Microstructured fiber optic oscillators and waveguides for fiber scanners.

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 of and priority to U.S. Provisional Application No. 62 / 438,898, filed December 23, 2016, and U.S. Provisional Application No. 62 / 464,298, filed February 27, 2017, the entireties of which are incorporated herein by reference. [Background technology]

[0002] Optical fibers are employed in a variety of applications, including communications, 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, with additional buffer and outer skin layers optionally included to provide protection during handling or exposure to environmental conditions. Additional optical fiber designs and optimizations are needed to improve and expand the variety of applications in which optical fibers are or can be employed. Summary of the Invention [Means for solving the problem]

[0003] This application relates to optical waveguides. More particularly, but not by way of limitation, this application relates to optical fibers and fiber optic oscillators such as those used in scanning fiber displays, where the optical fiber includes a waveguiding element and a mechanical region with one or more mass-reducing elements positioned between the waveguiding element and the outer periphery of the optical fiber. The inclusion of the mass-reducing elements advantageously provides scanning fiber displays incorporating optical fibers with an improved field of view, such as when compared to the use of conventional fiber optic oscillators.

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

[0005] However, range may be important to the field of view for a given projector design. For example, the maximum amplitude or range of an emitting fiber may provide a limit to the width of the output image that can be produced by the fiber. Increasing the emitting range may provide a wider field of view.

[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 field is required to obtain high-frequency scanning devices with high scanning ranges. The presently described optical fibers enable improved field of view projectors while maintaining a small form factor. As an example, by incorporating the disclosed optical fiber 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 microstructured optical fiber. Exemplary optical fibers include those comprising a waveguide element extending along an axis, a mechanical region surrounding the waveguide element, such as a mechanical region positioned between the waveguide element and the periphery, and including a first material having a first density, and multiple mass tuning regions positioned within the mechanical region, such as multiple mass tuning regions including a second material having a second density less than the first density. Such mass tuning regions may optionally include air or correspond to regions where material is removed or otherwise absent from the mechanical region. 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 an optical fiber comprising a waveguide element extending along an axis, a mechanical region surrounding the waveguide element, such as a mechanical region positioned between the waveguide element and an outer periphery and including a first material, and a plurality of second moment of area tuning regions positioned within the mechanical region, such as a plurality of second moment of area tuning regions, that serve to modify the overall second moment of area of ​​the mechanical region compared to an identical optical fiber except that the corresponding mechanical region of the same optical fiber does not include a second moment of area tuning region positioned between the corresponding waveguide element and the corresponding outer periphery of the same optical fiber. As an example, the second moment of area tuning regions may exhibit a mass per unit cross-sectional area that is different from that of the first material, resulting in a modification of the overall second moment of area of ​​the mechanical region. As a further example, the second moment of area tuning regions may exhibit a density that is different from that of the first material, resulting in a modification of the overall second moment of area of ​​the mechanical region. The term "moment of inertia" 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 may be used synonymously with moment of inertia, including area moment of inertia, second area moment, and planar area moment of inertia.

[0009] Various 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 unitary 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 multiple core regions and a cladding layer surrounding the multiple core regions. Optionally, each of the multiple core regions may be the same or different materials. Other waveguide elements are also contemplated, including those comprising hollow (i.e., vacuum) or gas- or air-filled regions, such as gas-filled core regions. It should be understood that hollow or gas- or air-filled cores may be useful in high-power applications because gas or air may absorb less energy than glass or another solid material. Optionally, vacuum regions (i.e., vacuum-filled regions) may also be utilized. It should also be understood that the core and cladding regions may 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 region may include, but is 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 multiple mass adjustment regions comprise multiple rows of mass adjustment elements. For example, the multiple rows may be arranged concentrically around a central waveguide element. Optionally, the multiple mass adjustment regions are arranged in a symmetrical configuration around an axis. Optionally, each of the multiple 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 about 1 μm to about 25 μm. Optionally, the plurality of mass tuning regions traverse the length of the optical fiber, such that each mass tuning 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 those in which individual cells or regions of mass-reducing material are contained within a section of the optical fiber. The mass tuning regions may optionally extend the entire length of the optical fiber or only a portion of the fiber. Alternatively, the mass tuning regions are randomly or evenly distributed throughout the mechanical region, or extend perpendicular to or at an angle to the optical or waveguide axis. Optionally, the pitch between the plurality of mass-reducing regions is between about 1 μm and about 25 μm. Optionally, the plurality of mass tuning regions occupy between about 30% and about 90% of the volume of the mechanical region. Such a percentage or percentage volume may be referred to herein as a mass-reducing fraction or a mass-reducing fill fraction. In the case of a mass-reducing region containing air or gas, such a percentage or percentage volume may be referred to as an air-filled fraction or a gas-filled fraction.

[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 sections that are microstructured and sections that are not microstructured. The sectioned optical fiber may be fabricated as a single fiber with varying cross-sectional configurations. The sectioned optical fiber may also be constructed by splicing optical fibers of different cross-sectional configurations.

[0013] It should be appreciated that the inclusion of mass-reduced regions may allow for 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-tuning fill fraction of the mechanical region is proportional to the pointing angle of the optical fiber. Optionally, the mass-tuning fill fraction is expressed by the ratio of the diameter of the mass-tuning regions to the pitch between the mass-tuning regions.

[0014] It should be understood that the multiple mass adjustment regions can reduce the mass of the optical fiber per unit length compared to an equivalent optical fiber, which comprises a corresponding waveguide element and a corresponding mechanical region that is the same as the waveguide element and the corresponding mechanical region that 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 circumference 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, the equivalent optical fiber having an effective cantilever length and comprising corresponding waveguide elements and corresponding mechanical regions, the corresponding waveguide elements being the same as the waveguide elements and the corresponding mechanical regions being the same as the mechanical regions except that the corresponding mechanical regions do not include mass adjustment regions positioned between the corresponding waveguide elements and the corresponding outer circumference of the equivalent optical fiber. Optionally, the plurality of mass adjustment regions increase the effective cantilever length of the optical fiber for a given operating or resonant frequency compared to an equivalent optical fiber, the equivalent optical fiber having corresponding waveguide elements and corresponding mechanical regions, the corresponding waveguide elements being the same as the waveguide elements and the corresponding mechanical regions being the same as the mechanical regions except that the corresponding mechanical regions do not include mass adjustment regions positioned between the corresponding waveguide elements and the corresponding outer circumference of the equivalent optical fiber.

