Patent Publication Number: US-2012026591-A1

Title: Optical element, display device, and anti-reflective optical component, and master

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is National Stage of International Application No. PCT/JP2009/071521 filed on Dec. 17, 2009, which claims priority to Japanese Patent Application No. 2008-335103 filed in the Japanese Patent Office on Dec. 26, 2008, the entire contents of which are being incorporated herein by reference. 
    
    
     BACKGROUND 
     Conventionally, in an optical element that uses a light-transmissive substrate composed of glass, plastic, or the like, surface treatment is performed to suppress the surface reflection of light. A method in which a minute and dense uneven structure (moth-eye structure) is formed on the surface of the optical element is exemplified as the surface treatment (e.g., refer to “Optical and Electro-Optical Engineering Contact” Vol. 43, No. 11 (2005), 630-637). 
     In general, in the case where a periodic uneven shape is formed on the surface of an optical element, diffraction is generated when light passes through the periodic uneven shape, which considerably reduces the amount of the light component of transmitted light that goes straight. However, when the pitch of the uneven shape is shorter than the wavelength of light transmitted, diffraction is not generated. For example, if the uneven shape is rectangular, an anti-reflection effect that is effective for light having a single wavelength corresponding to the pitch, depth, or the like can be achieved. 
     Since the above-described optical element has good anti-reflection characteristics, it is expected that the optical element is applied to solar cells and display devices. The following is proposed as the uneven structure in which anti-reflection characteristics are taken into account. 
     Minute tent-shaped uneven structures (pitch: about 300 nm, depth: about 400 nm) have been proposed as structures manufactured using electron-beam exposure (e.g., refer to NTT Advanced Technology Corporation, “Master Mold for Forming Anti-reflection (Moth-eye) Structures having no wavelength dependence”, [online], [accessed Sep. 1, 2008], Internet &lt;http://keytech.ntt-at.co.jp/nano/prd — 0033.html&gt;). 
     Structures having no wavelength dependence”, [online], [accessed Sep. 1, 2008], Internet &lt;http://keytech.ntt-at.co.jp/nano/prd — 0033.html&gt;). 
     Furthermore, a Super-RENS Technology Team, the Center for Applied Near-Field Optics Research of the Advanced Industrial Science and Technology has proposed nano-hole structures with a diameter of 100 nm and a depth of 500 nm or more (e.g., refer to the National Institute of Advanced Industrial Science and Technology, “Development of Desktop Device Enabling Nanometer-scale Microfabrication”, [online], [accessed Sep. 1, 2008], Internet &lt;http://aist.go.jp/aist_i/press_release/pr2006/pr20060306/pr20060306.html&gt;). Such structures can be formed by a microstructure formation method that uses an optical disc recording apparatus. Specifically, such structures can be formed using a nanomachining device based on a thermal lithography technology in which a visible light laser lithography method using a semiconductor laser (wavelength 406 nm) is combined with a thermally nonlinear material (e.g., refer to the National Institute of Advanced Industrial Science and Technology, “Development of Desktop Device Enabling Nanometer-scale Microfabrication”, [online], [accessed Sep. 1, 2008], Internet &lt;http://aist.go.jp/aist_i/press_release/pr2006/pr20060306/pr20060306.html&gt;). 
     In addition, the inventors of the present disclosure have proposed structures having a hanging bell shape or a truncated elliptic cone-like shape (e.g., refer to International Publication No. 08/023816 Pamphlet). In the structures, anti-reflection characteristics close to those of structures obtained by electron-beam exposure are achieved. Furthermore, the structures can be manufactured by a method in which a process for making a master of optical discs is combined with an etching process. 
     SUMMARY 
     In recent years, it has been demanded that the visibility of various display devices such as a liquid crystal display device is further improved. To satisfy such a demand, it is important to further improve the above-described anti-reflection characteristics of optical elements. 
     Accordingly, an object of the present disclosure is to provide an optical element having good anti-reflection characteristics, a display device, an anti-reflective optical component, and a master. 
     To solve the problems described above, a first disclosure provides an anti-reflective optical element including: 
     a base; and 
     a large number of structures arranged on a surface of the base, 
     wherein the structures are depressions or projections with a conical form, 
     the structures are arranged at a pitch shorter than or equal to a wavelength range of light in a use environment and lower portions of the structures adjacent to one another are connected to one another, and 
     an effective refractive index in a depth direction of the structures gradually increases toward the base and draws an S-shaped curved line. 
     A second disclosure provides an optical element including: 
     a base; and 
     a large number of structures arranged on a surface of the base, 
     wherein the structures are pillar-shaped depressions or projections that extend in a single direction on the surface of the base, 
     the structures are arranged at a pitch shorter than or equal to a wavelength range of light in a use environment and lower portions of the structures adjacent to one another are connected to one another, and 
     an effective refractive index in a depth direction of the structures gradually increases toward the base and draws an S-shaped curved line. 
     A third disclosure provides an anti-reflective optical component including: 
     an optical component; and 
     a large number of structures arranged on a surface of the optical component, 
     wherein the structures are depressions or projections with a conical form, 
     the structures are arranged at a pitch shorter than or equal to a wavelength of light in a use environment and lower portions of the structures adjacent to one another are connected to one another, and 
     an effective refractive index in a depth direction of the structures gradually increases toward the base and draws an S-shaped curved line. 
     A fourth disclosure provides a master including: 
     a large number of structures arranged on a surface of a base, 
     wherein the structures are depressions or projections with a conical form, 
     the structures are arranged at a pitch shorter than or equal to a wavelength of light in a use environment and lower portions of the structures adjacent to one another are connected to one another, and 
     a change in an effective refractive index in a depth direction of an optical element shaped using the structures gradually increases toward a base of the optical element and draws an S-shaped curved line. 
     In the present disclosure, the S-shape includes an inverse S-shape, that is, a Z-shape. Furthermore, in the case where the structures are projections that protrude from the surface of the base, the lower portion of the structures refers to a portion on the base side of the structures. In the case where the structures are depressions that sink from the surface of the base, the lower portion of the structures refers to a portion on the opening side of the structures. 
     In the first, third, and fourth disclosures, primary structures are preferably periodically arranged in a tetragonal lattice pattern or in a quasi-tetragonal lattice pattern. Herein, the tetragonal lattice means a regular tetragonal lattice. The quasi-tetragonal lattice means, unlike a regular tetragonal lattice, a distorted regular tetragonal lattice. Specifically, when the structures are arranged linearly, the quasi-tetragonal lattice is a tetragonal lattice obtained by stretching and distorting a regular tetragonal lattice in the direction of the linear arrangement. When the structures are arranged in an arc-like shape, the quasi-tetragonal lattice is a tetragonal lattice obtained by distorting a regular tetragonal lattice in an arc-like shape or a tetragonal lattice obtained by distorting a regular tetragonal lattice in an arc-like shape and stretching and distorting it in the direction of the arc-shaped arrangement. 
     In the first, third, and fourth disclosures, the structures are preferably periodically arranged in a hexagonal lattice pattern or in a quasi-hexagonal lattice pattern. Herein, the hexagonal lattice means a regular hexagonal lattice. The quasi-hexagonal lattice means, unlike a regular hexagonal lattice, a distorted regular hexagonal lattice. Specifically, when the structures are arranged linearly, the quasi-hexagonal lattice is a hexagonal lattice obtained by stretching and distorting a regular hexagonal lattice in the direction of the linear arrangement. When the structures are arranged in an arc-like shape, the quasi-hexagonal lattice is a hexagonal lattice obtained by distorting a regular hexagonal lattice in an arc-like shape or a hexagonal lattice obtained by distorting a regular hexagonal lattice in an arc-like shape and stretching and distorting it in the direction of the arc-shaped arrangement. 
     In the first to fourth disclosures, the structures with a conical form or the pillar-shaped structures are arranged at a pitch shorter than or equal to a wavelength range of light in a use environment and the lower portions of the structures adjacent to one another are connected to one another. This can smooth the change in an effective refractive index in the depth direction of the structures. Thus, the effective refractive index in the depth direction of the structures can be changed so as to gradually increase toward the base and draw an S-shaped curved line. Furthermore, by changing the effective refractive index in the depth direction of the structures so that the effective refractive index gradually increases toward the base and draws an S-shaped curved line, the boundary for light becomes unclear, which can reduce the reflected light on the surface of the base. 
     As described above, according to the present disclosure, an optical element having good anti-reflection characteristics can be provided. In particular, when the structures are tall, good anti-reflection characteristics can be achieved. 
     Additional features and advantages are described herein, and will be apparent from the following Detailed Description and the figures. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1A  is a schematic plan view showing an example of a configuration of an optical element according to a first example embodiment of the present disclosure.  FIG. 1B  is a partially enlarged plan view of the optical element shown in  FIG. 1A .  FIG. 1C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 1B .  FIG. 1D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 1B . 
         FIG. 2  is a graph showing an example of a refractive index profile of the optical element according to the first example embodiment of the present disclosure. 
         FIG. 3  is a partially enlarged perspective view of the optical element shown in  FIG. 1 . 
         FIG. 4A  is a schematic view showing an exemplary arrangement of structures  3  having a cone-like shape or a truncated cone-like shape.  FIG. 4B  is a schematic view showing an exemplary arrangement of structures  3  having an elliptic cone-like shape or a truncated elliptic cone-like shape. 
         FIG. 5  is a sectional view showing an example of a shape of a structure. 
         FIGS. 6A to 6C  are diagrams for describing the definition of a changing point. 
         FIG. 7A  is a perspective view showing an example of a configuration of a roll master for manufacturing the optical element according to the first example embodiment of the present disclosure.  FIG. 7B  is an enlarged plan view of a surface of the roll master in  FIG. 7A . 
         FIG. 8  is a schematic view showing an example of a configuration of an exposure apparatus used in a moth-eye pattern exposure step. 
         FIGS. 9A to 9C  are process diagrams for describing an example of a method for manufacturing the optical element according to the first example embodiment of the present disclosure. 
         FIGS. 10A to 10C  are process diagrams for describing an example of a method for manufacturing the optical element according to the first example embodiment of the present disclosure. 
         FIG. 11A  is a schematic plan view showing an example of a configuration of an optical element according to a second example embodiment of the present disclosure.  FIG. 11B  is a partially enlarged plan view of the optical element shown in  FIG. 11A .  FIG. 11C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 11B .  FIG. 11D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 11B . 
         FIG. 12A  is a plan view showing an example of a configuration of a disc master for manufacturing the optical element according to the second example embodiment of the present disclosure.  FIG. 12B  is an enlarged plan view of a surface of the disc master in  FIG. 12A . 
         FIG. 13  is a schematic view showing an example of a configuration of an exposure apparatus used in a moth-eye pattern exposure step. 
         FIG. 14A  is a schematic plan view showing an example of a configuration of an optical element according to a third example embodiment of the present disclosure.  FIG. 14B  is a partially enlarged plan view of the optical element shown in  FIG. 14A .  FIG. 14C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 14B .  FIG. 14D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 14B . 
         FIG. 15A  is a schematic plan view showing an example of a configuration of an optical element according to a fourth example embodiment of the present disclosure.  FIG. 15B  is a partially enlarged plan view of the optical element shown in  FIG. 15A .  FIG. 15C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 15B .  FIG. 15D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 15B . 
         FIG. 16  is a partially enlarged perspective view of the optical element shown in  FIG. 15 . 
         FIG. 17A  is a schematic plan view showing an example of a configuration of an optical element according to a fifth example embodiment of the present disclosure.  FIG. 17B  is a partially enlarged plan view of the optical element shown in  FIG. 17A .  FIG. 17C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 17B .  FIG. 17D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 17B . 
         FIG. 18  is a partially enlarged perspective view of the optical element shown in  FIG. 17 . 
         FIG. 19  is a sectional view showing an example of a shape of structures of an optical element according to a sixth example embodiment of the present disclosure. 
         FIG. 20  is a sectional view showing an example of a configuration of an optical element according to a seventh example embodiment of the present disclosure. 
         FIG. 21  is a schematic view showing an example of a configuration of a liquid crystal display device according to an eighth example embodiment of the present disclosure. 
         FIG. 22  is a schematic view showing an example of a configuration of a liquid crystal display device according to a ninth example embodiment of the present disclosure. 
         FIG. 23  is a graph showing the refractive index profiles of Examples 1 to 3 and Comparative Example 1. 
         FIGS. 24A to 24C  are diagrams showing the shapes of structures in Examples 1 to 3. 
         FIG. 25  is a graph showing the reflection characteristics of Examples 1 to 3 and Comparative Example 1. 
         FIG. 26  is a graph showing the reflection characteristics of Example 3 and Comparative Example 1 in the case where the height of structures is changed from 200 nm to 500 nm. 
         FIGS. 27A to 27C  are diagrams showing the shapes of structures in Examples 4 to 6. 
         FIG. 28  is a graph showing the refractive index profiles of Comparative Examples 2 to 4. 
         FIG. 29  is a graph showing the reflection characteristics of Example 7 and Comparative Examples 2 and 3. 
         FIG. 30A  is an AFM image of a formed surface of a master in Example 8.  FIG. 30B  shows a sectional profile of the AFM image shown in  FIG. 30A . 
         FIG. 31  is a graph showing the anti-reflection characteristics of Example 8 and Comparative Examples 5 and 6. 
     
