Optical devices that emit optical radiation have a wide range of applicability, including in Light Detection And Ranging (LIDAR), communications, and biomedical devices. Light with a micron-scale wavelength allows for 0.001° angular resolution, when used for imaging, and antenna gain of more than 100 dB from a modest 10 cm×10 cm aperture, when used for communication. Such light has a frequency in the hundreds of terahertz range and wide operating bandwidths, allowing for high-speed data-transmission and three-dimensional imaging with sub-millimeter range resolution. In addition, optical beams at this wavelength have wide windows of low atmospheric absorption, allowing for long-range propagation over terahertz of optical bandwidth.
An example of an optical device includes: a first waveguide having a first propagation constant; a second waveguide parallel to the first waveguide and having a second propagation constant that is different from the first propagation constant; a first grating antenna having a first grating period; and a second grating antenna having a second grating period different from the first grating period. The first grating antenna is configured to emit first light from the first waveguide, and the second grating antenna is configured to emit second light from the second waveguide. The first grating period and the second grating period are configured to emit the first light and the second light at a same emission angle.
Implementations of such an optical device may include one or more of the following features. The first propagation constant of the first waveguide may be a first function of a position along a length of the first waveguide. The second propagation constant of the second waveguide is a second function of a position along a length of the second waveguide. A value of the first propagation constant at most points along the length of the first waveguide may be different from a value of the second propagation constant at a corresponding point along the length of the second waveguide. The first grating period may be configured to emit the first light a first emission angle that is a function of the position along the length of the first waveguide. The second grating period is configured to emit the second light at a second emission angle that is a function of the position along the length of the second waveguide. A value of the first emission angle at every point along the length of the first waveguide may be equal to a value of the second emission angle at a corresponding point along the length of the second waveguide.
Implementations of such an optical device may further include one or more of the following features. The optical device may include a plurality of waveguides including the first waveguide and the second waveguide and at least one additional waveguide. Each waveguide of the plurality of waveguides may have a propagation constant that is different from a respective propagation constant of an adjacent waveguide. the first propagation constant of the first waveguide is a first vector ({right arrow over (β)}1), the second propagation constant of the second waveguide is a vector ({right arrow over (β)}2), a first wavenumber vector of the first grating antenna ({right arrow over (K)}1), and a second wavenumber vector of the second grating antenna ({right arrow over (K)}2) satisfy the following equation: {right arrow over (β)}1+{right arrow over (K)}1={right arrow over (β)}2+{right arrow over (K)}2. The first grating antenna may be etched into a core of the first waveguide. The second grating antenna may be etched into a core of the second waveguide. The first grating antenna may be above or below a core of the first waveguide. The second grating antenna may be above or below a core of the second waveguide. The first grating antenna may be adjacent to a core of the first waveguide at a same depth as the core of the first waveguide. The second grating antenna may be adjacent to a core of the second waveguide at a same depth as the core of the second waveguide.
Implementations of such an optical device may further include one or more of the following features. A width of a waveguide core of the first waveguide may be different from a width of a waveguide core of the second waveguide. A height of a waveguide core of the first waveguide may be different from a height of a waveguide core of the second waveguide. A material that forms a waveguide core of the first waveguide may have a different index of refraction from a material that forms a waveguide core of the second waveguide. A waveguide core of the first waveguide may be a distance from a waveguide core of the second waveguide, the distance being less than a single wavelength of the first light which the first waveguide is configured to guide. The optical device may include an antenna layer that includes the first waveguide, the second waveguide, the first grating antenna, and the second grating antenna. The optical device may include a phase shifter layer that includes a third waveguide, a fourth waveguide, a first phase shifter configured to apply a phase shift to the third waveguide, and a second phase shifter configured to apply a phase shift to the fourth waveguide. The third waveguide may be optically coupled to the first waveguide and the fourth waveguide may be optically coupled to the second waveguide. The third waveguide may have a third propagation constant, and the fourth waveguide may have a fourth propagation constant that is different from the third propagation constant. The optical device may include a splitting distribution network coupled to the first waveguide and the second waveguide. The optical device may further include: a first plurality of waveguides including the first waveguide, each waveguide of the first plurality of waveguides having the first propagation constant; and a second plurality of waveguides including the second waveguide, each waveguide of the second plurality of waveguides having the second propagation constant. The first plurality of waveguides and the second plurality of waveguides may be arranged in an alternating pattern such that each of the first plurality of waveguides is adjacent to at least one of the second plurality of waveguides.
An example of an optical device includes: a first optical path that includes a first waveguide having a first propagation constant; a second optical path that includes a second waveguide parallel to the first waveguide and having a second propagation constant that is different from the first propagation constant; a first antenna configured to emit first light from the first optical path; and a second antenna configured to emit second light from the second optical path. The first waveguide includes a first phase shifter configured to apply a phase shift along the first waveguide. The second waveguide includes a second phase shifter configured to apply a phase shift along the second waveguide.
Implementations of such an optical device may include one or more of the following features. The first optical path may include a third waveguide located at a different depth level than the first waveguide. The first antenna may be configured to emit first light from the third waveguide. The second optical path may include a fourth waveguide located at a different depth level than the fourth waveguide. The second antenna may be configured to emit second light from the fourth waveguide. A total optical path length of the first waveguide may be equal to a total optical path length of the second waveguide. The first propagation constant of the first waveguide may change smoothly over the majority of a total length of the first waveguide. The second propagation constant of the second waveguide may change smoothly over the majority of a total length of the second waveguide. The first waveguide may include a first plurality of sections, the first propagation constant for each section of the first plurality of sections being uniform, and each section of the first plurality of sections being connected to an adjacent section of the first plurality of sections by a taper. The second waveguide may include a second plurality of sections, the second propagation constant for each section of the second plurality of sections being uniform, and each section of the second plurality of sections being connected to an adjacent section of the second plurality of sections by a taper.
Implementations of such an optical device may further include one or more of the following features. A width of a waveguide core of the first waveguide may be different from a width of a waveguide core of the second waveguide. A height of a waveguide core of the first waveguide may be different from a height of a waveguide core of the second waveguide. A material that forms a waveguide core of the first waveguide may have a different index of refraction from a material that forms a waveguide core of the second waveguide. The first antenna and the second antenna may be selected from a group consisting of a plasmonic antenna, a waveguide-termination antenna, and a resonant antenna.
