Optical deflector including separated piezoelectric portions on piezoelectric actuators and its designing method

In an optical deflector including a mirror, a frame, torsion bars, first and second piezoelectric actuators coupled to both of the torsion bars, and first and second coupling bars, each of the first and second piezoelectric actuators is divided into first, second and third areas in accordance with a polarization polarity distribution obtained by performing a simulation upon the optical deflector where piezoelectric portions with no slits are hypothetically provided in the first and second piezoelectric actuators while a predetermined rocking operation is performed upon the mirror. First piezoelectric portions are formed in the first and third areas of the first piezoelectric actuator, and second piezoelectric portions are formed in the first and third areas of said second piezoelectric actuator. A first drive voltage applied to the first piezoelectric portions is opposite in phase to a second drive voltage applied to the second piezoelectric portions.

This application claims the priority benefit under 35 U.S.C. §119 to Japanese Patent Application No. JP2013-112342 filed on May 28, 2013, which disclosure is hereby incorporated in its entirety by reference.

BACKGROUND

The presently disclosed subject matter relates to an optical deflector used in a projector, a headlamp, a bar code reader, a laser printer, a laser head amplifier, a head-up display unit and the like, and its designing method.

2. Description of the Related Art

FIG. 1Ais a perspective view illustrating a first prior art one-dimensional optical deflector, andFIG. 1Bis a partial enlargement of the optical deflector ofFIG. 1Aenclosed by a dotted line B inFIG. 1A(see: FIG. 5 of JP2008-20701A).

As illustrated inFIGS. 1A and 1B, the first prior art one-dimensional optical deflector is constructed by a circular mirror1, a pair of torsion bars2aand2boppositely arranged along a Y-axis (rocking axis) each having an end coupled to the circumference of the mirror1, a pair of semi-circular piezoelectric actuators3-1and3-2opposite to each other with respect to the mirror1each coupled to both of the torsion bars2aand2bfor rocking the mirror1around the Y-axis, a rectangular fixed frame4surrounding the semi-circular piezoelectric actuators3-1and3-2each including one piezoelectric portion3-11(3-21) made of lead titanate zirconate PbZrTi02(PZT), and a pair of coupling bars5-1and5-2arranged along an X-axis perpendicular to the Y-axis having ends coupled to the inner circumference of the fixed frame4and other ends coupled to the outer circumference of the semi-circular piezoelectric actuators3-1and3-2.

InFIGS. 1A and 1B, in a resonance state, when the rocking frequency “f” of the semi-circular piezoelectric actuators3-1and3-2is close to the natural frequency of a mechanically-vibrating system of the mirror1, the rocking angle of the mirror1with respect to the Y-axis can be increased.

In the above-mentioned resonance state, the inventors found that, portions of the semi-circular piezoelectric actuators3-1and3-2where the torsion bars2aand2band the coupling bars5-1and5-2are coupled form loops having maximum amplitudes of a resonant vibration, while portions of the semi-circular piezoelectric actuators3-1and3-2having 45°-angled diameter directions with respect to a diameter line between the torsion bars2aand2band a diameter line between the coupling bars5-1and5-2form nodes having essentially zero amplitudes of the resonant vibration.

The loop portions and node portions of the semi-circular piezoelectric actuators3-1and3-2are discussed in more detail below.

InFIG. 1B, radial axes C1, C2, . . . , C16are defined at intervals 22.5° centered at a point “0” on a plane of the fixed frame4. Also, a circumferential line L is defined at a center line between the outer and inner circumferences of the semi-circular piezoelectric actuators3-1and3-2. Further, P1, P2, . . . , P16are defined as locations at intersections between the circumferential line L and the radial axes C1, C2, . . . , C16, respectively.

The X-axis is defined as the direction of the radial axis C5, and the Y-axis is defined as the direction of the radial axis C1. In this case, the Y-axis is shifted from the rocking direction of the mirror1by a half thickness of the mirror1; however, since this half thickness is very thin, the Y-axis is substantially the same as the rocking direction of the mirror1. Also, a Z-axis is defined as a direction perpendicular to the X-axis and the Y-axis.

