Optical deflector

An optical deflector made of an electro-optic material has one or more pairs of electrodes on opposite surfaces. Each pair of electrodes defines an interaction region in which an electric field applied from the electrodes produces a linear refractive-index gradient in the direction of the electric field. An incident light beam is refracted in this direction within the interaction region. The interaction region is shaped so that the light beam is also refracted in an orthogonal direction when it enters or leaves the interaction region. The light beam is thereby deflected three-dimensionally.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical deflector capable of deflecting an input beam three-dimensionally and outputting the deflected beam.

2. Description of the Related Art

Technology for deflecting light beams is used in many fields, in devices such as scanning electron microscopes, laser printers, bar-code scanners, optical cross-connects, and so on.

Known methods of deflecting light beams make use of rotating mirrors, the acousto-optic effect, and the electro-optical effect. The optical cross-connects used in optical communication, for example, employ micro-electromechanical systems (MEMS) with micromirrors. These optical cross-connects are capable of switching up to a thousand channels by mechanically controlling the tilt angles of the micromirrors.

The optical deflectors implemented by MEMS technology, however, require mechanical driving of a mirror. Accordingly, it is impossible to shorten the switching time to less than about one millisecond (1 ms).

Deflection devices that operate by using the electro-optical effect are intrinsically faster. Known examples of such devices are disclosed in U.S. Pat. No. 6,449,084 to Guo and U.S. Pat. No. 6,947,625 to Nishizawa et al. A more recent technique deflects an optical beam by injecting a space charge into a dielectric body to create a refractive index distribution aligned with the resulting electric field, as described by Nakamura et al. in ‘Wide-angle, low-voltage electro-optic beam deflection based on space-charge-controlled mode of electrical conduction in KTa1-xNbxO3’, Applied Physics Letters89, 131115 (2006).

A problem common to these known electro-optical deflectors is that they can only deflect light beams two-dimensionally, in a single plane including the incident beam.

SUMMARY OF THE INVENTION

An object of the present invention is to provide an optical deflector that can deflect and output an incident beam three-dimensionally.

In one aspect, the invention provides an optical deflector having an interaction region comprising an electro-optic material in which an applied electric field produces a refractive-index distribution that varies lineally in a first direction aligned with the electric field. Because of the refractive-index distribution, the optical deflector deflects a light beam by refraction in the first direction within the interaction region. In addition, the optical deflector deflects the light beam in a second direction orthogonal to the first direction by refraction at an interface where the light beam enters or leaves the interaction region. The light beam is thereby deflected three-dimensionally.

The deflection angle is controllable by varying the strength of the applied electric field.

In some embodiments, the refractive index of the electro-optic material varies by the Kerr effect and the interaction region comprises a first region, a second region, and a third region disposed in series the direction of propagation of the light beam.

The first region has a first surface at which the beam enters and a second surface from which the beam exits. The first surface and the second surface are mutually nonparallel.

The second region has a third surface at which the beam enters and a fourth surface from which the beam exits. The third surface and the fourth surface are mutually nonparallel.

The third region has a fifth surface at which the beam enters and a sixth surface from which the beam exits. The fifth surface and the sixth surface are mutually parallel.

The first surface is parallel to the fourth surface. The second surface is parallel to and faces the third surface.

The first region of the optical deflector preferably has a first facet and a second facet that are mutually parallel and orthogonal to both the first surface and the second surface, and have mutually congruent triangular shapes.

The second region preferably has a third facet and a fourth facet that are mutually parallel and orthogonal to both the third surface and the fourth surface, and have mutually congruent triangular shapes.

The first region, the second region, and a space between the second and third surfaces preferably combine to form a rectangular parallelepiped.

The third region preferably has a fifth facet and a sixth facet that are mutually parallel and orthogonal to both the fifth surface and the sixth surface. The third region preferably has the form of a rectangular parallelepiped.

The third region may comprise two sub-regions with shapes identical to the shapes of the first and second regions.

The optical deflector preferably further comprises first to sixth electrodes respectively disposed on the first to sixth facets.

In some other embodiments, the refractive index of the electro-optic material of the optical deflector varies by the Pockels effect and the interaction region comprises a first region and a second region disposed in series in the direction of propagation of the light beam.

The first region has a first surface at which the beam enters and a second surface from which the beam exits. The first surface and the second surface are mutually nonparallel.

The second region has a third surface at which the beam enters and a fourth surface from which the beam exits. One of the following two conditions is satisfied.

Condition 1: the first surface is parallel to the fourth surface and the second surface is parallel to and faces the third surface.

Condition 2: the third surface is parallel to the fourth surface.

The first region preferably has a first facet and a second facet that are mutually parallel and orthogonal to both the first surface and the second surface. The second region preferably has a third facet and a fourth facet that are mutually parallel and orthogonal to both the third surface and the fourth surface. The first and third facets are disposed in one major surface of the electo-optic material, while the second and fourth facets are disposed in the opposite major surface of the electro-optic material.

When condition 1 is satisfied, the first and second regions may have mutually congruent triangular prismatic shapes, the second and third surfaces may be mutually facing, and the first region, the second region, and a space between the second and third surfaces may combine to form a parallelepiped. The interaction region may further comprise a third region and a fourth region respectively identical in shape and orientation to the first region and second region, the third region and fourth region being disposed in series in the direction of propagation of the light beam.

When condition 2 is satisfied, the first and second facets may be triangular, so that the first region is a triangular prism, and the third and fourth facets may be rectangular, so that the second region is a rectangular parallelepiped.

In either case, the optical deflector may have first to fourth electrodes disposed respectively on the first to fourth facets. Alternatively, the optical deflector may have a first electrode disposed on the first facet, a second electrode disposed on the third facet, and a third electrode disposed on the opposite major surface of the electro-optic material, facing both the first and second electrodes.

To cause the refractive index to change linearly in the direction of the electric field, the electro-optic material forming the optical deflector may have a varying composition, or a varying ratio of domains with a first polarization or crystal geometry to domains with a second polarization or crystal geometry.

An array of optical deflectors of any of the above types may be formed in a slab of electro-optic material.

In another aspect, the invention provides an optical deflector having an interaction region comprising an electro-optic material in which an applied electric field produces a refractive-index distribution that varies linearly in the direction of the applied electric field by the Kerr effect. The interaction region comprises a first region and a second region to which electric fields are applied in mutually orthogonal directions. The optical deflector deflects a light beam three-dimensionally by refraction one direction in the first region and refraction an orthogonal direction in the second region. The direction and amount of deflection are controllable by varying the strengths of the applied electric fields, and the angle of incidence of the light beam.

DETAILED DESCRIPTION OF THE INVENTION

Illustrative embodiments of the invention will now be described with reference to the attached drawings, in which like elements are indicated by like reference characters. The drawings are schematic, and the invention is not limited to the configurations shown in the drawings, or the dimensions and materials mentioned in the description.

Before the embodiments are described, a model optical deflector with a minimal configuration in accordance with the invention will be described. In this model, there is only one interaction region. The model is shown in perspective view inFIG. 1, in plan view inFIG. 2, and in side view inFIG. 3.

The model optical deflector11is formed in an electro-optic material12comprising an interaction region14and a non-interaction region15.

