Abstract:
An optical modulation device includes following elements. Bus lines are extended in a first direction, wherein each bus line supplies a respective voltage. A first plate includes first lower electrodes extended in a second direction crossing the first direction, wherein a rightmost first lower electrode is connected to a first bus line of the bus lines and a leftmost first lower electrode is connected to a second bus line of the bus lines. A second plate faces the first plate, and includes at least one upper electrode. A liquid crystal layer is positioned between the first plate and the second plate and includes liquid crystal molecules. A first resistor string includes first resistors, wherein each resistor positioned between two adjacent first lower electrodes connects electrically the two adjacent first lower electrodes, causing a voltage drop between the two adjacent first electrodes.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority under 35 U.S.C. §119 to Korean Patent Application No. 10-2015-0018149 filed on Feb. 5, 2015 in the Korean Intellectual Property Office, the disclosure of which i8s incorporated herein by reference. 
       TECHNICAL FIELD 
       [0002]    The present invention relates to an optical modulation device including a liquid crystal, a driving method thereof, and an optical device using the same. 
       DISCUSSION OF THE RELATED ART 
       [0003]    Recently, an optical device using an optical modulation device which modulates optical characteristics has been actively developed. For example, an optical display device which may display a three dimensional (3D) image has drawn much attention and an optical modulation device for separating an image at different timings and transmitting the separated images to enable a viewer to recognize an image as a three-dimensional image is needed. As the optical modulation device which may be used in an autostereoscopic image display device, there are a lens, a prism, and the like which changes a path of light of an image of a display device and transmits the light at a desired viewpoint. 
         [0004]    As such, to change a direction of incident light, a diffraction of light by phase modulation of light may be used. 
         [0005]    When polarized light transmits the optical modulation device such as a phase delayer, a polarization state is changed. For example, when circularly polarized light is incident on a half-wavelength plate, a rotating direction of the circularly polarized light is changed reversely and thus light is emitted. For example, when light which is circularly polarized to the right transmits the half-wavelength plate, light which is circularly polarized to the left is emitted. In this case, a phase of the circularly polarized light which is emitted depending on an angle of an optical axis of the half-wavelength plate, that is, a slow axis is changed. In detail, when the optical axis of the half-wavelength plate rotates as much as φ on an in-plane, the phase of the output light is changed as much as 2φ. Therefore, when the optical axis of the half-wavelength plate rotates as much as 180° (it radian) in an x-axis direction on a space, the emitted light is subjected to a phase modulation or a phase change of 360° (2π radian) in the x-axis direction and may then be emitted. As such, when the optical modulation device changes the phase of light from 0 to 2π depending on a position, a diffraction lattice or a prism which may change or bend the direction of transmitted light ma be implemented. 
         [0006]    To control the optical axis depending on the position of the optical modulation device such as the half-wavelength plate, a liquid crystal may be used. The optical modulation device implemented as the phase delayer using the liquid crystal may rotate major axes of aligned liquid crystal molecules by applying an electric field to a liquid crystal layer to generate other phase modulations depending on the position. The phase of light which is emitted by transmitting the optical modulation device may be determined depending on a direction of the major axis of the aligned liquid crystal, that is, an azimuthal angle. 
       SUMMARY 
       [0007]    According to an exemplary embodiment of the present invention, an optical modulation device includes following elements. Bus lines are extended in a first direction, wherein each bus line supplies a respective voltage. A first plate includes first lower electrodes extended in a second direction crossing the first direction, wherein a rightmost first lower electrode is connected to a first bus line of the bus lines and a leftmost first lower electrode is connected to a second bus line of the bus lines. A second plate faces the first plate, and includes at least one upper electrode. A liquid crystal layer is positioned between the first plate and the second plate and includes liquid crystal molecules. A first resistor string includes first resistors, wherein each resistor positioned between two adjacent first lower electrodes connects electrically the two adjacent first lower electrodes, causing a voltage drop between the two adjacent first electrodes. 
         [0008]    According to an exemplary embodiment of the present invention, an optical device includes the following elements. An optical modulation device includes spiral zones, wherein each spiral zone includes a plurality of lower electrodes. Bus lines are connected to the lower electrodes in a predetermined manner. A voltage control device generates voltages applied to the optical modulation device through the bus lines. A number of lower electrodes of each zone is different from a number of lower electrodes of a neighboring spiral zone. 
         [0009]    According to an exemplary embodiment of the present invention, a driving method of an optical modulation device includes the following steps. A first voltage is received through a first bus line connected to a leftmost first lower electrode of first lower electrodes. A second voltage is received through a second bus line connected to a rightmost first lower electrode of the first lower electrodes. A voltage difference between the first voltage and the second voltage is divided through first resistors positioned between the first lower electrodes. The divided voltage is applied to the first lower electrodes. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    These and other features of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the accompanying drawings of which: 
           [0011]      FIG. 1  is a perspective view of an optical modulation device according to an exemplary embodiment of the present invention; 
           [0012]      FIG. 2  is a plan view illustrating an alignment direction in a first plate and a second plate included in the optical modulation device of  FIG. 1  according to an exemplary embodiment of the present invention; 
           [0013]      FIG. 3  is a diagram illustrating a process of bonding the first plate and the second plate of  FIG. 2  according to an exemplary embodiment of the present invention; 
           [0014]      FIG. 4  is a perspective view illustrating an alignment of liquid crystal molecules when a voltage difference is not applied to the first plate and the second plate of the optical modulation device of  FIG. 1  according to an exemplary embodiment of the present invention; 
           [0015]      FIGS. 5A to 5C  are cross-sectional views of the optical modulation device of  FIG. 4  taken along lines I, II, and III according to an exemplary embodiment of the present invention; 
           [0016]      FIG. 6  is a perspective view illustrating the alignment of the liquid crystal molecules when the voltage difference is applied to the first plate and the second plate of the optical modulation device of  FIG. 1  according to an exemplary embodiment of the present invention; 
           [0017]      FIG. 7  is a cross-sectional view of the optical modulation device of  FIG. 6  taken along lines I, II, and III according to an exemplary embodiment of the present invention; 
           [0018]      FIG. 8  is a perspective view of the optical modulation device according to the exemplary embodiment; 
           [0019]      FIG. 9  is a timing diagram of a driving signal of an optical modulation device according to an exemplary embodiment of the present invention; 
           [0020]      FIGS. 10A and 10B  are cross-sectional views taken along line IV of  FIG. 8  illustrating the alignment of liquid crystal molecules before a voltage difference is applied to the first plate and the second plate of the optical modulation device according to the exemplary embodiment and after a driving signal of step  1  is applied; 
           [0021]      FIG. 11  is a cross-sectional view taken along the line V of  FIG. 8  illustrating a stabilized alignment of the liquid crystal molecules after the driving signal of the step  1  is applied to the optical modulation device according to an exemplary embodiment and is a graph illustrating a phase change of light passing through the liquid crystal molecules; 