    
    
     DETAILED DESCRIPTION 
     Example Embodiments of the present disclosure will be described with reference to the attached drawings in the following order. 
     1. First Example Embodiment (an example in which structures are two-dimensionally arranged linearly in a hexagonal lattice pattern) 
     2. Second Example Embodiment (an example in which structures are two-dimensionally arranged in an arc-like shape in a hexagonal lattice pattern) 
     3. Third Example Embodiment (an example in which structures are two-dimensionally arranged linearly in a tetragonal lattice pattern) 
     4. Fourth Example Embodiment (an example in which secondary structures are arranged in addition to primary structures) 
     5. Fifth Example Embodiment (an example in which depressed structures are formed on the surface of a base) 
     6. Sixth Example Embodiment (an example in which pillar-shaped structures are one-dimensionally arranged) 
     7. Seventh Example Embodiment (an example in which a thin film is formed instead of structures) 
     8. Eighth Example Embodiment (a first application example to display devices) 
     9. Ninth Example Embodiment (a second application example to display devices) 
     1. First Example Embodiment 
     Configuration of Optical Element 
       FIG. 1A  is a schematic plan view showing an example of a configuration of an optical element according to a first example embodiment of the present disclosure.  FIG. 1B  is a partially enlarged plan view of the optical element shown in  FIG. 1A .  FIG. 1C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 1B .  FIG. 1D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 1B . 
     An optical element  1  is suitably applied to various optical components used for displays, optoelectronics, optical communications (optical fibers), solar cells, luminaires, and the like. Specifically, one of a polarizing element, a lens, an optical waveguide, a window material, and a display element can be exemplified as the optical component, for example. Examples of the polarizing element include a polarizer and a reflection polarizer. 
     The optical element  1  includes a base  2  and structures  3  formed on the surface of the base  2 . The structures are projections with a conical form. The lower portions of the structures  3  adjacent to one another are connected to one another so as to overlap one another. Among the adjacent structures  3 , the most adjacent structures  3  are preferably arranged in a track direction. This is because structures  3  arranged so as to be most adjacent to each other in such a position are easily manufactured by the method described below. The optical element  1  has an anti-reflection function against light that enters the surface of the base on which the structures  3  have been formed. Hereinafter, as shown in  FIG. 1 , two axes orthogonal to each other in one principal surface of the base  2  are referred to as an X axis and a Y axis and an axis perpendicular to the principal surface of the base  2  is referred to as a Z axis. Furthermore, when gaps  2   a  are present between the structures  3 , a minute uneven shape is preferably provided to the gaps  2   a . By providing such a minute uneven shape, the reflectivity of the optical element  1  can be further reduced. 
       FIG. 2  shows an example of a refractive index profile of the optical element according to the first example embodiment of the present disclosure. As shown in  FIG. 2 , the effective refractive index in the depth direction (−Z axis direction in  FIG. 1 ) of the structures  3  gradually increases toward the base  2  and changes so as to draw an S-shaped curved line. That is, the refractive index profile has a single inflection point N. The inflection point corresponds to the shape of a side face of the structures  3 . By changing the effective refractive index in such a manner, the boundary for light becomes unclear. This reduces reflected light, which can improve the anti-reflection characteristics of the optical element  1 . The change in the effective refractive index in the depth direction is preferably a monotonic increase. Herein, the S-shape includes an inverse S-shape, that is, a Z-shape. 
     Furthermore, the change in the effective refractive index in the depth direction is preferably greater on at least one of the top side and base side of the structures  3  than an average of a slope of the effective refractive index, and is more preferably greater on both the top side and base side of the structures  3  than the average. This can provide good anti-reflection characteristics. 
     Hereinafter, the base  2  and the structures  3  constituting the optical element  1  are described in order. 
     Base 
     The base  2  is a transparent base having transparency. The base  2  is mainly composed of, for example, a transparent synthetic resin such as polycarbonate (PC) or polyethylene terephthalate (PET) or glass, but the material of the base  2  is not particularly limited to these materials. 
     The base  2  is, for example, in the shape of a film, sheet, plate, or block, but the shape of the base  2  is not particularly limited to these shapes. The shape of the base  2  is preferably selected and determined in accordance with the shape of the main body of various optical devices that require predetermined anti-reflection functions such as displays, optoelectronic devices, optical communication devices, solar cells, and illuminating devices or in accordance with the shape of a sheet- or film-shaped anti-reflective component attached to these optical devices. 
     Structure 
       FIG. 3  is a partially enlarged perspective view of the optical element shown in  FIG. 1 . A large number of structures  3  that are projections are arranged on the surface of the base  2 . The structures  3  are periodically and two-dimensionally arranged at a short pitch shorter than or equal to the wavelength range of light in a use environment, for example, at a pitch substantially equal to the wavelength of visible light. The wavelength range of light in a use environment is, for example, a wavelength range of ultraviolet light, a wavelength range of visible light, or a wavelength range of infrared light. Herein, the wavelength range of ultraviolet light is a wavelength range of 10 nm to 360 nm. The wavelength range of visible light is a wavelength range of 360 nm to 830 nm. The wavelength range of infrared light is a wavelength range of 830 nm to 1 mm 
     The structures  3  of the optical element  1  has a configuration including multiple rows of tracks T 1 , T 2 , T 3 , . . . (hereinafter may be collectively referred to as “track T”) provided on the surface of the base  2 . Herein, the track is a region where the structures  3  are linearly arranged in rows. 
     In the two adjacent tracks T, the structures  3  arranged on one track are shifted by half a pitch from the structures  3  arranged on the other track. Specifically, in the two adjacent tracks T, at the intermediate positions (at the positions shifted by half a pitch) between the structures  3  arranged on one track (e.g., T 1 ), the structures  3  arranged on the other track (e.g., T 2 ) are disposed. Consequently, as shown in  FIG. 1B , in the three adjacent rows of tracks (T 1  to T 3 ), the structures  3  are arranged so as to form a hexagonal lattice pattern or a quasi-hexagonal lattice pattern with the centers of the structures  3  being positioned at points a 1  to a 7 . In the first example embodiment, the hexagonal lattice pattern means a regular hexagonal lattice pattern. In addition, the quasi-hexagonal lattice pattern means, unlike a regular hexagonal lattice pattern, a hexagonal lattice pattern that is stretched and distorted in the track extending direction (X axis direction). 
     When the structures  3  are arranged so as to form a quasi-hexagonal lattice pattern, as shown in  FIG. 1B , the arrangement pitch P 1  (distance between a 1  and a 2 ) of the structures  3  on the same track (e.g., T 1 ) is preferably longer than the arrangement pitch of the structures  3  between the two adjacent tracks (e.g., T 1  and T 2 ), that is, the arrangement pitch P 2  (e.g., distance between a 1  and a 7  or a 2  and a 7 ) of the structures  3  in the ±θ direction with respect to the track extending direction. By arranging the structures  3  in such a manner, the packing density of the structures  3  can be further improved. 
     The lower portions of the structures  3  are connected to, for example, some or all of lower portions of the adjacent structures  3 . By connecting the lower portions of structures to one another in such a manner, the effective refractive index in the depth direction of the structures  3  can be smoothly changed. As a result, an S-shaped refractive index profile can be provided. Furthermore, by connecting the lower portions of structures to one another, the packing fraction of the structures can be increased. Herein, in  FIG. 1B , the positions of connecting portions formed in the case where all the adjacent structures  3  are connected to one another are denoted by “solid-black circles”. Specifically, the connecting portions are formed between all the adjacent structures  3 , between the adjacent structures  3  on the same track (e.g., between a 1  and a 2 ), or between the structures  3  on the adjacent tracks (e.g., between a 1  and a 7  and between a 2  and a 7 ). To achieve a smooth refractive index profile and good anti-reflection characteristics, the connecting portions are preferably formed between all the adjacent structures  3 . To easily form the connecting portions by the manufacturing method described below, the connecting portions are preferably formed between the adjacent structures  3  on the same track. In the case where the structures  3  are periodically arranged in a hexagonal lattice pattern or in a quasi-hexagonal lattice pattern, for example, the structures  3  are connected to one another in directions of 6-fold symmetry. 
       FIG. 4A  shows an exemplary arrangement of the structures  3  having a cone-like shape or a truncated cone-like shape.  FIG. 4B  shows an exemplary arrangement of the structures  3  having an elliptic cone-like shape or a truncated elliptic cone-like shape. As shown in  FIGS. 4A and 4B , the structures  3  are preferably connected to one another so that the lower portions thereof overlap one another. By connecting the structures  3  to one another in such a manner, an S-shaped refractive index profile can be obtained and the packing fraction of the structures  3  can be increased. The structures are preferably connected to one another at portions smaller than or equal to ¼ the maximum value of the wavelength range of light in a use environment on the basis of an optical path length adopted in consideration of a refractive index. Thus, good anti-reflection characteristics can be achieved. 
     Preferably, the height of the structures  3  is suitably set in accordance with the wavelength region of light to be transmitted. Specifically, the height of the structures  3  is preferably 5/14 or more and 10/7 or less the maximum value of the wavelength range of light in a use environment, more preferably 2/5 or more and 10/7 or less the maximum value, and further preferably 3/7 or more and 10/7 or less the maximum value. When the height is 5/14 or more the maximum value, the reflectivity can be suppressed to 0.3% or less in substantially the entire visible range of 400 nm to 700 nm. When the height is 2/5 or more the maximum value, the reflectivity can be suppressed to 0.1% or less in the visible range of 400 nm to 700 nm. When the height is 10/7 or less the maximum value, the structures  3  are easily formed by the manufacturing method described below. When visible light is transmitted, the height of the structures  3  is preferably 150 nm to 500 nm. The aspect ratio (height H/arrangement pitch P) of the structures  3  is preferably set in the range of 0.81 to 1.46. If the aspect ratio is less than 0.81, the reflection characteristics and transmission characteristics tend to degrade. If the aspect ratio is more than 1.46, the releasing property degrades during the manufacturing of the optical element  1  and it tends to be difficult to remove a replicated replica properly. 
     Note that, in the present disclosure, the aspect ratio is defined by formula (1) below: 
       Aspect ratio= H/P   (1)
 
