Microstructured fiber optic oscillator and waveguide for fiber scanner

Abstract

To provide a favorable microstructured fiber optic oscillator and waveguide for a fiber scanner.SOLUTION: Described are optical fibers and scanning fiber displays comprising the optical fibers. The disclosed optical fibers include a plurality of mass adjustment regions, such as gas-filled regions, positioned between a central waveguiding element and an outer periphery for reducing the mass of the optical fiber compared to an optical fiber lacking the plurality of mass adjustment regions.SELECTED DRAWING: None

Description

Technical Field

[0001] (Cross - Reference to Related Applications) This application claims the benefit and priority of U.S. Provisional Application No. 62 / 438,898, filed on Dec. 23, 2016, and U.S. Provisional Application No. 62 / 464,298, filed on Feb. 27, 2017, and the entire contents of these are incorporated herein by reference.

Background Art

[0002] Optical fibers are employed in a variety of applications, including communication, sensors, and imaging. Optical fibers of various structures exist and generally include a waveguide structure such as a waveguide made from a central core and a surrounding cladding layer, and additional buffer layers and outer skin layers are optionally included to provide protection during handling or exposure to environmental conditions. Additional optical fiber design and optimization are needed to improve and expand the diversity of applications in which optical fibers are or can be employed.

Summary of the Invention

Means for Solving the Problems

[0003] This application relates to an optical waveguide. More specifically, but not limited thereto, this application relates to optical fibers and optical fiber oscillators such as those used in scanning fiber displays, where the optical fiber includes a waveguide element and a mechanical region with one or more mass - reducing elements positioned between the waveguide element and the outer perimeter of the optical fiber. The inclusion of the mass - reducing elements advantageously provides a scanning fiber display incorporating the optical fiber with improved field of view, as compared to the use of conventional optical fiber oscillators.

[0004] Scanning devices generally compromise the scanning range for frequency. For example, generally, as the frequency increases, the scanning range decreases. Similarly, as the scanning range increases, the frequency decreases. However, in many applications such as scanning optical projectors, it is desirable to have a larger operating frequency and a wide range. Frequency can be important for both resolution and refresh rate. For example, in a scanning fiber display, since the repetitive oscillation of the fiber can determine how frequently the output field of view can be changed, the frequency can directly affect the refresh rate.

[0005] However, the range can be important for the field of view for a given projector design. For example, the maximum amplitude or range of the oscillating fiber can provide the limit of the width of the output image that can be generated by the fiber. As the oscillation range is increased, a wider field of view can be provided.

[0006] Scanning devices can also be useful as display devices due to their small form factor and useful resolution and field of view. However, innovation within the art is required to obtain high-frequency scanning devices with a high scanning range. The optical fibers currently described enable an improved field of view projector while maintaining a small form factor. As an example, by incorporating the disclosed optical fibers into a scanning fiber display projector, the field of view of the projector can be increased relative to conventional scanning fiber display devices.

[0007] In a first aspect, an optical fiber is provided. The disclosed optical fiber may also be referred to herein as a microstructure optical fiber. An exemplary optical fiber includes a waveguide element extending along an axis, a mechanical region surrounding the waveguide element, such as a mechanical region that is positioned between the waveguide element and an outer periphery and includes a first material having a first density, and a plurality of mass adjustment regions positioned within the mechanical region, such as a plurality of mass adjustment regions that include a second material having a second density less than the first density. Such mass adjustment regions may optionally correspond to regions that contain air, or from which material has been removed from the mechanical region, or are otherwise absent. It should be understood that the first and second materials may also have different optical properties, such as different refractive indices.

[0008] As another example, the disclosed optical fiber includes a waveguide element extending along an axis, a mechanical region surrounding the waveguide element, such as a mechanical region that is positioned between the waveguide element and an outer periphery and includes a first material, and a plurality of cross-sectional second moment adjustment regions positioned within the mechanical region, such as a plurality of cross-sectional second moment adjustment regions that serve to modify the overall cross-sectional second moment of the mechanical region, except that the corresponding mechanical region of the same optical fiber does not include a cross-sectional second moment adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the same optical fiber. As an example, the cross-sectional second moment adjustment region may exhibit a mass per unit cross-sectional area different from that of the first material and may result in a modification of the overall cross-sectional second moment of the mechanical region. As a further example, the cross-sectional second moment adjustment region may exhibit a density different from that of the first material and may result in a modification of the overall cross-sectional second moment of the mechanical region. The term "cross-sectional second moment" refers to a geometric property of an area or object as known in the field of mechanical engineering, and it should be understood that other terms, including the moment of inertia of an area, the second moment of area, and the moment of inertia of a planar area, may also be used synonymously with cross-sectional second moment.

[0009] A variety of waveguide elements are useful with the optical fibers described herein. The waveguide element may comprise a central core region and a cladding layer surrounding the central core region. Optionally, the central core region has a diameter of about 5 μm to about 25 μm. Optionally, the cladding layer has a diameter of about 5 μm to about 200 μm. Optionally, the cladding layer comprises a first material. Optionally, the central core region comprises a third material. Optionally, the central core region comprises a second material. Optionally, the cladding layer comprises a third material. Optionally, the cladding layer and the mechanical region comprise a single body. For example, the mass adjustment region may optionally be positioned within or as part of the cladding layer.

[0010] Optionally, the waveguide element corresponds to a single-mode waveguide element or a multimode waveguide element. Other useful waveguide elements include those comprising a plurality of core regions and a cladding layer surrounding the plurality of core regions. Optionally, each of the plurality of core regions may be of the same or different materials. Other waveguide elements are also contemplated, including those having a hollow (i.e., vacuum) or gas or air-filled region such as a gas-filled core region. It should be understood that a hollow or gas or air-filled core can be useful in high-power applications because the gas or air can absorb less energy than glass or another solid material. Optionally, a vacuum region (i.e., a vacuum-filled region) may also be utilized. It should also be understood that the core and cladding regions can exhibit different optical properties such as different refractive indices.

[0011] Various mass adjustment regions may be employed with the optical fibers described herein. For example, the mass adjustment regions may include, but are not limited to, one or more gas or air filled regions, one or more polymer filled regions, one or more glass filled regions, one or more vacuum regions, or any combination thereof. As an example, the mechanical region may include a first glass, and the mass adjustment region may include a second glass different from the first glass. Optionally, the plurality of mass adjustment regions comprise a plurality of columns of mass adjustment elements. For example, the plurality of columns may be arranged concentrically around a central waveguide element. Optionally, the plurality of mass adjustment regions are arranged in a symmetric configuration around an axis. Optionally, each of the plurality of mass adjustment regions has a circular cross-sectional shape, an oval cross-sectional shape, or a polygonal cross-sectional shape. Combinations of cross-sectional shapes may also be utilized. Optionally, each mass adjustment region has a cross-sectional shape with a lateral dimension or diameter of from about 1 μm to about 25 μm. Optionally, the plurality of mass adjustment regions traverse the length of the optical fiber such as where each mass adjustment region has its own longitudinal axis. Optionally, each longitudinal axis is arranged with an axis parallel to the axis of the optical fiber. Other configurations are possible including where individual cells or regions of mass reducing material are included within segments of the optical fiber. The mass adjustment regions may optionally extend over the entire length of the optical fiber or only a portion of the fiber. Alternatively, the mass adjustment regions are randomly or evenly dispersed throughout the mechanical region, or extend perpendicular to or at an angle from the optical or waveguide axis. Optionally, the pitch between the plurality of mass reducing regions is from about 1 μm to about 25 μm. Optionally, the plurality of mass adjustment regions occupy from about 30% to about 90% of the volume of the mechanical region. Such a ratio or percentage volume may be referred to herein as a mass reduction ratio or mass reduction fill ratio. In the case of a mass reducing region containing air or gas, such a ratio or percentage volume may be referred to as an air fill ratio or gas fill ratio.

