Spiral integrated optical phased arrays for tunable near-field-focusing emission

Abstract

An integrated optical phased array system includes at least one spiral-shaped waveguide antenna on a substrate, with perturbations positioned along the spiral path of each antenna to enable light scattering, and phase shifters coupled to the spiral-shaped waveguide antenna to control beam profiles for enhanced functionality. Each spiral-shaped waveguide antenna is configured to emit wavelength-tunable focusing beams with variable focal distances for applications in optical tweezers, chip-based three-dimensional printing, quantum systems, LiDAR, and optical communication, whereby tunable focus is achieved by varying the input wavelength.

Description

[0001] mit-26247pct

[0002] SPIRAL INTEGRATED OPTICAL PHASED ARRAYS FOR TUNABLE NEAR-FIELD-FOCUSING EMISSION RELATED APPLICATION ABSTRACT

[0003] This application claims the benefit of US Provisional Application No. 63 / 720,651, filed 14 November 2024, the entire content of which is incorporated herein by reference.

[0004] BACKGROUND

[0005] The development of integrated optical phased arrays (OP As) has enabled cutting-edge applications where optical beam steering can benefit from chip-scale integration. Typical integrated OP As can achieve non-mechanical solid-state beam steering and, as a result, have promise to reduce the cost and complexity associated with applications such as light detection and ranging (LiDAR) and optical wireless communication. Motivated by these initial applications, the majority of integrated OP A demonstrations to date have been limited to showing far-field beam forming and steering.

[0006] There are, how ever, many emerging applications of integrated photonics where emission of focused light from a chip is desirable, such as in integrated optical tweezers for biophotonics, chip-based three-dimensional (3D) printers, and trapped-ion or neutral-atom quantum systems. To address this need, we have previously demonstrated the first integrated OP As capable of focusing radiated light to a focal spot in the radiative near field [J. Notaros, et al., " Near-Field-Focusing Integrated Optical Phased Arrays," 36 J. Lightwave Technol. 5912-5920 (2018)]. These focusing integrated OP As’ elements were encoded with a radially-dependent focusing phase distribution, thus allowing them to emit a focusing wavefront. However, because this radially-dependent phase was hard coded, this preliminary demonstration was limited to emission at only one focal plane above the chip. Thus far. an integrated OPA capable of emitting focusing beams with tunable variable focal distances (e.g., heights) has not been previously shown.

[0007] Spiral grating-based antennas integrated in an OPA configuration could offer a solution to enable emission of focusing beams with w avelength-tunable variable focal distances.

[0008] Previously, spiral-like electromagnetic structures have been utilized to enable unique radiation properties across the radio-frequency to optical spectrum. For example, bulk-optical spiral-like metasurfaces, metalenses, freeform lenses, and masks have been shown as polarization-sensitive or anomalous focusing structures with applications in imaging and the emission of light with orbital angular momentum (0AM). Similarly, spiral grating-based integrated optical antennas have been shown for the emission of 0AM beams, but the demonstration was limited to the emission of diverging beams in the far field and utilized only a single antenna. Moreover, similar spiral-like concepts have also been traditionally explored in the radio-frequency domain to realize wideband microwave antennas capable of 0AM emission. mit-26247pct

[0009] SUMMARY

[0010] An integrated optical phased array system and related methods are described herein, wherein various embodiments of the apparatus and methods may include some or all of the elements, features, and steps disclosed herein.

[0011] An integrated optical phased array system is disclosed, comprising at least one integrated optical phased array formed on a substrate and at least one spiral-shaped waveguide antenna mounted on or in the substrate. Each spiral-shaped waveguide antenna is positioned along a spiraled path with an outermost end remote from a center of the array and an innermost end near the center, and includes a plurality of antenna perturbations that emit light via scattering positioned along the spiral shape. The system is configured to emit wavelength-tunable focusing beams of variable focal distances when light is fed in from an end of the spiralshaped waveguide antenna.

[0012] In certain embodiments, the system includes a plurality of spiral-shaped waveguide antennas spiraling outward from a point near the center of the array. The system may further comprise a light source and a plurality of waveguides connecting the light source with the ends of the spiral-shaped waveguide antennas to deliver light from the light source to the antennas. Phase shifters may be positioned in the paths of the waveguides between the light source and the outermost ends of the spiral-shaped waveguide antennas to control the phase of light delivered to each antenna.

[0013] Other embodiments include a single bus waveguide that compactly encircles the array in a cascade-ring architecture, with evanescent tap couplers for tapping off a fraction of the available light in the bus waveguide for emission, and phase shifters for controlling the phase accumulation between adjacent antenna elements. Alternatively, the system may include a splitter tree configured to split an optical signal into a plurality’ of waveguides in a wound architecture, with each waveguide fed through a loop-back path to achieve length matching for each waveguide feeding each antenna in the spiral, and each waveguide routed from the respective phase shifter into the spiral-shaped path of one of the spiral-shaped waveguide antennas.

[0014] Further embodiments provide a path-length-matched splitter tree distributed around the array in a web pattern, with each splitter position chosen to path-length match each waveguide feeding the next splitter in the tree, and each waveguide fed through a phase shifter addressed by an independent control voltage before being routed to one of the spiral-shaped waveguide antennas. The array of spiral-shaped waveguide antennas may have dimensions less than 100 nm and may comprise at least four spiral-waveguide antennas spiraling outward from a common central region. The spiral-shaped waveguide antenna may be formed of silicon or silicon nitride, and the substrate may comprise silicon dioxide.

[0015] A processor-configured method of tunably focusing light in the radiative near field is also disclosed. The method includes utilizing the integrated optical phased array system, mit-26247pct

[0016] injecting coherent light of a first wavelength into one of the ends of each spiral-shaped waveguide antenna, propagating the light inward toward a spiral center or outward from the spiral center such that the perturbations collectively emit a first optical beam that focuses at a first focal distance from the array, changing the wavelength of the injected light to a second wavelength while maintaining relative drive phases of the perturbations to shift the focus to a second focal distance, and repeating the wavelength change to scan the focal distance without mechanical motion of the spiral-shaped waveguide antenna.

[0017] Additional embodiments of the method include injecting coherent light into an array of spiral-shaped waveguide antennas spiraling outward from a common central region, applying programmed electrical signals to integrated phase shifters disposed between successive spiralshaped waveguide antennas to impose a selectable azimuthal phase gradient that removes polarization-induced nulls at the focus, varying the wavelength over at least 40 nanometers to scan the focal distance over at least 0.3 millimeters, and producing a focused beam with orbital angular momentum that is positionable in three dimensions. The focused beam may be used, e.g., to trap microparticles in an optical-tweezers application, to initialize, manipulate, or read a trapped-ion or neutral-atom quantum bit, for chip-based 3D printing to cure a liquid resin and produce a solid programmed 3D structure, for light detection and ranging (LiDAR), or for w ireless optical communication using orbital angular momentum modes for channel encoding.

[0018] The following Detailed Description references the accompanying drawings, which form a part of this application, and which show, by way of illustration, specific exemplary implementations. Other implementations may be made without departing from the scope of the disclosure.

[0019] BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a simplified conceptual diagram of the spiral integrated optical phased array (OP A) 12 of a plurality of antennas 14 on a substrate 16, depicting emission of two focusing beams (Xi 18 and Z220) at two different focal distances corresponding to two different input wavelengths (not to scale).

[0020] FIG. 2 is a top-view schematic of a spiral grating-based waveguide antenna with critical dimensions annotated (not to scale), showing the light input 21 and the direction of light propagation 23.

[0021] FIG. 3 provides a comparison of the relative radial phase distribution of the desired parabolic focusing wavefront (22) and the exact wavefront formed by a spiral grating-based antenna (24) with Ao = 1480 nm, neff = 2.5, AAg= 616 nm, and = 12.5 pm / rad.