     where H is the height of the structures  3 , and P is the average arrangement pitch (average period). 
     Herein, the average arrangement pitch P is defined by formula (2) below: 
       Average arrangement pitch  P =( P 1 +P 2 +P 2)/3  (2)
 
     where P 1  is the arrangement pitch in the track extending direction (period in the track extending direction), and P 2  is the arrangement pitch in the ±θ direction with respect to the track extending direction (where θ=60°−δ, where δ is preferably 0°&lt;δ≦11° and more preferably 3°≦δ≦6°) (period in the θ direction). 
     Furthermore, the height H of the structures  3  is the height H 2  in the column direction of the structures  3  (refer to  FIG. 3 ). Herein, the column direction means a direction (Y axis direction) orthogonal to the track extending direction (X axis direction) in the surface of the base. The height H 1  in the track extending direction of the structures  3  is preferably smaller than the height H 2  in the column direction. This is because, when the optical element  1  is manufactured by the manufacturing method described below, the height H 1  in the track extending direction of the structures  3  is easily decreased compared with the height H 2  in the column direction. 
     In  FIG. 3 , each of the structures  3  has the same shape. However, the shape of the structures  3  is not limited thereto. The structures  3  having two or more different shapes may be formed on the surface of the base. Furthermore, the structures  3  may be formed integrally with the base  2 . 
     In addition, the structures  3  do not necessarily have the same aspect ratio. The structures  3  may be configured so as to have a certain height distribution (e.g., in the range of about 0.81 to 1.46 in terms of an aspect ratio). By disposing the structures  3  having a height distribution, the wavelength dependence of reflection characteristics can be reduced. Consequently, an optical element  1  having good anti-reflection characteristics can be realized. 
     Herein, the height distribution means that the structures  3  having two or more heights (depths) are disposed on the surface of the base  2 . That is, it means that structures  3  having a reference height and structures  3  having a height different from the reference height are disposed on the surface of the base  2 . The structures  3  having a height different from the reference height are disposed, for example, on the surface of the base  2  periodically or aperiodically (at random). For example, the track extending direction, the column direction, or the like may be exemplified as the direction of the periodicity. 
     Preferably, the structures  3  are mainly composed of, for example, an ionizing radiation curable resin that is cured through ultraviolet rays or electron beams or a thermosetting resin that is cured through heat. Most preferably, the structures  3  are mainly composed of an ultraviolet curable resin that is cured through ultraviolet rays. 
       FIG. 5  is an enlarged sectional view showing an example of a shape of structures. Preferably, the side face of the structures  3  gradually widens toward the base  2  and changes so as to draw a shape of the square root of the S-shaped curved line shown in  FIG. 2 . Such a side face shape can provide good anti-reflection characteristics and improve ease of transference of the structures  3 . 
     The top  3   t  of the structures  3  has, for example, a flat shape or a tapered protruding shape. When the top  3   t  of the structures  3  has a flat shape, the area ratio (St/S) of the area St of the flat surface on the top of the structures relative to the area S of a unit lattice is preferably decreased along with an increase in the height of the structures  3 . This can improve the anti-reflection characteristics of the optical element  1 . Herein, the unit lattice is, for example, a hexagonal lattice or a quasi-hexagonal lattice. The area ratio of the bottom of the structures (the area ratio (Sb/S) of the area Sb of the bottom of the structures relative to the area S of a unit lattice is preferably close to the area ratio of the top  3   t . Furthermore, a low refractive index layer having a lower refractive index than the structures  3  may be formed on the top  3   t  of the structures  3 . By forming such a low refractive index layer, the reflectivity can be reduced. 
     The side face of the structures  3  excluding the top  3   t  and the lower portion  3   b  preferably has a pair of first changing point Pa and second changing point Pb formed in that order in the direction from the top  3   t  to the lower portion  3   b . As a result, the effective refractive index in the depth direction (−Z axis direction in  FIG. 1 ) of the structures  3  can have a single inflection point. 
     Herein, the first changing point and the second changing point are defined as follows. 
     As shown in  FIGS. 6A and 6B , in the case where the side face from the top  3   t  to the lower portion  3   b  of the structures  3  is formed by joining a plurality of smooth curved surfaces in a discontinuous manner in the direction from the top  3   t  to the lower portion  3   b  of the structures  3 , the joining points are the changing points. The changing points coincide with inflection points. Although differentiation cannot be performed accurately at the joining points, such an inflection point taken as a limit is also referred to as an inflection point herein. When the structures  3  have the above-described curved surface, the slope in the direction from the top  3   t  to the lower portion  3   b  of the structures  3  preferably becomes gentler at the first changing point Pa and then becomes steeper at the second changing point Pb. 
     As shown in  FIG. 6C , in the case where the side face from the top  3   t  to the lower portion  3   b  of the structures  3  is formed by joining a plurality of smooth curved surfaces in a continuous manner in the direction from the top  3   t  to the lower portion  3   b  of the structures  3 , the changing point is defined as follows. As shown in  FIG. 7C , the point, on the curved line, closest from an intersection point at which tangent lines of two inflection points that are present on the side face of structures intersect with each other is referred to as a changing point. 
     The structures  3  preferably have a single step St on the side face between the top  3   t  and the lower portion  3   b . When the structures  3  have a single step St, the above-described refractive index profile can be achieved. In other words, the effective refractive index in the depth direction of the structures  3  can be gradually increased toward the base  2  and at the same time can be changed so as to draw an S-shaped curved line. Examples of the step include a slope step and a parallel step, and a slope step is preferred. This is because, when the step St is a slope step, ease of transference can be improved compared with the case where the step St is a parallel step. 
     The slope step is a step that is not parallel to the surface of the base, but is inclined so that the side face widens in the direction from the top to the lower portion of the structures  3 . The parallel step is a step that is parallel to the surface of the base. Herein, the step St is a section defined by the above-described first changing point Pa and second changing point Pb. Note that the step St does not include the flat surface of the top  3   t  or the curved surface or flat surface between the structures. 
     In view of ease of formation, the structures  3  preferably have a conical form that is axially symmetric except for the lower portion connected to the adjacent structures  3  or a conical form obtained by stretching or shrinking a conical form in the track direction. Examples of the conical form include a cone-like shape, a truncated cone-like shape, an elliptic cone-like shape, and a truncated elliptic cone-like shape. Herein, as described above, the conical form has a concept including an elliptic cone-like shape and a truncated elliptic cone-like shape, in addition to a cone-like shape and a truncated cone-like shape. Moreover, the truncated cone-like shape is a shape obtained by removing the top of a cone-like shape from the cone-like shape. The truncated elliptic cone-like shape is a shape obtained by removing the top of an elliptic cone-like shape from the elliptic cone-like shape. Furthermore, the entire shape of the structures  3  is not limited to these shapes, and needs only to be a shape in which the effective refractive index in the depth direction of the structures  3  gradually increases toward the base  2  and changes so as to draw an S-shape. Moreover, as described above, the conical form includes not only a complete conical form, but also a conical form having a step St on the side face. 
     The structures  3  having an elliptic cone-like shape are structures having a conical form in which the bottom is in the shape of an ellipse, an oblong, or an oval with a major axis and a minor axis, and the top has a tapered protruding shape. The structures  3  having a truncated elliptic cone-like shape are structures having a conical form in which the bottom is in the shape of an ellipse, an oblong, or an oval with a major axis and a minor axis, and the top has a flat surface. When the structures  3  have an elliptic cone-like shape or a truncated elliptic cone-like shape, the structures  3  are preferably disposed on the surface of the base such that the major axis of the bottom of the structures  3  is directed in the track extending direction (X axis direction). 
     The cross section of the structures  3  changes in the depth direction of the structures  3  so as to correspond to the above-described refractive index profile. Preferably, the cross section of the structures  3  monotonically increases along with an increase in the depth of the structures  3 . Herein, the cross section of the structures  3  means an area of a section that is parallel to the surface of the base where the structures  3  have been arranged. The cross section of the structures preferably changes in the depth direction so that the cross sectional ratio of the structure  3  at different depths corresponds to the effective refractive index profile at those depths. 
     Configuration of Roll Master 
       FIG. 7  shows an example of a configuration of a roll master for manufacturing the optical element having the above-described configuration. As shown in  FIG. 7 , a roll master  11  includes a large number of depressed structures  13  arranged on the surface of a cylinder- or column-shaped master  12 . The structures  13  are periodically and two-dimensionally arranged at a pitch shorter than or equal to a wavelength of light in an environment where the optical element  1  is used, for example, at a pitch substantially equal to a wavelength of visible light. The structures  13  are arranged on the surface of the cylinder- or column-shaped master  12 , for example, in a concentric or spiral manner. For example, the structures  13  are connected to the lower portions of some or all of the adjacent structures  3 . Herein, in  FIG. 7B , the positions of connecting portions formed in the case where all the adjacent structures  3  are connected to one another are denoted by “solid-black circles”. The structures  13  are used for forming the protruding structures  3  on the surface of the above-described base  2 . The master  12  can be composed of, for example, glass, but the material is not particularly limited thereto. 
     Method for Manufacturing Optical Element 
     Next, an example of a method for manufacturing the optical element having the above-described configuration will be described with reference to  FIGS. 8 to 10 . 
     A method for manufacturing the optical element according to the first example embodiment is a method in which a process for making a master of optical discs is combined with an etching process. The manufacturing method includes a resist layer formation step of forming a resist layer on a master, an exposure step of forming a latent image of a moth-eye pattern on the resist layer, a development step of developing the resist layer on which the latent image has been formed, an etching step of making a roll master, and a replication step of making a replica substrate. 
     Configuration of Exposure Apparatus 
     First, a configuration of an exposure apparatus used in the moth-eye pattern exposure step will be described with reference to  FIG. 8 . The exposure apparatus is configured on the basis of an optical disc recording apparatus. 
     A laser light source  21  is a light source for exposing a resist formed on the surface of the master  12  serving as a recording medium, and oscillates, for example, a laser beam  15  for recording with a wavelength λ of 266 nm. The laser beam  15  emitted from the laser light source  21  travels in a straight line as a collimated beam and enters an electro optical modulator (EOM)  22 . The laser beam  15  transmitted through the electro optical modulator  22  is reflected by a mirror  23  and guided to an optical modulation system  25 . 
     The mirror  23  includes a polarization beam splitter and has a function that reflects one polarized component and transmits the other polarized component. The polarized component transmitted through the mirror  23  is received by a photodiode  24 , and the electro optical modulator  22  is controlled in accordance with the signal of the received polarized component to perform phase modulation of the laser beam  15 . 
