Abstract:
In an optical deflector apparatus including a mirror, an inner frame, an outer frame, an inner piezoelectric actuator adapted to flex the mirror around an axis of the mirror, an outer piezoelectric actuator adapted to flex the mirror around the axis of the mirror, and a driver adapted to generate an offset drive voltage and a rocking drive voltage. The offset drive voltage is applied to a first piezoelectric actuator selected from the inner piezoelectric actuator and the outer piezoelectric actuator. The rocking drive voltage is applied to a second piezoelectric actuator different from the first piezoelectric actuator.

Description:
This application claims the priority benefit under 35 U.S.C. §119 to Japanese Patent Application No. JP2014-121658 filed on Jun. 12, 2014, which disclosure is hereby incorporated in its entirety by reference. 
     BACKGROUND 
     1. Field 
     The presently disclosed subject matter relates to an optical deflector apparatus. The optical deflector apparatus can be applied as an optical scanner to a laser pico projector, a laser radar, a bar code reader, an area sensor, an adaptive front-lighting system (AFS) type head lamp, a head-up display unit, and other optical apparatuses, to generate scanning light. 
     2. Description of the Related Art 
     Generally, in an optical scanner or the like, an optical deflector apparatus is constructed by a micro electro mechanical system (MEMS) device manufactured by using semiconductor manufacturing processes and micro machine technology. 
     A prior art optical deflector apparatus as a MEMS device is constructed by a mirror, an outer frame (fixed frame) surrounding the mirror, piezoelectric actuators coupled between the mirror and the outer frame, serving as cantilevers for rocking the mirror with respect to an axis (X-axis) of the mirror in a rocking operation mode (see: JP2012-198314A). 
     On the other hand, in an AFS control, when a steering angle read from a steering angle sensor or the like is larger than a predetermined value, the area of high luminous intensities needs to be shifted from a central position of the head lamp to a right side or a left side of the head lamp, to substantially decline the optical axis of the head lamp while the visibility in a high-beam mode is maintained. If such an AFC control is applied to the above-described prior art optical deflector apparatus, an offset voltage is applied to the piezoelectric actuators to deflect the mirror around the X-axis. This is called an offset operation mode. 
     In the above-described prior art optical deflector apparatus, when a rocking operation mode and an offset operation are simultaneously carried out, rocking drive voltages are offset by an offset voltage corresponding to the shifted amount of the optical axis of the head lamp, for example. In other words, the offset voltage is combined with the rocking drive voltages to generate combined drive voltages which are applied to the piezoelectric actuators (see:  FIGS. 14, 15, 16 and 17  of JP2012-198314A). In this case, the piezoelectric actuators are used commonly for a rocking operation mode and an offset operation mode. 
     In the above-described prior art optical deflector apparatus, however, when the combined drive voltages become larger than a threshold value corresponding to the maximum rocking angle of the mirror with respect to the X-axis of the mirror, the piezoelectric actuators would be damaged. Therefore, the offset voltage is limited, so that the combined drive voltages do not exceed the threshold value. As a result, the offset deflecting amount of the mirror cannot be increased. Otherwise, if the offset voltage is caused to be increased, the rocking drive voltages need to be decreased. In this case, it is impossible to increase the rocking amount of the mirror. 
     SUMMARY 
     The presently disclosed subject matter seeks to solve the above-described problems. 
     According to the presently disclosed subject matter, an optical deflector apparatus includes a mirror, an inner frame surrounding the mirror, an outer frame surrounding the inner frame, an inner piezoelectric actuator coupled between the mirror and the inner frame and adapted to flex the mirror around an axis of the mirror, an outer piezoelectric actuator coupled between the inner frame and the outer frame and adapted to flex the mirror around the axis of the mirror, and a driver adapted to generate an offset drive voltage and a rocking drive voltage. The offset drive voltage is applied to a first piezoelectric actuator selected from the inner piezoelectric actuator and the outer piezoelectric actuator. The rocking drive voltage is applied to a second piezoelectric actuator different from the first piezoelectric actuator, selected from the inner piezoelectric actuator and the outer piezoelectric actuator. 