InFIG. 2, which illustrates the amplitudes at the locations P9, P10, P11, P12and P13along the Z-axis ofFIG. 1Bin a resonant state whose resonant frequency is 18.877 kHz, three or four amplitudes at three or four X-coordinate values and at one Y-coordinate value were measured. As illustrated inFIG. 2, the amplitude at the location P9was about 4.4 mm, the amplitude at the location P10was about 1.6 mm, the amplitude at the location P11was about 0.3 mm, the amplitude at the location P12was about 1.5 mm, and the amplitude at the location P13was about 2.2 mm. Therefore, the amplitude at the location P11was minimum, while the amplitude at the location P9was maximum. Also, the amplitudes at the locations P10and P12were medium.

The amplitude at the location P13is smaller than the amplitude at the location P9, because the coupling bar5-2is located at the location P13to suppress the vibration of the portion of the semi-circular piezoelectric actuator3-2at the location P13. That is, if no coupling bar is present at the location P13, the amplitude at the location P13would be considered to be the same as the amplitude at the location P9, i.e., larger than 2.2 mm.

As is understood fromFIG. 2, the amplitudes at the locations P1, P2, . . . , P16of the circumferential line L in a resonant state can be as shown inFIG. 3. Thus, although the amplitudes at the locations P1, P9, P10and P16are opposite in phase to those at the locations P12, P13and P14, a drive voltage VY1is applied to the entire semi-circular piezoelectric actuator3-1. Also, although the amplitudes at the locations P1, P2, P8and P9are opposite in phase to those at the locations P4, P5and P6, a drive voltage VY2opposite in phase to the drive voltage VY1is applied to the entire semi-circular piezoelectric actuator3-2. As a result, the drive power by the drive voltages VY1and VY2would be decreased.

FIG. 4is a perspective view illustrating a second prior art one-dimensional optical deflector (see: FIGS. 26, 27, 28 and 29 of JP2010-197994A and US2010/0195180A1).

As illustrated inFIG. 4, the second prior art one-dimensional optical deflector is constructed by a circular mirror101, a pair of torsion bars102aand102barranged along a Y-axis each having an end coupled to the circumference of the mirror101, a pair of linear piezoelectric actuators103a-1and103a-2each having an end coupled to the torsion bar102a, a pair of linear piezoelectric actuators103b-1and103b-2each having an end coupled to the torsion bar102b, and a rectangular fixed frame104coupled to other ends of the linear piezoelectric actuators103a-1,103a-2,103b-1and103b-2.

InFIG. 4, piezoelectric portions103a-11,103a-21,103b-11and103b-21made of PZT are formed on only two-thirds of the linear piezoelectric actuators103a-1,103a-2,103b-1and103b-2, respectively. That is, if a length between the torsion bar102a(102b) and the fixed frame4is L, the piezoelectric portions103a-11,103a-21,103b-11and103b-21are formed in length portions having a length LP(=2L/3) from the torsion bar102a(102b). In this case, a drive voltage VY1is applied to the piezoelectric portions103a-11and103b-11, while a drive voltage VY2opposite in phase to the drive voltage VY1is applied to the piezoelectric portions103a-21and103b-21. Thus, the rocking angle of the mirror1can be maximum under the same drive voltages VY1and VY2.

InFIG. 5, further piezoelectric portions103a-12,103a-22,103b-12and103b-22separated from the piezoelectric portions103a-11,103a-21,103b-11and103b-21are formed on the linear piezoelectric actuators103a-1,103a-2,103b-1and103b-2, respectively, ofFIG. 4. In this case, the drive voltage VY1is applied to the piezoelectric portions103a-22and103b-22, while the drive voltage VY2is applied to the piezoelectric portions103a-12and103b-12. Thus, the rocking angle of the mirror1can be further increased under the same drive voltages VY1and VY2.

InFIGS. 4 and 5, the length LPof the piezoelectric portions103a-11,103a-21,103b-11and103b-22is determined in accordance with the maximum value of the flexing angle of the linear piezoelectric actuators103a-1,103a-2,103b-1and103b-2when no torsion bar is coupled thereto or the maximum value of the moment of the linear piezoelectric actuators103a-1,103a-2,103b-1and103b-2when the torsion bars102aand102bare fixed.

Therefore, even if the one-dimensional optical deflector ofFIG. 1is combined with the one-dimensional optical deflector ofFIG. 4 or 5, the drive power cannot always be increased. As a result, the drive power cannot be increased and the reliability cannot be enhanced.