The interaction region14is a part of the electro-optic material12across which an external voltage is applied, creating an electric field. The refractive index of the electro-optic material12varies linearly in the direction of the electric field, at a rate that increases as the applied voltage is increased. The interaction region14is defined by the shape of the electrodes that generate the electric field. In this model, these electrodes17a,17bhave congruent right triangular shapes, and the interaction region14has the shape of a right triangular prism extending between two major surfaces12c,12dof the electro-optic material12. The non-interaction region15comprises all parts of the electro-optic material12not disposed within this prism.

Application of appropriate voltages to the electrodes17a,17bgenerates an electric field in the interaction region14, directed from the first or upper major surface12cof the electro-optic material12toward the second or lower major surface12d. The refractive index of the interaction region14accordingly varies linearly from the upper major surface12cto the lower major surface12d. The direction from the upper major surface12cto the lower major surface12d, marked by the letter ‘a’ inFIG. 1, will be referred to as the depth direction. Directions parallel to major surfaces12cand12d, such as the directions marked ‘b’ inFIG. 1, will be referred to as horizontal directions.

The interaction region14has an entry interface19athrough which a light beam L enters the interaction region14and an exit interface19bthrough which the light beam leaves the interaction region14. In this model, the entry interface19ais normal (orthogonal) to the direction of propagation of the incident light L, while the exit interface19bis oriented at an oblique angle to the light propagation direction.

When voltage is applied, due to the change in refractive index of the interaction region14, a difference in refractive index arises between the interaction region14and the non-interaction region15. As a result, the light L is refracted horizontally at the exit interface19b, as shown inFIG. 2. The horizontal deflection angle of the light can be varied by changing the applied voltage.

If the entry interface19awere not normal to the incident light beam, the light would also be refracted at the entry interface19a. In general, the light beam L may be refracted at either the entry interface19aor the exit interface19bor at both interfaces.

The linearly varying refractive index in the interaction region14also causes the light beam L to bend in the direction of increasing index within the interaction region14. The light beam L is accordingly deflected (refracted) in the depth direction, as shown inFIG. 3. Like the horizontal deflection angle, the depth deflection angle can be varied by changing the applied voltage.

In the model optical deflector11, accordingly, the application of a voltage deflects the incident light beam both horizontally and in the depth direction. That is, the light is deflected three-dimensionally. In the following embodiments, a plurality of interaction areas are provided to provide greater control over the direction in which the light is deflected. In some of the embodiments, the applied voltage causes the refractive index in the interaction region to vary by the Kerr effect, while in other embodiments the Pockels effect is used.

First Embodiment

An optical deflector according to the first embodiment will be described with reference toFIGS. 4 to 14.

FIG. 4is a perspective view showing the general structure of the optical deflector. For simplicity, electrodes inFIG. 4are depicted as having no thickness.

The optical deflector10is a block of an electro-optic material12. The interaction region14consists of three mutually separated regions: a first region16, a second region18, and a third region20.

The block of electro-optic material12is a rectangular solid having two end facets12a,12bwith a flat square shape. Light L propagating in the direction of arrow A enters the electro-optic material12at end facet12a. Deflected light exits the electro-optic material12from the opposite end facet12b, having passed through the first region16, second region18, and third region20in this sequence.

The electro-optic material12has a first or upper major surface12con which first to third front electrodes22a,24a,26aare formed and a second or lower major surface12don which first to third back electrodes22b,24b,26bare formed. The direction perpendicular to the major surfaces12c,12d, that is, the direction from the upper major surface12cto the lower major surface12d, will be referred to below as the depth direction (a). Directions perpendicular to the depth direction, that is, directions in any plane parallel to the upper major surface12c, will be referred to as horizontal (b).

The electro-optic material12is formed of a material the refractive index of which can be changed linearly by an electric field applied in the depth direction. In this embodiment, ‘linearly’ means that the refractive index of the electro-optic material12is a linear function of distance from the upper major surface12c.

According to the Kerr effect, the linear change in refractive index of the material of which the electro-optic material12is made is proportional to the square of the intensity of the applied electric field. The change in refractive index is due to the injection of electrical charge by the electric field. An exemplary preferred material for the electro-optic material12is potassium tantalum niobate (KTa1-xNbxO3, where 0≦x≦1).

The first front electrode22aand first back electrode22bform a first electrode pair22. The first front electrode22ais a flat right triangle disposed on the upper major surface12c. The part of the upper major surface12cbelow the first front electrode22aforms the first facet or upper facet16aof the first region16.

The first back electrode22bis congruent in shape to the first front electrode22aand is disposed on the lower major surface12d, in an area that forms an orthographic projection of the first front electrode22a. The part of the lower major surface12dabove the first back electrode22bforms the second facet or lower facet16bof the first region16.

The first region16is accordingly a right triangular prismatic region in the electro-optic material12disposed between the first front electrode22aand the first back electrode22b, that is, between the upper facet16aand lower facet16b.

The first region16has a first surface16cor incident boundary interface through which light L enters the first region16. The first surface16cis disposed near the incident end facet12aof the electro-optic material12and is parallel to the incident end facet12a. In this exemplary structure, the incident light beam L is normal to the first surface16c.

The first region16also has a second surface16dor exit boundary interface through which light L leaves the first region16. As seen from the first surface16c, the second surface16dextends at an oblique angle toward the exit end facet12bof the electro-optic material12, following the hypotenuse of the right triangular first front electrode22a. The second surface16dis not parallel to the first surface16c, and is not normal to the direction of propagation of the light beam L.

The first region16also has a side surface16ethat extends parallel to a side facet of the block of the electro-optic material12.

The second front electrode24aand second back electrode24bform a second electrode pair24. The second front electrode24ais a flat right triangle disposed on the upper major surface12c. The part of the upper major surface12cbelow the second front electrode24aforms the third facet or the upper facet18aof the second region18.

The second back electrode24bis congruent to the second front electrode24aand is disposed on the lower major surface12d, in an area that forms an orthographic projection of the second front electrode24a. The part of the lower major surface12dabove the second back electrode24bforms the fourth facet or the lower facet18bof the second region18.

The second region18has a third surface18cor incident boundary interface through which light L enters the second region18. The third surface18cparallels the second surface16dof the first region16and faces the incident end facet12aof the electro-optic material12at an oblique angle, following the hypotenuse of the right-triangular second front electrode24a. Light entering the second region18from the first region16crosses the third surface18cat an oblique angle.

The second region18also has a fourth surface18dor exit boundary interface through which light L leaves the second region18. The fourth surface18dis parallel to and faces the exit end facet12bof the electro-optic material12, and is not parallel to the third surface18c.

The second region18also has a side surface18ethat extends parallel to a side facet of the electro-optic material12.

The second region18has the form of a right triangular prism congruent to the right triangular prism formed by the first region16. The first surface16cof the first region16and the fourth surface18dof the second region18are mutually parallel. The second surface16dof the first region16and the third surface18cof the second region18are mutually parallel and face each other. Taken together, the first region16, the second region18, and the space between them essentially form two halves of a rectangular parallelepiped.

The third front electrode26aand third back electrode26bform a third electrode pair26. The third front electrode26ais a flat rectangle disposed on the upper major surface12c. The part of the upper major surface12cbelow the third front electrode26aforms the fifth facet or the upper facet20aof the third region20.

The third back electrode26bis congruent to the third front electrode26aand is disposed on the lower major surface12d, in an area that forms an orthographic projection of the third front electrode26a. The part of the lower major surface12dabove the third back electrode26bforms the sixth facet or the lower facet20bof the third region20.

The third region20forms a rectangular parallelepiped or rectangular prism within the electro-optic material12, disposed between the third front electrode26aand the third back electrode26b.