An example integrated optical device includes: a waveguide cladding volume; a waveguide layer within the waveguide cladding volume, the waveguide layer including at least one waveguide core that is elongated in a longitudinal direction, and the at least one waveguide core and the waveguide cladding volume forming a waveguide; and a perturbation layer within the waveguide cladding volume. The perturbation layer includes: a first emitter layer that includes a first plurality of emitters displaced from the at least one waveguide core in a first direction perpendicular to the longitudinal direction; and a second emitter layer that includes a second plurality of emitters, the second emitter layer being farther from the waveguide core in the first direction than the first emitter layer.
Implementations of such an integrated optical device may include one or more of the following features. The perturbation layer may be separated from the waveguide layer by a first separation distance that is greater than zero. The first separation distance may be less than a single wavelength of the first light which the first waveguide is configured to guide. The first emitter layer may be separated from the second emitter layer by a second separation distance that is greater than zero. The second plurality of emitters may be offset by an offset distance in the longitudinal direction relative to the first plurality of emitters. The offset distance and the separation distance may be configured to emit light from the waveguide in a single direction. The offset distance may be approximately ±λeff/4+m λeff/2, wherein λeff is an effective wavelength of light guided by the waveguide and m is an integer. The second separation distance is approximately λc/4+nλc/2, wherein n is an integer and λc is an effective wavelength of light in the cladding volume.
Implementations of such an integrated optical device may further include one or more of the following features. Each of the first plurality of emitters may have a first length in the longitudinal direction, and each of the second plurality of emitters may have a second length in the longitudinal direction. The second length may be different from the second length. A first thickness of the first plurality of emitters may be less than a second thickness of the second plurality of emitters. The first thickness and the second thickness may be in the depth direction. The first plurality of emitters may be formed from a first material and the second plurality of emitters may be formed from a second material that is different from the first material. A dielectric constant of the second material may be greater than a dielectric constant of the first material.
An example optical phase shifter includes: a waveguide core comprising a top surface and a bottom surface; and a semiconductor contact that is laterally displaced relative to the waveguide core and is electrically connected to the waveguide core. A top surface of the semiconductor contact is above the top surface of the waveguide core or a bottom surface of the semiconductor contact is below the bottom surface of the waveguide core.
Implementations of such an optical phase shifter may include one or more of the following features. The semiconductor contact may be a first semiconductor contact that is an n-type semiconductor contact. The optical phase shifter may include a second semiconductor contact that is n-type semiconductor contact that is laterally displaced relative to the waveguide core and is electrically connected to the waveguide core. A top surface of the second semiconductor contact may be above the top surface of the waveguide core or a bottom surface of the second semiconductor contact may be below the bottom surface of the waveguide core. A width of the semiconductor contact may be less than a width of the waveguide core. A first concentration of a dopant of the semiconductor contact at the top surface of the semiconductor contact may be greater than a second concentration of the dopant of the semiconductor contact at the bottom surface of the semiconductor contact. A doping profile of the semiconductor contact may smoothly transition from the first concentration of the dopant of the semiconductor contact at the top surface of the semiconductor contact to the second concentration of the dopant of the semiconductor contact at the bottom surface of the semiconductor contact.
Implementations of such an optical phase shifter may further include one or more of the following features. The semiconductor contact may include epitaxially grown semiconductor, deposited semiconductor, or etched semiconductor. The semiconductor contact may include silicon or silicon germanium. The waveguide core may include the same material as the semiconductor contact. The waveguide core may be a first waveguide core having a first propagation constant. The optical phase shifter may include a second waveguide core having a second propagation constant that is different from the first propagation constant. The second waveguide core may be adjacent to the first waveguide core. The semiconductor contact may be electrically connected to the second waveguide core.
An example integrated optical phase shifter includes: a waveguide core comprising a p-type core region and an n-type core region; a p-type semiconductor region in physical contact with the n-type core region of the waveguide core; an n-type semiconductor region in physical contact with the p-type core region of the waveguide core; a first electrical contact in contact with the p-type semiconductor region; and a second electrical contact in contact with the n-type semiconductor region.
Implementations of such an integrated optical phase shifter may include one or more of the following features. A level of a top surface of the waveguide core may be above a level of a top surface of the p-type semiconductor region and may be above a level of a top surface of the n-type semiconductor region. The n-type semiconductor region may be in physical contact with the n-type core region. The p-type semiconductor region may be in physical contact with the p-type core region.
An example integrated optical device includes: a plurality of waveguide cores disposed in an array oriented perpendicular to a longitudinal direction, each waveguide core of the plurality of waveguide cores being elongated in the longitudinal direction; a plurality of diode signal contacts disposed in a first signal contact array oriented in a transverse direction that is perpendicular to the longitudinal direction, a respective waveguide core of the plurality of waveguide cores separating each signal contact of the plurality of signal contacts; a plurality of diode ground contacts disposed in a first ground contact array oriented in the transverse direction, a respective waveguide core of the plurality of waveguide cores separating each ground contact of the plurality of ground contacts; and a plurality of diodes disposed in an array perpendicular to the longitudinal direction. Each diode of the plurality of diodes includes: a first diode ground contact of the plurality of diode ground contacts; and a first diode signal contact of the plurality of signal contacts.
Implementations of such an integrated optical device may include one or more of the following features. The first diode ground contact may be at a first position in the transverse direction, and the first diode signal contract may be at a second position in the transverse direction adjacent to the first position. The integrated optical device may include: a plurality of signal contact arrays comprising the first signal contact array; and a plurality of ground contact arrays comprising the second signal contact array. Each signal contact array of the plurality of signal contact arrays may be configured to be independently controlled. Each diode signal contact of the plurality of diode signal contacts may be electrically isolated from the other diode signal contacts of the plurality of diode signal contacts. A length of each diode signal contact of the plurality of diode signal contacts in the longitudinal direction may be different from a length of each diode ground contact of the plurality of diode ground contacts in the longitudinal direction. The plurality of diode signal contacts and the plurality of diode ground contacts may be epitaxially grown.
An example integrated optical device includes: a phase shifter layer that includes an array of phase shifter regions, each phase shifter region including a first plurality of waveguides and at least one phase shifter for at least a portion of the first plurality of waveguides. Each phase shifter region of the array of phase shifter regions is located at a respective position within the array of phase shifter regions. The integrated optical device also includes an antenna layer above or below the phase shifter layer, the antenna layer including an array of light-emitting regions, each light-emitting region including a second plurality of waveguides. Each light-emitting region of the array of light-emitting regions is located at a respective position within the array of light-emitting regions. Each light-emitting region of the array of light-emitting regions is configured to emit light received from a phase shifter region located at a position adjacent to a position of the light-emitting region.