[0022] FIG. 4 plots a theoretically calculated focal distance of a spiral grating-based waveguide antenna as the input wavelength is varied for neff = 2.5, AAg= 616 nm, and / ? = 12.5 pm / rad, while also showing the vertical Bragg condition 26. mit-26247pct

[0023] FIG. 5 is a top-view schematic of the antenna aperture of a spiral integrated OP A 14 with N = 8 spiral grating-based waveguide antennas 14 with important parameters annotated (not to scale).

[0024] FIG. 6 shows simulated array -factor intensity emissions in the x-z plane and in the x-y focal plane for a spiral integrated OP A with To = 1500 nm and 1 = 0 (at left), To = 1500 nm and 1 = 1 (at center), and Ao = 1520 nm and t = 1 (at right), where On = 2n:ln / N all simulations assume N — 8, θ_min = 2, θ_max = 4, R_min = 25 μm, R_max = 50 μm, n_eff = 2.5, and A_g = 616 nm. The dashed line denotes the approximate focal plane.

[0025] FIG. 7 plots a simulated focal distance 28 and a theoretically predicted focal distance 30 versus input wavelength for a spiral integrated OPA assuming Rmax = 50 pm.

[0026] FIG. 8 plots a simulated radial spot size [full width at half maximum (FWHM)] versus input wavelength of the focal spot versus input wavelength, assuming Rmax = 50 pm.

[0027] FIG. 9 plots an axial spot size (FWHM) of the focal spot versus input wavelength, assuming Rmax = 50 pm.

[0028] FIG. 10 plots a simulated radial spot size (FWHM) versus aperture radius (Rmax) assuming f ~ 0.25 mm. All simulations for FIGS. 7-10 assume N = 8, 0mln ~ 2, dmax — 4, eff — 2.5, £ = 1, and A# = 616 nm.

[0029] FIG. 11 shows a simulated array -factor emission intensity in the x-y focal plane for a spiral integrated OPA with N — 8, Omin — 2, Omax — 4, Rmin — 25 J,m, Rmax — 50 pm, and Ao = 1500 nm.

[0030] FIG. 12 shows a simulated array-factor emission intensity in the x-y focal plane for a spiral integrated OPA with N = 8, θ_min = 1, θ_max = 4, Rmin = 12.5 pm, Rmax = 50 pm, and Ao = 1500 nm.

[0031] FIG. 13 shows a simulated array -factor emission intensity in the x-y focal plane for a spiral integrated OPA with N — 8, Omin ~ 2, Omax ~ 4, Rmin = 50 pm, Rmax = 100 pm, and Ao = 1470 nm.

[0032] FIG. 14 shows a simulated array-factor emission intensity in the x-y focal plane for a spiral integrated OPA with N — 32, Omin — 2, Omax — 4, R_min = 50 μm, R_max = 100 μm, and Ao = 1470 nm. Each of the simulations shown in FIGS. 11-14 assumes f ~ 0.2 mm, neff = 2.5, £ = 1, and Ag= 616 nm. Simplified top-view schematics of the spiral integrated OPA apertures are included as insets in white in each of FIGS. 11-14.

[0033] FIG. 15 (not to scale) is a simplified top- view schematic showing a wound spiral integrated OPA architecture with phase shifters 32, loopbacks 34 and with inputs 38 from a splitter tree (not shown). The spiral OPA aperture 36 is shown via the dashed line.

[0034] FIG. 16 is a distributed-splitter-tree spiral integrated OPA architecture (not to scale) with a single input 38 and splitters 40 on each of three sides.

[0035] FIG. 17 is a cascaded-ring spiral integrated OPA architecture (not to scale) with a single input 38, a bus wav eguide 42, phase shifters 32, and a tap coupler 44. mit-26247pct

[0036] FIG. 18 is a micrograph of a fabricated spiral integrated OPA system.

[0037] FIG. 19 shows experimentally measured intensity above the chip in the x-z plane and in the x-y focal plane for the fabricated spiral integrated OPA with Ao = 1515 nm and £ = 0 phase calibration (at left), with Ao = 1515 nm and 1 = 1 phase calibration (at center), and with Ao = 1525 nm and £ = 1 phase calibration (at right); the dashed lines denote the approximate focal plane.

[0038] FIG. 20 plots a comparison of the theoretically predicted focal distance 46 and experimentally measured focal distance 48 versus input wavelength for the fabricated spiral integrated OPA.

[0039] FIG. 21 shows a top view of a grating-based waveguide antenna 14 of a particular width 52 and with perturbations 53 in the form of indents of specific width 54 and length along the antenna 14. The light input 50 into the antenna 14 is shown.

[0040] In the accompanying drawings, like reference characters refer to the same or similar parts throughout the different views. The drawings are not necessarily to scale; instead, an emphasis is placed on illustrating particular principles in the exemplifications discussed below. For any drawings that include text (words, reference characters, and / or numbers), alternative versions of the draw ings w ithout the text are to be understood as being part of this disclosure; and formal replacement drawings without such text may be substituted therefor.

[0041] DETAILED DESCRIPTION

[0042] The foregoing and other features and advantages of various aspects of the invention(s) will be apparent from the following more particular description of various concepts and specific implementations within the broader bounds of the invention(s). Various aspects of the subject matter introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the subject matter is not limited to any particular manner of implementation. Examples of specific implementations and applications are provided primarily for illustrative purposes.

[0043] Unless otherwise herein defined, used, or characterized, terms that are used herein (including technical and scientific terms) are to be interpreted as having a meaning that is consistent with their accepted meaning in the context of the relevant art and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein. For example, if a particular composition is referenced, the composition may be substantially (though not perfectly) pure, as practical and imperfect realities may apply; e.g., the potential presence of at least trace impurities (e.g., at less than 1 or 2%) can be understood as being within the scope of the description. Likewise, if a particular shape is referenced, the shape is intended to include imperfect variations from ideal shapes, e.g., due to manufacturing tolerances. Percentages or concentrations expressed herein can be in terms of weight or volume. Processes, procedures, and phenomena described below can occur at ambient pressure (e.g., mit-26247pct

[0044] about 50-120 kPa— for example, about 90-110 kPa) and temperature (e.g., -40 to 6o°C— for example, about o-4O°C) unless otherw ise specified.

[0045] Although the terms, first, second, third, etc., may be used herein to describe various elements, these elements are not to be limited by these terms. These terms are simply used to distinguish one element from another. Thus, a first element, discussed below, could be termed a second element without departing from the teachings of the exemplar}’ implementations.

[0046] Spatially relative terms, such as “above,” “below,” “left,” “right,” “in front,” and “behind,” may be used herein for ease of description to describe the relationship of one element to another element, as illustrated in the figures. It will be understood that the spatially relative terms, as well as the illustrated configurations, are intended to encompass different orientations of the apparatus in use or operation in addition to the orientations described herein and depicted in the figures. For example, if the apparatus in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term “above” may encompass both an orientation of above and below. The apparatus may be otherwise oriented (e.g., rotated 90 degrees or at other orientations), and the spatially’ relative descriptors used herein should be interpreted accordingly. The term “about” can mean within ± 10% of the value recited. In addition, w here a range of values is provided, each subrange and each individual value between the upper and lower ends of the range is contemplated and, therefore, disclosed.

[0047] Further still, in this disclosure, when an element is referred to as being “on,” “connected to,” “coupled to,” “in contact with,” etc., another element, it may be directly on, connected to, coupled to, or in contact with the other element or intervening elements may be present unless otherwise specified.