     According to the presently disclosed subject matter, since the first piezoelectric actuator for an offset operation mode is independent of the second piezoelectric actuator for a rocking operation mode, the offset deflecting amount (angle) can be increased, and also, the rocking amount (angle) can be increased. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other advantages and features of the presently disclosed subject matter will be more apparent from the following description of certain embodiments, taken in conjunction with the accompanying drawings, wherein: 
         FIG. 1  is a plan view illustrating a first embodiment of the optical deflector apparatus according to the presently disclosed subject matter; 
         FIGS. 2A and 2B  are views for explaining the operation of the inner piezoelectric actuator of  FIG. 1 ; 
         FIG. 3  is a cross-sectional view of the optical deflector of  FIG. 1 ; 
         FIG. 4  is a graph for explaining the relationship between the deflection angle and offset angle of the mirror of  FIG. 1 ; 
         FIGS. 5A, 5B, 5C and 5D  are timing diagrams of the drive voltages applied to the piezoelectric actuators of  FIG. 1 ; 
         FIG. 6  is a plan view illustrating a second embodiment of the optical deflector apparatus according to the presently disclosed subject matter; 
         FIGS. 7A, 7B, 7C and 7D  are timing diagrams of the drive voltages applied to the piezoelectric actuators of  FIG. 6 ; 
         FIG. 8  is a plan view illustrating a first modification of the optical deflector apparatus of  FIG. 6 ; 
         FIG. 9  is a plan view illustrating a second modification of the optical deflector apparatus of  FIG. 6 ; 
         FIG. 10  is a plan view illustrating a third modification of the optical deflector apparatus of  FIG. 6 ; 
         FIG. 11  is a plan view illustrating a fourth modification of the optical deflector apparatus of  FIG. 6 ; 
         FIG. 12  is a plan view illustrating a fifth modification of the optical deflector apparatus of  FIG. 6 ; 
         FIG. 13  is a plan view illustrating a sixth modification of the optical deflector apparatus of  FIG. 6 ; 
         FIG. 14  is a plan view illustrating a third embodiment of the optical deflector apparatus according to the presently disclosed subject matter; 
         FIGS. 15A and 15B  are timing diagrams of the drive voltages applied to the piezoelectric actuators of  FIG. 14 ; 
         FIG. 16  is a plan view illustrating a fourth embodiment of the optical deflector apparatus according to the presently disclosed subject matter; and 
         FIGS. 17A and 17B  are timing diagrams of the drive voltages applied to the piezoelectric actuators of  FIG. 16 . 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     In  FIG. 1 , which illustrates a first embodiment of the optical deflector apparatus according to the presently disclosed subject matter as a one-dimensional MEMS device, reference numeral  10  designates a one-dimensional optical deflector,  20  designates a driver for driving the optical deflector  10 , and  30  designates a laser light source. 
     The optical deflector  10  is constructed by a rectangular mirror  1  for reflecting incident light L from the laser light source  30 , a rectangular inner frame (movable frame)  2  surrounding the mirror  1 , and a rectangular outer frame (fixed frame) surrounding the inner frame  2 . 
     Also, in order to realize an offset operation mode, a pair of meander-type inner piezoelectric actuators  4   a  and  4   b  are coupled between coupling portions  1   a  and  1   b  of the mirror  1  and inner coupling portions  2   a  and  2   b  of the inner frame  2  and serving as cantilevers for rocking the mirror  1  around an X-axis on the plane of the mirror  1  centered at the center  0  of the mirror  1 . The inner piezoelectric actuators  4   a  and  4   b  are arranged opposite to each other with respect to the mirror  1 . 
     Further, in order to realize a rocking operation mode, a pair of torsion bars  5   a  and  5   b  are coupled to outer circumferences of the inner frame  2  along the X-axis. Also, linear outer piezoelectric actuators  6   a - 1  and  6   a - 2  are coupled between the torsion bar  5   a  and the outer frame  3 , and linear outer piezoelectric actuators  6   b - 1  and  6   b - 2  are coupled between the torsion bar  5   b  and the outer frame  3 . In this case, the flexing direction of the outer piezoelectric actuators  6   a - 1  and  6   b - 1  are opposite to that of the outer piezoelectric actuators  6   b - 1  and  6   b - 2 , so that the outer piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  serve as cantilevers for rocking the mirror  1  around the X-axis. Note that the torsion bars  5   a  and  5   b  can be coupled to the outer frame  3 . 
     The mirror  1  can be square, rectangular, polygonal or elliptical. 
     The meander-type inner piezoelectric actuators  4   a  and  4   b  are symmetrical to each other with respect to the Y-axis. 
     In more detail, the meander-type inner piezoelectric actuator  4   a  is constructed by piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  which are serially-coupled from the coupling portion  1   a  of the mirror  1  to a coupling portion  2   a  of the inner frame  2  via folded portions Fa 12  and Fa 23 . Also, each of the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  is in parallel with the Y-axis. Therefore, the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  are folded at their ends or meandering from the mirror  1  to the inner frame  2 , so that the amplitudes of the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  can be changed along directions perpendicular to the X-axis. 
     Similarly, the meander-type inner piezoelectric actuator  4   b  is constructed by piezoelectric cantilevers  4   b - 1   s ,  4   b - 2  and  4   b - 3   s  which are serially-coupled from the coupling portion  1   b  of the mirror  1  to an inner coupling portion  2   b  of the inner frame  2  via folded portions Fb 12  and Fb 23 . Also, each of the piezoelectric cantilevers  4   b - 1   s ,  4   b - 2  and  4   b - 3   s  are in parallel with the Y-axis. Therefore, the piezoelectric cantilevers  4   b - 1   s ,  4   b - 2  and  4   b - 3   s  are folded at their ends or meandering from the mirror  1  to the inner frame  2 , so that the piezoelectric cantilevers  4   b - 1   s ,  4   b - 2  and  4   b - 3   s  can be changed along directions perpendicular to the X-axis. 
     The meander-type inner piezoelectric actuators  4   a  ( 4   b ) operate as follows. 
     In the inner piezoelectric actuators  4   a  ( 4   b ), the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  ( 4   b - 1   s ,  4   b - 2  and  4   b - 3   s ) are divided into an odd-numbered group of the piezoelectric cantilevers  4   a - 1   s  and  4   a - 3   s  ( 4   b - 1   s  and  4   b - 3   s ), and an even-numbered group of the piezoelectric cantilever  4   a - 2  ( 4   b - 2 ) alternating with the odd-numbered group of the piezoelectric cantilevers  4   a - 1   s  and  4   a - 3   s  ( 4   b - 1   s  and  4   b - 3   s ). 
     When no drive voltages are applied to the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s,  the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  are as illustrated in  FIG. 2A . 