[0012] Optionally, the optical fiber comprises a composite optical fiber having a plurality of different cross-sectional configurations. For example, the optical fiber may comprise a first section having a first cross-sectional configuration and a second section having a second cross-sectional configuration. Thus, the optical fiber may comprise a section that is microstructured and a section that is not microstructured. The sectioned optical fiber may be manufactured as a single fiber with a varying cross-sectional configuration. The sectioned optical fiber may also be constructed by joining optical fibers of different cross-sectional configurations.

[0013] It should be understood that the inclusion of mass reduction regions may enable the selection, tuning, or otherwise modification of the mechanical properties of the optical fiber. For example, the outer diameter of the optical fiber may be proportional to the pointing angle of the optical fiber. Optionally, the mass regulation filling ratio of the mechanical region is proportional to the pointing angle of the optical fiber. Optionally, the mass regulation filling ratio is represented by the ratio of the diameter of the mass regulation region to the pitch between the mass regulation regions.

[0014] It should be understood that a plurality of mass regulation regions may reduce the mass of the optical fiber per unit length compared to an equivalent optical fiber, where the equivalent optical fiber comprises a corresponding waveguide element and a corresponding mechanical region, the corresponding waveguide element being the same as the waveguide element, and the corresponding mechanical region being the same as the mechanical region except that the corresponding mechanical region does not include a mass regulation region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber.

[0015] The optical fiber may exhibit an effective cantilever length. Optionally, the plurality of mass adjustment regions increase the resonant oscillation frequency of the optical fiber compared to an equivalent optical fiber, which has an effective cantilever length and includes a corresponding waveguide element and a corresponding mechanical region, where the corresponding waveguide element is the same as the waveguide element and the corresponding mechanical region is the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber. Optionally, the plurality of mass adjustment regions increase the effective cantilever length of the optical fiber for a given operation or resonance frequency compared to an equivalent optical fiber, which includes a corresponding waveguide element and a corresponding mechanical region, where the corresponding waveguide element is the same as the waveguide element and the corresponding mechanical region is the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber.

[0016] An optical fiber, such as one having an effective cantilever length, may have a resonance frequency. Optionally, the plurality of mass adjustment regions increase the effective cantilever length of the optical fiber compared to an equivalent optical fiber, which has a resonance frequency and includes a corresponding waveguide element and a corresponding mechanical region, where the corresponding waveguide element is the same as the waveguide element and the corresponding mechanical region is the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber.

[0017] In another aspect, a scanning fiber display is provided. For example, the scanning fiber display may optionally include any one of the optical fibers described above and an actuator that mechanically contacts the optical fiber and induces oscillation of the optical fiber. As an example, the optical fiber in the scanning fiber display may optionally include a waveguide element extending along an axis and a mechanical region surrounding the waveguide element, such as a mechanical region positioned between the waveguide element and the outer periphery and including a first material having a first density, and a plurality of mass adjustment regions positioned within a mechanical region, such as a plurality of mass adjustment regions including a second material having a second density less than the first density.

[0018] Various actuators and actuator configurations are useful with the scanning fiber displays described herein. For example, the actuator may optionally include a piezoelectric transducer, an electromagnetic voice coil, or a thermal actuator. Optionally, the actuator includes a two-dimensional actuator for controlling the movement of the end of the optical fiber in two dimensions. Useful actuators include those that oscillate at a controllable frequency and are configured to operate at or about the natural or resonant frequency of the optical fiber.

[0019] The disclosed scanning fiber display may optionally further include a visible light source in optical communication with the waveguide element of the optical fiber. For example, a multi-color switchable light source in optical communication with the waveguide element of the optical fiber may be used. In this way, a color image may be output by the scanning fiber display by controlling the light input to the waveguide element, such as by adjusting the color or intensity as a function of the position of the optical fiber.

[0020] The foregoing will become more apparent, together with other features and embodiments, upon reference to the following description, claims, and accompanying drawings. It should be understood that the optical fibers and scanning fiber displays of the above aspects may optionally include the features and aspects described in the following description. The present invention provides, for example, the following. (Item 1) An optical fiber comprising: a waveguide element extending along an axis; a mechanical region surrounding the waveguide element, the mechanical region being positioned between the waveguide element and an outer periphery, the mechanical region including a first material having a first density; a plurality of mass adjustment regions positioned within the mechanical region, the plurality of mass adjustment regions including a second material having a second density less than the first density. The optical fiber comprising the above. (Item 2) The optical fiber according to Item 1, wherein the waveguide element includes a central core region and a cladding layer surrounding the central core region. (Item 3) The optical fiber according to Item 2, wherein the cladding layer includes the first material and the central core region includes a third material. (Item 4) The optical fiber according to Item 2, wherein the cladding layer and the mechanical region form a single body. (Item 5) The optical fiber according to Item 1, wherein the waveguide element includes a plurality of core regions and a cladding layer surrounding the plurality of core regions. (Item 6) The optical fiber according to Item 1, wherein the plurality of mass adjustment regions include one or more gas-filled regions, air-filled regions, one or more polymer-filled regions, one or more glass-filled regions, one or more vacuum regions, or any combination thereof. (Item 7) The optical fiber according to Item 1, wherein the plurality of mass adjustment regions include a plurality of columns of mass adjustment elements, the plurality of columns being arranged concentrically around the waveguide element. (Item 8) The optical fiber according to Item 1, wherein the plurality of mass adjustment regions are arranged in a symmetric configuration around the axis. (Item 9) The optical fiber according to item 1, wherein the plurality of mass adjustment regions are arranged with an axis parallel to the axis. (Item 10) The optical fiber according to item 1, wherein the plurality of mass adjustment regions occupy from about 30% to about 90% of the volume of the mechanical region. (Item 11) The optical fiber according to item 1, wherein the plurality of mass adjustment regions reduce the mass per unit length of the optical fiber as compared with an equivalent optical fiber, the equivalent optical fiber comprising a corresponding waveguide element and a corresponding mechanical region, the corresponding waveguide element being the same as the waveguide element, and the corresponding mechanical region being the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber. (Item 12) The optical fiber has an effective cantilever length, and the plurality of mass adjustment regions increase the resonance oscillation frequency of the optical fiber as compared with an equivalent optical fiber, the equivalent optical fiber having the effective cantilever length and comprising a corresponding waveguide element and a corresponding mechanical region, the corresponding waveguide element being the same as the waveguide element, and the corresponding mechanical region being the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber. (Item 13) The optical fiber according to item 1, wherein the plurality of mass adjustment regions increase the effective cantilever length of the optical fiber for a given operating frequency as compared with an equivalent optical fiber, the equivalent optical fiber comprising a corresponding waveguide element and a corresponding mechanical region, the corresponding waveguide element being the same as the waveguide element, and the corresponding mechanical region being the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer periphery of the equivalent optical fiber. (Item 14) The optical fiber has a resonant frequency, and the plurality of mass adjustment regions increase the effective cantilever length of the optical fiber compared to an equivalent optical fiber. The equivalent optical fiber has the resonant frequency and includes a corresponding waveguide element and a corresponding mechanical region. The corresponding waveguide element is the same as the waveguide element, and the corresponding mechanical region is the same as the mechanical region except that the corresponding mechanical region does not include a mass adjustment region positioned between the corresponding waveguide element and the corresponding outer circumference of the equivalent optical fiber. The optical fiber according to item 1. (Item 15) A scanning fiber display, An optical fiber, the optical fiber A waveguide element extending along an axis, and A mechanical region surrounding the waveguide element, the mechanical region being positioned between the waveguide element and the outer circumference, and the mechanical region including a first material having a first density, the mechanical region, and A plurality of mass adjustment regions positioned within the mechanical region, the plurality of mass adjustment regions including a second material having a second density less than the first density, the plurality of mass adjustment regions An optical fiber including, and An actuator in mechanical contact with the optical fiber, the actuator being for inducing oscillation of the optical fiber, the actuator and A scanning fiber display including. (Item 16) The scanning fiber display according to item 15, wherein the actuator includes a piezoelectric transducer, an electromagnetic voice coil, or a thermal actuator. (Item 17) The scanning fiber display according to item 15, wherein the actuator includes a two-dimensional actuator for controlling movement of an end portion of the optical fiber in two dimensions. (Item 18) The scanning fiber display according to item 15, further including a visible light source in optical communication with the waveguide element of the optical fiber. (Item 19) The scanning fiber display according to item 15, further comprising a multi-color switchable light source that is in optical communication with the waveguide element of the optical fiber. (Item 20) An optical fiber comprising: A waveguide element extending along an axis; and A mechanical region surrounding the waveguide element, the mechanical region being positioned between the waveguide element and an outer circumference, the mechanical region including a first material, the mechanical region; and A plurality of cross-sectional second moment adjustment regions positioned within the mechanical region, the plurality of cross-sectional second moment adjustment regions including a second material for generating a cross-sectional second moment of the mechanical region different from that of an equivalent optical fiber, the equivalent optical fiber comprising a corresponding mechanical region, the corresponding mechanical region being the same as the mechanical region except that the corresponding mechanical region does not include the plurality of cross-sectional second moment adjustment regions positioned between the corresponding waveguide element and the corresponding outer circumference of the equivalent optical fiber, a plurality of cross-sectional second moment adjustment regions. An optical fiber comprising.