     In the optical modulation system  25 , the laser beam  15  is focused by a collective lens  26  on an acoust-optic modulator (AOM)  27  composed of glass (SiO 2 ) or the like. After the laser beam  15  is intensity-modulated by the acoust-optic modulator  27  and diverged, the laser beam  15  is collimated by a collimating lens  28 . The laser beam  15  emitted from the optical modulation system  25  is reflected by a mirror  31  and guided onto a moving optical table  32  in a horizontal and parallel manner. 
     The moving optical table  32  includes a beam expander  33  and an objective lens  34 . The laser beam  15  guided to the moving optical table  32  is shaped into a desired beam form by the beam expander  33 , and then applied to the resist layer on the master  12  through the objective lens  34 . The master  12  is placed on a turntable  36  connected to a spindle motor  35 . Subsequently, the exposure step of the resist layer is performed by intermittently irradiating the resist layer with the laser beam  15  while the master  12  is rotated and the laser beam  15  is moved in the height direction of the master  12 . The resulting latent image has, for example, a substantially elliptical shape having a major axis in the circumferential direction. The laser beam  15  is moved by moving the moving optical table  32  in the direction indicated by an arrow R. 
     The exposure apparatus includes a control mechanism  37  for forming, on the resist layer, a latent image corresponding to the two-dimensional pattern of the hexagonal lattice or quasi-hexagonal lattice shown in  FIG. 1B . The control mechanism  37  includes a formatter  29  and a driver  30 . The formatter  29  includes a polarity inversion unit, and the polarity inversion unit controls the timing when the resist layer is irradiated with the laser beam  15 . The driver  30  controls the acoust-optical modulator  27  in response to the output from the polarity inversion unit. 
     In the exposure apparatus, a polarity inversion formatter signal is synchronized to a rotation controller of the recording apparatus to generate a signal for each track so that two-dimensional patterns are spatially linked to one another, and intensity modulation is performed by the acoust-optical modulator  27 . By performing patterning at constant angular velocity (CAV) and at an appropriate number of revolutions, an appropriate modulation frequency, and an appropriate feed pitch, a hexagonal or quasi-hexagonal lattice pattern can be recorded on the resist layer. 
     Hereinafter, the individual steps in the method for manufacturing the optical element according to the first example embodiment of the present disclosure will be described one by one. 
     Resist Layer Formation Step 
     First, as shown in  FIG. 9A , a cylinder- or column-shaped master  12  is prepared. The master  12  is, for example, a glass master. Next, as shown in  FIG. 9B , a resist layer  14  is formed on a surface of the master  12 . The resist layer  14  can be composed of, for example, either an organic resist or an inorganic resist. Examples of the organic resist include novolac resists and chemically-amplified resists. Furthermore, examples of the inorganic resist include metal oxides containing one or more transition metals such as tungsten and molybdenum. 
     Exposure Step 
     Next, as shown in  FIG. 9C , using the exposure apparatus described above, the resist layer  14  is irradiated with the laser beam (exposure beam)  15  while the master  12  is rotated. In this step, the entire surface of the resist layer  14  is exposed by intermittently irradiating the resist layer  14  with the laser beam  15  while the laser beam  15  is moved in the height direction of the master  12 . As a result, a latent image  16  following the trajectory of the laser beam  15  is formed over the entire surface of the resist layer  14 , for example, at a pitch substantially equal to a wavelength of visible light. 
     Development Step 
     Next, a developer is dropwise applied onto the resist layer  14  while the master  12  is rotated, whereby the resist layer  14  is subjected to development treatment as shown in  FIG. 9A . In the case where the resist layer  14  is formed using a positive resist, an exposed portion exposed to the laser beam  15  has an increased rate of dissolution in the developer compared with a non-exposed portion. As a result, as shown in  FIG. 10A , a pattern corresponding to the latent image (exposed portion)  16  is formed on the resist layer  14 . 
     Etching Step 
     Next, for example, the surface of the master  12  is etched using, as a mask, the pattern (resist pattern) of the resist layer  14  formed on the master  12 . Specifically, an etching treatment and an ashing treatment are alternately performed. Consequently, as shown in  FIG. 10B , there can be obtained depressions having an elliptic cone-like shape or a truncated elliptic cone-like shape with a major axis directed in the track extending direction, that is, structures  13 . Furthermore, a glass master having a depth of three times or more the thickness of the resist layer  14  (selectivity: 3 or more) can be produced to achieve a high aspect ratio of structures  3 . Moreover, by appropriately adjusting the treatment time of the etching treatment and the ashing treatment, a step can be formed on the side face of the structures  13 . The etching is preferably performed by dry etching. Examples of the dry etching that can be used include plasma etching and reactive ion etching (RIE). In addition, for example, isotropic etching or anisotropic etching can be used as the etching method. 
     Thus, a roll master  11  having a hexagonal lattice pattern or a quasi-hexagonal lattice pattern can be obtained. 
     Replication Step 
     Next, the roll master  11  and the base  2  such as an acrylic sheet to which an ultraviolet curable resin has been applied are brought into close contact with each other. After the ultraviolet curable resin is cured by irradiation with ultraviolet rays, the base  2  is detached from the roll master  11 . Consequently, as shown in  FIG. 10C , an intended optical element  1  is manufactured. 
     According to the first example embodiment, the structures  3  have a conical form, and the effective refractive index in the depth direction of the structures  3  gradually increases toward the base  2  and changes so as to draw an S-shaped curved line. Consequently, the boundary for light becomes unclear due to the shape effect of the structures  3 , which can reduce reflected light. Thus, good anti-reflection characteristics can be achieved. In particular, when the structures  3  are tall, good anti-reflection characteristics can be achieved. Specifically, when the height of the structures  3  is preferably 5/14 or more and 10/7 or less, more preferably 2/5 or more and 10/7 or less, and further preferably 3/7 or more and 10/7 or less the maximum value of the wavelength range of light in a use environment, particularly good anti-reflection characteristics can be achieved. Furthermore, since the lower portions of the adjacent structures  3  are connected to one another so as to overlap one another, the packing fraction of the structures  3  can be increased and the structures  3  can be easily formed. 
     Preferably, the effective refractive index profile in the depth direction of the structures  3  is changed so as to draw an S-shape, and the structures are arranged in a (quasi-)hexagonal lattice pattern or a (quasi-)tetragonal lattice pattern. Furthermore, each of the structures  3  preferably has an axially symmetric structure or a structure obtained by stretching or shrinking the axially symmetric structure in the track direction. Moreover, the adjacent structures  3  are preferably connected to one another near the base. Such a configuration can provide high-performance anti-reflection structures that can be manufactured more easily. 
     When the optical element  1  is manufactured by a method in which a process for making a master of optical discs is combined with an etching process, the time (exposure time) required in the process for making a master can be considerably shortened compared with the case where the optical element  1  is manufactured by electron-beam exposure. Thus, the productivity of the optical element  1  can be significantly improved. 
     When the shape of the top of the structures  3  is a flat shape but not a tapered shape, the durability of the optical element  1  can be improved. The releasing property of the optical element  1  from the roll master  11  can also be improved. When a step of the structures  3  is a slope step, ease of transference can be improved compared with the case where a parallel step is used. 
     Second Example Embodiment 
     Configuration of Optical Element 
       FIG. 11A  is a schematic plan view showing an example of a configuration of an optical element according to a second example embodiment of the present disclosure.  FIG. 11B  is a partially enlarged plan view of the optical element shown in  FIG. 11A .  FIG. 11C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 11B .  FIG. 11D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 11B . 
     In an optical element  1  according to the second example embodiment, tracks T have an arc-like shape and structures  3  are arranged in an arc-like manner. As shown in FIG.  11 B, in the three adjacent rows of tracks (T 1  to T 3 ), the structures  3  are arranged so as to form a quasi-hexagonal lattice pattern with the centers of the structures  3  being positioned at points a 1  to a 7 . Herein, the quasi-hexagonal lattice pattern means, unlike a regular hexagonal lattice pattern, a hexagonal lattice pattern distorted along an arc-like shape of the tracks T. Alternatively, the quasi-hexagonal lattice pattern means, unlike a regular hexagonal lattice pattern, a hexagonal lattice pattern that is distorted along an arc-like shape of the tracks T and stretched and distorted in the track extending direction (X axis direction). 
     Except for the configuration of the optical element  1  described above, the configuration is the same as that in the first example embodiment, and the description thereof is omitted. 
     Configuration of Disc Master 
       FIG. 12  shows an example of a configuration of a disc master for manufacturing the optical element having the above-described configuration. As shown in  FIG. 12 , a disc master  41  has a configuration in which a large number of depressed structures  43  are arranged on a surface of a disc-shaped master  42 . The structures  13  are periodically and two-dimensionally arranged at a pitch shorter than or equal to a wavelength range of light in an environment where the optical element  1  is used, for example, at a pitch substantially equal to a wavelength of visible light. For example, the structures  43  are disposed on concentric tracks or on a spiral track. 
     Except for the configuration of the disc master  41  described above, the configuration is the same as that of the roll master  11  in the first example embodiment, and the description thereof is omitted. 
     Method for Manufacturing Optical Element 
     First, an exposure apparatus used for making the disc master  41  having the above-described configuration will be described with reference to  FIG. 13 . 
     A moving optical table  32  includes a beam expander  33 , a mirror  38 , and an objective lens  34 . The laser beam  15  guided to the moving optical table  32  is shaped into a desired beam form by the beam expander  33 , and then applied to the resist layer on the disc-shaped master  42  through the mirror  38  and the objective lens  34 . The master  42  is placed on a turntable (not shown) connected to a spindle motor  35 . Subsequently, the exposure step of the resist layer is performed by intermittently irradiating the resist layer on the master  42  with the laser beam while the master  42  is rotated and the laser beam  15  is moved in the radial direction of rotation of the master  42 . The resulting latent image has a substantially elliptical shape having a major axis in the circumferential direction. The laser beam  15  is moved by moving the moving optical table  32  in the direction indicated by an arrow R. 
     The exposure apparatus shown in  FIG. 13  includes a control mechanism  37  for forming, on the resist layer, a latent image of the two-dimensional hexagonal lattice or quasi-hexagonal lattice pattern shown in  FIG. 11 . The control mechanism  37  includes a formatter  29  and a driver  30 . The formatter  29  includes a polarity inversion unit, and the polarity inversion unit controls the timing when the resist layer is irradiated with the laser beam  15 . The driver  30  controls an acoust-optical modulator  27  in response to the output from the polarity inversion unit. 
     The control mechanism  37  synchronizes the intensity modulation of the laser beam  15  performed by the AOM  27 , the driving rotational speed of the spindle motor  35 , and the moving speed of the moving optical table  32  for each track so that the two-dimensional patterns of the latent image are spatially linked to one another. The rotation of the master  42  is controlled at a constant angular velocity (CAV). In addition, patterning is performed using an appropriate number of revolutions of the master  42  provided by the spindle motor  35 , appropriate frequency modulation of laser intensity provided by the AOM  27 , and an appropriate feed pitch of the laser beam  15  provided by the moving optical table  32 . Thus, a latent image having a hexagonal lattice pattern or a quasi-hexagonal lattice pattern is formed on the resist layer. 
