Abstract:
A tunable microlens uses a layer of photo-conducting material which results in a voltage differential between at least one of a plurality of electrodes and a droplet of conducting liquid when a light beam is incident upon the photo-conducting material. Such a droplet, which forms the optics of the microlens, moves toward an electrode with a higher voltage relative to other electrodes in the microlens. In one embodiment, when a misalignment of the beam and microlens occurs, an electronic circuit creates the aforementioned differential. In a second embodiment, two layers of electrodes are used, an upper layer and a lower layer. Each electrode in a lower layer of electrodes is electrically coupled to an electrode in the upper layer directly opposed to the lower-layer electrode. When the light beam is misaligned with the microlens, a voltage differential between the droplet and the electrodes in the upper layer automatically causes the droplet, and hence the microlens, to realign itself with the beam.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to microlenses, and more particularly, to liquid microlenses.  
         BACKGROUND OF THE INVENTION  
         [0002]    Lasers, photoconductors, and other optical components are widely used in many optoelectronic applications such as, for example, optical communications systems. Traditionally in such applications, manual positioning and tuning is required to maintain the desired optical coupling between the system components. However, such manual positioning can be slow and quite expensive.  
           [0003]    More recently, in attempts to eliminate this manual positioning, small tunable lenses (also known as tunable microlenses) were developed to achieve optimal optical coupling. Typically, these microlenses are placed between an optical signal transmitter, such as a laser, and an optical signal receiver, such as a photodetector. The microlens acts to focus the optical signal (e.g., that is emitted by the laser) onto its intended destination (e.g., the photodetector). In some cases the refraction index of these microlenses is automatically varied in order to change the focus characteristics of the microlens when the incidence of a light beam upon the microlens varies from its nominal, aligned incidence. Thus, the desired coupling is maintained between components of the microlens. Therefore, the manual positioning and adjustment required in previous systems is eliminated.  
           [0004]    Most tunable microlenses are either gradient index (GRIN) lenses with the refractive index controlled electrostatically or flexible polymeric lenses with the shape (and, therefore, the focal length) controlled mechanically. Both technologies have inherent limitations that impose severe restrictions on the performance of these existing tunable microlenses.  
           [0005]    Tunable gradient index lenses have inherent limitations associated with the relatively small electro-optic coefficients found in the majority of electro-optic materials. This results in a small optical path modulation and, therefore, requires thick lenses or very high voltages to be employed. In addition, many electro-optic materials show strong birefringence that causes polarization dependence of the microlens, which distorts light with certain polarization.  
           [0006]    Mechanically adjustable flexible lenses typically have a substantially wider range of tunability than the gradient index lenses. However, they require external actuation devices, such as micropumps, to operate. Integration of such actuation devices into optoelectronic packages involves substantial problems associated with their miniaturization and positioning. These become especially severe in the case where a two-dimensional array of tunable microlenses is required.  
           [0007]    Attempts have also been made to use other technologies to produce tunable microlenses, such as liquid microlenses controlled through self-assembled monolayers. Some of these attempts are described in U.S. Pat. No. 6,014,259, issued Jan. 11, 2000, the entirety of which is hereby incorporated by reference herein. Microlenses utilizing self-assembled monolayers, however, also suffer from several problems, including severe limitations on material selection and strong hysteresis often leading to the failure of the microlens to return to an original shape after a tuning voltage is disconnected.  
           [0008]    None of the above-described microlenses allow for both lens position adjustment and focal length tuning. Therefore, more recent attempts have involved developing liquid microlenses that permit such lens position and focal length adjustments. Examples of such microlenses, which utilize electrowetting principles coupled with external electronic control systems to accomplish these adjustments, are described in Applicants&#39; copending U.S. patent applications Ser. No. 09/884,605, filed Jun. 19, 2001, entitled “Tunable Liquid Microlens” and Ser. No. 09/951,637, filed Sep. 13, 2001, entitled “Tunable Liquid Microlens With Lubrication Assisted Electrowetting.” 