           [0022]      FIG. 12  is a diagram illustrating a stabilized alignment of the liquid crystal molecules after the driving signal of the step  1  is applied to an optical modulation device according to an exemplary embodiment; 
           [0023]      FIG. 13  is a cross-sectional view taken along the line IV of  FIG. 8  and a cross-sectional views taken along the line V as a cross-sectional view illustrating the alignment of the liquid crystal molecules before the voltage difference is applied to the first plate and the second plate of the optical modulation device according to an exemplary embodiment; 
           [0024]      FIG. 14  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules when the driving signal of the step  1  is applied to the optical modulation device according to an exemplary embodiment; 
           [0025]      FIG. 15  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules before being stabilized, after the driving signal of the step  1  is applied to the optical modulation device according to an exemplary embodiment; 
           [0026]      FIG. 16  is a cross-sectional view taken along the line IV of  FIG. 8  and is a cross-sectional view taken along the line V as a cross-sectional view illustrating the alignment of the stabilized liquid crystal molecules after the driving signal of the step  1  is applied to the optical modulation device according to an exemplary embodiment; 
           [0027]      FIG. 17  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules before the voltage difference is applied to the first plate and the second plate of the optical modulation device according to an exemplary embodiment and after the driving signals of first to third steps, respectively, are applied; 
           [0028]      FIGS. 18 and 19  are cross-sectional views taken along the line of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules in which the alignment is stabilized, after the driving signals of the first to third steps are sequentially applied to the optical modulation device according to an exemplary embodiment; 
           [0029]      FIG. 20  is a diagram illustrating a phase change depending on a position of a lens which may be implemented using the optical modulation device according to an exemplary embodiment; 
           [0030]      FIGS. 21 and 22  each are diagrams illustrating a structure schematically illustrating a stereoscopic optical device as an example of an optical device using the optical modulation device according to an exemplary embodiment and a method for displaying a 2D image and a 3D image; 
           [0031]      FIG. 23  is a diagram illustrating a case in which a resistor string for voltage division is formed in the optical modulation device according to an exemplary embodiment; 
           [0032]      FIG. 24  is a diagram illustrating a case of performing RC modeling on a spiral zone of  FIG. 23 ; 
           [0033]      FIG. 25  is a spice simulation graph illustrating a voltage applied to an electrode of  FIG. 24 ; and 
           [0034]      FIG. 26  is a diagram illustrating a case in which a resistor string is formed in a voltage control device controlling a voltage applied to the optical modulation device according to an exemplary embodiment. 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0035]    Exemplary embodiments of the present invention will be described below in detail with reference to the accompanying drawings. However, the present invention may be embodied in different forms and should not be construed as limited to the embodiments set forth herein. In the drawings, the thickness of layers and regions may be exaggerated for clarity. It will also be understood that when an element is referred to as being “on” another element or substrate, it may be directly on the other element or substrate, or intervening layers may also be present. It will also be understood that when an element is referred to as being “coupled to” or “connected to” another element, it may be directly coupled to or connected to the other element, or intervening elements may also be present. Like reference numerals may refer to the like elements throughout the specification and drawings. 
         [0036]    An optical modulation device according to an exemplary embodiment will be described with reference to  FIGS. 1 to 3 . 
         [0037]      FIG. 1  is a perspective view of an optical modulation device according to an exemplary embodiment,  FIG. 2  is a plan view illustrating an alignment direction in a first plate and a second plate included in the optical modulation device of  FIG. 1 , and 
         [0038]      FIG. 3  is a diagram illustrating a process of bonding the first plate and the second plate of  FIG. 2 . 
         [0039]    Referring to  FIG. 1 , an optical modulation device  1  according to an exemplary embodiment includes a first plate  100  and a second plate  200  which face each other and a liquid crystal layer  3  positioned therebetween. 
         [0040]    The first plate  100  may include a first substrate  110  and a plurality of lower electrodes  191 . The first substrate  110  may be made of glass, plastic, etc. The first substrate  110  may be rigid or flexible and may be flat or at least partially bent. 
         [0041]    The lower electrodes  191  are positioned on the first substrate  110 . The lower electrodes  191  may include a conductive material or transparent conductive materials. For example, the lower electrodes  191  may include indium tin oxide (ITO), indium zinc oxide (IZO), metal, or the like. The lower electrodes  191  may be applied with a voltage from a voltage applying configuration (not illustrated). For example, each lower electrode may be applied with different voltages. 
         [0042]    The plurality of lower electrodes  191  may be arranged in a predetermined direction, for example, an x-axis direction and each lower electrode  191  may extend long in a vertical direction to the arrangement direction, for example, a y-axis direction. 
         [0043]    A width of a space G between the adjacent lower electrodes  191  may be variously controlled depending on a design condition of the optical modulation device. A ratio of the width of the lower electrode  191  and the width of the space G adjacent thereto may be approximately N:1 (N is a real number which is equal to or more than 1). 
         [0044]    The second plate  200  may include a second substrate  210  and an upper electrode. The second substrate  210  may be made of glass, plastic, etc. The second substrate  210  may be rigid or flexible and may be flat or at least partially bent. 
         [0045]    The upper electrode  290  is formed on the second substrate  210 . The upper electrode  290  may include a conductive material or transparent conductive materials. For example, the upper electrode  290  may include ITO, IZO, metal, or the like. The upper electrode  290  may be applied with a voltage from a voltage applying configuration (not illustrated). The upper electrode  290  may be applied with a ground voltage. In an exemplary embodiment, various voltages other than the ground voltage may apply to the upper electrode  290 . The upper electrode  290  may be formed on the second substrate  210  as a whole body. In an exemplary embodiment, the upper electrode  290  may be patterned to include a plurality of spaced portions. 
         [0046]    The liquid crystal layer  3  includes a plurality of liquid crystal molecules  31 . The liquid crystal molecules  31  may have a negative dielectric anisotropy to be aligned in a transverse direction to an electric field generated in the liquid crystal layer  3 . The liquid crystal molecules  31  may be aligned in approximately a vertical direction to the second plate  200  and the first plate  100  in the state in which an electric field is not generated in the liquid crystal layer  3 . In an exemplary embodiment, the liquid crystal molecules  31  may pre-tilted in a specific direction. The liquid crystal molecule  31  may be a nematic liquid crystal molecule. 
         [0047]    A height d of a cell gap of the liquid crystal layer  3  may substantially satisfy the Equation 1 for light having a specific wavelength  2 . As a result, the optical modulation device  1  according to an exemplary embodiment may serve as approximately a half-wavelength plate and may be used as a diffraction lattice, a lens, or the like. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       λ 
                       2 
                     
                     × 
                     1.3 
                   
                   ≥ 
                   
                     Δ 
                      
                     
                         
                     
                      
                     nd 
                   
                   ≥ 
                   
                     λ 
                     2 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
         [0048]    In the above Equation 1, Δnd is a phase delay value of light transmitting the liquid crystal layer  3 . 