     Furthermore, the control signal of the polarity inversion unit is gradually changed such that the spatial frequency (pattern density of the latent image, P 1 : 330, P 2 : 300 nm; P 1 : 315 nm, P 2 : 275 nm; or P 1 : 300 nm, P 2 : 265 nm) becomes uniform. More specifically, exposure is performed while an irradiation period of the resist layer with the laser beam  15  is changed for each track, and frequency modulation of the laser beam  15  is performed by the control mechanism  37  such that P 1  becomes about 330 nm (315 nm, or 300 nm) on each track T. That is, the modulation is controlled such that the irradiation period of the laser beam becomes shorter as the track position becomes distant from the center of the disc-shaped master  42 . Thus, a nano-pattern in which the spatial frequency is uniform over the entire substrate can be formed. 
     Hereinafter, an example of a method for manufacturing the optical element according to the second example embodiment of the present disclosure will be described. 
     First, a disc master  41  is made by the same method as in the first example embodiment, except that a resist layer formed on a disc-shaped master is exposed using the exposure apparatus having the above-described configuration. Next, the disc master  41  and the base  2  such as an acrylic sheet to which an ultraviolet curable resin has been applied are brought into close contact with each other. After the ultraviolet curable resin is cured by irradiation with ultraviolet rays, the base  2  is detached from the disc master  41 . Thus, a disc-shaped optical element is obtained. Subsequently, the disc-shaped optical element is cut into optical elements  1  having a desired shape such as a rectangle. Accordingly, an intended optical element  1  is manufactured. 
     According to the second example embodiment, as in the case where the structures  3  are linearly arranged, an optical element  1  having good anti-reflection characteristics and high productivity can be obtained. 
     Third Example Embodiment 
       FIG. 14A  is a schematic plan view showing an example of a configuration of an optical element according to a third example embodiment of the present disclosure.  FIG. 14B  is a partially enlarged plan view of the optical element shown in  FIG. 14A .  FIG. 14C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 14B .  FIG. 14D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 14B . 
     An optical element  1  according to the third example embodiment differs from that of the first example embodiment in that, in the three adjacent rows of tracks, structures  3  form a tetragonal lattice pattern or a quasi-tetragonal lattice pattern. Herein, the quasi-tetragonal lattice pattern means, unlike a regular tetragonal lattice pattern, a tetragonal lattice pattern that is stretched and distorted in the track extending direction (X axis direction). When the structures  3  are periodically arranged in a tetragonal lattice pattern or in a quasi-tetragonal lattice pattern, for example, the structures  3  lie adjacent to one another in directions of 4-fold symmetry. Moreover, by further stretching and distorting the tetragonal lattice, a structure  3  can also be laid adjacent to structures  3  on the same track, and an arrangement with high packing density is achieved in which one structure lies adjacent to structures not only in directions of 4-fold symmetry but also at two positions on the same track. 
     In the two adjacent tracks T, at the intermediate positions (at the positions shifted by half a pitch) between the structures  3  arranged on one track (e.g., T 1 ), the structures  3  on the other track (e.g., T 2 ) are disposed. Consequently, as shown in  FIG. 14B , in the three adjacent rows of tracks (T 1  to T 3 ), the structures  3  are arranged so as to form a tetragonal lattice pattern or a quasi-tetragonal lattice pattern with the centers of the structures  3  being positioned at points a 1  to a 4 . 
     Preferably, the height of the structures  3  is appropriately set in accordance with the wavelength range of light to be transmitted. For example, when visible light is transmitted, the height of the structures  3  is preferably 150 nm to 500 nm in this manufacturing method. The pitch P 2  in the 0 direction with respect to the track T is, for example, about 275 nm to 297 nm. In addition, the structures  3  may be configured so as to have a certain height distribution. 
     The arrangement pitch P 1  of the structures  3  on the same track is preferably longer than the arrangement pitch P 2  of the structures  3  between the two adjacent tracks. Furthermore, the ratio P 1 /P 2  preferably satisfies the relationship 1.4&lt;P 1 /P 2 ≦1.5, where P 1  is the arrangement pitch of the structures  3  on the same track and P 2  is the arrangement pitch of the structures  3  between the two adjacent tracks. By selecting such a numerical range, the packing fraction of the structures having an elliptic cone-like shape or a truncated elliptic cone-like shape can be increased. Therefore, anti-reflection characteristics can be improved. 
     In the third example embodiment, an optical element  1  having good anti-reflection characteristics and high productivity can be obtained as in the first example embodiment. 
     Fourth Example Embodiment 
       FIG. 15A  is a schematic plan view showing an example of a configuration of an optical element according to a fourth example embodiment of the present disclosure.  FIG. 15B  is a partially enlarged plan view of the optical element shown in  FIG. 15A .  FIG. 15C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 15B .  FIG. 15D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 15B .  FIG. 16  is a partially enlarged perspective view of the optical element shown in  FIG. 15 . 
     An optical element  1  according to the fourth example embodiment differs from that of the first example embodiment in that the optical element  1  further includes secondary structures  4  formed on the surface of the base  2 , and the structures are connected to one another with the secondary structures  4  therebetween. The same parts as those in the first example embodiment are designated by the same reference numerals, and the descriptions thereof are omitted. Note that, in the fourth example embodiment, the structures  3  are referred to as primary structures  3  to avoid the confusion between the structures  3  and the secondary structures  4 . 
     The secondary structures  4  are depressions or projections that are smaller than the primary structures. For example, the secondary structures  4  are minute protruding portions having a height smaller than that of the primary structures  3 . Furthermore, when the height of the secondary structures  4  is smaller than or equal to about ¼ the maximum value of the wavelength range of light in a use environment on the basis of an optical path length adopted in consideration of a refractive index, the secondary structures  4  contribute to an anti-reflection function. For example, the height of the secondary structures  4  is about 10 nm to 150 nm. The secondary structures  4  can be composed of, for example, the same material as that of the base  2  and the primary structures  3 , but are preferably composed of a material having a lower refractive index than the materials constituting the base  2  and the primary structures  3 . This is because the reflectivity can be further reduced. Furthermore, in the above description, the case where both the primary structures  3  and the secondary structures  4  are projections has been mainly described, but the primary structures  3  and the secondary structures  4  may be depressions. Moreover, the projection-depression relationship may be reversed between the primary structures  3  and the secondary structures  4 . Specifically, when the primary structures  3  are projections, the secondary structures  4  may be depressions. When the primary structures  3  are depressions, the secondary structures  4  may be projections. 
     The secondary structures  4  are disposed, for example, in some or all of portions between the primary structures. Specifically, preferably, the secondary structures  4  are provided in the most adjacent portions between the primary structures  3 , and the primary structures  3  are connected to one another by the secondary structures  4  provided in the most adjacent portions. In such a manner, the packing fraction of the primary structures  3  can be increased. Furthermore, the secondary structures  4  may be disposed in portions other than the portions between the primary structures. The spatial frequency component of the secondary structures  4  is preferably higher than the frequency component converted from the period of the primary structures  3 . Specifically, the spatial frequency component of the secondary structures  4  is preferably two times or higher and more preferably four times or higher the frequency component converted from the period of the primary structures  3 . Preferably, the spatial frequency component of the secondary structures  4  is not an integral multiple of the frequency component of the primary structures  3 . 
     From the standpoint of ease of formation of the secondary structures  4 , as shown in  FIG. 15B , the secondary structures  4  are preferably arranged at some or all of the positions indicated by “solid-black circles” where the primary structures  3  having an elliptic cone-like shape, a truncated elliptic cone-like shape, or the like lie adjacent to one another. In such an arrangement, the secondary structures  4  are formed between all the adjacent structures  3 , between the adjacent structures  3  on the same track (e.g., between a 1  and a 2 ), or between the structures  3  on the adjacent tracks (e.g., between a 1  and a 7  and between a 2  and a 7 ). When the primary structures  3  are arranged periodically in a hexagonal lattice pattern or in a quasi-hexagonal lattice pattern, for example, the primary structures  3  lie adjacent to one another in directions of 6-fold symmetry. In this case, preferably, the secondary structures  4  are provided in the adjacent portions, and the primary structures  3  are connected to one another by the secondary structures  4 . Furthermore, when gaps  2   a  are present between the primary structures  3  as shown in  FIG. 15B , from the standpoint of increasing the packing fraction, the secondary structures  4  are preferably formed in the gaps  2   a  between the primary structures  3 . The secondary structures  4  may be formed both in the adjacent portions of the primary structures  3  and in the gaps  2   a . Furthermore, the positions at which the secondary structures  4  are formed are not particularly limited to the examples described above. The secondary structures  4  may be formed on the entire surfaces of the primary structures  3 . 
     Furthermore, from the standpoint of improving the reflection characteristics and transmission characteristics, at least one type of minute projections and depressions, for example, a minute uneven portion  4   a  is preferably formed on the surfaces of the secondary structures  4 . 
     Furthermore, in order to obtain an optical element  1  having a good anti-reflection function and small wavelength dependence, the minute uneven portion  4   a  of the secondary structures  4  is preferably formed so as to have a spatial frequency component with high frequency that is shorter than the period of the primary structures  3 . For example, as shown in  FIG. 16 , a corrugated minute uneven portion  4   a  is preferably provided. The minute uneven portion  4   a  can be formed, for example, by appropriately selecting the conditions of etching such as RIE (reactive ion etching) in the optical element manufacturing process or the material for the master. For example, the uneven portion  4   a  can be formed using Pyrex (registered trademark) glass as the material for the master. 
     In the fourth example embodiment, since the secondary structures  4  are further formed on the surface of the base  2 , an S-shaped refractive index profile can be obtained. Thus, good anti-reflection characteristics can be achieved. However, since the optical element  1  according to the first example embodiment includes adjacent structures directly connected to one another, the packing fraction of the optical element  1  is higher than that of the optical element  1  according to the fourth example embodiment. Therefore, the optical element  1  according to the first example embodiment has an S-shaped refractive index profile that changes more smoothly than that of the optical element  1  according to the fourth example embodiment. Thus, when the structures  3  are tall, the optical element  1  according to the first example embodiment can have better anti-reflection characteristics than the optical element  1  according to the fourth example embodiment. 
     Fifth Example Embodiment 
       FIG. 17A  is a schematic plan view showing an example of a configuration of an optical element according to a fifth example embodiment of the present disclosure.  FIG. 17B  is a partially enlarged plan view of the optical element shown in  FIG. 17A .  FIG. 17C  is a sectional view taken along track T 1 , T 3 , . . . of  FIG. 17B .  FIG. 17D  is a sectional view taken along track T 2 , T 4 , . . . of  FIG. 17B .  FIG. 18  is a partially enlarged perspective view of the optical element shown in  FIG. 17 . 
     An optical element  1  according to the fifth example embodiment differs from that of the first example embodiment in that a large number of depressed structures  3  are arranged on the surface of the base. The shape of the structures  3  is a depression obtained by reversing the projection of the structures  3  in the first example embodiment. Therefore, the effective refractive index in the depth direction (−Z axis direction in  FIG. 17 ) of the structures  3  gradually increases toward the base  2  and changes so as to draw an S-shaped curved line. Note that, when the structures  3  are depressions as described above, the opening portions (the entrance portions of the depressions) of the depressed structures  3  are defined as lower portions and the lowermost portions (the deepest portions of the depressions) in the depth direction of the base  2  are defined as tops. In other words, the top and lower portion are defined using structures  3  that are insubstantial spaces. In this case, the effective refractive index shown in  FIG. 2  gradually increases in the direction from the lower portion to the top. Furthermore, in the fifth example embodiment, since the structures  3  are depressions, the height H of the structures  3  in formula (1) or the like is replaced with the depth H of the structures  3 . 