[0016] An optical fiber, such as one having an effective cantilever length, may have a resonant frequency. Optionally, a plurality of mass tuning regions increase the effective cantilever length of the optical fiber compared to an equivalent optical fiber, the equivalent optical fiber having a resonant frequency and comprising a corresponding waveguide element and a corresponding mechanical region that is identical to the waveguide element and that is identical to the mechanical region except that the corresponding mechanical region does not include a mass tuning region located between the corresponding waveguide element and a corresponding circumference 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 of the optical fibers described above and an actuator in mechanical contact with the optical fiber for inducing 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, a mechanical region surrounding the waveguide element, such as a mechanical region positioned between the waveguide element and an outer periphery, the mechanical region including a first material having a first density, and a plurality of mass tuning regions positioned within the mechanical region, such as a plurality of mass tuning regions including a second material having a second density less than the second density.

[0018] Various actuators and actuator configurations are useful with the scanning fiber displays described herein. For example, the actuator optionally comprises a piezoelectric transducer, an electromagnetic voice coil, or a thermal actuator. Optionally, the actuator comprises 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 can be configured to operate at or about the natural or resonant frequency of the optical fiber.

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

[0020] The foregoing, together with other features and embodiments, will become more apparent upon reference to the following description, claims, and accompanying drawings. It will be understood that the optical fiber and scanning fiber display of the above aspects may optionally include features and aspects described in the following description. The present invention provides, for example, the following. (Item 1) An optical fiber, 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 comprising a first material having a first density; 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; An optical fiber comprising: (Item 2) Item 1. The optical fiber of item 1, wherein the waveguide element comprises a central core region and a cladding layer surrounding the central core region. (Item 3) Item 3. The optical fiber of item 2, wherein the cladding layer comprises the first material and the central core region comprises a third material. (Item 4) Item 3. The optical fiber of item 2, wherein the cladding layer and the mechanical region comprise a single body. (Item 5) Item 1. The optical fiber according to item 1, wherein the waveguide element comprises a plurality of core regions and a cladding layer surrounding the plurality of core regions. (Item 6) Item 1, wherein the plurality of mass-adjusting regions comprise 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) Item 1. The optical fiber of item 1, wherein the plurality of mass tuning regions comprises a plurality of rows of mass tuning elements, the plurality of rows being arranged concentrically around the waveguide element. (Item 8) Item 2. The optical fiber of item 1, wherein the plurality of mass tuning regions are arranged in a symmetrical configuration around the axis. (Item 9) Item 2. The optical fiber described in item 1, wherein the plurality of mass adjustment regions are arranged with an axis parallel to the axis. (Item 10) 2. The optical fiber according to item 1, wherein the plurality of mass adjusting regions occupy about 30% to about 90% of the volume of the mechanical region. (Item 11) Item 1, the optical fiber of item 1, wherein the plurality of mass adjustment regions reduce the mass of the optical fiber per unit length compared to 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 located between the corresponding waveguide element and a corresponding circumference of the equivalent optical fiber. (Item 12) Item 1, the optical fiber having an effective cantilever length, the plurality of mass adjustment regions increasing a resonant oscillation frequency of the optical fiber compared to 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 a corresponding circumference of the equivalent optical fiber. (Item 13) Item 1, the optical fiber of item 1, wherein the plurality of mass adjustment regions increase the effective cantilever length of the optical fiber for a given operating frequency compared to 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 located between the corresponding waveguide element and a corresponding circumference of the equivalent optical fiber. (Item 14) Item 1, wherein the optical fiber has a resonant frequency, and the plurality of mass tuning regions increase an effective cantilever length of the optical fiber compared to an equivalent optical fiber, the equivalent optical fiber having the resonant frequency 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 tuning region positioned between the corresponding waveguide element and a corresponding circumference of the equivalent optical fiber. (Item 15) 1. A scanning fiber display, comprising: An optical fiber, the 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 comprising a first material having a first density; 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; an optical fiber including: an actuator in mechanical contact with the optical fiber, the actuator for inducing oscillation of the optical fiber; and 1. A scanning fiber display comprising: (Item 16) Item 16. The scanning fiber display of item 15, wherein the actuator comprises a piezoelectric transducer, an electromagnetic voice coil, or a thermal actuator. (Item 17) Item 16. The scanning fiber display of item 15, wherein the actuator comprises a two-dimensional actuator for controlling movement of the end of the optical fiber in two dimensions. (Item 18) Item 16. The scanning fiber display of item 15, further comprising a visible light source in optical communication with the optical fiber waveguiding element. (Item 19) Item 16. The scanning fiber display of item 15, further comprising a multi-color switchable light source in optical communication with the optical fiber waveguiding element. (Item 20) An optical fiber, 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 comprising a first material; and a plurality of area second moment of area tuning regions positioned within the mechanical region, the plurality of area second moment of area tuning regions including a second material for producing a different area second moment of area of ​​the mechanical region than 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 area second moment of area tuning regions positioned between the corresponding waveguiding element and a corresponding circumference of the equivalent optical fiber; An optical fiber comprising: [Brief explanation of the drawings]

[0021] [Figure 1] 1A and 1B provide schematic diagrams of an exemplary fiber optic system, according to some embodiments.

[0022] [Figure 2] Figure 2A provides a schematic representation of the cross section of an exemplary conventional optical fiber, and Figure 2B provides a schematic representation of the cross section of an exemplary microstructured optical fiber.

[0023] [Figure 3] 3A, 3B, 3C, and 3D provide schematic illustrations of different cross sections of a microstructured optical fiber.

[0024] [Figure 4]4A and 4B provide schematic diagrams of an exemplary optical fiber system showing a comparison between the use of conventional optical fibers and microstructured optical fibers.

[0025] [Figure 5] Figure 5A provides a schematic illustration of a spiral output pattern achieved by a scanning fiber display using conventional optical fibers, and Figure 5B provides a schematic illustration of a spiral output pattern achieved by a scanning fiber display using microstructured optical fibers.

