Patent Publication Number: US-2003234180-A1

Title: Process for preparation of optical element, electrolytic solution used for the same and apparatus for preparation of optical element

Description:
BACKGROUND OF THE INVENTION  
       [0001] 1. Field of the Invention  
       [0002] The present invention relates to a process for preparing a polymer thin film to be patterned in the order of micrometers. More particularly, the present invention relates to a process for preparing an optical element in the form of thin film which changes in color and refractive index along its in-plane length or thickness.  
       [0003] 2. Description of the Related Art:  
       [0004] There is known a conventional method for patterning a polymer thin film in the order of micrometers. This method has steps of coating a flat substrate with a photocurable resin (as a raw material for polymer thin film) by spin coating or the like, exposing the coated film after drying to ultraviolet rays, and developing the cured film. A similar method is also used for a polymer thin film formed from a non-photocurable resin. In this case, the polymer thin film is coated with a photocurable resin in the same way as mentioned above and the coated film is patterned by exposure and development.  
       [0005] These methods work well in preparation of a polymer thin film containing a functional material, such as fine particles (e.g., pigment and highly refractive material), molecules (e.g., dye), and polymer of a different kind, which is uniformly dispersed therein. However, with these methods, it is impossible to prepare a polymer thin film in which the concentration of the functional material changes stepwise or continuously along its in-plane length or thickness, because the polymer thin film itself is formed uniformly by spin coating. It is possible to prepare a thin film in which the concentration of the functional material changes along its thickness, if coating is repeated several times with coating solutions each containing the functional material in different concentrations. In this case, the variation of concentration is stepwise and it is difficult to change the concentration continuously.  
       [0006] By the way, the present inventors proposed processes for forming an image with high resolution and for preparing a color filter from an electrodeposition material containing a coloring agent by electrodeposition or photovoltaic electrodeposition at a low voltage. Details of these processes are disclosed in Japanese Published Unexamined Patent Applications Nos. Hei 10-119414, 11-189899, 11-15418, 11- 174790, 11-133224 , and 11-335894. These methods are characterized by simplicity in preparation of colored film with high-resolution. They are used mainly in the application area of liquid crystal display units.  
       [0007] The above-mentioned photovoltaic electrodeposition process and its related technology make it possible to continuously change the concentration of the functional material in the film (such that the concentration of the functional material increases in proportion to the film thickness) if an adequate control is exerted on at least one of such variables as (a) bias voltage to be applied, (b) duration of irradiation with light, and (c) intensity of light for irradiation. Consequently, with this process, we can obtain a thin film in which the concentration of the functional material continuously changes in the in-plane direction. On the other hand, however, it poses some problems. That is, the resulting polymer thin film is poor in flatness and cannot be transferred to another surface satisfactorily because the thicker part of the thin film tends to blur. Needless to say, this process does not give a thin film in which the concentration of the functional material changes continuously in the thickness direction.  
       [0008] There is a conventional process called photobleaching which permits the concentration of the functional material to change from place to place in a polymer thin film. This process employs special molecules which change in color or disappear upon irradiation with light having a specific wavelength. This process gives a uniformly thick thin film (such as the one produced by spin coating) in which the refractive index changes from place to place. This process, however, is not generally acceptable because the material for photobleaching is limited.  
       [0009] As mentioned above, there has been no process for preparing a polymer thin film and a patterned polymer thin film which is made up mainly of a polymer and which contains a functional material (such as pigment fine particles, dye, and highly refractive fine particles) such that the concentration of the functional material changes continuously along the in-plane length or the thickness of the thin film.  
       SUMMARY OF THE INVENTION  
       [0010] The present invention was completed in view of the-foregoing and provides a process for preparation of an optical element, an electrolytic solution used for the process, and an apparatus for preparation of the optical element. According to the present invention, the optical element is a polymer thin film containing a functional material such that the concentration of the functional material changes somewhat stepwise or continuously in the in-plane and/or thickness direction. According to the present invention, the process permits easy production of such an optical element.  
       [0011] The foregoing is dealt with by providing a process for preparation of an optical element, an electrolytic solution used for the process, and an apparatus for preparation of the optical element as follows.  
       [0012] One aspect of the present invention resides in a process for preparation of an optical element which includes the steps of: preparing a substrate having an insulating substrate and a conductive thin film formed thereon; preparing an electrolytic solution containing a film forming polymer decreasing in solubility or dispersibility in an aqueous liquid as a pH value changes and a functional material in a certain concentration; contacting the conductive thin film with the electrolytic solution in a presence of a counter electrode in the electrolytic solution and applying a voltage between the conductive thin film and the counter electrode for changing the pH value; and varying the concentration of the functional material near the conductive thin film.  
       [0013] Another aspect of the present invention resides in a process for preparation of an optical element which includes the steps of: preparing a substrate having an insulating substrate, a conductive thin film and a photosemiconductive film formed thereon; preparing an electrolytic solution containing a film forming polymer decreasing in solubility or dispersibility in an aqueous liquid as a pH value changes and a functional material in a certain concentration; contacting the photosemiconductive film with the electrolytic solution and applying a light to the photosemiconductive film for changing the pH value; and varying the concentration of the functional material near the conductive thin film.  
       [0014] Another aspect of the present invention resides in an apparatus for preparing an optical element on a substrate having conductive thin film, including: an electrodeposition vessel holding an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as the pH value changes; a counter electrode which is placed in the electrodeposition vessel and is electrically connected to the conductive thin film; a unit that irradiates with light the photosemiconductor thin film on the optical element preparing substrate, and a mechanism to cause a flow of an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as a pH value changes.  
       [0015] Another aspect of the present invention resides in an apparatus for preparing an optical element on a substrate having an clectroconductive thin film, including: an electrodeposition vessel holding an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as a pH value changes; a counter electrode which is placed in the electrodeposition vessel and is electrically connected to the conductive thin film; a voltage application unit that applies a voltage across the conductive thin film and the counter electrode, and a mechanism to cause a flow of an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as a pH value changes. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0016] Preferred embodiments of the present invention will be described in detail on the followings, wherein:  
     [0017]FIG. 1 is a diagram showing the steps of preparing the optical element according to one embodiment of the present invention.  
     [0018]FIGS. 2A and 2B are a plan view and a sectional view, respectively, of the optical element obtained by the process of the present invention,  
     [0019]FIG. 3 is a schematic diagram showing the apparatus to prepare the optical element by using a projection exposure unit.  