         [0049]    An inner surface of the first plate  100  is provided with a first aligner  11  and an inner surface of the second plate  200  is provided with a second aligner  21 . The first aligner  11  and the second aligner  21  may be a vertical alignment layer and may have an alignment force by various methods such as a rubbing process and a photo alignment process to determine a pre-tilt direction of the liquid crystal molecules  31  which are close to the first plate  100  and the second plate  200 . In the case of the rubbing process, the vertical alignment layer may be an organic vertical alignment layer. In the case of using the photo alignment process, an alignment material including a photosensitive polymer material is applied to the inner surfaces of the first plate  100  and the second plate  200  and then light such as ultraviolet rays is irradiated thereto to form a photopolymerization material. 
         [0050]    Referring to  FIG. 2 , alignment directions R 1  and R 2  of two aligners  11  and  21  which are positioned on the inner surfaces of the first plate  100  and the second plate  200  are substantially parallel with each other. Further, the alignment directions R 1  and R 2  are constant. 
         [0051]    When considering a misalign margin between the first plate  100  and the second plate  200 , a difference between an azimuthal angle of the first aligner  11  of the first plate  100  and an azimuthal angle of the second aligner  21  of the second plate  200  may be approximately ±5°, but the present invention is not limited thereto. 
         [0052]    Referring to  FIG. 3 , the first plate  100  and the second plate  200  in which the aligners  11  and  21  are substantially aligned in parallel with each other may be aligned and bonded to each other to form the optical modulation device  1  according to an exemplary embodiment. 
         [0053]    Differently from the illustrated case, the upper and lower position of the first plate  100  and the second plate  200  may be changed 
         [0054]    As described above, according to the exemplary embodiment, the aligners  11  and  21  which are formed in the first plate  100  and the second plate  200  of the optical modulation device  1  including the liquid crystal are parallel with each other and the alignment directions of each aligner  11  and  21  are constant, and as a result, the alignment process of the optical modulation device is simple and the complicated alignment process is not required, thereby simplifying the manufacturing process of the optical modulation device  1 . Therefore, the badness of the optical modulation device or the optical device including the same due to the alignment badness may be prevented. Therefore, a size of the optical modulation device may be easily large. 
         [0055]    Next, an operation of the optical modulation device according to an exemplary embodiment will be described with reference to  FIGS. 4 to 7  along with  FIGS. 1 to 3  which are described above. 
         [0056]    Referring to  FIGS. 4 and 5 , when a voltage difference is not applied between the lower electrode  191  of the first plate  100  and the upper electrode  290  of the second plate  200  and thus no electric field is not applied to the liquid crystal layer  3 , the liquid crystal molecules  31  are aligned, having an initial pre-tilt.  FIGS. 5A to 5C  are cross-sectional views of the optical modulation device  1  of  FIG. 4  taken along lines I, II and III, respectively. The cross-sectional view of  FIG. 5A  is taken crossing a first lower electrodes  191 . The cross-sectional view of  FIG. 5C  is taken crossing a second lower electrode  191 . The cross-sectional view of  FIG. 5B  is taken crossing the space G interposed between the first and second lower electrodes  191 . In this case, the alignment of the liquid crystal molecules  31  may be approximately constant. [Note to client: uniform]. 
         [0057]    The drawings of  FIG. 5 , or the like illustrate that some of the liquid crystal molecules  31  are penetrated into an area of the first plate  100  or the second plate  200 , which is illustrated for convenience. Actually, the liquid crystal molecules  31  are not penetrated into the area of the first plate  100  or the second plate  200 , which is the same even in the following drawings. 
         [0058]    The liquid crystal molecules  31  adjacent to the first plate  100  and the second plate  200  are initially aligned along the parallel alignment direction of the aligners  11  and  21 . The pre-tilt direction of the liquid crystal molecules  31  adjacent to the first plate  100  and the pre-tilt direction of the liquid crystal molecules  31  adjacent to the second plate  200  are opposite to each other while not being in parallel. For example, the liquid crystal molecules  31  adjacent to the first plate  100  and the liquid crystal molecule  31  adjacent to the second plate  200  may be tilted in a symmetrical direction to each other with respect to a horizontal central line which horizontally extends along a center of the liquid crystal layer  3  on the cross-sectional view. For example, when the liquid crystal molecules  31  adjacent to the first plate  100  are tilted to the right, the liquid crystal molecules  31  adjacent to the second plate  200  may be tilted to the left. 
         [0059]    Referring to  FIGS. 6 and 7 , a voltage difference which is equal to or more than a threshold voltage is applied between the lower electrode  191  of the first plate  100  and the upper electrode  290  of the second plate  200 , and thus the liquid crystal molecules  31  having a negative dielectric anisotropy immediately after an electric field is generated in the liquid crystal layer  3  may be tilted in a vertical direction to the direction of the electric field. Therefore, as illustrated in  FIGS. 6 and 7 , the liquid crystal molecules  31  are tilted in approximately parallel with the surface of the first plate  100  or the second plate  200  to form an in-plane alignment and a major axis of the liquid crystal molecule  31  are arranged with rotating on an in-plane. The in-plane alignment means that the major axis of the liquid crystal molecule  31  is arranged to be parallel with the surface of the first plate  100  or the second plate  200 . 
         [0060]    In this case, a voltage is applied to the lower electrode  191  and the upper electrode such that the rotating angle (azimuthal angle) of the liquid crystal molecule  31  on the in-plane may be changed in a spiral shape depending on the position of the x-axis direction. 
         [0061]    Next, a method for implementing a forward phase tilt using an optical modulation device according to an exemplary embodiment will be described with reference to  FIGS. 8 to 12  along with the drawings described above. 
         [0062]      FIG. 8  illustrates the optical modulation device  1  including the liquid crystal according to the exemplary embodiment which may have the same structure as the foregoing exemplary embodiment. The optical modulation device  1  may include a plurality of unit region, in which each unit region may include at least one lower electrode  191 . The exemplary embodiment describes an example in which each unit region includes one lower electrode  191 . The two lower electrodes  191   a  and  191   b  which are each positioned in two adjacent unit regions will be described herein. The two lower electrodes  191   a  and  191   b  are each called a first electrode  191   a  and a second electrode  191   b.    
         [0063]    Referring to  FIG. 10A , when a voltage is not applied to the first and second electrodes  191  and  191   b  and the upper electrode  290 , the liquid crystal molecules  31  are initially aligned in a substantially vertical direction to a plane of the first plate  100  and the second plate  200  and as described above, may have the pre-tilt along the alignment direction of the first plate  100  and the second plate  200 . In this case, a voltage of 0V with reference to the voltage of the upper electrode  290  may be applied to the first and second electrodes  191   a  and  191   b  and a voltage which is equal to or less than a threshold voltage Vth at which the alignment of the liquid crystal molecules  31  starts to change may also be applied thereto. 
