WO2006096534A1

WO2006096534A1 - Electrooptic bragg grating modulator array for imaging

Info

Publication number: WO2006096534A1
Application number: PCT/US2006/007669
Authority: WO
Inventors: Richard W. Ridgway; Steven M. Risser
Original assignee: Optimer Photonics, Inc.
Priority date: 2005-03-04
Filing date: 2006-03-03
Publication date: 2006-09-14

Abstract

According to the present invention, electrooptic modulators are configured to form one or more Bragg-grating modulators, which are in turn configured to control and direct light in imaging systems, exposure systems, laser printers, or other types of systems where the control and direction of light forms an integral part of the operation of the system. By way of illustration, and not limitation, a disclosed embodiment relates to an imaging system capable of exposing spots in photoresist or a photoreceptor. Applications may include, but are not limited to, laser printing, laser copiers, or direct laser exposure of photoresist. Additional embodiments are contemplated.

Description

ELECTROOPTIC BRAGG GRATING MODULATOR ARRAY

FOR IMAGING

Technical Field. The present invention relates to imaging systems and other types of systems configured to control and direct light.

Disclosure of Invention.

According to the present invention, electrooptic modulators are configured to form one or more Bragg-grating modulators, which are in turn configured to control and direct light in imaging systems, exposure systems, laser printers, or other types of systems where the control and direction of light forms an integral part of the operation of the system. By way of illustration, and not limitation, a disclosed embodiment relates to an imaging system capable of exposing spots in photoresist or another type of photoreceptor. Applications may include, but are not limited to, laser printing, laser copiers, or direct laser exposure of photoresist. Additional embodiments are contemplated.

In accordance with one embodiment of the present invention, an optical system is provided comprising at least one light source, a planar waveguide, and a photoreceptor. The light source and the planar waveguide are configured such that light generated by the light source propagates in the waveguide in the direction of an electrooptic functional region of the waveguide. The electrooptic functional region of the waveguide is configured to define an array of electrooptic gratings aligned along a lateral dimension of a cross section of the propagating light. The light source and the planar waveguide are configured such that an angle at which the propagating light is oriented relative to the array of electrooptic gratings comprises a Bragg angle. The planar waveguide comprises an array of grating control elements configured to control the array of electrooptic gratings so as to direct selective portions of the propagating light to the photoreceptor. The electrooptic functional region may comprise an electrooptic polymer and the array of grating control elements may comprise an array of interdigital control electrodes configured such that a control signal can be applied to the electrooptic functional region in the form of an electric field, hi which case, the array of interdigital control electrodes defines a metal period Bragg angle and the metal period Bragg angle is different than the Bragg angle defined by the propagating light and the array of electrooptic gratings.

The electrooptic functional region of the waveguide can be configured to define at least one additional array of electrooptic gratings. The additional array of electrooptic gratings can be oriented such that light directed by the first array of gratings impinges the additional grating at its Bragg angle.

The electrooptic functional region of the waveguide can also be configured to define cascading arrays of electrooptic gratings. The cascading arrays can be oriented such that light directed by an upstream array of gratings impinges a downstream array of gratings at the Bragg angle of the downstream array. Further, the planar waveguide can be configured to comprise an additional array of grating control elements configured to control the downstream array of electrooptic gratings so as to direct selective portions of the propagating light to the photoreceptor.

The upstream array of gratings can be configured as a bit select grating and the downstream array of gratings can be configured as a position select grating, hi addition, the planar waveguide can be configured such that portions of the propagating light selective directed by the bit select grating are directed to the photoreceptor regardless of whether the selectively directed portions are further selectively directed by the position select grating to the photoreceptor. The bit select grating and the position select grating can also be configured to direct respective portions of the propagating light to different portions of the photoreceptor, to interlace respective portions of the propagating light on the photoreceptor, or both. Where the cascading arrays of gratings comprise at least two position select gratings downstream of the bit select grating, the planar waveguide can be configured such that the position select gratings are independently configured to selectively direct light impinging from the bit select grating to the photoreceptor.

The electrooptic functional region may comprise a Kerr Effect medium characterized by a dominant electrooptic response where the application of an electric field produces a birefringence in a propagating optical signal that varies with a square of the magnitude of a control signal in the grating control elements, biased by a DC voltage. More specifically, the Kerr Effect medium can be configured to induce a phase shift Aφ in an optical signal propagating through the electrooptic functional region in response to a control signal such that successive phase shifts Aφ of 180° are induced in the optical signal as a magnitude of the control signal is increased in successive increments and the successive increments decrease in magnitude as the magnitude of the control voltage is increased.