Brief Description of the Drawings

[0021]

Figure 1

[0022]

Figure 2

[0023]

Figure 3

[0024]

Figure 4

[0025]

Figure 5

[0026]

Figure 6

[0027] Embodiments of optical fibers, optical fiber oscillators, and scanning fiber displays are described herein. The disclosed optical fibers advantageously have the same fixed oscillation frequency or resonance frequency and provide an improvement in the oscillation amplitude or pointing angle for the fixed oscillation frequency or resonance frequency when compared, for example, to an optical fiber oscillator that utilizes a conventional optical fiber.

[0028] The disclosed optical fibers possess mechanical properties different from those of conventional fibers due to their structure and material properties. For example, a conventional optical fiber may include a core region and a cladding region so as to define a waveguide element. These regions may be solid bodies of optical materials having different refractive indices so as to achieve total internal reflection and waveguiding of an optical beam along the axis of the optical fiber.

[0029] The optical fibers disclosed herein, also referred to as microstructured optical fibers, may optionally utilize, for example, similar waveguide elements of materials having different refractive indices, but they are also mainly used not to guide light beams, but instead to surround waveguide elements such as mechanical regions used to tune, select, or otherwise modify the mechanical properties of the optical fiber, for example, to achieve desired mechanical properties. As an example, one or more cross-sectional second moment adjustment regions that can play a role in modifying the cross-sectional second moment of the optical fiber may be included in the mechanical region, compared to an optical fiber that is otherwise the same except for not including one or more cross-sectional second moment adjustment regions. In a specific embodiment, the cross-sectional second moment may be adjusted by modifying the mass of the mechanical region. For example, one or more mass adjustment regions that can play a role in reducing the mass or the mass per unit length of the optical fiber may be included in the mechanical region, compared to an optical fiber that is otherwise the same except for not including one or more mass reduction regions. Exemplary mass adjustment regions include air-filled regions (or other gas-filled regions), or regions containing other materials having a density less than that of the materials used for the waveguide elements or the mechanical region. For example, plastics, polymers, or glasses having a density less than that of the materials used in the waveguide elements or the mechanical region may be employed. The reduction in the intrinsic mass may, for example, enable an optical fiber with desired mechanical properties to be fabricated and used. Additionally, the reduction in mass may correspond to a modification of the moment of area of the mechanical region.

[0030] The same optical fiber may refer to two optical fibers having the same geometry, material, and / or structure, and it should be understood that an exception reference between the same optical fibers may indicate that the exception is one characteristic of one fiber that differs from the other fiber, such as one microstructured optical fiber and one non-microstructured optical fiber. For example, an optical fiber may include a core, such as a core having a first cross-sectional dimension (e.g., diameter) and made of a first optical material, and a cladding surrounding the core, such as a cladding having a second cross-sectional dimension (e.g., outer diameter) and made of a second optical material. An optical fiber that is the same except for including one or more mass adjustment regions, such as an air or gas filling region, may refer to a microstructured optical fiber that includes a core having a first cross-sectional dimension and made of a first optical material, a cladding surrounding the core having a second cross-sectional dimension and made of a second optical material, and one or more mass adjustment regions located within the cladding. It should be understood that the same optical fiber may have other characteristic differences other than the mass reduction region, which may result from the presence of a mass reduction region, such as different mass per unit length, or different resonance frequencies for a fixed oscillating fiber length, or different oscillating fiber lengths for a fixed resonance frequency.

[0031] Furthermore, it should be understood that the same optical fiber may have slightly different characteristics depending on whether a particular attribute is identical between the same optical fibers. For example, two optical fibers that are identical except for the inclusion of a microstructured mechanical region and have the same oscillation length will have different resonance frequencies, such as when the microstructured optical fiber has a higher resonance frequency. As another example, two optical fibers that are identical except for the inclusion of a microstructured mechanical region and have the same resonance frequency will have different oscillation lengths, such as when the microstructured optical fiber has a longer oscillation length.

[0032] Advantageously, the disclosed optical fiber can provide an improved field of view for a given scanning frequency. For example, a scanning fiber display using a microstructure optical fiber that includes one or more mass reduction regions can have an increased field of view compared to a scanning fiber display using an optical fiber with the same resonant frequency that is the same except for not including one or more mass reduction regions (i.e., a non-microstructure optical fiber). Since the field of view can be a limiting factor in consumer acceptance of augmented reality devices, increasing the field of view can be beneficial for increasing consumer adoption. In some scanning fiber display embodiments, it should be understood that the field of view can be increased thereby because increasing the length of the oscillating fiber for a given operating frequency will result in an increase in the maximum angular orientation of the oscillating fiber.

[0033] FIG. 1A provides a schematic view of an exemplary optical fiber system 100. The exemplary optical fiber system includes a light source 105, a coupling optics 110, and an optical fiber 115. The light source 105 may include, for example, a light emitting diode, a laser, or other visible light source. The light source 105 may optionally include a plurality of sub-light sources or a multi-color light source such as a light source that outputs electromagnetic radiation of different wavelengths. In an embodiment, the light source 105 may be switchable, for example, to enable control of the output or intensity of the light source 105 as a function of time.

