative permittivity value which are/is unobtainable with a substance in the natural world. Further, with respect for example to a microwave having a wavelength of 6 cm (frequency: 5 GHz), a large number of small split-ring resonators having a negative relative permeability and a large number of thin metallic lines having a negative relative permittivity and arranged in parallel are combined and thus a substance (structure) having a negative refractive index is realized (see, for example, Non-patent Literature 1). 
     In the recent years, in order to realize a substance having a negative refractive index to lights in the infrared to visible regions, for example, such a substance is theoretically proposed having a plurality of minute split-ring resonators and a relative permeability that is greatly different from 1 (including a negative value) with respect to a light of which wavelength is about 1,000 nm to about 400 nm (see, for example, Non-patent Literature 2). By combining the minute split-ring resonators (having the relative permeability in a negative range) and another substance having a negative relative permittivity, it is possible to realize the substance having the negative refractive index to the lights in the infrared to visible regions. 
     CITATION LIST 
     Non-Patent Literature 
     [Non-Patent Literature 1] 
     D. R. Smith et al.: “Composite medium with simultaneously negative permeability and permittivity”, Phys. Rev. Lett. (the United States), 84, pp. 4184-4187 (2000). 
     [Non-Patent Literature 2] 
     A. Ishikawa, T. Tanaka and S. Kawata: “Frequency dependence of the magnetic response of split-ring resonators”, J. Opt. Soc. Am. B (the United States), Vol. 24, No. 3, pp. 510-515 (2007). 
     SUMMARY 
     According to a first aspect of the present teaching, there is provided an optical material which is used as a component of a liquid or solid to which an illumination light is irradiated, the optical material comprising: 
     a plurality of minute resonators each of which is formed of a conductor having a width approximately same as or smaller than a wavelength of the illumination light; and 
     a protective film which is formed of an insulator or a semi-conductor, wherein each of the minute resonators is covered by the protective film. 
     According to a second aspect of the present teaching, there is provided an optical material which is used as a component of a liquid or solid to which an illumination light is irradiated, the optical material comprising a plurality of resonating elements each of which includes: 
     a plurality of minute resonators each of which is formed of a conductor having a width approximately same as or smaller than a wavelength of the illumination light and which are arranged apart from each other; and 
     a protective film which is formed of an insulator or a semi-conductor and which covers the minute resonators. 
     According to a third aspect of the present teaching, there is provided an optical liquid comprising a liquid; and the optical material of the first or second aspect of the present teaching which is mixed in the liquid. 
     Further, according to a fourth aspect of the present teaching, there is provided an optical element comprising the optical material of the first or second aspect of the present teaching which is solidified. 
     Furthermore, according to a fifth aspect of the present teaching, there is provided a method for producing an optical material composed of a plurality of minute resonators each of which is formed of a conductor, and is covered by a protective film formed of an insulator or a semi-conductor, the method comprising the steps of: 
     forming a sacrifice layer on a substrate; 
     forming a first protective layer formed of the insulator or the semi-conductor on the sacrifice layer; 
     forming a conductive layer formed of the conductor on the first protective layer; 
     patterning the minute resonators in the conductive layer; 
     forming a second protective layer formed of the insulator or the semi-conductor so as to cover the patterned minute resonators; and 
     removing the sacrifice layer. 
     According to a sixth aspect of the present teaching, there is provided a method for producing an optical material having a plurality of optical elements each of which is composed of a plurality of minute resonators formed of a conductor and is arranged apart from each other, and which are covered by a protective film formed of an insulator or a semi-conductor, the method comprising the steps of: 
     forming a sacrifice layer on a substrate; 
     forming a first protective layer formed of the insulator or the semi-conductor on the sacrifice layer; 
     forming a first conductive layer formed of the conductor on the first protective layer; 
     patterning the minute resonators in the first conductive layer; 
     forming a second protective layer formed of the insulator or the semi-conductor so as to cover the patterned minute resonators; 
     removing a part of the first protective layer and a part of the second protective layer based on an arrangement of the minute resonators in each of the optical elements; and 
     removing the sacrifice layer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1(A)  is a perspective view of powder of an optical material of a first embodiment,  FIG. 1(B)  is an enlarged perspective view of a plurality of resonating elements  14  (each of which is a split-ring resonator (SRR) covered by a protective layer) constructing the powder, and  FIG. 1(C)  is an enlarged perspective view showing one SRR. 
         FIG. 2  is a diagram showing an example of relative permeability of the SRR. 
         FIG. 3  is a flowchart showing an example of a method for producing a large number of the resonating elements  14 . 
         FIG. 4(A)  is a diagram showing an exposure apparatus which is used in an exposure step,  FIG. 4(B)  is an enlarged plan view of a part of a pattern of a first reticle, and  FIG. 4(C)  is an enlarged plan view of a part of a pattern of a second reticle. 
         FIG. 5  ( FIGS. 5(A) to 5(G) ) is an enlarged cross-sectional view showing a construction of a part of a wafer in a plurality of steps during production process until a large number of the resonating elements  14  are produced. 
         FIG. 6(A)  is a diagram showing a liquid in which a large number of the resonating elements  14  are mixed,  FIG. 6(B)  is an enlarged view of a B portion shown in  FIG. 6(A) ,  FIG. 6(C)  is a diagram showing an optical lens including a large number of the resonating elements  14 , and  FIG. 6(D)  is an enlarged view of a D portion shown in  FIG. 6(C) . 
         FIG. 7(A)  is an enlarged perspective view of a resonating element  14  of a first modification, and  FIG. 7(B)  is an enlarged perspective view of a split-ring resonator  17  shown in  FIG. 7(A) . 
         FIG. 8(A)  is an enlarged plan view of a part of a pattern of a reticle R 1 A which is used in a second modification,  FIG. 8(B)  is an enlarged plan view of a part of a pattern of a reticle R 1 B. 
         FIG. 9(A)  is an enlarged perspective view of a resonating element  14 B of a third modification, and  FIG. 9(B)  is an enlarged plan view of a part of a pattern of a reticle which is used for producing the resonating element  14 B. 
         FIG. 10(A)  is an enlarged perspective view of a resonating element  14 C of a second embodiment,  FIG. 10(B)  is a side view of the resonating element  14 C shown in  FIG. 10(A) , and  FIG. 10(C)  is a perspective view of powder of an optical material of the second embodiment. 
         FIG. 11(A)  is an enlarged perspective view of another resonating element  14 D of the second embodiment,  FIG. 11(B)  is a side view of the resonating element  14 D shown in  FIG. 11(A) . 
         FIG. 12(A)  is an enlarged perspective view of a plurality of split-ring resonators (SRRs) in the resonating element  14 D, and  FIG. 12(B)  is an enlarged perspective view of one SRR. 
         FIG. 13  ( 13 A,  13 B) is a flowchart showing an example of a method for producing the resonating elements  14 C,  14 D. 
         FIG. 14(A)  is an enlarged view of a pattern for SRR,  FIG. 14(B)  is an enlarged plan view of a part of a pattern of a first reticle, and  FIG. 14(C)  is an enlarged plan view of a part of a pattern of a second reticle. 
         FIG. 15  ( FIGS. 15(A) to 15(G) ) is an enlarged cross-sectional view showing a construction of a part of the upper surface of a wafer in a plurality of first half steps during a process for producing the resonating element  14 D. 
         FIG. 16  ( FIGS. 16(A) to 16(G) ) is an enlarged cross-sectional view showing the construction of the part of the upper surface of the wafer in a plurality of latter half steps during the process for producing the resonating element  14 D. 
         FIG. 17(A)  is an enlarged perspective view of a resonating element  14 E of a modification, and  FIG. 17(B)  is an enlarged plan view of a part of a pattern of a reticle for producing the resonating element  14 E. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     [First Embodiment] 
     A preferred first embodiment of the present teaching will be explained with reference to  FIGS. 1 to 6 . 
       FIG. 1(A)  shows powder  12  of an optical material of the embodiment,  FIG. 1(B)  is an enlarged perspective view of a plurality of resonating elements  14  which are a part or portion composing the powder  12  and each of which is a split-ring resonator covered by a protective layer. In the following description, the split-ring resonator is also referred to as “SRR”. In  FIG. 1(B) , each of the plurality of resonating elements  14  is formed or constructed, for example, by covering entire faces of a split ring-shaped SRR (split-ring resonator)  16 , which is made of a metal such as silver (Ag), gold (Au), copper (Cu), aluminum (Al) or the like, with a protective layer  18  having a disc-shape and formed of an insulator (insulating material) such as silicon dioxide (SiO 2 ), aluminum oxide (Al 2 O 3 ), or the like. Note that the protective layer  18  may have, for example, a square plate-shape. 
     In  FIG. 1(B) , two resonating elements  14  adjacent in the x-direction and the y-direction are periodically arranged with a period of “a” and two resonating elements 14 adjacent in the z direction are periodically arranged with a period of “b” in the rectangular coordinate system (x, y, z). Note that the arrangement state of the plurality of resonating elements  14  in  FIG. 1(B)  is a virtual arrangement for calculating the relative permeability (to be discussed later), and a large number of the resonating elements  14  in the powder  12  shown in  FIG. 1(A)  are randomly arranged. In this embodiment, since each of the SRRs  16  is covered by the protective layer  18 , average spacing distances or gaps (arrangement periods) of the plurality of SRRs  16  in the lateral and thickness directions thereof respectively are substantially defined by an outer shape of the protective layer  18 . 
       FIG. 1(C)  shows one of the SRRs (split-ring resonators)  16  in one resonating element  14  as shown in  FIG. 1(B) . In  FIG. 1(C) , the SRR  16  is constructed of four fan-shaped members  16 A,  16 B,  16 C and  16 D obtained by splitting or dividing a ring, of which center is an axis parallel to the z axis, in the circumference direction of the circle with a spacing distance g. Note that a split number N (N=2, 3, 4, 5, . . . ) by which the SRR is split is arbitrary, and the SRR  16  may be constructed of a plurality of arbitrary number of fan-shaped members. 
     The inner diameter of the SRR  16  is r (diameter is  2   r ), the width in the radial direction of the SRR  16  is w, the thickness of the SRR  16  is T. In this case, according to the document by A. Ishikawa, T. Tanaka and S. Kawata and entitled “Frequency dependence of the magnetic response of split-ring resonators”, J. Opt. Soc. Am. B (the United States), Vol. 24, No. 3, pp. 510-515 (2007) (hereinafter referred to as “Reference Literature A”), an effective relative permeability μeff of the plurality of SRRs  16  arranged as shown in  FIG. 1(B)  with respect to an illumination light having a predetermined wavelength λ (angular frequency is ω) is as follows. The real part of the relative permeability is μRe, the imaginary part of the relative permeability is μIm, and i is the imaginary unit. 
     