Brief Description of Drawings.

Figure 1. A schematic illustration of electrooptic grating modulator array in a laser printer application.

Figure 2. A schematic illustration of an electrooptic Bragg Grating formed in a planar optical waveguide.

Figures 3A and 3B. A schematic illustration of the manner in which a refractive index grating is formed in a planar waveguide when a voltage is applied to the interdigital electrodes.

Figure 4. A cross-sectional schematic illustration of a Bragg-grating modulator employing electrooptic polymer waveguide layers.

Figure 5. A schematic illustration of the manner in which light diffracted from one grating can be made to diffract a second or third time. Figure 6. A schematic illustration showing bit select gratings diffracting portions of an input collimated optical signal.

Figure 7. A schematic illustration of the manner in which a bit select grating can be configured to diffract portions of an incoming optical beam and a position select grating can be used to change the position of the diffracted dots in the image plane.

Figure 8. A schematic illustration of bit select gratings and four position select gratings configured to change the angle of a diffracted beam.

Figure 9. A schematic illustration showing position select gratings configured to interlace diffracted dots in the image plane.

Modes for Carrying Out the Invention. Figure 1 shows a schematic representation of one embodiment, where a single laser diode is used to form a linear series of dots. Light from a laser diode is coupled into an optical waveguide formed in an electrooptic material, which has an index of refraction that can be controlled with electric field. The laser light is confined in the plane of the waveguide, but is unconfined in the lateral direction. The light is first collimated in the lateral direction using a lens that is either internal or external to the waveguide. The broad collimated beam then propagates to an array of interdigital electrooptic gratings. The light is oriented so that the light impinges the grating at the Bragg angle. If an appropriate voltage is applied to the electrooptic grating, a refractive index grating will be induced and the laser light will be diffracted in a preferred direction. Non-diffracted light In the configuration shown in Figure 1, the first set of electrooptic gratings are referenced herein as bit select gratings and are configured to diffract portions of the input optical beam. The segments that are diffracted will ultimately form spots in the image plane.

Once the light propagates through the bit select gratings, the diffracted beams will encounter one or more electrooptic gratings, denoted position select gratings. If an appropriate voltage is applied to the position select gratings, the light will be diffracted a second time by the position select gratings. The light that is diffracted by both the bit select grating and position select grating will propagate through a lens where the collimated segments of light will be focused to a focal plane. The image will form at a position slightly closer to, or farther than, the focal plane. The image is a series of dots that could be binary (on or off) or gray scale, depending on the application.

Figure 2 shows a schematic representation of a Bragg Grating modulator formed on an electrooptic planar waveguide. The planar waveguide confines the light in the vertical direction but does not confine the light in the horizontal direction, allowing it to propagate in any direction in the plane. A set of interdigital electrodes are placed on the surface of the electrooptic material or on top a thin buffer layer which serves to optically isolate the electrodes from the waveguide layer. When a voltage is applied to the electrodes, an alternating electric field is formed between the fingers of the grating, as shown in Figure 3. This electric field interacts with the electrooptic material to form a refractive index grating. If the light impinges the grating at the appropriate angle, then the refractive index grating will cause the light to be diffracted. The appropriate incidence angle is the Bragg angle, which is given by:

0,, = siπf¹!'—] (!)

* {2AJ

where λ is the wavelength of the light in the waveguide and Λ is the period of the index change.

The refractive index grating will be formed using the electrooptic effect, which causes the refractive index to change with electric field. In the case where the waveguide is formed from lithium niobate, the change in refractive index can be approximated by the expression:

where, r_tj is the appropriate electrooptic coefficient, E is the induced electric field, V is the applied voltage, and n is the refractive index of the electrooptic material. Similar expressions can be derived when other electrooptic materials are used.

The amount of light that gets diffracted is dependent on the applied voltage. The diffraction efficiency is given by:

where d is the length of the electrodes. Table 1 shows typical parameters for the electrooptic gratings considered in this application. Electrooptic gratings can be formed in a variety of materials, including, but not limited to, lithium niobate, and electrooptic polymer materials.

Table 1. Typical Parameters for electrooptic grating modulators.