         SUMMARY OF THE INVENTION  
         [0009]    We have recognized that, while the &#39;605 and &#39;637 applications provide exemplary electrowetting-based tunable liquid microlenses, there remains a need to provide a tunable liquid microlens that does not rely on an external electronic control system to detect out of alignment conditions and adjust the position and/or focal length of the microlens. In particular, in certain applications it may be advantageous to have a microlens that is self-tunable. Such a microlens would eliminate the cost and effort associated with integrating the microlens control electronics previously necessary to tune electrowetting-based microlenses and would potentially reduce the tuning time.  
           [0010]    Therefore, we have invented a microlens that uses a layer of photo-conducting material (such as a conjugated polymer, a doped charge transporting polymer, or certain inorganic semiconductors) to create a voltage differential between at least one of a plurality of electrodes and a droplet of conducting liquid. Such a droplet, which forms the optics of the microlens, will move toward an electrode with a higher voltage relative to other electrodes in the microlens.  
           [0011]    One embodiment of such a self-tunable microlens comprises a transparent conducting substrate of a material (such as transparent glass) that is transparent to at least one wavelength of light useful in an optical system. A plurality of electrodes is disposed on the aforementioned photo-conducting material in a way such that they may be selectively biased to create a respective voltage potential between the droplet and each of the plurality of electrodes. The photo-conducting material is, in turn, disposed on the transparent conducting substrate between the light beam source and the plurality of electrodes. A layer of dielectric insulating material separates the plurality of electrodes and the photo-conducting material from the droplet of conducting liquid.  
           [0012]    When light is incident upon the photo-conducting material, a leakage current results. When a light beam is equally incident on the photo-conducting material associated with each electrode in the layer of electrodes, the leakage current through each electrode is equal and the droplet remains in its initial, centered position. However, when the light beam becomes misaligned with the electrode pattern such that it is incident more upon one segment of photoconducting material than the others, a greater leakage current develops in that segment than otherwise would be present when the light beam is incident equally upon all segments. This greater current also causes the voltage across the electrode associated with that segment to decrease. An electrical circuit coupled with each electrode detects this change in current (or voltage) and then adjusts the voltages applied to each electrode in such a manner as to ensure that a higher voltage is applied to the electrode(s) toward which the droplet must move in order for the microlens to be aligned with the light beam.  
           [0013]    In another embodiment of the present invention, the microlens requires no electrical circuit to adjust the voltages across the electrodes to achieve the droplet&#39;s desired location. Instead, two layers of electrodes are used, an upper layer and a lower layer. Each electrode in the lower layer of electrodes is electrically coupled to the electrode in the upper layer directly opposed to that electrode in the lower layer. Thus, as described above, when a light beam becomes more incident upon the photo-conducting layer of material associated with one electrode in the lower layer, the larger leakage current through this electrode develops and, as a result, the voltage across that electrode drops. The result is that the voltage also drops in the opposing electrode in the upper layer to which that electrode in the lower layer is connected. The resulting voltage differential between the droplet and the electrodes in the upper layer is such that the droplet moves automatically toward the lower layer electrode with the lowest voltage (i.e., toward the position of greatest incidence with the light beam). 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWING  
       [0014]    [0014]FIG. 1 shows a prior art microlens and its operational effect on a beam of light.  
         [0015]    [0015]FIG. 2 shows a prior art microlens wherein a voltage differential between an electrode and a droplet of conducting liquid is used to adjust the focal length of the lens.  
         [0016]    [0016]FIGS. 3A and 3B show a prior art microlens wherein the droplet of conducting liquid is electrically coupled to a substrate via a well.  
         [0017]    [0017]FIG. 4 shows the prior art microlens of FIGS. 3A and 3B wherein a voltage selectively applied to one or more electrodes results in a movement of the droplet away from its centered position relative to the electrodes.  
         [0018]    [0018]FIG. 5 shows a microlens in accordance with the present invention wherein a layer of photo-conducting material is used with a single layer of electrodes to create a voltage difference to adjust the position of the microlens.  