         [0064]    Referring to  FIG. 9 , first, for a forward phase tilt of liquid crystal molecules, the adjacent lower electrodes  191   a  and  191   b  and the upper electrode  290  may be applied with a driving signal of step  1  for one frame. In the step  1 , a voltage difference is also formed between the first electrode  191   a  and second electrode  191   b  which are adjacent to each other while the voltage difference is formed between the lower electrodes  191   a  and  191   b  of the first plate  100  and the upper electrode  290  of the second plate  200 . For example, a size of an absolute value of a second voltage applied to the second electrode  191   b  may be larger than that of a first voltage applied to the first electrode  191   a . Further, a third voltage applied to the upper electrode  290  is different from the first voltage and the second voltage applied to the lower electrodes  191   a  and  191   b . For example, the third voltage applied to the upper electrode  290  may be smaller than the absolute value of the first voltage and the absolute value of the second voltage which are applied to the first and second electrodes  191   a  and  191   b . For example, 5V may be applied to the first electrode  191   a,  6V may be applied to the second electrode  191   b , and 0V may be applied to the upper electrode  290 . 
         [0065]    Unlike the illustrated case, when the unit region includes a plurality of lower electrodes  191 , the same voltage may also be applied to all the plurality of lower electrodes  191  of a single unit region. In an exemplary embodiment, a voltage which is sequentially changed based on at least one lower electrode  191  as a unit may be applied. In this case, a voltage gradually increasing based on at least one lower electrode  191  as a unit may be applied to the lower electrode  191  in one unit region based on a boundary of the adjacent unit regions oe a voltage gradually decreasing based on at least one lower electrode  191  as a unit may be applied to the lower electrode  191  of the other unit region. 
         [0066]    The voltage applied to the lower electrodes  191  of all the unit regions may have the same polarity as positive polarity or negative polarity with reference to the voltage of the upper electrode  290   
         [0067]    Further, the polarity of the voltage applied to the lower electrode  191  may be inverted based on at least one frame. 
         [0068]    Next, as illustrated in  FIG. 10B  and  FIG. 11 , the liquid crystal molecules  31  are re-aligned depending on the electric field generated in the liquid crystal layer  3 . For example, the liquid crystal molecules  31  are tilted in approximately parallel with the surface of the first plate  100  or the second plate  200  to form an in-plane alignment. In the in-plane alignment, the major axis rotates on a plane to form an spiral alignment of  FIGS. 11 and 12  showing an u-letter alignment. The azimuthal angle of the major axis of the liquid crystal molecules  31  may be changed from approximately 0° to approximately 180° based on a pitch of the lower electrode  191 . A portion where the azimuthal angle of the major axis of the liquid crystal molecules  31  is changed from approximately 0° to approximately 180° may form one u-letter alignment. 
         [0069]    A predetermined time may be required until the optical modulation device  1  is applied with the driving signal of the step  1  and then the alignment of the liquid crystal molecules  31  is stabilized and the optical modulation device  1  forming the forward phase tilt may be continuously applied with the driving signal of the step  1  unlike one illustrated in  FIG. 9 . 
         [0070]    Referring to  FIG. 11 , a region in which the liquid crystal molecules  31  may be arranged with rotating by 180° along the x-axis direction may be as one unit region. In the case of the exemplary embodiment, the single unit region may include the space G between the first electrode  191   a  and the second electrode  191   b  adjacent thereto. 
         [0071]    As described above, when the optical modulation device  1  satisfies the above Equation 1 to implement approximately the half-wavelength plate, the rotating direction of the input circularly polarized light is changed reversely.  FIG. 11  illustrates a phase change depending on the position of the x-axis direction, for example, in the case in which the right circularly polarized light is incident on the light modulation device  1 . The right circularly polarized light transmitting the optical modulation device  1  is emitted with being changed to the left circularly polarized light and a phase delay value of the liquid crystal layer  3  is changed depending on the x-axis direction and therefore the phase of the emitted circularly polarized light is continuously changed. 
         [0072]    If the optical axis of the half-wavelength plate rotates as much as φ on the in-plane, the phase of emitted light is changed as much as 2φ. As illustrated in  FIG. 11 , the phase of light emitted from one unit region in which the azimuthal angle of the major axis of the liquid crystal molecule  31  is changed 180° is changed from 0 to 2π (radian) along the x-axis direction. This is called the forward phase tilt. The phase change may be repeated every the unit region to implement the forward phase tilt portion of the lens which changes the direction of light using the optical modulation device  1 . 
         [0073]    Next, the method for implementing a forward phase tilt using the optical modulation device  1  according to the exemplary embodiment as illustrated in  FIG. 11  will be described with reference to  FIGS. 13 to 16  along with the drawings described above. 
         [0074]      FIG. 13  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules  31  before the voltage difference is applied between the first and second electrodes  191   a  and  191   b  of the first plate and the upper electrode  290  of the second plate  200  of the optical modulation device  1  according to the exemplary embodiment. Unlike the foregoing drawings,  FIGS. 13 to 16  illustrate a portion where one unit region moves in a horizontal direction. 
         [0075]    The liquid crystal molecules  31  are initially aligned in a direction approximately vertical to the plane of the first plate  100  and the second plate  200  and may have the pre-tilt along the alignment directions R 1  and R 2  of the first plate  100  and the second plate  200  as described above. An equi-potential line VL is illustrated in the liquid crystal layer  3 . 
         [0076]      FIG. 14  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules  31  when the driving signal of the step  1  is applied between the first and second electrodes  191   a  and  191   b  of the first plate and the upper electrode  290  of the second plate  200  of the optical modulation device  1  according to the exemplary embodiment and illustrates a portion where one unit region horizontally moves. An electric field E is generated between the first plate  100  and the second plate  200  and thus the equi-potential line VL is represented. In this case, the first and second electrodes  191   a  and  191   b  have edge sides, and therefore as illustrated in  FIG. 14 , a fringe field is formed between edge sides of the first and second electrodes  191   a  and  191   b  and the upper electrode  290 . 
         [0077]    When the driving signal of the step  1  is applied to the first and second electrodes  191   a  and  191   b  and the upper electrode  290 , in the liquid crystal layer  3  of the unit region including the second electrode  191   b , a strength of electric field in a region D 1  adjacent to the first plate  100  is stronger than that of electric field in a region S 1  adjacent to the second plate  200  and in the liquid crystal layer  3  of the unit region including the first electrode  191   a , a strength of electric field in a region S 2  adjacent to the first plate  100  is weaker than that of a strength of electric field in a region D 2  adjacent to the second plate  200 . 
         [0078]    There is a difference between the voltage applied to the first electrode  191   a  and the voltage applied to the second electrode  191   b  in the two adjacent unit regions and therefore as illustrated in  FIG. 14 , the strength of the electric field in the region S 2  adjacent to the first electrode  191   a  may be weaker than that of the electric field in the region D 1  adjacent to the second electrode  191   b . For this purpose, as illustrated in  FIG. 9  described above, the voltage applied to the second electrode  191   b  may be larger than the voltage applied to the first electrode  191   a . The upper electrode  290  may be applied with a voltage different from the voltage applied to the first and second electrodes  191   a  and  191   b , in more detail, a voltage smaller than the voltage applied to the first and second electrodes  191   a  and  191   b.    