       
         
           
             
               
                 
                   
                     
                       μ 
                       eff 
                     
                     = 
                     
                       
                         
                           μ 
                           Re 
                         
                         + 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             μ 
                             Im 
                           
                         
                       
                       = 
                       
                         1 
                         - 
                         
                           
                             F 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               2 
                             
                           
                           
                             
                               ω 
                               2 
                             
                             - 
                             
                               1 
                               CL 
                             
                             + 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   Z 
                                   ⁢ 
                                   
                                     ( 
                                     ω 
                                     ) 
                                   
                                   ⁢ 
                                   ω 
                                 
                                 L 
                               
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Further, provided that the space permeability (vacuum permeability) is μ 0 , the permittivity is ε 0 , and the relative permittivity of the SRR  16  is εr, then the parameters F, C, L and the impedance Z (ω) in the formula (1) are represented as follows: 
     
       
         
           
             
               
                 
                   
                     F 
                     = 
                     
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           2 
                         
                       
                       
                         a 
                         2 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     C 
                     = 
                     
                       
                         1 
                         N 
                       
                       ⁢ 
                       
                         ϵ 
                         0 
                       
                       ⁢ 
                       
                         ϵ 
                         r 
                       
                       ⁢ 
                       
                         wT 
                         g 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     t 
                     = 
                     
                       g 
                       
                         
                           2 
                           ⁢ 
                           w 
                         
                         + 
                         g 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     L 
                     = 
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           2 
                         
                       
                       b 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Z 
                       ⁡ 
                       
                         ( 
                         ω 
                         ) 
                       
                     
                     = 
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             rZ 
                             s 
                           
                           ⁡ 
                           
                             ( 
                             ω 
                             ) 
                           
                         
                       
                       w 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Z 
                       s 
                     
                     ⁡ 
                     
                       ( 
                       ω 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         R 
                         s 
                       
                       ⁡ 
                       
                         ( 
                         ω 
                         ) 
                       