It should be noted that there is another Bragg angle associated with period of the metal fingers. This period is one half of the period associated with the electrooptically induced refractive index grating described above. Buffer layers are often used to keep the light from directly impinging the metal electrodes. Furthermore, since the Bragg angle associated with the electrooptically-induced refractive index grating and angle associated with the periodic pattern of the metal fingers is different, usually only one of the Bragg conditions are met by the impinging optical beam and only the electrooptically-induced refractive index grating results in diffraction. However, as will be described in the next section, there are configurations where these two angles are equal. In this case, it is difficult to completely eliminate the fixed diffraction caused by the metallic fingers.

Bragg Diffraction using Electrooptic Polymers. The device structure shown in Figure 3 a can be associated with devices fabricated from LiNbO3, where the nonlinearities are intrinsic to the crystal structure. For many applications, the preference would be to use an electrooptic polymer as the waveguide layer, where the electrooptic response is either first order in the applied field (Pockels effect) or quadratic in the applied field (Kerr effect). Pockels material requires prior poling while Kerr material can be aligned during operation.

A major deterrent to the use of electrooptic polymers as the waveguide layer is the period of the refractive index changes that occur in the polymer layer. In a grating device, such a shown in Figure 3 a, the electric field is oriented from the positive electrodes to the negative electrodes. When this electric field interacts with an electrooptic material that has a uniform nonlinearity, such as lithium niobate, the refractive index modulation has a period that is equal to the period of the positive electrodes. The light diffracted by the grating formed by the electrooptic effect then has a different diffraction angle from the light that may be diffracted by the simple presence of the metal electrodes, allowing for easy resolution of the electrooptic performance.

Use of an electrooptic polymer as the waveguide layer requires the application of a large DC field to the polymer, either before operation in the case of a Pockels material, or during operation in the case of a Kerr material. In either case, the use of the grating electrodes to provide both the DC field and the drive signal leads to a refractive index period that is the same as the metal period. Referring again to Figure 3, the arrows show the direction of the electric field caused by application of a voltage across the electrodes. If the waveguide material is a Kerr material, the refractive index change is proportional to the square of the electric field, hi this case, the refractive index change is largest between the electrodes and is zero directly beneath the center of the electrodes. This pattern of index changes has a period that is the same as the metal period. A similar analysis can be performed for electrooptic waveguide materials using the Pockels effect, where the grating electrodes are used to pole the polymer prior to use. The equal period for the electrooptic grating and the spacing between electrodes leads to difficulties in completely extinguishing light diffracted at the Bragg angle. The metal pattern will always diffract light along the Bragg angle of the electrodes unless a very thick buffer layer is interposed between the waveguide layer and the electrodes, which leads to reduced electrooptic efficiency.

A second component of this invention, therefore, is the design of a Bragg grating device which uses electrooptic polymers as the optical waveguide, but which has a refractive index period and an electrooptic Bragg diffraction angle different from that of the Bragg angle associated with the metal period. The cross section of this device is shown in Figure 4.

The device is fabricated by forming a metal ground plane on a suitable (silica, silicon) substrate, then applying a lower buffer layer to the metal ground plane. This buffer layer serves to optically isolate the waveguide layer from the ground plane, preventing excess loss. The refractive index of the buffer must be less than that of the electrooptic polymer layer, with the minimum thickness of the buffer determined by the refractive index difference between the buffer layer and electrooptic polymer, and the acceptable level of optical loss due to the metal. The electrooptic polymer waveguide layer is then applied to the buffer layer, with a thickness sufficient to allow for single- mode propagation of light in the electrooptic polymer layer. An upper buffer layer (same or different as lower buffer) is then applied to the electrooptic polymer layer, and the grating electrodes are applied to this upper buffer layer. The electrodes may be directly patterned onto the upper buffer, or may be formed onto a superstrate, and this superstrate applied to the upper buffer layer. If a superstrate is used, the upper buffer layer may alternately be applied to the electrodes, and the placed onto the electrooptic polymer waveguide layer.

The workings of the device will be explained assuming the electrooptic polymer layer is formed from a Kerr material. The functioning in the case of a Pockels material is similar except that the material is poled with the DC bias field prior to operation.