SUMMARY

The presently disclosed subject matter seeks to solve one or more of the above-described problems.

According to the presently disclosed subject matter, in an optical deflector including: a mirror; a frame surrounding the mirror; first and second torsion bars oppositely arranged along a first axis of the frame, the first and second torsion bars having an end coupled to a circumference of the mirror; first and second piezoelectric actuators opposite to each other with respect to the mirror, for rocking the mirror around the first axis, each of the first and second piezoelectric actuators being coupled to both of the first and second torsion bars; and first and second coupling bars each coupled between the frame and one of the first and second piezoelectric actuators, each of the first and second piezoelectric actuators is divided into first, second and third areas from the first torsion bar to the second torsion bar in accordance with a polarization polarity distribution obtained by performing a predetermined simulation upon the optical deflector where piezoelectric portions with no slits are hypothetically provided in the first and second piezoelectric actuators while a predetermined rocking operation is performed upon the mirror. First piezoelectric portions are formed in the first and third areas of the first piezoelectric actuator, while second piezoelectric portions are formed in the first and third areas of the second piezoelectric actuator. A first drive voltage applied to the first piezoelectric portions is opposite in phase to a second drive voltage applied to the second piezoelectric portions.

Also, in a method for designing an optical deflector comprising: a mirror; a frame surrounding the mirror; first and second torsion bars oppositely arranged along a first axis of the frame, the first and second torsion bars having an end coupled to a circumference of the mirror; first and second piezoelectric actuators opposite to each other with respect to the mirror, for rocking the mirror around the first axis, each of the first and second piezoelectric actuators being coupled to both of the first and second torsion bars; and first and second coupling bars each coupled between the frame and one of the first and second piezoelectric actuators, a predetermined simulation is performed upon the optical deflector where piezoelectric portions with no slits are hypothetically provided in the first and second piezoelectric actuators while a predetermined rocking operation is performed upon the mirror to obtain a polarization polarity distribution. Then, each of the first and second piezoelectric actuators is divided into first, second and third areas from the first torsion bar to the second torsion bar in accordance with boundaries of the polarization polarity distribution. Finally, first piezoelectric portions are formed in the first and third areas of the first piezoelectric actuator, and second piezoelectric portions are formed in the first and third areas of the second piezoelectric actuator. In this case, a first drive voltage applied to the first piezoelectric portions is opposite in phase to a second drive voltage applied to the second piezoelectric portions.

According to the presently disclosed subject matter, the drive power can be increased and the reliability can be enhanced.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

InFIG. 6, which illustrates a first embodiment of the one-dimensional optical deflector according to the presently disclosed subject matter, the semi-circular piezoelectric actuators3-1and3-2ofFIG. 1are replaced by semi-circular piezoelectric actuators3′-1and3′-2, respectively. Also, inFIG. 6, radial axes C1′, C2′, C3′, C4′, C5′ and C6′ are defined at 60° intervals centered at a point “0” on a plane of the fixed frame4. In this case, an X-axis is defined by a radial line between the radial axes C2′ and C3′, and a Y-axis is defined by the radial axis C1′. Also, a Z-axis is defined to be perpendicular to the X-axis and the Y-axis.

The semi-circular piezoelectric actuator3′-1includes piezoelectric portions3′-11,3′-12and3′-13made of PZT separated by slits S1and S2arranged on the radial axes C2′ and C3′, respectively. Similarly, the semi-circular piezoelectric actuator3′-2includes piezoelectric portions3′-21,3′-22and3′-23made of PZT separated by slits S3and S4arranged on the radial axes C5′ and C6′, respectively.

The positions of the slits S1, S2, S3and S4are determined by a polarization polarity distribution on the semi-circular piezoelectric actuators3′-1and3′-2as illustrated inFIG. 7obtained by performing a predetermined polarization simulation upon the one-dimensional optical deflector ofFIG. 6where piezoelectric portions with no slits are hypothetically provided in the semi-circular piezoelectric actuators3′-1and3′-2and a predetermined rocking operation is performed on the mirror1.