[0048] Some of the terminology used herein is associated with particular implementations and is not intended to limit more generic exemplifications of the invention. As used herein, singular forms, such as those introduced with the articles, “a” and “an,” are intended to include the plural forms as well, unless the context indicates otherwise. Additionally, the terms “includes,” “including,” “comprises,” and “comprising” specify the presence of the stated elements or steps but do not preclude the presence or addition of one or more other elements or steps.

[0049] Herein, we propose and experimentally demonstrate spiral-based integrated optical phased arrays (OP As), enabling emission of focusing beams with tunable variable focal distances. To enable this functionality, we propose and develop the theory for an Archimedean-spiral grating-based waveguide antenna with a wavelength-tunable focal distance. Using these spiral grating-based waveguide antennas, we construct an azimuthally -tiled OPA aperture and simulate the theoretical performance of such an OPA to verify its w avelength-tunable focusing capabilities. Additionally’, we define and explore the design parameters and performance metrics of this new spiral integrated OPA aperture. Furthermore, to realize such an OPA aperture, we propose several novel OPA architectures for integration. Finally, we experimentally demonstrate mit-26247pct

[0050] an example spiral integrated OPA system fabricated using a standard silicon-photonics process, showing wavelength-tunable variable-focal-distance focusing emission. This work introduces a first-of-its-kind integrated OPA architecture not previously explored or demonstrated in literature and, as such, enables new functionality for emerging applications of OP As that require focusing operation.

[0051] I. Integrated Spiral Grating-Based Antenna: Theory and Design:

[0052] For an OPA to emit focused light, the light emitters in the plane of the OPA are encoded with a radially dependent hyperbolic phase distribution that matches a desired focal wavefront. In our prior work, this radial dependence was hard coded into the emitters by careful design of the grating-based antenna element pattern and the phase fed to each element. However, that approach limits the beam forming of the focal spot to only one focal plane, as the radial phase curvature cannot be modified after fabrication. In this section, we introduce a spiral gratingbased waveguide antenna with a radial phase curvature that depends on wavelength, thus enabling the emission of a focused beam having a focal distance that can be controlled by vary ing the input w avelength.

[0053] As shown in FIG. 1, this functionality can be achieved by curving an array 12 of gratingbased w aveguide antennas 14 along a spiraled path on a substrate. For this discussion, we treat each grating-based w aveguide antenna 14 as a subarray of elements with the same phases and positions as the antenna’s scattering perturbations 53 (see FIG. 21). The phase gradient sampled by the grating-based w aveguide antenna’s perturbations is equivalent to the component of the scattered w avevector in the longitudinal direction (the propagation direction) of the antenna (kz), which can be theoretically predicted in terms of its perturbation period (A5) and the weighted effective index (neff) of the propagating mode in the grating-based waveguide antenna structure:

[0054]

[0055] If we allow this phase to accumulate along a noncolinear path defined by a spiral, we can map the linear phase accumulation inherent to the grating-based waveguide antenna 14 onto a specified path that conformally maps to a desired phase curvature. As our focusing system has radial symmetry, we choose to define the points along the path taken by the grating-based waveguide antenna 14 with polar coordinates ( / ?, 9). Specifically, we consider a path for the grating that is defined by an Archimedean spiral with the polar equation:

[0056] R(9) = pe, (2) where the spiral rate ( / ?) is a design constant that can be modified to produce differently scaled spiral paths. As shown in FIG. 2, which also shows the input light 21 and the direction of light propagation 23 through the antenna 14, this path is defined with several design parameters in consideration. The grating-based waveguide antenna is formed along the path described in Eq. 2 mit-26247pct

[0057] with light fed in at the outermost end of the spiral, forming an angle (9 max) from the x axis, at which point it propagates inward toward the center until the grating is terminated at another angle (9m ), from the x axis. The angular domain of the spiral curve defines a sector angle (0), an inner radius defined by Rmtn = [39min, and an outer radius defined by Rmax = (39max. The grating-based waveguide antenna is defined to have an unperturbed waveguide width of ITT, with perturbations of width WPspaced at a pitch of A5= Lu+ LP, where Lu is the length of the unperturbed regions and LPis the length of the perturbed regions. At the end of the path, the antenna is terminated with an inverse taper to reduce undesired back reflections.

[0058] If we choose to feed the grating-based waveguide antenna from the outside of the spiral, the phase (< >) accumulated and emitted by a perturbation along this curve at any angle (9) can be represented as the product of the longitudinal component of the wavevector scattered by the grating-based waveguide antenna (kt) and the arc length traveled by the light inward through the spiral path:

[0059] - z3-j 4>( 0) J y / R( O")2+ R’ ( 0’ )2d0',

[0060]

[0061] where R(9) and R'(9) are the spiral path function and its first derivative, respectively. Evaluation of this expression yields an exact solution (< ><?) to the angular phase accumulation along the spiral path, which (neglecting a constant phase offset) can be represented as follows:

[0062] = (faJl + R2+ In + v / 1 + 02)). (4)

[0063]

[0064] To understand how this phase distribution can be used for focusing, we can further reduce Eq. 4 by keeping only the dominant term (9 ~l + ~92) and taking 9 > 1, giving the following equation:

[0065] (5)

[0066]

[0067] approximately mapping Eq. 4 to a parabolic function. The nature of this approximation can be visualized by plotting an example of Eq. 4 and Eq. 5 against each other as a function of radius (shown in FIG. 3, which includes a parabolic plot 22 and an exact plot 24). This approximation ultimately dictates 9mtn and will be discussed further in Sec. II, infra.

[0068] Using this approximation, we now evaluate this phase distribution by substitution of Eq.

[0069] 2 to find the approximate radial phase curvature ((j>fr.

[0070] (R\=hJ^LLfr=frd,1(2 )_AV (6)

[0071]

[0072] ’ 2 / 3 fr / 3 Av;From this, we observe that the approximate parabolic curvature of the radial phase distribution can be made more or less pronounced by tuning the wavelength illuminating the grating-based mit-26247pct

[0073] waveguide antenna. The theoretical focus of this parabolic phase curvature (and therefore the spiral grating-based waveguide antenna) in the Fresnel propagation regime (when f R) can be computed based on the coefficient associated with the parabolic phase term in Eq. 6 as:

[0074]

[0075] This equation represents a variable focus ( ) that depends on the geometry of the gratingbased waveguide antenna (neff, A.g), the path of the grating-based waveguide antenna ( / ?), and, most importantly, the free-space wavelength of the source (To). We plot this result for a hypothetical spiral grating-based waveguide antenna with a constant neff of 2.5, a grating perturbation pitch (A5) of 616 nm, and a spiral rate ( / ?) of 12.5 pm / rad in FIG. 4. We observe that the predicted spiral grating-based waveguide antenna will have a focus that is wavelength sensitive, increasing (as the wavelength is increased) to infinity at the vertical Bragg condition 26. where the phase curvature of the grating-based waveguide antenna is flat. Beyond this point, the curvature of the phase gradient is inverted, and a virtual focus beneath the antenna (negative focus) can be achieved.

[0076] II. Spiral Integrated OP A: Theory, Design, and Metrics:

[0077] One spiral grating-based waveguide antenna, while capable of focusing light at the desired point, is too sparse to form a well-defined focal spot with useful resolution. In this section, we propose an azimuthal tiling scheme to form an integrated OPA using the spiral grating-based waveguide antennas discussed in Sec. I. Furthermore, we explore the parameter space of this spiral integrated OPA by evaluating a reference design.

[0078] Note that providing an array of antennas enables greater manipulation of the light emission (e.g., shifting of phases and switching between different modes of orbital angular momentum). However, the use of just a single antenna can still provide variable focal-distance functionality via wavelength tuning (but without the added functionality of switching between different modes of orbital angular momentum).