Implementations of such an integrated optical device may include one or more of the following features. Each waveguide of the first plurality of waveguides of a phase shifter region at a first position within the array of phase shifter regions may be coupled to a respective waveguide of the second plurality of waveguides of a light-emitting region at a second position within the array of light-emitting regions via an optical layer transition. The second position is adjacent to the first position. The optical layer transition is selected from through group consisting of an inverse taper element, a grating-to-grating coupler, and a periscope. The integrated optical device may include a transition layer between the phase shifter layer and the emitting layer. The transition layer may include an array of transition regions, each transition region including a third plurality of waveguides. Each transition region of the array of transition regions may be located at a respective position within the array of transition regions, and each light-emitting region of the array of light-emitting regions may be configured to couple light received from a respective phase shifter region to a respective light-emitting region. The integrated optical device may include a plurality of splitting distribution networks, each splitting distribution network being configured to couple light to a respective phase shifter region. The plurality of splitting distribution networks may be at a same level as the phase shifter layer or at a level farther from the antenna layer than the phase shifter layer. Each waveguide of the second plurality of waveguides of a first light-emitting region may be above or below a respective waveguide of the first plurality of waveguides of a first phase shifter region array. Each waveguide of the first plurality of waveguides of the first phase shifter region may have a different propagation constant than the respective waveguide of the second plurality of waveguides of the first light-emitting region that is above or below each waveguide of the first plurality of waveguides.
Various aspects and embodiments will be described with reference to the following figures. The figures are not necessarily drawn to scale. For purposes of clarity, not every component may be labeled in every drawing.
The inventors have recognized and appreciated a need for optical devices for emitting optical radiation (referred to simply as “light” herein) that are compact and can emit coherent optical radiation with control over the angle of emission of the emitted optical radiation. Applications of such a device include LIDAR, communications and biomedical imaging, but applications are not limited to these fields. For example, implementations of one such optical device may be used to perform frequency modulated continuous wave (FMCW) LIDAR. The optical device may receive a multimode return signal. The optical device may also be used as a high-speed free-space optical communication link. The optical device may produce a single phased beam across a wide aperture (e.g., 100 cm2) and/or numerous independent beams. Some implementations of the optical device may be integrated into a mobile communication system. Alternatively, the optical device may be integrated into a vehicle, such as an automobile, an aircraft or a ship.
Techniques are discussed herein for emitting light from an optical device that includes multiple waveguides, antennas and/or phase shifters configured to shift the phase of light guided by at least a subset of the waveguides. Such an optical device may be an optical phased array, but other optical devices may also benefit from the techniques described herein.
The inventors have recognized that there is a need for a light emitting optical device that is allows unidirectional emission of light in a controllable direction and is robust to variations that commonly occur during fabrication, such as proximity and rounding effects that can alter the physical geometry of a device in an unpredictable way when compared to a desired geometry. For example, some implementations of an optical device may include antennas that are distinct from the waveguides. The antennas may include multiple emitter elements that may, for example, be separated from the waveguides by a gap. By separating the guiding and emitting function of a perturbation layer of the optical device the emitter elements can cause light guided by the waveguides to be emitted without using emitter elements formed directly in the waveguide using partial or full etching. Instead, the emitter elements can be formed in a separate perturbation layer using full etching. By reducing the use of directly etching the waveguide in forming the optical device, the rounding and proximity effects are restricted to regions that are far from the optical mode of the light guided by the waveguides.
The inventors have also recognized and appreciated that using a single layer of emitter elements (a “single emitting layer”) that is separate from the layer of waveguides (“the waveguide layer”), up to 50% of the optical power may be lost due to light emission occurring in both an upward and downward direction. By including multiple emitting layers, the amount of optical power emitted in the desired direction can be increased to greater than 90%, and in some cases higher than 99%.
The inventors have further recognized that a light emitting optical device that is compact may need to overcome several obstacles that have not been addressed by conventional optical devices. For example, making a compact optical device may include using a phase shifters that are scalable to large arrays. For phase shifters to be considered scalable, the phase shifters should have approximately the same pitch as the emitter elements used to cause the light to be emitted from the optical device. Optical devices that include phase shifters that have approximately the same pitch as the emitter elements of the optical device may have large fill factors, where the fill factor is defined as the ratio of the light emitting/receiving area of the optical device to the total area of the optical device. As a result of including phase shifters that have approximately the same pitch as the emitter elements, the fill factor is less dependent on the number of antennas included as compared to optical devices that include phase shifters that have a larger pitch than the emitter elements.
The inventors have also recognized that the fill factor of an optical device can be further increased by forming the optical device using a “unit cell” approach where particular regions of the device are repeated in an array and stacked together in a “Tetris-style” building block approach. The optical device, for example, can include, on a top layer, multiple light-emitting regions in an antenna layer that are formed above multiple phase shifter regions in a phase shifter layer that is below the antenna layer. Each light-emitting region emits light from a phase shifter region from which light is received. A particular light-emitting region does not emit light from the phase shifter region immediately below the light-emitting region. Instead, a particular light-emitting region emits light from a phase shifter region that is in a different position in the array of regions such that the majority of the top layer of the optical device includes light-emitting regions. Thus, the surface area of the optical device is not wasted with regions that do not emit light. Instead, the phase shifter regions, which do not emit light, may be located beneath the antenna regions.
The inventors have further recognized that a light emitting optical device that is compact may include multiple waveguides in close proximity. When waveguides of an optical device are sufficiently close, there is cross-talk between waveguides where light from a first waveguide evanescently couples to a second waveguide and vice versa. Such cross-talk can make it difficult to control the light emitted from an optical device. The inventors have recognized and appreciated that by using waveguides that are phase mismatched, the crosstalk between waveguides can be reduced. Waveguides can be phase mismatched by ensuring that adjacent waveguides have different propagation constants for the wavelength of light that the waveguides are designed to guide. The inventors have also recognized and appreciated that emitter elements used to form an antenna for each waveguide can be formed in a way that compensates for the phase mismatch in the waveguides and results in emitted light that is coherent and emits in a single direction. For example, if the optical device include a grating antenna, the grating period of the grating antenna for a first waveguide with a first propagation constant can be selected to be different from the grating period of a second waveguide with a second propagation constant such that the overall angle of the emitted light is the same, while maintaining a phase mismatch for the light within the two waveguides. Techniques described herein for phase mismatching waveguides can be used for any adjacent waveguides of the optical device. For example, adjacent waveguides in a waveguide layer of an antenna layer of the optical device may be phase mismatched. Alternatively or additionally, adjacent waveguides in a phase shifter layer of the optical device may be phase mismatched. Alternatively or additionally, a waveguide in the antenna layer may be phase mismatched with a waveguide from the phase shifter layer of the optical device.