[0026] [Figure 6] FIG. 6 provides a plot showing the pointing angle gain of an optical fiber as a function of the ratio of diameter to pitch of the reduced mass regions and as a function of the diameter of the reduced mass regions. DETAILED DESCRIPTION OF THE INVENTION

[0027] Described herein are embodiments of optical fibers, fiber optic oscillators, and scanning fiber displays. The disclosed optical fibers advantageously provide improved oscillation amplitude or beam angle for a fixed oscillation or resonant frequency, such as when compared to fiber optic oscillators that have the same fixed oscillation or resonant frequency but utilize conventional optical fibers.

[0028] The disclosed optical fibers possess different mechanical properties than conventional fibers due to their structure and material properties. For example, conventional optical fibers may include a core region and a cladding region to define a waveguiding element. These regions may be solid bodies of optical material possessing different refractive indices to achieve total internal reflection and waveguiding of a light beam down the axis of the optical fiber.

[0029] The optical fibers disclosed herein, also referred to as microstructured optical fibers, may optionally utilize similar waveguiding elements, e.g., of materials having different refractive indices, but they may also include mechanical regions surrounding the waveguiding elements, such as mechanical regions that are not primarily used to guide the light beam, but instead are used to tune, select, or otherwise modify the mechanical properties of the optical fiber, such as to achieve desired mechanical properties. As an example, one or more second moment of area tuning regions may be included within a mechanical region, which may serve to modify the second moment of area of ​​the optical fiber compared to an otherwise identical optical fiber that does not include one or more second moment of area tuning regions. In a specific example, the second moment of area may be tuned by modifying the mass of the mechanical region. For example, one or more mass tuning regions may be included within a mechanical region, which may serve to reduce the mass or mass per unit length of the optical fiber compared to an otherwise identical optical fiber that does not include one or more mass-reducing regions. Exemplary mass tuning regions include air-filled regions (or other gas-filled regions), or regions comprising other materials having a density less than that of the materials used for the waveguiding elements or mechanical regions. For example, plastics, polymers, or glasses having densities less than the materials used in the waveguide elements or mechanical regions may be employed. This reduction in mass may allow, for example, optical fibers with desired mechanical properties to be created and used. In addition, the reduction in mass may correspond to a modification of the moment of area of ​​the mechanical region.

[0030] It should be understood that the term "same optical fiber" may refer to two optical fibers having the same geometry, material, and / or structure, and that reference to an exception between the same optical fibers may indicate that the exception is a characteristic of one fiber that differs from the other fiber, such as one optical fiber that is microstructured and one optical fiber that is not microstructured. For example, an optical fiber may include a core, such as a core having a first cross-sectional dimension (such as a diameter) and made from a first optical material, and a cladding surrounding the core, such as a cladding having a second cross-sectional dimension (such as an outer diameter) and made from a second optical material. Optical fibers that are the same except for including one or more mass-tuning regions, such as air- or gas-filled regions, may refer to a microstructured optical fiber that includes a core, such as a core having a first cross-sectional dimension and made from a first optical material, a cladding surrounding the core, such as a cladding having a second cross-sectional dimension and made from a second optical material, and one or more mass-tuning regions located within the cladding. It should be understood that the same optical fiber may have other characteristic differences besides the mass-reduced region that arise due to the presence of the mass-reduced region, such as different mass per unit length, or different resonant frequencies for a fixed oscillating fiber length, or different oscillating fiber lengths for a fixed resonant frequency.

[0031] Furthermore, it should be understood that identical optical fibers may have slightly different properties depending on whether certain attributes are 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 resonant frequencies, such as if the microstructured optical fiber has a higher resonant frequency. As another example, two optical fibers that are identical except for the inclusion of a microstructured mechanical region and have the same resonant frequency will have different oscillation lengths, such as if the microstructured optical fiber has a longer oscillation length.

[0032] Advantageously, the disclosed optical fiber can provide an improved field of view of a scanning fiber display for a given scanning frequency. For example, a scanning fiber display using a microstructured optical fiber including a mechanical region that includes one or more mass-reduced regions can have an increased field of view compared to a scanning fiber display using an optical fiber with the same resonant frequency but without the one or more mass-reduced regions (i.e., a non-microstructured optical fiber). Because 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. It should be understood that in some scanning fiber display embodiments, the field of view can be increased by increasing the length of the oscillating fiber for a given operating frequency, as this will result in an increase in the maximum directivity angle of the oscillating fiber.

[0033] 1A provides a schematic diagram of an exemplary fiber optic system 100. The exemplary fiber optic system includes a light source 105, 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 multiple sub-light sources or polychromatic light sources, such as light sources that output electromagnetic radiation of different wavelengths. In an embodiment, the light source 105 may be switchable, such as to allow control over 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 waveguiding. Thus, the light source 105 may be positioned in optical communication with the waveguiding element of the optical fiber 115. It should be understood that the coupling optics required to efficiently couple light from the light source 105 may depend on the geometry, material, and / or numerical aperture of the light source 105 and the optical fiber 115.

[0035] As shown, the optical fiber 115 includes a core 120 and a cladding 125 and has an axis 130 that may correspond, for example, to an optical axis or a waveguide axis. Light from the light source 105 that is coupled into the core 120 and guided along the length of the optical fiber 115 may be output at the opposite end of the optical fiber 115. It should be understood that the spot shape and direction of the light output from the optical fiber 115 may depend on the geometry, material, and / or numerical aperture of the optical fiber 115. Typically, the output from the optical fiber exhibits a cone shape 135, the angle of which is again defined by the geometry, material, and / or numerical aperture of the optical fiber 115. In terms of field of view, the optical fiber 115 in the non-oscillating configuration exhibits no increase in field of view 140 beyond the angle of the cone 135. In terms of deflection angle, the optical fiber 115 in the non-oscillating configuration exhibits a deflection angle of zero.

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

[0037] FIG. 1B omits 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 correspond to a cantilevered oscillator with a fixed end and a free end. The actuator 160 may be or include, for example, a piezoelectric actuator, an electromagnetic voice coil, or a thermal actuator. The actuator 160 may enable control over the oscillatory motion of the optical fiber 155 in two dimensions and may include two or more independently actuable axes. The extent 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 increased field of view beyond the output cone of the optical fiber 155. In terms of 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] 2A provides a schematic cross-sectional view of optical fiber 200. Optical fiber 200 may correspond to a conventional optical fiber and includes a core 205 and a cladding 210 surrounding core 205. Core 205 is illustrated as having a core diameter 215, and cladding 210 is illustrated as having an outer diameter 220. It should be understood that core diameter 215 and outer diameter 220 may be characteristic of a particular optical fiber embodiment and, therefore, may take any suitable values.