     On the other hand, when a first drive voltage is applied to the odd-numbered group of the piezoelectric cantilevers  4   a - 1   s  and  4   a - 3   s  and a second drive voltage opposite in phase to the first drive voltage is applied to the even-numbered group of the piezoelectric cantilever  4   a - 2 , for example, the odd-numbered group of the piezoelectric cantilever  4   a - 1   s  and  4   a - 3   s  are flexed in one direction, for example, in an upward direction U, and the even-numbered group of the piezoelectric cantilever  4   a - 2  is flexed in the other direction, i.e., in a downward direction D. Otherwise, the odd-numbered group of the piezoelectric cantilevers  4   a -is and  4   a - 3   s  are flexed in the downward direction D, the even-numbered group of the piezoelectric cantilever  4   a - 2  is flexed in the upward direction U. In this case, since the length of each of the piezoelectric cantilever  4   a - 1   s  and  4   a - 3   s  is about half of that of the piezoelectric cantilever  4   a - 2 , the flexing amounts of the piezoelectric cantilevers  4   a - 1   s  and  4   a - 3   s  are about half of that of the piezoelectric cantilever  4   a - 2 ; however, the flexing center of the piezoelectric actuator  4   a  is close to the center thereof. 
     Thus, the mirror  1  is flexed around the X-axis by the inner piezoelectric actuators  4   a  and  4   b.    
     Note that the number of piezoelectric cantilevers in each of the inner piezoelectric actuators  4   a  and  4   b  can be other values such as 4, 5, . . . . 
     Returning to  FIG. 1 , the torsion bars  5   a  and  5   b  have ends coupled to the outer circumference of the inner frame  2 . Therefore, the torsion bars  5   a  and  5   b  are twisted by the outer piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  to rock the mirror  1  around the X-axis. Other ends of the torsion bars  5   a  and  5   b  can be coupled to the inner circumference of the outer frame  3 . 
     A method for manufacturing the optical deflector  10  of  FIG. 1  is explained with reference to  FIG. 3 . 
     First, a silicon-on-insulator (SOI) structure constructed by a monocrystalline silicon support layer (“Handle” layer)  301 , an intermediate (buried) silicon dioxide layer (“Box” layer)  302 , and a monocrystalline silicon active layer (“Device” layer)  303  is prepared. Also, by a thermal oxidation process, a silicon dioxide layer  304  is formed on the support layer  301 , and a silicon dioxide layer  305  is formed on the active layer  303 . Further, piezoelectric actuator cantilevers  4   a - 1   s ,  4   a - 2 ,  4   a - 3   s,    4   b - 1   s ,  4   b - 2 ,  4   b - 3   s  and the piezoelectric actuators  6   b - 1  and  6   b - 2  are formed on the silicon dioxide layer  305 . 
     Next, a Pt/Ti lower electrode layer  306  consisting of an about 50 nm thick Ti and an about 150 nm thick Pt on Ti is formed by a sputtering process. Then, an about 3 μm thick PZT layer  307  is deposited on the lower electrode layer  306  by an arc discharge reactive ion plating (ADRIP) process at a temperature of about 500° C. to 600° C. Then, an about 150 nm thick Ti upper electrode layer  308  is formed on the PZT layer  307  by a sputtering process. 
     Next, the upper electrode layer  308  and the PZT layer  307  are patterned by a photolithography and etching process. Then, the lower electrode layer  306  and the silicon dioxide layer  305  are patterned by a photolithography and etching process. 
     Next, an about 500 nm thick silicon dioxide interlayer  309  is formed on the entire surface by a plasma chemical vapor deposition (CVD) process. 
     Next, contact holes are perforated in the silicon dioxide interlayer  309  by a photolithography and dry etching process. The contact holes correspond to the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2 ,  4   a - 3   s,    4   b - 1   s ,  4   b - 2  and  4   b - 3   s,  the piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  and the pads P formed on the outer frame  3 . 
     Next, wiring layers  310  made of AlCu (1% Cu) are formed by a photolithography process, a sputtering process, and a lift-off process. The wiring layers  310  are electrically connected between the upper electrode layers  308  of the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2 ,  4   a - 3   s,    4   b - 1   s ,  4   b - 2  and  4   b - 3   s  and the piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  and their corresponding pads P. 
     Next, the silicon dioxide layer  304  is etched by a photolithography and dry etching process, so that the silicon dioxide layer  304  is left in an area corresponding to the inner frame  2  and the outer frame  3 . 
     Next, the support layer  301  is etched by a dry etching process using the silicon dioxide layer  304  as an etching mask. Then, the silicon dioxide layer  302  is etched by a wet etching process using the support layer  301  as an etching mask. 
     Finally, an aluminum (Al) reflective metal layer  311  is formed by an evaporation process on the active layer  303 , and is patterned by a photolithography and etching process, thus completing the optical deflector  10 . 
     In Fig,  3 , the torsion bars  5   a  and  5   b  are formed by the active layer  303 . 
       FIG. 4  is a graph for explaining the deflection angle and offset angle of the mirror  1  of  FIG. 1 . 
     The driver  20  controls the outer piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  using sinusoidal-wave voltages V X1  and V X2  opposite in phase to each other, so that the rocking angle of the mirror  1  is from −θ to +θ with respect to a normal line n 1  normal to the plane m 1  of the mirror  1  as illustrated in  FIG. 4 . 