     The fifth example embodiment is the same as the first example embodiment except for the above description. 
     In the fifth example embodiment, since the depressions obtained by reversing the projections of the structures  3  in the first example embodiment are used, the same effects as in the first example embodiment can be achieved. 
     Furthermore, in the fifth example embodiment, the lower portions of the adjacent structures  3  are connected to one another so that the adjacent structures are penetrated in the lower portions thereof. Therefore, the optical element  1  according to the fifth example embodiment has low possibility that the walls between the structures are damaged, compared with an optical element having thin walls formed between all the adjacent structures. Accordingly, the durability can be improved. 
     Sixth Example Embodiment 
       FIG. 19  is a perspective view showing an example of a configuration of an optical element according to a sixth example embodiment of the present disclosure. As shown in  FIG. 19 , an optical element  1  according to the sixth example embodiment differs from that of the first example embodiment in that the optical element  1  includes pillar-shaped structures  5  that extend in a single direction on the surface of the base and the structures  5  are one-dimensionally arranged on the base  2 . Note that the same parts as those in the first example embodiment are designated by the same reference numerals, and the descriptions thereof are omitted. 
     The effective refractive index in the depth direction (−Z axis direction in  FIG. 19 ) of the structures  5  gradually increases toward the base  2  and changes so as to draw an S-shaped curved line. That is, the refractive index profile has a single inflection point N. Furthermore, the pillar-shaped structures may be connected to one another such that portions of the pillar-shaped structures overlap one another or may be connected to one another such that portions between the pillar-shaped structures are secondary structures. In this case, by modifying the width of the pillar-shaped structures themselves, the pillar-shaped structures may be connected to one another such that portions of the structures overlap one another. 
     The structures  5  have a cylindrical surface that uniformly extends in a single direction (Y axis direction). The section (XZ section) obtained by cutting the structures  5  in the direction perpendicular to the ridgeline direction has a sectional shape that is the same as or similar to the refractive index profile shown in  FIG. 2 . 
     According to the sixth example embodiment, a change in the effective refractive index of the ridgeline direction in the depth direction gradually increases toward the base  2  and draws an S-shaped curved line. Therefore, the boundary for light becomes unclear due to the shape effect of the structures  5 , which can reduce reflected light. Thus, an optical element  1  having good anti-reflection characteristics can be obtained. 
     Seventh Example Embodiment 
       FIG. 20  is a sectional view showing an example of a configuration of an optical element according to a seventh example embodiment of the present disclosure. As shown in  FIG. 20 , an optical element  1  according to the seventh example embodiment differs from that of the first example embodiment in that a gradient film  6  is formed on the base instead of the structures  3 . Note that the same parts as those in the first example embodiment are designated by the same reference numerals, and the descriptions thereof are omitted. 
     The gradient film  6  is a film composed of a material whose composition is gradually changed in the depth direction (thickness direction), whereby the refractive index in the depth direction is gradually changed. The refractive index on the surface side of the gradient film  6  is lower than that on the base side (interface side). The effective refractive index in the depth direction gradually increases toward the base  2  and changes so as to draw an S-shaped curved line. Consequently, the boundary for light becomes unclear, which can reduce reflected light. Thus, the anti-reflection characteristics of the optical element can be degraded. 
     The gradient film  6  can be formed by, for example, sputtering. Examples of the film formation method performed by sputtering include a method in which two types of target materials are simultaneously sputtered at a certain ratio and a method in which the content of process gas contained in the film is appropriately changed by performing reactive sputtering while the flow rate of the process gas is changed. 
     According to the seventh example embodiment, the same effects as in the first embodiment can be achieved. 
     Eighth Example Embodiment 
     Configuration of Liquid Crystal Display Device 
       FIG. 21  shows an example of a configuration of a liquid crystal display device according to an eighth example embodiment of the present disclosure. As shown in  FIG. 21 , the liquid crystal display device includes a backlight  53  that emits light and a liquid crystal panel  51  that temporally and spatially modulates the light emitted from the backlight  53  to display an image. Polarizers  51   a  and  51   b , which are optical components, are respectively disposed on two surfaces of the liquid crystal panel  51 . An optical element  1  is disposed on the polarizer  51   b  disposed on the display surface side of the liquid crystal panel  51 . In the present disclosure, the polarizer  51   b  having the optical element  1  disposed on one principal surface thereof is referred to as an anti-reflective polarizer  52 . The anti-reflective polarizer  52  is an example of anti-reflective optical components. 
     Hereinafter, the backlight  53 , the liquid crystal panel  51 , the polarizers  51   a  and  51   b , and the optical element  1  constituting the liquid crystal display device will be described one by one. 
     Backlight 
     For example, a direct-type backlight, an edge-type backlight, or a planar light source-type backlight can be used as the backlight  53 . The backlight  53  includes, for example, a light source, a reflecting plate, and an optical film. For example, a cold cathode fluorescent lamp (CCFL), a hot cathode fluorescent lamp (HCFL), an organic electroluminescence (OEL), an inorganic electroluminescence (TEL), a light emitting diode (LED), or the like is used as the light source. 
     Liquid Crystal Panel 
     Examples of the display mode that can be used for the liquid crystal panel  51  include a twisted nematic (TN) mode, a super twisted nematic (STN) mode, a vertically aligned (VA) mode, an in-plane switching (IPS) mode, an optically compensated birefringence (OCB) mode, a ferroelectric liquid crystal (FLC) mode, a polymer dispersed liquid crystal (PDLC) mode, and a phase change guest host (PCGH) mode. 
     Polarizers 
     The polarizers  51   a  and  51   b  are respectively provided on two surfaces of the liquid crystal panel  51  so that the transmission axes thereof are orthogonal to each other, for example. Each of the polarizers  51   a  and  51   b  allows only one of orthogonal polarized components of incident light to pass through and blocks the other component by absorption. Each of the polarizers  51   a  and  51   b  may be a uniaxially stretched hydrophilic polymer film such as a polyvinyl alcohol film, a partially formalized polyvinyl alcohol film, or an ethylene-vinyl acetate copolymer partially saponified film, with a dichroic substance, such as iodine or a dichroic dye, adsorbed to the hydrophilic polymer film. A protective layer such as a triacetyl cellulose (TAC) film is preferably formed on two surfaces of each of the polarizers  51   a  and  51   b . When the protective layer is formed in such a manner, the base  2  of the optical element  1  preferably also serves as the protective layer. This is because, in such a configuration, the anti-reflective polarizer  52  can be thinned. 
     Optical Element 
     The optical element  1  is the same as one of those in the first to seventh example embodiments, and the descriptions thereof are omitted. 
     According to the eighth example embodiment, since the optical element  1  is disposed on the display surface of the liquid crystal display device, the anti-reflection function of the display surface of the liquid crystal display device can be improved. Thus, the visibility of the liquid crystal display device can be improved. 
     Ninth Example Embodiment 
     Configuration of Liquid Crystal Display Device 
       FIG. 22  shows an example of a configuration of a liquid crystal display device according to a ninth example embodiment of the present disclosure. The liquid crystal display device differs from that of the eighth example embodiment in that the liquid crystal display device includes a front member  54  on the front side of the liquid crystal panel  51  and also includes the optical element  1  on at least one of the front surface of the liquid crystal panel  51  and the front and rear surfaces of the front member  54 .  FIG. 22  shows an example in which the optical element  1  is provided to all the front surface of the liquid crystal panel  51  and the front and rear surfaces of the front member  54 . For example, an airspace is formed between the liquid crystal panel  51  and the front member  54 . The same parts as those in the eighth example embodiment are designated by the same reference numerals, and the descriptions thereof are omitted. Note that, in the present disclosure, the front surface is a surface on the display surface side, that is, a surface on the viewer&#39;s side, and the rear surface is a surface on the side opposite the display surface. 
     The front member  54  is a front panel or the like used for the purpose of providing mechanical, thermal, and weather-resistant protections and a design function to the front surface (viewer&#39;s side) of the liquid crystal panel  51 . The front member  54  has, for example, a sheet shape, a film shape, or a plate shape. Examples of the material of the front member  54  include glass, triacetyl cellulose (TAC), polyester (TPEE), polyethylene terephthalate (PET), polyimide (PI), polyamide (PA), aramid, polyethylene (PE), polyacrylate, polyethersulfone, polysulfone, polypropylene (PP), diacetyl cellulose, polyvinyl chloride, acrylic resin (PMMA), and polycarbonate (PC). However, the material is not particularly limited to these materials and any material having transparency can be used. 
     According to the ninth example embodiment, the visibility of the liquid crystal display device can be improved as in the eighth example embodiment. 
     EXAMPLES 
     Hereinafter, the present disclosure is specifically described based on Examples, but is not limited to only Examples. 
     Examples of the present disclosure are described in the following order. 
     1. Investigation about the refractive index profile and the shape of structures 
     2. Investigation about other shapes of structures 
     3. Investigation about the number of steps in refractive index profile 
     4. Investigation about reflection characteristics using actually manufactured samples 
     1. Investigation about the Refractive Index Profile and the Shape of Structures 
     An S-shaped refractive index profile was assumed, and the shape of structures that achieves the refractive index profile was determined through simulation. Furthermore, the relationship between the refractive index profile and reflectivity was investigated through simulation. 
     Example 1 
     As shown in  FIG. 23 , a refractive index profile whose effective refractive index draws an S-shaped curved line was assumed. Subsequently, the shape of structures that achieves the above-described refractive index profile was determined.  FIG. 24A  shows the result. 
     Example 2 
     As shown in  FIG. 23 , a refractive index profile whose effective refractive index draws an S-shape and in which the tip changes more steeply than that of Example 1 was assumed. Subsequently, the shape of structures that achieves the above-described refractive index profile was determined.  FIG. 24B  shows the result. 
     Example 3 
     As shown in  FIG. 23 , a refractive index profile whose effective refractive index draws an S-shape and in which the tip changes much more steeply than that of Example 1 was assumed. Subsequently, the shape of structures that achieves the above-described refractive index profile was determined.  FIG. 24C  shows the result. 
     Comparative Example 1 
     As shown in  FIG. 23 , a linear refractive index profile was assumed. Subsequently, the shape of structures that achieves the above-described refractive index profile was determined. As a result, structures having a hanging bell shape (not shown) were obtained. 
     Evaluation of Reflectivity 1 
     First, the reflectivity of each of the above-described refractive index profiles in the case where the height of structures was 300 nm was determined.  FIG. 25  shows the results. Note that, in  FIG. 23 , since the optical thickness is determined on the basis of the bottom surface of the structures, the relationship between increase and decrease in the refractive index profile is opposite to that shown in  FIG. 2 . 