     [0020]FIG. 4 is a schematic diagram showing the apparatus to prepare the optical element by using a proximity exposure unit.  
     [0021]FIG. 5 is a schematic diagram showing the apparatus to prepare the optical element by using a scanning laser exposure unit.  
     [0022]FIG. 6 is a schematic diagram showing the apparatus to prepare the optical element by electrodeposition. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
     [0023] According to the present invention, the process for preparation of an optical element is based the technology disclosed in Japanese Published Unexamined Patent Applications Nos. Hei 10-119414, 11-189899, 11-15418, 11-174790, 11-133224, and 11-335894. This technology is designed to form a thin film by electrodeposition or photovoltaic electrodeposition. The process of the present invention is characterized by performing electrodeposition in such a way that the concentration of the functional material in the electrolytic solution changes in the vicinity of the optical element preparing substrate so that the resulting thin film contains the functional material whose concentration gradationally changes. The following deals mainly with optical waveguides (of core-cladding type) and lenses as the typical examples of the optical element.  
     [0024] The process of the present invention makes it possible to easily prepare a thin-film optical element in which the concentration of the functional material changes gradationally. The advantage of this process is that the concentration changes continuously instead of stepwise (as in the conventional technology) and moreover the concentration changes not only in the thickness direction but also in the in-plane direction. A combination of these modes of change may give a three-dimensional gradation. In addition, the thin film proper which is formed by deposition is flat and uniform in thickness regardless of the changing concentration of the functional material therein. This facilitates transfer and eliminates blurs and other defects.  
     [0025] The electrodeposition process basically has a step of preparing a substrate for electrodeposition, which is made up of an insulating substrate and a conductive thin film formed thereon, in an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as the pH value changes, in such a way that at least the conductive thin film comes into contact with the electrolytic solution, and a step of applying a voltage across the conductive thin film and its counter electrode, thereby causing the materials to deposit on the conductive thin film.  
     [0026] The photovoltaic electrodeposition process utilizes photoelectromotive force that is generated in a photosemiconductor thin film. It has a step of preparing a substrate for photovoltaic electrodeposition, which is made up of an insulating substrate and a conductive thin film and a photosemiconductor thin film sequentially laminated thereon, in an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as the pH value changes, in such a way that at least the photosemiconductor thin film comes into contact with the electrolytic solution, and a step of applying a voltage across the photosemiconductor thin film and its counter electrode in a selected region while irradiating the selected region in the photosemiconductor thin film with light, thereby causing the materials to deposit on the selected region of the photosemiconductor thin film.  
     [0027] The electrodeposition process and photovoltaic electrodeposition process make it possible to accurately form an optical element having fine patterns without the necessity of applying a high voltage (over 5 V). Whereas the conventional process that uses a photosensitive resin to prepare an optical element needs a thin film with an accurately controlled thickness on the substrate and poses a problem with alkaline waste liquids resulting from etching, the process of the present invention makes it possible to easily control the thickness of the thin film by adjusting the duration of light irradiation or voltage application and needs no etching for patterning (and hence poses no environmental problem).  
     [0028] The process for preparation of an optical element which is based on photovoltaic electrodeposition will be described first in the following. This process uses an optical element preparing substrate, which is made up of an insulating substrate and a conductive thin film and a photosemiconductor thin film sequentially laminated thereon. The insulating substrate includes glass plate, quartz plate, plastic film, epoxy resin sheet, and the like. The conductive thin film includes those of ITO, indium oxide, nickel, and aluminum. The photosemiconductor thin film includes titanium oxide thin film, zinc oxide thin film, and the like, which will be explained in the following. Incidentally, the insulating substrate and conductive thin film should be transparent to light in the case where the photosemiconductor thin film is irradiated with light through the insulating substrate. This is not applied to the case in which irradiation with light is carried out through the electrolytic solution.  
     [0029] The electrolytic solution will be explained later because it is used in common for the photovoltaic electrodeposition process and the electrodeposition process.  
     [0030] The term “selected region” as used in the present invention denotes the entire region as well as the partial region in the optical element preparing substrate. For example, in the case where a cladding layer is formed on the entire surface of the substrate, the selected region means the entire surface which is irradiated with light.  
     [0031] The process of the present invention may be applied in the following manner to the preparation of an optical element including a cladding layer and a core layer laminated on one the-other. First, the cladding layer is formed on the entire surface from the electrolytic solution for the cladding layer. Second, the selected region (or the entire surface) of the substrate is irradiated with light. Third, the core layer is formed on the selected region (or the core-forming region) from the electrolytic solution for the core layer. Finally, the selected region is irradiated with light. Another cladding layer may be formed on the core layer by repeating the same steps as above without drying the cladding layer and the core layer. The resulting optical element is made up of a lower cladding layer, a core layer, and an upper cladding layer.  
     [0032] Moreover, the above-mentioned cladding layer may also be formed by electrodeposition even though irradiation with light is replaced by application of a voltage exceeding the Schottky barrier of the photosemiconductor thin film on the optical element preparing substrate. This process is simpler because it dispenses with the step for exposure.  
     [0033] The process for preparing an optical element according to the present invention will be illustrated below with reference to the accompanying drawings. FIGS. 1A to  1 D show the steps of preparing a waveguide in which a cladding layer is formed on the entire surface of a substrate, with a core layer interposed between them, the core layer containing a functional material (such as fine particles to control the refractive index) such that its concentration changes gradationally in the thickness direction.  
     [0034]FIG. 1A shows an example of the optical element preparing substrate  10 , which has an insulating substrate  12 , a conductive film  14 , and a photosemiconductor thin film  16 . FIG. 1B shows a cladding layer  18  (not yet dried) which has been formed from an electrolytic solution for the cladding layer. The entire surface of the cladding layer  18  has been irradiated with light or alternatively it has been given a voltage exceeding the Schottky barrier of the photosemiconductor thin film.  
     [0035]FIG. 1C shows a core layer  20  formed in the selected region on the cladding layer  18  (not yet dried) from an electrolytic solution for the core layer. The core layer  20  has been irradiated with light. The core layer contains the functional material such that its concentration gradationally changes. This is accomplished by changing the concentration of the functional material in the electrolytic solution in the vicinity of the optical element preparing substrate, as mentioned later. In the case where the functional material is fine particles to control the refractive index, the resulting core layer has a refractive index which changes from place to place. FIG. 1C shows that the concentration of the functional material is high at the center of the thickness of the core layer.  