                     
                     + 
                     
                       
                         iX 
                         s 
                       
                       ⁡ 
                       
                         ( 
                         ω 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Note that in this embodiment, the parameter t in the formula (4) is not used. Further, the split number N in the formula (3) is 4 regarding the SRR  16 ; Rs(ω) in the formula (7) is the surface resistance of the SRR  16  and Xs(ω)in the formula (7) is the inner reactance of the SRR  16 ; and as disclosed in Reference Literature A, in a case that, for example, the wavelength λ is in the visible region, the Rs(ω) takes a value in a range from about 0.2 to about 1.7 depending on the material of the SRR  16 , and the Xs(ω) takes a large negative value regardless of the material. 
     Further, according to the formula (1), the real part μRe of the effective relative permeability μeff becomes considerably greater than 1 in predetermined ranges in each of which a frequency f [THz] of the illumination light is smaller than a predetermined resonance frequency (f 1 , f 2 , f 3 , etc.) and takes a negative value in predetermined ranges in each of which the frequency f is greater than the predetermined resonance frequency, as shown in  FIG. 2 , depending on the shape and arrangement of the SRRs  16 . Furthermore, as the resonance frequency f becomes higher from f 1  to f 3 , the absolute value of the real part μRe becomes smaller. Note that the resonance frequency is substantially defined by the parameters of the shape of SRR  16  (r, w, T, etc.), and the contribution by the arrangement periods a, b of the SRRs  16  are considered as relatively small. 
     According to Reference Literature A, in a case that the radius r of the SRR  16  is same as the width w of the SRR  16 , that the period b is 350 nm, the spacing distance g is 33 nm, the thickness T is 2.5 times the penetration depth, and the relative permittivity εr is 2.25, the resonance frequency f 1  is 300 THz (the wavelength λ 1  corresponding thereto is 1000 nm (1 μm)), the resonance frequency f 2  is 500 THz (the wavelength λ 2  corresponding thereto is 600 nm), and the resonance frequency f 3  is 700 THz (the wavelength λ 3  corresponding thereto is 420 nm). Namely, the wavelength λ 1  corresponding to the resonance frequency f 1  is in the infrared region, the wavelengths λ 2 , λ 3  corresponding to the resonance frequencies f 1 , f 2 , respectively are in the visible region. 
     Further, in the formulae (1) to (5), when the resonance frequency f 1  (wavelength λ 1 : 1000 nm) can be obtained, the period a, the radius r and outer diameter  4   r  (which is the width of the outer diameter) of the SRR  16  (=2(r+w)), are 875 nm, 125 nm and 600 nm, respectively. Furthermore, when the resonance frequency f 2  (wavelength λ 2 : 600 nm) can be obtained, the period a, the radius r and the outer diameter  4   r  are 525 nm, 75 nm and 300 nm, respectively; and when the resonance frequency f 3  (wavelength λ 3 : 420 nm) can be obtained, the period a, the radius r and the outer diameter  4   r  are 350 nm, 50 nm and 200 nm, respectively. In this case, since the thickness T of the SRR  16  is about the radius r or thinner than the radius r, the maximum width of the outer shape of the SRR  16  is  4   r  and the size of the outer shape of the SRR  16  (maximum width ( 4   r )) is approximately ½ of the wavelength λ 1  to λ 3  corresponding thereto. 
     Moreover, in the embodiment, in a case that the relative permeability of the protective layer  18  is approximately 1 and the resonating element  14  is used as a substance having the real part μRe of the relative permeability that is considerably greater than 1 (for example, greater than 2), the wavelength of the illumination light may be set to λ 1   b,  λ 2   b  (frequencies f 1   b,  λ 2   b  corresponding thereto are lower than the resonance frequencies f 1 , f 2 ), etc. in a range slightly longer than λ 1 , λ 2  (similarly regarding λ 3  as well). On the other hand, in a case that the resonating element  14  is used as a substance having the real part μRe of the relative permeability that is negative, the wavelength of the illumination light may be set to λ 1   a,  λ 2   a  (frequencies f 1   a,  f 2   a  corresponding thereto are higher than the resonance frequencies f 1 , f 2 ), etc. in a range slightly shorter than λ 1 , λ 2 . By doing so, the resonating element  14  can be used as a substance (meta-material) in which the real part μRe of the relative permeability is considerably different from 1. 
     As an example shown in  FIG. 6(A) , a large number of the resonating elements  14  may be mixed (or dissolved) in a predetermined solvent to thereby produce an optical liquid  30 . As shown in  FIG. 6(B)  which is an enlarged view, the liquid  30  is obtained, for example, by mixing (dissolving) a large number of the resonating elements  14  in a solvent  30   a  such as a pure water (purified water). Further, in a case that the solvent  30   a  is water (relative permittivity is positive), the resonating elements  14  are used, for example, under a condition that the wavelength is set to be λ 1   b  or λ 2   b,  etc. with which the real part μRe of the relative permeability is considerably greater than 1 as shown in  FIG. 2 . Under this condition, since the refractive index of the water  30  takes a value that is greater than, for example, 2, the liquid  30  can be used as a liquid having a high refractive index. Such a liquid having the high refractive index is usable, for example, as an immersion liquid for a liquid immersion type microscope, an immersion liquid for a liquid immersion type exposure apparatus (to be described later on), etc. The orientations (directions) of the respective resonators mixed in the liquid are random, and thus the liquid can have an isotropic optical characteristic. 
     Further, in a case that the solvent  30   a  is, for example, a liquid having a negative relative permittivity, the resonating elements  14  are used under a condition, for example, that the wavelength is set to be λ 1   a  or λ 2   a,  etc. with which the real part μRe of the relative permeability is negative as shown in  FIG. 2 . Under this condition, the refractive index of the liquid  30  takes a negative value. Such a liquid having the negative refractive index is, for example, filled in a cell and thus becomes usable as a super lens such as an optical element having a negative refractive index, as will be described later on. 
     Furthermore, as shown in  FIG. 6(C)  as another example, a plate-shaped optical element  32  can be produced by solidifying the large number of resonating elements  14 . As shown in  FIG. 6(D)  that is an enlarged view, the optical element  32  is obtained, for example, by mixing a medium  32   a  in a powdery form (filling agent) and the powder of the resonating elements  14  uniformly and then by solidifying the mixture by means of sintering, etc. Further, in a case that the protective layer  18  of each of the resonating elements  14  is formed of silicon dioxide (having positive relative permittivity) in a state that the medium  32   a  is absent, then the resonating elements  14  are used under a condition that the wavelength is set to be λ 1   b  or λ 2   b,  etc. with which the real part μRe of the relative permeability is considerably greater than 1 as shown in  FIG. 2 . Under this condition, since the refractive index of the optical element  32  takes, for example, a value greater than 2, it is possible to produce an optical lens having, for example, a refractive index greater than 2 by processing the optical element  32  into a spherical or aspherical lens. 
     On the other hand, in a case that the medium  32   a  is, for example, a substance having a negative relative permittivity (for example, a large number of minute thin metallic lines, or a dielectric having a small bandgap), the resonating elements  14  are used under a condition, for example, that the wavelength is set to be λ 1   a  or λ 2   a,  etc. with which the real part μRe of the relative permeability is negative as shown in  FIG. 2 . Under this condition, the refractive index of the optical element  32  takes a negative value. When an illumination light IL comes into such an optical element  32  having the negative refractive index from an external object point  34  as shown in  FIG. 6(C) , then the illumination light IL is imaged precisely to an external image point  36 . Accordingly, the optical element  32  can be used as a so-called super lens. 
     Next, an example of a method for producing the powder  12  composed of the large number of resonating elements  14  as shown in  FIG. 1(A)  will be explained with reference to a flow chart shown in  FIG. 3 . This producing method uses a photolithography step, and an exposure apparatus  50  shown in  FIG. 4(A)  is used in the photolithography step. 
     In  FIG. 4(A) , the exposure apparatus  50  which is a scanning-exposure and liquid immersion type and is constructed of a scanning stepper includes, for example, an exposure light source (not shown) which generates an illumination light or illumination light beam (exposure light or exposure light beam) IL such as, for example, an ArF excimer laser (wavelength: 193 nm) or a KrF excimer laser (wavelength: 248 nm), etc.; an illumination optical system ILS which illuminates a reticle R 1  (or a reticle R 2 , etc.) with the illumination light IL; a reticle stage RST which moves (scans) the reticle R 1 , etc.; a projection optical system PL which projects a pattern of the reticle R 1 , etc., onto a wafer P at a predetermined projection magnification β (for example, a reduction magnification of ¼, etc.); and a wafer stage WST which moves (scans and step-moves) the wafer P in a plane perpendicular to an optical axis AX of the projection optical system PL. The wafer P is, for example, a disc-shaped substrate (base member) having a diameter of 200 mm, 300 mm or 450 mm, etc., and formed of silicon, etc., and a predetermined plurality of numbers of layers of thin films and a photoresist (photosensitive material) are formed on the wafer P. 
     The exposure apparatus  50  is further provided with a local immersion mechanism including a nozzle head  51  which is arranged to surround a tip (end) portion of an optical member located at the lower end of the projection optical system PL; a liquid supply device  52  which supplies a liquid Lq such as a pure water (purified water) allowing the illumination light IL to transmit therethrough to a local space between the wafer P and the optical member arranged inside the nozzle head  51 ; and a liquid recovery device  53  which recovers the liquid Lq in the local space. Note that as the local liquid immersion mechanism, it is allowable to use, for example, the mechanism as disclosed in United States Patent Application Publication No. 2007/242247 or European Patent Application Publication No. 1420298, etc. Further, as the liquid Lq, it is also allowable to use the liquid  30  shown in  FIG. 6(A)  (in a case that the liquid is used in the wavelength region at which the liquid  30  exhibits a high refractive index). 
     As described above, the exposure apparatus  50  is a liquid immersion-type exposure apparatus. Therefore, it is possible to produce the SRR (split-ring resonator)  16  in  FIG. 1(C)  having the radius r of about 50 nm easily and highly precisely. 
     Further,  FIG. 4(B)  is an enlarged plane view showing a part or portion of a pattern formed in a pattern area in the reticle R 1  shown in  FIG. 4(A) . In  FIG. 4(B) , a first pattern  55 , which is formed of a light-shielding film and which is magnification of the SRR  16  shown in  FIG. 1(C)  by the reciprocal ratio of the projection magnification β, is formed in the pattern area in the reticle R 1  in mutually orthogonal two directions at a predetermined period. 
       FIG. 4(C)  is an enlarged plan view showing a part or portion of a pattern formed in the reticle R 2  shown in  FIG. 4(A) . In  FIG. 4(C) , a second pattern  57 , which is formed of a light-shielding film and which is magnification of the outer shape of the protective layer  18  of the resonating element  14  shown in  FIG. 1(B)  by the recipriocal ratio of the projection magnification β, is formed in the pattern area of the reticle R 2  in mutually orthogonal two directions at a predetermined period which is same as the arrangement period for the first pattern  55 . During the exposure, the second pattern  57  on the reticle R 2  is positioned at a location same as a location  55 A at which the first pattern  55  on the reticle R 1  is arranged. Further, an area  58  between the second patterns  57  on the reticle R 2  corresponds to a separation band for separating the plurality of resonating elements  14  away from one another. 
     Further, in Step  101  of  FIG. 3 , one lot of wafers each of which is, for example, a silicon wafer having a disc-shape and diameter of 300 mm is prepared. Although the following processes or steps are sequentially executed for processing the one lot of wafers, the processes will be explained as follows regarding one piece of the wafers P.  FIGS. 5(A) to 5(G)  are each an enlarged cross-sectional view showing a part of the construction of a multi-layered thin film (plurality of layered thin films) formed on the wafer P. At first, in a thin-film forming apparatus (not shown), a first photoresist layer  22 A is formed on an entire surface of the wafer P as shown in  FIG. 5(A) . The first photoresist layer  22 A is used not as a photosensitive layer for forming a resist pattern, but is used as a sacrifice layer for separating the large number of resonating elements  14  away from the wafer P at the end of the processes. 