         [0079]      FIG. 15  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the liquid crystal molecules  31  reacting to the electric field E generated in the liquid crystal  3  after the driving signal of the step  1  is applied to the optical modulation device  1  illustrated in  FIG. 8  and illustrates the portion where one unit region horizontally moves. As described above, in the liquid crystal layer  3  corresponding to the second electrode  191   b , the electric field in the region D 1  adjacent to the second electrode  191   b  is the strongest and therefore the tilted direction of the liquid crystal molecules  31  of the region D 1  determines the in-plane alignment direction of the liquid crystal molecules  31  corresponding to the second electrode  191   b . Therefore, in the region corresponding to the second electrode  191   b , the liquid crystal molecules  31  are tilted in the initial pre-tilt direction of the liquid crystal molecules  31  adjacent to the first plate  100  to form the in-plane alignment. 
         [0080]    To the contrary, in the liquid crystal layer  3  corresponding to the first electrode  191   a , the electric field in the region D 2  adjacent to the upper electrode  290  facing the first electrode  191   a , not the first electrode  191   a , is the strongest and therefore the tilted direction of the liquid crystal molecules  31  in the region D 2  determines the in-plane alignment direction of the liquid crystal molecules  31 . Therefore, in the region corresponding to the first electrode  191   a , the liquid crystal molecules  31  are tilted in the initial pre-tilt direction of the liquid crystal molecules  31  adjacent to the second plate  200  to form the in-plane alignment. The initial pre-tilt direction of the liquid crystal molecules  31  adjacent to the first plate  100  and the initial pre-tilt direction of the liquid crystal molecules  31  adjacent to the second plate  200  are opposite to each other and therefore the tilted direction of the liquid crystal molecules  31  corresponding to the first electrode  191   a  is opposite to the tilted direction of the liquid crystal molecules  31  corresponding to the second electrode  191   b.    
         [0081]      FIG. 16  is a cross-sectional view taken along the line IV of  FIG. 8  as a cross-sectional view illustrating the alignment of the stabilized liquid crystal molecules  31  after the driving signal of the step  1  is applied to the optical modulation device  1  illustrated in  FIG. 8  and illustrates the portion where one unit region horizontally moves. The in-plane alignment direction of the liquid crystal molecules  31  corresponding to the first electrode  191   a  is opposite to the in-plane alignment direction of the liquid crystal molecules  31  corresponding to the second electrode  191   b  and the liquid crystal molecules  31  corresponding to the space G between the first electrode  191   a  and the second electrode  191   b  which are adjacent to each other continuously rotate along the x-axis direction to form the spiral alignment. 
         [0082]    Finally, the liquid crystal layer  3  of the optical modulation device  1  may give the phase delay changed along the x-axis direction to the incident light. 
         [0083]    Referring to  FIG. 16 , the region in which the liquid crystal molecules  31  are aligned with rotating 180° along the x-axis direction is defined as one unit region, in which one unit region may include the space G between one lower electrodes  191   a  and  191   b  and the other lower electrodes  191   a  and  191   b  adjacent thereto. For example, when the right circularly polarized light is incident on the optical modulation device  1  forming the forward phase tilt like the exemplary embodiment, the phase change depending on the position in the x-axis direction is represented, the right circularly polarized light is emitted with being changed to the left circularly polarized light, and the phase delay value of the liquid crystal layer  3  is changed depending on the x-axis direction and therefore the phase of the emitted circularly polarized light is continuously changed. 
         [0084]    Next, a method for implementing a reverse phase tilt using the optical modulation device  1  according to the exemplary embodiment will be described with reference to  FIGS. 17 to 19  along with the drawings described above, in particular,  FIGS. 9 to 11 . 
         [0085]    Referring to the upper left of  FIG. 17 , when a voltage is not applied to the first and second electrodes  191  and  191   b  and the upper electrode  290 , the liquid crystal molecules  31  are initially aligned in approximately a vertical direction to a plane of the first plate  100  and the second plate  200  and as described above, may have the pre-tilt along the alignment direction of the first plate  100  and the second plate  200 . 
         [0086]    Referring to  FIG. 9  described above, the optical modulation device  1  according to the exemplary embodiment is applied with the driving signal of the step  1  and then the lower electrodes  191   a  and  191   b  and the upper electrode  290  may be applied with the driving signal of the step  2  after a predetermined time lapses (for example, 50 ms). 
         [0087]    In the step  2 , the first electrode  191   a  and the second electrode  191   b  which are adjacent to each other may be applied with a voltage having opposite polarity to the voltage applied to the upper electrode  290 . For example, the first electrode  191   a  may be applied with a voltage of −6V based on the voltage of the upper electrode  290  and the second electrode  191   b  may be applied with a voltage of 6V, and vice versa. 
         [0088]    Next, as illustrated in the left lower of  FIG. 17 , the equi-potential line VL is formed and the liquid crystal molecules  31  of a region A corresponding to the space G between the first and second electrodes  191   a  and  191   b  are aligned in an approximately vertical direction to the substrates  100  and  200  and do not have the in-plane spiral alignment. 
         [0089]    A section of the step  2  may be, for example, 20 ms, but is not limited thereto. 
         [0090]    Unlike the illustrated case, when the unit region includes the plurality of lower electrodes  191 , the same voltage may also be applied to all the plurality of lower electrodes  191  of a single unit region and a voltage which is sequentially changed based on at least one lower electrode  191  as a unit may be applied. The voltage applied to the lower electrode  191  of the adjacent unit regions may be applied with a voltage having an opposite polarity to each other based on the voltage of the upper electrode  290   
         [0091]    Further, the polarity of the voltage applied to the lower electrode  191  may be inverted every at least one frame. 
         [0092]    Next, the optical modulation device  1  according to the exemplary embodiment is applied with a driving signal of step  2  and then the lower electrodes  191   a  and  191   b  and the upper electrode  290  is applied with a driving signal of step  3  after a predetermined time (e.g., 20 ms) lapses and may be maintained for the remaining section of the corresponding frame. 
         [0093]    A voltage level applied to the lower electrodes  191   a  and  191   b  and the upper electrode in the step  3  is similar to the step  1  but a relative size of the voltage applied to the first electrode  191   a  and the second electrode  191   b  may be changed inversely. That is, when the voltage applied to the first electrode  191   a  in the step  1  is smaller than the voltage applied to the second electrode  191   b , the voltage applied to the 1 st  first electrode  191   a  in the step  3  may be larger than the voltage applied to the second electrode  191   b . For example, in the step  3 , 10V may be applied to the first electrode  191   a,  6V may be applied to the second electrode  191   b , and 0V may be applied to the upper electrode  290 . 