     [0036]FIG. 1D shows an additional cladding layer  22  (not yet dried) which has been formed on the core layer  20  (not yet dried) from an electrolytic solution for the cladding layer. The entire surface of the cladding layer  20  has been irradiated with light or alternatively it has been given a voltage exceeding the Schottky barrier of the photosemiconductor thin film. The desired optical element is completed by drying these layers.  
     [0037] The foregoing example demonstrates a case in which the core layer has the gradation of concentration. Needless to say, there may be another case in which the cladding layer or both the core layer and the cladding layer have the gradation of concentration.  
     [0038]FIGS. 2A and 2B show an example of an optical element (such as lens) which is characterized in that the concentration of the functional material in the thin film changes in the in-plane direction. FIGS. 2A and 2B show how the concentration of the functional material decreases in going from the center to the periphery in the flat circular thin film  24  formed on the optical element preparing substrate  10 . The change of concentration is represented by the density of dots.  
     [0039] The above-mentioned photovoltaic electrodeposition process may employ an optical element preparing substrate made up of a conductive substrate and a photosemiconductor thin film formed thereon. The conductive substrate may be the one which is formed from at least one member selected from iron, nickel, zinc, copper, or titanium, or compounds thereof, or mixtures thereof. The conductive substrate may also include conductive plastics film.  
     [0040] The photosemiconductor may be formed from titanium oxide or zinc oxide by the process mentioned later. Alternatively, it is also possible to form a photosemiconductor thin film on a plate of metallic titanium or zinc by oxidation of its surface. In this case, the optical element preparing substrate or the deposition substrate is made up of a conductive substrate and a photosemiconductor thin film formed thereon.  
     [0041] Oxidation may be accomplished inexpensively by heating at a high temperature in the air or by anodization. In other words, it is possible to form a transparent semiconductor thin film without using the expensive sputtering method. Incidentally, it is desirable that the unoxidized part of the underlying metal substrate should be coated with an insulating film to avoid formation of an unnecessary electrodeposition film thereon.  
     [0042] Now, the process for preparation of an optical element which is based on electrodeposition will be described in the following. This process uses an optical element preparing substrate, which is made up of an insulating substrate and a conductive thin film or a patterned conductive thin film formed thereon. The optical element preparing substrate is arranged in an aqueous electrolytic solution, which contains a film-forming polymer and a functional material, the former decreasing in solubility or dispersibility in an aqueous liquid as the pH value changes, in such a way that at least the conductive thin film comes into contact with the electrolytic solution. Then a voltage is applied across the conductive thin film and its counter electrode, so that the materials deposit on the conductive thin film. During voltage application, the concentration of the functional material in the electrolytic solution is changed in the vicinity of the optical element preparing substrate. Thus, the resulting thin film contains the functional material gradationally. The foregoing process may be used to form on the optical element preparing substrate a core layer in which the concentration of the functional material changes gradationally.  
     [0043] The insulating substrate may be the same one as used in the photovoltaic electrodeposition method. The patterned conductive thin film may be formed by patterning the conductive film in the usual way or coating the conductive substrate with an insulating film so that a conductive part is exposed in a desired pattern. These substrates may be used to form the cladding layer or core layer by the electrodeposition process.  
     [0044] The optical element prepared as mentioned above may be transferred to another substrate in the following manner.  
     [0045] First, the method of transferring the optical element prepared by photovoltaic electrodeposition to an optical element substrate is explained. (The optical element in this case denotes the core layer and the cladding layer individually or in combination.) The substrate to which transfer is made may be the one which functions also as a cladding layer. In this way it is possible to reduce the total number of steps including the step of electrodeposition. If an optical element is prepared by repeating transfer of the core layers and cladding layers, which have been formed separately by electrodeposition, there may be the possibility that loss increases at the interface between the core layer and the cladding layer and the resulting waveguide is slightly deformed.  
     [0046] The optical element substrate includes those of glass, epoxy resin, and the like which are in general use. The optical element substrate which functions also as a cladding layer includes polyethylene film, polyester film, polycarbonate film, acrylic resin film, fluoropolymer film, and the like.  
     [0047] The cladding layer or core layer formed by electrodeposition as mentioned above may also be transferred to another substrate. In this case, the substrate should preferably be one which functions as the cladding layer.  
     [0048] Transfer of an optical element (which has been prepared by the above-mentioned photovoltaic electrodeposition) to another substrate may be accomplished easily if a release layer is previously formed on the optical element preparing substrate. This release layer obviates the necessity of using heat or pressure at the time of transfer and hence eliminates the possibility of damage to the substrate and optical element.  
     [0049] The release layer should preferably be one which has a critical surface tension not higher than 30 dyne/cm and has no influence on electrodeposition current. Its typical examples include commercial fluoropolymer spray for waterproofing, silicone resin, silicone oil, and unsaturated fatty acid such as oleic acid.  
     [0050] The electrodeposition uses a film-forming polymer which decreases in solubility or dispersibility in an aqueous liquid as the pH value changes. Such a material is exemplified by a substance which preferably contains such ionic groups as carboxyl group and amino group in the molecule. These groups change in ionic dissociation as the pH value changes. However, the presence of ionic groups is not necessarily essential, and the polarity of ionic groups does not matter.  
     [0051] The property that solubility or dispersibility in an aqueous liquid decreases as the pH value changes is important for the film-forming polymer from the standpoint of the mechanical strength of the thin film (optical element). Examples of such a material include ionic polymers having ionic groups as mentioned above. The ionic polymer should be highly soluble or dispersible in an aqueous liquid (with or without pH adjustment) and also highly transparent.  
     [0052] The polymer should have both hydrophilic groups and hydrophobic groups in the molecule so that it decreases in solubility or dispersibility in an aqueous solution as the pH value changes. Examples of the hydrophilic groups include carboxyl group (anionic) and amino group (cationic) which are capable of ionization. (These groups are simply referred to as “ionizable groups” hereinafter.) A polymer having carboxyl groups dissolves in an aqueous solution when the pH value is in the alkaline region because the carboxyl groups dissociate. On the other hand, it precipitates out in the acid region because the carboxyl groups do not dissociate any longer.  
     [0053] The hydrophobic groups in the polymer permit the polymer to separate out (in the form of thin film) instantaneously as the pH value changes and hence the dissociated groups become non-ionic. The hydrophobic groups absorb the fine particles to control refractive index and help the polymer to disperse while the optical element is being prepared according to the present invention as mentioned later. The hydrophilic group also includes hydroxyl groups in addition to the ionizable groups.  