[0034] The coupling optics 110 may include one or more optical elements such as lenses, mirrors, reflectors, etc. arranged in a configuration to enable light from the light source 105 to be suitably directed into the core 120 of the optical fiber 115 for waveguide. Thus, the light source 105 may be positioned in optical communication with the waveguide element of the optical fiber 115. It should be understood that the coupling optics required to efficiently couple the light from the light source 105 may depend on the light source 105, and the geometry, material, and / or numerical aperture of the optical fiber 115.

[0035] As shown, optical fiber 115 includes a core 120 and a cladding 125 and has an axis 130 that can correspond to, for example, an optical axis or a waveguide axis. Light from light source 105 that is coupled into core 120 and guided along the length of optical fiber 115 may be output at the opposite end of optical fiber 115. It should be understood that the spot shape and direction of the light output from optical fiber 115 can depend on the geometry, material, and / or numerical aperture of optical fiber 115. Typically, the output from the optical fiber exhibits a conical shape 135, and the angle of cone 135 is again defined by the geometry, material, and / or numerical aperture of optical fiber 115. From a field of view perspective, optical fiber 115 in a non-oscillating configuration does not exhibit an increase in the field of view 140 that exceeds the angle of cone 135. From a deflection angle perspective, optical fiber 115 in a non-oscillating configuration exhibits a zero deflection angle.

[0036] FIG. 1B provides a schematic view of an optical fiber system 150 such as may be present in a scanning fiber display system. General details of scanning fiber display systems can be found, for example, in U.S. Patent Application No. 14 / 156,366, filed Jan. 15, 2014, and published under Publication No. US2015 / 0268415 (incorporated herein by reference in its entirety).

[0037] FIG. 1B omits the depiction of any light source or coupling element from the optical fiber system 150 so as not to obscure other details. The optical fiber system 150 includes an optical fiber 155, which may correspond to the optical fiber 115, and an actuator 160. The actuator 160 may be used to impart an oscillatory motion into the optical fiber 155. The oscillation of the optical fiber 155 may be modeled as, or may correspond to, an oscillator held in a cantilever-like fashion with a fixed end and a free end. The actuator 160 may be, or may include, for example, a piezoelectric actuator, an electromagnetic voice coil, or a thermal actuator. The actuator 160 may enable control of the oscillatory motion of the optical fiber 155 in two dimensions and may include two or more independent operable axes. The degree of the oscillatory motion of the optical fiber 155 is depicted by a dashed line in FIG. 1B. Due to the oscillatory motion, the optical fiber 155 exhibits an increase in the field of view beyond the output cone of the optical fiber 155. From the perspective of the field of view, the optical fiber system 150 exhibits a field of view 165 that exceeds the output cone of the optical fiber 155.

[0038] FIG. 2A provides a schematic cross-sectional view of an optical fiber 200. The optical fiber 200 may correspond to a conventional optical fiber and includes a core 205 and a cladding 210 that surrounds the core 205. The core 205 is illustrated as having a core diameter 215, and the cladding 210 is illustrated as having an outer diameter 220. It is to be understood that the core diameter 215 and the outer diameter 220 may be characteristic of a particular optical fiber embodiment and, thus, may take on any suitable values.

[0039] Unless otherwise indicated, the dimensions of the features illustrated in the accompanying drawings may not be to scale, but it is to be understood that particular aspects of the figures or different figures are depicted to illustrate differences in dimensions between different configurations or elements. It is also to be understood that additional materials, such as buffers, jackets, or other coated or protective materials, may be constructed outside of the cladding or mechanical regions but may not be shown in the accompanying drawings.

[0040] Figure 2B provides a schematic cross-sectional view of an embodiment of the microstructured optical fiber 230. The microstructured optical fiber 230 includes a waveguide element 235 and a mechanical region 240 surrounding the waveguide element. For illustrative purposes, a dashed line is shown in Figure 2B to better distinguish the transition between the waveguide element 235 and the mechanical region 240. In Figure 2B, the waveguide element 235 includes a core 245 and a cladding 250 surrounding the core 245. The core 245 is depicted as having a core diameter 255, the waveguide element 235 is depicted as having a cladding diameter 260, and the optical fiber 230 is depicted as having an outer diameter 265.

[0041] The mechanical region 240 is depicted in Figure 2B as including a solid region 270 and a mass reduction region 275 positioned between the waveguide element 235 and the outer perimeter of the mechanical region 240 and the microstructured optical fiber 230. Exemplary mass adjustment regions include, but are not limited to, fluid-filled regions, gas or air-filled regions, polymer-filled regions, glass-filled regions, and / or vacuum regions (e.g., vacuum filling), where the fluid, gas or air, polymer, glass filling, or vacuum region has a density less than that of the solid region 270, the cladding 250, the core 245, or any combination thereof. Optionally, the solid region 270 includes the same material as the cladding 250 and / or has similar or the same optical and / or mechanical properties. Optionally, the solid region 270 and the cladding 250 include different materials and / or have different optical and / or mechanical properties. Additional materials such as buffers, jackets, or other coated or protective materials may be constructed outside the outer perimeter of the mechanical region 240, but it should be understood that these are not shown here.

[0042] The mass reduction regions 275 may be uniformly and / or regularly distributed throughout the mechanical region 240, and any suitable or desirable geometric shape and distribution may be used to obtain specific targeted mechanical properties for the microstructured optical fiber 230. It should be understood that the mass reduction regions 275 may be arranged along axes parallel to each other and / or along an axis parallel to the axis of the optical fiber such as the waveguide axis or the optical axis. Optionally, the mass reduction regions 275 may be arranged along other directions, such as along intersecting axes, perpendicular to the optical axis, or at an angle to the optical axis, however, at least a portion of the mechanical region 240 includes the mass reduction regions. The mass reduction regions 275 may also be randomly, uniformly, or non-uniformly (optionally, not along any particular axis) distributed throughout the mechanical region 240. As shown in FIG. 2B, the mass reduction regions 275 are shown as circular and exhibit a uniform cross-section having a diameter 280. The pitch 285 corresponds to the center-to-center spacing between adjacent mass reduction regions 275. The mass reduction regions 275 may exhibit symmetry such as cylindrical symmetry about the axis of the microstructured optical fiber 230 such as the waveguide axis or the optical axis. The optical fiber 230 may optionally exhibit rotational symmetry.

[0043] Although not limiting, the microstructured optical fiber 230 may be constructed by stacking several appropriately sized materials so as to form an overall preform structure that is targeted to produce the microstructured optical fiber 230, such as by using a solid tube and / or a hollow tube of suitable diameter, wall thickness, material, shape, etc. In some embodiments, a glass material is used. Exemplary glasses may include, but are not limited to, silica glass, fluoride glass, phosphate glass, chalcogenide glass. In some embodiments, a plastic or polymer such as polymethylmethacrylate, polystyrene, fluoropolymer, or polysiloxane may be used. Depending on the processing method and material, the preform may be placed in a furnace to heat and fuse the different components of the preform, and the heated preform may be drawn into strands of optical fiber. Optionally, an extrusion method may be used for fibers containing polymer or plastic materials. It should be understood that various techniques, materials, and methods may be used to manufacture optical fibers, that there are several commercial fiber manufacturers, and that services may be provided to manufacture optical fibers based on specified parameters.