         [0094]    Next, as illustrated in the lower right of  FIG. 17  and  FIG. 11 , the liquid crystal molecules  31  are re-aligned depending on the electric field generated in the liquid crystal layer  3 . In detail, most of the liquid crystal molecules  31  are tilted in approximately parallel with the surface of the first plate  100  or the second plate  200  to form the in-plane alignment and the major axis rotates on the in-plane to form the spiral alignment as illustrated in  FIGS. 18 and 19 , in more detail, an n-letter alignment. The azimuthal angle of the major axis of the liquid crystal molecules  31  may be changed from approximately 180° to approximately 0° based on a pitch of the lower electrode  191 . A portion where the azimuthal angle of the major axis of the liquid crystal molecules  31  is changed from approximately 180° to approximately 0° may form one n-letter alignment. 
         [0095]    A predetermined time may be required until the optical modulation device  1  is applied with the driving signal of the step  3  and then the alignment of the liquid crystal molecules  31  is stabilized and the optical modulation device  1  forming the reverse phase tilt may be continuously applied with the driving signal of the step  3 . 
         [0096]    As described above, when the optical modulation device  1  satisfies the above Equation 1 to implement approximately the half-wavelength plate, the rotating direction of the input circularly polarized light is changed reversely.  FIG. 18  illustrates a phase change depending on the position in the x-axis direction, for example, in the case in which the right circularly polarized light is incident on the light modulation device  1 . The right circularly polarized light transmitting the optical modulation device  1  is emitted with being changed to the left circularly polarized light and a phase delay value of the liquid crystal layer  3  is changed depending on the x-axis direction and therefore the phase of the emitted circularly polarized light is continuously changed. 
         [0097]    Generally, when the optical axis of the half-wavelength plate rotates as much as φ on the in-plane, the phase of emitted light is changed as much as 2φ and therefore as illustrated in  FIG. 18 , the phase of light emitted from one unit region in which the azimuthal angle of the major axis of the liquid crystal molecule  31  is changed from 2π (radian) to 0 along the x-axis direction. This is called a reverse phase tilt. The phase change may be repeated every the unit region to implement the reverse phase tilt portion of the lens which changes the direction of light using the optical modulation device  1 . 
         [0098]    A method for implementing a reverse phase tilt has the same principle as the method for implementing a forward phase tilt and therefore a detailed description thereof will be omitted. 
         [0099]    According to the exemplary embodiment as described above, the in-plane rotating angle of the liquid crystal molecules  31  is easily controlled according to the method for applying a driving signal to variously modulate the optical phase and form various diffraction angles of light. 
         [0100]      FIG. 20  is a diagram illustrating a phase change depending on a position of a lens which may be implemented using an optical modulation device according to an exemplary embodiment. 
         [0101]    The optical modulation device  1  of  FIG. 1  may implement both of the forward phase tilt and the reverse phase tilt to form a Fresnel lens.  FIG. 20  illustrates the phase change depending on a position of the Fresnel lens implemented by the optical modulation device  1  of  FIG. 1 . The Fresnel lens is a lens using optical characteristics of a Fresnel zone plate, in which a phase distribution is periodically repeated and thus an effective phase delay may be the same as or similar to a solid convex lens or a green lens. 
         [0102]    As illustrated in  FIG. 20 , based on a center O of a single Fresnel lens, a left portion La includes a plurality of forward phase tilt regions of which the width in the x-axis direction may be different and a right portion Lb includes a plurality of reverse phase tilt regions of which the width in the x-axis direction may be different. Therefore, a portion of the optical modulation device  1  corresponding to the left portion La of the Fresnel lens may apply only the driving signal of the step  1  described above to form the forward phase tilt and a portion of the optical modulation device  1  corresponding to the right portion Lb of the Fresnel lens may sequentially apply the driving signals of the step  1 , the step  2 , and the step  3  described above to form the reverse phase tilt. 
         [0103]    The plurality of forward phase tilts performed by the left portion La of the Fresnel lens may have different widths depending on the position. For this purpose, the width of the lower electrode  191  of the optical modulation device  1  corresponding to each forward phase tilt portion and/or the number of lower electrodes  191  included in one unit region, and the like may be properly controlled. Similarly, the plurality of reverse phase tilts performed by the right portion Lb of the Fresnel lens may have different widths depending on the position. For this purpose, the width of the lower electrode  191  of the optical modulation device  1  corresponding to each reverse phase tilt portion and/or the number of lower electrodes  191  included in one unit region, and the like may be properly controlled. 
         [0104]    When the voltage applied to the lower electrode  191  and the upper electrode  290  is controlled, a phase curvature of the Fresnel lens may also be changed. 
         [0105]      FIGS. 21 and 22  each illustrates a structure of a stereoscopic optical device using an optical modulation device  1  according to an exemplary embodiment and a method for displaying a 2D image and a 3D image. 
         [0106]    Referring to  FIGS. 21 and 22 , an optical device according to an exemplary embodiment is a stereoscopic optical device including a display panel  300  and the optical modulation device  1  positioned in front of a front surface on which an image of the display panel  300  is displayed. The display panel  300  includes a plurality of pixels which display images and may be arranged in a matrix form. 
         [0107]    As illustrated in  FIG. 21 , the display panel  300  may display a 2D image of each frame in a 2D mode and as illustrated in  FIG. 22 , the display panel  300  may divide images corresponding to multi views such as a right-eye image, a left-eye image, etc., in a 3D mode by a spatial division method and display the divided images. In the 3D mode, some of the plurality of pixels may display an image corresponding to any one view and the others thereof may display images corresponding to other views. The number of views may be equal to or more than two. 
         [0108]    The optical modulation device  1  may repeatedly implement the Fresnel lens including the plurality of forward phase tilt portions and the plurality of reverse phase tilt portions to divide the imaged displayed on the display panel  300  at each view. 
         [0109]    The optical modulation device  1  may be switched on/off. When the optical modulation device  1  is switched on, the stereoscopic optical device is operated in the 3D mode and as illustrated in  FIG. 22  may form the plurality of Fresnel lenses which refract the image displayed on the display panel  300  to display an image at the corresponding view. On the other hand, when the optical modulation device  1  is switched off, as illustrated in  FIG. 21 , the image displayed on the display plane  300  is transmitted without being refracted and thus the 2D image may be observed. 
         [0110]      FIG. 23  is a diagram illustrating a resistor string for voltage division in the optical modulation device  1  of  FIG. 1  according to an exemplary embodiment. 
         [0111]    For an in-plane spiral mode panel, a resistor string may be formed within spiral zones SZ 1 , SZ 2 , and SZ 3  of the optical modulation device  1 . Here, each spiral zone SZ 1  to SZ 3  may correspond to a region in which the liquid crystal molecules  31  are aligned with rotating along the x-axis direction. For example, each spiral zone SZ 1  to SZ 3  may correspond to the region in which the spiral alignment (for example, the u-letter alignment of  FIGS. 11 and 12  and the n-letter alignment of  FIGS. 18 and 19 ) of the liquid crystal molecules  31  is formed. For convenience of explanation,  FIG. 23  illustrates some  192   a  to  192   c ,  193   a  to  193   e , and  194   a  to  194   f  of the plurality of lower electrodes included in the first plate  100 . The lower electrodes  192   a  to  192   c ,  193   a  to  193   e , and  194   a  to  194   f  of  FIG. 23  are the same as/similar to the foregoing lower electrodes  191 ,  191   a , and  191   b.    