     [0054] The polymer having both hydrophobic groups and hydrophilic groups should preferably be one in which the number of hydrophobic groups accounts for 30% to 80% of the total number of hydrophobic groups and hydrophilic groups. The one in which the number of hydrophobic groups is less than 30% of the total number of hydrophobic groups and hydrophilic groups gives rise to a film which is easily soluble and poor in water resistance and strength. The one in which the number of hydrophobic groups is more than 80% of the total number of hydrophobic groups and hydrophilic groups is poor in solubility in an aqueous solution and hence it gives rise to an electrolytic solution which is viscous or turbid with precipitation. It is more desirable that the number of hydrophobic groups should account for 55 to 70% of the total number of hydrophobic groups and hydrophilic groups. The polymer containing hydrophobic groups in such a range forms film efficiently at a low clectrodeposition potential of the order of photoelectromotive force and gives rise to a stable electrolytic solution.  
     [0055] An example of the above-mentioned polymer is a copolymer made up of a polymerizable monomer having hydrophilic groups and a polymerizable monomer having hydrophobic groups.  
     [0056] Examples of the polymerizable monomer having hydrophilic groups include methacrylic acid, acrylic acid, hydroxyethyl methacrylate, acrylamide, maleic anhydride, fumaric acid, propionic acid, itaconic acid, and derivatives thereof, but they are not limited thereto. Of these examples, methacrylic acid and acrylic acid are useful hydrophilic monomers because they contribute to the film-forming efficiency due to pH changes.  
     [0057] Examples of the polymerizable monomer having hydrophobic groups include alkene, styrene, a-methylstyrene, a-ethylstyrene, methyl methacrylate, butyl methacrylate, acryronitrile, vinyl acetate, ethyl acrylate, butyl acrylate, lauryl methacrylate, and derivatives thereof. These examples are not limitative. Of these examples, styrene and c-methylstyrene are useful hydrophobic monomers because they contribute to the hysteresis characteristics for re-dissolution.  
     [0058] A preferred polymer used in preparation of the optical element according to the present invention is a copolymer made up of acrylic acid or methacrylic acid, as the monomer containing hydrophilic groups, and styrene or c-styrene, as the monomer containing hydrophobic groups.  
     [0059] The process for preparing the optical element according to the present invention uses a polymer which is made up of polymerizable monomers each containing hydrophilic groups and hydrophobic groups. This polymer should preferably be a copolymer which contains hydrophilic groups and hydrophobic group in a certain ratio as specified above. There may be more than one kind each of hydrophilic groups and hydrophobic groups.  
     [0060] The functional material used in the present invention include fine particles to control refractive index, fine particles of pigment, dye, and electrically conductive fine particles.  
     [0061] The fine particles to control refractive index are either those of high refractive index which are added to the core layer and those of low refractive index which are added to the cladding layer. The former are exemplified by titanium oxide and zinc oxide and the latter are exemplified by magnesium fluoride.  
     [0062] The above-mentioned fine particles should have a number-average particle diameter of 0.2 to 150 nm, preferably 2 to 20 nm, so that they readily disperse in the electrolytic solution and keep clear the electrodeposited film. With a number-average particle diameter smaller than 0.2 nm, the fine particles are high in production cost and poor in quality uniformity. On the other hand, with a number-average particle diameter larger than 150 nm (which is one-tenth of the wavelength (1.5 μm) used for communications), the fine particles produce adverse effects such as decreased clarity, internal irregular reflection, and internal loss.  
     [0063] For adjustment of refractive index, the above-mentioned functional material may be selected from one kind of film-forming polymer which differs in refractive index from the main film-forming polymer.  
     [0064] According to the present invention, the process for preparing the optical element should work in such a way as to give a thin film in which the content of the functional material changes gradationally in the thickness direction. To achieve the foregoing, it is necessary to change the concentration of the functional material in the electrolytic solution in the vicinity of the optical element preparing substrate (or in the vicinity of the conductive thin film or photosemiconductor thin film, or in the vicinity of a thin film if it has already been formed). One way to meet this requirement is made to flow a secondary electrolytic solution toward the optical element preparing substrate in a primary electrode deposition solution, the former differing from the latter in the concentration of the functional material. If the concentration of the functional material is to be uniform in the in-plane direction of the resulting thin film, it is necessary to keep uniform the concentration of the functional material in the electrolytic solution in the vicinity of the entire film-forming region of the optical element preparing substrate. The foregoing may be achieved by making a flow of the electrolytic solution whose shape conforms to the film-forming region, or by causing the electrolytic solution to flow through small holes evenly arranged over the film-forming region. For example, in the case where a core optical waveguide is to be formed, the foregoing is achieved by flowing the electrolytic solution toward the core-forming region on the optical element preparing substrate through slits or small holes which are arranged in conformity with the core shape. If a voltage is applied to the film-forming region while the electrolytic solution is flowing, the electrolytic solution, which differs in the concentration of the functional material from its surrounding one, comes into contact with the optical element preparing substrate. Thus the resulting electrodeposited thin film has a different concentration of the functional material than it would have if the surrounding electrolytic solution alone were used.  
     [0065] If it is desirable to form a thin film on a previously formed thin film (the former differing from the latter in the concentration of the functional material) as in the case where a core layer is formed subsequently on a cladding layer, it is not necessary to entirely replace the electrolytic solution in the vessel (for example, replacing the solution for the cladding layer with the solution for the core layer). Instead, it is only necessary to flow a second electrolytic solution, which differs from a first one in the concentration of the functional material, toward the film-forming region. In this way it is possible to form a thin film with a different concentration of the functional material on a previously formed thin film. The result is process simplification and cost reduction.  
     [0066] An alternative process is also possible which employs plural electrolytic solutions differing in the concentration of the functional material. In this case the electrolytic solutions are sequentially made to flow toward the optical element preparing substrate so that the concentration of the functional material changes with time in the vicinity of the substrate. The thus formed thin film changes gradationally in the concentration of the functional material. If the electrolytic solution is made to flow in such a way that the concentration of the functional material therein changes continuously, the resulting thin film will contain the functional material in continuously changing concentrations. For example, if plural electrolytic solutions are made to flow in an adequate order with respect to the concentration of the functional material, it would be possible to form a core layer in which the concentration of the functional material is higher at its center. Alternatively, if plural electrolytic solutions are flown continuously such that the concentration of the functional material gradually increases and then a voltage is applied steadily (with the flow of the electrolytic solution suspended), the concentration of the functional material to be electrodeposited decreases. Thus, in this way it is possible to form a core layer in which the concentration of the functional material is higher at its center. (The concentration of the functional material is lower in the previously formed cladding layer than in the core layer.)  