[0039] Unless otherwise indicated, it should be understood that dimensions of features illustrated in the accompanying drawings may not be to scale, but that certain aspects of the figures or different views are depicted to illustrate dimensional differences between different configurations or elements. It should also be understood that additional materials, such as buffers, skins, 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] 2B provides a schematic cross-sectional view of an embodiment of a 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, dashed lines are shown in FIG. 2B to better distinguish the transition between the waveguide element 235 and the mechanical region 240. In FIG. 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] 2B as including a solid region 270 and a mass-reduced region 275 positioned between the waveguide element 235 and the outer periphery of the mechanical region 240 and microstructured optical fiber 230. Exemplary mass-adjusted regions include, but are not limited to, a fluid-filled region, a gas- or air-filled region, a polymer-filled region, a glass-filled region, and / or a vacuum region (e.g., vacuum-filled), where the fluid, gas- or air-filled, polymer-filled, glass-filled, 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 comprises 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 comprise different materials and / or have different optical and / or mechanical properties. It should be understood that additional materials, such as cushioning, skins, or other coated or protective materials, may be constructed outside the perimeter of mechanical region 240, but are not shown here.

[0042] The mass-reduced regions 275 may be uniformly and / or regularly distributed throughout the mechanical region 240, and any suitable or desired geometry and distribution may be used to obtain particular mechanical properties of interest for the microstructured optical fiber 230. It should be understood that the mass-reduced regions 275 may be arranged along axes parallel to one another and / or along an axis parallel to the axis of the optical fiber, such as the waveguide axis or optical axis. Optionally, the mass-reduced regions 275 may be arranged along other directions, such as along a cross axis, perpendicular to the optical axis, or at an angle relative to the optical axis, provided that at least a portion of the mechanical region 240 comprises a mass-reduced region. The mass-reduced regions 275 may also be distributed randomly, uniformly, or non-uniformly (optionally not along any particular axis) throughout the mechanical region 240. As illustrated in FIG. 2B , the mass-reduced 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 reduced-mass regions 275. The reduced-mass regions 275 may exhibit symmetry, such as cylindrical symmetry, about an axis of the microstructured optical fiber 230, such as the waveguide axis or optical axis. The optical fiber 230 may optionally exhibit rotational symmetry.

[0043] Without limitation, the microstructured optical fiber 230 may be constructed by stacking several appropriately sized lengths of material to form an overall preform structure targeted to produce the microstructured optical fiber 230, such as by using solid and / or hollow tubes of suitable diameters, wall thicknesses, materials, shapes, etc. In some embodiments, glass materials are used. Exemplary glasses may include, but are not limited to, silica glass, fluoride glass, phosphate glass, and chalcogenide glass. In some embodiments, plastics or polymers such as polymethyl methacrylate, polystyrene, fluoropolymers, or polysiloxanes may be used. Depending on the processing method and materials, 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 a strand of optical fiber. Optionally, extrusion methods may be used, such as for fibers comprising polymer or plastic materials. It should be understood that a variety of techniques, materials, and methods can be used to manufacture optical fiber, and several commercial fiber manufacturers exist and may offer services for manufacturing optical fiber based on specified parameters.

[0044] For comparative illustrative purposes, 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 core 205 and the core 255 may optionally be made of the same material. The cladding 210 and the cladding 250 and the solid region 270 (non-mass-reduced 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 the mass-reduced region 275, while the optical fiber 200 includes a solid cladding 210 that does not include a mass-reduced region.

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

[0046] As another example, waveguide element 235 may have a diameter of about 5 μm to about 200 μm, such as, but not limited to, about 5 μm to about 125 μm. In some embodiments, cladding 250 may have a diameter or thickness of about 5 μm to about 200 μm, such as, but not limited to, about 5 μm to about 125 μm, and may optionally be considered to encompass or be integral with or monolithic with mechanical region 240, and thus may have a diameter or thickness corresponding to outer diameter 265. Outer diameter 265 may also have any suitable value, such as, but not limited to, about 10 μm to about 200 μm, and may match outer diameter 220 of 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 mass-reduced region 275 may have any suitable size or shape, for example, but not limited to, a cross-sectional dimension, 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 mass-reduced regions 275 may also have any suitable size and may be limited by the cross-sectional dimension of the mass-reduced regions 275. For example, the pitch 280 may be greater than the diameter of the mass-reduced region 275. The pitch 280 may have a length, 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 percentage of optical fiber 230 and / or mechanical region 240 may be any suitable value based on the size, number, spacing, and arrangement of the mass-reduced regions. In embodiments, the multiple mass-reduced regions occupy between about 1% and about 90% of the volume of optical fiber 230 or the volume of mechanical region 240. Optionally, the multiple mass-reduced regions occupy between about 30% and 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 optical fiber 230 or the volume of mechanical region 240.

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

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

[0050] While the waveguiding elements of the microstructured optical fiber described above correspond to conventional core / cladding designs, other waveguiding 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 scanning fiber displays (also referred to as fiber scanning displays). U.S. Patent Application No. 14 / 156,366 describes hexagonally filled multicore fibers, such as those containing 7 or 19 cores in a hexagonally arranged configuration, as well as arrays of oscillating fibers for fiber scanning displays. It should be understood that in embodiments, a change in refractive index between the core and cladding or between materials, such as glass and air, may provide a waveguiding effect, such as through the process of total internal reflection. Thus, a transition between materials may be all that is needed to achieve waveguiding, and thus the bulky cladding of a conventional optical fiber may be modified to include a mass-reduced region while still retaining a solid central portion surrounding a core of higher refractive index material that provides waveguiding. Various fiber configurations are possible, including single-mode and multimode configurations. For the purpose of producing optical displays, it is beneficial for optical fibers to have high transparency / low loss in the visible electromagnetic range.