InFIG. 7, the polarization polarity of polarization areas as indicated by G1is opposite to the polarization polarity of polarization areas as indicated by G2. Note that one of the polarization polarities represents a compression stress state, while the other represents a tension stress state. That is, the positions of the slits S1, S2, S3and S4ofFIG. 6correspond to boundaries between the polarization polarity areas indicated by G1and the polarization polarity areas indicated by G2inFIG. 7. Therefore, as illustrated inFIG. 8, a drive voltage VY1is applied to the piezoelectric portions3′-11and3′-13of the semi-circular piezoelectric actuator3′-1and the piezoelectric portion3′-22of the semi-circular piezoelectric actuator3′-2, while a drive voltage VY2opposite in phase to the drive voltage VY1is applied to the piezoelectric portion3′-12of the semi-circular piezoelectric actuator3′-1and the piezoelectric portions3′-21and3′-23of the semi-circular piezoelectric actuator3′-2.

Note that the boundaries between the polarization polarities of the polarization polarity distribution indicated by G1and G2theoretically correspond to the nodes of the resonance state as indicated by P3, P7, P11and P15inFIG. 3. However, these boundaries actually differ slightly from the nodes P3, P7, P11and P15due to the difference between the actual resonance state and the simulation.

The drive voltage VY1is a sinusoidal-wave voltage whose frequency fRis a resonant frequency as illustrated inFIG. 9A, and the drive voltage VY2is a sinusoidal-wave voltage as illustrated inFIG. 9Bwhich is opposite in phase to the sinusoidal-wave drive voltage VY1.

InFIGS. 9A and 9B, note that the sinusoidal-wave voltages VY1and VY2are monopolar. As a result, the areas indicated by G1and G2of the semi-circular piezoelectric actuators3′-1and3′-2are moved in the same phase with respect to the Y-axis, to thereby effectively rock the mirror1with respect to the Y-axis.

For example, in order to realize the rocking angle of the mirror1by a resonant frequency fRsuch as about 20 kHz at a rocking angle of 10°, the amplitudes of the drive voltages VY1and VY2were required to be 10V in the one-dimensional optical deflector ofFIG. 6, while the amplitudes of the drive voltages VY1and VY2were required to be 20V or more in the one-dimensional optical deflector ofFIG. 1. In other words, the rocking angle of the mirror1by the same amplitudes of the drive voltages VY1and VY2can be larger in the one-dimensional optical deflector ofFIG. 6than in the one-dimensional optical deflector ofFIG. 1. Also, in the one-dimensional optical deflector ofFIG. 6, since the same rocking angle of the mirror1can be realized by smaller amplitudes of the drive voltages VY1and VY2, the power consumption can be decreased, and the deterioration of the piezoelectric portions made of PZT can be suppressed to enhance the reliability.

The structure of each element of the optical deflector ofFIG. 6is explained next with reference toFIGS. 10A, 10B, 10C and 10Dwhich are cross-sectional views of the optical deflector ofFIG. 6. Note thatFIG. 10Ais a cross-sectional view of the entire optical deflector ofFIG. 6, andFIGS. 10B, 10C and 10Dare cross-sectional views of the semi-circular piezoelectric actuator3′-1(3′-2) ofFIG. 6.

InFIGS. 10A and 10B, a monocrystalline silicon support layer1001, an intermediate silicon dioxide layer1002and a monocrystalline silicon active layer1003are formed by a silicon-on-insulator (SOI) substrate. Also, reference numeral1004designates a silicon dioxide layer,1005designates a lower electrode layer of a double layer made of Ti, Ti02or Ti0X(0<x<2) and Pt, LaNi02or SrRu02,1006designates a PZT layer,1007designates an upper electrode layer made of Pt, Au or the like, and1008designates an about 100 to 500 nm thick metal layer made of Al, Ag, Au, Pt or the like.

The mirror1is constructed by the monocrystalline silicon active layer1003serving as a vibration plate and the metal layer1008serving as a reflector.

The semi-circular piezoelectric actuators3′-1and3′-2are constructed by the intermediate silicon layer1002, the monocrystalline silicon active layer1003, the silicon dioxide layer1004, the lower electrode layer1005, the PZT layer1006and the upper electrode layer1007. Particularly, the lower electrode layer1005, the PZT layer1006and the upper electrode layer1007form the piezoelectric portions3′-11,3′-12,3′-13,3′-21,3′-22and3′-23.