The third region20has a fifth surface20cor incident boundary interface through which light. L enters, and a sixth surface20dor exit boundary interface through which light L exits. The fifth surface20cis parallel to and faces toward the incident end facet12aof the electro-optic material12. The sixth surface20dis parallel to and faces toward the exit end facet12bof the electro-optic material12. The fifth surface20cand sixth surface20dare mutually parallel.

The front electrodes22a,24a,26aand back electrodes22b,24b,26bmake ohmic contact with the first to third regions16,18,20so that they can inject charge effectively into these regions. The front electrodes22a,24a,26aand back electrodes22b,24b,26bare preferably made from a metal such as titanium (Ti) or chromium (Cr) having a work function that does not differ greatly from the work function of the electro-optic material12.

Next the operation of the optical deflector10will be described.

First the operation when a voltage is applied only to the first electrode pair22will be described. This operation is shown in plan view inFIG. 5and in side viewFIGS. 6 and 7, looking from the direction of arrow B inFIG. 5.

In this operation, a positive voltage (+V) is applied to the first front electrode22aand the first back electrode22bis grounded. No voltage is applied across the second and third electrode pairs24,26. The regions between the second and third electrode pairs24,26become non-interaction regions with a constant refractive index since no electric field is present in them. In the first region16, the refractive index varies as follows.

The applied voltage injects electrons into the electro-optic material12from the first back electrode22b, thereby reducing the electric field near the first back electrode22bso that the electric field increases from the first back electrode22btoward the first front electrode22a. Because of the Kerr effect, the electric field reduces the refractive index, so the refractive index in the first region16is lower than in the surrounding non-interaction region, as indicated by the ‘LOWER INDEX’ notation and hatching inFIG. 5. The refractive index increases linearly from the first front electrode22ato the first back electrode22b, as indicated by the ‘HI’ and ‘LO’ notations on the ‘INDEX’ arrow inFIG. 6.

Because the refractive index is lower in the first region16than in the surrounding parts of the electro-optic material12, when light L exits the first region16through its second surface16d, the light is refracted, that is, deflected, to the right as shown inFIG. 5. No refraction or deflection occurs at the first surface16c, because this surface is normal to the incident light beam.

In addition, because of the refractive index gradient in the first region16, as the light beam L passes through the first region16it is deflected in the depth direction as shown inFIG. 6. The deflection is in the direction of increasing refractive index, that is, toward the first back electrode22b. This deflection is orthogonal to the horizontal deflection inFIG. 5. Having been deflected in two mutually orthogonal directions, the light exiting the first region16has been deflected three-dimensionally.

Since no voltage is applied to the second and third electrode pairs24,26inFIGS. 5 and 6, the light beam passes straight through the second and third regions18,20without undergoing further deflection.

If the electric field is reversed as shown inFIG. 7, by applying a positive voltage to the first back electrode22band grounding the first front electrode22a, then the same horizontal deflection occurs as shown inFIG. 5, but the direction of depth deflection is reversed. The refractive index now decreases linearly from the first front electrode22ato the first back electrode22b, so the light beam is now deflected toward the first front electrode22a.

Next the operation when a voltage is applied only to the second electrode pair24will be described. This operation is shown in plan view inFIG. 8and in side viewFIG. 9, looking from the direction of arrow C inFIG. 8. No voltage is applied to the first and third electrode pairs22,26. Now the regions between the first and third electrode pairs22,26become non-interaction regions with a constant refractive index since no electric field is present in them. In the second region18, the refractive index varies in the same way as when a voltage is applied to the first electrode pair22.

If a positive voltage is applied to the second front electrode24aand the second back electrode24bis grounded, the resulting charge injection and the Kerr effect cause the refractive index in the second region18to increase linearly from the second front electrode24ato the second back electrode24b, as indicated inFIG. 9, while the refractive index in the second region18as a whole becomes lower than in the surrounding parts of the electro-optic material12. Accordingly, light L entering the second region18through the third surface18cis refracted or deflected to the left inFIG. 8. When the light L exits the second region18from the fourth surface18d, it is again deflected to the left. In this case the light beam L is deflected horizontally at both the third surface18cor incident boundary interface and the fourth surface18dor exit boundary interface.

Light L passing through the second region18is also refracted downward in the depth direction as shown inFIG. 9because of the refractive index distribution in the second region18. This depth deflection is similar to the depth deflection shown inFIG. 6.

Though not illustrated in the drawings, the behavior of the second region18if the second front electrode24ais grounded and a positive voltage is applied to the second back electrode24bis similar to the behavior of the first region16. That is, the horizontal deflection of the light beam is the same as inFIG. 8, but the depth deflection is opposite to the deflection inFIG. 9: the light L is deflected upward toward the24a.

Next the operation when the same voltage is applied in the same direction to both the first and second electrode pairs22,24will be described. This operation is shown in plan view inFIG. 10and in the sectional viewFIG. 11taken along line D inFIG. 10. No voltage is applied to the third electrode pair26, so the region between the third electrode pair26is a non-interaction region with no electric field and a constant refractive index.

InFIGS. 10 and 11, a positive voltage is applied to the first and second front electrodes22a,24aand the first and second back electrodes22b,24bare grounded.

Referring toFIG. 10, the triangular prisms of the first region16and second region18and the space between them combine to form an essentially rectangular parallelepiped having flat square ends16cand18d. Incident light L enters and leaves this parallelepipedical region without being deflected horizontally.

As indicated inFIG. 11, light L is deflected in the depth direction in both the first and second regions16,18. Light L is thus deflected at a larger angle in the depth direction than when either the first region16or second region18is used alone.

Though not illustrated in the drawings, when a voltage is applied in the reverse direction, that is, when the first and second front electrodes22a,24aare grounded and a positive voltage is applied to the first and second back electrodes22b,24b, the light L is deflected upward in the depth direction, opposite to the direction indicated inFIG. 11. That is, the light beam L is deflected at a comparatively large angle toward the first and second front electrodes22a,24a, without being deflected horizontally.

Next the operation when a prescribed voltage is applied to the first and third electrode pairs22,26will be described with reference toFIGS. 12 to 14. This operation is shown in plan view inFIG. 12and in side views inFIGS. 13 and 14, looking from the direction of arrow B inFIG. 12.

As indicated inFIG. 12, in the third region20, the fifth surface20c, which is the incident interface, and the sixth surface20d, which is the exit interface, are mutually parallel. Accordingly, the light beam L is not deflected horizontally in the third region20. The third region20deflects light L only in the depth direction.

InFIG. 13, the voltages applied across the first and third electrode pairs22,26are identical in magnitude and direction. More specifically, identical positive voltages are applied to the first and third front electrodes22a,26aand the first and third back electrodes22b,26bare grounded.

In this case, as indicated inFIGS. 12 and 13, incident light L is deflected downward and to the right in the first region16and enters the third region20. The light beam L passes through the third region20without further horizontal deflection, but is again deflected downward in the depth direction, because the third region20and the first region16have the same refractive index gradient, increasing from the upper major surface12cto the lower major surface12d. The total effect of the combined action of the first and third regions16,20is to deflect the light beam L by a moderate amount horizontally (to the right) and by a large amount in the depth direction (downward).

InFIG. 14, opposite voltages are applied across the first and third electrode pairs22,26: a positive voltage is applied to the first front electrode22aand the first back electrode22bis grounded; the third front electrode26ais grounded and a positive voltage is applied to the third back electrode26b.