     Next, in Step  102 , a first silicon dioxide (SiO 2 ) layer  24 A is formed on the first photoresist layer  22 A on the wafer P. Then, in Step  103 , a metallic thin film  26  made of a metal (in this case, for example, silver or aluminum, etc.) is formed on the first silicon dioxide layer  24 A. Next, in Step  104 , a second, positive-type photoresist layer  22 B is formed on the metallic thin film  26 . The second photoresist layer  22 B and the first photoresist layer  22 A are different types from each other, and the first photoresist layer  22 A is not dissolved by a developing liquid and a dissolving liquid for the second photoresist layer  22 B (and a photoresist layer  22 C which will be described later on). Next, in Step  105 , the wafer P is loaded on the exposure apparatus  50  shown in  FIG. 4(A) , and the second photoresist layer  22 B in each of all the shot areas on the wafer P is exposed with a pattern of the minute SRR (split-ring resonator) composed of a large number of images  55 P of the first patterns  55  of the reticle R 1 , by the exposure apparatus  50 . Note that in this example, in  FIG. 5(A) , areas between the large number of images  55 P are exposed by the illumination light. 
     Next, in Step  106 , the wafer P is transported to a coater/developer (not shown), and the second photoresist layer  22 B on the wafer P is developed. By doing so, a resist pattern  22 BP corresponding to the pattern of the SRR is formed, as shown in  FIG. 5(B) . Next, in Step  107 , the wafer P is transported to an etching device (not shown) and the metallic thin film  26  on the wafer P is etched with the resist pattern  22 BP serving as a mask, thereby forming a large number of minute SRRs  16  as shown in  FIG. 5(C) . Then, the resist pattern  22 BP is removed. 
     Next, in Step  108 , the thin-film forming apparatus (not shown), a second silicon dioxide layer  24 B is formed so as to cover the large number of minute SRRs  16  on the wafer P, as shown in  FIG. 5(D) . Then, in Step  109 , a third, positive-type photoresist layer  22 C is formed on the second silicon dioxide layer  24 B of the wafer P at the coater/developer (not shown). Next, in Step  110 , the wafer P is loaded on the exposure apparatus  50  shown in  FIG. 4(A) , and the third photoresist layer  22 C on the wafer P is exposed with images  57 P of the second patterns  57  of the reticle R 2 , by the exposure apparatus  50 . By doing so, the area (separation band) between the large number of SRRs  16  on the wafer P is exposed. After that, the third photoresist layer  22 C on the wafer P is developed in the coater/developer (not shown). With this, as shown in  FIG. 5(E) , a resist pattern  22 CP is formed at an area at which the protective layer  18  as shown in  FIG. 1(B)  is to be formed, so as to cover the large number of the SRRs  16  on the wafer P. 
     Next, in Step  111 , the first and second silicon dioxide layers  24 A,  24 B are etched at the etching device (not shown) with the resist pattern  22 CP on the wafer P serving as a mask, as shown in  FIG. 5(F) . By doing so, the large number of SRRs  16  are each covered entirely by silicon dioxide films  24 AP and  24 BP. Then, in Step  112 , the wafer P is transported to the coater/developer (not shown), and the first photoresist layer  22 A (sacrifice layer) on the wafer P is dissolved and removed. In order to remove the first photoresist layer  22 A, it is allowable to perform the plasma asking. With this, as shown in  FIG. 5(G) , a large number of resonating elements  14 , each of which is constructed of the SRR  16  covered by the protective layer  18  which is formed of the silicon dioxide films  24 AP and  24 BP, are produced in a state that the resonating elements  14  are separated from the wafer P. The powder  12  shown in  FIG. 1(A)  is obtained by collecting the large number of resonating elements  14  produced on one lot of the wafers P. 
     Note that in a case of producing further a greater number of the resonating elements  14 , it is possible to re-use the one lot of wafers used in the production steps as described above. Accordingly, the wafers are not burden on the production cost. 
     Afterwards, in a case of producing the liquid  30  (optical liquid) shown in  FIG. 6(A) , the powder composed of the large number of resonating elements  14  is dissolved in a solvent  30   a  such as water, etc. inside a predetermined container in Step  121 , followed by being agitated with an agitating device (not shown), as necessary. 
     On the other hand, in a case of producing the optical element  32  as shown in  FIG. 6(C) , the powder composed of the large number of resonating elements  14  is placed in a predetermined mould, followed by being sintered in Step  131 . In this procedure, it is also allowable to previously and uniformly mix the powder of the resonating elements  14  and the medium  32   a  in a powdery state (filling agent). 
     The effects, etc. of the embodiment are as follows. 
     (1) The powder  12  of the embodiment is an optical material which is used as a component (a part or a portion) of a liquid or solid to which the illumination light is irradiated and includes a large number of the resonating elements  14 ; the resonating elements  14  are each formed by covering the minute SRR (split-ring resonator)  16  made of the metal (conductor) having the width smaller than the wavelength of the illumination light with the protective layer  18  formed of silicon dioxide, etc. (insulator). 
     According to the optical material of the embodiment, the SRR  16  is formed to have the size or dimension not more than about the wavelength of the visible light, thereby making it possible that the SRR  16  has the real part of the relative permeability different from 1 to a light having a wavelength which is in the infrared region or smaller than the infrared region. Further, since each of the SRRs  16  is covered by the protective layer  18 , the plurality of SRRs  16  do not contact with one another, and thus are structurally stable. 
     Note that it is allowable to use, as the material for the protective layer  18 , a semi-conductor such as silicon nitride (Si 3 N 4 ), etc., other than the insulator. 
     (2) Further, in the large number of resonating elements  14  constructing the powder  12 , the real part of the relative permeability (and consequently permeability) of the SRR  16  with respect to the illumination light may be negative and the real part of the relative permittivity (and consequently permittivity) of the protective layer  18  which covers each of the SRRs  16  with respect to the illumination light may be negative. With this, the resonating elements  14  or the liquid or solid containing the resonating elements  14  therein becomes an optical material having a negative refractive index to the illumination light. 
     (3) Further, the liquid  30  obtained by dissolving the powder  12  in the solvent  30   a  can be used as an optical liquid having, for example, a refractive index greater than 2 or having a negative refractive index. 
     (4) Furthermore, the optical element  32  formed by solidifying the powder  12  can be used as the optical material having, for example, a refractive index greater than 2 or having a negative refractive index. 
     (5) Moreover, the method for producing the large number of resonating elements  14  of the embodiment includes: Step  101  of forming the first photoresist layer  22 A (sacrifice layer) on the wafer P; Step  102  of forming the first silicon dioxide layer  24 A on the first photoresist layer  22 A; Step  103  of forming the metallic thin film  26  on the first silicon dioxide film  24 A; Steps  104  to  107  of patterning the plurality of SRRs  16  on the thin film  26 ; Steps  108  to  111  of forming the second silicon dioxide layer  24 B so as to cover the plurality of SRRs  16 ; and Step  112  of removing the first photoresist layer  22 A. 
     Accordingly, it is possible to mass-produce the powder  12  composed of the large number of resonating elements  14  of the embodiment with high precision by using the photolithography step. 
     (6) Further, the step of forming the second silicon dioxide layer  24 B includes Steps  109  to  111  of removing the silicon dioxide layers  24 A,  24 B between the plurality of SRRs  16 . Accordingly, by removing the first photoresist layer  22 A next, the plurality of resonating elements  14  can be separated easily from one another. 
     (7) Furthermore, the optical liquid  30  shown in  FIG. 6(A)  can be produced by the step of mixing the powder  12  composed of the large number of resonating elements  14  in the solvent  30   a  (liquid such as water, etc.); and the step of agitating the solvent  30   a  in which the powder  12  is mixed. Accordingly, the liquid can be produced easily. 
     (8) Moreover, the optical element  32  shown in  FIG. 6(C)  can be produced by including the step of sintering the powder  12  composed of the large number of resonating elements  14 . Accordingly, the optical element  32  can be produced easily. 
     Note that the following modifications can be made for the embodiment described above. 
     (1) It is allowable to use, instead of the resonating element  14  of the embodiment, a resonating element  14 A (split-ring resonator provided with a protective film) having a construction in which a double split-ring resonator  17  is covered with the protective layer  18 , as in a first modification shown in  FIG. 7(A) . As shown in  FIG. 7(B) , the split-ring resonator  17  is obtained by surrounding a first split-ring  17 A having a radius of r and a width of w in the radial direction with a second split-ring  17 B having a width of w at a spacing distance or gap g. Further, the thickness of each of the split-rings  17 A,  17 B is T. This resonating element  14 A can also be easily produced by a production method similar to the production method of  FIG. 3 . Accordingly, the construction of the SRR (split-ring resonator) is arbitrary. 
     (2) Further, in a case that the image of the pattern of the first reticle R 1  shown in  FIG. 4(B)  is exposed in Step  105  of  FIG. 3  by using, for example, a dry-type exposure apparatus of which resolution is lower than that of the liquid-immersion type exposure apparatus  50  of the above-described embodiment, there is a fear that the resolution might not be sufficient. In such a case, it is allowable to divide the large number of first patterns  55  of the reticle R 1  into two simpler-shaped patterns and to perform double-exposure with these two divided patterns. By doing so, it is possible to produce the large number of resonating elements  14  including the minute SRRs  16  highly precisely by using an exposure apparatus having a low resolution. As an example, the large number of first patterns  55  of the reticle R 1  can be divided into circular patterns (annular patterns)  551  (first portion) constructed of a large number of light-shielding films formed on a reticle R 1 A of  FIG. 8(A) ; and a pattern (second portion) which is formed in a light-shielding film of a reticle R 1 B of  FIG. 8(B)  and which includes, as light-transmitting portions, a plurality of vertical line patterns  553 , a plurality of horizontal line patterns  554  and a large number of small circular patterns  552  each arranged at the intersection of the line patterns  553  and  554 . The patterns of the reticles R 1 A and R 1 B of the second modification are simpler than the pattern of the reticle  1  and the pattern period is wide, which in turn makes it possible to expose the patterns of the reticles R 1 A and R 1 B on the wafer with a required resolution with an exposure apparatus having a lower resolution than that of the exposure apparatus  50 . 
     Note that the large number of first pattern  55  of the reticle R 1  may be divided into two or more patterns having simpler shapes, and the two or more simpler-shaped pattern may be subjected to the multiple-exposure. 
     (3) Further, in a case of producing the optical element  32  of  FIG. 6(C) , it is allowable to use, as the medium  32   a  to be mixed with the large number of resonating elements  14 , a solid obtained by solidifying a liquid in the sol state by the Sol-Gel process. The Sol-Gel process is a chemical reaction in which the sol is turned into the gel state by heating, etc. and then ceramics, etc., is synthesized. In this case also, in the step of mixing the large number of resonating elements  14  (powder  12 ) and the medium  32   a,  the medium  32   a  is a liquid in the sol state, and thus the large number of resonating elements  14  and the medium  32   a  can be mixed uniformly. 
     As the liquid in the sol state for the medium  32   a,  it is possible to use, as an example, tetraethoxysilane (Si(OR 4 ). Here, —OR is ethoxy group (—OC 2 H 5 ), and —R is ethyl group (—C 2 H 5 ). The reaction in this case is, for example, as follows. 
     At first, when the powder  12  of the resonating elements  14  is mixed to a pure water solution (Sol) of tetraethoxysilane and is then heated, the aqueous solution of tetraethoxysilane becomes colloid of triethoxysilane hydroxide and ethanol as follows, due to the hydrolysis. The heating temperature is, for example, 600 degrees Celsius to 1,100 degrees Celsius, and ethanol is evaporated and recovered.
 