The device functions in the following manner. A large DC bias voltage is applied to both sets of grating electrodes while the lower metal plane is grounded, creating a large vertical electric field. The drive voltage is then superimposed onto this DC bias voltage leading to an alternating voltage pattern on the grating electrodes. This alternating voltage pattern gives rise to refractive index changes in the electrooptic polymer layer that occur at both the spacing of the electrodes (due to the voltage between the grating electrodes) and at twice the spacing between the grating electrodes (due to the alternating pattern of V_DC+V_RF, V_DC-V_RF).

To better illustrate this invention, finite element electrostatic calculations were performed for a model system where the electrooptic polymer layer is 3 microns thick, with top and bottom buffer layers also 3 microns thick. The grating electrodes were 8 microns wide with 8 microns between the electrodes. The dielectric constant of all three layers was the same. A DC bias of 1000V was applied to the grating electrodes, and the drive voltage of 100V was applied across the grating, leading to voltages of 1050V and 950V on the grating electrodes. The refractive index of the EOP was then determined as n. = n + KE^: n. = n -~KE² (4)

where 7t_e is along the direction of the electric field, and the y-direction is the layer normal. The Kerr constant was taken to be X=0.03pm/V². The resulting refractive index variation in the x direction through the center of the waveguide layer was Fourier decomposed to determine the components with a period equal to the metal period and the component with period equal to twice the metal period. A second simulation was performed with a bias voltage of only 500V. A comparison was also run without the lower metal ground plane and four times the voltage applied to the grating. The results are shown in Table 2.

Table 2. Refractive index variation through the center of the waveguide layer.

The results in Table 2 show the inclusion of the metal ground plane leads to a substantial refractive index variation at twice the metal period, while this response is absent in the control system without the lower ground plane. The magnitude of the response at twice the metal period scales approximately linearly with the magnitude of the bias voltage.

Cascading Electrooptic Bragg Grating Modulators. Figure 5 shows that light diffracted from one electrooptic grating can be subsequently diffracted by a second diffraction grating. By appropriately orienting the gratings, the diffracted light from the left grating impinges the second grating at its Bragg angle. If voltage is applied to the second grating, the light will be diffracted a second time. The light can be further diffracted by subsequent gratings, as long as the Bragg criteria are met. It should be noted that these gratings need not have the same period and same Bragg angles, as long as these design features are taken into consideration when the grating layout and orientation is defined.

Description of Electrooptic Imaging Device. Figure 6 shows the schematic layout of a series of segmented gratings that can diffract portions of the incoming collimated optical signal. These gratings have been denoted as bit select gratings (BSG). Each segment diffracts a portion of the input optical beam. The diffracted light stays relatively collimated. In this example, each diffracted segment is 100 μm in width. If a lens is used to focus the diffracted segments, each segment will be focused to the same spot in the focal plane. However, just before the focal plane (or just after) lies an image plane where each segment impinges the image plane at a separate location. The size of the spots in the image plane will depend on the focal length of the lens and the image plane position. Typical spots will be 2 to5 μm in width.

It should be noted that if the light leaves the confinement of the planar waveguide, the beam will diverge in the vertical direction. In this case, a cylindrical lens can be used to collimate the beam in the vertical direction.

Figure 7 shows a large unsegmented grating that is denoted as a position select grating (PSG), in addition to the bit select grating and lens described in the previous figure. This grating is used select the position of the image spots. If there is no voltage on the PSG, then the light diffracted from the BSG will continue to the lens and image plane. However, if the PSG is energized, then the light diffracted from the BSGs will be diffracted a second time. The lens will then send the twice-diffracted beams to a different position than the single-diffracted beams. Note that the light that was not diffracted by the BSGs will not be diffracted by the PSGs, since the undiffracted light will not impinge the PSG at the appropriate Bragg angle.

Figure 8 shows a variation of the position select gratings where the angle of the diffracted beam is changed. In this example, the bit select gratings still diffract segments of the input light, depending on which of the grating segments are energized. In this example, one, and only one, PSG is energized at a time. Each PSG has a slightly different grating period so that the diffraction angle is slightly different. The light diffracted from the PSGs impinge the lens at the same position, but at different angles. These different angles will cause the light to focus at different locations. Furthermore, the light will impinge the image plane in different locations.

Figure 9 shows another variation of the position select gratings, where they are positioned to interlace the dots. The position, grating period and orientation can be adjusted to position the dots in the image plane. In the image plane, the dots are 2 μm in diameter and positioned 1 μm apart.