     The following is clear from  FIG. 25 . 
     In the linear refractive index profile (Comparative Example 1), the reflectivity R is more than 0.1% in substantially the entire visible range of 400 nm to 700 nm. In contrast, in the S-shaped refractive index profiles (Examples 1 to 3), the reflectivity R is less than 0.1% in substantially the entire visible range of 400 nm to 700 nm. In particular, the S-shaped refractive index profiles (Examples 2 and 3) that steeply change at the ends on the base side and the air side are satisfactory in terms of reflectivity prevention effects in the visible range. 
     Evaluation of reflectivity 2 
     Regarding the linear refractive index profile (Comparative Example 1) and the refractive index profile (Example 3) having the best characteristics in Examples 1 to 3, the reflection characteristics obtained when the height of structures was changed were determined  FIG. 26  shows the results. 
     The following is clear from  FIG. 26 . 
     When the height of structures is 200 nm, the reflectivity of the S-shaped refractive index profile (Example 3) is higher than that of the linear refractive index profile (Comparative Example 1). Therefore, the reflection characteristics of the S-shaped refractive index profile are degraded. 
     When the height of structures is 250 nm, the reflectivity of the S-shaped refractive index profile (Example 3) is decreased at shorter wavelengths, and the average value of the reflectivity in the visible range of 400 nm to 700 nm is improved compared with the linear refractive index profile (Comparative Example 1). Therefore, when the height of structures is 5/14 (250 nm) or more of the wavelength 700 nm, the S-shaped refractive index profile effectively functions and the reflectivity R&lt;0.3% can be achieved in substantially the entire visible range of 400 nm to 700 nm. Furthermore, in a wavelength range of 400 nm to 550 nm, when the height of structures is 5/14 (below 200 nm) or more of the wavelength 550 nm, the reflectivity R&lt;0.3% can be achieved. 
     When the height of structures is 300 nm, 400 nm, or 500 nm, the reflectivity of the S-shaped refractive index profile (Example 3) is decreased in the visible range of 400 nm to 700 nm compared with the reflectivity of the linear refractive index profile. Therefore, the reflection characteristics of the S-shaped refractive index profile are improved. Specifically, better anti-reflection effects (R&lt;0.1%) can be produced in the visible range of 400 nm to 700 nm. 
     When the height of structures is 300 nm, the reflectivity at 700 nm, which is the longer wavelength edge of the wavelength range, is about 0.08%. Thus, when the height of structures is 2/5 (280 nm) or more and preferably 3/7 (300 nm) or more of the wavelength 700 nm, the S-shaped refractive index profile effectively functions and the reflectivity R&lt;0.1% can be achieved in substantially the entire visible range of 400 nm to 700 nm. 
     In terms of ease of manufacturing, the maximum value of the height of structures is preferably about 1.0 μm (at a pitch of 700 nm, the aspect is 1.4) in the visible range. Thus, the height of structures is preferably 10/7 (1 μm) or less of the wavelength 700 nm. 
     In consideration of the above description, the height of structures is preferably 5/14 or more and 10/7 or less the maximum value of the wavelength range of light in a use environment, more preferably 2/5 or more and 10/7 or less the maximum value, and further preferably 3/7 or more and 10/7 or less the maximum value. 
     Evaluation of Shape of Structures 
     The following is clear from  FIGS. 24A to 24C  and  25 . 
     The shape of structures that achieves the refractive index profile shown in  FIG. 23  is a sectional shape of the square root of the S-shaped refractive index profile, and the shape gradually widens toward the base. In addition, among the structures shown in  FIGS. 24A to 24C , the structures having a truncated cone-like shape whose top is flat (Example 2:  FIG. 24B  and Example 3:  FIG. 24C ) can achieve particularly good anti-reflection characteristics. 
     Furthermore, as shown in  FIG. 24 , the lower portions of the adjacent structures are connected to one another, which is indicated by the presence of flat portions  3   a  formed in the lower portions of the structures. This can achieve a refractive index profile that gradually increases toward the base and draws an S-shaped curved line. Note that minute structures such as secondary structures may be formed on the surface of the base without bringing the lower portions of structures into contact with one another. 
     2. Investigation about Other Shapes of Structures 
     The shapes of the structures other than those shown in  FIGS. 24A to 24C  were determined by calculation. 
     Example 4 
     Structures obtained by stretching the structures  3  of Example 3 1.5 times in the Y axis direction were determined.  FIG. 27A  shows the result. 
     Example 5 
     Structures obtained by stretching the structures  3  of Example 3 1.5 times in the X axis direction were determined.  FIG. 27B  shows the result. 
     Example 6 
     The shape of structures obtained by reversing the depressions and projections of the structures  3  of Example 2 was determined.  FIG. 27C  shows the result. 
     Evaluation of Shape of Structures 
     Even in the structures stretched in the X and Y axis directions or the structures whose depressions and projections are reversed, a refractive index profile similar to those of Examples 2 and 3 is obtained. Therefore, the shapes (Examples 4 to 6) of the structures shown in  FIGS. 27A to 27C  also achieve good anti-reflection characteristics. 
     Moreover, the structures stretched in the X and Y axis directions as in Examples 4 and 5 can be easily manufactured, and the packing fraction can be increased. 
     3. Investigation about the Number of Steps in Refractive Index Profile 
     The reflection spectra of a refractive index profile having two or more inflection points and a refractive index profile having a single inflection point (S-shaped refractive index profile) were determined, and the results were compared with each other. 
     Example 7 
     The same S-shaped refractive index profile as that of Example 3, that is, a refractive index profile having a single inflection point was assumed. 
     Comparative Example 2 
     As shown in  FIG. 28 , the same refractive index profile as that of Comparative Example 1, that is, a linear refractive index profile was assumed. 
     Comparative Example 3 
     As shown in  FIG. 28 , a refractive index profile having three inflection points was assumed. 
     Comparative Example 4 
     As shown in  FIG. 28 , a refractive index profile having five inflection points was assumed. 
     Evaluation of Reflectivity 
     The reflectivity of each of the above-described refractive index profiles in the case where the height of structures was 500 nm was determined.  FIG. 29  shows the results. Note that, in  FIG. 28 , since the optical thickness is determined on the basis of the bottom surface of the structures, the relationship between increase and decrease in the refractive index profile is opposite to that shown in  FIG. 2 . 
     The following is clear from  FIG. 29 . 
     When the height of structures is 500 nm, the S-shaped refractive index profile (Example 7) produces better anti-reflection effects than the refractive index profiles having two or more inflection points (Comparative Examples 3 and 4) and the linear refractive index profile 
     Comparative Example 2 
     Herein, when the height of structures is 500 nm or more, the S-shaped refractive index profile (Example 7) tends to produce better anti-reflection effects than the refractive index profiles having two or more inflection points (Comparative Examples 3 and 4) and the linear refractive index profile (Comparative Example 2). 
     4. Investigation about Reflection Characteristics Using Actually Manufactured Samples 
     In Example 8 below, the height H of structures of an optical sheet, the arrangement pitches P 1  and P 2 , and the aspect ratio were determined as follows. 
     First, the surface shape of an optical sheet manufactured was observed with an atomic force microscope (AFM). Subsequently, the height H and arrangement pitches P 1  and P 2  of structures were determined from the sectional profile obtained with the AFM. Furthermore, the aspect ratio (=Height H/Arrangement pitch P 2 ) was determined using the height H and the arrangement pitch P 2 . 
     Example 8 
     First, a glass roll master having an outer diameter of 126 mm was prepared, and a resist layer was formed on the surface of the glass roll master as follows. That is to say, a photoresist was diluted with a thinner by a factor of 1/10, and the diluted resist was applied on the columnar surface of the glass roll master by dipping so as to have a thickness of about 70 nm, whereby the resist layer was formed. Next, the glass roll master serving as a recording medium was transferred to the roll master exposure apparatus shown in  FIG. 8 . By exposing the resist layer, a latent image having a quasi-hexagonal lattice pattern in the three adjacent rows of tracks was patterned on the resist layer so as to form a single spiral shape. 
     Specifically, a region where a quasi-hexagonal lattice exposure pattern was to be formed was irradiated with laser beams having a power of 0.50 mW/m that reach the surface of the glass roll master to form a depressed quasi-hexagonal lattice exposure pattern. Note that the thickness of the resist layer in the column direction of track rows was about 60 nm and the thickness of the resist layer in the track extending direction was about 50 nm. 
     Subsequently, by subjecting the resist layer on the glass roll master to development treatment, an exposed portion of the resist layer was dissolved to perform development. Specifically, an undeveloped glass roll master was placed on a turntable of a developing apparatus (not shown). A developer was dropwise applied onto the surface of the glass roll master while the glass roll master was rotated together with the turntable, to develop the resist layer on the surface. Thus, a resist glass roll master whose resist layer has openings in a quasi-hexagonal lattice pattern was obtained. 
     Next, etching treatment and ashing treatment were alternately performed on the resist glass roll master using a roll etching machine. Thus, a pattern of conical structures (depressions) was formed. Herein, by suitably adjusting the treatment time of the etching treatment and ashing treatment, a single step was formed on the side face of the structures. This provided a shape whose effective refractive index in the depth direction of the structures gradually increases toward a base and changes so as to draw an S-shaped curved line.  FIGS. 30A and 30B  show the shape of the formed surface of a master manufactured. Such a shape of structures can also be measured by observation with a SEM (scanning electron microscope) or the like, instead of the evaluation with the AFM (scanning atomic force microscope). 
     Herein, the roll etching machine is a plasma etching apparatus having a columnar electrode, and is configured such that the columnar electrode is inserted into the hollow of the cylindrical glass roll master and plasma etching is performed on the cylindrical surface of the glass roll master. 
     Finally, by completely removing the resist layer by O 2  ashing, a moth-eye glass roll master having a depressed quasi-hexagonal lattice pattern was obtained. The depth of the depressions in the column direction was larger than those in the track extending direction. 
     Subsequently, the moth-eye glass roll master was brought into close contact with a TAC (triacetyl cellulose) sheet to which an ultraviolet curable resin had been applied, and then they were detached from each other while being cured by applying ultraviolet rays. Consequently, an optical sheet having a principal surface on which a plurality of structures were arranged was obtained. The height H of the structures of the optical sheet was 230 nm, the arrangement pitch P 1  was 300 nm, the arrangement pitch P 2  was 270, and the aspect ratio (H/P 2 ) was 0.9. 
     Through the processes above, an intended optical sheet was manufactured. 
     Evaluation of Reflectivity 
     The reflectivity of the optical sheet manufactured as described above was evaluated using an evaluation apparatus (V-550) available from JASCO Corporation.  FIG. 31  shows the results. 
     Comparative Example 5 
     The reflection characteristics of an optical sheet having a surface on which a plurality of structures having a cone-like shape had been arranged were determined through simulation.  FIG. 31  shows the result. 
     The conditions of the simulation are shown below. 
     Arrangement: hexagonal lattice 
     Height H: 200 nm 
     Arrangement pitches P 1  and P 2 : 300 nm 
     Aspect ratio (H/P 2 ): 0.7 
     Shape: cone-like shape (shape without an S-shaped refractive index profile) 
     Polarization: none 
     Comparative Example 6 
     The reflection characteristics of an optical sheet having a surface on which a plurality of structures having a hanging bell shape had been arranged were determined through simulation.  FIG. 31  shows the result. 
     The conditions of the simulation are shown below. 
     Arrangement: hexagonal lattice 
     Height H: 300 nm 
     Arrangement pitches P 1  and P 2 : 300 nm 
     Aspect ratio (H/P 2 ): 1.0 
     Shape: hanging bell shape (shape without an S-shaped refractive index profile) 
     Polarization: none 
     Table 1 shows the configurations of Example 8 and Comparative Examples 5 and 6. 
     