Si(OR) 4 +H 2 O+Powder→Si(OR) 3 (OH)+ROH+Powder  (11A)
 
     When the hydrolysis is continued further, the triethoxysilane hydroxide, uniformly mixed with the powder (resonating elements  14 ) assumes a structure such as that of silicon dioxide, due to the following polymerization reaction.
 
2×Si(OR) 3 (OH)+Powder→(OR) 3 Si—O—Si(OR) 3 +H 2 O+Powder  (11B)
 
     Accordingly, in the optical element  32  which is finally formed, the resonating elements  14  and the solvent  32   a  are uniformly mixed and the refractive index of the medium  32   a  is approximately same as the refractive index of the protective layer  18  (provided that the protective layer  18  is formed of silicon dioxide) of the resonating elements  14 . Therefore, the reflection on the interface is lowered and the transmittance with respect to the illumination light becomes high. 
     Note that in this reaction, when the amount of the pure water is too much and the concentration of the solid in the solvent  32   a  is small, then the pure water may be evaporated. 
     (4) Further, in the resonating elements  14  of the embodiment described above, the real part of the permittivity is positive and the real part of the relative permittivity is also positive (for example, real number greater than 1). Therefore, even when a large number of the resonating elements  14  are merely collected, the refractive index remains to be positive. 
     In view of this, as a resonating element  14 B of a third modification shown in  FIG. 9(A) , it is allowable to form a pair of line patterns  81 X elongated in the y-direction and a pair of line patterns  81 Y elongated in the x-direction so as to sandwich (interpose) each of the SRRs (split-ring resonators)  16  therebetween in the x-direction and the y-direction, respectively, inside the protective layer  18 . The line patterns  81 X,  81 Y are minute thin lines formed of a conductor (metal, etc.) which is same as that forming the SRR  16 . 
     In this modification, it is assumed that the wavelength of a light (light beam) ILY is within a range in which the real part μRe of the relative permeability of  FIG. 2  takes a negative value (for example, a value slightly smaller than the wavelength λ 3 ) provided that the light ILY is a light in which a vibration direction EVY of the electric field vector is parallel to the x-axis (linearly polarized in the x-direction) and the vibration direction of the magnetic field vector is parallel to the z-axis and that the light ILY comes into the resonating element  14 B in the y-direction. In this case, the line width (cross-sectional area) and the length in the x-direction of the line pattern  81 Y and the arrangement such as the x-direction and y-direction period, etc. of the large number of line patterns  81 Y are set so that the real part of the permittivity of the resonating elements  14 B to the light ILY is negative (the real part of the relative permittivity is also negative). 
     As a result, the resonating element  14 B (or a substance obtained by collecting the resonating elements  14 B) becomes a meta-material in which the refractive index to the light ILY takes a negative value. 
     Note that an example of construction of the plurality of thin metallic lines, in which the real part of the permittivity is negative with respect to a microwave, is described in Literature by D. R. Smith et al. and entitled “Composite medium with simultaneously negative permeability and permittivity”, Phys. Rev. Lett. (the United States), 84, pp. 4184-4187 (2000) (hereinafter referred to as “Reference Literature B”). The line patterns  81 Y of the modification shown in  FIG. 9(A)  is formed to have the minute shape and arrangement so that the real part of the permittivity to the visible light takes a negative value. 
     Further, it is presumed that the shape and arrangement of the large number of line patterns  81 X elongated in the y-direction inside the resonating element  14 B are same as the shape and arrangement of the line patterns  81 Y. In this case, when a light ILX (provided that the light ILX has a wavelength same as that of the light ILY), in which a vibration direction EVX of the electric field vector is parallel to the y-axis (linearly polarized in the y-direction) and the vibration direction of the magnetic field vector is parallel to the z-axis, comes into the resonating element  14 B in the x-direction, then the real part of the permittivity of the resonating element  14 B to the light ILX also becomes negative, due to the line pattern  81 X. Accordingly, the refractive index of the resonating element  14 B to the light ILX also takes a negative value. Therefore, by mixing the large number of resonating elements  14 B in the liquid or by solidifying the large number of resonating elements  14 B to thereby form an optical element, it is possible to produce an optical liquid or optical element having a negative refractive index to a light having a predetermined wavelength. 
     Next, in a case that the resonating element  14 B of  FIG. 9(A)  is produced, it is allowable to use, in Step  105  of  FIG. 3 , a reticle R 3  in which line patterns  58 X,  58 Y formed of a light-shielding film and corresponding to the line patterns  81 X,  81 Y are formed around each of the first patterns  55  as shown in  FIG. 9(B) , instead of using the reticle R 1  of  FIG. 4(B) . 
     By doing so, the line patterns  81 X,  81 Y can be patterned together and at the same time with the large number of SRRs  16  in the metallic thin film  26  of the wafer P. 
     [Second Embodiment] 
     Next, a second embodiment will be explained with reference to  FIGS. 10 to 16 . In the following description, components or parts which are shown in  FIGS. 10(A) to 12(B)  and  FIGS. 14(A)  to  16  and which correspond to those shown in  FIGS. 1(A) to 1(C)  and  FIGS. 4(B)  to  13 , are designated by the same reference numerals, and any detailed explanation therefor will be simplified or omitted. 
       FIG. 10(C)  shows powder  12 A of an optical material of the second embodiment. The powder  12 A is obtained by collecting a large number of minute resonating elements  14 C or  14 D.  FIG. 10(A)  is an enlarged perspective view of one resonating element  14 C constituting the powder  12 A, and  FIG. 10(B)  is a side view of the resonating element  14 C shown in  FIG. 10(A) . In  FIG. 10(A) , there is assumed x-axis and y-axis in a rectangular coordinate system in a plane, and z-axis is assumed as an axis perpendicular to the plane. The resonating element  14 C is constructed by covering a plurality of minute split-ring resonators  16  (or SRRs  16 ), which are arranged in the x-direction and the y-direction at a period (pitch) of “a” to be arranged in K rows×L columns, with a rectangular plate-shaped protective layer  18 A composed of an insulator such as silicon dioxide (SiO 2 ), aluminum oxide (Al 2 O 3 ), or the like. 
     “K” is an arbitrary integer not less than 1, and “L” is an arbitrary integer not less than 2. Note that K and L may be same integers not less than 2. In the embodiment, as an example, K=L=10. In this case, 100 pieces of the SRR  16  are arranged in 10 rows×10 columns in the resonating element  14 C. Note that the protective layer  18 A may be, for example, formed such that four corner portions thereof are rounded. Each of the SRRs  16  is made of a metal such as silver (Ag), gold (Au), copper (Cu) or aluminum (Al), etc., and has a shape obtained by dividing a ring axisymmetric with respect to an axis parallel to the z-axis into four portions (see  FIG. 12(B) ). As shown in  FIG. 10(B) , a thickness (width in the z-direction) T of the SRR  16  is smaller than the pitch “a”, and a thickness Tp of the protective layer  18 A is about three times the thickness T. 
     Note that it is allowable to use a resonating element  14 D as shown in  FIG. 11(A)  and having a plurality of layers each including a plurality of the SRRs  16  as the optical material for the powder  12 A as shown in  FIG. 10(C) , instead of using the resonating element  14 C as shown in  FIG. 10(A)  and having one layer of the plurality of SRRs  16  formed therein. In  FIG. 11(A) , the resonating element  14 D is obtained by covering, with the protective layer  18 A, a plurality of SRRs  16  which are arranged at the period (pitch) of “a” in K rows×L columns in the x-direction and the y-direction and are arranged in M layers such as a first layer  15 A, a second layer  15 B, a third layer  15 C, etc., in the z-direction at a period (pitch) of “b”. In this case, K is an arbitrary integer not less than 1, and M are each an arbitrary integer not less than 2. Note that K and L may be same integers not less than 2, and that the resonating element  14 C shown in  FIG. 10(A)  corresponds to the arrangement in which M=1. 
     As shown in the side view of  FIG. 10(B) , the thickness Tp 3  of the protective layer  18 A of the resonating element  14 D is approximately (3×T+(M−1)b). Note that in  FIG. 11(A) , the resonating element  14 D has a three-layered structure (L=3). Other than this, as an example, the relationship among K, L and M may be K=L=M=10. In such a case, 1000 pieces of the SRRs  16  are arranged in 10 rows×10 columns×10 layers in the resonating element  14 D. 
       FIG. 12(A)  is an enlarged view showing a portion of the resonating element  14 D (note that the resonating element  14 D has a two-layered structure). The resonating element  14 D can be considered as a plurality of the resonating elements  14 C which are overlaid (stacked) in the z-direction. Note that although the large number of resonating elements  14 D in the powder  12 A of  FIG. 10(C)  are arranged randomly, the resonating elements  14 D approximately arranged as shown in  FIG. 12(A)  are included in the powder  12 A at a certain ratio. 
       FIG. 12(B)  shows one of the SRRs (split-ring resonators)  16  shown in  FIG. 12(A) . The shape and material of the SRR  16  is same as those of the SRR  16  shown in  FIG. 1(B)  of the first embodiment. Namely, in  FIG. 12(B) , the SRR  16  is constructed of four fan-shaped members  16 A,  16 B,  16 C and  16 D obtained by splitting or dividing a ring, which has an inner radius r, a width w in the radial direction and a thickness T, in the circumference direction of the ring with a spacing distance g. Note that a split number N (N=2, 3, 4, 5, . . . ) by which the SRR is split is arbitrary. 
     The arrangement of the plurality of SRRs  16 , in the resonating element  14 D of  FIG. 12(A) , on the rectangular coordinate system (x, y, z) is same as the arrangement of the plurality of SRRs  16  in the resonating element  14  of  FIG. 1(B)  of the first embodiment. Accordingly, similarly to the first embodiment, the effective relative permeability μeff of the plurality of SRR  16  arranged as shown in  FIG. 12(A)  with respect to an illumination light having a predetermined wavelength λ (provided that the angular frequency is ω) is represented by the formula (1). 
     According to the formula (1), the real part μRe of the effective relative permeability μeff becomes considerably greater than 1 in the predetermined ranges in each of which the frequency f [THz] of the illumination light is smaller than the predetermined resonance frequency (f 1 , f 2 , f 3 , etc.) and takes a negative value in the predetermined ranges in each of which the frequency f is greater than the predetermined resonance frequency, as shown in  FIG. 2 , depending on the shape and arrangement of the SRRs  16 . Furthermore, as the resonance frequency f becomes higher from f 1  to f 3 , the absolute value of the real part μRe becomes smaller. Note that the resonance frequency is substantially defined by the parameters of the shape of SRR  16  (r, w, T, etc.), and the contribution by the arrangement periods a, b of the SRRs  16  are considered as relatively small. 
     Similarly to the first embodiment, according to Reference Literature A, in a case that the radius r of the SRR  16  is same as the width w of the SRR  16 , the period b is 350 nm, the spacing distance g is 33 nm, the thickness T is 2.5 times the penetration depth, and the relative permittivity εr is 2.25, the resonance frequency f 1  is 300 THz (the wavelength λ 1  corresponding thereto is 1000 nm (1 μm)), the resonance frequency f 2  is 500 THz (the wavelength λ 2  corresponding thereto is 600 nm), and the resonance frequency f 3  is 700 THz (the wavelength λ 3  corresponding thereto is 420 nm). 