[0079] In this scheme (depicted in FIGS. 1 and 5), the spiral grating-based waveguide antennas 14 are rotated about the origin and repeated N times to form the antenna array aperture. The antennas are fed with light from the outside of each spiral curve (alternatively, light can be fed from the inside of each spiral curve), with each antenna having a starting phase of

[0080]

[0081] The antennas may have a minimum feature dimension in the 10's of nanometers (e.g., less than 100 nm). The length of the antennas are typically on the order of 100's of micrometers; larger or smaller antenna lengths may also be used, as the array size is primarily determined by design considerations, such as available chip area, emission aperture, or desired beam characteristics, rather than by any inherent physical limitation.

[0082] To successfully integrate the spiral grating-based waveguide antennas into this array configuration, we must constrain some of the properties of the antennas. Firstly, we constrain the mit-26247pct

[0083] sector angle (0) to limit the undesired effects of allowing the grating to wrap over more than half a rotation. If the antenna spans over a sector angle of more than it rad, the geometrical rotation of the perturbations at the end of the antenna with respect to the perturbations at the beginning of the antenna will approach n rad. If this occurs, the light at the focus emitted by perturbations at opposite ends of the antenna would be rotated out of phase, resulting in an undesirable null (or OAM) at the focus. For the sake of this demonstration, we limit 0 to 2 rad.

[0084] Next, the minimum angle (Omin) defining the grating-based waveguide antenna’s spiral path is dictated by limiting the error in the concavity of the exact phase distribution (< / >e) of the integrated spiral waveguide antenna when compared to the approximate (desired) parabolic focusing phase distribution (< / >a) discussed previously. Analytically, we define this concavity as the second derivative of the phase distribution with respect to polar angle. We choose to evaluate these expressions with respect to 6 in order to determine a value for Omin [because our chosen spiral function (Eq. 2) is a linear function of 0 (an Archimedean spiral), the phase concavity with respect to 0 and radius are linearly related]. We define the concavity error (e) as the unitless absolute value of the difference in the concavity between the exact and approximate phase distributions relative to the approximate phase concavity:

[0085] d~< / >ad2< / )ede2de2\ d2

[0086] (8) d2< / >aIdO2

[0087]

[0088] de2Equation 8 can be evaluated over the polar angle (0) to find the minimum polar angle (Omin) that corresponds to a desired worst-case concavity error. In our reference example, we limit the concavity error to approximately 0.1. corresponding to a Omin of approximately 2 rad. However, in certain regimes, the benefits of filling the center of the array to a smaller inner radius can mandate a relaxed concavity error constraint and will be explored further later in this section.

[0089] With 0 and Omin constrained, we find the value for Omax from the expression

[0090] Omax = Omin + 0. In our reference example, Omax is found to be 4 rad. Finally, we chose a desired aperture diameter to inform the value for Rmax. In this demonstration, choosing an aperture diameter of 100 pm, we constrain Rmax to 50 pm. Having already constrained Omax, we can then determine a value for / ? that satisfies Eq. 2 (? = Rmax I Omax ). In this case, is found to be 12.5 pm / rad. With / ? determined, Rmin can also be evaluated using Eq. 2, and is found to be 25 pm in this case.

[0091] Having determined the grating geometry of our reference design, we define a spiral integrated OPA having N = 8 antennas 14 (similar to FIG. 5) with a weighted effective index neff) of 2.5 and a perturbation pitch (A5) of 616 nm. We now use this hypothetical system to explore the parameter space of this design. To facilitate this exploration, we model the spiral mit-26247pct

[0092] integrated OPA system in the MATLAB computing platform (from The MathWorks, Inc., of Natick, Massachusetts, US), motivated by the theory developed in Sec. I. We propagate the light emitted by the antennas 14 into the radiative near field of the OPA using standard numerical Rayleigh-Sommerfeld propagation techniques, taking into consideration the following points. Firstly, each antenna 14 is fed with an independent starting phase of On, as illustrated in FIG. 5. Furthermore, the model makes some small approximations for simplicity. It does not consider waveguide dispersion in the grating-based waveguide antenna structure (neff is held constant) as it has negligible effects on the simulation outcome. Similarly, bending of the grating-based waveguide antenna 14 is assumed to have a negligible impact on the weighted effective index of its propagating mode. Finally, each grating perturbation is modeled as an isotropic light emitter that has a phase determined by the exact phase distribution (< >e) derived in Sec. I, where its amplitude contribution to all points in the radiative near field of the OPA is approximated to be constant. The polarization of each emitter is assumed to be oriented within the plane of the OPA normal to the spiral curve. The simulation model produces intensity plots of the spiral integrated OPA’s array factor in both the focal plane (x-y plane) and the x-z plane of the simulation.

[0093] First, we run the simulation with each grating-based waveguide antenna fed in phase. The simulation results are shown in FIG. 6 (at left). Although a pattern forms at a focal distance of 0.18 mm as expected, a null in the center of the focus is observed. As each w aveguide grating-based w aveguide antenna is rotated about the origin, so is the polarization direction of its radiated field at the focus. As a result, if all elements in the array are fed in phase, the contributions to the field at the focus from opposing elements will be effectively out of phase, resulting in a null at the focus. However, for most applications, a focal "‘spot” is more desirable and can be achieved by allowing the starting phase in each grating-based w aveguide antenna to wrap such that On =

[0094]

[0095] where I>n is the input phase to the nth antenna, I is an integer representing different emission regimes, n is an integer representing the index of each antenna, and N is the total number of antennas. When T = 1, the null is removed and replaced with a well-defined spot.

[0096] Phasing of the elements in this way ensures that opposing light emitters are fed completely out of phase to counteract the effects of their rotating polarizations. This can be clearly observed in the simulation outputs shown in FIG. 6 (at center and right). When £ = 1, the array forms mostly left-hand-circularly-polarized (LHCP) light at the focus (much like a turnstile antenna) and right-hand-circularly-polarized (RHCP) light w hen / = -1. The polarization of emission from this array may be used to enable the generation of tunable higher-order focused 0AM beams. As such, each element is subject to a phase shift to encode the element phase ( n) and gain control over the field profile at the focus. This phase shift can be achieved passively by geometrically skewing the spiral paths or with passive phase-delay structures. However, active phase shifters are ideal for this function, as they both allow' for active encoding of the element phase distributions to change / (to electrically tune the field mit-26247pct

[0097] profile at the focus) and are advantageous for correcting random fabrication-variation-induced phase errors that can occur as the array is scaled in size. Accordingly, the phase shifters are configured to control the relative phase of light delivered to each spiral antenna to compensate for fabrication-induced phase variations and to selectively encode phase wrappings for a desired I, thereby enabling adjustment between different focusing regimes (e.g., a central null or a centered focal spot). The primary focusing behavior is determined by the geometry of the spiral antenna itself, which defines the hyperbolic phase front required for focusing.

[0098] Next, we vary the simulation wavelength to confirm our theoretical understanding of the spiral integrated OPA’s capability to achieve wavelength-tunable focal distance. Altering the wavelength from 1500 nm to 1520 nm is shown to have the desired effect of increasing the focal distance of the spot formed by the array to 0.46 mm, as shown in FIGS. 6 (at right). To further explore this effect, we sweep the simulation wavelength and determine the focal distance numerically as a function of wavelength over a range from 1480 nm to 1520 nm. The corresponding results are shown in FIG. 7 and match closely with the theoretical estimate from Sec. I, albeit with some error induced by the fitness of our phase approximation.

[0099] As the wavelength is tuned and the focal distance changes, diffraction theory also mandates that the spot size will change. To quantify this, we sweep the simulation wavelength and record the radial spot size in the focal plane, as well as the axial spot size along the z'axis.