         [0019]    [0019]FIG. 6 shows a top plan view of the microlens of FIG. 5, wherein the droplet of conducting liquid moves in response to a distribution of voltages from an electrical circuit to align itself with a light beam.  
         [0020]    [0020]FIG. 7 shows a microlens in accordance with the present invention wherein a layer of photo-conducting material is used with two layers of electrodes to automatically adjust the position of the droplet of conducting liquid.  
         [0021]    [0021]FIG. 8 shows a top plan view of the microlens of FIG. 7 wherein the droplet of conducting liquid moves in response to a voltage differential within the microlens to align itself with a light beam.  
         [0022]    [0022]FIG. 9 shows a three dimensional representation of the two layers of electrodes of the microlens in FIGS. 7 and 8. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]    [0023]FIG. 1 shows a prior art embodiment of a liquid microlens  101  including a small droplet  102  of a transparent liquid, such as water, typically (but not necessarily) with a diameter from several micrometers to several millimeters. The droplet is disposed on a transparent substrate  103  which is typically hydrophobic or includes a hydrophobic coating. The droplet  102  and substrate  103  need only be transparent to light waves having a wavelength within a selected range. Light waves  104  pass through the liquid microlens focal point/focal spot  105  in a focal plane  106  that is a focal distance “f” from the contact plane  107  between the droplet  102  and the substrate  103 .  
         [0024]    The contact angle θ between the droplet and the substrate is determined by interfacial surface tensions (also known as Interfacial energy) “γ”, generally measured in milli-Newtons per meter (mN/m). As used herein, γ S-V  is the interfacial tenson between the substrate  103  and the air, gas or other liquid that surrounds the substrate, γ L-V  is the interfacial tension between the droplet  102  and the air, gas or other liquid that surrounds the droplet, and γ S-L  is the interfacial tension between the substrate  103  and the droplet  102 . The contact angle θ may be determined from equation (1):  
         cos θ=(γ S-V −γ S-L )/γ L-V   Equation (1)  
         [0025]    The radius “R” in meters of the surface curvature of the droplet is determined by the contact angle θ and the droplet volume in cubic meters (m 3 ) according to equation (2) as follows:  
           R   3 =3* (Volume)/[π*(1−cos θ)(2−cos 2 θ−cos θ)]  Equation (2)  
         [0026]    The focal length in meters is a function of the radius and the refractive indices “n”, where n Liquid  is the refractive index of the droplet and n Vapor  is the refractive index of the air, gas or other liquid that surrounds the droplet  102 . The focal length f may be determined from Equation (3):  
           f=R /( n   Liquid   −n   Vapor )  Equation (3)  
         [0027]    The refractive index of the substrate  103  is not critical because of the parallel entry and exit planes of the light waves. The focal length of the microlens  101 , therefore, is a function of the contact angle θ.  
         [0028]    [0028]FIG. 2 shows a prior art microlens  201  whereby the phenomenon of electrowetting may be used to reversibly change the contact angle θ between a droplet  202  of a conducting liquid (which may or may not be transparent) and a dielectric insulating layer  203  having a thickness “d” and a dielectric constant ε r . An electrode  204 , such as metal electrode is positioned below the dielectric layer  203  and is insulated from the droplet  202  by that layer. The droplet  202  may be, for example, a water droplet, and the dielectric insulating layer  203  may be, for example, a Teflon/Parylene surface.  
         [0029]    When no voltage difference is present between the droplet  202  and the electrode  204 , the droplet  202  maintains its shape defined by the volume of the droplet and contact angle θ 1 , where θ 1  is determined by the interfacial tensions γ as explained above. When a voltage V is applied to the electrode  204 , the voltage difference betweeen the electrode  204  and the droplet  202  causes the droplet to spread. The dashed line  205  illustrates that the droplet  202  spreads equally across the layer  203  from its central position relative to the electrode  204 . Specifically, the contact angle θ decreases from θ 1  to θ 2  when the voltage is applied between the electrode  204  and the droplet  202 . The voltage V necessary to achieve this spreading may range from several volts to several hundred volts. The amount of spreading, i.e., as determined by the difference between θ 1  and θ 2 , is a function of the applied voltage V. The contact angle θ 2  can be determined from equation (4):  
         cos θ( V )=cos θ( V= 0)+ V   2 (ε 0  ε r )/(3 dγ   L-V )  Equation (4)  
         [0030]    where cos θ(V=0) is the contact angle between the insulating layer  203  and the droplet  202  when no voltage is applied between the droplet  202  and electrode  204 ; γ L-V  is the droplet interfacial tension described above; ε r  is the dielectric constant of the insulating layer  203 ; and ε 0  is 8.85×10 −12  F/M—the permissivity of a vacuum.  