     Further, the period a, the radius r and the outer diameter  4   r  in the formulae (1) to (5) when the resonance frequency f 3  (the wavelength λ 3 : 420 nm) can be obtained are 350 nm, 50 nm and 200 nm, respectively. In this case, since the thickness T of the SRR  16  is approximately same as or thinner than the radius r, the maximum width of the outer shape of the SRR  16  is  4   r,  and the size or dimension of the outer shape (the maximum width ( 4   r )) of the SRR  16  is approximately ½ of the wavelengths λ 1  to λ 3  corresponding thereto. 
     As described above, provided that the arrangement of the SRRs  16  in the resonating element  14 D is 100 rows×100 columns×100 layers in a case that each of the periods a and b are 350 nm, then the size of the resonating element  14 D is approximately 35×35×35 μm 3 . Accordingly, the resonating element  14 C,  14 D has a size of μm-order, and thus the resonating element  14 C,  14 D can be easily handled, thereby making it possible to suppress, for example, inadvertent aggregation of a plurality of the elements. 
     Further, in the embodiment, in a cases that the relative permittivity of the protective layer  18 A is approximately 1 and that the resonating elements  14 C (or  14 D) are used as a substance having the real part μRe of the relative permeability which is considerably greater than 1 (for example, greater than 2), the wavelength of the illumination light may be set, for example, to λ 1   b,  λ 2   b  (frequencies f 1   b,  f 2   b  corresponding thereto are lower than the resonance frequencies f 1 , f 2 ), etc. in a range slightly longer than λ 1 , λ 2  (similarly regarding λ 3  as well). On the other hand, in a case that the resonating elements  14 C (or  14 D) are used as a substance having the real part μRe of the relative permeability that is negative, the wavelength of the illumination light may be set to λ 1   a,  λ 2   a  (frequencies f 1   a,  f 2   a  corresponding thereto are higher than the resonance frequencies f 1 , f 2 ), etc. in a range slightly shorter than λ 1 , λ 2 . By doing so, the resonating element  14 D (or  14 C) can be used as a substance (meta-material) in which the real part μRe of the relative permeability is considerably different from 1. 
     As an example shown in  FIG. 6(A) , a large number of the resonating elements  14 C (or  14 D) may be mixed (or dissolved) in a predetermined solvent to thereby produce an optical liquid  30 . The liquid  30  is obtained, for example, by mixing (dissolving) a large number of the resonating elements  14 C (or  14 D) in a solvent such as a pure water (purified water). Further, in a case that the solvent is water (relative permittivity is positive), the resonating elements  14 C are used, for example, under a condition that the wavelength is set to be λ 1   b  or λ 2   b,  etc. with which the real part μRe of the relative permeability is considerably greater than 1 as shown in  FIG. 2 . Under this condition, since the refractive index of the water  30  is greater than, for example, 2, the liquid  30  can be used as a liquid having a high refractive index. Such a liquid having the high refractive index is usable, for example, as an immersion liquid for a liquid immersion type microscope, an immersion liquid for a liquid immersion type exposure apparatus (to be described later on), etc. The orientations (directions) of the respective resonators mixed in the liquid are random, and thus the liquid can have an isotropic optical characteristic. 
     Further, in a case that the solvent is, for example, a liquid having a negative relative permittivity, the resonating elements  14 C (or  14 D) are used, for example, under a condition that the wavelength is set to be λ 1   a  or λ 2   a,  etc. with which the real part μRe of the relative permeability is negative as shown in  FIG. 2 . Under this condition, the refractive index of the liquid  30  takes a negative value. Such a liquid having the negative refractive index is, for example, filled in a cell and thus becomes usable as a super lens such as an optical element having a negative refractive index, as will be described later on. 
     Furthermore, as shown in  FIG. 6(C)  as another example, a plate-shaped optical element  32  can be produced by solidifying the large number of resonating elements  14 C (or  14 D). The optical element  32  is obtained, for example, by mixing a medium in a powdery form (filling agent) and the powder of the resonating elements  14 C,  14 D uniformly and then by solidifying the mixture by means of sintering, etc. Further, in a case that the protective layer  18 A of each of the resonating elements  14 C,  14 D is formed of silicon dioxide (having positive relative permittivity) in a state that the medium is absent, then the resonating elements  14 C,  14 D are used under a condition that the wavelength is set to be λ 1   b  or λ 2   b,  etc. with which the real part μRe of the relative permeability is considerably greater than 1 as shown in  FIG. 2 . Under this condition, since the refractive index of the optical element  32  takes, for example, a value greater than 2, it is possible to produce an optical lens having, for example, a refractive index greater than 2 by processing the optical element  32  into a spherical or aspherical lens. 
     On the other hand, in a case that the medium is, for example, a substance having a negative relative permittivity (for example, a large number of minute thin metallic lines, or a dielectric having a small bandgap), the resonating elements  14 C (or  14 D) are used, for example, under a condition that the wavelength is set to be λ 1   a  or λ 2   a,  etc. with which the real part μRe of the relative permeability is negative as shown in  FIG. 2 . Under this condition, the refractive index of the optical element  32  takes a negative value. When an illumination light IL comes into such an optical element  32  having the negative refractive index from an external object point  34  as shown in  FIG. 6(C) , then the illumination light IL is imaged precisely to an external image point  36 . Accordingly, the optical element  32  can be used as a so-called super lens. 
     Next, an example of a method for producing the powder  12 A composed of the large number of single-layered resonating elements  14 C as shown in  FIG. 10(A)  or the large number of multi-layered resonating elements  14 D as shown in  FIG. 11(A)  will be explained with reference to a flow chart shown in  FIG. 13  ( FIGS. 13A, 13B ). This producing method uses a photolithography step, and the exposure apparatus  50  of the liquid-immersion type and shown in  FIG. 4(A)  is used in the photolithography step. Since the exposure apparatus  50  is a liquid immersion-type exposure apparatus as described above, the SRRs (split-ring resonators)  16  having the diameter r of about 50 nm in  FIG. 12(B)  can be produced easily and highly precisely. 
     Further,  FIG. 14(B)  is an enlarged plane view showing a part or portion of a pattern formed in a pattern area in a first reticle R 4  used in the exposure apparatus  50  shown in  FIG. 4(A) . In  FIG. 14(B) , first patterns  56 , each of which is formed of a light-shielding film and is magnification of the SRRs  16  arranged for example in 10 rows×10 columns in the resonating element  14 C as shown in  FIG. 10(A)  by the reciprocal ratio of the projection magnification β, are formed in the pattern area of the reticle R 4  while being arranged in mutually orthogonal two directions at a predetermined spacing distance. Each of the first patterns  56  is formed by arranging a ring-shaped pattern  55 , which is formed of a split-ring shaped, light-shielding film as shown in  FIG. 14(A)  that is an enlarged view and corresponding to one piece of the SRRs  16 , for examples in 10 rows×10 columns. 
       FIG. 14(C)  is an enlarged plan view showing a part or portion of a pattern formed in a second reticle R 5  which is used in the exposure apparatus  50 . In  FIG. 14(C) , second patterns  57 A, each of which is formed of a light-shielding film and is magnification of the outer shape of the protective layer  18 A on the xy-plane of the resonating element  14 C,  14 D by the reciprocal ratio of the projection magnification β, are formed in the pattern area of the reticle R 5  while being in mutually orthogonal two directions at a predetermined period which is same as the arrangement period for the first patterns  56 . During the exposure, each of the second patterns  57 A on the reticle R 5  is positioned at a location same as a location  56 A (including locations  55 A at which a large number of the ring-shaped patterns  55  are arranged respectively) at which one of the first patterns  56  on the reticle R 4  is arranged. Further, an area between the second patterns  57 A on the reticle R 5  corresponds to a separation band for separating the plurality of resonating elements  14 C,  14 D away from one another. 
     Further, in Step  141  of  FIG. 13 , one lot of wafers each of which is, for example, a silicon wafer having a disc-shape and diameter of 300 mm is prepared. Although the following processes or steps are sequentially executed for processing the one lot of wafers, the processes will be explained as follows regarding one piece of the wafers P.  FIGS. 15(A) to 15(G)  and  FIGS. 16(A) to 16(G)  are each an enlarged cross-sectional view showing a part of the construction of a multi-layered thin film (plurality of layered thin films) formed on the wafer P. At first, in a thin-film forming apparatus (not shown), a first photoresist layer  22 A is formed on an entire surface of the wafer P as shown in  FIG. 15(A) . The first photoresist layer  22 A is used not as a photosensitive layer for forming a resist pattern, but is used as a sacrifice layer for separating the large number of resonating elements  14 C,  14 D away from the wafer P at the end of the processes. 
     Next, in Step  142 , a first silicon dioxide (SiO 2 ) layer  24 A is formed on the first photoresist layer  22 A on the wafer P. Then, in Step  143 , a first metallic thin film  26 A formed of a metal (in this case, for example, silver or aluminum, etc.) on the first silicon dioxide layer  24 A. Next, in Step  144 , a second, positive-type photoresist layer  22 B is formed on the metallic thin film  26 . The second photoresist layer  22 B and the first photoresist layer  22 A are different types from each other, and the first photoresist layer  22 A is not dissolved by a developing liquid and a dissolving liquid for the second photoresist layer  22 B (and a photoresist layer  22 C, etc. which will be described later on). Next, in Step  145 , the wafer P is loaded on the exposure apparatus  50  shown in  FIG. 4(A) , and the second photoresist layer  22 B in each of all the shot areas on the wafer P is exposed with images of a large number of the first patterns  56  (a large number of images  55 P of the ring-shaped patterns  55  for the SRRs  16 ) of the reticle R 4 , by the exposure apparatus  50 . Note that in this example, areas between the large number of images  55 P are exposed by the illumination light in  FIG. 15(A) . 
     Next, in Step  146 , the wafer P is transported to a coater/developer (not shown), and the second photoresist layer  22 B on the wafer P is developed. By doing so, a resist pattern  22 BP corresponding to the SRRs  16  (images  55 P) is formed, as shown in  FIG. 15(B) . Next, in Step  147 , the wafer P is transported to an etching device (not shown) and the metallic thin film  26 A on the wafer P is etched with the resist pattern  22 BP serving as a mask, thereby forming a large number of minute SRRs  16  of the first layer  15 A as shown in  FIG. 15(C) . Then, the resist pattern  22 BP is removed. 
     Next, in Step  148 , in the thin-film forming apparatus (not shown), a second silicon dioxide layer  24 B is formed so as to cover the large number of minute SRRs  16  on the wafer P, as shown in  FIG. 15(D) . Next, in Step  149 , a surface of the silicon dioxide layer  24 B is planarized (flattened) by the chemical-mechanical polishing (CMP), as shown in  FIG. 15(E) . Next, in Step  150 , confirmation is made whether or not a layer of the SRRs  16  (here, a second layer of SRRs  16 ) is to be formed on the first layer  15 A. In a case that the second layer is not to be formed, namely in a case that a single-layered resonating element  14 C of  FIG. 10(A)  is to be produced, then the procedure proceeds to Step  151 . Here, provided that the second layer is to be formed, the procedure returns to Step  143  and a metallic thin film  26 B which is same as the metallic thin film  26 A is formed on the silicon dioxide layer  24 B and then a third photoresist layer  22 C is formed on the metallic thin film  26 B (Step  144 ), as shown in  FIG. 15(F) . Next, the photoresist layer  22 C in each of all the shot areas on the wafer P is exposed with the large number of images of the first patterns  56  (images  55 P of the ring-shaped patterns  55 ) of the reticle R 4 , by the exposure apparatus  50 . 