The refractive index distributions in the third region20and first region16are now mutually opposite. Accordingly, light L that has been deflected downward toward the lower major surface12din the first region16is deflected upward toward the upper major surface12cin the third region20. The result is that the light beam L exits the optical deflector10with no net deflection in the depth direction.

As described above, the optical deflector10in the first embodiment has a simple structure with electrodes on only its upper and lower major surfaces12c,12d, but can deflect light L three-dimensionally: in the horizontal direction, the depth direction, or both the horizontal and depth directions.

Since the electrodes are located only on the upper major surface12cand lower major surface12dof the electro-optic material12, the optical deflector10can be mass-produced at a low cost by conventional semiconductor fabrication methods, such as photolithography.

If the first, second, and third front electrodes22a,24a,26aare too close to each other, interference effects may occur among the applied voltages. This is also true of the first, second, and third back electrodes22b,24b,26b. To avoid such voltage interference, the first, second, and third front electrodes22a,24a,26aare preferably separated from each other by a distance greater than the thickness (the depth dimension) of the electric optical material forming them. The same separation should naturally be provided for the first, second, and third back electrodes22b,24b,26b.

If it would be difficult to separate the first, second, and third front electrodes22a,24a,26aor the first, second, and third back electrodes22b,24b,26bby the necessary amount, grooves may be provided between the electrodes to avoid voltage interference. The grooves can be formed easily by conventional semiconductor fabrication techniques such as dicing or dry etching.

Although the optical deflector10in this embodiment has three electrode pairs22,24,26, the number of electrode pairs is a design choice and is not limited to three.

In order to obtain substantially the same deflection in the depth direction in the third region20as in the first region16and second region18, the length of the third electrode pair26in the light propagation direction may be shorter than the combined length of the first electrode pair22and second electrode pair24in this direction. More specifically, the length of the third electrode pair26in the light propagation direction may be the same as the distance through which the light actually propagates in the first region16or the second region18: for example, half the length of the first region16or second region18.

Next, a deflector array based on the first embodiment will be described.

Referring toFIG. 15, the deflector array28comprises a plurality of optical deflectors10of the type shown inFIG. 4arranged in parallel in a large flat panel of electro-optic material13disposed on a substrate (not shown). This structure is possible because of the structure of the optical deflectors10, having electrodes only on their upper and lower major surfaces. As there are no electrodes or other electrical components on the side surfaces of the optical deflectors10, a plurality of optical deflectors10can be created in the same slab of electro-optic material13. The deflector array28can be fabricated at a low cost as an integrated device by the same photolithographic processes as used in fabricating semiconductor integrated circuit devices.

Second Embodiment

An optical deflector according to a second embodiment will be described with reference toFIGS. 16 to 20.

FIG. 16is a perspective view showing the general structure of the optical deflector. For simplicity, electrodes inFIG. 16are depicted as having no thickness.

This optical deflector32is similar in structure to optical deflector10in the first embodiment except for the shape and arrangement of the regions formed in the electro-optic material12. The following description will focus on the differences between the optical deflector32and the optical deflector10.

The optical deflector32comprises a block of electro-optic material12having three interaction regions34disposed in series in the direction of propagation of the light beam L. From upstream to downstream, the three interaction regions34are a first region36, a second region38, and a third region40.

The third region40is separated into two sub-regions: a first sub-region42and a second sub-region43. In shape, the first sub-region42and the second sub-region43are mutually congruent, the first sub-region42is congruent to the first region36, and the second sub-region43is congruent to the second region38.

The first region36has a first front electrode44aand first back electrode44b, which form a first electrode pair44. The first front electrode44ais a flat isosceles triangle disposed on the upper major surface12cof the electro-optic material12with its base parallel to the direction of propagation of the light beam L. The part of the upper major surface12cbelow the first front electrode44aforms the first facet or upper facet36aof the first region36.

The first back electrode44bis congruent in shape to the first front electrode44a, and is disposed on the lower major surface12din an area that forms an orthographic projection of the first front electrode44a. The part of the lower major surface12dabove the first back electrode44bforms the second facet or lower facet36bof the first region36.

The first region36is accordingly an isosceles triangular prismatic region in the electro-optic material12disposed between the first front electrode44aand the first back electrode44b, that is, between the upper facet36aand the lower facet36b.

The first region36has a first surface36cor incident boundary interface through which light L enters the first region36. The first surface36cis disposed near the incident end facet12aof the electro-optic material12. Incident light L meets the first surface36cat an oblique angle.

The first region36also has a second surface36dor exit boundary interface through which light L leaves the first region36. The second surface36dis disposed near the other end facet12bof the electro-optic material12and is not parallel to the first surface36c. Light L exits through the second surface36dat an oblique angle.

The first region36also has a side surface36ethat is parallel to a side facet of the electro-optic material12.

The second region38has a second front electrode46aand second back electrode46b, which form a second electrode pair46. The second front electrode46ais a flat isosceles triangle congruent in shape to the first front electrode44a, disposed on the upper major surface12c. The base of the isosceles triangle is parallel to the direction of propagation of the light beam L. The part of the upper major surface12cbelow the second front electrode46aforms the third facet or the upper facet38aof the second region38.

The second back electrode46bis congruent to the second front electrode46a, and is disposed on the lower major surface12d, in an area that forms an orthographic projection of the second front electrode46a. The part of the lower major surface12dabove the second back electrode46bforms the fourth facet or the lower facet38bof the second region38.

The second region38is accordingly an isosceles triangular prismatic region in the electro-optic material12disposed between the second front electrode46aand the second back electrode46b, that is, between the upper facet38aand lower facet38b.

The second region38has a third surface38cor incident boundary interface through which light L enters the second region38. The third surface38cis disposed comparatively near the incident end facet12aof the electro-optic material12. Incident light L meets the third surface38cat an oblique angle.

The second region38also has a fourth surface38dor exit boundary interface through which light L leaves the second region38. The fourth surface38dis disposed comparatively near the other end facet12bof the electro-optic material12. The fourth surface38dis not parallel to the third surface38c, and is not parallel to the end facet12bof the electro-optic material12. Light L exits through the fourth surface38dat an oblique angle.

The second region38also has a side surface38ethat is parallel to a side facet of the electro-optic material12.

The first sub-region42of the third region40is three-dimensionally congruent in shape to the first region36, but is located in a position translated parallel to the light propagation direction from the position of the first region36.

The first sub-region42has a first front sub-electrode48aand first back sub-electrode48b, which form a third electrode pair48.

The first front sub-electrode48ais a flat isosceles triangle congruent in shape to the first front electrode44a, disposed on the upper major surface12c. The base of the isosceles triangle is parallel to the direction of propagation of the light beam L. The part of the upper major surface12cbelow the first front sub-electrode48aforms the upper facet42aof the first sub-region42.

The first back sub-electrode48bis congruent in shape to the first front sub-electrode48aand is disposed on the lower major surface12d, in an area that forms an orthographic projection of the first front sub-electrode48a. The part of the lower major surface12dabove the first back sub-electrode48bforms the lower facet42bof the first sub-region42.

The first sub-region42is an isosceles triangular prismatic region in the electro-optic material12disposed between the first front sub-electrode48aand the first back sub-electrode48b, that is, between its upper facet42aand lower facet42b.