Overview of an Optical Device According to Some Embodiments
Referring to
Each reticle field of the optical device 1 includes four macro-cells, each macro-cell including 16 unit cells (e.g., a 4×4 array that includes a unit cell 8 of
Referring to
The splitting distribution network 15 may be, for example, a binary tree network or a star coupler that is optically connected to the light source 14 and each waveguide of the phase shifter region 12. A binary tree network may include a cascade of 1×2 couplers formed by splitting an initial waveguide that is connected to the light source 14 into two waveguide, each of those two waveguides splitting into two more waveguides, and so on until 2n waveguides are formed, where n is the number of levels of the tree. Referring to
The “Tetris-style” approach to an example optical device is illustrated by the unit cell 10, which includes the phase shifter region 12 and the light-emitting region 13 offset from one another in a longitudinal direction defined by the orientation of the waveguides with in the phase shifter region 12 and the light-emitting region 13. The different regions are disposed at different layers within the optical device 1. A phase shifter layer 18 of the optical device 1 includes an array of phase shifter regions (e.g., phase shifter region 12), each phase shifter region comprising a first plurality of waveguides and at least one phase shifter for at least a portion of the first plurality of waveguides. Each phase shifter region of the array of phase shifter regions is located at a respective position within the array of phase shifter regions. An antenna layer 20 of the optical device 1 is above or below the phase shifter layer 18. The antenna layer 20 includes an array of light-emitting regions (e.g., light-emitting region 13), each light-emitting region including a second plurality of waveguides. Each light-emitting region of the array of light-emitting regions is located at a respective position within the array of light-emitting regions. Additionally, each light-emitting region of the array of light-emitting regions is configured to emit light received from a phase shifter region located at a position adjacent to a position of the light-emitting region. For example, phase shifter region 12 is located at a position in the array that is one position to the left of the light-emitting region 13. In other words, the center of the phase shifter region 12 is to the left of the center of the light-emitting region 13. It should be understood, that the directional terms left and right are being used in reference to
Referring to
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An optical layer transition is used to optically couple a waveguide from a first layer to a waveguide located in a second layer that is above or below the first layer. Non-limiting examples of optical layer transitions include an inverse taper element, a grating-to-grating coupler, or a periscope. The periscope includes an arrangement of at least two reflective surfaces that guide light from the waveguide of the first layer to the waveguide of the second layer using reflection. An example of an inverse taper element is an “optical escalator.” Referring to
Referring to
While the components of
The phase shifter layer 56 includes multiple waveguide cores that, together with the cladding volume 62 form waveguides that guide light through the optical device 1. The metal contact layer 60 includes multiple metal contacts that deliver electrical signals from the electrodes 4 to multiple semiconductor contacts of the semiconductor contact layer 58. Each of the waveguides of the phase shifter layer 56 includes at least one phase shifter that, based on the received electrical signal, applies a phase shift along the waveguide such that light guided by a particular waveguide experiences a phase shift that depends on the received electrical signal. Each phase shifter of the phase shifter layer 56 may be independently controlled such that light guided by each waveguide of the phase shifter layer 56 experiences a phase shift that is individually controlled and may be different from the phase shifts experienced by other waveguides. Any type of phase shifter may be used to induce a phase shift along the waveguides of the phase shifter layer 56, including thermal phase shifters and electro-optical phase shifters. A particular example of an electro-optical phase shifter is described in more detail below.
The waveguide layer 54 includes multiple waveguides, which may be referred to as antenna waveguides to distinguish them from phase the phase shifter waveguides of the phase shifter layer 56. Light from the phase shifter layer 56 is coupled to the antenna waveguides of the waveguide layer 54 using an optical layer transition, such as the escalator 16. The perturbation layer 52 includes multiple antennas that cause light guided by the antenna waveguides to be emitted in a vertical direction, away from the phase shifter layer 56. While not illustrated in
Having described an overview of an optical device according to some embodiments, particular details of example optical devices are described below.
Phase Mismatched Waveguides
When two or more waveguide cores are brought sufficiently close to one another, light guided by one waveguide may couple to a different waveguide. This crosstalk can limit the ability to precisely tune optical devices that emit optical radiation for purposes such as LIDAR. To reduce crosstalk from occurring, adjacent waveguides can be phase mismatched from one another. Two waveguides are phase mismatched, for example, when the propagation constants of the two waveguides are different. The maximum optical power that is transferred between two neighboring guides is
where κ is a coupling coefficient between the two waveguides and Δβ is the different in propagation constants between the two waveguides. Thus, a large Δβ prevents significant coupling of light between the two guides.
The propagation constant of a waveguide depends on the effective index of refraction of the waveguide via the following equation:
where β is the propagation constant, neff is the effective index of refraction, and λ is the wavelength of the light guided by the waveguide. The effective index of refraction, neff, is dependent on a number of parameters, including a cross-sectional area and the cross-sectional shape of the waveguide, a material that forms the waveguide core, and a material that forms the waveguide cladding. For example, increasing the width of the waveguide core increases the effective index of refraction, resulting in an increased propagation constant. Similarly, increasing the height of the waveguide core increases the effective index of refraction, resulting in an increased propagation constant. Using a material with a larger intrinsic index of refraction (e.g., the index of refraction of the bulk material) also increases the propagation constant.
Based on the waveguide above factors that affect the index of refraction, an entire array of waveguides can be phase mismatched by ensuring that adjacent waveguides in the array of waveguides are phase mismatched with each other. This may be achieved by forming each waveguide in the array with its own unique propagation constant. Alternatively, two, three or more types of waveguides can be used, each type having its own propagation constant. The array of waveguides can be formed by alternating the multiple different types of waveguides, e.g., periodically, to form the array.