         [0031]    [0031]FIGS. 3A and 3B illustrate a prior art tunable liquid microlens  301  that is capable of varying both position and focal length. Referring to FIG. 3A, a tunable liquid microlens  301  includes a droplet  302  of a transparent conductive liquid disposed on a first surface of a transparent, dielectric insulating layer  303 . The microlens  301  includes a plurality of electrodes  305  insulated from the droplet  302  by the insulating layer  303 . A conducting transparent substrate  304  supports the electrodes  305  and the insulating layer  303  and is connected to the droplet  302  via a well  306  running through the dielectric insulating layer  303 . Thus, when voltage V O  is passed over the conducting transparent substrate  304 , the droplet  302  also experiences voltage V O .  
         [0032]    [0032]FIG. 3B is a top plan view of an illustrative configuration for the electrodes  305 . Each electrode is coupled to a respective voltage V 1  through V 4  and the droplet  302 , which is centered initially relative to the electrodes, is coupled to a voltage V O  via the well  306 . When there is no voltage difference between the droplet  302  and any of the electrodes  305  (i.e., V 1 =V 2 =V 3 =V 4 =V O ), and the droplet  302  is centered relative to the electrodes and quadrants I thru IV, the droplet  302  assumes a shape as determined by contact angle θ 1  and the volume of droplet  302  in accordance with equations (1)-(3) expained above. The position of the droplet  302  and the focal length of the microlens can be adjusted by selectively applying a voltage potential between the droplet  302  and the electrodes  305 . If equal voltages are applied to all four electrodes (i.e., V 1 =V 2 =V 3 =V 4 ≠V O ), then the droplet  302  spreads equally within quadrants I, II, III and IV (i.e., equally along lateral axes X and Y). Thus, the contact angle θ between the droplet  302  and insulating layer  303  decreases from θ 2  to θ 1  in FIG. 3A. The resulting shape of the droplet  302  is shown as the dashed line  307  in FIG. 3A. This new shape of the droplet  302  with contact angle θ 1  increases the focal length of the microlens  301  from the focal length of the microlens with the initial contact angle θ 2  (i.e., when V 1 =V 2 =V 3 =V 4 =V O ).  
         [0033]    [0033]FIG. 4 shows the prior art microlens of FIG. 3A and FIG. 3B wherein the lateral positioning of the droplet,  301  in FIGS. 3A and 3B, along the X and Y axes can also be changed relative to the initial location of the droplet by selectively applying voltages to one or more of the electrodes,  305  in FIGS. 3A and 3B. For example, referring to FIG. 4, by making V 1 =V 3 =V O  and by making V 2  greater than V 4 , the droplet  402  is attracted toward the higher voltage of the electrode  404  and thus moves in direction  407  toward quadrant II. As discussed above, by adjusting the lateral position of the droplet  402 , the lateral position of the focal spot of the microlens  401  in that microlens&#39; focal plane is also adjusted. Thus, by selectively adjusting the voltage applied to one or more of the electrodes  403 ,  404 ,  405  and  406  relative to the droplet  402  in different combinations, the focal length and the lateral position of the microlens  401  can be selectively adjusted.  