     [0067] An adequate flow rate of the electrolytic solution should be 0.1 to 10 mm/s so that the flow does not damage the deposited film and the concentration of the functional material changes in proportion to the film-forming rate.  
     [0068] The above-mentioned process gives rise to a thin film which is flat and uniform in thickness regardless of the changing concentration of the functional material. Therefore, the thin film permits transfer easily and has few blurs and flaws.  
     [0069] According to the present invention, the process for preparation of an optical element may be modified in the way of changing the concentration of the functional material in the electrolytic solution in the vicinity of the optical element preparing substrate, so that the resulting thin film contains the functional material whose concentration changes gradationally in the in-plane direction of the thin film. The foregoing is achieved by causing the electrolytic solution to flow in such a way that the concentration of the functional material changes in the in-plane direction. To be concrete, such a flow is made by directing an electrolytic solution, which differs in the concentration of the functional material from its surrounding electrolytic solution, toward a specific part of the film-forming region on the optical element preparing substrate. The flow made in this manner impinges upon the substrate and then spreads along the substrate surface and eventually diffuses into its surrounding electrolytic solution. Thus the concentration of the functional material in the electrolytic solution in the vicinity of the substrate changes in the direction in which the electrolytic solution flows along the substrate. It is also possible to produce a thin film in which the content of the functional material changes in the in-plane direction if plural electrolytic solutions, which differ in the concentration of the functional material from one another, are directed toward the optical clement preparing substrate from plural outlets.  
     [0070] It is also possible to form an optical element in which the concentration of the functional material differs three-dimensionally if the above-mentioned methods for gradation in the thickness direction and the in-plane direction of the functional material are combined with each other.  
     [0071] A detailed mention is made below of the process and apparatus for preparing the optical element of the present invention.  
     [0072]FIG. 3 is a schematic diagram showing an example of the apparatus for preparing the optical element by the photovoltaic electrodeposition process.  
     [0073] There is shown a vessel  80  holding an electrolytic solution  20 , in which is placed an optical element preparing substrate  10  (formed of a transparent insulating substrate  12  and a transparent conductive film  14  and a photosemiconductor thin film  16  sequentially laminated thereon) such that at least the photosemiconductor thin film  16  comes into contact with the electrolytic solution  20 . Above the electrolytic solution is an exposure system (of projection type) has a first image-forming optical lens  73 , a photomask  71 , a second image-forming optical lens  72 , and a light source (not shown) which are arranged from the side of the vessel  80 . The light source emits a beam of light  70  which passes through the second image-forming lens  72  and forms an image at the photomask  71 . The photomask  71  produces a patterned beam of light which passes through the first image-forming lens  73  and forms an image on the surface of the photosemiconductor thin film.  
     [0074] In FIG. 3, there is also shown a plate  100  which permits another electrolytic solution which differs in the concentration of the functional material from the electrolytic solution  20  to flow at a controlled flow rate. There are shown a flow outlet  102  formed in the plate  100 , a container  106  to hold the electrolytic solution, and a pump  104  to steadily feed under pressure the electrolytic solution from the container  106 . These components constitute the flow-forming mechanism. The electrolytic solution is discharged from the flow outlet  102  at an-adequate flow rate which is controlled by the pump. The pump, which causes a flow as mentioned above, may be any commercial one which produces the desired flow rate even though it sometimes suffers pulsation. The flow outlet  102  of the plate  100  discharges an electrolytic solution which differs in the concentration of the functional material from the electrolytic solution  20 , so that the concentration of the functional material changes in the electrolytic solution in the vicinity of the optical element preparing substrate. The flow outlet should be positioned such that it is a certain distance away from the position where the thin film is formed on the optical element preparing substrate. The distance should be about  0 . 2  to  10  mm in order to prevent the flow outlet from coming into contact with the substrate and in order to ensure a uniform flow rate.  
     [0075] In this embodiment, the plate  100  functions also as a counter electrode  91 , which is electrically connected to a voltage application unit  90  such as a potentiostat that applies a bias voltage. The voltage application unit  90  is connected further to a reference electrode  92  such as a saturated calomel electrode, and is constituted in a tripolar manner. The voltage application unit  90  is connected further to the conductive film  14  of the substrate on which the thin film is formed. Needless to say, the counter electrode may be installed separately in an adequate position in the vessel  80  without it functioning also as the plate. Incidentally, application of a bias voltage from the voltage application unit is not necessary and hence the voltage application unit itself is not necessary in the case where photoelectromotive force is strong enough to change the hydrogen ion concentration required for film deposition. However, it is desirable to install the voltage application unit so that the process works satisfactorily for any film-forming substrate under any electrodeposition condition.  
     [0076] The method of forming a flow of the electrolytic solution is disclosed in the specification of Japanese Unexamined Patent Application No. 2001-353725 filed by the present applicant. This method can be used in the present invention.  
     [0077] The preparation of the optical element is illustrated below by way of example. In this example, an optical waveguide is prepared by using the photovoltaic electrodeposition apparatus as shown in FIG. 3. This optical waveguide is made up of a cladding layer (lower), which is laminated on the entire surface of a substrate, a core layer, and a cladding layer (upper), which is laminated on the entire surface of a substrate. The core layer contains a functional material (fine particles to control refractive index) such that its concentration changes in the thickness direction.  
     [0078] The process starts with filling the vessel  80  with the electrolytic solution  20  from which the lower cladding layer is formed. The lower cladding layer is formed on the entire surface of the substrate by application of a voltage across the voltage application unit  90  and the counter electrode  91  (the plate  100 ), without irradiation with light. This voltage is higher than the Schottky barrier of the photosemiconductor thin film on the substrate on which the optical element preparing substrate.  