The fixed frame4is constructed by the monocrystalline silicon layer1001, the intermediate silicon layer1002, the monocrystalline silicon active layer1003and the silicon dioxide layer1004.

Note that the semi-circular piezoelectric actuators3′-1(3′-2) can entirely include the lower electrode layer1005as illustrated inFIG. 10C, or can entirely include the lower electrode layer1005and the PZT layer1006as illustrated inFIG. 10D. InFIGS. 10C and 10D, portions of the PZT layer1006without the upper electrode layer1007are inactivated, so that the semi-circular piezoelectric actuators3′-1(3′-2) ofFIG. 10C or 10Dcan serve as the semi-circular piezoelectric actuators3′-1(3′-2) ofFIG. 10B.

The structure of the one-dimensional optical deflector as illustrated inFIG. 10can be manufactured by semiconductor manufacturing technology and micro electro mechanical systems (MEMS) technology (see: JP 2009-169326 and JP 2009-223165).

A method for designing the one-dimensional optical deflector ofFIG. 6is as follows.

First, a one-dimensional optical deflector ofFIG. 6without slits S1, S2, S3and S4is designed. In this case, piezoelectric portions are provided at least on the piezoelectric actuators3′-1and3′-2.

Next, a predetermined polarization simulation is performed upon the designed one-dimensional deflector without slits S1, S2, S3and S4to obtain a polarization polarity distribution as illustrated inFIG. 7while a predetermined rocking operation is performed upon the mirror1.

Next, the locations of the slits S1, S2, S3and S4are determined in accordance with boundaries between the polarization polarity areas of the polarization polarity distribution.

Finally, the piezoelectric portions3′-11,3′-12,3′-13,3′-21,3′-22and3′-23are determined in accordance with the slits S1, S2, S3and S4.

InFIG. 11, which illustrates a second embodiment of the one-dimensional optical deflector according to the presently disclosed subject matter, a semi-diamond (or semi-lozenge)-shaped piezoelectric actuator3″-1including piezoelectric portions3″-11,3″-12and3″-13and a semi-diamond-shaped piezoelectric actuator3″-2including piezoelectric portions3″-21,3″-22and3″-23and a diamond-shaped fixed frame4′ are provided instead of the semiconductor piezoelectric actuator3′-1including the piezoelectric portions3′-11,3′-12and3′-13and the semi-circular piezoelectric actuator3′-2including piezoelectric portions3′-21,3′-22and3′-23and the rectangular fixed frame4, respectively, ofFIG. 6.

InFIG. 11, the width of the semi-diamond-shaped piezoelectric actuators3′-1and3″-2is gradually increased from the coupling portions5-1and5-2as indicated by A (see:FIG. 12) to the torsion bars2aand2bas indicated by B (see:FIG. 12). As a result, since the areas of the piezoelectric portions3″-11,3″-12,3″-13,3″-21,3″-22and3″-23are increased around the torsion bars2aand2b, the rocking angle of the mirror1can be increased under the same drive voltage VY1and VY2.

The piezoelectric portions3″-11,3′-12and3′-13made of PZT are separated by slits S1′ and S2′ arranged on the radial axes C2′ and C3′, respectively. Similarly, the piezoelectric portions3′-21,3″-22and3″-23made of PZT are separated by slits S3′ and S4′ arranged on the radial axes C5″ and C6″, respectively.

The positions of the slits S1′, S2′, S3′ and S4′ are determined by a polarization polarity distribution on the semi-diamond-shaped piezoelectric actuators3″-1and3″-2as illustrated inFIG. 12obtained by performing a predetermined polarization simulation upon the one-dimensional optical deflector ofFIG. 11where piezoelectric portions with no slits are hypothetically provided in the semi-diamond-shaped piezoelectric actuators3″-1and3″-2and a predetermined rocking operation is performed on the mirror1.