         [0034]    While the prior art electrowetting-based microlens embodiments described above are useful in certain applications, they are also limited in certain aspects of their usefulness. For example, all prior art electrowetting microlenses rely on an external control system to detect out of alignment conditions and vary the voltage differential between the droplet and the electrodes. Such control systems tend to be expensive to manufacture. Also, integration of these systems into an optoelectronic package (for use, e.g., in an optical telecommunications switch) is difficult. Additionally, since the position of the light beam is not a priori known, some sort of a search and optimization algorithm has to be employed to discover the ideal alignment conditions. This might result in a substantial increase in the time necessary to complete the tuning process. Thus, there remains a need to provide a tunable liquid microlens that does not rely on an external electronic control system to detect out of alignment conditions and adjust the position and/or focal length of the microlens. In particular, in certain applications it may be advantageous to have a microlens that is self-tunable. Such a microlens would eliminate the cost and effort associated with integrating the microlens control electronics previously necessary to tune electrowetting-based microlenses.  
         [0035]    [0035]FIG. 5 shows a first embodiment of the present invention wherein a self-tunable liquid microlens  501  includes a droplet  502  of a transparent conductive liquid disposed on a first surface of a hydrophobic layer  503  which is in turn disposed on a dielectric insulating layer  504 . Illustrative dielectric insulating materials include the aforementioned Teflon/Parylene surface. Alternatively, the dielectric insulating layer  504  could be made of a hydrophobic material, thus eliminating the need for a separate hydrophobic layer  503 . The microlens  501  includes a plurality of electrodes  505 , shown in cross section in FIG. 5 as electrodes  505   a  and  505   b , each of which is disposed on a layer of photoconducting material  507 . Suitable photoconducting materials include, but are not limited to, conjugated polymers, doped charge transporting polymers (such as poly[2-methoxy-5-(2′-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV)+C60), or certain inorganic semiconductors (such as PbS, HgCdTe, or Cd 1-x Mn x Te). Alternatively, a photovoltaic material, such as InP, CdX, GaAs, or CdTe, may be used. The electrodes  505  and the photoconducting material  507  are insulated from the droplet  502  by the dielectric insulating layer  504 . A conducting transparent substrate  506 , such as a substrate made from transparent glass, supports the electrodes  505 , the insulating layer  504  and the photo-conducting material  507 , and is connected to the droplet  502  via a well  512  running through the hydrophobic layer  503  and the dielectric insulating layer  504 . A voltage V O  is applied to the conducting transparent substrate  506  and, hence, the droplet  502 . The droplet  502  may advantageously be enclosed in an enclosure liquid or gas  509 .  
         [0036]    When a light beam  511  of a selected wavelength, such as that generated by a laser, is incident upon a particular segment of photo-conducting material, such as segment  510 , a current  514  develops between the conducting transparent substrate  506  and the electrode  505   a  associated with the segment of photo-conducting material  510 . As the light beam  511  overlaps a larger portion of the photo-conducting material  510  and electrode  505   a  (which would occur, for example, if the light beam becomes misaligned with the microlens), current  514  rises. If a photovoltaic material is used, instead of the photoconducting material, when light is incident upon the material a voltage is created in that material. The photovoltaic material is oriented such that the voltage over the electrode drops. Thus, when either a photoconducing material or a photovoltaic material is used, the voltage difference between electrode  505   a  and the conducting transparent substrate  506  (and, hence, the droplet  502 ) drops. Since the conducting droplet will tend to move toward an electrode with a higher voltage, the tendency in this case would be for the droplet to move toward electrode  505   b  (i.e, because the voltage across electrode  505   a  is lower than that across electrode  505   b ). However, this movement would be the opposite of the movement necessary to align the droplet with the light beam. Therefore, in response to a drop in voltage across electrode  505   a , electronic circuit  508  raises the voltage applied to electrode  505   a  relative to electrode  505   b , causing the droplet to be attracted toward electrode  505   a  and, thus, aligning the droplet  502  with the beam  511 . The electronics necessary achieve this variation in voltage are readily apparent to one skilled in the art. It is noteworthy that, unlike in prior art embodiments, electronic circuit  508  does not serve as an external control mechanism to detect out-of-alignment conditions between the beam  511  and the microlens  501  and, as a result, adjust voltages. Rather, in this embodiment of the present invention, the electronic circuit only distributes a higher voltage to electrode  505   a  or a lower voltage to electrode  505   b  in response to the voltage changes in the microlens itself in order to move the droplet in direction  513  to align it with the light beam  511 .  