     [0079] Then, the photomask  71  for the core layer is set as shown in FIG. 3. The container  106  to hold the electrolytic solution is filled with the electrolytic solution for the lower core layer, and the electrolytic solution is allowed to flow out of the outlet  102  at a controlled flow rate. Subsequently, the photosemiconductor thin film  16  is exposed to light by the exposure unit in such a way that the light forms an image in the selected region on the surface thereof. Simultaneously with exposure, a bias voltage is applied by the voltage application unit  90 . The bias voltage should be high enough so that the sum of the bias voltage and the photo-electromotive force generated in the photosemiconductor thin film exceeds the threshold voltage necessary for film deposition. Application of the bias voltage greatly changes the hydrogen ion concentration of the electrolytic solution in the vicinity of the selected region which has been exposed. Since the above-mentioned electrolytic solution contains an electrodepositing material which decreases in solubility or dispersibility in an aqueous solution as the hydrogen ion concentration changes, an electrodeposition film (lower core layer) containing fine particles to control refractive index separates out on the surface of the lower cladding layer as the result of decrease in solubility in the electrolytic solution near the selected region. After that, irradiation with light and voltage application are suspended. Subsequently, the electrolytic solution for the core layer in the container  106  to hold the electrolytic solution is replaced by the electrolytic solution for the upper core layer. The latter solution differs from the former solution in the concentration of fine particles to control refractive index. The replaced electrolytic solution is allowed to flow out of the outlet  102  and irradiation with light and application of bias voltage are carried out in the same way as mentioned above, so that a thin film (upper core layer) is formed. Thus there is formed the core layer in which the content of fine particles to control refractive index changes gradationally in the thickness direction. Incidentally, in the case where the liquid flow forming mechanism is so constructed as to continuously flow electrolytic solutions differing in the concentration of the functional material, it is not necessary to suspend irradiation with light and replace the electrolytic solution for the upper core in the container to hold the electrolytic solution as mentioned above after the lower core layer has been formed. Instead, all that is necessary is to permit the electrolytic solution for the upper core to flow continuously.  
     [0080] Then, the electrolytic solution in the electrolytic vessel  80  is replaced with the electrolytic solution for the upper cladding layer. The upper cladding layer is formed, without irradiation with light, over the entire surface in the same way as the lower cladding layer.  
     [0081] A mention is made below of another apparatus for preparing the optical element by photovoltaic electrodeposition. FIG. 4 is a schematic diagram showing another apparatus for preparing the optical element which is the same as that shown in FIG. 3 except that it employs an exposure unit of proximity exposure type. The apparatus shown in FIG. 4 is designed such that the photomask is placed near the photosemiconductor thin film (or in contact with the insulating substrate). Therefore, it gives a highly resolved pattern without resorting to an exposure system having a focusing optical system and reflecting optical system (mirror) unlike the apparatus shown in FIG. 3. The exposure unit  75  may be that of parallel light type or contact type. The light source for irradiation may be a uniformly emitting Hg—Xe lamp. In this case, it is desirable that the insulating substrate be thinner than 0.2 mm so that the diffraction of light is minimized.  
     [0082] For preparation of the optical element, this apparatus is operated in the same way as that shown in FIG. 3. In addition, photovoltaic electrodeposition may be performed over the entire surface of the optical element preparing substrate by irradiation with light in order to form the lower and upper cladding layers.  
     [0083]FIG. 5 is a schematic diagram showing another apparatus for preparing the optical element. This apparatus is the same as that shown in FIG. 3 except that it employs a laser writing unit of scanning type as the exposure unit. In FIG. 5, there is shown the laser writing unit  78  which emits He—Cd laser or the like.  
     [0084] In addition, FIG. 6 is a schematic diagram showing another apparatus for preparing the optical element by electrodeposition. This apparatus is the same as those shown in FIGS.  3  to  5  except that it does not have the exposure unit.  
     [0085] According to the present invention, the process for preparation of the optical element should preferably be followed by a step of heat treatment after all the optical elements have been formed. This heat treatment reduces the transmission loss of the finished optical element.  
     [0086] Incidentally, “all the optical elements” means one or all optical elements in the case where one or more optical elements (for example, more than one core layer and more than one cladding layer) are formed. “After all the optical elements have been formed” means that “after the optical element has been formed by deposition” in the case where the optical element is formed on the optical element-preparing substrate by (photo)-electrodeposition and the thus obtained optical element is used as such as the optical element. However, it is usually understood that the above-mentioned heat treatment follows a drying step to remove water from the optical element. “After . . . ” also means “after the optical element has been transferred to the optical element substrate” in the case where the process for preparation of the optical element involves transfer to the optical element substrate.  
     [0087] The optical element formed by (photo)-electrodeposition usually contains a trace amount of water caught in the film. Therefore, the optical element formed by deposition is dried to remove water from the film. Removal of water results in film defects (such as pinholes) in the optical element. This is a possible cause that increases the transmission loss of the optical element. It is expected that the above-mentioned heat treatment repairs such defects and smoothens the surface of the optical element and reduces the surface roughness of the core-clad interface, thereby decreasing the transmission loss.  
     [0088] The above-mentioned heat treatment is not specifically restricted in temperature and duration so long as it reduces the transmission loss of the optical element. The heating temperature may be determined in consideration of the glass transition temperature and flow point of the film-forming polymer.  
     [0089] For efficient heat treatment, the heating temperature should preferably be higher than the flow point of the polymer. “Plow point” means that defined in “Method for testing polymers” (Lectures on Polymer Technology, vol. 14, pp. 364 to 369, compiled by Institute of Polymer Science, issued by Chijin Shokan, 1963). The polymer used in the present invention should be one which has a flow point in the range of 50 to 200° C., preferably 80 to 150° C., and more preferably 110 to 130° C.  
     [0090] The heating temperature may be lowered or the heating time may be reduced if pressure is applied to the optical element at the time of heat treatment.  
     [0091] The above-mentioned polymer for electrodeposition should be one which has a refractive index ranging from 1.45 to 1.6 and is transparent in its deposited state. It suits the optical element because it does not absorb the light with a wavelength of 0.8 to 1.6 μm which is used for the optical element.  
     [0092] Moreover, the polymer after dissolution in water to give the electrolytic solution does not absorb UV light; therefore, it permits the photosemiconductor to be irradiated with UV light for patterning through the electrolytic solution. In addition, it is capable of electrodeposition with a low potential (5V or below). This facilitates forming the electrodeposition pattern with the photoelectromotive force generated by the photosemiconductor.  
     EXAMPLES  
     [0093] The present invention will be described in more detail with reference to the following examples which are not intended to restrict the scope thereof.  
     Example 1  
     [0094] This example demonstrates the preparation of an optical waveguide of clad-core-clad structure. (The cladding layer is formed by application of a voltage exceeding the Schottky barrier of the photosemiconductor instead of irradiation with light.)  