The first sub-region42has a first sub-surface42cor incident boundary interface through which light L enters the first sub-region42. The first sub-surface42cis disposed comparatively near the incident end facet12aof the electro-optic material12and is oblique to the incident light beam L. The first sub-surface42cis also the ‘fifth surface’ of the third region40.

The first sub-region42also has a second sub-surface42dor exit boundary interface through which light L leaves the first sub-region42. The second sub-surface42dis disposed comparatively near the other end facet12bof the electro-optic material12, and is not parallel to the first sub-surface42c. Light L exits through the second sub-surface42dat an oblique angle.

The first sub-region42also has a side surface42ethat is parallel to a side facet of the electro-optic material12.

The second sub-region43is three-dimensionally congruent to the second region38, but is located in a position translated parallel to the light propagation direction from the position of the second region38.

The second sub-region43has a second front sub-electrode50aand second back sub-electrode50b, which form a third electrode pair50.

The second front sub-electrode50ais a flat isosceles triangle congruent in shape to the second front electrode46a, disposed on the upper major surface12c. The base of the isosceles triangle is parallel to the direction of propagation of the light beam L. The part of the upper major surface12cbelow the second front sub-electrode50aforms the upper facet43aof the second sub-region43.

The second back sub-electrode50bis congruent to the second front sub-electrode50a, and is disposed on the lower major surface12d, in an area that forms an orthographic projection of the second front sub-electrode50a. The part of the lower major surface12dabove the second back sub-electrode50bforms the lower facet43bof the second sub-region43.

The second sub-region43is an isosceles triangular prismatic region in the electro-optic material12disposed between the second front sub-electrode50aand the second back sub-electrode50b, that is, between its upper facet43aand lower facet43b.

The second sub-region43has a third sub-surface43cor incident boundary interface through which light L enters the second sub-region43. The third sub-surface43cis disposed near the incident end facet12aof the electro-optic material12. Incident light L meets the third sub-surface43cat an oblique angle.

The second sub-region43also has a fourth sub-surface43dor exit boundary interface through which light L leaves the second sub-region43. The fourth sub-surface43dis disposed near the other end facet12bof the electro-optic material12and is not parallel to the third sub-surface43c. Light L exits through the fourth sub-surface43dat an oblique angle. The fourth sub-surface43dis the ‘sixth surface’ of the third region40.

The second sub-region43also has a side surface43ethat is parallel to one side facet of the block of electro-optic material12.

Next the operation of the optical deflector32when a positive voltage is applied to the first front electrode44aand first back sub-electrode48b, and the first back electrode44band first front sub-electrode48aare electrically grounded will be described. This operation is shown in plan view inFIG. 17and in side viewFIG. 18, which is a sectional view through line D inFIG. 17.

In the first region36, the refractive index of the electro-optic material12increases linearly in the depth direction from the first front electrode44ato the first back electrode44b, as in the first embodiment. In the first sub-region42, the refractive index of the electro-optic material12decreases linearly in the depth direction from the first front sub-electrode48ato the first back sub-electrode48b. In both the first region36and the first sub-region42the refractive index is lower in than in the surrounding parts of the electro-optic material12.

Because the first region36has a lower refractive index than the surrounding parts of the electro-optic material12, light L is refracted horizontally, toward the left inFIG. 17, both when it enters the first region36at the first surface36cand when it exits the first region36at the second surface36d.

After exiting the first region36, the light beam L passes through the second region38without deflection and enters the first sub-region42. Because the first sub-region42has a lower refractive index than the surrounding part of the electro-optic material12, the light beam L is again refracted horizontally toward the left inFIG. 17when it enters the first sub-region42at the first sub-surface42cand when it exits the first sub-region42at the second sub-surface42d.

As a result, both the first region36and the first sub-region42deflect the light beam L horizontally toward the left.

In the depth direction, as shown inFIG. 18, the light beam L is refracted downward in the first region36, passes through the second region38without deflection, and is refracted upward in the first sub-region42. In both cases the deflection is in the direction of increasing refractive index. The light beam L exits the optical deflector32with no net deflection in the depth direction, having been deflected by equal amounts in opposite directions in the first region36and the first sub-region42.

Next, the operation when same voltage is applied across the first region36and second region38with no voltage applied across the first and second sub-regions42,43will be described. This operation is shown in plan view inFIG. 19and in side viewFIG. 20, which is a sectional view through line D inFIG. 19.

As shown inFIGS. 19 and 20, a positive voltage is applied to the first and second front electrodes44a,46a, the first and second back electrodes44b,46bare electrically grounded, and no voltage is applied across the first sub-region42and second sub-region43. This time, the light beam L is deflected downward by a large amount, but there is no net horizontal deflection.

In the opposite case (not illustrated) in which the first and second front electrodes44a,46aare electrically grounded, a positive voltage is applied to the first and second back electrodes44b,46b, and no voltage is applied across the first and second sub-regions42,43, the light beam L is deflected upward by a large amount with no net horizontal deflection.

Next, the operation when same voltage is applied across the second region38and second sub-region43and no voltage is applied across the first region36and first sub-region42will be described. This operation is shown in plan view inFIG. 21and in side viewFIG. 22, which is a sectional view through line D inFIG. 21.

As shown inFIGS. 21 and 22, the second front electrode46aand second front sub-electrode50aare electrically grounded, a positive voltage is applied to the second back electrode46band second back sub-electrode50b, and no voltage is applied across the first region36and first sub-region42. The light beam L is deflected horizontally toward the right and upward in the depth direction.

In the opposite case (not illustrated) in which a positive voltage is applied to the second front electrode46aand second front sub-electrode50a, the second back electrode46band second back sub-electrode50bare grounded, and no voltage is applied across the first region36and first sub-region42, the light beam L is deflected horizontally toward the left and downward in the depth direction.

The optical deflector32in the second embodiment produces substantially the same effects as the optical deflector10in the first embodiment.

As in the first embodiment, the electrodes are preferably separated from each other by a distance greater than the thickness of the electro-optic material12, or by grooves between the electrodes if this separation distance is not feasible.

The number of the electrode pairs is a design choice and is not limited to the four electrode pairs44,46,48,50shown in the drawings. The optical deflector32may have any suitable number of electrode pairs. For example, one set of electrode pairs44,46,48, and50may followed by one or more further similar sets of electrode pairs arranged in the direction of propagation of the light beam L in the electro-optic material12.

An array of optical deflectors32may be fabricated, similar to the optical deflector array28inFIG. 15.

Third Embodiment

An optical deflector according to a third embodiment will be described with reference toFIGS. 23 to 31.

The third embodiment differs from the first and second embodiments in that the optical deflector employs the Pockels effect instead of the Kerr effect.

The Pockels effect is an effect in which the refractive index of a medium changes in direct proportion to the magnitude of the voltage applied across the medium.

FIG. 23is a perspective view showing the general structure of the optical deflector52. For simplicity, electrodes inFIG. 23are depicted as having no thickness.

As shown inFIG. 23, the optical deflector52comprises a block of an electro-optic material54and two or more mutually separated interaction regions56in the electro-optic material54.

The structure of the optical deflector52is similar to the structure of the optical deflector10in the first embodiment except for the following points.

(1) The optical deflector52uses an electro-optic material54with an electro-optic coefficient that varies linearly in the depth direction.

(2) The two front electrodes62a,64aface a single shared back electrode66.

(3) The optical deflector52lacks the third region20that was present in the first embodiment.

(4) The first front electrode62a, the second front electrode64aand the back electrode66are non-ohmic electrodes, or they are reverse biased so as to oppose carrier injection.