[0051] For comparison purposes, FIGS. 4A and 4B provide schematic diagrams of optical fiber systems 400 and 450. Optical fiber systems 400 and 450 may be used, for example, in a scanning fiber display system. FIGS. 4A and 4B omit depictions of any light sources or coupling elements from optical fiber systems 400 and 450 so as not to obscure other details. In FIG. 4A, optical fiber system 400 includes optical fiber 405 and actuator 410. A cross section 415 of optical fiber 405 is also shown in FIG. 4A, illustrating that optical fiber 405 is a conventional optical fiber including a core and a cladding layer. Actuator 410 may be used to impart an oscillatory motion into optical fiber 405. The extent of the oscillatory motion of optical fiber 405 is depicted by a dashed line in FIG. 4A. From a field of view perspective, optical fiber system 400 exhibits field of view 420. The cantilevered portion of optical fiber 405 has a length 425.

[0052] In FIG. 4B , optical fiber system 450 includes a microstructured optical fiber 455 and an actuator 460. A cross section 465 of the microstructured optical fiber 455 is also shown in FIG. 4A , illustrating that the microstructured optical fiber 465 includes a waveguiding element and a microstructured mechanical region surrounding the waveguiding element, the microstructured optical fiber including multiple mass-reduced regions. The actuator 460 may be used to impart an oscillatory motion into the microstructured optical fiber 455. The actuator 460 may oscillate at or near a resonant frequency of the microstructured optical fiber 455, such as within 5% of the natural frequency of the microstructured optical fiber 455 or within 1% of the resonant frequency of the microstructured optical fiber 455. In an embodiment, the resonant frequency may correspond to a natural frequency or a natural frequency. In an embodiment, the actuator 460 operates at a frequency that provides a gain in the pointing angle or deflection of the microstructured optical fiber 455. The extent of the oscillatory motion of the microstructured optical fiber 455 is depicted by a dashed line in FIG. 4B . From a field of view perspective, the microstructured optical fiber system 450 exhibits a field of view 470. The cantilevered portion of the microstructured optical fiber 455 has a length 475.

[0053] It should be understood that the resonant frequency of a cantilevered optical fiber may generally be proportional to the square of the cantilever length. 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 microstructured optical fiber 455 is halved, a four-fold decrease in the resonant frequency of the microstructured optical fiber 475 would be expected.

[0054] It should also be understood that the distribution of mass of the cantilevered optical fiber can affect the resonant frequency. For example, assuming that optical fiber 405 and microstructured optical fiber 455 are the same (diameter, material, etc.) except for the mass-reduced region of microstructured optical fiber 455, the inclusion of the mass-reduced region can reduce the mass per unit length of microstructured optical fiber 455 compared to optical fiber 405. Thus, for the resonant frequencies of optical fiber 405 and microstructured optical fiber 455 to be identical, optical fiber 405 and microstructured optical fiber 455 will exhibit different lengths, with length 425 being less than length 475. Advantageously, this length difference will allow field of view 470 and / or beam angle of microstructured optical fiber 455 to exceed field of view 420 and / or beam angle of optical fiber 405.

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

[0056] In some embodiments, a scanning fiber display utilizes the oscillating motion of a cantilevered optical fiber to project an image using the optical fiber. For example, the oscillating motion of the cantilevered optical fiber may be controlled in two dimensions to generate a spiral pattern, such as by appropriately driving an actuator. In some embodiments, input light may be controlled and timed so that the output of the oscillating optical fiber generates the desired image in the spiral pattern, and the repetitive oscillating motion and timed optical output are used to generate a series of images. U.S. Patent Application No. 14 / 156,366 describes how a cantilevered fiber can be used to generate a projected image or series of images. However, the embodiments described herein advantageously allow the field of view, beam angle, and projected output image size and / or resolution of a scanning fiber display to be increased by using microstructured optical fiber.

[0057] For example, Figure 5A depicts a spiral pattern 500 for a conventional scanning fiber display incorporating conventional optical fiber with a core and cladding, but without mass-reduced regions within the cladding material, similar to the optical fiber system 400 of Figure 4A. The diameter 505 of the spiral pattern is limited by the maximum beam angle of the scanning fiber display being used.

[0058] In contrast, Figure 5B depicts an equivalent spiral pattern 550 for a scanning fiber display incorporating an equivalent microstructured optical fiber including a waveguiding element and a microstructured mechanical region surrounding the waveguiding element, the microstructured mechanical region including multiple mass-reduced regions, similar to the optical fiber system 450 of Figure 4B. The spiral pattern 550 exhibits a diameter 555 limited by the maximum beam angle of the scanning fiber display being used.

[0059] For the same conventional optical fiber and microstructured optical fiber (i.e., identical except for the inclusion of a mass-reduced region in the microstructured optical fiber) operating at the same resonant frequency (implying an increase in cantilever length), diameter 555 of spiral pattern 550 will be larger than diameter 505 of spiral pattern 500, corresponding to the increase in field of view and / or maximum beam angle achieved through the use of the microstructured optical fiber. Without limitation, the use of a microstructured optical fiber may advantageously increase the field of view and / or beam angle by up to about 30%. In some cases, increases in field of view and / or beam angle of up to about 50% or up to about 70% may be achieved. In some embodiments, increases in field of view and / or beam angle of about 30% to about 40% may 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: an optical transmission range of about 435 nm to about 645 nm; a red, green, and / or blue output mode field diameter of about 1.4 μm with a tolerance of about ±0.15 μm; a red, green, and / or blue numerical aperture of about 0.25; an optical transmission loss of about 30 dB / km or less for any or all wavelengths from about 435 to 645 nm; and low splicing loss to single mode (φ1.2 μm, NA).

[0061] In some embodiments, the microstructured optical fiber may have one or more of the following mechanical specifications: an outer diameter of about 80 μm to about 125 μm or about 40 μm to about 200 μm; a mechanical region diameter of about 40 μm to about outer diameter; a mass reduction percentage (e.g., gas or air-filled percentage) within the mechanical region of about 70% or greater; a concentric 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 (z is the fiber longitudinal axis); and a weight change due to water collection within the air-filled region of about 1% or less.

[0062] It should be understood that rotational symmetry can be useful for the optical fibers disclosed herein and can be advantageous for some embodiments, and thus the microstructured optical fiber can optionally possess rotational symmetry. Rotational symmetry allows for the stiffness (K) of the optical fiber to be the same in all radial directions (θ). r ) (see Figure 2A for directional reference). In other words, for a force acting along any radial direction defined by θ, the optical fiber will undergo a purely radial translation. In the static case, Hooke's law states that 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 directions of the optical fiber are not unique.