     [0095] (1) Preparation of Electrolytic Solution for Clad  
     [0096] In 100 g of pure water was dispersed 5 g of styrene-acrylic acid copolymer (having a molecular weight of 13,000, a molar ratio of 65:35 for styrene and acrylic acid, and an acid value of 150). [This copolymer will be referred to as “electrodepositable polymer A” hereinafter.] To the resulting dispersion was added dimethylaminoethanol in a ratio of 180 ml/l. (This reagent is a water-soluble liquid having a boiling point no lower than 110° C. and a vapor pressure no higher than 100 mmHg.) The resulting solution was given tetramethylammoniumhydroxide and ammonium chloride so that it had pH 7.8 and a conductivity of 8 mS/cm. The thus obtained solution was used as the electrolytic solution from which the cladding layer was formed.  
     [0097] (2) Preparation of Electrolytic Solution 1 for Cure  
     [0098] In 100 g of pure water were dispersed 5 g of electrodepositable polymer A (mentioned above) and 5 g of titanium oxide having a particle diameter of 2 nm. To the resulting dispersion was added dimethylaminoethanol in a ratio of 180 mmol/l. The resulting solution was given tetramethylammoniumhydroxide and ammonium-chloride so that it had pH 7.8 and a conductivity of 8 mS/cm. The thus obtained solution was used as an electrolytic solution 1 from which the core was formed.  
     [0099] (3) Preparation of Electrolytic Solution 2 for Core  
     [0100] The same procedure to prepare the electrolytic solution 1 for the core was repeated except that the amount of titanium oxide was increased to 25 g to prepare an electrolytic solution 2 for the core.  
     [0101] (4) Preparation of Optical Element Preparing Substrate  
     [0102] An alkali-free #7059 glass substrate (0.5 mm thick) underwent sputtering for coating with a transparent ITO conductive film (100 nm thick) and further underwent RF sputtering for coating with TiO 2  film (200 nm thick).  
     [0103] ( 5 ) Preparation of Optical Waveguide  
     [0104] An apparatus for photovoltaic electrodeposition was used which has a mechanism to flow the electrolytic solution as shown in FIG. 4. The plate has a slit-like outlet corresponding to the core to be formed. The plate was used as the counter electrode (platinum) and a TiO 2  electrode was used as the working electrode for the saturated calomel electrode. The photomask  71  has an opening corresponding to the core to be formed. The exposure unit is that of proximity exposure type (made by Yamashita Denso Co., Ltd.). The outlet in the plate is 1 mm away from the substrate on which the core is formed.  
     [0105] First, the electrodeposition vessel was filled with the electrolytic solution for the cladding layer (mentioned above). A bias voltage of 3.5 V was applied for 10 seconds to the working electrode, without the exposure unit emitting light. Thus there was formed the lower cladding layer (5 μm thick) over the entire TiO 2  surface.  
     [0106] With the optical element preparing substrate remaining in the electrodeposition vessel, the electrolytic solution 2 for the core started to flow at a flow rate of 0.1 mm/s toward the core forming position from the slit-like outlet in the plate. After 10 seconds, with a bias voltage (1.8 V) applied to the working electrode, the exposure unit was activated to emit UV light (365 nm in wavelength and 50 mW/cm 2  in intensity) for 15 seconds. There was formed a lower core layer (5 μm thick and 10 μm wide) only on that region of the cladding layer which was irradiated with UV light.  
     [0107] Irradiation with UV light and application of bias voltage were suspended. The electrolytic solution was replaced with the electrolytic solution 1 for the core. The electrolytic solution 1 started to flow at a flow rate of 0.1 mm/s toward the core forming position from the slit-like outlet in the plate. After 10 seconds, with a bias voltage (1.8 V) applied to the working electrode, the exposure unit was activated to emit UV light (365 nm in wavelength and 50 mW/cm 2  in intensity) for 15 seconds. There was formed an upper core layer (5 μm thick and 10 μm wide) on the lower core layer.  
     [0108] The electrolytic solution in the vessel was replaced with the electrolytic solution for the clad (mentioned in (1) above). Without irradiation with light from the exposure unit, a bias voltage of 4 V was applied to the working electrode for 35 seconds. There was formed the upper cladding layer (8 μm thick) over the entire surface.  
     [0109] The optical element preparing substrate was taken out of the electrodeposition vessel and then washed by dipping in pure water for 3 minutes so as to remove a trace amount of residual salt from the film. Washing was followed by drying with clean air. Thus the substrate for optical waveguide was completed.  
     [0110] The thus obtained optical waveguide was cut to a length of 50 mm by using a dicing saw. The sample was tested for insertion loss. The transmission loss of the sample was about 5 dB for a wavelength of 0.85 μm.  
     Example 2  
     [0111] The optical waveguide prepared in Example 1 underwent heat treatment at 140° C. for 3 minutes. The heat-treated sample was tested for transmission loss in the same way as in Example 1. The result indicated that the heat treatment reduced transmission loss by about 1.5 dB. A probable reason for this is that the heat treatment removes a few pinholes remaining in the film of the optical waveguide..  
     [0112] The optical waveguide constructed as mentioned above produces a profound effect of confining light even though its cladding layer is thin in the thickness direction. This leads to an improvement in transmission loss over the conventional optical waveguide of simple step-index type.  
     Example 3  
     [0113] (1) Preparation of Electrolytic Solution for Clad  
     [0114] In 100 g of pure water was dispersed 5 g of styrene-acrylic acid copolymer (having a molar ratio of 20:80 for styrene and acrylic acid, an acid value of 160, and a molecular weight of 12,000). [This copolymer will be referred to as “electrodepositable polymer B” hereinafter.] To the resulting dispersion was added dimethylaminoethanol in a ratio of 180 ml/l. The resulting solution was given tetramethylammoniumhydroxide and ammonium chloride so that it had pH 7.8 and a conductivity of 8 mS/cm. The thus obtained solution was used as the electrolytic solution from which the cladding layer was formed.  
     [0115] (2) Preparation of Electrolytic Solution 1 for Core  
     [0116] In 100 g of pure water were dispersed 5 g of electrodepositable polymer A (used in Example 1) and 5 g of electrodepositable polymer B (mentioned above). To the resulting dispersion was added dimethylaminoethanol in a ratio of 180 mmol/l. The resulting solution was given tetramethylammoniumhydroxide and ammonium chloride so that it had pH 7.8 and a conductivity of 8 mS/cm. The thus obtained solution was used as an electrolytic solution 1 from which the core layer was formed.  