The following description deals mainly with these differences.

The electro-optic material54is a flat rectangular solid having end facets54aand54bwith a flat square shape. Light propagating in the direction of arrow A enters the electro-optic material54at end facet54aand exits at end facet54b.

The electro-optic material54has a first or upper major surface54con which the first and second front electrodes62a,64aare formed and a second or lower major surface54don which the back electrode66is formed as described below. The direction from the upper major surface54cto the lower major surface54dwill be referred to as the depth direction; directions parallel to the upper major surface54c, perpendicular to the depth direction, will be referred to as horizontal directions.

The electro-optic material54differs from the electro-optic material12in the first and second embodiments in that it is formed of a material with an electro-optic coefficient that is linearly graded in the depth direction.

More specifically, the electro-optic material54has a composition that varies in the depth direction, causing its electro-optic coefficient to increase linearly in the depth direction. An exemplary preferred material for the electro-optic material12is potassium tantalum niobate (KTa1-xNbxO3, where 0≦x≦1).

The Pockels effect enables the refractive index of the electro-optic material54to be controlled by an applied positive or negative voltage. When a positive voltage is applied, the refractive index of the electro-optic material increases linearly in the depth direction; when a negative voltage is applied, the refractive index decreases linearly in the depth direction.

The electro-optic material54is not limited to the KTa1-xNbxO3material mentioned above. Another material that can be provided with an electro-optic coefficient that varies linearly in the depth direction is the compound semiconductor material indium gallium arsenide phosphide (InGaAsP). The electro-optic material lithium niobate (LiNbO3) can also be used; in this case it is the ratio of domains with a first polarization or crystal geometry to domains with a second polarization or crystal geometry that varies in the depth direction.

Two interaction regions56, a first region58and a second region60, are disposed in the electro-optic material54. In relation to the propagation of light L, the first region58is upstream and the second region60is downstream.

The first region58is defined by the first front electrode62a, which is a flat right triangle disposed on the upper major surface54c. The part of the upper major surface54cbelow the first front electrode62aforms the first facet or upper facet58aof the first region58, while the orthographic projection of the first front electrode62aonto the lower major surface54dforms the second facet or lower facet58bof the first region58. The first region58is a right triangular prismatic region in the electro-optic material54disposed between the upper facet58aand lower facet58b.

The first region58has a first surface58cor incident boundary interface through which light L enters the first region58. The first surface58cis disposed near the incident end facet54aof the electro-optic material54and is normal to the incident light L.

The first region58also has a second surface58dor exit boundary interface through which light L leaves the first region58. The second surface58dis disposed closer to the other end facet54bof the electro-optic material54and follows the hypotenuse of the right triangular first front electrode62a. The second surface58dis not normal to the exiting light L.

The first region58also has a side surface58ethat extends parallel to a side facet of the electro-optic material54.

The second region60is defined by the second front electrode64a, which is a flat right triangle that is congruent to the first front electrode62a, and is disposed on the upper major surface54c. The part of the upper major surface54cbelow the second front electrode64aforms the third facet or the upper facet60aof the second region60, while the orthographic projection of the second front electrode64aonto the lower major surface54dforms the fourth facet or the lower facet60bof the second region60.

The second region60is a right triangular prismatic region in the electro-optic material54disposed between the upper facet60aand the lower facet60b.

The second region60has a third surface60cor incident boundary interface through which light L enters the second region60. The third surface60cis the nearest side of the second region60to the incident end facet54aof the electro-optic material54and follows the hypotenuse of the second front electrode64a, which is not parallel to the end facets54a,54bof the electro-optic material54. Light L enters the second region60through the third surface60cat an oblique angle.

The second region60also has a fourth surface60dor exit boundary interface through which light L leaves the second region60. In this exemplary structure, the fourth surface60dis disposed near end facet54bof the electro-optic material54. If not deflected, light L exits the second region60normal to the fourth surface60d.

The second region60also has a side surface60ethat extends parallel to a side facet of the electro-optic material54.

The first surface58cof the first region58and the fourth surface60dof the second region60are parallel. The second surface58dof the first region58and the third surface60cof the second region60are parallel and face each other. Taken together, accordingly, the second region60and first region58essentially form two halves of a rectangular parallelepiped.

The back electrode66covers the entire lower major surface54dof the electro-optic material54, facing both the first and second front electrodes62a,64a.

In order to facilitate the Pockels effect, the front and back electrodes62a,64a,66are formed so as to make non-ohmic contact with the electro-optic material54. The front and back electrodes62a,64a,66are preferably formed by depositing films of a metal such as platinum (Pt) or gold (Au). The front electrodes62a,64amay be patterned by photolithography.

Next the operation of the optical deflector52will be described with reference toFIGS. 24 to 31. In all of the operations described, the back electrode66is electrically grounded.

First, the operation when a voltage is applied to the first front electrode62awill be described. This operation is shown in plan view inFIG. 24and in side viewFIG. 25, looking from the direction of arrow B inFIG. 24.

When a positive voltage is applied to the first front electrode62a, the electro-optic coefficient of the electro-optic material54increases linearly in the depth direction, from the first front electrode62ato the back electrode66. Due to the Pockels effect caused by the applied voltage, the refractive index of the first region58increases linearly in the depth direction.

As a result, the refractive index is higher in the first region58than in the surrounding parts of the electro-optic material54. As shown inFIG. 24, light L is refracted or deflected towards the left at the second surface58d. In this case, light L is deflected horizontally at the second surface58d(exit interface) but not at the first surface58c(incident interface).

As shown inFIG. 25, as the refractive index of the first region58increases linearly in the depth direction, light L is refracted or deflected downward while passing through the first region58.

Next, the operation when a negative voltage (−V) is applied to the first front electrode62awill be described. This operation is shown in plan view inFIG. 26and in side viewFIG. 27, looking from the direction of arrow B inFIG. 26.

Due to the Pockels effect, the refractive index in the first region58now decreases linearly in the depth direction from the first front electrode62ato the back electrode66. The refractive index is accordingly lower in the first region58than in the surrounding parts of the electro-optic material54. As shown inFIG. 26, light L is refracted or deflected horizontally towards the right at the second surface58d. As before, light L is deflected horizontally at the second surface58d(exit interface) but not at the first surface58c(incident interface).

As shown inFIG. 27, as the refractive index of the first region58decreases linearly in the depth direction, light L is refracted or deflected upward in the depth direction while passing through the first region58.

Next, an operation using both the first and second front electrodes62a,64awill be described. This operation is shown in plan view inFIG. 28and in side viewFIG. 29, which is a sectional view along line D inFIG. 28.

The operation when positive voltages with the same magnitude are applied to the first and second front electrodes62a,64awill be described. In this case, the first and second front electrodes62a,64aoperate as if they were a single rectangular electrode.

Therefore, as shown inFIG. 28, light L passes through without horizontal deflection. As shown inFIG. 29, the first region58and the second region60have the same refractive index gradation in the depth direction, increasing from the upper major surface54cto the lower major surface54d. The light beam L is therefore deflected downward in both the first region58and the second region60. The total angle of downward deflection is larger than inFIG. 25.

Although not illustrated, a similar effect is obtained when negative voltages with the same magnitude are applied to the first and second front electrodes62a,64a. Light L is deflected upward by a large amount without horizontal deflection.