[0063] The terms and expressions which have been employed are used as terms of description rather than of limitation, and the use of such terms and expressions is not intended to exclude any equivalents of the features or portions thereof shown and described, but it is recognized that various modifications are possible within the scope of the invention as claimed. Thus, while the present invention has been specifically disclosed by preferred embodiments and optional features, it will be understood that modifications and variations of the concepts disclosed herein may be employed by those skilled in the art, and that 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 exemplary embodiments of the present 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 form described, and many modifications and variations are possible in light of the above teachings. The embodiments have been chosen and described 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 may be suitable for the particular use contemplated.

[0065] When groups of substitutions are disclosed herein, it is understood that all individual members of the groups and all subgroups and classes that can be formed using the substitutions are separately disclosed. When Markush groups or other groupings are used herein, all individual members of the groups and all possible combinations and subcombinations of the groups are intended to be included individually within the disclosure. As used herein, "and / or" means that one, all, or any combination of the items in the 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 present invention unless otherwise stated. Specific names of materials are intended to be exemplary, as it is known that those skilled in the art may name the same materials 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 present invention without undue experimentation. All art-known functional equivalents of any such methods, device elements, starting materials, and synthetic methods are intended to be encompassed within the present invention. Whenever a range, e.g., a temperature range, a time range, or a composition range, is recited herein, all intermediate ranges and subranges, and all individual values ​​encompassed within the recited range, are intended to be encompassed within the present disclosure. Specific details of particular embodiments may 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 may be directed to specific embodiments relating to each individual aspect or specific combinations of these individual aspects.

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

[0068] (Explanation of the mechanical merit function: a cantilevered optical fiber oscillator) This example describes how to maximize the beam angle at the end of an optical fiber, thus increasing the field of view, while keeping the natural frequency of the oscillator constant. In some embodiments, this can be accomplished by minimizing the mass of the cantilevered oscillator while maximizing the second moment of area. This example derives how, for a given size fiber, the optical performance (maximum deflection for a given operating frequency) can be achieved relative to a thin-walled tube fiber. Advantageously, microstructured optical fibers incorporating this technology can exhibit a merit function increase (i.e., increased beam angle) of approximately 30% or better compared to the same conventional fiber.

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

[0070] For solid rods, I T =d 4 / 64. As a constraint, the natural frequency f nis fixed to be the same for direct comparison of the solid and microstructured designs. For the cantilevered beam, the natural frequency is obtained from Euler's equation: [ka]

[0071] For high refresh rates of the display, it is useful to have a high operating frequency of the scanning fiber. At the same time, it is desirable to achieve a large deflection of the oscillator, as this is proportional to the field of view and resolution.

[0072] Because 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 chosen such that the system natural frequency, as estimated by the equation above, remains high.

[0073] From the perspective of a microstructured fiber, the above equations provide direct insight into the influence of the second moment of area I and the solid cross-sectional area A of the solid fiber minus the area of ​​the holes on the natural frequency and associated length of the oscillator.

[0074] By examination of this equation, increasing the ratio of I to A increases the natural frequency. This property can be exploited in microstructured fibers by removing mass near the neutral axis (small effect on I) by inserting holes near the neutral axis, since this has a small effect on I due to keeping the mass near the outer diameter or periphery, which is a function of the square of the distance from the neutral axis. This is further derived from the following equation, which shows that the contribution of a 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 microstructured fiber is: [ka] Thus, a section can be removed (i.e., a hole or reduced mass region is inserted) farthest from the neutral axis to increase the natural frequency or increase the oscillator length L for a given natural frequency. Inserting a hole allows the oscillator natural frequency to be increased or the oscillator length (L) to be increased for a given natural frequency. Note that while all holes have the same effect on the area (A) regardless of their location, holes closest to the neutral axis increase the natural frequency more than holes farther away from the neutral axis.

[0076] The merit function analysis below explains how a microstructured fiber compares to a solid fiber in terms of deflection angle. In this analysis, frequency is held constant and the second moment of area and area of ​​the beam section are varied. The merit function quantifies the gain in deflection angle. Using the above equation for the natural frequency, [ka] Finding a value for L that constrains the frequency to be a constant yields: [ka] Frequency (f n ), density (ρ), mode constant (βL(n i )) (comparing first mode to first mode, second mode to second mode, etc.), and fixing the coefficient (E) constant, the above equation becomes: [ka]

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

[0078] Calculate the inclination of a beam with a concentrated load at the end: [ka] where α is the deflection angle, E is the Young's modulus, I is the moment of inertia, L is the cantilever length, and F is the force. Calculating the tilt of a beam with a distributed load is: [ka] where W is the load per unit length.

[0079] The equation for the angular deflection gain of a constant frequency oscillator is derived as follows: In terms of the concentrated force model, E MS =E T Assuming that, [ka] This represents a gain relationship that allows calculations using the area and second moment of area of ​​the segments.

[0080] Regarding the dispersion force model, [ka] [ka] This represents a gain relationship that allows calculations using the area and second moment of area of ​​the segments.

[0081] The dynamic mode shapes are approximated as distributed loads for relative stress calculations: [ka] Assuming z and ρ are constant, [ka] This indicates that for the same oscillation frequency, the reduced mass fiber has a longer cantilever length.