     Next, the photoresist layer  22 C on the wafer P is developed (Step  146 ), thereby forming a resist pattern  22 CP corresponding to the SRRs  16  (images  55 P), as shown in  FIG. 15(G) . Next, the metallic thin film  26 B on the wafer P is etched with the resist pattern  22 CP serving as a mask (Step  147 ), thereby forming a large number of minute SRRs  16  of the second layer  15 B as shown in  FIG. 16(A) . Then, the resist pattern  22 CP is removed. 
     Next, a third silicon dioxide layer  24 C is formed so as to cover the large number of SRRs  16  of the second layer  15 B, as shown in  FIG. 16(B)  (Step  148 ). Next, a surface of the silicon dioxide layer  24 C is planarized as shown in  FIG. 16(C) . Next, in Step  150 , provided that a third layer is not to be formed on the second layer  15 B in this case, and the procedure proceeds to Step  151  in which a fourth, positive-type photoresist layer  22 D is formed on the silicon dioxide layer  24 C of the wafer P in the coater/developer (not shown), as shown in  FIG. 16D . Next, in Step  152 , the wafer P is loaded on the exposure apparatus  50  shown in  FIG. 4(A) , and the photoresist layer  22 D on the wafer P is exposed with the images  57 P of the second patterns  57  of the reticle R 5 , by the exposure apparatus  50 . By doing so, the area (separation band) between the large number of resonating elements  14 D (or  14 C, same as the following description) on the wafer P is exposed. After that, the photoresist layer  22 D on the wafer P is developed in the coater/developer (not shown). With this, as shown in  FIG. 16(E) , a resist pattern  22 DP is formed at an area, at which the protective layer  18 A as shown in  FIG. 11(A)  or  FIG. 10(A)  is to be formed, so as to cover the large number of the SRRs  16  in each of the resonating elements  14 D on the wafer P. 
     Next, in Step  153 , the plurality of silicon dioxide layers  22 A to  24 C are etched at the etching device (not shown) with the resist pattern  22 DP on the wafer P serving as a mask, as shown in  FIG. 16(F) . By doing so, the large number of SRRs  16  in the resonating element  14 D are each covered entirely by the silicon dioxide films  24 AP,  24 BP and  24 CP. Then, in Step  154 , the wafer P is transported to the coater/developer (not shown), and the first photoresist layer  22 A (sacrifice layer) is dissolved and removed. In order to remove the first photoresist layer  22 A, it is allowable to perform the plasma asking. With this, as shown in  FIG. 16(G) , a large number of resonating elements  14 D, each constructed of the large number of SRRs  16  of the first and second layers  15 A,  15 B which are covered by the protective layers  18 A formed of the silicon dioxide films  24 AP,  24 BP and  24 CP, are produced in a state that the resonating elements  14 D are separated from the wafer P. Note that in a case wherein the second layer  15 B is not formed, a large number of the resonating elements  14 C is produced. The powder  12 A shown in  FIG. 10(C)  is obtained by collecting the large number of resonating elements  14 D (or  14 C) produced on one lot of the wafers P. 
     Note that in a case of producing a resonating element  14 D including three or more layers of the large number of SRRs  16 , the operations in Steps  143  to  149  may be repeated as the number of the layers. Further, note that in a case of producing further a greater number of the resonating elements  14 C,  14 D, it is possible to re-use the one lot of wafers used in the production steps as described above. Accordingly, the wafers are not burden on the cost. 
     Afterwards, in a case of producing the liquid  30  (optical liquid) shown in  FIG. 6(A) , the powder composed of the large number of resonating elements  14 C or  14 D is dissolved in a solvent  30   a  such as water, etc. inside a predetermined container in Step  161 , followed by being agitated with an agitating device (not shown), as necessary. 
     On the other hand, in a case of producing the optical element  32  as shown in  FIG. 6(C) , the powder composed of the large number of resonating elements  14 C or  14 D is placed in a predetermined mould, followed by being sintered. In this procedure, it is also allowable to previously and uniformly mix the powder of the resonating elements  14 C,  14 D and the medium  32   a  (filling agent) in a powdery state. Note that in the powder  12 A, the liquid  30  and the optical element  32 , it is allowable to use a large number of the single-layered resonating elements  14 C and the large number of the multiple-layered resonating elements  14 D in a mixed manner. 
     The effects, etc. of the embodiment are as follows. 
     (1) The powder  12 A of the embodiment is an optical material which is used as a component (a part or a portion) of a liquid or solid to which the illumination light is irradiated and includes the plurality of minute resonating elements  14 C,  14 D; the resonating elements  14 C,  14 D each include the plurality of SRRs (split-ring resonator)  16  made of the metal (conductor) having the width that is approximately same as or smaller than the wavelength of the illumination light and arranged apart from one another and the protective layer  18 A which is formed of silicon dioxide, etc. (insulator) and which covers the plurality of SRRs  16 . 
     According to the optical material of the embodiment, the SRR  16  is formed to have the size or dimension not more than about the wavelength of the visible light, thereby making it possible that the SRR 16  has the real part of the relative permeability different from 1 to a light having a wavelength which is in the infrared region or smaller than the infrared region. Further, since each of the SRRs  16  is covered by the protective layer  18 , the plurality of SRRs  16  do not contact with one another, and thus are structurally stable. Furthermore, since the relative positions of the plurality of SRRs  16  are substantially fixed, the characteristics such as the resonating frequencies f 1  to f 3 , etc. can be easily controlled by controlling the relative positions. 
     Note that it is allowable to use, as the material for the protective layer  18 A, a semi-conductor such as silicon nitride (Si 3 N 4 ), etc., other than the insulator. 
     (2) Further, the plurality of SRRs  16  in the resonating element  14 C are arranged at the period “a” along the x- and y-axes perpendicular to each other; and the plurality of SRRs  16  in the resonating element  14 D are arranged at the period “a” along the x- and y-axes perpendicular to each other and arranged at the period b along the z-axis. Thus, according to the resonating elements  14 C or  14 D, since the two-dimensional or three-dimensional arrangement of the SRRs  16  are fixed, it is possible to control the characteristics such as the resonating frequency, etc., further easily and precisely. 
     (3) Furthermore, in the large number of resonating elements  14 C,  14 D constructing the powder  12 A, the real part of the relative permeability (and consequently permeability) of the SRRs  16  with respect to the illumination light may be negative and the real part of the relative permittivity (and consequently permittivity) of the protective layer  18 A which covers the SRRs  16  with respect to the illumination light may be negative. With this, the resonating elements  14 C,  14 D or the liquid or solid containing the resonating elements  14 C,  14 D therein becomes an optical material having a negative refractive index to the illumination light. 
     (4) Moreover, the liquid  30  obtained by dissolving the powder  12 A in the solvent can be used as an optical liquid having a refractive index for example greater than 2 or having a negative refractive index. 
     (5) Further, the optical element  32  formed by solidifying the powder  12 A can be used as the optical material having a refractive index for example greater than 2 or having a negative refractive index. 
     (6) Furthermore, the method for producing the large number of resonating elements  14 C of the embodiment includes: Step  141  of forming the first photoresist layer  22 A (sacrifice layer) on the wafer P; Step  142  of forming the first silicon dioxide layer  24 A on the first photoresist layer  22 A; Step  143  of forming the metallic thin film  26 A on the first silicon dioxide layer  24 A; Steps  144  to  147  of patterning the plurality of SRRs  16  on the thin film  26 A; Steps  148  and  149  of forming the second silicon dioxide layer  24 B so as to cover the plurality of SRRs  16 ; Steps  151  to  153  of removing a portion or part of the silicon dioxide layer  24 A and a portion or part of the silicon dioxide layer  24 B in accordance with the arrangement of the SRRs  16 ; and Step  154  of removing the first photoresist layer  22 A. 
     According to this producing method, it is possible to highly precisely mass-produce the powder  12 A composed of the large number of resonating elements  14 C of the embodiment by using the lithography step. 
     (7) Further, between the operation of Step  148  performed for the first time and the operations of Steps  151  to  153 , this producing method is capable of performing Step  149  of planarizing (flattening) the surface of the silicon dioxide layer  24 B, Step  143  of forming the second metallic thin film  26 B on the silicon dioxide layer  24 B which has been planarized, Steps  144  to  147  of patterning the plurality of SRRs  16  in the second metallic thin film  26 B, and Step  148  of forming the silicon dioxide layer  24 C so as to cover the plurality of SRRs  16  which have been patterned. 
     By repeating the operations of Steps  143  to  148  as described above, it is possible to produce the resonating elements  14 D including a large number of the SRRs  16  arranged in multiple layers. 
     Note that following modifications can be made to the respective embodiments described above. 
     (1) First, it is allowable to apply (coat) a surfactant to surfaces of the protective layers  18 ,  18 A of the respective resonating elements  14 ,  14 A to  14 D of the respective embodiments. By doing so, it is possible to prevent the plurality of resonating elements  14 ,  14 A to  14 D from fixing to one another when the resonating elements  14 ,  14 A to  14 D are in the powdery state. 
     (2) Next, instead of the first photoresist layer  22 A on the wafer P in  FIG. 5(A)  of the first embodiment or the first photoresist layer  22 A on the wafer P in  FIG. 15(A)  of the second embodiment, it is allowable to form, for example, a layer of silicon dioxide as the sacrifice layer. In such a case, it is possible to use, for example, fluorinated acid as a dissolving liquid for dissolving the sacrifice layer in Step  112  or Step  154 . Namely, the wafer P may be immersed in the fluorinated acid. As the material for forming the protective layer  18 ,  18 A in this case (material used instead of the material forming the silicon dioxide layers  24 A to  24 C), it is allowable to use a material which is not dissolved by the fluorinated acid, such as silicon nitride, aluminum oxide or aluminum nitride (AlN), etc. 
     (3) Further, instead of using the SRRs  16  inside the resonating elements  14 C,  14 D of the second embodiment, it is allowable to use the double split-ring resonator  17  shown in  FIG. 7(B) , in a similar manner as in the first embodiment. A resonating element in which a plurality of double split-ring resonators  17  are covered by the protective film  18 A, etc., can also be easily produced by a producing method similar to the producing method of  FIG. 13 . Accordingly, the construction of the split-ring resonator is arbitrary. 
     (4) Furthermore, in the second embodiment, in a case that the exposure is performed with the image of the pattern of the first reticle R 4  shown in  FIG. 14(B)  in Step  145  of  FIG. 13  by using, for example, a dry-type exposure apparatus of which resolution is lower than that of the liquid-immersion type exposure apparatus  50 , there is a fear that the resolution might not be sufficient. In such a case, it is allowable to divide the large number of ring-shaped patterns  55  of the reticle R 4  into two simpler-shaped patterns and to perform double-exposure with these two divided patterns, in a similar manner to the first embodiment. By doing so, it is possible to produce the large number of resonating elements  14 C,  14 D including the minute SRRs  16  highly precisely by using an exposure apparatus having a low resolution. 