       
         
           
               
               
               
               
             
               
                   
               
               
                   
                   
                 Comparative 
                 Comparative 
               
               
                   
                 Example 8 
                 Example 5 
                 Example 6 
               
               
                   
               
             
            
               
                 Result of surface 
                 FIG. 30A 
                 — 
                 — 
               
               
                 observation 
                 FIG. 30B 
                   
                   
               
               
                   
                 (AFM image) 
                   
                   
               
               
                 Lattice pattern 
                 quasi-hexagonal  
                 hexagonal 
                 hexagonal 
               
               
                   
                 lattice 
                 lattice 
                 lattice 
               
               
                 Shape of bottom 
                 ellipse 
                 circle 
                 circle 
               
               
                 Pitch P1 (nm) 
                 300 
                 300 
                 300 
               
               
                 Pitch P2 (nm) 
                 270 
                 300 
                 300 
               
               
                 Height H (nm) 
                 230 
                 200 
                 300 
               
               
                 Aspect ratio  
                 0.9 
                 0.7 
                 1.0 
               
               
                 (H/P2) 
                   
                   
                   
               
               
                 Shape 
                 S-shape 
                 cone-like 
                 hanging bell 
               
               
                   
                 (refractive index profile)  
                 shape 
                 shape 
               
               
                 Polarization 
                 none 
                 none 
                 none 
               
               
                   
               
            
           
         
       
     
     The following is clear from  FIG. 31 . 
     In Example 8, the reflectivity tends to slightly increase at longer wavelengths in the wavelength range of 400 nm to 650 nm, but is much lower than that of Comparative Example in the wavelength range of about 400 nm to 650 nm. Specifically, the low-reflection characteristics such as a reflectivity of 0.2% or less are achieved at a wavelength of 550 nm, at which the visibility of human beings is the highest. Note that the increase in reflectivity at longer wavelengths is caused by the height of structures. Therefore, the increase in reflectivity can be suppressed by changing the height of structures in Example 8 to about 300 nm, which is the height of structures in Comparative Example 6. 
     In contrast, in Comparative Example 5, the reflectivity tends to gradually increase along with an increase in wavelength in the wavelength range of 400 nm to 650 nm. Furthermore, in Comparative Example 6, an increase in reflectivity is suppressed at longer wavelengths in the wavelength range of 400 nm to 650 nm, but the anti-reflection characteristics of Example 8 are better than those of Comparative Example 6 in the entire above-described wavelength range. In particular, Example 8 is better than Comparative Example 6 in terms of anti-reflection characteristics at a wavelength of 550 nm, at which the visibility of human beings is the highest. Herein, when the height of structures in Example 8 is changed to about 300 nm, which is the height of structures in Comparative Example 6, the structures having an S-shaped refractive index profile have considerably better anti-reflection characteristics. 
     It is clear from the above description that good anti-reflection characteristics can be achieved when an effective refractive index in the depth direction of structures gradually increases toward a base and draws an S-shaped curved line. 
     The example embodiments and Examples of the present disclosure have been specifically described above. However, the present disclosure is not limited to the above-described example embodiments and Examples, and various modifications can be made in accordance with different desired performances on the basis of the technical ideas of the present disclosure. 
     For example, the numerical values, shapes, materials, and configurations exemplified in the example embodiments and Examples are mere examples, and different numerical values, shapes, materials, and configurations may be optionally used. 
     Furthermore, the configurations of the above-described example embodiments can be combined with each other as long as they do not depart from the spirit of the present disclosure. 
     Furthermore, in the above-described example embodiments, the case where the present disclosure is applied to a liquid crystal display device has been described as an example, but the present disclosure can also be applied to various display devices other than the liquid crystal display device. For example, the present disclosure can be applied to various display devices such as a CRT (cathode ray tube) display, a plasma display panel (PDP), an electro luminescence (EL) display, and a surface-conduction electron-emitter display (SED). 
     Furthermore, in the above-described example embodiments, the case where the optical element  1  is manufactured by a method in which a process for making a master of optical discs is combined with an etching process has been described as an example. However, the method for manufacturing the optical element  1  is not limited thereto, and any method may be adopted as long as an optical element having an S-shaped refractive index profile whose effective refractive index in the depth direction gradually increases toward a base can be manufactured. For example, the optical element may be manufactured using electron-beam exposure or the like. Alternatively, the optical element may be manufactured by performing coating with a gradient film obtained by blending hollow silica or the like while the ratio of the hollow silica is changed such that the effective refractive index gradually changes, or with a gradient film obtained through reactive sputtering. 
     Furthermore, in the above-described example embodiments, a low refractive index layer may be further formed on the surface of the base  2  where the structures  3  have been formed. Preferably, the low refractive index layer is mainly composed of a material having a lower refractive index than the materials constituting the base  2 , the structures  3 , and the secondary structures  4 . Examples of the material of such a low refractive index layer include organic materials such as fluorocarbon resins and inorganic low refractive index materials such as LiF and MgF 2 . 
     Furthermore, in the above-described example embodiments, the optical element may be manufactured by thermal transfer. Specifically, the optical element  1  may be manufactured by heating a base mainly composed of a thermoplastic resin and then by pressing a stamp (mold) such as the roll master  11  or the disc master  41  against the base sufficiently softened by the heat treatment. 
     Furthermore, in the above-described example embodiments, the case where an anti-reflective polarizer is provided by applying the present disclosure to a polarizer has been described as an example, but the present disclosure is not limited to the example. Anti-reflective optical components other than the polarizer can be provided by applying the present disclosure to a lens, an optical waveguide, a window material, a display element, and the like. 
     Furthermore, in the above-described example embodiments, the case where the refractive index profile has an S-shape with a single inflection point has been described, but another inflection point may be further provided to at least one of ends of the S-shaped refractive index profile. Even in such a substantially S-shaped refractive index profile, good anti-reflection characteristics can be achieved. In particular, when the height of structures is small, the effects of anti-reflection characteristics are significantly produced. The inflection point at one end of the refractive index profile can be obtained by, for example, forming the top of the structures  3  so that the top is a protrusion with a curved surface. The inflection point at the other end can be obtained by, for example, forming a hem in the lower portion of the structures  3  so that the hem widens toward the base. 
     It should be understood that various changes and modifications to the presently preferred example embodiments described herein will be apparent to those skilled in the art. Such changes and modifications can be made without departing from the spirit and scope of the present subject matter and without diminishing its intended advantages. It is therefore intended that such changes and modifications be covered by the appended claims.