[0100] FIGS. 8 and 9 show that both the radial and axial full-width-at-half-maximum (FWHM) spot sizes increase as the wavelength is increased. This defines an inherent tradeoff of focal distance with spot size as expected.

[0101] In addition, we scale the spiral integrated OPA’s aperture size by scaling the parameter Rmax. Specifically, we scale the value of / ? while leaving all other angle and grating parameters fixed. For each simulated aperture size, the focal distance is held approximately constant at 250 pm by varying the simulation wavelength alongside ft in accordance with Eq. 7. / ? is scaled to render a range of OPA apertures with radii varying from 50 pm to 125 pm. As expected, the inverse relationship between aperture size and radial spot size is apparent in the simulation outputs plotted in FIG. 10. This aperture size can be further increased so long as the focal distance desired remains reasonably within the Fresnel focusing regime. Beyond the approximate limit where the array diameter exceeds the focal distance, the spot is poorly resolved due to an error in the Fresnel approximation.

[0102] Scaling the spiral integrated OPA aperture size without filling the gaps between antennas results in a reduction of the OPA’s fill factor. Interestingly, we do not observe the formation of true grating lobes along the focusing contour (as expected from a traditional OPA architecture) as a result of the aperiodic light emiter placement inherent to the spiral geometry'. Nevertheless, a sparser emiter arrangement wall give rise to increased sidelobe energy at distances far away from the z axis. mit-26247pct

[0103] To explore this effect, we simulate the optical intensity in the same focal plane (at a focal distance of 0.2 mm) for a variety of different spiral integrated OPA parameters. For each parameter, we explore changes in the focal-plane pattern and in the approximate focusing efficiency (77), which we conservatively define as the power in the focal plane integrated within a circle whose radius coincides with the first null of the focal spot as a percentage of the total radiated power. Note that, since these simulations only consider the array factor of the OPA and do not account for the element factor of each grating perturbation, these efficiency values are a low conservative estimate. Furthermore, because our grating-based waveguide antennas are vertically symmetric, they radiate equally upward and downward; this fundamentally limits 77 to 50% for this particular antenna geometry.

[0104] Beginning with our reference design, we observe (in FIG. 11) that the sidelobes resulting from reduced fill factor appear in annular rings around the central focal spot. This configuration has a focusing efficiency (77) of approximately 1%. These sidelobes can be marginally suppressed by filling in the center of the array (shown in FIG. 12). This increases the 77 to approximately 1.4%, albeit sacrificing some phase error, as described previously. The effects of the OPA's sparsity are more pronounced as the array is scaled in size while fixing the number of elements. In FIG. 13, we display the focal-plane intensity7of a spiral integrated OPA that has all the same parameters as our initial reference design but scaled in radius by a factor of two. We observe that the array is too sparse and that the beam formed has a poor sidelobe rejection ratio. This reduces the 77 to less than 0.5%. Since there are large gaps between the antennas, we can remedy this by placing more antennas in the gaps around the aperture, thus increasing the fill factor. The resulting focal-plane intensity from simulation of a similar array now having 32 antenna elements is depicted in FIG. 14. Notably, a considerable amount of the sidelobe energy can be removed from the focal plane with additional antennas, thus restoring the focusing efficiency to approximately 1.8%. By controlling each of these design parameters, this spiral integrated OPA system can be tailored to meet the requirements of a wide variety of applications requiring focused light emission from a chip.

[0105] III. Spiral Integrated OPA: System Architectures:

[0106] In Sec. I and Sec. II, we discussed the illumination of each spiral grating-based waveguide antenna in the spiral integrated OPA abstractly. The spiral integrated OPA inherently relies on having a specific waveguide feed structure to distribute on-chip light to each antenna in the array. In this section, we propose a variety of ways that such an OPA can be fed.

[0107] Generally, most integrated OPA architectures can be grouped into two subcategories: splitter-tree-based architectures and cascade-fed architectures. Splitter trees lend themselves well to feeding arrays of integrated optical antennas because they scale reasonably and maintain phase matching over a wide bandwidth as a result of being inherently path-length matched. One potential way a splitter-tree-based feed could be implemented for a spiral integrated OPA takes the form of a “wound” architecture. In this architecture (shown in FIG. 15), light is coupled on mit-26247pct

[0108] chip and routed to a splitter tree that splits the optical signal into N waveguides. Each resulting waveguide is then fed through a loopback path to length-match each waveguide feeding each antenna in the spiral. This length-matching avoids imparting a wavelength-sensitive phase offset between each antenna. Each resulting waveguide is then fed through a phase shifter driven with an independent control voltage. After a phase shift is imparted, the light is routed into an array of waveguides that trace the wound paths of each antenna feed, eventually illuminating each antenna in the array. This architecture is somewhat area-efficient but requires a significant amount of additional area to successfully path-length match and feed each element in the array. Moreover, an array of N elements will involve N control voltages.

[0109] Another potential splitter-tree-based feed architecture is the "di s tn buted-spl i tter-tree" architecture. In this architecture (depicted in FIG. 16), an input waveguide is split into N waveguides using a specifically path-length-matched splitter tree distributed around the aperture in a web pattern. Each splitter position is chosen to path-length match each waveguide feeding the next splitter in the tree. Before each spiral arm, each of the N waveguides is fed through a phase shifter addressed by an independent control voltage. After imparting a phase shift, each waveguide is routed to its respective antenna. This architecture is inherently path-length matched as well but requires a larger area overhead to implement successfully compared to the wound architecture. In general, both of these splitter-tree architectures do not scale efficiently, both requiring A control voltages and occupying a large amount of area outside of the OPA’s emitting aperture. One redeemable feature of these splitter-tree-based architectures is, however, their abi 1 i ty to maintain phase calibration over a broad bandwidth. This allows for the spiral integrated OP A to shift its focus over a wide range using wavelength tuning without needing to reprogram each phase shifter.

[0110] A “cascaded-ring” spiral integrated OPA architecture offers a potential solution to the scaling issues inherent to the splitter-tree-based architectures. In this architecture (shown in FIG.

[0111] 17), a single bus waveguide is routed in a circular path around the spiral integrated OPA. At each antenna, an evanescent coupler taps off a fraction of the available light in the bus waveguide for emission. Uniform power distribution into each antenna element can be achieved using common cascade-architecture apodization techniques. In between each tap coupler, a phase shifter in the bus waveguide is used to control the phase accumulation between adjacent antenna elements. In this way, all phase shifters in the ring can be driven with the same single voltage to reduce the control complexity of the spiral integrated OPA. As this feed structure compactly fits around the spiral integrated OPA emission aperture and occupies very' little additional area, it is much more suitable for scalable and dense spiral OPA integration - so long as the sector distance between each tap coupler in the bus waveguide ring is long enough to support the desired phase shifter. However, the inherent path-length mismatch between antennas in the cascaded-ring architecture may require readjustment of the phase-shifter voltages as the mit-26247pct

[0112] focus is shifted with wavelength. More optimized versions of these architectures could be explored in future work.

[0113] IV. Spiral Integrated OPA: Fabricated System and Experimental Results:

[0114] Next, we apply the theory and architectures developed in Sec. I and Sec. II to experimentally demonstrate a spiral integrated OPA fabricated in the American Institute for Manufacturing (AIM) Photonics Active process.

[0115] Our fabricated design targets an aperture diameter of 100 pm and uses N = 8 gratingbased waveguide antennas arranged with the same geometry as described in Sec. II. Each grating-based waveguide antenna is formed out of a 610-nm-wide (Wu) and 220-nm-thick silicon waveguide with 504-nm-wide (V / P) perturbations spaced at a pitch (A5) of 616 nm. Each perturbation has a length (LP) of 316 nm, with the remaining length in the pitch occupied by 300-nm-long Lu unperturbed regions. These grating-based waveguide antennas have a weighted effective index (neff) of approximately 2.5 at a wavelength of 1550 nm, similar to the antennas explored theoretically in Sec. I and Sec. II. Rmax is set to be 50 pm, and constraining the sector angle range between 2 and 4 rad determines to be 12.5 pm / rad. These parameters define the exact path taken by the spiral given Eq. 2 and should perform well for focal distances (f) greater than 0.1 mm.