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The above examples of waveguide arrays used two different types of waveguides in an alternating pattern to create an array of phase mismatched waveguides. It is possible to create similar arrays of phase mismatched waveguides using more than two types of waveguides. Referring to
While
The above mentioned techniques for phase mismatching waveguides, as described in connection with
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The aforementioned waveguide mismatching techniques may be used in any array of waveguides of an optical device. For example, referring back to
In some embodiments, it may be desirable to have the total optical path of a first type of waveguide equal to the total optical path of a second type of waveguide. This may be desirable, for example, when the phase mismatching techniques are used for phase shifter waveguides. In this type of embodiment, the overall phase shift imparted on light guided by the waveguides by the geometry of the two types of waveguides should be equal to ensure the phase shift imparted on the light is controlled precisely by the phase shifters themselves.
Compensating for Phase Mismatch with the Perturbation Layer
An optical device that emits light from an array of waveguides may include multiple antennas that combine and superpose the light from each waveguide of the array of waveguides, enhancing radiation in certain directions while suppressing radiation in other directions. Using multiple antennas in this way creates a radiation pattern that could not be achieved by a single antenna.
When the aforementioned phase mismatching technique is used to form a waveguide array with adjacent waveguides having different propagation constants, a problem arises in ensuring that the direction of emission from a one waveguide is the same as the direction of emission from another waveguide with a different propagation constant. For example, the direction of emission for a grating antenna depends on the propagation constant of the waveguide. Thus, a large difference in propagation constant between neighboring waveguides of the array causes the emitted light from the optical device to become out of phase. This phase mismatch in the emitted light can be compensated by adjusting the grating period of the grating antenna used for each waveguide. Specifically, if the propagation constant vector of a first waveguide {right arrow over (β)}1 and the propagation constant vector of a second waveguide is {right arrow over (β)}2 (both of the propagation constant vectors directed toward the direction of propagation), then the difference in propagation constant vectors is Δ{right arrow over (β)}={right arrow over (β)}2−{right arrow over (β)}1. Further, if a grating antenna for the first waveguide has a first grating wavenumber vector {right arrow over (K)}1 and a grating antenna for the second waveguide has a second grating wavenumber vector {right arrow over (K)}2, then the difference in grating wavenumber vectros between the two grating antennas is Δ{right arrow over (K)}={right arrow over (K)}2−{right arrow over (K)}1. The amplitude of the grating wavenumber vector of a grating antenna is |{right arrow over (K)}|=2 π/Λ, where Λ is the grating period of the grating antenna and the direction of the vector is against the direction of propagation of light in the grating (i.e., in the opposite direction as the propagation constant vector). For the emitted light from the two waveguides to be emitted at the same angle, the grating period of the grating antennas should be adjusted such that Δ{right arrow over (K)}=Δ{right arrow over (β)}. In other words, the following equation should be satisfied:
{right arrow over (β)}1+{right arrow over (K)}1={right arrow over (β)}2+{right arrow over (K)}2. (Eqn. 2)
The wavenumber vectors {right arrow over (K)}2 and {right arrow over (K)}2 point in the opposite direction as the propagation constant vectors {right arrow over (β)}1 and {right arrow over (β)}2. As a result, if the widths of the waveguide cores are used to control the propagation constants of two neighboring waveguides, then the wider of the two waveguides has the larger propagation constant and, therefore, the grating antenna associated with the wider waveguide should have a smaller grating period.
As mentioned above, the propagation constant of a particular waveguide is dependent on the wavelength of the light guided by the waveguide. Equation 2, above, should be satisfied for first light guided by a first waveguide and second light guided by a second waveguide for the grating antennas associated with the two waveguides to emit light in the same direction. To emphasize the wavelength dependence of Eqn. 2, it can be rewritten in scalar form as:
where n1(λ) is the wavelength dependent effective index of refraction of the first waveguide, n2(λ) is the wavelength dependent effective index of refraction of the second waveguide, Λ1 is the grating period of the first grating antenna, and Λ2 is the grating period of the second grating antenna. If λp is defined as the wavelength at which both the first waveguide and the second waveguide are configured to emit the light perpendicularly, |{right arrow over (K1)} |=2 π/Λ1 and |{right arrow over (K2)}|=2 π/Λ2 can be written as 2πn1,2(λp)/λp (known as the Bragg condition). Thus, the Eqn. 3 can be further rewritten as:
In some embodiments, Eqn. 4 is satisfied for the wavelengths of light (λ) for for which the optical device is operational. The period of each grating antenna may be set, for example, so that the emitted light from a first emitter element of a particular grating antenna is in phase with the light emitted from a second emitter element (adjacent to the first emitter element in the particular grating antenna along a waveguide) for the operational wavelength. Further, the emission angle from the first emitter element may also be equal with the emission angle of the second emitter element. Additionally, at the operational wavelength, the emission angles from adjacent antennas may be equal.
Grating antennas are formed in a perturbation layer and includes multiple emitter elements spaced at a periodic interval (i.e., the grating period). The emitter elements may be made from the same material as the associated waveguide core or from a different material. The material may be a dielectric, a semiconductor, or a metal. The grating antennas are configured to emit light from an associated waveguide. In some embodiments, the perturbation layer may be part of the same layer as the waveguide layer by being partially or fully etched into the waveguide core itself. Alternatively or additionally, the perturbation layer may be above or below the waveguide layer. If the perturbation layer is above the waveguide layer, the perturbation layer may be immediately above the waveguide layer, with no gap between the waveguide layer and the perturbation layer. Alternatively, there may be a gap between the waveguide layer and the perturbation layer. The perturbation layer may also include multiple emitter layers, each emitter layer including multiple emitter elements spaced at a periodic interval. The grating period of each emitter layer may be the same or different. Additionally, the emitter elements of each emitter layer may be offset from each other by some distance.
Referring to
Separate Perturbation Layer and Waveguide Layer
As mentioned above, the perturbation layer may be at the same depth level as the waveguide layer or at a different level. Separating the perturbation layer and the waveguide layer may have a number of advantages. For example, embodiments that separate the perturbation layer and the waveguide layer may allow an optical device to have a larger fill factor as compared to forming the perturbation layer and the waveguide layer at the same depth level. Separating the layers also reduces or eliminates the need to use partial etching in forming the antennas, resulting in more precisely formed, robust antennas.