The drive signals needed to energize these gratings require a voltage between 5 and 10 volts to provide nearly 100% diffraction efficiency. The electrodes themselves are capacitive in nature and have a response time dependent on this capacitance. The capacitance of these electrodes tend to be around 10 pF for a bit select grating to 1000 pF for the unsegmented position select grating. In general, the speed of dot delivery is dictated by the speed of the PSGs. Typical PSGs can operate at rates up to 10 MHz. Table 3 shows typical system parameters for delivering the spots to the image plane. Table 3. Typical System Parameters.

For the purposes of describing and defining the present invention, it is noted that an electrooptic functional region is a region of an optical waveguide structure where application of an electrical control signal to the region alters the characteristics of an optical signal propagating along an optical axis defined in the waveguide structure to a significantly greater extent than in non-electrooptic regions of the structure. For example, electrooptic functional regions according to the present invention may be formed from lithium niobate or another non-linear optical material or may comprise an electrooptic polymer configured to define an index of refraction that varies under application of a suitable electric field generated by control electrodes. Such a polymer may comprise a poled or un-poled electrooptic polymer dominated by the Pockels Effect, the Kerr Effect, or some other electrooptic effect. These effects and the various structures and materials suitable for their creation and use are described in detail in the context of waveguide devices in the following published and issued patent documents: U.S. Pat. Nos. 6,931,164 for Waveguide Devices Incorporating Kerr-Based and Other Similar Optically Functional Mediums, 6,610,219 for Functional Materials for use in Optical Systems, 6,687,425 for Waveguides and Devices Incorporating Optically Functional Cladding Regions, and 6,853,758 for Scheme for Controlling Polarization in Waveguides; and U.S. PG Pub. Nos. 2004/0184694 Al for Electrooptic Modulators and Waveguide Devices Incorporating the Same and 2004/0131303 Al for Embedded Electrode Integrated Optical Devices and Methods of Fabrication. Further, it is noted that, various teachings regarding materials and structures suitable for generating the Pockels Effect, the Kerr Effect, and other electrooptic effects in an optical waveguide structure are represented in the patent literature as a whole, particularly those patent documents in the waveguide art assigned to Optimer Photonics Inc. or naming Richard W. Ridgway, Steven M. Risser; Vincent McGinniss, and/or David W. Nippa as inventors.

The specific values suitable for the variety of control signals described herein will vary widely depending upon the specific waveguide structure at issue and the preferred operational characteristics of that structure. Guidance regarding values of such voltages may be gleaned from the collection of teachings noted above and through routine experimentation.

For the purposes of defining and describing the present invention, it is noted that the term "photoreceptor" is utilized herein to refer to any object that is configured to receive one or more distinct optical images, or components of an optical image, regardless of whether the optical image, or component thereof, is received within its focal plane. For example, and not by way of limitation, a photoreceptor may comprise a photoreceptor drum in a laser printer, a linear or multi-dimensional photodetector array, etc. In addition, it is noted that the wavelength of "light" or an "optical signal" is not limited to any particular wavelength or portion of the electromagnetic spectrum. Rather, "light" and "optical signals," which terms are used interchangeably throughout the present specification and are not intended to cover distinct sets of subject matter, are defined herein to cover any wavelength of electromagnetic radiation capable of propagating in an optical waveguide. For example, light or optical signals in the visible and infrared portions of the electromagnetic spectrum are both capable of propagating in an optical waveguide. An optical waveguide may comprise any suitable signal propagating structure. Examples of optical waveguides include, but are not limited to, optical fibers, slab waveguides, and thin-films used, for example, in integrated optical circuits. It is noted that terms like "preferably," "commonly," and "typically" are not utilized herein to limit the scope of the claimed invention or to imply that certain features are critical, essential, or even important to the structure or function of the claimed invention. Rather, these terms are merely intended to highlight alternative or additional features that may or may not be utilized in a particular embodiment of the present invention.

For the purposes of describing and defining the present invention it is noted that the term "substantially" is utilized herein to represent the inherent degree of uncertainty that maybe attributed to any quantitative comparison, value, measurement, or other representation. The term "substantially" is also utilized herein to represent the degree by which a quantitative representation may vary from a stated reference without resulting in a change in the basic function of the subject matter at issue.