[0116] The antennas are fed with a distributed splitter tree (described in Sec. Ill) including seven silicon multi-mode-interference splitters. Before each antenna, we utilize an integrated thermo-optic phase shifter (provided in the AIM active PDK) to control the phase of each grating-based waveguide antenna element. One electrode of each phase shifter is connected to a common ground bus routed around the structure that interfaces with one of the electrical pads associated with this system. The signal electrodes corresponding to each phase shifter are routed to the eight remaining electrical pads. A micrograph of the chip containing the fabricated spiral integrated OPA system is shown in FIG. 18.

[0117] To test the performance of the spiral integrated OPA system, we constructed an experimental setup, including power supplies for phase-shifter modulation, a microscope train, a microchip, optical fiber, and electronic probes. The experimental setup is based on a custom infrared microscope. We derive the optical signal for this experiment with a benchtop tunable laser routed through a single-mode optical fiber. This fiber is routed through an off-chip polarization controller, and then the light is coupled onto the chip and fed into the spiral integrated OPA system using an integrated edge coupler. Electrical probes are landed on the chip to control each of the 8 integrated phase shifters independently. The control voltages for each phase shifter are derived from a set of bench-top programmable direct-current power supplies and commanded by a Python script. The emission from the spiral integrated OPA is imaged by the microscope train, which can be translated vertically to capture a transverse (x-y plane) cross section of the emitted beam over a range of distances (z) above or below the chip. mit-26247pct

[0118] Before data is captured, we phase calibrate the spiral integrated OPA using a simple local-search-based calibration algorithm. However, in this case, the microscope stage is translated vertically so that the approximate focal plane is imaged, so that the calibration is performed to optimize the emission in the expected focal plane in the radiative near field of the chip (instead of in the far field as is typically done). Additionally, we modify the figure of merit in the calibration routine to be the maximum value in the two-dimensional cross correlation of a desired focal-plane pattern (derived from the MATLAB model described in Sec. II) and the experimentally captured image of the spiral integrated OPA’s focal plane captured by the microscope. For this architecture, this calibration needs to be performed only once whenever T is changed to encode the necessary element phase distribution and to account for random fabrication-variation-induced phase errors. For non-path-length -matched architectures (such as the cascaded-ring architecture), this calibration would need to be redone over a range of wavelengths to account for dispersion in the bus waveguide around the aperture.

[0119] First, we calibrate the spiral integrated OPA to produce the beam associated with f - 0 at a wavelength of 1515 nm. Then, we sweep the vertical translation of the microscope over a z-axis range of 1.27 mm, starting at the plane of the spiral integrated OPA elements and translating upward in steps of 0.0127 mm. For each step, the intensity in the x-y plane is captured. FIG. 19 (at left) depict the x-y- and x-z-plane cross sections of the emission from the fabricated system in this state. Here, we observe a focusing beam having a null in the center as predicted theoretically in Sec. II.

[0120] Next, we recalibrate the phases of the elements to form a spot ( / = 1). We note that the OPA can successfully form a spot at a focal distance of approximately 0.21 mm (depicted in FIG. 19 (at center). In this state, the radial and axial FWHM spot sizes are measured to be approximately 3 pm and 0.1 mm, respectively.

[0121] Then, without changing the phase calibration, we tune the wavelength of the laser source to 1525 nm and cross-section the emission pattern of the spiral integrated OPA again, the results of which are depicted in FIG. 19 (at right). At this longer wavelength, we observe the focus to shift up to a distance of 0.57 mm, exhibiting radial and axial FWHM spot sizes of approximately 7 pm and 0.4 mm, respectively. We also note that the emission patterns displayed in FIG. 19 agree well with those predicted by our theoretical model in Sec. II.

[0122] Finally, we explore the wavelength-tuning dynamics of the focus by taking (without changing the phase calibration) cross sections of the spiral integrated OPA's emission patterns over a range of wavelengths from 1500 nm to 1560 nm in 5-nm steps. For each wavelength, we locate the focus of the array and plot the resulting (experimentally measured) estimate of focus distance 48 as a function of wavelength in FIG. 20. For wavelengths beyond the vertical Bragg condition, a virtual focus was found beneath the plane of the chip by incrementing the focus of the microscope downward. In FIG. 20, we also plot the theoretically predicted focal distance 46 as a function of wavelength, assuming the same parameters discussed in Sec. I. The measured mit-26247pct

[0123] wavelength-tuning curve 48 closely resembles the nature of this theoretically predicted focus curve 46, albeit with some differences due to both a fabrication-bias-induced shift in the gratingbased waveguide antenna’s weighted effective index and waveguide dispersion not being considered in the theoretical focal-distance calculation 46. In general, all behaviors of the fabricated spiral integrated OPA system closely match our theoretical model.

[0124] V. Conclusion:

[0125] Herein, we proposed and experimentally demonstrated spiral-based integrated OP As, enabling emission of focusing beams with tunable variable focal distances. To enable this functionality, we proposed and developed the theory for an Archimedean-spiral grating-based waveguide antenna with a wavelength-tunable focal distance. Using these spiral grating-based waveguide antennas, we constructed an azimuthally tiled OPA aperture and simulated the theoretical performance of such an OPA to verify its wavelength-tunable focusing capabilities. Additionally, we defined and explored the design parameters and performance metrics of this new spiral integrated OPA aperture. Furthermore, to realize such an OPA aperture, we proposed several novel OPA architectures for integration. Finally, we experimentally demonstrated an example spiral integrated OPA system fabricated in a standard silicon-photonics process, showing wavelength-tunable variable-focal-distance focusing emission.

[0126] In additional exemplifications, using spiral grating-based waveguide antennas and spiral integrated OP As can enhance the functionality of the architectures presented here by enabling emission of higher-order structured light with orbital angular momentum (OAM), enabling emission of focusing beams that can be positioned arbitrarily in three dimensions, utilizing more optimal spiral paths that may enable focusing beyond the Fresnel limit, and enabling larger-scale demonstrations of these spiral integrated OP As through further feed-structure and antennaelement development. Moreover, the spiral integrated OPAs developed in this work may be applied to a variety of applications. For example, the polarization diversity of the spiral integrated OPAs may be utilized to enable novel advanced cooling and detection schemes for integrated-photonics-based trapped-ion or neutral-atom quantum systems. Similarly, the variable-focal-distance functionality of the spiral integrated OPAs may be applied to enable volumetric chip-based 3D printing or multi-plane chip-based optical tweezing of cells -capabilities not previously attainable with prior integrated OPA-based demonstrations.

[0127] This integrated OPA architecture enables an advantageous beam-steering degree of freedom for near-field-focusing integrated OPAs. In particular, the beam can be controlled in the near-field regime of the chip. As such, this w ork enables advancements in functionality for new emerging applications of integrated OPAs that require focusing operation. For example, the integrated OPA can be used as integrated optical tweezers for biophotonics [see T. Sneh, et al., " Optical tw eezing of microparticles and cells using silicon-photonics-based optical phased arrays," 15 Nat Commun 8493 (2024)], wherein microparticles can be held and manipulated by the small forces produced by the incident light beam from the OPA. In additional mit-26247pct

[0128] exemplifications, the integrated OP As can be used in chip-based 3D printers, wherein the light beam produced by the OPA cures a liquid resin to produce a programmed 3D structure of a desired shape [see S. Corsetti, et al., " Silicon-photonics-enabled chip-based 3D printer," 13 Light Sci Appl 132 (2024)].