[0082] Figure 6 provides a merit function plot showing the beam angle gain of a microstructured optical fiber compared to a solid or conventional optical fiber, based on a fiber outer diameter of 125 μm according to the equation above. While this example describes mass reduction in terms of air-filled regions, it should be understood that other mass-reducing materials could be used under similar analysis. The plot provides a surface showing the maximum beam angle gain of an optical fiber as a function of the ratio of the diameter to the pitch of the air-filled regions and as a function of the diameter of the air-filled regions, illustrating the effect of the fiber. While the greatest possible gain is desirable, it should be understood that certain mechanical considerations must be taken into account. For example, the fiber must be able to oscillate without breakage. Therefore, the diameter of the microstructured area should be less than the outer diameter of the fiber in order for the fiber to have mechanical integrity. Additionally, the ratio of the diameter of the air-filled regions to the pitch of the air-filled regions should be less than 1; otherwise, the air-filled regions will overlap and occupy an unusable amount of fiber. As illustrated in FIG. 6, a microstructured (air-filled) region diameter 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 pointing angle. [Example]

[0083] (Microstructured Fiber Performance Analysis) The requirement to maximize the natural frequency of a mechanical system is simple: for a lumped parameter system, such as a mass connected to a single degree of freedom spring that contains no damping, the natural frequency f n (Hz) is the modal stiffness [ka] and is a function of the modal mass m (kg). The natural frequency is: [ka] In this case, for a given constraint on the problem, there are only two parameters: either stiffness can be increased or mass can be decreased to increase the natural frequency. For a real continuous system, such as the cantilevered beam of the fiber scanner illustrated in Figure 1B (with coefficient E, density ρ, cross-sectional area A, and second moment of area I), the relationship between mass distribution, material properties, boundary conditions (the method of support for the fiber), and beam dimensions, as well as the display's operating parameters (field of view, refresh rate, resolution), should also be considered. It is also possible to modify the beam's length as a geometric function. This is classically done for tapered beams, but is not considered here. Rather, microstructured or photonic bandgap fibers are considered for their potential benefits. A brief background on oscillators is first provided.

[0084] The natural frequency equation for the lateral motion of an Euler-Bernoulli beam is, [ka] During the ceremony, α: Directivity angle and end of the cantilevered fiber I,I T,MS : Moment of inertia of cross section T : Subscript for standard straight cylindrical fiber MS : Subscript for microstructured fiber A,A T,MS : cross-sectional area of ​​the cantilever (constant over the length, i.e., not a tapered fiber) A H_i : Area of ​​the pores in the microstructure (not constant for a given design) r i : Perpendicular distance from hole to neutral axis T : Subscript indicating solid conventional fiber MS : Subscript indicating microstructured fiber i: number of vibration modes (e.g., first, second, and third modes of vibration and natural frequency) β(i): modal constant of the i-th mode, depends on the boundary condition (cantilevered, free, simply supported) D: Oscillator (fiber) outer diameter d: inner diameter of the tube oscillator (fiber) δ: Side beam deflection L: cantilever length E: Young's modulus ρ: Density f n : natural frequency of the beam, only the first mode is considered [ka] [ka] ξ: damping ratio of the oscillator The turning radius is defined above as: [ka] By examining Equation 2, the influence of the independent variables on the beam natural frequency can be seen as follows: Increasing Young's modulus (E) increases the natural frequency Increasing the moment of inertia (I) increases the natural frequency Increasing density decreases the natural frequency Increasing the cross-sectional area (A) decreases the natural frequency Increasing the length (L) decreases the natural frequency The natural frequency varies linearly with the modal constant (β), which is a function of the boundary conditions. Any one or more of the following may be implemented to increase the natural frequency:

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

[0086] Modify material properties. Increase the Young's modulus (E), which is difficult due to the limited availability of optical waveguide materials. Decrease the density (ρ), which is also difficult due to the limited availability of optical waveguide materials, especially in the context of mass production. These objectives are: [ka] This is combined by introducing the concept of specific modulus or specific stiffness, defined as: Therefore, it may be desirable to maximize specific stiffness, but this is limited by commercially available materials. This balances the variability of material properties and allows for direct material comparison.

[0087] Modify the mass distribution. Shorten the cantilever length (L). This is possible, but such a change may reduce the lateral deflection (if the static deflection for an applied end load is L 3(proportional to ). Reduce the area of ​​the cross section (A). This reduces the mass, but also reduces the moment of inertia (I) and, correspondingly, the stiffness. Increase the moment of inertia (I). This increases the natural frequency to the extent that the increase in moment of inertia exceeds the increase in area. Increase the cross section, and therefore the mass, and decrease the natural frequency. Therefore, the ratio of I to A is the important factor here. [ka] Therefore, it is advantageous to normalize the second moment of area (I) to (A). Recall from Equation 3 that this is the definition of the radius of gyration. This is a useful approach when designing microstructure oscillators. See Equation 14. Therefore, it is useful to normalize the mass distribution effect on the natural frequency, as well as the material properties. Advantageously, this is done by the properties of the radius of gyration, which is used to describe the distribution of area about a central axis.

[0088] From Equation 2, a proportional relationship (where the factor removed from the relationship is constant) may be used to define the oscillator design trade space. The proportional relationship is used because the relative performance between different oscillator types is of interest. Based on Equation 2, natural frequency of the beam, f n From the perspective of [ka] For a fixed frequency, the cantilever length (L) is: [ka]

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

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

[0091] For quasi-static analysis, recall that the deflection of a cantilevered beam with a distributed load (w) per unit length is: [ka] However, the distributed load increases with the cantilever length (L 1 ), and therefore the deflection (δ) and cantilever length are related as follows: [ka] Therefore, the merit function is the radius of gyration (R g ), it can be written as follows: [ka] [ka] To compare two oscillators with the same natural frequency (subscripts 1 and 2), the deflection gain is: [ka] The beam angle gain is: [ka] These merit functions are applied to microstructured fibers to track the expected relative gain compared to a conventional non-tapered optical fiber oscillator.

[0092] The radius of gyration of a hollow fiber with outer diameter (D) and inner diameter (d) is: [ka] Thus, for microstructured fibers, the highest turning radius is achieved for thin-walled tubes.

[0093] The turning radius of a solid fiber is: [ka] Since the natural frequency of the oscillator is proportional to the turning radius, this parameter can be maximized for a given fiber diameter. The second moment of area is: [ka] The cross-sectional fiber area is: [ka]

[0094] To illustrate the gain achieved by microstructured fibers, examples of several common fiber sizes and microstructured sections (limits) based on thin-walled tubes are considered: a 125 μm diameter solid fiber and a simplified model of a 125 μm diameter microstructured fiber with a 10 μm wall thickness (105 μm inner diameter). The second moment of area of ​​a solid fiber is: [ka] The cross-sectional area of ​​the solid fiber is: [ka] The second moment of area of ​​the microstructured fiber is: [ka] The cross-sectional area of ​​the microstructured fiber is: [ka] The turning radius ratio is: [ka]

[0095] Using the relative deflection gain from Equation 14 and substituting the result from Equation 23 to get 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: [ka] This change therefore results in approximately a 50% increase in deflection for a given natural frequency and material.