     On the other hand, the driver  20  controls the inner piezoelectric actuators  4   a  and  4   b  using saw-tooth drive voltages V OFFSET1  and V OFFSET2  opposite in phase to each other, so that the rocking angle of the mirror  1  is shifted by θ OFFSET  , so that the plane m 1  of the mirror  1  is rotated by θ OFFSET  to a plane m 2  with a normal line n 2  as illustrated in  FIG. 4 . In this state, the driver  20  also controls the outer piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  using the above-mentioned sinusoidal-wave voltages V X1  and V X2 , so that the rocking angle of the mirror  1  is from −θ to +θ with respect to the normal line n 2 , i. e. , from −θ−θ OFFSET  to +θ−θ OFFSET  with respect to the normal line n 1 . For example, the rocking angle of the mirror  1  from −10° to +10° with respect to the normal line n 1  is changed by the offset angle θ OFFSET 5° of the inner piezoelectric actuators  4   a  and  4   b  to the rocking angle of the mirror  1  from −15° to +5° with respect to the normal line n 1 . 
     The rocking operation of the mirror  1  by the outer piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  in a rocking operation mode around the X-axis will be explained below. 
     Rocking sinusoidal-wave drive voltages V X1  and V X2  opposite in phase to each other as illustrated in  FIGS. 5A and 5B  are applied by the driver  20  to the outer piezoelectric actuators  6   a - 1  and  6   a - 2 , respectively, so that the outer piezoelectric actuators  6   a - 1  and  6   a - 2  carry out flexing operations in opposite directions to each other, which would distort the torsion bar  5   a  in a direction to cause a torque in the mirror  1  around the X-axis. Simultaneously, the above-mentioned rocking sinusoidal-wave drive voltages V X1  and V X2  are applied by the driver  20  to the outer piezoelectric actuators  6   b - 1  and  6   b - 2 , respectively, so that the outer piezoelectric actuators  6   b - 1  and  6   b - 2  carry out flexing operations in opposite directions to each other, which also would distort the torsion bar  5   b  in the above-mentioned direction to cause a torque in the mirror  1  around the X-axis. As a result, the torsion bars  5   a  and  5   b  are twisted to rock the mirror  1  around the X-axis. In this case, if the frequency f X  of the sinusoidal-wave drive voltages V X1  and V X2  is a resonant frequency such as 20 kHz of a mechanical vibrating system of the mirror  1  with respect to the X-axis depending upon the mirror  1 , the inner frame  2  and the inner piezoelectric actuators  4   a  and  4   b,  the rocking angle of the mirror  1  can further be enhanced. 
     The offset operation of the mirror  1  by the inner piezoelectric actuators  4   a  and  4   b  in an offset operation mode will be explained below. 
     An offset saw-tooth drive voltage V OFFSET1  as illustrated in  FIG. 5C  is applied by the driver  20  to the odd-numbered piezoelectric cantilevers  4   a - 1   s  and  4   a - 3   s  of the inner piezoelectric actuator  4   a  and the odd-numbered. piezoelectric cantilevers  4   b - 1   s  and  4   b - 3   s  of the inner piezoelectric actuator  4   b.  Simultaneously, an offset drive voltage V OFFSET2  as illustrated in  FIG. 5D  opposite in phase to the offset drive voltage V OFFSET1  is applied by the driver  20  to the even-numbered piezoelectric cantilever  4   a - 2  of the inner piezoelectric actuator  4   a  and the even-numbered piezoelectric cantilever  4   b - 2  of the inner piezoelectric actuator  4   b.  Therefore, the odd-numbered piezoelectric cantilevers  4   a - 1   s ,  4   a - 3   s;    4   b - 1   s ,  4   b - 3   s  and the even-numbered piezoelectric cantilevers  4   a - 2  and  4   b - 2  carry out flexing operations in opposite directions to each other. As a result, the mirror  1  is flexed in one direction. 
     For example, in a positive offset angle, the offset drive voltage V OFFSET1  is rectangular-wave shaped as indicated by a solid line in  FIG. 5C , while the offset drive voltage V OFFSET2  is pulse-shaped as indicated by a solid line in  FIG. 5D . In this case, the offset drive voltage V OFFSET2  can be L(low level). Contrary to this, in a negative offset angle, the offset drive voltage V OFFSET1  is pulse-shaped as indicated by a dotted line in  FIG. 5C , while the offset drive voltage V OFFSET2  is rectangular-wave shaped as indicated by a dotted line  FIG. 5D . In this case, the offset drive voltage V OFFSET1  can be L (low level). The offset drive voltages V OFFSET1  and V OFFSET2  have the same frequency f X  of the rocking sinusoidal-wave drive voltages V X1 , and V X2 . The amplitude of the rectangular-waved offset drive voltage V OFFSET1  or V OFFSET2  corresponds to an offset angle of the mirror  1 . 
     In  FIGS. 5A, 5B, 5C and 5D , T A  is an image active period, and T B  is a blanking period. That is, in a horizontal scanning by the rocking sinusoidal-wave drive voltages V X1 and V X2 , the scanning speed is constant in the image active period T A , while the scanning speed is low in the blanking period T B . Therefore, since image display is impossible in the blanking period T B , the offset drive voltages V OFFSET1  and V OFFSET2  are inactive or pulse-shaped. 