[0129] Further, the integrated OPA can be used in trapped-ion or neutral-atom quantum systems [see S. Corsetti, et al., " Integrated Polarization-Diverse Grating Emitters for Trapped-Ion Quantum Systems," Frontiers in Optics JTu7A.3 (2023); R. J. Niffenegger, et al., " Integrated multi- wavelength control of an ion qubit," 586 Nature 7830, 538-542 (2020); A. Hattori, et al., " Integrated-Photonics-Based Architectures for Polarization-Gradient and EIT Cooling of Trapped Ions," in Frontiers in Optics + Laser Science 2022 (FIO. LS) Optica Publishing Group FM4B.3 (2022); and A. Hattori, et al.. " Integrated visible-light polarization rotators and splitters for atomic quantum systems." 49 Opt. Lett. 1794-1797 (2024)], wherein quantum bits (qubits, which are the basic unit of quantum information, which can exist in a superposition of states — a qubit can be 0, 1. or any portion of both simultaneously, and which can engage in quantum entanglement), for example, can be initialized, controlled / manipulated, and read out, by focused light beams produced by the OPA; light-qubit interactions can be used for, e.g., quantum communication, quantum computing, quantum networks, and quantum metrology7.

[0130] Further still, the OPA can also be used for light detection and ranging (LiDAR), wherein the OPA-generated light is sent out and the time required for the light to return after bouncing back after hitting an object is measured; via this scanning of the surrounding environment with the OPA-generated light, the surrounding environment can be mapped. The near-fi eld-focusing operation of this integrated OPA would be particularly advantageous for short-range LiDAR applications.

[0131] In yet another application, the OPA can be used to direct light for optical wireless communications using the light beam as the medium for communication signals. The 0AM-generation capabilities of this integrated OPA can be particularly advantageous for optical wireless communications in turbulent conditions.

[0132] The OPA of this disclosure can produce a tunable focused light beam, wherein the distance of the focal point from the OPA can be adjusted by changing the wavelength of the light. For some applications, such as 3D printing, a broad range of wavelengths can serve the purpose of curing the resin; in other applications, such as interacting with qubits, the range of suitable light wavelengths may be significantly more restricted. The OPA can also generate orbital angular momentum (0AM), where the light w ave spirals as it propagates and generates a twisting light polarization.

[0133] It should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific implementations described above. The specific implementations described above are disclosed as examples only. mit-26247pct

[0134] In describing implementations herein, specific terminology is used for the sake of clarity. For the purpose of description, specific terms are intended to at least include technical and functional equivalents that operate in a similar manner to accomplish a similar result.

[0135] Additionally, in some instances where a particular implementation includes a plurality of system elements or method steps, those elements or steps may be replaced with a single element or step. Likewise, a single element or step may be replaced with a plurality of elements or steps that serve the same purpose. Further, where parameters for various properties or other values are specified herein for implementations, those parameters or values can be adjusted up or down by 1 / lOOth, l / 5Oth, l / 20th, l / 10th, l / 5th, l / 3rd. 1 / 2, 2 / 3rd, 3 / 4th. 4 / 5th, 9 / 10th, 19 / 20th. 49 / 50th, 99 / 1 OOth, etc. (or up by a factor of 1, 2, 3. 4, 5, 6, 8. 10. 20. 50, 100, etc.), or by rounded-off approximations thereof or within a range of the specified parameter up to or down to any of the variations specified above (e.g., for a specified parameter of 100 and a variation of 1 / 1 OOth, the value of the parameter may be in a range from 0.99 to 1.01), unless otherwise specified. Further still, where methods are recited and where steps / stages are recited in a particular order — with or without sequenced prefacing characters added for ease of reference — the steps / stages are not to be interpreted as being temporally limited to the order in which they are recited unless otherw ise specified or implied by the terms and phrasing.

[0136] Additional examples consistent with the present teachings are set out in the following numbered clauses:

[0137] 1. A system comprising at least one integrated optical phased array, comprising:

[0138] a substrate; and

[0139] at least one spiral-shaped w aveguide antenna mounted on or in the substrate, wherein the spiral-shaped w aveguide antenna is positioned along a spiraled path with an outermost end remote from a center of the array and an innermost end proximate the center of the array, wherein each spiral-shaped waveguide antenna includes a plurality of antenna perturbations that emit tight via scattering positioned along the spiral shape, and wherein the system is configured to emit wavelength-tunable focusing beams of variable focal distances when tight is fed in from an end of the spiral-shaped waveguide antenna.

[0140] 2. The system of clause 1, wherein the system comprises a plurality of the spiral-shaped waveguide antennas spiraling outward from a point proximate the center of the array. 3. The system of clause 2, further comprising:

[0141] a tight source; and

[0142] a plurality of waveguides connecting the tight source w ith the ends of the spiralshaped waveguide antennas to deliver tight from the light source to the waveguide antennas.

[0143] 4. The system of clause 3, further comprising phase shifters positioned in the paths of the waveguides between the tight source and the outermost ends of the spiral-shaped waveguide antennas. mit-26247pct

[0144] 5. The system of clause 2, further comprising a single bus waveguide that compactly encircles the array in a cascade-ring architecture, wherein the single bus waveguide comprises:

[0145] evanescent tap couplers, wherein each coupler taps off a fraction of the available light in the bus waveguide for emission; and

[0146] phase shifters, wherein each phase shifter controls the phase accumulation between adjacent antenna elements.

[0147] 6. The system of clause 2 or 3, further comprising a splitter tree configured to split an optical signal into a plurality of waveguides in a wound architecture, wherein:

[0148] each waveguide is fed through a loop-back path to length match each waveguide feeding each antenna in the spiral;

[0149] each resulting waveguide is fed through a phase shifter driven with an independent control voltage; and

[0150] each resulting waveguide is routed from its respective phase shifter into the spiral-shaped path of one of the spiral-shaped waveguide antennas to illuminate that spiral-shaped waveguide antenna.

[0151] 7. The system of clause 2 or 3, further comprising a path-length-matched splitter tree distributed around the array in a web pattern, wherein:

[0152] each splitter position is chosen to path-length match each waveguide feeding the next splitter in the tree;

[0153] each of the waveguides is fed through a phase shifter addressed by an independent control voltage; and

[0154] after passing through the phase shifter, each waveguide is routed to one of the spiral-shaped waveguide antennas.

[0155] wherein the path-length matching provides phase matching among all spiralshaped waveguide antennas over a w avelength tuning range.

[0156] 8. The system of any of clauses 2-7, wherein the array of spiral-shaped waveguide antennas has dimensions less than 100 nm.

[0157] 9. The system of any of clauses 2-8, wherein the array of spiral-shaped waveguide antennas comprises at least 4 spiral-waveguide antennas spiraling outward from a common central region.

[0158] 10. The system of any of clauses 1 -9, wherein the spiral-shaped w aveguide antenna is formed of at least one of silicon and silicon nitride, and wherein the substrate comprises silicon dioxide on or in which the spiral-shaped waveguide antenna is mounted.

[0159] 11. A processor-configured method of tunably focusing light in the radiative near field, the method comprising: mit-26247pct

[0160] utilizing the system of claim 1, including the at least one spiral-shaped waveguide antenna, and;

[0161] injecting coherent light of a first wavelength into one of the ends of each spiralshaped waveguide antenna;

[0162] propagating the light inward toward a spiral center or outward from the spiral center such that the perturbations collectively emit a first optical beam that focuses at a first focal distance from the array;

[0163] changing the wavelength of the injected light to a second wavelength while maintaining relative drive phases of the perturbations, thereby shifting the focus to a second focal distance different from the first focal distance; and

[0164] repeating the wavelength change to scan the focal distance without mechanical motion of the spiral-shaped waveguide antenna.