Referring to
Referring to
An optical device with a grating antenna formed from a single emitter layer, as illustrated in
While a mirror could be used to redirect the light emitted downward from a single emitter layer upwards, the spacing of the mirror would need to be set at a well-defined spacing d=λ/4+λ/2 m, where m=0, 1, 2 . . . , with small values of m being more desirable due to reduced angular and wavelength dependence. It is challenging to find a distance d that meets this condition and fits within the process layer stack sufficiently far away from a waveguide layer so as not to induce absorption in the guided mode of the waveguide. Accordingly, it is preferable not to use mirrors for this purpose in an optical device. Instead of using a metal layer to reflect the downward light emission upwards, a second emitter layer is included in the perturbation layer. For example, to emit light vertically upward (i.e., the direction of emission is normal to the plane of the optical device), the emitter elements of the second emitter layer are shifted by π/2 in their temporal phase from the first layer and are additionally separated by a distance λ/4 from the first emitter layer. This configuration is mathematically similar to a pair of dipole radiators separated by a distance λ/4 with a π/2 phase advance in the bottom dipole's excitation waveform. The result is that light emitted in the downward direction from the emitter layers is π out of phase with one another and the light emitted in the upward direction is in phase with one another thereby increasing the amount of optical power directed in the upward direction. Additionally, the offset and separation of the emitter layers can be adjusted to different values in order to emit light at angles other than zero degrees, i.e., an emission direction that is not directly upward.
Referring to
Each emitter element of the first emitter layer 154 have a first length in a longitudinal direction along the length of the waveguide core 150 and each emitter element of the second emitter layer 156 have a second length in the longitudinal direction. The lengths of the emitters in each emitter layer may be different. For example, as illustrated, the emitter element length of the first emitter layer 154 is greater than the emitter element length of the second emitter layer 156. However, the emitter element length of the first emitter layer 154 may also be less than or equal to the emitter element length of the second emitter layer 156.
The first emitter layer 154 has a first thickness, h1, in the depth direction and the second emitter layer 156 has a second thickness, h2, in the depth direction. The second thickness, h2, may be greater than the first thickness, h1, to ensure that the second emitter layer 156 perturbs the light guided by the waveguide with the same strength as the first emitter layer 154. This is due to the intensity of the light guided by the waveguide decreasing as a function of distance from the waveguide core 150. Other techniques for ensuring the perturbation of the two emitter layers are approximately equal may also be used. For example, instead of forming the first emitter layer 154 and the second layer 156 from the same material, as illustrated in
The direction light is emitted by the grating antenna 152 can be tuned by setting the gap distance, dg, the separation distance, ds, and also an offset distance, dg, which is a distance that the center of the emitter elements of the second emitter layer 156 are offset relative to the center of the emitter elements of the first emitter layer 154. For example, to tune the emission direction to be vertical in the upward direction, the offset distance, do, is approximately ±λeff/4+mλ/2, wherein λeff is an effective wavelength of light guided by the waveguide and m is an integer, and the separation distance, ds, is approximately λo/4+nλo/2, wherein n is an integer and λc is an effective wavelength of light in the cladding volume. Other angles of emission can be achieved by setting the offset distance, do, and the separation distance, ds, to different values. For example, as shown in
The emitter elements of any grating antenna used in example optical devices may be formed from various materials. For example, silicon, silicon nitride, poly/amorphous silicon, liquid crystals, aluminum nitride, indium titanium oxide, metals, or germanium may be used to form emitter elements. In some embodiments, a material used to form a grating antenna above a waveguide core may have a higher index of refraction than a material from which the waveguide core is formed. Additionally, as discussed above, if a perturbation layer of a grating antenna includes multiple emitter layers, then each emitter layer may be formed from different materials. For example, a first emitter layer that is nearer to a waveguide core than a second emitter layer may be formed from a material with an index of refraction that is less than the index of refraction of a material used to form the second emitter layer.
To change the emission rate along the waveguide core 150, the gap distance, ds, between the waveguide layer and the first emitter layer can be changed. Changing this distance is independent of the profile of the layers themselves so new lithography masks do not have to be fabricated to change the emission rate of the antenna from wafer to wafer. Furthermore, changing the gap distance, ds, does not change the directionality of the emission because the directionality is determined by the horizontal and vertical offset of the emitter layers 154 and 156. Changing the gap distance, ds, allows for a robust and inexpensive way to tune the emission of light from an optical device.
Phase Shifter Pitch Reduction
Electro-optic phase shifters are waveguides (e.g., formed from silicon waveguide cores) that are embedded with p-n and p-i-n diodes using, for example, ion implantation. Within the waveguides, electrical field based DC Kerr effect and/or plasma dispersion effect alter the refractive index of silicon waveguide core causing a controllable phase shift for light guided by the waveguide. To efficiently fabricate a compact optical device that includes an array of phase shifters, the phase shifters should be scalable to large arrays. Referring to
Referring to
Two contacts are required to drop a voltage potential across p and n sides of the diodes of a phase shifter. However, contacts are made out of metals that are not transparent to portions of the optical spectrum of interest (1.1λm<λ<3 μm). Thus, when tight pitched electro-optic phase shifters are used, metal contacts used to bring signals to the diode used to induce a phase shift create undesirable losses in the optical device 170. This is because the optical mode of the waveguide overlaps more with the volume occupied by the metal contact. When the pitch of the phase shifters is less than one wavelength of the light guided by the waveguide, and especially as the pitch approaches one-half of one wavelength of the light guided by the waveguide, the metal contacts should be moved farther from the waveguide core to ensure the metal contacts are isolated from the guided mode of the waveguide. One solution to efficiently bring the voltage potential from the metal contacts to the diodes is to use highly doped, low resistance semiconductor contact extension regions, which have less optical loss than metal, in the vicinity of the waveguide core. This may be achieved by extending the silicon of the diode in a vertical direction to form raised semiconductor pillars that are in contact with a metal contact at a distance greater than one-half wavelength from the waveguide core. The semiconductor pillars may be extended in an upward or a downward direction. The semiconductor pillars can be etched from a silicon wafer or epitaxially grown and are doped to with the same dopant type as the side of the diode in which it is in contact.
Referring to
A semiconductor contact for the p-type semiconductor region 184 is formed from a p-type semiconductor contact region 190 and a p-type semiconductor contact extension region 191, both having a higher dopant concentration than the p-type semiconductor region 184. The p-type semiconductor contact extension region 191 is extended in a downward vertical direction, such that a bottom surface of the p-type semiconductor contact extension region 191 is below a bottom surface of the waveguide core 181. The depth of the bottom surface of the p-type semiconductor contact extension region 191 may be, for example, 250 nm or 800 nm below the bottom surface of the waveguide core 181. A metal contact 192 is in physical contact with the bottom surface of the p-type semiconductor contact extension region 191 and is configured to bring electrical signals to the p-type semiconductor region 184.