         [0112]    The spiral zone SZ 1  includes the plurality of lower electrodes  192   a  to  192   c , the spiral zone SZ 2  includes the plurality of lower electrodes  193   a  to  193   e , and the spiral zone SZ 3  includes the plurality of lower electrodes  194   a  to  194   f.    
         [0113]    Each of the lower electrodes  192   a  to  192   c ,  193   a  to  193   e , and  194   a  to  194   f  has a bar shape, extending in a diagonal direction with respect to the arranged direction. 
         [0114]    The lower electrode  192   a  of the spiral zone SZ 1  is connected to a bus line B 1   a  and the lower electrode  192   c  of the spiral zone SZ 1  is connected to a bus line B 1   b . A first resistor string is formed between the lower electrodes  192   a  to  192   c  of the spiral zone SZ 1 . The first resistor string includes a plurality of resistors P 1   a  and P 1   b . Each resistor P 1   a  and P 1   b  may be formed by a deposition of a high resistance material. The resistance of the resistor P 1   a  and P 1   b  may correspond to the length of the resistor P 1   a  and P 1   b . The high resistance material may be deposited using a sheet of mask. The high resistance material may be directly contacted. For example, each resistor P 1   a  and P 1   b  may be made of nickel-chromium (Ni—Cr), indium zinc oxide (IZO), etc. Each resistor P 1   a  and P 1   b  may be formed between the lower electrodes  192   a  to  192   c . A connection of the resistors P 1   a  and P 1   b  formed between the lower electrodes  192   a  to  192   c  is a series-shunt connection of the resistors P 1   a  and P 1   b.    
         [0115]    The spiral zones SZ 2  and SZ 3  may be formed by the same method as the spiral zone SZ 1 . For example, the lower electrode  193   a  of the spiral zone SZ 1  is connected to a bus line B 1   c  and the lower electrode  193   e  of the spiral zone SZ 2  is connected to a bus line B 1   d . A second resistor string is formed between the lower electrodes  193   a  to  193   e  of the spiral zone SZ 2 . The second resistor string includes a plurality of resistors P 2   a  to P 2   d . Each resistor P 2   a  to P 2   d  may be formed by a deposition of a high resistance material. The resistance of the resistor P 2   a  to P 2   d  may correspond to a deposition length of the resistor P 2   a  to P 2   d . Each resistor P 2   a  to P 2   d  may be formed between two adjacent electrodes of the lower electrodes  193   a  to  193   e.    
         [0116]    The lower electrode  194   a  of the spiral zone SZ 3  is connected to a bus line B 1   e  and the lower electrode  194   f  of the spiral zone SZ 3  is connected to a bus line B 1   f . A third resistor string is formed between the lower electrodes  194   a  to  194   f  of the spiral zone SZ 3 . The third resistor string includes a plurality of resistors P 3   a  to P 3   e . Each resistor P 3   a  to P 3   e  may be formed by a deposition of a high resistance material. The resistance of each resistor P 3   a  to P 3   e  may correspond to a deposition length of the resistor P 3   a  to P 3   e . Each resistor P 3   a  to P 3   e  may be formed between two adjacent lower electrodes of the lower electrodes  194   a  to  194   f . For convenience of explanation,  FIG. 23  illustrates the case in which the resistors P 3   a  to P 3   e  are formed between all the lower electrodes  194   a  to  194   f , but the resistors need not be formed between some of the lower electrodes. For example, the resistor P 3   e  need not be formed between the lower electrode  194   e  and the lower electrode  194   f.    
         [0117]    A voltage control device  400  applies a voltage to the optical modulation device  1  through the bus lines B 1   a  to B 1   f . For example, the voltage control device  400  may include a driver integrated circuit (D-IC) and/or an external amplifier which directly applies a voltage to the optical modulation device  1  through a flexible printed circuit separated from the D-IC. The voltage control device  400  may be included in an optical device. 
         [0118]    When the bus line B 1   a  and the bus line B 1   b  are applied with a voltage from the voltage control device  400 , the voltage is divided by the first resistor string and the divided voltage is applied to the lower electrodes  192   a  to  192   c  of the spiral zone SZ 1 . For example, the voltage applied to the bus line B 1   a  is V 1   a  and the voltage applied to the bus line B 1   b  is V 1   b . Here, it is assumed that V 1   b  is greater than V 1   a . A voltage (e.g. voltage applied to the lower electrode  192   c ) of a node N 1   c  is V 1   b . A voltage (e.g. voltage applied to the lower electrode  192   b ) of a node N 1   b  is (V 1   b -voltage dropped by the resistor P 1   b ). A voltage (e.g. voltage applied to the lower electrode  192   a ) of a node N 1   a  is V 1   a  (e.g. V 1   b -voltage dropped by the resistor P 1   b -voltage dropped by the resistor P 1   a ). When the V 1   b  is larger than the V 1   a , a monotonically increasing voltage is applied to the lower electrodes  192   a  to  192   c . For example, the voltage applied to the lower electrode  192   b  is larger than the voltage applied to the lower electrode  192   a  and the voltage applied to the lower electrode  192   c  is larger than the voltage applied to the lower electrode  192   b . To the contrary, when the V 1   a  is larger than the V 1   b , a monotonically decreasing voltage is applied to the lower electrodes  192   a  to  192   c.    
         [0119]    When a voltage is applied to the bus lines B 1   c  and Bid for the spiral zone SZ 2 , similarly to the spiral zone SZ 1 , the voltage is divided through the second resistor string and the divided voltage is applied to the lower electrodes  193   a  to  193   e  of the spiral zone SZ 2 . The lower electrodes  193   a  to  193   e  may be applied with the monotonically increasing or decreasing voltage. 
         [0120]    When a voltage is applied to the bus lines B 1   e  and B 1   f  for the spiral zone SZ 3 , similarly to the spiral zone SZ 1 , the voltage is divided through the third resistor string and the divided voltage is applied to the lower electrodes  194   a  to  194   f  of the spiral zone SZ 3 . The lower electrodes  194   a  to  194   f  may be applied with the monotonically increasing or decreasing voltage. 
         [0121]    According to the exemplary embodiment, as illustrated in  FIG. 23 , the electrode structure may be simplified by using the resistor string for voltage division and the number of bus lines for each spiral zone SZ 1  to SZ 3  may be minimized. For example, though the spiral zone SZ 3  includes six lower electrodes  194   a  to  194   f , but to apply a voltage to the six lower electrodes  194   a  to  194   f , only the two bus lines B 1   e  and B 1   f  connected to the lower electrodes  194   a  and  194   f  of both ends of the spiral zone SZ 3  are needed. 
         [0122]      FIG. 24  is a diagram illustrating a RC modeling to the spiral zone SZ 1  of  FIG. 23 . 