         [0037]    [0037]FIG. 6 is a top plan view of microlens  501  in FIG. 5 and illustrates one illustrative configuration of the electrodes  505  in that figure. One skilled in the art will recognize that there are other equally advantageous configurations of electrodes  505  that are intended to be encompassed by the embodiments of the present invention. Referring to FIG. 6, each electrode  603 - 610  is coupled to a respective voltage V 1  through V 8 . Droplet  602 , which is centered initially relative to the electrodes  603 - 610 , is coupled to a voltage V O  via the well  612 . When there is no voltage difference between the droplet  602  and any of the electrodes (i.e., V 1 =V 2 =V 3 =V 4 =V 5 =V 6 =V 7 =V 8 =V O ) the droplet  602  is centered relative to the electrodes and each of segments I thru VIII. Additionally, the droplet  602  assumes a shape as determined by the contact angle θ in FIG. 5 and the volume in accordance with equations (1)-(3) expained above. Also as described above, the position of the droplet  602  and the focal length of the microlens  601  can be adjusted by selectively applying a voltage difference between the droplet  602  and selected individual electrodes  603 - 610 .  
         [0038]    Because the embodiment of FIG. 5 and FIG. 6 relies on an external electronic circuit to adjust the voltage of the electrodes, this embodiment is said to be an “active” microlens. FIGS. 7, 8 and  9  show an embodiment of the microlens of the present invention that is “passive”—that is, requires no external voltage-adjusting mechanism to adjust the position of the droplet. FIG. 7 shows that the microlens  701  of this embodiment is structurally similar to the microlens of FIGS. 5 and 6, with the addition of a second, upper layer  715  of electrodes (hereinafter referred to as “second layer”) that is electrically connected via leads  716  to the first, lower layer  705  of electrodes (hereinafter referred to as “first layer”). This connection is such that each of the first layer  705  of electrodes is electrically connected to an opposing electrode in the second layer  715 . This second layer  715  of electrodes is disposed within the dielectric insulating layer  704  above the first layer  705  of electrodes and is thus insulated by that dielectric layer from the droplet  702 , the first layer  705  of electrodes, the photo-conducting layer  707 , and the transparent conducting substrate  706 . The electrical connections between the first-layer electrodes and second-layer electrodes result in equal voltages between a particular electrode in the first layer (such as electrode  705   a ) and its counterpart opposing electrode in the upper layer (in this case, electrode  715   a ). Thus, when the light beam  711  is incident equally upon the photo-conducting material associated with electrodes in the first layer  705  (i.e., the light beam is aligned with the microlens), each of the electrodes in the first layer (and, hence, each of the corresponding opposing electrodes in the second layer) will be biased equally with respect to the conducting transparent substrate  706 . Thus, the droplet  702  is aligned with the beam  711  and will not move relative to the upper electrodes  715 .  
         [0039]    [0039]FIG. 8 is a top plan view of microlens  701  in FIG. 7 and illustrates one illustrative configuration of the second, upper layer  715  of electrodes in that figure. Referring to FIG. 8, each electrode  803  through  810  are disposed in a star pattern, with wedge-like gaps between each electrode, such that the surface area of the electrode decreases as the distance from the center well increases. One skilled in the art will recognize that there are other equally advantageous configurations of this upper layer  715  of electrodes hat are intended to be encompassed by the embodiments of the present invention. Each electrode  803 - 810  in the upper layer is coupled to its opposing electrode in the first, lower layer,  705  in FIG. 7, of electrodes. Referring to FIG. 9, showing an exemplary configuration of the upper and lower electrode planes  715  and  705  in FIG. 7, respectively, electrodes  808 ,  809 ,  810  and  803  are connected, respectively, to opposing electrodes  902 ,  903 ,  904  and  905 . This same illustrative connection configuration is followed for each of electrodes  803 - 810  in FIG. 8, wherein each is electrically coupled to its opposing electrode in the first, lower layer. Each of the electrodes in the first, lower layer of electrodes is, in turn, coupled to a voltage V 1  through V 8 . Droplet  802 , which is responsive to and initially centered relative to the electrodes  803 - 810  in the second, upper layer, is coupled to a voltage V O  via the well  812  leading to the conducting transparent substrate,  706  in FIG. 7.  