[0096] Now, all the parameters for the two designs are determined for verification. Solving Equation 2 for the cantilever length gives: [ka] The cantilever length of the solid fiber is calculated as follows: [ka] The cantilever length of the microstructured fiber is calculated as follows: [ka] To verify the merit function, these results are compared using Equation 8. [ka]

[0097] Finally, to check the results, the expected deflections are compared for a constant load using quasi-static analysis as the merit function from Equation 24. [ka] Finally, applying Equation 14 directly based on the turning radius ratio from Equation 23 provides the deflection gain. [ka]

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

[0099] Equation 2 can be solved for length as follows: [ka] from now, [ka] From equation 31 it is clear that when the ratio of the moment of inertia to the area is maximized, the length 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 microstructured optical fiber having an overall air-filling fraction 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 beam angle.

[0101] The second moment of area of ​​the microstructured fiber is: [ka] The cross-sectional area of ​​the microstructured fiber is: [ka] The length of the microstructured fiber is: [ka] The second moment of area of ​​a solid fiber is: [ka] The cross-sectional area of ​​the solid fiber is: [ka] The length of the solid fiber is: [ka] The ratio of the lengths of the microstructured fiber to the solid fiber, LMS / LT, is 1.12. Using Equation 16, the relative increase in beam angle is: [ka] Thus, by microstructuring an 80 μm fiber, the beam angle can be increased by 25%. [Example]

[0102] Exemplary Optical Fibers for Scanning Fiber Displays This example describes a microstructured optical fiber embodiment including multiple mass-reduced regions and the use of the optical fiber in a scanning fiber display. The microstructured optical fiber is fabricated by stacking several optical quartz tubes to form the overall preform structure. A single solid tube of optical material is positioned in the center of the preform and is used to correspond to the core of the waveguiding region of the final formed optical fiber. A series of solid quartz tubes are positioned around the solid tubes in the preform and are used to correspond to the cladding layers of the waveguiding region of the final formed optical fiber. A hollow quartz tube is positioned around the series of solid quartz tubes in the preform and is used to correspond to the mass adjustment region of the mechanical region of the final formed optical fiber. Finally, a ring-shaped solid quartz tube is positioned outside the hollow quartz tubes and is used to correspond to the outer solid edge or perimeter of the mechanical region of the final 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 microstructured optical fiber. The resulting optical fiber has a core region, such as one having a core 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 microstructured optical fiber, for example, exhibits an overall air-filling fraction of about 44%. The microstructured optical fiber exhibits a corresponding mass reduction in the mechanical region compared to a comparable non-microstructured optical fiber.

[0104] A scanning fiber display is created by positioning a microstructured optical fiber in a cantilevered configuration relative to a mechanical actuator so that a length of the microstructured optical fiber is free (i.e., unsupported). The length of the unsupported portion of the microstructured optical fiber is approximately 1.159 mm. A 1.159 mm cantilevered microstructured optical fiber exhibits a resonant frequency of approximately 60 kHz. The maximum beam angle of the microstructured optical fiber when oscillating at the resonant frequency is approximately 12.5 degrees.

[0105] By comparison, an equivalent non-microstructured (i.e., solid) optical fiber in a cantilevered configuration, having a resonant frequency of about 60 kHz (i.e., the same resonant frequency as the microstructured optical fiber described above), is about 1.037 mm long and has a maximum beam angle of about 10 degrees.

Claims

1. 1. A scanning fiber display, comprising: An optical fiber, the 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 comprising 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 and arranged within the mechanical region such that the optical fiber exhibits radially symmetric stiffness; an optical fiber including: an actuator in mechanical contact with the optical fiber, the actuator for inducing oscillation of the optical fiber; and 1. A scanning fiber display comprising:

2. The scanning fiber display of claim 1 , wherein the actuator comprises a piezoelectric transducer, an electromagnetic voice coil, or a thermal actuator.

3. 10. The scanning fiber display of claim 1, wherein the actuator comprises a two-dimensional actuator for controlling movement of the end of the optical fiber in two dimensions.

4. The scanning fiber display of claim 1 further comprising a visible light source in optical communication with the waveguiding element of the optical fiber.

5. The scanning fiber display of claim 1 , further comprising a multi-color switchable light source in optical communication with the waveguiding element of the optical fiber.

6. A scanning fiber display comprising an optical fiber, The optical fiber is 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 comprising 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 and arranged within the mechanical region such that the optical fiber exhibits radially symmetric stiffness; An optical fiber comprising: an optical fiber for use in mechanical contact with an actuator to induce oscillation of the optical fiber; Scanning fiber display.

7. 7. The scanning fiber display of claim 6, wherein the waveguide element comprises a central core region and a cladding layer surrounding the central core region.

8. The scanning fiber display of claim 7 , wherein the cladding layer comprises the first material and the central core region comprises a third material.

9. The scanning fiber display of claim 7 , wherein the cladding layer and the mechanical region comprise a unitary body.

10. 7. The scanning fiber display of claim 6, wherein the waveguide element comprises a plurality of core regions and a cladding layer surrounding the plurality of core regions.

11. The scanning fiber display of claim 6 , wherein the plurality of hollow or gas-filled regions comprises one or more gas-filled regions, one or more air-filled regions, one or more vacuum regions, or any combination thereof.

12. The scanning fiber display of claim 6 , wherein the plurality of rows are arranged concentrically around the waveguide element.

13. The scanning fiber display of claim 6 , wherein the plurality of hollow or gas-filled regions are arranged in a symmetrical configuration around the axis.

14. 7. The scanning fiber display of claim 6, wherein the plurality of hollow or gas-filled regions are arranged with axes parallel to the axis.

15. 7. The scanning fiber display of claim 6, wherein the plurality of hollow or gas-filled regions occupy between about 30% and about 90% of the volume of the mechanical region.

16. A scanning fiber display comprising an optical fiber, The optical fiber is 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 comprising quartz; and 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, occupying about 30% to about 90% of the volume of the mechanical region, and arranged within the mechanical region such that the optical fiber exhibits radially symmetric stiffness; An optical fiber comprising: an optical fiber for use in mechanical contact with an actuator to induce oscillation of the optical fiber; Scanning fiber display.

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