[0044] For illustrative purposes of comparison, the core diameter 215 of the core 205 of the optical fiber 200 may optionally be the same as the core diameter 255 of the core 245 of the microstructured optical fiber 230. The outer diameter 220 of the optical fiber 200 may optionally be the same as the outer diameter 265 of the microstructured optical fiber 230. The cores 205 and 255 may optionally be made of the same material. The claddings 210 and 250 and the solid region 270 (non-mass reduction region) of the mechanical region 240 may optionally be made of the same material. In this regard, the optical fiber 200 may be considered the same as the microstructured optical fiber 230, except that the microstructured optical fiber 230 includes a mass reduction region 275 while the optical fiber 200 includes a solid cladding 210 that does not include a mass reduction region.

[0045] The different components of the microstructure optical fiber 230 may have any suitable dimensions, and specific dimensions may be selected to provide specific properties such as optical and mechanical properties. For example, the core 245 may have a diameter of, but is not limited to, from about 5 μm to about 25 μm. As used herein, the term "about" is intended to include variations centered around a defined value, such as variations that would not modify the operational effect if the value were slightly smaller or slightly larger. It should be understood that in some embodiments, the term "about" may be related to the precision or tolerance of a value. In some embodiments, the term "about" may correspond to a variation of ±1% or less, ±5% or less, or ±10% or less.

[0046] As another example, the waveguide element 235 may have a diameter of, but is not limited to, from about 5 μm to about 200 μm, such as from about 5 μm to about 125 μm. In some embodiments, the cladding 250 may have a diameter or thickness of, but is not limited to, from about 5 μm to about 200 μm, such as from about 5 μm to about 125 μm, and optionally may be considered to include the mechanical region 240, or be integral with it, or be a single entity therewith, and thus may have a diameter or thickness corresponding to the outer diameter 265. The outer diameter 265 may also take on any suitable value, such as from about 10 μm to about 200 μm, and may match the outer diameter 220 of the conventional optical fiber 200. Exemplary outer diameters may include about 40 μm, about 50 μm, about 80 μm, about 100 μm, about 125 μm, about 150 μm, about 175 μm, and about 200 μm.

[0047] Each of the mass reduction regions 275 may have any suitable dimension or shape, for example, but not limited to, cross-sectional dimensions such as a diameter, radius, side length, or axial length of about 1 μm to about 25 μm, about 1 μm to about 5 μm, about 5 μm to about 10 μm, about 10 μm to about 15 μm, about 15 μm to about 20 μm, or about 20 μm to about 25 μm. The pitch 280 between the mass reduction regions 275 may also have any suitable dimension and may be limited by the cross-sectional dimensions of the mass reduction regions 275. For example, the pitch 280 may exceed the diameter of the mass reduction regions 275. The pitch 280 may have a length of, but not limited to, about 1 μm to about 25 μm, about 1 μm to about 5 μm, about 5 μm to about 10 μm, about 10 μm to about 15 μm, about 15 μm to about 20 μm, or about 20 μm to about 25 μm. The mass reduction ratio of the optical fiber 230 and / or the mechanical region 240 may take any suitable value based on the size, number, spacing, and arrangement of the mass reduction regions. In embodiments, the plurality of mass reduction regions occupy about 1% to 90% of the volume of the optical fiber 230 or the volume of the mechanical region 240. Optionally, the plurality of mass reduction regions occupy about 30% to about 90%, about 30% or more, about 40% or more, about 50% or more, about 60% or more, about 70% or more, about 80% or more, or about 90% of the volume of the optical fiber 230 or the volume of the mechanical region 240.

[0048] Depending on the particular configuration, in some embodiments, the mass reduction regions may exhibit four-fold or six-fold or other symmetries such as cylindrical symmetry, rotational symmetry, or radial symmetry about the axis of the microstructured optical fiber. Additionally, other cross-sectional shapes for the mass reduction regions may be utilized. For example, the cross-section of the mass reduction region may exhibit a polygon such as a triangle, square, rectangle, hexagon, a perfect circle, a circular shape, or an oval shape, or any other suitable shape. In some embodiments, the cross-section of the mass reduction region may have a shape with regular symmetry such as a circle, an oval, an ellipse, a polygon, etc. In embodiments, a combination of mass reduction regions with different cross-sectional shapes may be utilized. In embodiments, the spacing between adjacent mass reduction regions may be uniform or non-uniform. In embodiments, the cross-sectional dimensions such as the diameter, radius, axial length, side length, etc. of different mass reduction regions may be uniform or non-uniform.

[0049] Figures 3A - 3D depict schematic cross - sectional views of different microstructured optical fibers presenting waveguide elements surrounded by mechanical regions, according to various embodiments. The microstructured optical fiber 300A of FIG. 3A includes a plurality of rows of mass - reduction regions arranged concentrically around a central waveguide element. The microstructured optical fiber 300B of FIG. 3B includes circular mass - reduction regions arranged in a six - fold symmetric configuration. The microstructured optical fiber 300C of FIG. 3C includes square mass - reduction regions arranged in a four - fold symmetric configuration. The microstructured optical fiber 300D of FIG. 3D includes a concentric ring of oval mass - reduction regions.

[0050] The waveguide elements of the microstructured optical fibers described above are compatible with conventional core / cladding designs, but other waveguide element configurations are possible and contemplated. For example, in some embodiments, multiple core regions may be surrounded by a single cladding layer or region. Additionally, multiple optical fibers may be arranged in a side - by - side or two - dimensional array configuration to provide additional fields of view for a scanning fiber display (also referred to as a fiber - scanning display). U.S. Patent Application No. 14 / 156,366 describes multi - core fibers filled in a hexagonal pattern, such as those including an array of seven or nineteen cores in a hexagonal arrangement and oscillator fibers for a fiber - scanning display. It should be understood that in embodiments, a change in refractive index between materials, such as between a core and a cladding or between glass and air, can provide a waveguide effect, such as by the process of total internal reflection. Thus, the transition between materials may be all that is required to achieve waveguiding, and thus, the large cladding of a conventional optical fiber may still be modified to include mass - reduction regions while retaining a solid central portion surrounding a core of a higher refractive index material that provides waveguiding. Various fiber configurations are possible, including single - mode and multi - mode configurations. For the purpose of generating an optical display, it is beneficial for the optical fiber to have high transparency / low loss within the visible electromagnetic region.

[0051] Figures 4A and 4B provide schematic diagrams of optical fiber systems 400 and 450 for comparison purposes. Optical fiber systems 400 and 450 may be used, for example, in a scanning fiber display system. Figures 4A and 4B omit any depiction of a light source or coupling element from optical fiber systems 400 and 450 so as not to obscure other details. In Figure 4A, optical fiber system 400 includes optical fiber 405 and actuator 410. A cross-section 415 of optical fiber 405 is also shown in Figure 4A, illustrating that optical fiber 405 is a conventional optical fiber that includes a core and a cladding layer. Actuator 410 may be used to impart an oscillatory motion into optical fiber 405. The degree of oscillatory motion of optical fiber 405 is depicted by a dashed line in Figure 4A. From the perspective of the field of view, optical fiber system 400 presents a field of view 420. The cantilever-like held portion of optical fiber 405 has a length 425.