     In addition, the offset drive voltages V OFFSET1  and V OFFSET2  can always be active even in the blanking period T B ; however, in this case, charges may be stored in the PZT layer  308  so that the polarization within the PZT layer  308  would be decreased to decrease the offset angle of the mirror  1 . Contrary to this, as stated above, when the offset drive voltages V OFFSET1  and V OFFSET2  are caused to be inactive or pulse-shaped in the blanking period T B , the charges stored in the PZT layer  308  are emitted to recover the offset angle corresponding to the rectangular-waved offset drive voltage V OFFSET1  or V OFFSET2  in the active period T A . 
     In the meander type piezoelectric actuators  4   a  and  4   b  of  FIG. 1 , the lengths of the piezoelectric cantilevers can be the same, so that the flexing amounts of the piezoelectric cantilevers can be enhanced. Also, the piezoelectric cantilevers  4   a - 1   s ,  4   a - 2  and  4   a - 3   s  and the piezoelectric cantilevers  4   b - 1   s ,  4   b - 2  and  4   b - 3   s  can be symmetrical with respect to the center  0  of the mirror  1 . In this case, the offset drive voltage V OFFSET1  is applied to the piezoelectric cantilevers  4   a - 1   s ,  4   a - 3   s  and  4   b - 2 , while the offset drive voltage V OFFSET2  is applied to the piezoelectric cantilevers  4   b - 1   s ,  4   b - 3   s  and  4   a - 2 . Further, the meander-type piezoelectric cantilevers  4   a  and  4   b  can be provided between the inner frame  2  and the outer frame  3 , while the piezoelectric actuators  6   a - 1  and  6   a - 2  along with the torsion bars  4   a  and  4   b  can be provided between the mirror  1  and the inner frame  2 . 
     In  FIG. 6 , which illustrates a second embodiment of the optical deflector apparatus according to the presently disclosed subject matter, the torsion bars  5   a  and  5   b  and the outer piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b - 1  and  6   b - 2  of  FIG. 1  are replaced by a pair of meander-type outer piezoelectric actuators  7   a  and  7   b  which are symmetrical to each other with respect to the Y-axis. 
     In more detail, the meander-type outer piezoelectric actuator  7   a  is constructed by piezoelectric cantilevers  7   a - 1   s ,  7   a - 2  and  7   a - 3   s  which are serially-coupled from a coupling portion  2   c  of the inner frame  2  to a coupling portion  3   a  of the outer frame  3  via folded portions Fc 12  and Fc 23 . Also, each of the piezoelectric cantilevers  7   a - 1   s ,  7   a - 2  and  7   a - 3   s  is in parallel with the Y-axis. Therefore, the piezoelectric cantilevers  7   a - 1   s ,  7   a - 2  and  7   a - 3   s  are folded at their ends or meandering from the inner frame  2  to the outer frame  3  so that the amplitudes of the piezoelectric cantilevers  7   a - 1   s ,  7   a - 2  and  7   a - 3   s  can be changed along directions perpendicular to the X-axis. 
     Similarly, the meander-type outer piezoelectric actuator  7   b  is constructed by piezoelectric cantilevers  7   b - 1   s ,  7   b - 2  and  7   b - 3   s  which are serially-coupled from a coupling portion  2   d  of the inner frame  2  to a coupling portion  3   b  of the outer frame  3  via folded portions Fd 12  and Fd 23 . Also, each of the piezoelectric cantilevers  7   b - 1   s ,  7   b - 2  and  7   b - 3   s  are in parallel with the Y-axis. Therefore, the piezoelectric cantilevers  7   b - 1   s ,  7   b - 2  and  7   b - 3   s  are folded at their ends or meandering from the inner frame  2  to the outer frame  3  so that the piezoelectric cantilevers  7   b - 1   s ,  7   b - 2  and  7   b - 3   s  can be changed along directions perpendicular to the X-axis. 
     The meander-type outer piezoelectric actuators  7   a  ( 7   b ) operate in the same way as the inner piezoelectric actuators  4   a  ( 4   b ). 
     Thus, the mirror  1  is rocked around the X-axis by the outer piezoelectric actuators  7   a  and  7   b.    
     Note that the number of piezoelectric cantilevers in each of the outer piezoelectric actuators  7   a  and  7   b  can be other values such as 4, 5, . . . . 
     The rocking operation of the mirror  1  by the outer piezoelectric actuators  7   a  and  7   b  in a rocking operation mode around the X-axis will be explained below. 
     A rocking saw-tooth drive voltage V X1 ′ as illustrated in  FIG. 7A  is applied by the driver  20  to the odd-numbered piezoelectric cantilevers  7   a - 1   s  and  7   a - 3   s  of the outer piezoelectric actuator  7   a  and the odd-numbered piezoelectric cantilevers  7   b - 1   s  and  7   b - 3   s  of the inner piezoelectric actuator  7   b.  Simultaneously, a rocking saw-tooth drive voltage V X2 ′ as illustrated in  FIG. 7B  is applied by the driver  20  to the even-numbered piezoelectric cantilever  7   a - 2  of the outer piezoelectric actuator  7   a  and the even-numbered piezoelectric cantilever  7   b - 2  of the outer piezoelectric actuator  7   b.  Therefore, the odd-numbered piezoelectric cantilevers  7   s - 1   s ,  7   a - 3   s;    7   b - 1   s ,  7   b - 3   s  and the even-numbered piezoelectric cantilevers  7   a - 2  and  7   b - 2  carry out flexing operations in opposite directions to each other. As a result, the mirror  1  is rocked around the X-axis. 