         [0123]    A resistor P 1   a ′ of  FIG. 24  corresponds to the resistor P 1   a  of  FIG. 23  and a resistor P 1   b ′ of  FIG. 24  corresponds to the resistor P 1   b  of  FIG. 23 . A node N 1   a ′ of  FIG. 24  corresponds to the node N 1   a  of  FIG. 23 , a node N 1   b ′ of  FIG. 24  corresponds to the node N 1   b  of  FIG. 23 , and a node N 1   b ′ of  FIG. 24  corresponds to the node N 1   b  of  FIG. 23 . An electrode E 1  connected to the node N 1   a  corresponds to the lower electrode  192   a  of  FIG. 23 , an electrode E 2  connected to the node N 1   b ′ corresponds to the lower electrode  192   b  of  FIG. 23 , and an electrode E 3  connected to the node N 1   c ′ corresponds to the lower electrode  192   c  of  FIG. 23 . 
         [0124]    The RC equivalent to the lower electrode  192   a  may include a plurality of resistors P 6   a  to P 6   g  and a plurality of capacitors C 3   a  to C 3   g . The RC equivalent to the lower electrode  192   b  may include a plurality of resistors P 5   a  to P 5   g  and a plurality of capacitors C 2   a  to C 2   g . The RC equivalent to the lower electrode  192   c  may include a plurality of resistors P 4   a  to P 4   g  and a plurality of capacitors C 1   a  to C 1   g.    
         [0125]      FIG. 25  is a simulation program with integrated circuit emphasis (SPICE) simulation result illustrating a voltage applied to the electrodes E 1  to E 3  of  FIG. 24 . In  FIG. 25 , it is assumed that the V 1   b  is larger than Via. 
         [0126]    A graph G 1   a  represents a voltage applied to the electrode E 1 , a graph G 1   b  represents a voltage applied to the electrode E 2 , and a graph G 1   c  represents a voltage applied to the electrode E 3 . The V 1   b  and the Via are divided by the resistors P 1   a ′ and P 1   b ′ coupled in series and the divided voltage is applied to each electrode E 1  to E 3 . In detail, the monotonically increasing voltage is applied to the electrodes E 1  to E 3 . That is, the voltage applied to the electrode E 2  is larger than the voltage applied to the electrode E 1  and the voltage applied to the electrode E 3  is larger than the voltage applied to the electrode E 2 . 
         [0127]      FIG. 26  is a diagram illustrating a resistor string formed in a voltage control device  401  controlling a voltage applied to the optical modulation device  1  of  FIG. 1  according to an exemplary embodiment. The resistor string of  FIG. 23  is formed within the spiral zones SZ 1  to SZ 3  but is different from the resistor string of  FIG. 26  in that it is formed within the voltage control device  401 . For convenience of explanation,  FIG. 26  illustrates the two spiral zones SZ 1  and SZ 2  of the plurality of spiral zones included in the optical modulation device  1 . The voltage control device  401  may be included in an optical device. 
         [0128]    For example, each lower electrode  192   a  to  192   c  of the spiral zone SZ 1  is connected to different bus lines B 2   a  to B 2   c  and each lower electrode  193   a  to  193   e  of the spiral zone SZ 2  is connected to different bus lines B 2   d  to B 2   h.    
         [0129]    The voltage control device  401  directly applies a voltage to the bus lines B 2   a  to B 2   h  connected to the optical modulation device  1  through a connector  500 . The voltage control device  401  may be included in a control board. For example, the voltage control device  401  may include a resistor string (for example, fourth resistor string and fifth resistor string) formed by using a lumped resistor. The fourth resistor string may include a plurality of resistors P 7   a  and P 7   b  coupled in series and the fifth resistor string may include a plurality of resistors P 8   a  to P 8   d  coupled in series. The voltage control device  401  divides a voltage through the resistor string (fourth resistor string and fifth resistor string) and applies the divided voltage to the bus lines B 2   a  to B 2   h  through the connector  500 . The voltage of the node N 2   a  may be applied to the lower electrode  192   a  through the bus line B 2   a , the voltage of the node N 2   b  may be applied to the lower electrode  192   b  through the bus line B 2   b , and the voltage of the node N 2   c  may be applied to the lower electrode  192   c  through the bus line B 2   c . The voltage of the nodes N 2   a  to N 2   c  may be the monotonically increasing or decreasing voltage. The voltage of the node N 3   a  may be applied to the lower electrode  193   a  through the bus line B 2   d , the voltage of the node N 3   b  may be applied to the lower electrode  193   b  through the bus line B 2   f , the voltage of the node N 3   c  may be applied to the lower electrode  193   c  through the bus line B 2   h , the voltage of node N 3   d  may be applied to the lower electrode  193   d  through the bus line B 2   g , and the voltage of the node N 3   e  may be applied to the lower electrode  193   e  through the bus line B 2   e . The voltage of the nodes N 3   a  to N 3   e  may be the monotonically increasing or decreasing voltage. 
         [0130]    For example, the voltage V 2   a  is applied to the node N 2   a  and the voltage V 2   b  is applied to the node N 2   c . Herein, it is assumed that V 2   b  is greater than V 2   a . The voltage (e.g. V 2   b ) of the node N 2   c  is applied to the lower electrode  192   c  through the bus line B 2   c . The voltage (e.g. V 2   b -voltage dropped by the resistor P 7   b ) of the node N 2   b  is applied to the lower electrode  192   b  through the bus line B 2   b . The voltage (e.g. V 2   a =V 2   b -voltage dropped by the resistor P 7   b -voltage dropped by the resistor P 7   a ) of the node N 2   a  is applied to the lower electrode  192   a  through the bus line B 2   a . Accordingly, the monotonically increasing voltage is applied to the lower electrodes  192   a  to  192   c.    
         [0131]    In an exemplary embodiment, the voltage V 3   a  is applied to the node N 3   a  and the voltage V 3   b  is applied to the node N 3   e . Herein, it is assumed that V 3   a  is greater than V 3   b . The voltage (e.g. V 3   a ) of the node N 3   a  is applied to the lower electrode  193   a  through the bus line B 2   d . The voltage (e.g. V 3   a -voltage dropped by the resistor P 8   a ) of the node N 3   b  is applied to the lower electrode  193   b  through the bus line B 2   f . The voltage (e.g. V 3   a -voltage dropped by the resistors P 8   a  and P 8   b ) of the node N 3   c  is applied to the lower electrode  193   c  through the bus line B 2   h . The voltage (e.g. V 3   a —voltage dropped by the resistors P 8   a , P 8   b , and P 8   c ) of the node N 3   d  is applied to the lower electrode  193   d  through the bus line B 2   g . The voltage (e.g. V 3   b =V 3   a -voltage dropped by the resistors P 8   a , P 8   b , P 8   c , and P 8   d ) of the node N 3   e  is applied to the lower electrode  193   e  through the bus line B 2   e . Accordingly, the monotonically decreasing voltage is applied to the lower electrodes  193   a  to  193   e.    
         [0132]    While this invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.