[0052] In Figure 4B, optical fiber system 450 includes microstructured optical fiber 455 and actuator 460. A cross-section 465 of microstructured optical fiber 455 is also shown in Figure 4A, illustrating that microstructured optical fiber 465 includes a waveguide element and a microstructured mechanical region surrounding the waveguide element that includes a plurality of mass reduction regions. Actuator 460 may be used to impart an oscillatory motion into microstructured optical fiber 455. Actuator 460 may oscillate at or near the resonance frequency of microstructured optical fiber 455, such as within 5% of the natural frequency of microstructured optical fiber 455 or within 1% of the resonance frequency of microstructured optical fiber 455. In an embodiment, the resonance frequency may correspond to the eigenfrequency or natural frequency. In an embodiment, actuator 460 operates at a frequency that provides a gain in the steering angle or deflection of microstructured optical fiber 455. The degree of oscillatory motion of microstructured optical fiber 455 is depicted by a dashed line in Figure 4B. From the perspective of the field of view, microstructured optical fiber system 450 presents a field of view 470. The cantilever-like held portion of microstructured optical fiber 455 has a length 475.

[0053] It should be understood that the resonant frequency of an optical fiber held in a cantilever shape can generally be proportional to the square of the length of the cantilever. For example, if the length 425 of the optical fiber 405 is doubled, a four-fold increase in the resonant frequency of the optical fiber 405 would be expected. Similarly, if the length 475 of the microstructure optical fiber 455 is halved, a four-fold decrease in the resonant frequency of the microstructure optical fiber 475 would be expected.

[0054] It should also be understood that the mass distribution of an optical fiber held in a cantilever shape can also affect the resonant frequency. For example, assuming that the optical fiber 405 and the microstructure optical fiber 455 are the same (diameter, material, etc.) except for the mass reduction region of the microstructure optical fiber 455, the inclusion of the mass reduction region can reduce the mass per unit length of the microstructure optical fiber 455 compared to the optical fiber 405. Therefore, for the resonant frequencies of the optical fiber 405 and the microstructure optical fiber 455 to be the same, the optical fiber 405 and the microstructure optical fiber 455 exhibit different lengths, and the length 425 is smaller than the length 475. Advantageously, this difference in length will allow the field of view 470 and / or the orientation angle of the microstructure optical fiber 455 to exceed the field of view 420 and / or the orientation angle of the optical fiber 405.

[0055] It should be understood that other characteristics of the optical fiber can affect the resonant frequency of the optical fiber and / or the orientation angle such as the maximum orientation angle. Exemplary characteristics that can affect the frequency or orientation angle include fiber outer diameter, diameter of the waveguide element, mass reduction ratio, number of mass reduction regions, distribution, and cross-sectional dimensions (e.g., diameter), pitch between adjacent mass reduction regions, mass reduction region material density, waveguide element design, core material, cladding material, solid material in the mechanical region, and the like.

[0056] In some embodiments, a scanning fiber display utilizes the oscillatory motion of an optically fiber held in a cantilever-like manner and projects an image using the optical fiber. For example, the oscillatory motion of the optically fiber held in a cantilever-like manner may be two-dimensionally controlled to generate a helical pattern, such as by appropriately driving an actuator. In some embodiments, the input light may be controlled and timed such that the output of the oscillating optical fiber can generate a desired image within the helical pattern, and the repetitive oscillatory motion and timed optical output are used to generate a series of images. U.S. Patent Application No. 14 / 156,366 describes a method by which a fiber held in a cantilever-like manner can be used to generate a projected image or a series of images. However, the embodiments described herein advantageously enable the field of view, the steering angle, and the projected output image size and / or resolution of the scanning fiber display to be increased by using a microstructure optical fiber.

[0057] For example, FIG. 5A depicts a helical pattern 500 for a conventional scanning fiber display incorporating a conventional optical fiber with a core and cladding and without a mass reduction region within the cladding material, similar to the optical fiber system 400 of FIG. 4A. The diameter 505 of the helical pattern is limited by the maximum steering angle of the scanning fiber display used.

[0058] In contrast, FIG. 5B depicts an equivalent helical pattern 550 for a scanning fiber display incorporating an equivalent microstructure optical fiber including a waveguide element and a microstructure mechanical region surrounding the waveguide element including a plurality of mass reduction regions, similar to the optical fiber system 450 of FIG. 4B. The helical pattern 550 exhibits a diameter 555 that is limited by the maximum steering angle of the scanning fiber display used.

[0059] (Implies an increase in the cantilever length) For the same conventional optical fiber and microstructured optical fiber operating at the same resonant frequency (i.e., the same except for the inclusion of a mass reduction region within the microstructured optical fiber), the diameter 555 of the spiral pattern 550 will be greater than the diameter 505 of the spiral pattern 500 in correspondence with the increase in the field of view and / or maximum angular aperture achieved by the use of the microstructured optical fiber. Without limitation, the use of the microstructured optical fiber can advantageously increase the field of view and / or angular aperture by up to approximately 30%. In some cases, an increase in the field of view and / or angular aperture of up to approximately 50% or up to approximately 70% can be achieved. In some embodiments, an increase in the field of view and / or angular aperture of from about 30% to about 40% can be achieved.

[0060] Various microstructured optical fibers may have different optical and mechanical properties. In some embodiments, the microstructured optical fiber may have one or more of the following optical specifications, namely, a light transmission range of from about 435 nm to about 645 nm, an output mode field diameter of about 1.4 μm for red, green, and / or blue light with a tolerance of about ±0.15 μm, a numerical aperture of about 0.25 for red, green, and / or blue light, a light transmission loss of about 30 dB / km or less for any or all wavelengths from about 435 to 645 nm, and a low splicing loss to single mode (ф1.2 μm, NA).

[0061] In some embodiments, the microstructured optical fiber may have one or more of the following mechanical specifications, namely, an outer diameter of from about 80 μm to about 125 μm or from about 40 μm to about 200 μm, a diameter of the mechanical region from about 40 μm to the outer diameter, a mass reduction ratio (e.g., gas or air filling ratio) within the mechanical region of 70% or more, a concentricity core / outer diameter of about 500 nm or less, a percent difference between the vertical moments of inertia of about 0.4% or less indicating that the microstructured optical fiber is substantially symmetric about the x and y axes (where z is the fiber long axis), and a weight change due to water collection within the air filling region of about 1% or less.

[0062] Rotational symmetry can be useful for the optical fibers disclosed in this specification and can be advantageous for some embodiments. Thus, it should be understood that a microstructure optical fiber can optionally possess rotational symmetry. Rotational symmetry can refer to the stiffness (K r ) of an optical fiber that is the same in all radial directions (θ) (see Figure 2A for direction reference). In other words, with respect to a force acting along any radial direction defined by θ, the optical fiber would purely translate parallel to the radial direction. In the static case, Hooke's law results in F r =K r ·δ r . Note that with rotational symmetry, there is no translation perpendicular to the radial direction. This can also be characterized by stating that the principal direction of the optical fiber is not unique.

[0063] The terms and expressions employed are used as terms of description and not of limitation, and there is no intention, in the use of such terms and expressions, to exclude any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the claimed invention. Accordingly, although the invention has been specifically disclosed by the preferred embodiments and optional features, it should be understood that modifications and variations of the concepts disclosed herein may be used by those skilled in the art, and such modifications and variations are considered to be within the scope of the invention as defined by the appended claims.