Next, the operation when a positive voltage is applied to the first front electrode62aand a negative voltage with same magnitude is applied to the second front electrode64awill be described. This operation is shown in plan view inFIG. 30and in side viewFIG. 31, which is a sectional view along line D inFIG. 30.

In the depth direction, the first region58and second region60have opposite refractive index distributions, producing opposite deflections that cancel out as shown inFIG. 31. As a result, light L passes through the optical deflector52with no net deflection in the depth direction.

As shown inFIG. 30, however, the refractive index is higher in the first region58than in the surrounding parts of the electro-optic material54, so light L is deflected toward the left at the second surface58d. The refractive index is lower in the second region60than in the surrounding parts of the electro-optic material54, so the light beam L is further deflected toward the left at the third surface60cand fourth surface60d.

As a result, the light beam L is deflected by a large amount towards the left without deflection in the depth direction.

Although not illustrated, a similar effect is obtained when a negative voltage is applied to the first front electrode62aand a positive voltage with same magnitude is applied to the second front electrode64a. Light L is deflected by a large amount horizontally toward the right without deflection in the depth direction.

The optical deflector52in this embodiment provides substantially the same effects as the optical deflector10in the first embodiment, but by using the Pockels effect, the optical deflector52can deflect light L over the same range of angles with fewer electrodes than the optical deflectors10and32in the preceding embodiments, which used the Kerr effect.

As in the first embodiment, the electrodes are preferably separated from each other by a distance greater than the thickness of the electro-optic material54, or by grooves if this separation distance is not feasible.

The number of front electrodes is a design choice and is not limited to the two front electrodes shown in the drawings. The optical deflector52may have any suitable number of electrodes. For example, one pair of front electrodes62a,64amay be followed by one or more similar pairs of front electrodes arranged in the direction of propagation of light L in the electro-optic material54. Alternatively, isosceles triangular electrodes may be alternately disposed in series as in the second embodiment.

An array of optical deflectors52may be fabricated, similar to the deflector array28inFIG. 15.

In a variation of the third embodiment, the shared back electrode66is replaced by separate back electrodes facing the first front electrode62aand second front electrode64a. The same effects are obtained.

Fourth Embodiment

An optical deflector according to a fourth embodiment will be described with reference toFIGS. 32 to 40.

FIG. 32is a perspective view showing the general structure of the optical deflector. For simplicity, electrodes inFIG. 32are depicted as having no thickness.

The optical deflector70in the fourth embodiment is similar to the optical deflector52in the third embodiment except for the shape of the first region72and second region74in the electro-optic material54. The following description deals mainly with this difference.

As seen inFIG. 32, the first region72and the second region74in the optical deflector70are disposed in the electro-optic material54in series in the direction of propagation of light L, the first region72being upstream of the second region74.

The first region72has a first front electrode76awith a flat isosceles triangular shape disposed in the upper major surface54c, the base of the isosceles triangle being parallel to the direction of propagation of the light beam L.

The part of the upper major surface54cbelow the first front electrode76aforms the first facet or upper facet72aof the first region72, while the area defined by orthographic projection of the first front electrode76aonto the lower major surface54dforms the second facet or lower facet72bof the first region72. The first region72is a right triangular prismatic region in the electro-optic material54disposed between the upper facet72aand the lower facet72b.

The first region72has a first surface72cor incident boundary interface through which light L enters the first region72. The first surface72cis disposed near the incident end facet54aof the electro-optic material54and is not parallel to this end facet54a. The incident light L is not normal to the first surface72c.

The first region72has a second surface72dor exit boundary interface through which light L leaves the first region72. In this exemplary structure, the second surface72dis disposed comparatively near the other end facet54bof the electro-optic material54but is not parallel to this end facet54b, and is not parallel to the first surface72cof the first region72. Light L exits from the second surface72dat an oblique angle.

The first region72also has a side surface72ethat is parallel to a side facet of the electro-optic material54.

The second region74has a flat rectangular second front electrode78adisposed on the upper major surface54c, with two opposite sides normal to the direction of propagation of the light beam L.

The part of the upper major surface54cbelow the second front electrode78aforms the third facet or the upper facet74aof the second region74while the area defined by orthographic projection of the second front electrode78aonto the lower major surface54dforms the fourth facet or the lower facet74bof the second region74. The second region74is a rectangular prismatic region in the electro-optic material54disposed between the upper facet74aand lower facet74b.

The second region74has a third surface74cor incident boundary interface through which light L enters the second region74. The third surface74cis the nearest side of the second region74to the incident end facet54aof the electro-optic material54, and is parallel to this end facet54a. If not diffracted in the first region72, incident light L meets the third surface74cof the second region74at a normal angle.

The second region74has a fourth surface74dor exit boundary interface through which light L leaves the second region74. In this exemplary structure, the fourth surface74dis disposed near the other end facet54bof the electro-optic material54, and is parallel to this end facet54band to the third surface74cof the second region74. If not deflected, light L exits through the fourth surface74dat a normal angle.

The second region74also has side surfaces74e,74fthat extend parallel to side facets of the electro-optic material54.

Next the operation of the optical deflector70will be described with reference toFIGS. 33 to 40. In the operations described below, the back electrode66is electrically grounded.

First the operation when a positive voltage is applied to the first front electrode76awill be described. This operation is shown in plan view inFIG. 33and in side viewFIG. 34, looking from the direction of arrow B inFIG. 33.

Since the electro-optic coefficient of the electro-optic material54increases linearly in the depth direction, due to the Pockels effect, the refractive index of the first region72increases linearly in the depth direction from the first front electrode76ato the back electrode66, and is higher than in the surrounding parts of the electro-optic material54.

Since the refractive index is higher in the first region72than in the surrounding parts of the electro-optic material54, as shown inFIG. 33, light L is refracted or deflected towards the left at the first surface72cand the second surface72d. The light beam L is thus deflected horizontally at both the first surface72c(incident interface) and the second surface72d(exit interface).

Since the refractive index of the first region72increases linearly in the depth direction, as shown inFIG. 34, the light beam L is refracted or deflected downward while passing through the first region72.

Next, the operation when a negative voltage is applied to the first front electrode76awill be described. This operation is shown in plan view inFIG. 35and in side viewFIG. 36, looking from the direction of arrow B inFIG. 35. Due to the Pockels effect, the refractive index in the first region72decreases linearly in the depth direction.

The refractive index is now lower in the first region72than in the surrounding parts of the electro-optic material54. As shown inFIG. 35, light L is refracted or deflected towards the right at the first and second surfaces72c,72d. In this case also, the light beam L is deflected horizontally at both the first surface72c(incident interface) and the second surface72d(exit interface).

As shown inFIG. 36, since the refractive index of the first region72decreases linearly in the depth direction, the light beam L is refracted or deflected upward while passing through the first region72.

Next, operations when various voltages are applied to both the first front electrode76aand the second front electrode78awill be described.

First, the operation when the same voltage is applied to the first and second front electrodes76a,78awill be described. This operation is shown in plan view inFIG. 37and in side viewFIG. 38, looking from the direction of arrow B inFIG. 37. In these figures, a positive voltage is applied to the first and second front electrodes76a,78a.

In the horizontal direction, as shown inFIG. 37, light L is refracted towards the left in the first region72and then exits toward the second region74. Because the third surface74cand fourth surface74dof the second region74are mutually parallel, despite the altered refractive index of the second region74, the light beam L is not deflected horizontally by its passage through the second region74.

Referring toFIG. 38, because the first region72and the second region74have same refractive index distribution in the depth direction, the refractive index increasing linearly with depth, light L is deflected downwards in the depth direction as it passes through both regions72,74.