Even inFIG. 12, the polarization polarity of polarization areas as indicated by G1is opposite to the polarization polarity of polarization areas as indicated by G2. That is, the positions of the slits S1′, S2′, S3′ and S4′ ofFIG. 11correspond to boundaries between the polarization areas indicated by G1and the polarization areas indicated by G2inFIG. 12. Therefore, in the same way as inFIG. 8, a sinusoidal-wave drive voltage VY1is applied to the piezoelectric portions3″-11and3″-13of the semi-diamond-shaped piezoelectric actuator3″-1and the piezoelectric portion3″-22of the semi-diamond-shaped piezoelectric actuator3″-2, while a sinusoidal-wave drive voltage VY2opposite in phase to the drive voltage VY1is applied to the piezoelectric portion3″-12of the semi-diamond-shaped piezoelectric actuator3″-1and the piezoelectric portions3″-21and3′-23of the semi-diamond-shaped piezoelectric actuator3″-2. As a result, the areas indicated by G1and G2of the semi-diamond-shaped piezoelectric actuators3″-1and3″-2are moved in the same phase with respect to the Y-axis, thereby to effectively rock the mirror1with respect to the Y-axis.

The structure of the one-dimensional optical deflector ofFIG. 11is similar to that of the one-dimensional optical deflector ofFIG. 6as illustrated inFIG. 10. Also, the method for designing the one-dimensional optical deflector ofFIG. 11is similar to the method for designing the one-dimensional optical deflector ofFIG. 6.

InFIG. 13, which illustrates a third embodiment of the one-dimensional optical deflector according to the presently disclosed subject matter, the piezoelectric portions3′-12and3′-22are removed from the semi-circular piezoelectric actuators3′-1and3′-2ofFIG. 6.

Therefore, as illustrated inFIG. 14, a sinusoidal-wave drive voltage VY1as illustrated inFIG. 9Ais applied to the piezoelectric portions3′-11and3′-13of the semi-circular piezoelectric actuator3′-1, while a sinusoidal-wave drive voltage VY2as illustrated inFIG. 9Bopposite in phase to the drive voltage VY1is applied to the piezoelectric portions3′-21and3′-23of the semi-circular piezoelectric actuator3′-2. As a result, the areas indicated by G1and G2of the semi-circular piezoelectric actuators3′-1and3′-2are moved in the same phase with respect to the Y-axis, thereby to effectively rock the mirror1with respect to the Y-axis.

For example, in order to realize the rocking angle of the mirror1by a resonant frequency fRsuch as about 20 kHz at a rocking angle of 10°, the amplitudes of the drive voltages VY1and VY2were required to be 11 to 12V in the one-dimensional optical deflector ofFIG. 13. Therefore, in the same way as in the one-dimensional optical deflector ofFIG. 6, the power consumption can be decreased, and the deterioration of the piezoelectric portions made of PZT can be suppressed to enhance the reliability.

The structure of the one-dimensional optical deflector ofFIG. 13is similar to that of the one-dimensional optical deflector ofFIG. 6as illustrated inFIG. 10. Also, the method for designing the one-dimensional optical deflector ofFIG. 13is similar to the method for designing the one-dimensional optical deflector ofFIG. 6.

Note that the one-dimensional optical deflector ofFIG. 6where no drive voltage is applied to the piezoelectric portions3′-12and3′-22can be used as the one-dimensional optical deflector ofFIGS. 13 and 14. In this case, no drive voltage is applied to the piezoelectric portion3′-12of the semi-circular piezoelectric actuator3′-1and the piezoelectric portion3′-22of the semi-circular piezoelectric actuator3′-2.

InFIG. 15, which illustrates a fourth embodiment of the one-dimensional optical deflector according to the presently disclosed subject matter, torsion bars2′aand2′bare provided instead of the torsion bars2aand2b, respectively, ofFIG. 6. Since the torsion bars2′aand2′bare coupled between the outer circumference of the mirror1and the inner circumference of the fixed frame4through the semi-circular piezoelectric actuators3′-1and3′-2, the torsion bars2′aand2′bcan be stably twisted by the piezoelectric actuators3′-1and3′-2. Also, since the mirror1is supported by a four-point support at the fixed frame4, the support of the mirror1is more stable in the one-dimensional optical deflector ofFIG. 15than in the one-dimensional optical deflector ofFIG. 6.

InFIG. 15, a piezoelectric sensor1501is provided at a portion crossing between the torsion bar2band the semi-circular piezoelectric actuator3′-1.