[0064] The foregoing description of the exemplary embodiments of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed, and many modifications and variations are possible in light of the above teachings. The embodiments were chosen and described in order to explain the principles of the invention and its practical application, thereby enabling others skilled in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated.

[0065] When groups of substituents are disclosed herein, it is to be understood that all individual components of these groups, and all sub-groups and classes that can be formed using the substituents, are disclosed separately. When Markush groups or other groupings are used herein, all individual components of the group, and all possible combinations and sub-combinations of the group are intended to be individually included within the present disclosure. As used herein, "and / or" means that one, all, or any combination of the items in a list separated by "and / or" is included in the list. For example, "1, 2, and / or 3" is equivalent to " "1" or "2" or "3", or "1 and 2" or "1 and 3" or "2 and 3" or "1, 2, and 3" ".

[0066] All formulations or combinations of components described or exemplified can be used to practice the invention unless otherwise stated. Specific names of materials are intended to be exemplary since it is known that those skilled in the art may name the same material differently. Those skilled in the art will understand that methods, device elements, starting materials, and synthetic methods other than those specifically exemplified can be employed in the practice of the invention without undue experimentation. All known functional equivalents in the art of any such methods, device elements, starting materials, and synthetic methods are intended to be included within the present invention. When ranges, such as temperature ranges, time ranges, or composition ranges, are recited in this specification, all intermediate ranges and sub-ranges, and all individual values included within the recited ranges are intended to be included within the present disclosure. The specific details of particular embodiments can be combined in any suitable manner without departing from the spirit and scope of the embodiments of the present invention. However, embodiments of the present invention can be directed to specific embodiments, with respect to each individual aspect, or to specific combinations of these individual aspects.

[0067] The present invention can be further understood by reference to the following non-limiting examples. (Example)

Example

[0068] (Explanation of the mechanical merit function: An optical fiber oscillator held in a cantilever shape) This example describes a method of maximizing the angular divergence at the end of an optical fiber while keeping the natural frequency of the oscillator constant, thus increasing the field of view. In some embodiments, this can be accomplished by minimizing the mass of the oscillator held in a cantilever shape while maximizing the second moment of area. This example derives how the optical performance (maximum deflection for a given operating frequency) is achieved for a fiber of a given size with respect to a thin-walled tube fiber. Advantageously, a microstructure optical fiber incorporating this technology can exhibit an increase in the merit function (i.e., an increase in the angular divergence) of about 30% or better compared to the same conventional fiber.

[0069] To determine the merit function, the second moment of area of a section of the optical fiber is required. The following definitions are used in the calculation of the second moment of area. I T,MS : Second moment of area of the cross-section (T = standard fiber, MS = microstructure fiber) A T,MS : Area of the cross-section A H_i : Area of the holes (air-filled regions) within the microstructure r i : Perpendicular distance from the hole of the area segment to the neutral axis T : Subscript indicating a solid fiber MS : Subscript indicating a microstructure fiber j: Natural frequency mode / harmonic order β(j): Mode constant of the j-th mode d: Rod diameter

[0070] For a solid rod, I T = d 4 / 64. As a constraint, the natural frequency f nIt is fixed to be the same for direct comparison of the solid and microstructure designs. For a beam held in a cantilever shape, the natural frequency is obtained from the Euler equation.

Chem.

[0071] Regarding the high refresh rate of the display, it is useful for the operating frequency of the scanning fiber to be high. At the same time, since the large deflection of the oscillator is proportional to the field of view and resolution, it is desirable to achieve this.

[0072] Since the scanning fiber projector is a resonant device, the operating frequency is approximately equal to the natural frequency (within 1%). This means that the system parameters must be selected so that the system natural frequency remains high as estimated by the above equation.

[0073] From the perspective of the microstructure fiber, the above equation provides direct insight into the influence of the natural frequency of the oscillator and the solid cross-sectional area A of the solid fiber minus the second moment of area I of the cross-section and the area of the holes on the associated length.

[0074] Investigation of this equation shows that increasing the ratio of I to A increases the natural frequency. This property can be utilized in microstructure fibers by removing the mass near the neutral axis by inserting holes near the neutral axis (a small effect on I). This is because it is a function of the square of the distance from the neutral axis and has a small effect on I due to keeping the mass near the outer diameter or circumference. This further results from the following equation, showing that the contribution of the section (hole) to the second moment of area is a function of the square of the distance from the neutral axis.

[0075] From the parallel axis theorem, the second moment of area of the microstructure fiber is as follows.

Chem.

[0076] The following merit function analysis explains to what extent the microstructure fiber is comparable to the solid fiber from the perspective of the deflection angle. In this analysis, the frequency is held constant and the cross-sectional second moment of area and area of the beam segments are varied. The merit function quantifies the gain of the deflection angle. Using the above equation for the natural frequency,

Chemical formula

Chemical formula

Chemical formula

[0077] From the frequency response function, the response at resonance is identified as scaling with the static deflection. Therefore, the static deflections of the beam under point load and distributed load are considered. In each case, the ratio of the deflection of the structured device to the deflection of the solid optical fiber cantilever with respect to the deflection angle is determined. It should be noted that the pattern of the microstructure can be optimized for maximum deflection, but this must also be tuned for the transmission of visible light using a single mode.

[0078] When calculating the slope of a beam with a concentrated load at the end,

Chemical formula

Chemical formula

[0079] The formula for the angular deflection gain of a constant frequency oscillator is derived as follows. For the concentrated force model, assuming E MS =E T then,

Chemical formula

[0080] For the distributed force model,

Chemical formula

Chemical formula

[0081] Estimating the dynamic mode shape as that of a distributed load for relative stress calculation,

Chemical formula

Chemical formula

[0082] Figure 6 provides a plot of the merit function showing the gain in the steering angle of the microstructure optical fiber compared to a solid or conventional optical fiber based on a fiber outer diameter of 125 μm according to the above equation. This example explains the mass reduction from the perspective of the air-filled region, but it should be understood that other mass-reducing materials can also be used under similar analysis. The plot provides a surface showing the maximum gain in the steering angle of the optical fiber as a function of the ratio of the diameter to the pitch of the air-filled region and as a function of the diameter of the air-filled region, demonstrating the effect of the fiber. It is desirable to have the maximum gain possible, but it should be understood that certain mechanical considerations must be taken into account. For example, the fiber must be able to oscillate without breaking. Therefore, the diameter of the microstructure area should be less than the outer diameter of the fiber for the fiber to have mechanical integrity. In addition, the ratio of the diameter of the air-filled region to the pitch of the air-filled region should be less than 1; otherwise, the air-filled regions would overlap and occupy an unusable amount of the fiber. As shown in Figure 6, a diameter of the microstructure (air-filled) region of 102.9 μm with a diameter / pitch of 0.873 is expected to provide a gain of 1.725 corresponding to a 72.5% increase in the steering angle.

Example

[0083] (Analysis of Microstructure Fiber Performance) The requirements for maximizing the natural frequency of a mechanical system are simple. For a lumped-parameter system such as a mass connected to a single-degree-of-freedom spring without damping, the natural frequency f n (Hz) is a function of the modal stiffness

Chem.

Chem.

[0084] The equation for the natural frequency of the lateral motion of an Euler-Bernoulli beam is as follows,

Chem.