A semiconductor contact for the p-type semiconductor region 185 and the p-type semiconductor region 186 is formed from a p-type semiconductor contact region 193 and a p-type semiconductor contact extension region 194, both having a higher dopant concentration than the p-type semiconductor region 185 and the p-type semiconductor region 186. The p-type semiconductor contact extension region 194 is extended in a downward vertical direction, such that a bottom surface of the p-type semiconductor contact extension region 194 is below a bottom surface of the waveguide core 182 and a bottom surface of the waveguide core 183. The depth of the bottom surface of the p-type semiconductor contact extension region 194 may be, for example, 250 nm or 800 nm below the bottom surface of the waveguide core 182 and the bottom surface of the waveguide core 183. A metal contact 195 is in physical contact with the bottom surface of the p-type semiconductor contact extension region 194 and is configured to bring electrical signals to the p-type semiconductor region 185 and the p-type semiconductor region 186. The metal contact 195 is shared by the diode associated with waveguide core 182 and the diode associated with waveguide core 183 such that adjacent waveguide cores share one contact with each other.
A semiconductor contact for the n-type semiconductor region 189 is formed from an n-type semiconductor contact region 196 and an n-type semiconductor contact extension region 197, both having a higher dopant concentration the n-type semiconductor region 189. The n-type semiconductor contact extension region 197 is extended in a downward vertical direction, such that a bottom surface of the n-type semiconductor contact extension region 197 is below a bottom surface of the waveguide core 183. The depth of the bottom surface of the n-type semiconductor contact extension region 197 may be, for example, 250 nm or 800 nm below the bottom surface of the waveguide core 183. A metal contact 198 is in physical contact with the bottom surface of the n-type semiconductor contact extension region 197 and is configured to bring electrical signals to the p-type semiconductor region 189.
A semiconductor contact for the n-type semiconductor region 187 and the n-type semiconductor region 188 is formed from an n-type semiconductor contact region 199 and an n-type semiconductor contact extension region 200, both having a higher dopant concentration than the n-type semiconductor region 187 and the n-type semiconductor region 188. The n-type semiconductor contact extension region 200 is extended in a downward vertical direction, such that a bottom surface of the n-type semiconductor contact extension region 200 is below a bottom surface of the waveguide core 181 and a bottom surface of the waveguide core 182. The depth of the bottom surface of the n-type semiconductor contact extension region 200 may be, for example, 250 nm or 800 nm below the bottom surface of the waveguide core 181 and the bottom surface of the waveguide core 182. A metal contact 201 is in physical contact with the bottom surface of the n-type semiconductor contact extension region 200 and is configured to bring electrical signals to the n-type semiconductor region 187 and the n-type semiconductor region 188. The metal contact 201 is shared by the diode associated with waveguide core 181 and the diode associated with waveguide core 182 such that adjacent waveguide cores share one contact with each other.
While the optical device 180 may be formed using many different dimensions, one set of dimensions is provided as an example. The waveguides of the optical device 180 are configured to guide light with a wavelength equal to 1550 nm. The pitch of the optical device 180 (i.e., the distance between the center points of each metal contact) is approximately one-half of one wavelength. For example, the pitch may be 760 nm or 800 nm. The waveguide core width, ww, is approximately one-quarter of one wavelength. For example, the waveguide core width, ww, may be approximately 400 nm. The distance, d, between a side surface of each semiconductor contact extension region and a side surface of a respective waveguide core is approximately 100 nm. A semiconductor contact extension region width, ws, is approximately 200 nm. A metal contact width, wc, is approximately 160 nm. These widths may vary from waveguide to waveguide in order to introduce phase mismatch between adjacent waveguides. Accordingly, even within a single device, these widths may vary by ±50 nm.
In the semiconductor contact of the optical device 180, a concentration of a respective dopant may vary as a function of depth. For example, the concentration of a dopant of a particular semiconductor contact at the bottom surface of the semiconductor contact extension region may be greater than a second concentration of the dopant of the semiconductor contact at the top surface of the semiconductor contact. In other words, the dopant concentration of the semiconductor contact is higher near the metal contact and lower near the waveguide core. The dopant concentration may vary discontinuously or continuously with a smooth gradient. The semiconductor contact can be formed from, for example, silicon or silicon germanium and may be formed from the same or a different material than the waveguide cores.
While
A top surface of the p-type semiconductor contact extension region 215 and a top surface of the n-type semiconductor contact extension region 219 are at a depth level that is above the top surface of the waveguide core 212. For example, the depth of the top surface of each semiconductor contact extension region may be 250 nm or 800 nm above the top surface of the waveguide core 212. The optical device 210 of
Increased Depletion Within Waveguide Core
In some embodiments, phase shifter waveguides the waveguide core may be formed from an n-type semiconductor region and a p-type semiconductor region. The resulting n-p-n-p junction structure may result in a waveguide core with increased electron-hole depletion in the waveguide core resulting in less optical loss than the p-i-n structures described above. A phase shifter with the n-p-n-p junction may use the aforementioned semiconductor contact extension technique to keep the metal contact isolated from the vicinity of the waveguide core.
Referring to
Adjacent to the n-type semiconductor core region 233 is a p-type semiconductor region 235 that extends longitudinally along the length of the waveguide core 232. The p-type semiconductor region 235 is in physical contact with both the n-type semiconductor core region 233 and the p-type semiconductor core region 234. Specifically, p-type semiconductor region 235 is in physical contact with the longitudinal portion of the n-type semiconductor core region 233 and the transverse portion of the p-type semiconductor core region 234. A level of a top surface of the waveguide core 232 is above a level of a top surface of the p-type semiconductor region 235 in the depth direction.
Adjacent to the p-type semiconductor core region 234 is an n-type semiconductor region 238 that extends longitudinally along the length of the waveguide core 232. The n-type semiconductor region 238 is in physical contact with both the n-type semiconductor core region 233 and the p-type semiconductor core region 234. Specifically, n-type semiconductor region 238 is in physical contact with the longitudinal portion of the p-type semiconductor core region 234 and the transverse portion of the n-type semiconductor core region 233. A level of a top surface of the waveguide core 232 is above a level of a top surface of the n-type semiconductor region 238 in the depth direction.