     In  FIG. 6 , the meander-type outer piezoelectric actuators  7   a  and  7   b  are specialized for a rocking operation mode around the X-axis, and the meander-type inner piezoelectric actuators  4   a  and  4   b  are specialized for an offset operation mode around the X-axis. However, the meander-type inner piezoelectric actuators  4   a  and  4   b  can be specialized for a rocking operation mode around the X-axis, and the meander-type outer piezoelectric actuators  7   a  and  7   b  can be specialized for an offset operation mode around the X-axis. 
     In  FIG. 8 , which illustrates a first modification of the optical deflector apparatus of  FIG. 6 , the meander-type inner piezoelectric actuator  4   b  of  FIG. 6  is replaced by a meander-type inner piezoelectric actuator  4   b ′ which is symmetrical to the meander-type inner piezoelectric actuator  4   a  with respect to the center  0  of the mirror  1 , and the meander-type outer piezoelectric actuator  7   b  of  FIG. 6  is replaced by a meander-type outer piezoelectric actuator  7   b ′ which is symmetrical to the meander-type inner piezoelectric actuator  7   a  with respect to the center  0  of the mirror  1 . The operation of the optical deflector of  FIG. 8  is the same as that of the optical deflector of  FIG. 6 , except the following. The rocking saw-tooth drive voltage V X1 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 1   s ,  7   a - 3   s  and  7   b - 2 , and the rocking saw-tooth drive voltage V X2 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 2 ,  7   b - 1   s  and  7   b - 3   s.  Also, the offset saw-tooth drive voltage V OFFSET1  is applied by the driver  20  to the piezoelectric cantilevers  4   a - 1   s ,  4   a - 3   s  and  4   b - 2  and the offset saw-tooth drive voltage V OFFSET2  is applied by the driver  20  to the piezoelectric cantilevers  4   a - 2 ,  4   b - 1   s  and  4   b - 3   s.    
     In  FIG. 9 , which illustrates a second modification of the optical deflector apparatus of  FIG. 6 , the piezoelectric cantilevers  7   a - 1   s ,  7   a - 3   s,    7   b - 1   s  and  7   b - 3   s  of  FIG. 6  are replaced by piezoelectric cantilevers  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 , respectively, whose length is the same as that of the piezoelectric cantilevers  7   a - 2  and  7   b - 2 . The operation of the optical deflector of  FIG. 9  is the same as that of the optical deflector of  FIG. 6 , except that the rocking saw-tooth drive voltage V X1 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 . 
     In  FIG. 10 , which illustrates a third modification of the optical deflector apparatus of  FIG. 6 , the piezoelectric cantilevers  4   a - 1   s ,  4   a - 3   s,    4   b - 1   s  and  4   b - 3   s  of  FIG. 6  are replaced by piezoelectric cantilevers  4   a - 1 ,  4   a - 3 ,  4   b - 1  and  4   b - 3 , respectively, whose length is the same as that of the piezoelectric cantilevers  4   a - 2  and  4   b - 2 . The operation of the optical deflector of  FIG. 10  is the same as that of the optical deflector of  FIG. 6 , except that the offset saw-tooth drive voltage V OFFSET1  is applied by the driver  20  to the piezoelectric cantilevers  4   a - 1 ,  4   a - 3 ,  4   b - 1  and  4   b - 3 . 
     In  FIG. 11 , which illustrates a fourth modification of the optical deflector apparatus of  FIG. 6 , the piezoelectric cantilevers  4   a - 1   s ,  4   a - 3   s,    4   b - 1   s ,  4   b - 3   s,    7   a - 1   s ,  7   a - 3   s,    7   b - 1   s  and  7   b - 3   s  of  FIG. 6  are replaced by piezoelectric cantilevers  4   a - 1 ,  4   a - 3 ,  4   b - 1 ,  4   b - 3 ,  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 , respectively, whose length is the same as that of the piezoelectric cantilevers  4   a - 2  and  4   b - 2  and the piezoelectric cantilevers  7   a - 2  and  7   b - 2 . The operation of the optical deflector of  FIG. 11  is the same as that of the optical deflector of  FIG. 6 , except for the following. The rocking saw-tooth drive voltage V X1 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 . Also, the offset saw-tooth drive voltage V OFFSET1  is applied by the driver  20  to the piezoelectric cantilevers  4   a - 1 ,  4   a - 3 ,  4   b - 1  and  4   b - 3 . 
     In  FIG. 12 , which illustrates a fifth modification of the optical deflector apparatus of  FIG. 6 , the piezoelectric cantilevers  4   a - 1   s ,  4   a - 3   s,    4   b - 1   s  and  4   b - 3   s ,  7   a - 1   s ,  7   a - 3   s,    7   b - 1   s  and  7   b - 3   s  of  FIG. 6  are replaced by piezoelectric cantilevers  4   a - 1 ,  4   a - 3 ,  4   b - 1 ,  4   b - 3 ,  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 , respectively, whose length is the same as that of the piezoelectric cantilevers  4   a - 2  and  4   b - 2  and the piezoelectric cantilevers  7   a - 2 , and  7   b - 2 . Additionally, the meander-type inner piezoelectric actuator  4   b  of  FIG. 6  is replaced by a meander-type inner piezoelectric actuator  4   b ′ which is symmetrical to the meander-type inner piezoelectric actuator  4   a  with respect to the center  0  of the mirror  1 . The operation of the optical deflector of  FIG. 12  is the same as that of the optical deflector of  FIG. 6 , except for the following. The rocking saw-tooth drive voltage V X1 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 . Also, the offset saw-tooth drive voltage V OFFSET1  is applied by the driver  20  to the piezoelectric cantilevers  4   a - 1 ,  4   a - 3  and  4   b - 2 , and the offset saw--tooth drive voltage V OFFSET2  is applied by the driver  20  to the piezoelectric cantilevers  4   a - 2 ,  4   b - 1  and  4   b - 3 . 