Chemical formula

Chemical formula

Chemical formula

[0085] Modify the boundary conditions. Change the waveguide holding method to increase the constant βL(i). The holding method is limited by stability requirements, drive energy coupling, and processing techniques.

[0086] Modify the material properties. Increase the Young's modulus (E). This is difficult because the optical waveguide material is limited. Reduce the density (ρ). This is also difficult, especially in relation to mass production, because the optical waveguide material is limited. These objectives

Chemical formula

[0087] Modify the mass distribution. Reduce the cantilever length (L). This is possible, but such a change can reduce lateral deflection (the static deflection with respect to the applied end load is proportional to L 3 ). Reduce the cross-sectional area (A). This reduces the mass but also reduces the second moment of area (I) and, correspondingly, the stiffness. Increase the second moment of area (I). This increases the natural frequency to the extent that the increase in the second moment of area exceeds the increase in area. Increase the cross-sectional area and thus the mass, reducing the natural frequency. Therefore, the ratio of I to A is an important factor here

Chemical formula

[0088] From Equation 2, the proportional relationships (the elements removed from the relationship are constant) that define the oscillator design trade space may be used. The proportional relationships are used because the relative performance between different oscillator types is of interest. Based on Equation 2, the natural frequency f of the beam n from the perspective of

Chemical formula

Chemical formula

[0089] The frequency gain between different oscillators is proportional to the square root of the ratio coefficient, the radius of rotation (square root of I / A), and the boundary constant, and inversely proportional to the square root of the cantilever length.

Chemical formula

[0090] In fiber scanner applications, it is desirable to maximize both the natural frequency (f n ) and the lateral deflection (δ) simultaneously. The maximum achievable deflection is identified by Equation 11, and generally, an increase in the natural frequency corresponds to a reduction in the lateral deflection. Therefore, a change in length is not always useful in increasing the overall system performance without accompanying other changes.

[0091] Regarding the quasi-static analysis, recall that the deflection of a beam held in a cantilever shape with a distributed load (w) per unit length is as follows.

Chemical formula

Chemical formula

Chemical formula

Chemical formula

Chem.

Chem.

[0092] The radius of rotation of a hollow fiber with an outer diameter (D) and an inner diameter (d) is as follows.

Chem.

[0093] The radius of rotation of a solid fiber is as follows.

Chem.

Chem.

Chem.

[0094] To illustrate the gain achieved by the microstructured fiber, some examples of microstructured segments (limits) based on several common fiber sizes and thin-walled tubes are considered. A simplified model of a solid fiber with a diameter of 125 μm and a microstructured fiber with a diameter of 125 μm with a wall thickness of 10 μm (inner diameter 105 μm) is considered. The second moment of area of the solid fiber is as follows.

Chem.

Chem.

Chem.

Chem.

Chem.

[0095] Using the relative deflection gain from Equation 14 and substituting the result from Equation 23 to obtain the best-case gain for a 125 μm outer diameter fiber (hollow) with a 10 μm wall thickness, the deflection gain of the microstructured fiber compared to the solid fiber is as follows.

Chem.

[0096] Here, all the parameters for the two designs are determined for verification. Solving Equation 2 for the cantilever length gives

Chem.

Chem.

Chem.

Chem.

[0097] Finally, to check the results, the expected deflection is compared for a constant load using the quasi-static analysis as the merit function from Equation 24.

Chem.

Chem.

[0098] Note that the approximately 1.5-fold gain described here is based on an ideal 10-μm wall thickness for a fiber with an outer diameter of 125 μm. In practice, the results for actual fibers with the same dimensions are slightly less.

[0099] Equation 2 can be solved with respect to length as follows. [Chemistry] From this, [Chemistry] From Equation 31, it is clear that the length is maximized when the ratio of the second moment of area to the cross-sectional area is maximized.

[0100] As another example, a solid optical fiber with an outer diameter of 80 μm and a natural frequency of about 60 kHz is considered and compared to a microstructure optical fiber having an overall air filling ratio of about 43.7% (modeled as above using an 80 μm fiber with a 10 μm wall thickness) and a natural frequency of about 60 kHz to determine the increase in the angle of incidence.

[0101] The second moment of area of the microstructure fiber is as follows. [Chemistry] The cross-sectional area of the microstructure fiber is as follows. [Chemistry] The length of the microstructure fiber is as follows. [Chemistry] The second moment of area of the solid fiber is as follows. [Chemistry] The cross-sectional area of the solid fiber is as follows.

Chem.

Chem.

Chem.

Example

[0102] (Exemplary optical fiber for a scanning fiber display) This example describes a microstructured optical fiber embodiment that includes a plurality of mass reduction regions and the use of an optical fiber within a scanning fiber display. The microstructured optical fiber is fabricated by stacking several optical quartz tubes to form an overall preform structure. A single solid tube of optical material is positioned at the center of the preform and used to correspond to the core of the waveguide region of the finally formed optical fiber. A series of solid quartz tubes are positioned around the solid tube within the preform and used to correspond to the cladding layer of the waveguide region of the finally formed optical fiber. Hollow quartz tubes are positioned around the series of solid quartz tubes within the preform and used to correspond to the mass adjustment regions of the mechanical region of the finally formed optical fiber. Finally, a ring-shaped solid quartz tube is positioned outside the hollow quartz tube and used to correspond to the outer solid edge or periphery of the mechanical region of the finally formed optical fiber. The assembled preform is heated to fuse the components together and then drawn into an optical fiber according to known optical fiber drawing techniques.

[0103] The resulting optical fiber corresponds to a microstructure optical fiber. The resulting optical fiber has a core region such as one having a core with a diameter of about 5 μm, a cladding region such as one having an outer diameter of about 25 μm, and a mechanical region having a diameter of about 80 μm. The microstructure optical fiber exhibits, for example, an overall air filling ratio of about 44%. The microstructure optical fiber exhibits a reduction in the corresponding mass within the mechanical region as compared to an equivalent non-microstructure optical fiber.

[0104] The scanning fiber display is created by positioning the microstructure optical fiber in a configuration held in a cantilever shape with respect to a mechanical actuator such that the length of the microstructure optical fiber is free (i.e., not supported). The length of the unsupported portion of the microstructure optical fiber is about 1.159 mm. The microstructure optical fiber held in a cantilever shape with a length of 1.159 mm exhibits a resonance frequency of about 60 kHz. The maximum angular deflection of the microstructure optical fiber when oscillating at the resonance frequency is about 12.5 degrees.

[0105] For comparison, an equivalent non-microstructure (i.e., solid) optical fiber in a cantilever-held configuration having a resonance frequency of about 60 kHz (i.e., the same resonance frequency as the microstructure optical fiber described above) has a length of about 1.037 mm and a maximum angular deflection of about 10 degrees.

Claims

Claim 1 A scanning fiber display, comprising: An optical fiber, wherein the optical fiber comprises: A waveguide element extending along an axis; A mechanical region surrounding the waveguide element, the mechanical region being positioned between the waveguide element and an outer periphery, the mechanical region including a first material having a first density; A plurality of hollow or gas-filled regions positioned within the mechanical region, the plurality of hollow or gas-filled regions comprising a plurality of rows of hollow or gas-filled elements, the plurality of hollow or gas-filled regions being arranged within the mechanical region such that the optical fiber exhibits radially symmetric rigidity; An optical fiber including; An actuator in mechanical contact with the optical fiber, the actuator being for inducing oscillation of the optical fiber; A scanning fiber display comprising.

Images