[0165] 12. The processor-configured method of clause 11, wherein the coherent light is injected into an array of the spiral-shaped waveguide antennas, wherein each of the spiral-shaped waveguide antennas spiral outward from a common central region.

[0166] 13. The processor-configured method of clause 12, further comprising applying programmed electrical signals to integrated phase shifters disposed between successive spiral-shaped waveguide antennas to impose a selectable azimuthal phase gradient that removes polarization-induced nulls at the focus.

[0167] 14. The processor-configured method of clause 12 or 13, wherein the focused beam has orbital angular momentum and is positionable in three dimensions.

[0168] 15. The processor-configured method of any of clauses 12-14, further comprising:

[0169] directing the beam for wireless optical communication, wherein light in the beam is used as a medium for communication signals; and

[0170] using orbital angular momentum modes enabled by the array as an encoding for various communication channels.

[0171] 16. The processor-configured method of any of clauses 11-15, wherein the wavelength is varied over at least 40 nanometers to scan the focal distance over at least 0.3 millimeters.

[0172] 17. The processor-configured method of any of clauses 11-16, wherein the focused beam produced at the scanned focal distance is used to trap microparticles in an optical- tweezers application.

[0173] 18. The processor-configured method of any of clauses 11-17, further comprising using the focused beam to initialize, manipulate, or read a trapped-ion or neutral-atom quantum bit.

[0174] 19. The processor-configured method of any of clauses 11-16, wherein the focused beam is used for chip-based 3D printing, the method further comprising using the focused beam to cure a liquid resin to produce a solid programmed 3D structure of a desired shape. mit-26247pct

[0175] 20. The processor-configured method of any of clauses 11-16, further comprising using the focused beam for light detection and ranging (LiDAR).

[0176] While this invention has been shown and described with references to particular implementations thereof, those skilled in the art will understand that various substitutions and alterations in form and details may be made therein without departing from the scope of the invention. Further, other aspects, functions, and advantages are also within the scope of the invention, and all implementations of the invention need not necessarily achieve all of the advantages or possess all of the characteristics described above. Additionally, steps, elements, and features discussed herein in connection with one implementation can likewise be used in conjunction with other implementations. The contents of references, including reference texts, journal articles, patents, patent applications, etc., cited throughout the text are hereby- incorporated by reference in their entirety for all purposes; and all appropriate combinations of implementations, features, characterizations, and methods from these references and the present disclosure may be included in implementations of this invention. Further still, the components and steps identified in the Background section are integral to this disclosure and can be used in conjunction with or substituted for components and steps described elsewhere in the disclosure within the scope of the invention.

Claims

mit-26247pctCLAIMSWhat is claimed is:

1. A system comprising at least one integrated optical phased array, comprising:a substrate; andat least one spiral-shaped waveguide antenna mounted on or in the substrate, wherein the spiral-shaped waveguide antenna is positioned along a spiraled path with an outermost end remote from a center of the array and an innermost end proximate the center of the array, wherein each spiral-shaped waveguide antenna includes a plurality of antenna perturbations that emit light via scattering positioned along the spiral shape, and wherein the system is configured to emit wavelength-tunable focusing beams of variable focal distances when light is fed in from an end of the spiral-shaped waveguide antenna.

2. The system of claim 1, wherein the system comprises a plurality of the spiral-shaped waveguide antennas spiraling outward from a point proximate the center of the array.

3. The system of claim 2, further comprising:a light source; anda plurality of waveguides connecting the light source with the ends of the spiralshaped waveguide antennas to deliver light from the light source to the waveguide antennas.

4. The system of claim 3, further comprising phase shifters positioned in the paths of the waveguides between the light source and the outermost ends of the spiral-shaped waveguide antennas.

5. The system of claim 2, further comprising a single bus waveguide that compactly encircles the array in a cascade-ring architecture, wherein the single bus waveguide comprises:evanescent tap couplers, wherein each coupler taps off a fraction of the available light in the bus waveguide for emission; andphase shifters, wherein each phase shifter controls the phase accumulation between adjacent antenna elements.

6. The system of claim 2, further comprising a splitter tree configured to split an optical signal into a plurality of waveguides in a w ound architecture, wherein:each w aveguide is fed through a loop-back path to length match each waveguide feeding each antenna in the spiral;mit-26247pcteach resulting waveguide is fed through a phase shifter driven with an independent control voltage; andeach resulting waveguide is routed from its respective phase shifter into the spiral-shaped path of one of the spiral-shaped waveguide antennas to illuminate that spiral-shaped waveguide antenna.

7. The system of claim 2, further comprising a path-length-matched splitter tree distributed around the array in a web pattern, wherein:each splitter position is chosen to path-length match each waveguide feeding the next splitter in the tree;each of the waveguides is fed through a phase shifter addressed by an independent control voltage; andafter passing through the phase shifter, each waveguide is routed to one of the spiral-shaped waveguide antennas,wherein the path-length matching provides phase matching among all spiralshaped waveguide antennas over a wavelength tuning range.

8. The system of claim 2, wherein the array of spiral-shaped waveguide antennas has dimensions less than 100 nm.

9. The system of claim 2, wherein the array of spiral-shaped waveguide antennas comprises at least 4 spiral-waveguide antennas spiraling outward from a common central region.

10. The system of claim 1, wherein the spiral-shaped waveguide antenna is formed of at least one of silicon and silicon nitride, and wherein the substrate comprises silicon dioxide on or in which the spiral-shaped waveguide antenna is mounted.

11. A processor-configured method of tunably focusing light in the radiative near field, the method comprising:utilizing the system of claim 1, including the at least one spiral-shaped waveguide antenna, and;injecting coherent light of a first wavelength into one of the ends of each spiralshaped waveguide antenna;propagating the light inward toward a spiral center or outward from the spiral center such that the perturbations collectively emit a first optical beam that focuses at a first focal distance from the array;changing the wavelength of the injected light to a second wavelength while maintaining relative drive phases of the perturbations, thereby shifting the focus to a second focal distance different from the first focal distance; andmit-26247pctrepeating the wavelength change to scan the focal distance without mechanical motion of the spiral-shaped waveguide antenna.

12. The processor-configured method of claim 11. wherein the coherent light is injected into an array of the spiral-shaped waveguide antennas, wherein each of the spiral-shaped waveguide antennas spiral outward from a common central region.

13. The processor-configured method of claim 12, further comprising applying programmed electrical signals to integrated phase shifters disposed between successive spiral-shaped waveguide antennas to impose a selectable azimuthal phase gradient that removes polarization-induced nulls at the focus.

14. The processor-configured method of claim 12. wherein the focused beam has orbital angular momentum and is positionable in three dimensions.

15. The processor-configured method of claim 12, further comprising:directing the beam for wireless optical communication, wherein light in the beam is used as a medium for communication signals; andusing orbital angular momentum modes enabled by the array as an encoding for various communication channels.

16. The processor-configured method of claim 11, wherein the wavelength is varied over at least 40 nanometers to scan the focal distance over at least 0.3 millimeters.

17. The processor-configured method of claim 11, wherein the focused beam produced at the scanned focal distance is used to trap microparticles in an optical-tweezers application.

18. The processor-configured method of claim 11, further comprising using the focused beam to initialize, manipulate, or read a trapped-ion or neutral-atom quantum bit.

19. The processor-configured method of claim 11, wherein the focused beam is used for chip-based 3D printing, the method further comprising using the focused beam to cure a liquid resin to produce a solid programmed 3D structure of a desired shape.

20. The processor-configured method of claim 11, further comprising using the focused beam for light detection and ranging (LiDAR).

Images