     In  FIG. 13 , which illustrates a sixth modification of the deflector apparatus of  FIG. 6 , the meander-type outer piezoelectric actuator  7   b  of  FIG. 12  is replaced by a meander-type outer piezoelectric actuator  7   b ′ which is symmetrical to the meander type outer piezoelectric actuator  7   a  of  FIG. 12  with respect to the center  0  of the mirror  1 . The operation of the optical deflector of  FIG. 13  is the same as that of the optical deflector of  FIG. 12 , except that the rocking saw-tooth drive voltage V X1 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 1 ,  7   a - 3 ,  7   b - 1  and  7   b - 3 , and the rocking saw-tooth drive voltage V X3 ′ is applied by the driver  20  to the piezoelectric cantilevers  7   a - 2 ,  7   b - 1  and  7   b - 2 . 
     Even in  FIGS. 8, 9, 10, 11, 12 and 13 , the meander-type outer piezoelectric actuators  7   a  and  7   b  ( 7   b ′) are specialized for a rocking operation mode around the X-axis, and the meander-type inner piezoelectric actuators  4   a  and  4   b  ( 4   b ′) are specialized for an offset operation mode around the X-axis. However, the meander-type inner piezoelectric actuators  4   a  and  4   b  ( 4   b ′) can be specialized for a rocking operation mode around the X-axis, and the meander-type outer piezoelectric actuators  7   a  and  7   b  ( 7   b ′) can be specialized for an offset operation mode around the X-axis. 
     In  FIG. 14 , which illustrates a third embodiment of the optical deflector apparatus according to the presently disclosed subject matter as a two-dimensional MEMS device, reference numeral  100  designates a two-dimensional optical deflector,  200  designates a driver, and  300  designates a laser light source. 
     The optical deflector  100  includes the optical deflector  10  of  FIG. 1 . Additionally, in order to carry out another rocking operation mode around the Y-axis, the optical deflector  100  includes another outer frame (fixed frame)  101 , a pair of torsion bars  102   a  and  102   b  coupled to the outer circumference of the outer frame  3  along the Y-axis, and linear outer piezoelectric actuators  103   a - 1  and  103   a - 2  coupled between the torsion bar  102   a  and the outer frame  101 , and linear outer piezoelectric actuators  103   b - 1  and  103   b - 2  coupled between the torsion bar  102   b  and the outer frame  101 . In this case, the outer frame  3  serves as a movable frame. The flexing direction of the outer piezoelectric actuators  103   a - 1  and  103   b - 1  is opposite to that of the outer piezoelectric actuators  103   a - 2  and  103   b - 2 , so that each of the outer piezoelectric actuators  103   a - 1 ,  103   a - 2 ,  103   b - 1  and  103   b - 2  serves as cantilevers for rocking the mirror  1  around the Y-axis. Note that the torsion bars  102   a  and  102   b  can be coupled to the outer frame  101 . 
     The outer frame  101  has the same structure as the outer frame  3  as illustrated in  FIG. 3 . In this case, the pads P are formed on the outer frame  101 , not on the outer frame  3 . Also, the torsion bars  102   a  and  102   b  have the same structure as the torsion bars  5   a  and  5   b  as illustrated in  FIG. 3 . Further, the linear piezoelectric actuators  103   a - 1 ,  103   a - 2 ,  103   b - 1  and  103   b - 2  have the same structure as the linear piezoelectric actuators  6   a - 1 ,  6   a - 2 ,  6   b -a and  6   b - 2  as illustrated in  FIG. 3 . 
     The rocking operation of the mirror  1  by the outer piezoelectric actuators  103   a - 1 ,  103   a - 2 ,  103   b - 1  and  103   b - 2  in a rocking operation mode around the Y-axis will be explained below. 
     Rocking sinusoidal-wave drive voltages V Y1  and V Y2  opposite in phase to each other as illustrated in  FIGS. 15A and 15B  are applied by the driver  200  to the outer piezoelectric actuators  103   a - 1  and  103   a - 2 , respectively, so that the outer piezoelectric actuators  103   a - 1  and  103   a - 2  carry out flexing operations in opposite directions to each other, which would distort the torsion bar  102   a  in a direction to cause a torque in the mirror  1  around the Y-axis. Simultaneously, the above-mentioned rocking sinusoidal-wave drive voltages V Y1  and V Y2  are applied by the driver  200  to the outer piezoelectric actuators  103   b - 1  and  103   b - 2 , respectively, so that the outer piezoelectric actuators  103   b - 1  and  103   b - 2  carry out flexing operations in opposite directions to each other, which would distort the torsion bar  102   b  in the above-mentioned direction to cause a torque in the mirror  1  around the Y-axis. As a result, the torsion bars  102   a  and  102   b  are twisted to rock the mirror  1  around the Y-axis. The frequency f Y  of the rocking sinusoidal-wave drive voltages V Y1  and V Y2  is 60 Hz, for example, much lower than the resonant frequency f X  of the sinusoidal-wave drive voltages V X1  and V X2 . 