         [0040]    When there is no voltage difference between the droplet  802  and any of the electrodes in the first, lower layer (i.e., V 1 =V 2 =V 3 =V 4 =V 5 =V 6 =V 7 =V 8 =V O ), the droplet  802  will remain centered relative to the upper level electrodes and each of segments I thru VIII. However, when a voltage difference exists between the droplet  802  and individual electrodes in the first layer, the position of the droplet  802  is automatically adjusted.  
         [0041]    For example, referring once again to FIG. 7, the light beam  711  is not initially aligned with the microlens  701 . A greater portion of the light beam  711  is, for example, incident upon electrode  705   a . Thus, the leakage current  714  that develops in the segment of photo-conducting material corresponding to electrode  705   a  is greater than the current  717  corresponding to electrode  705   b . It follows that the voltage V 1  applied to electrode  705   b  is greater than the voltage V 2  applied to electrode  705   a . Since electrode  715   b  is electrically connected to electrode  705   b , and electrode  715   a  is connected to electrode  705   a , electrode  715   b  also experiences voltage V 1  and electrode  715   a  experiences voltage V 2 . The droplet  702 , with applied voltage V O , will move toward the higher voltage V 1 , in direction  713 . Thus, the microlens  701  in this embodiment is self-aligning in that the droplet  702  will automatically move to align itself with the light beam with no external control apparatus.  
         [0042]    Referring once again to FIG. 8, which shows a top plan view of FIG. 7, a greater portion of the cross-section of the mis-aligned light beam  811  is incident upon the first, lower layer of electrodes in segments I, II, III and IV, than is incident upon the first, lower layer of electrodes in segments V, VI, VII and VIII, respectively. Thus, the voltages V 5 , V 6 , V 7  and V 8  across the lower layer of electrodes are higher than the voltages V 1 , V 2 , V 3  and V 4 , respectively. As previously discussed, therefore, the upper electrodes  803 - 806  in segments I, II, III and IV, respectively, will experience a higher voltage than the upper electrodes  807 - 810  in segments V, VI, VII and VIII respectively. Since the droplet  802  will move toward those upper electrodes with the highest voltage, the droplet will move in approximately direction  813  to align itself with the light beam  811 . The driving force needed to move the droplet in direction  813  is directly proportional to the square of the voltage (V 2 ) across each electrode multiplied by the intersection L n  between the outer circumference of the droplet and each of the electrodes. The upper electrodes are disposed in a star-like pattern with wedge-like gaps between the electrodes (or other equally advantageous configuration) in a way such that the length of the intersection of the circumference of the droplet and a particular electrode will decrease as the droplet moves in the direction of that particular electrode. As a result, the driving force will decrease as the droplet  802  moves in direction  813 . The droplet  802  will move in direction  813  until V 1   2 *L 5 =V 2   2 *L 6 =V 3   2 *L 7 =V 4   2 *L 8 =V 5   2 *L 1 =V 6   2 *L 2 =V 7   2 *L 3 =V 8   2 *L 4  (i.e., the droplet  802  is aligned with the beam  811 ). In other words, the droplet  802  will move until the continuous reduction in the driving force due to the decrease in the length of contact between the circumference of the droplet and the individual electrodes  805  and  804  results in the equilibrium of the forces acting on the droplet. The size and number of the wedge-like gaps between the electrodes is designed in such a way as to insure that the motion of the droplet halts at the point where it is aligned with the light beam.  
         [0043]    The foregoing merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are within its spirit and scope. Furthermore, all examples and conditional language recited herein are intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting aspects and embodiments of the invention, as well as specific examples thereof, are intended to encompass functional equivalents thereof.