     [0117] (3) Preparation of Electrolytic Solution 2 for Core  
     [0118] The same procedure to prepare the electrolytic solution 1 for the core was repeated except that the amount of electrodepositable polymer B was increased to 25 g to prepare an electrolytic solution  2  for the core.  
     [0119] (4) Preparation of Optical Element Preparing Substrate  
     [0120] An alkali-free #7059 glass substrate (0.5 mm thick) underwent sputtering for coating with a transparent ITO conductive film (100 nm thick) and further underwent RF sputtering for coating with TiO 2  film (200 nm thick).  
     [0121] (5) Preparation of Optical Waveguide  
     [0122] An apparatus for photovoltaic electrodeposition was used which has a mechanism to flow the electrolytic solution which-is the same one as used in Example 1.  
     [0123] First, the electrodeposition vessel was filled with the electrolytic solution for the cladding layer (mentioned in (1) above). A bias voltage of 3.5 V was applied for 10 seconds to the working electrode, without the exposure unit emitting light. Thus there was formed the lower cladding layer (5 μm thick) over the entire TiO 2  surface.  
     [0124] With the optical element preparing substrate remaining in the electrodeposition vessel, the electrolytic solution 2 for the core started to flow at a flow rate of 0.1 mm/s toward the core forming position from the slit-like outlet in the plate. After 10 seconds, with a bias voltage (1.8 V) applied to the working electrode, the exposure unit was activated to emit UV light (365 nm in wavelength and 50 mW/cm 2  in intensity) for 15 seconds. There was formed a lower core layer (5 μm thick and 10 μm wide) only on that region of the cladding layer which was irradiated with UV light.  
     [0125] Irradiation with UV light and application of bias voltage were suspended. The electrolytic solution was replaced with the electrolytic solution 1 for the core (mentioned in (2) above). The electrolytic solution 1 started to flow at a flow rate of 0.1 mm/s toward the core forming position from the slit-like outlet in the plate. After 10 seconds, with a bias voltage (1.8 V) applied to the working electrode, the exposure unit was activated to emit UV light (365 nm in wavelength and 50 mW/cm 2  in intensity) for 15 seconds. There was formed an upper core layer (5 μm thick and 10 μm wide) only on that region of the TiO 2  surface which was irradiated with UV light.  
     [0126] The electrolytic solution in the vessel was replaced with the electrolytic solution for the clad (mentioned in (1) above). Without irradiation with light from the exposure unit, a bias voltage of 4 V was applied to the working electrode for 35 seconds. There was formed the upper cladding layer (8 μm thick) over the entire surface.  
     [0127] The optical element preparing substrate was taken out of the electrodeposition vessel and then washed by dipping in pure water for 3 minutes so as to remove a trace amount of residual salt from the film. Washing was followed by drying with clean air. Thus the substrate for optical waveguide was completed.  
     [0128] The thus obtained optical waveguide was cut to a length of 50 mm by use of a dicing saw. The sample was tested for insertion loss. The transmission loss of the sample was about 4.5 dB for a wavelength of 0.85 μm.  
     Example 4  
     [0129] The optical waveguide prepared in Example 3 underwent heat treatment at 140° C. for 3 minutes. The heat-treated sample was tested for transmission loss in the same way as in Example 3. The result indicated that the heat treatment reduces transmission loss by about 1.5 dB.  
     [0130] The optical waveguide constructed as mentioned above produces a profound effect of confining light even though its cladding layer is thin in the thickness direction. This leads to an improvement in transmission loss over the conventional optical waveguide of simple step-index type.  
     Example 5  
     [0131] This example demonstrates the preparation of an optical element preparing substrate and a circular thin film (10 mm in diameter) formed thereon.  
     [0132] The optical element preparing substrate is the same one as used in Example 1. The optical element was prepared by use of an apparatus provided with the scanning laser exposure unit (He—Cd laser) as shown in FIG. 5. This exposure unit has an optical system which spirally scans the entire surface of the substrate at a rate of 0.05 mm/s with an He—Cd laser beam focused to a spot diameter of 100 μm. The electrolytic solution flowed from a round outlet (1 mm in diameter) formed in the plate. The outlet is 1 mm away from the substrate on which the thin film is formed.  
     [0133] The electrodeposition vessel was filled with the electrolytic solution for the cladding layer (which is the same one as used in Example 1). The electrolytic solution for the cladding layer (which is the same one as used in Example 1) was made to flow at a rate of 0.1 mm/s from the outlet toward the center of the round area of the substrate on which a round thin film is formed. After 10 seconds, the round area was spirally scanned (around the center) with an He—Cd laser from a position 10 mm away from the center. Thus there was formed a round thin film, 10 mm in diameter and 1 μm thick. (See FIG. 2.) This thin film has refractive indices of 1.7 at its center and 1.5 at its periphery. With the refractive index continuously changing from the center to the periphery, this thin film is expected to find use as a lens.  
     Example 6  
     [0134] The sample obtained in Example 5 was passed through two rolls (roll surface temperature: 170° C.; linear pressure: 300 g/cm; and linear speed: 20 mm/s) under pressure with heating under the following conditions, with a separately prepared polyethylene film (0.2 mm thick) placed on the round thin film. This rolling step made it possible to form on the polyethylene film a round polymeric thin film which has a distribution of refractive index. The round thin film formed in Example  5  was so flat that it was easily transferred without deformation.  
     [0135] The process according to the present invention permits easy preparation of an optical element with a thin film which contains a functional material with gradationally changing concentrations. The change of concentration is not stepwise as in the conventional technology but is moderate or continuous. In addition, the change of concentration takes place not only in the thickness direction but also in the in-plane direction of the thin film. Combination of changing concentrations in two directions gives a three-dimensional gradation. The thin film formed by deposition is flat (with a uniform thickness) despite the changing concentration of the functional material, and hence it can be transferred easily without appreciable blurring and defect. Moreover, the distribution of the functional material is more accurate than that achieved by the conventional technology which employs a developing sleeve to make inorganic conductive fine particles to unevenly distribute in the resin (as disclosed in Japanese Published Unexamined Patent Applications No. Hei 8-160737).  
     [0136] The entire disclosure of Japanese Patent Application No. 2002-179857 filed on Jun. 20, 2002 including specification, claims, drawings and abstract is incorporated herein by reference in its entirety.