The p-type semiconductor region 235 is in physical contact with a p-type semiconductor contact region 236, which is in contact with a metal contact 237. The n-type semiconductor region 238 is in physical contact with an n-type semiconductor contact region 239, which is in contact with a metal contact 240.
Staggered Phase Shifter Contacts
By staggering the contacts of the phase shifters, the pitch of the phase shifter may be decreased in contrast to when the contacts of the phase shifters are not staggered. Referring to
Multiple diode signal contacts (Si, Si+1, etc.) are disposed in a first signal contact array 255 oriented in a transverse direction that is perpendicular to the longitudinal direction. A respective waveguide core separates each signal contact from an adjacent signal contact. For example, waveguide core 251 separates signal contact Si from signal contacts Si+1. The array of signal contacts is oriented in the horizontal direction such that each signal contact of the array is to the left of the right of at least one other signal contact of the array. Thus, each signal contact has a position within the array, the positions being labeled across the bottom of
Multiple diode ground contacts (Gi, Gi+1, etc.) are disposed in a first ground contact array 256 oriented in the transverse direction. A respective waveguide core separates each ground contact from an adjacent ground contact. For example, waveguide core 253 separates signal contact Gi+1 from signal contacts Gi+2. The array of ground contacts is oriented in the horizontal direction such that each ground contact of the array is to the left of the right of at least one other ground contact of the array. Thus, each ground contact has a position within the array, the positions being labeled across the bottom of
Multiple diodes are formed in an array perpendicular to the longitudinal direction, wherein each diode of the plurality of diodes includes a first diode ground contact from the first ground contact array 256, and a first diode signal contact from the first signal contact array 255. For example, a first diode is formed from the signal contact Si, which at a first position within the array of signal contacts, and the ground contact Gi, which at a second position within the array of ground contacts. Thus, in the example shown, the diodes are formed using contacts that are staggered relative to one another because they are not at the same position within their respective array.
In some embodiments, the signal contact array 255 is one of multiple signal contact arrays and the ground contact array 256 is one of multiple signal contact arrays.
In the optical device 250, diodes within a column are isolated from one another using an electrical isolation material. Thus, each column of diodes, which corresponds to a respective waveguide, are independently controlled. In other embodiments, each signal contact array of the multiple signal contact arrays is independently controlled. This can be achieved by including an additional electrical isolation component that is formed from the same material as the waveguides between each array of diodes. Referring to
Other Considerations
Other examples and implementations are within the scope and spirit of the disclosure and appended claims. For example, individual elements of optical devices described above may be used in other application or devices not discussed. Additionally, individual elements of optical devices described above may be combined in ways not described in detail above.
Some of the example embodiments described above were described as using light with a wavelength of approximately 1550 nm. Embodiments are not limited, however, to any particular wavelength. For example, some embodiments may use light at longer wavelengths, such as approximately 10 μm, which penetrates fog better than light with a wavelength of 1550 nm. As a further example, it may be advantageous for some applications to use light in the visible spectrum. Accordingly, light with a wavelength in the range of 550 nm-750 nm may be used. It should be understood that if different wavelengths of light are used, the materials and dimensions of different components will be different from those described above in connection with particular example embodiments.
Also, as used herein, “or” as used in a list of items prefaced by “at least one of” or prefaced by “one or more of” indicates a disjunctive list such that, for example, a list of “at least one of A, B, or C,” or a list of “one or more of A, B, or C,” or “A, B, or C, or a combination thereof” means A or B or C or AB or AC or BC or ABC (i.e., A and B and C), or combinations with more than one feature (e.g., AA, AAB, ABBC, etc.).
As used herein, unless otherwise stated, a statement that a function or parameter is “based on” an item or condition means that the function or parameter is based on the stated item or condition and may be based on one or more items and/or conditions in addition to the stated item or condition.
As used herein, unless otherwise stated, a statement that a parameter is “approximately” equal to a value means that the parameter is equal to the value or some other value within a 20% range of the stated value. For example, if a distance is “approximately equal” to 1000 nm, then the distance may be equal to any value within the inclusive range 800 nm to 1200 nm.
Specific details are given in the description to provide a thorough understanding of example configurations (including implementations). However, configurations may be practiced without these specific details. For example, well-known fabrication techniques, processes, and structures, have been shown without unnecessary detail in order to avoid obscuring the configurations. This description provides example configurations only, and does not limit the scope, applicability, or configurations of the claims. Rather, the preceding description of the configurations provides a description for implementing described techniques. Various changes may be made in the function and arrangement of elements without departing from the spirit or scope of the disclosure.
Components, functional or otherwise, shown in the figures and/or discussed herein as being connected or optically coupled with each other are may be directly or indirectly connected or optically coupled. Meaning, there may be additional elements, not shown or described, between the components that are connected or optically coupled. Components, functional or otherwise, discussed herein as being in physical contact do not have additional elements between the components that are in physical contact with one another.
Having described several example configurations, various modifications, alternative constructions, and equivalents may be used without departing from the spirit of the disclosure. For example, the above elements may be components of a larger system, wherein other rules may take precedence over or otherwise modify the application of the invention. Also, a number of operations may be undertaken before, during, or after the above elements are considered. Accordingly, the above description does not bound the scope of the claims.
When describing embodiments in reference to the drawings, direction references (“above,” “below,” “top,” “bottom,” “left,” “right,” “horizontal,” “vertical,” etc.) may be used. Such references are intended merely as an aid to the reader viewing the drawings in a normal orientation. These directional references are not intended to describe a preferred or only orientation of an embodied device. A device may be embodied in other orientations.
Several example configures include waveguides. Not all descriptions and drawings include a discussion of the cladding of the waveguides. It is to be understood that a waveguide is formed from a waveguide core and a cladding that is in physical contact with the waveguide core. The cladding may be a cladding volume that surrounds multiple waveguide cores and is formed from a material that has a lower index of refraction than a material used to form the waveguide cores.
Further, more than one invention may be disclosed.
This application is a continuation of U.S. patent application Ser. No. 16/361,152 filed 21 Mar. 2019, which is a continuation of U.S. patent application Ser. No. 15/499,468 filed 27 Apr. 2017 which claims the benefit of U.S. Provisional Application No. 62/329,178, filed Apr. 28, 2016, each of which is incorporated herein by reference.
Number | Date | Country | |
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62329178 | Apr 2016 | US |
Number | Date | Country | |
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Parent | 16361152 | Mar 2019 | US |
Child | 17443971 | US | |
Parent | 15499468 | Apr 2017 | US |
Child | 16361152 | US |