Having described the invention in detail and by reference to specific embodiments thereof, it will be apparent that modifications and variations are possible without departing from the scope of the invention defined in the appended claims. More specifically, although some aspects of the present invention are identified herein as preferred or particularly advantageous, it is contemplated that the present invention is not necessarily limited to these preferred aspects of the invention. For example, although electrooptic functional regions according to specific embodiments of the present invention can be selected such that the variation of the index of refraction is dominated by an electrooptic response resulting from the Kerr Effect because Kerr Effect mediums can, in specific configurations, have the capacity for significantly higher changes in index of refraction than mediums dominated by the Pockels Effect, it is understood that electrooptic region may be dominated by the Pockels Effect, the Kerr Effect, or some other electrooptic effect, including electrooptic effects attributable to lithium niobate and other non-linear optical materials.

Claims

1. An optical system comprising at least one light source, a planar waveguide, and a photoreceptor, wherein: said light source and said planar waveguide are configured such that light generated by said light source propagates in said waveguide in the direction of an electrooptic functional region of said waveguide; said electrooptic functional region of said waveguide is configured to define an array of electrooptic gratings aligned along a lateral dimension of a cross section of said propagating light; said light source and said planar waveguide are configured such that an angle at which said propagating light is oriented relative to said array of electrooptic gratings comprises a Bragg angle; and said planar waveguide comprises an array of grating control elements configured to control said array of electrooptic gratings so as to direct selective portions of said propagating light to said photoreceptor.

2. An optical system as claimed in claim 1 wherein said electrooptic functional region comprises an electrooptic polymer.

3. An optical system as claimed in claim 2 wherein said array of grating control elements comprises an array of interdigital control electrodes configured such that a control signal can be applied to said electrooptic functional region in the form of an electric field.

4. An optical system as claimed in claim 3 wherein: said array of interdigital control electrodes defines a metal period Bragg angle; and said metal period Bragg angle is different than the Bragg angle defined by said propagating light and said array of electrooptic gratings.

5. An optical system as claimed in claim 1 wherein: said electrooptic functional region of said waveguide is configured to define at least one additional array of electrooptic gratings aligned along said lateral dimension of a cross section of said propagating light; said at least one additional array of electrooptic gratings is oriented such that light directed by said first array of gratings impinges the additional grating at its Bragg angle.

6. An optical system as claimed in claim 1 wherein: said electrooptic functional region of said waveguide is configured to define cascading arrays of electrooptic gratings aligned along said lateral dimension of a cross section of said propagating light; said cascading arrays of electrooptic gratings are oriented such that light directed by an upstream array of gratings impinges a downstream array of gratings at the Bragg angle of the downstream array; and said planar waveguide comprises an additional array of grating control elements configured to control said downstream array of electrooptic gratings so as to direct selective portions of said propagating light to said photoreceptor.

7. An optical system as claimed in claim 6 wherein said upstream array of gratings is configured as a bit select grating and said downstream array of gratings is configured as a position select grating.

8. An optical system as claimed in claim 7 wherein said planar waveguide is configured such that portions of said propagating light selective directed by said bit select grating are directed to said photoreceptor regardless of whether the selectively directed portions are further selectively directed by said position select grating to said photoreceptor.

9. An optical system as claimed in claim 7 wherein said bit select grating and said position select grating are configured to direct respective portions of said propagating light to different portions of said photoreceptor.

10. An optical system as claimed in claim 7 wherein said bit select grating and said position select grating are configured to interlace respective portions of said propagating light on said photoreceptor.

11. An optical system as claimed in claim 7 wherein: said cascading arrays of gratings comprise at least two position select gratings downstream of said bit select grating; and said planar waveguide is configured such that said position select gratings are independently configured to selectively direct light impinging from said bit select grating to said photoreceptor.

12. An optical system as claimed in claim 1 wherein said electrooptic functional region comprises a Kerr Effect medium.

13. An optical system as claimed in claim 12 wherein said Kerr Effect medium is characterized by a dominant electrooptic response where the application of an electric field produces a birefringence in a propagating optical signal that varies with a square of the magnitude of a control signal in said grating control elements, biased by a DC voltage.

14. An optical system as claimed in claim 12 wherein: said Kerr Effect medium is configured to induce a phase shift Δφ in an optical signal propagating through said electrooptic functional region in response to a control signal; successive phase shifts Aφ of 180° are induced in said optical signal as a magnitude of said control signal is increased in successive increments; and said successive increments decrease in magnitude as said magnitude of said control voltage is increased.

15. An optical system as claimed in claim 1 wherein said optical system further comprises optical elements configured to collimate and focus light generated by said light source.