InFIG. 16, which is a partial enlargement of the optical deflector ofFIG. 15near the piezoelectric sensor1501, the piezoelectric sensor1501is constructed by the lower electrode layer1005, the PZT layer1006and the upper electrode layer1007in the same way as those ofFIG. 10, in order to sense rocking vibrations of the torsion bar2bcaused by the semi-circular piezoelectric actuator3′-1. In this case, the piezoelectric sensor1501senses a strong stress due to the rocking vibrations of the torsion bar2bwhich would be concentrated at an inner side portion of the semi-circular piezoelectric actuator3′-1in the vicinity of the torsion bar2b.

The piezoelectric sensor1501has a length L which is defined by
L=L1+L2
L1=L0/8
L2≦L0/8

where L1is a distance between the inner edge of the piezoelectric sensor1501and an edge of the torsion bar2bon the side of the semi-circular piezoelectric actuator3′-1;

L2is a distance between the outer edge of the piezoelectric sensor1501and the edge of the torsion bar2bon the semi-circular piezoelectric actuator3′-1; and

L0is a width of the torsion bar2b.

Also, if W is defined by a width of the semi-circular piezoelectric actuator3′-1, the piezoelectric sensor1501is arranged at a width portion having a width of less than 0.18·W from the inner circumference of the semi-circular piezoelectric actuator3′-1.

A sense conductive layer1601is connected from the upper electrode layer (not shown) of the piezoelectric sensor1501over the torsion bar2bto a sense pad PSon the fixed frame4.

Two ground conductive layers1602and1603are arranged to sandwich the sense conductive layer1601, so that the sense conductive layer1601is electrostatically shielded by the ground conductive layers1602and1603, thus preventing the sense conductive layer1601from crosstalking with the drive voltages VY1and VY2at the piezoelectric portion3′-13of the semi-circular piezoelectric actuator3′-1and the piezoelectric portion3′-21of the semi-circular piezoelectric actuator3′-2. The ground conductive layers1602and1603are connected over the torsion bar2bto a ground pad PGNDon the fixed frame4.

A sense voltage VSof the piezoelectric sensor1501is supplied from the sense conductive layer1601to the sense pad PS, and then is supplied to a control unit (not shown) which controls the drive voltages VY1and VY2. Therefore, the frequency of the drive voltages VY1and VY2is controlled by the control unit, so that the sense voltage VSis brought close to its maximum value, thus realizing a resonance state.

The structure of the one-dimensional optical deflector ofFIG. 15is similar to that of the one-dimensional optical deflector ofFIG. 6as illustrated inFIG. 10. Also, the method for designing the one-dimensional optical deflector ofFIG. 15is similar to the method for designing the one-dimensional optical deflector ofFIG. 6.

The one-dimensional optical deflector ofFIG. 6is applied to a light scanning system as illustrated inFIG. 17. InFIG. 17, a light source1701emits a light beam BM and transmits it to the mirror1of the one-dimensional optical deflector ofFIG. 6. A control unit1702controls the light source1701, so that the control unit1702turns ON and OFF the light source1701, as occasion demands. Also, the control unit1702controls the sinusoidal-wave drive voltages VY1and VY2as illustrated inFIGS. 9A and 9Bin accordance with a sense voltage VSoutputted from the piezoelectric sensor (not shown) of the one-dimensional optical deflector, and transmits them to the piezoelectric portions of the piezoelectric actuators3′-1and3′-2. For example, the control unit1702turns ON the light source1701for a half period of the sinusoidal-wave voltage VY1and turns OFF the light source1701for the other half period of the sinusoidal-wave voltage VY1. As a result, the light beam BM is reflected by the mirror1to emit a scanning light beam SB. Note that the control unit1702is constructed by a microcomputer including a central processing unit (CPU), a read-only memory (ROM), a random access memory (RAM) and the like.

Note that the one-dimensional optical deflector ofFIG. 11, 13 or 15can also be applied to the light scanning system ofFIG. 17.

In the above-described embodiments, the mirror1is circular; however, the mirror1can be an ellipse.