The horizontal deflection is accordingly the same as when the positive voltage is applied only to the first front electrode76a, but that the deflection in the depth direction is greater.

Next, the operation when voltages with opposite signs are applied to the first front electrode76aand second front electrode78awill be described. This operation is shown in plan view inFIG. 39and in side viewFIG. 40, looking from the direction of arrow B inFIG. 39. In these figures, a positive voltage is applied to the first front electrode76awhile a negative voltage is applied to the second front electrode78a.

As shown inFIG. 39, light L is deflected horizontally towards the left and exits toward the second region74. Because the third surface74cand the fourth surface74dof the second region74are parallel, the light beam L is not deflected horizontally in the second region74, despite its altered refractive index.

The second region74now has a refractive index distribution opposite to that of the first region72in the depth direction. The refractive index increases linearly with depth in the first region72and decreases linearly with depth in the second region74. As shown inFIG. 40, light L is deflected downward in the first region72and upward in the second region74. The upward and downward deflections cancel out, so the light beam L exits the optical deflector70with no net deflection in the depth direction.

Overall, compared to the case where voltage is applied only to the first front electrode76a, the deflection of light is the same in the horizontal direction but there is no deflection in the depth direction.

The optical deflector70in the fourth embodiment provides substantially the same effects as the optical deflector10in the second embodiment. By using the Pockels effect instead of the Kerr effect, however, the optical deflector70in the fourth embodiment can deflect light L over the same range of angles with fewer electrodes than the optical deflector32in the second embodiment.

As in the first embodiment, the electrodes are preferably separated from each other by a distance greater than the thickness of the electro-optic material54, or by grooves between the electrodes if this separation distance is not feasible.

The number of front electrodes is a design choice and is not limited to the two front electrodes76aand78ashown in the drawings. The optical deflector70may have any suitable number of front electrodes.

An array of optical deflectors70may be fabricated, similar to the deflector array28inFIG. 15.

The first front electrode76aand the second front electrode78amay be paired with separate back electrodes, as in the first and the second embodiments, instead of having a shared back electrode66. InFIG. 32, reference numerals72band74bmay be considered to indicate such separate back electrodes.

Fifth Embodiment

An optical deflector according to a fifth embodiment will be described with reference toFIGS. 41 to 45.

FIG. 41is a perspective view showing the general structure of the optical deflector. For simplicity, electrodes inFIG. 41are depicted as having no thickness.

Like the preceding embodiments, the optical deflector80in the fifth embodiment comprises a block of an electro-optic material12with two or more interaction regions. The fifth embodiment differs from the preceding embodiments in that the optical deflector80has electrodes not only on its upper and lower major surfaces12c,12dbut also on both side surfaces.

In the example shown inFIG. 41, the optical deflector80has two mutually separated interaction regions82: a first region84and a second region86. The first region84precedes the second region86in the light propagation direction.

The electro-optic material12is similar to the electro-optic material12in the first and second embodiments, having two end facets12a,12b, a first major surface or upper major surface12c, a second major surface or lower major surface12d, a left side facet12e, and a right side facet12f.

The first region84has a pair of electrodes88including a left side electrode88aformed on the left side facet12eof the electro-optic material12and a right side electrode88bformed on the right side facet12f.

The left side electrode88ahas flat rectangular shape. The part of the left side facet12ebelow the left side electrode88aforms the first facet or the left facet84aof the first region84.

The right side electrode88bis congruent to the left side electrode88a, and is disposed on the right side facet12fin an area that forms an orthographic projection of the left side electrode88a. The part of the right side facet12fbelow the right side electrode88bforms the second facet or the right facet84bof the first region84.

The first region84accordingly is a rectangular prismatic region in the electro-optic material12disposed between the left side electrode88aand the right side electrode88b, that is, between the left facet84aand right facet84b.

When a voltage is applied across the left side electrode88aand right side electrode88b, a horizontal electric field is generated in the first region84of the electro-optic material12. The applied voltage causes the refractive index of the first region84to vary linearly in the horizontal direction. As a result, the first region84can deflect light L horizontally.

The second region86has a pair of electrodes90including a front electrode90aformed on the upper major surface12cof the electro-optic material12and a back electrode90bformed on the lower major surface12d.

The front electrode90ahas a flat rectangular shape. The part of the upper major surface12cbelow the front electrode90aforms the third facet or the upper facet86aof the second region86.

The back electrode90bis congruent to the front electrode90a, and is disposed in an area of the lower major surface12dthat forms an orthographic projection of the front electrode90a. The part of the lower major surface12dbelow the back electrode90bforms the fourth facet or the lower facet86bof the second region86.

The second region86is accordingly a rectangular prismatic region in the electro-optic material12disposed between the front electrode90aand the back electrode90b, or between the upper facet86aand lower facet86b.

When a voltage is applied across the front and back electrodes90a,90b, an electric field oriented in the depth direction is generated in the second region86of the electro-optic material12. This electric field is orthogonal to the electric field generated in the first region84. Since the applied voltage causes the refractive index of the second region86to vary linearly in the depth direction, the second region86can deflect light L in the depth direction.

Next the operation of the optical deflector80will be described.

First the operation when a positive voltage is applied to the left side electrode88aand front electrode90aand the right side electrode88band back electrode90bare electrically grounded will be described. This operation is shown in plan view inFIG. 42and in side viewFIG. 43, looking from the direction of arrow B inFIG. 42.

The refractive index of the first region84increases linearly from the left side electrode88ato the right side electrode88b. Therefore, as shown inFIG. 42, light L is deflected horizontally towards the right without deflection in the depth direction.

In the second region86, the refractive index increases linearly from the front electrode90ato the back electrode90b. Therefore as shown inFIG. 43, light entering the second region86from the first region84is deflected downward in the depth direction without deflection in the horizontal direction.

In this example, accordingly, light L is deflected downward and toward the right.

Next, the operation when a positive voltage is applied to the right side electrode88band back electrode90band the left side electrode88aand front electrode90aare electrically grounded will be described. This operation is shown in plan view inFIG. 44and in side viewFIG. 45, looking from the direction of arrow B inFIG. 44.

In this example, the refractive index in the first region84decreases linearly from the left side electrode88ato the right side electrode88b. As shown inFIG. 44, light L is deflected horizontally toward the left without deflection in the depth direction in the first region84.

In the second region86, the refractive index decreases linearly from the front electrode90ato the back electrode90b. As shown inFIG. 45, light L entering the second region86from the first region84is deflected upward without deflection in the horizontal direction.

In this example, accordingly, light L is deflected upward and towards the left.

Although not illustrated, it is possible to deflect light upward and toward the right, or downward and toward the left, by applying suitable voltages to the electrode pairs88,90.

The amount of deflection in each direction can be controlled by controlling the magnitude of the applied voltages.

The optical deflector80according to this embodiment can deflect a light beam L three-dimensionally with a simple structure having electrodes on the upper and lower major surfaces12c,12dand the left and right side facets12e,12fof the electro-optic material12.

In a variation of the fifth embodiment, there are multiple interaction regions with electrodes on the upper and lower major surfaces12c,12d, and multiple interaction regions with electrodes on the left and right side facets12e,12f. The amount of deflection can then be varied by varying the number of interaction regions to which voltages are applied.

Those skilled in the art will recognize that further variations are possible within the scope of the invention, which is defined in the appended claims.