     Note that it is allowable to divide the large number of ring-shaped patterns  55  of the reticle R 4  into two or more pieces of simpler-shaped patterns and to perform multiple-exposure with these two or more divided patterns. 
     (5) Moreover, in the first embodiment, in a case that a large number of the resonating elements  14 ,  14 A,  14 B are mixed in the solvent  30   a  to thereby produce the liquid  30  as shown in  FIG. 6(B)  or in the second embodiment, in a case that a large number of the resonating elements  14 C,  14 D, etc. are mixed in the solvent  30   a  to thereby produce the liquid  30 , it is allowable to use, as the solvent  30   a,  for example a solvent obtained by mixing a coloring matter which absorbs the illumination light in pure water (purified water) so that the real part of the permittivity of the solvent  30   a  to the illumination light is made to be negative. Since the coloring matter functions as a substance having a negative permittivity, the refractive index of the liquid  30  to the illumination light is negative when the real part of the relative permeability of the resonating elements  14 ,  14 A to  14 D, etc. to the illumination light is negative. 
     (6) Further, in a case that the liquid  30  is produced by mixing the large number of resonating elements  14 ,  14 A to  14 D, etc. in the solvent  30   a,  the refractive index of the solvent  30   a  may be made to be similar to the refractive index of the protective layers  18 ,  18 A of the resonating elements  14 ,  14 A to  14 D. In a case that the protective layers  18 ,  18 A is formed of silicon dioxide, it is allowable to use, for example, a hydrocarbon-based liquid (high-refractive index liquid) such as decalin or dicyclohexyl, etc. as a solvent having the refractive index similar to that of silicon dioxide. By doing so, the difference between the refractive index of the solvent  30   a  and the refractive index of the protective layers  18 ,  18 A is made to be small, which in turn reduces the light loss (optical loss) due to the reflection of the illumination light at the interface between the solvent  30   a  and the protective layers  18 ,  18 A. 
     (7) Furthermore, in a case that the optical element  32  is produced by mixing the large number of resonating elements  14 ,  14 A and  14 B with the medium  32   a  (filling agent) of  FIG. 6(D)  and by solidifying the mixture of the large number of resonating elements  14 ,  14 A,  14 B and the medium  32   a  in the first embodiment, or in a case that the optical element  32  is produced by mixing the large number of resonating elements  14 C,  14 D with the medium  32   a  (filling agent) and by solidifying the mixture of the large number of resonating elements  14 C,  14 D and the medium  32   a  in the second embodiment, it is allowable to use, as the medium  32   a,  a thermo-curable resin such as silicon resin. In this case, by performing a step of mixing the thermo-curable resin in liquid form and a large number of the resonating elements  14 ,  14 A to  14 D followed by being uniformly agitated and a step of heating the mixture to solidify the thermo-curable resin, it is possible to easily produce an optical element  32  in which the large number of resonating elements  14 ,  14 A to  14 D and the solid medium  32   a  are uniformly mixed. 
     (8) Moreover, in the second embodiment, it is allowable to use, as the medium  32   a  which is to be mixed with a large number of the resonating elements  14 C (or  14 D), a solid obtained by solidifying a liquid in the sol state by the Sol-Gel process, similarly in the first embodiment. 
     (9) Further, in the resonating elements  14 C,  14 D of the second embodiment, the real part of the permittivity is positive and the real part of the relative permittivity is also positive (for example, real number greater than 1). Therefore, even when a large number of the resonating elements  14 C,  14 D are merely collected, the refractive index remains to be positive. 
     In view of this, similarly as in the first embodiment, as a resonating element  14 E of a modification shown in  FIG. 17(A) , it is allowable to form line patterns  81 X elongated in the y-direction and line patterns  81 Y elongated in the x direction so as to sandwich (interpose), in the y-direction and the x-direction, each of a large number of SRRs (split-ring resonators)  16 , which are arranged inside the protective layer  18 A along the x-axis and y-axis at the period “a”, therebetween. The line patterns  81 X,  81 Y are minute thin lines formed of a conductor (metal, etc.) which is same as that forming the SRR  16 . 
     In this modification, it is assumed that the wavelength of the light ILY is within a range in which the real part μRe of the relative permeability of the light ILY of  FIG. 2  takes a negative value (for example, a value slightly smaller than the wavelength λ 3 ) provided that the light ILY is a light in which the vibration direction EVY of the electric field vector is parallel to the x-axis (linearly polarized in the x-direction) and the vibration direction of the magnetic field vector is parallel to the z-axis and that the light ILY comes into the resonating element  14 E in the y-direction. In this case, the line width (cross-sectional area) and the length in the x-direction of the line pattern  81 Y and the arrangement such as the x-direction and y-direction period, etc. of the large number of line patterns  81 Y are set so that the real part of the permittivity of the resonating elements  14 E to the light ILY is negative (the real part of the relative permittivity is also negative). 
     As a result, the resonating element  14 E (or a substance obtained by stacking the resonating elements  14 E in the z-direction) becomes a meta-material in which the refractive index to the light ILY takes a negative value. Note that the example of construction of the plurality of thin metallic lines having a negative real part of the permittivity with respect to the microwave is disclosed in Reference Literature B as described above. The line patterns  81 Y of the modification shown in  FIG. 17(A)  is formed to have the minute shape and arrangement so that the real part of the permittivity to the visible light takes a negative value. 
     Further, it is presumed that the shape and arrangement of the large number of line patterns  81 X elongated in the y-direction inside the resonating element  14 E are same as the shape and arrangement of the line patterns  81 Y. In this case, when a light ILX (presumed as having a same wavelength as that of the light ILY) in which the vibration direction EVX of the electric field vector is parallel to the y-axis (linearly polarized in the y-direction) and the vibration direction of the magnetic field vector is parallel to the z-axis comes into the resonating element  14 E in the x-direction, the real part of the permittivity of the resonating element  14 E to the light ILX also becomes negative, due to the line pattern  81 X. Accordingly, the refractive index of the resonating element  14 E to the light ILX also takes a negative value. Therefore, by mixing the large number of resonating elements  14 E in the liquid or by solidifying the large number of resonating elements  14 E to thereby form an optical element, it is possible to produce an optical liquid or optical element having a negative refractive index to a light having a predetermined wavelength. 
     Also in the resonating element  14 D of  FIG. 11(A) , it is possible to make the real part of the permittivity of the resonating element  14 D to the light having the predetermined wavelength take a negative value by arranging a plurality of the line patterns formed of conductor in the vicinity of the respective SRRs  16 . As a result, the refractive index of the resonating element  14 D to the light having the predetermined wavelength becomes negative. 
     Next, in a case that the resonating element  14 E of  FIG. 17(A)  is produced, it is allowable to use, in Step  145  of  FIG. 13 , a reticle R 3  in which line patterns  58 X,  58 Y formed of a light-shielding film and corresponding to the line patterns  81 X,  81 Y are formed around each of the ring-shaped patterns  55  as shown in  FIG. 17(B) , instead of using the reticle R 4  of  FIG. 14(B) . 
     By doing so, the line patterns  81 X,  81 Y can be patterned together with the large number of SRRs  16  in the metallic thin film  26 A,  26 B, etc. 
     Note that the present teaching is not limited to the above-described embodiments, and may take a various kinds of construction or configuration within a scope without deviating from the gist or essential characteristics of the present teaching. Further, the contents including the specification, the claims, the drawings and the abstract of each of U.S. Provisional Application Ser. No. 61/202,845 filed on Apr. 10, 2009, Japanese Patent Application No. 2009-243438 filed on Oct. 22, 2009 and Japanese Patent Application No. 2009-243439 filed on Oct. 22, 2009 are incorporated herein by reference in their entireties. 
     It is theoretically possible to realize a substance having the relative permeability greatly different from 1 to the lights in the infrared to visible regions and further to realize a substance having the relative permeability with a negative value to the lights in the infrared to visible regions by using the conventional minute split-ring resonators. However, in order to apply the substance, for example, to a visible light, the split-ring resonators are formed to have a radius of about not more than 100 nm, and there arises a problem of how to produce the respective split-ring resonators highly precisely and in a large quantity. Further, when simply producing a large number of split-ring resonators, there is a fear that these split-ring resonators might be brought into contact with one another, and further that the structure of the split-ring resonators might be destroyed or damaged, thereby making it impossible to exhibit a desired relative permeability characteristic with respect to a light as the application objective of the split-ring resonators. 
     Further, when merely producing the minute split-ring resonators by using the lithography technique, the respective resonators are formed while being aligned or arranged in a two-dimensional plane, which in turn causes a problem such that the obtained resonators as they are cannot be used as an optical material having a three-dimensional volume. Furthermore, even if two-dimensional planes, in each of which a large number of split-ring resonators are arranged, are stacked so that the stacked two-dimensional planes have a three-dimensional volume, the respective resonators are aligned in one and same direction (orientation), which in turn causes a problem such that the obtained material is anisotropic as an optical material and thus is not a isotropic optical material. 
     The present invention has been made in view of the above-described situation, and has an object to provide an optical material (a kind of meta-material) which is for example capable of having a relative permeability different from 1 to a light having a wavelength in the infrared region or shorter than the infrared region and which has a stable structure, and to provide a liquid and solid (optical element) using the optical material. 
     Another object of the present invention is to provide a method capable of mass-producing such an optical material with high precision, and a method for producing the liquid and solid using the optical material. 
     According to the optical material of the present invention, the minute resonators are formed to have a size or dimension which is, for example, about not more than the wavelength of visible light, thereby making it possible to realize the relative permeability which is different from 1 to a light in the infrared region or a light having a wavelength shorter than the infrared region. Further, since each of the minute resonators is covered by the protective film, the plurality of minute resonators do not make contact with each other, thereby realizing the stable structure. 
     According to the method for producing the optical material of the fifth or sixth aspect of the present invention, it is possible to mass-produce the optical material of the first or second aspect of the present invention with high precision, by using, for example, the photolithography process.