Also, the slits S1, S2, S3and S4(S1′, S2′, S3′ and S4′) are arranged along a 60°, 120°, 240° and 300°-angled direction with respect to the rocking direction of the mirror1. However, as illustrated inFIG. 18, the slit S1(S1′) can be arranged along a first radial direction which is +30° to +60°-angled with respect to the rocking direction, the slit S2(S2′) can be arranged along a second radial direction which is +120° to +150°-angled with respect to the rocking direction, the slit S3(S3′) can be arranged along a third radial direction which is +210° to +240°-angled with respect to the rocking direction, and the slit S4(S4′) can be arranged along a fourth radial direction which is +300° to +330°-angled with respect to the rocking direction. In other words, the slits S1and S3(S1′ and S3′) are arranged along a first diameter direction which is obtained by inclining the rocking direction (axis) by a first predetermined angle between +30° and +60°, while the slits S2and S4(S2′ and S4′) are arranged along a second diameter direction which is obtained by inclining the rocking direction (axis) by a second predetermined angle between −30° and −60°.

InFIG. 19, which is a perspective view illustrating a two-dimensional optical deflector to which the one-dimensional optical deflector ofFIG. 6is applied, the rectangular fixed frame4ofFIG. 6serves as a movable frame4M. Also, a rectangular fixed frame11is provided to surround the movable frame4M. Further, a pair of outer meander-type piezoelectric actuators12and13between the fixed frame11and the movable frame4M and serving as cantilevers for rocking the mirror1around the X-axis. The piezoelectric actuators12and13are arranged opposite to each other with respect to the X-axis.

The outer piezoelectric actuator12is constructed by piezoelectric cantilevers12-1,12-2,12-3and12-4which are serially-coupled from the fixed frame11to the movable frame4M. Also, each of the piezoelectric cantilevers12-1,12-2,12-3and12-4are in parallel with the Y-axis. Therefore, the piezoelectric cantilevers12-1,12-2,12-3and12-4are folded at every cantilever or meandering from the fixed frame11to the movable frame4M, so that the amplitudes of the piezoelectric cantilevers12-1,12-2,12-3and12-4can be changed along directions perpendicular to the X-axis.

Similarly, the outer piezoelectric actuator13is constructed by piezoelectric cantilevers13-1,13-2,13-3and13-4which are serially-coupled from the fixed frame11to the movable frame4M. Also, each of the piezoelectric cantilevers13-1,13-2,13-3and13-4are in parallel with the Y-axis. Therefore, the piezoelectric cantilevers13-1,13-2,13-3and13-4are folded at every cantilever or meandering from the fixed frame11to the movable frame4M, so that the amplitudes of the piezoelectric cantilevers13-1,13-2,13-3and13-4can be changed along directions perpendicular to the X-axis.

Note that the number of piezoelectric cantilevers in each of the outer piezoelectric actuators12and13can be other values such as 2, 6, 8, . . . .

Also, provided on the fixed frame11are pads PX1and PX2. The pads PX1and PX2are connected to a control unit1901which applies a drive voltage VX1to the pad PX1, and applies a drive voltage VX2to the pad PX2. In this case, the drive voltages VX1and VX2opposite in phase to each other are saw-tooth-shaped, and have a frequency of 15 kHz.

The pad PX1is connected via conductive layers (not shown) to the upper electrode layers of the odd-numbered piezoelectric cantilevers12-1,12-3,13-1and13-3of the outer piezoelectric actuators12and13.

The pad PX2is connected via conductive layers to the upper electrode layers of the even-numbered piezoelectric cantilevers12-2,12-4,13-2and13-4of the outer piezoelectric actuators12and13.

The pad PY1is connected via conductive layers (not shown) to the upper electrode layer of the semi-circular piezoelectric actuator3′-1.

The pad PY2is connected via conductive layers (not shown) to the upper electrode layer of the semi-circular piezoelectric actuator3′-2.

The pad PSis connected via conductive layers (not shown) to the upper electrode layer of the piezoelectric sensor (not shown).

The pad PGNDis connected via conductive layers (not shown) to the lower electrode layers of all the piezoelectric actuators and the piezoelectric sensor.

InFIG. 19, a light source1901corresponding to the light source1701ofFIG. 17and a control unit1902corresponding to the control unit1702ofFIG. 17are provided. The control unit1902further controls the drive voltages VY1and VY2in accordance with the sense voltage VSand also, controls the drive voltages VX1and VX2.

Also, note that the one-dimensional optical deflector ofFIG. 11, 13 or 15can also be applied to the two-dimensional optical deflector ofFIG. 19.

Further, in the above-described embodiments, the piezoelectric actuators are semi-circular or semi-diamond-shaped; however, the piezoelectric actuators can be of another bent-type.

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.