     In  FIG. 16 , which illustrates a fourth embodiment of the optical deflector apparatus according to the presently disclosed subject matter as a two-dimensional MEMS device, the torsion bars  102   a  and  102   b  and the linear piezoelectric actuators  103   a - 1 ,  103   a - 2 ,  103   b - 1  and  103   b - 2  of  FIG. 14  are replaced by a pair of meander-type piezoelectric actuators  104   a  and  104   b  which are symmetrical to each other with respect to the X-axis. 
     In more detail, the piezoelectric actuator  104   a  is constructed by piezoelectric actuators  104   a - 1   s ,  104   a - 2  and  104   a - 3   s  which are serially coupled from an outer coupling portion  3   c  of the outer frame  3  to a coupling portion  101   a  of the outer frame  101  via folded portions Fe 12  and Fe 23 . Also, each of the piezoelectric cantilevers  104   a - 1   s ,  104   a - 2  and  104   a - 3   s  are in parallel with the X-axis. Therefore, the piezoelectric actuators  104   a - 1   s ,  104   a - 2  and  104   a - 3   s  are folded at their ends or meandering from the outer frame  3  to the outer frame  101 , so that amplitudes of the piezoelectric actuators  104   a - 1   s ,  104   a - 2  and  104   a - 3   s  can be changed along directions perpendicular to the Y-axis. 
     Similarly, the piezoelectric actuator  104   b  is constructed by piezoelectric actuators  104   b - 1   s ,  104   b - 2  and  104   b - 3   s  which are serially coupled from an outer coupling portion  3   d  of the outer frame  3  to a coupling portion  101   a  of the outer frame  101  via folded portions Ff 12  and Ff 23 . Also, each of the piezoelectric cantilevers  104   b - 1   s ,  104   b - 2  and  104   b - 3   s  are in parallel with the X-axis. Therefore, the piezoelectric actuators  104   b - 1   s ,  104   b - 2  and  104   b - 3   s  are folded at their ends or meandering from the outer frame  3  to the outer frame  101 , so that amplitudes of the piezoelectric actuators  104   b - 1   s ,  104   b - 2  and  104   b - 3   s  can be changed along directions perpendicular to the Y-axis. 
     The meander-type piezoelectric actuators  104   a  and  104   b  operate in the same way as the meander-type piezoelectric actuators  4   a  and  4   b.    
     Thus, the mirror  1  is rocked around the Y-axis by the piezoelectric actuators  104   a  and  104   b.    
     Note that the number of piezoelectric cantilevers  104   a  and  104   b  can be other values such as 4, 5, . . . . 
     The meander-type piezoelectric actuators  104   a  and  104   b  have the same structure as the meander-type piezoelectric actuators  4   a  and  4   b  as illustrated in  FIG. 3 . 
     The rocking operation by the piezoelectric actuators  104   a  and  104   b  in a rocking operation around the Y-axis will be explained below. 
     A rocking saw-tooth drive voltage V Y1 ′ as illustrated in  FIG. 17A  is applied by the driver  200  to the odd-numbered piezoelectric cantilevers  104   a - 1   s  and  104   a - 3   s  of the outer piezoelectric actuator  104   a  and the odd-numbered piezoelectric cantilevers  104   b - 1   s  and  104   b - 3   s  of the outer piezoelectric actuator  104   b.  Similarly, a rocking saw-tooth drive voltage V Y2 ′ as illustrated in  FIG. 17B  is applied by the driver  200  to the even-numbered piezoelectric cantilever  104   a - 2  of the outer piezoelectric actuator  104   a  and the even-numbered piezoelectric cantilever  104   b - 2  of the outer piezoelectric actuator  104   b.  Therefore, the odd-numbered piezoelectric cantilevers  104   a - 1   s ,  104   a - 3   s,    104   b - 1   s ,  104   b - 3   s  and the even-numbered piezoelectric cantilevers  104   a - 2  and  104   b - 2  carry out flexing operations in phase with each other. As a result, the mirror  1  is rocked around the Y-axis. Even in this case, the frequency f y  of the rocking saw-tooth drive voltages V Y1 ′ and V Y2 ′ is 60 Hz, for example, much lower than the resonant frequency f X  of the sinusoidal-wave drive voltages V X1  and V X2 . 
     In  FIG. 16 , the length of piezoelectric cantilevers  104   a - 1   s ,  104   a - 3   s,    104   b - 1   s  and  104   b - 3   s  is half of the piezoelectric cantilever  104   a - 2  and  104   b - 2 ; however, the length of piezoelectric cantilevers  104   a - 1   s ,  104   a -- 3   s,    104   b - 1   s  and  104   b - 3   s  can be the same as that of the piezoelectric cantilever  104   a - 2  and  104   b - 2 . Also, the piezoelectric actuators  104   a  and  104   b  can be symmetrical to each other with respect to the center  0  of the mirror  1 . 
     It will be apparent to those skilled in the art that various modifications and variations can be made in the presently disclosed subject matter without departing from the spirit or scope of the presently disclosed subject matter. Thus, it is intended that the presently disclosed subject matter covers the modifications and variations of the presently disclosed subject matter provided they come within the scope of the appended claims and their equivalents. All related or prior art references described above and in the Background section of the present specification are hereby incorporated in their entirety by reference.