Photonic integrated circuit based beam scanner

Abstract

A photonic integrated circuit (PIC) 400A e.g. for LiDAR ranging may be configured to provide a beam scanner comprising an output light beam switchable between a plurality of out-coupling ports (output

Description

TECHNICAL FIELD

[0001] The present disclosure relates to photonic integrated circuits, and in particular to beam scanners based on photonic integrated circuits. BACKGROUND

[0002] Light Detection And Ranging (LiDAR) is a remote sensing technology that uses pulsed or continuous light beams to provide three-dimensional maps of surroundings and outside objects. A light source emits light toward a target. The target scatters the light, reflecting a portion of it towards a receiver of a LiDAR system. The LiDAR system then determines the distance to the target in the direction of the light beam based on one or more characteristics associated with the reflected / scattered light, such as arrival time, modulation phase, and / or optical frequency of the reflected / scattered light. LiDAR may be used in a wide variety of applications, from 3D imaging by a smartphone to automotive and even atmospheric sensing applications.

[0003] It is desirable for a LiDAR system to be able to operate over large distances, and to measure not only the distance to objects but also their relative velocities. It is further desirable to reduce the size, weight, complexity, and power consumption of a LiDAR device while providing a high degree of reliability and fidelity of obtained 3D images and data. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] Exemplary embodiments will now be described in conjunction with the drawings, in which:

[0005] FIG. lisa schematic view of a beam scanner including a single-output photonic integrated circuit (PIC) coupled to a collimator and a pair of scanning mirrors;

[0006] FIG. 2 is a cross-sectional view of areas scanned by the scanner of FIG. 1 at different locations along the light path;

[0007] FIG. 3 is a plan view of a beam scanner including a multiple-output PIC coupled to a collimator, with output ports located at a straight edge of the PIC for emitting parallel output light beams;

[0008] FIG. 4A is a plan view of a beam scanner including a multiple-output PIC coupled to a collimator, with output ports located at a straight edge of the PIC for emitting non-parallel output light beams aimed at the collimator, the PIC comprising an optical switch;

[0009] FIG. 4B is a plan view of a beam scanner including a multiple-output PIC coupled to a collimator, with output ports located at a straight edge of the PIC for emitting non-parallel output light beams aimed at the collimator, the PIC comprising a plurality of independent LiDAR channels;

[0010] FIG. 5A is a plan view of a beam scanner including a multiple-output PIC coupled to a collimator, with output ports located at a curved edge of the PIC for emitting non-parallel output light beams aimed at the collimator, the PIC comprising an optical switch;

[0011] FIG. 5B is a plan view of a beam scanner including a multiple-output PIC coupled to a collimator, with output ports located at a curved edge of the PIC for emitting non-parallel output light beams aimed at the collimator, the PIC comprising a plurality of independent LiDAR channels;

[0012] FIG. 6A is a plan view of a PIC with a curved edge portion;

[0013] FIGs. 6B and 6C are cross-sectional views of the PIC of FIG. 6 A;

[0014] FIG. 7 is a plan view of a beam scanner with the PIC of FIG. 5 A and a tiltable reflector;

[0015] FIG. 8 is a plan view of a beam scanner with the PIC of FIG. 5 A and a pair of coaxial tiltable reflectors;

[0016] FIG. 9 is a plan view of a beam scanner with a pair of non-coaxial tiltable reflectors;

[0017] FIG. 10 is a field of view diagram of the beam scanner of FIG. 9 for LiDAR sensing to the left and right side of a vehicle;

[0018] FIG. 11 is a field of view diagram of the beam scanner of FIG. 8 or FIG. 9 with different scanning ranges for individual PIC chips;

[0019] FIG. 12 is a field of view diagram of the beam scanner of FIG. 9 for high- beam and low-beam LiDAR sensing;

[0020] FIG. 13 is a plan view of LiDAR angular scanning ranges corresponding to the field of view diagram of FIG. 12;

[0021] FIG. 14 is a plan view of a beam scanner with a plurality of the PICs of FIG. 5A or 5B in a fan configuration and a common tiltable reflector;

[0022] FIG. 15A is a plan view of a beam scanner with a plurality the PICs of FIG. 5A or 5B in a fan configuration, each PIC chip equipped with a dedicated tiltable reflector;

[0023] FIG. 15B is a side view of the beam scanner of FIG. 15 A; and

[0024] FIG. 16 is a flow chart of a method for manufacturing a PIC chip with a photolithographically defined curved edge portion. DETAILED DESCRIPTION

[0025] While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives and equivalents, as will be appreciated by those of skill in the art. All statements herein reciting principles, aspects, and embodiments of this disclosure, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure.

[0026] As used herein, the terms "first", "second", and so forth are not intended to imply sequential ordering, but rather are intended to distinguish one element from another, unless explicitly stated. Similarly, sequential ordering of method steps does not imply a sequential order of their execution, unless explicitly stated. In FIGs. 1 and 3, FIGs. 4A-4B, FIGs. 5A-5B, FIGs. 6A-6C, FIGs. 7-9, FIG. 14, and FIGs. 15A-15B, similar reference numerals refer to similar elements.

[0027] A Light Detection And Ranging (LiDAR) beam scanner may use a photonic integrated circuit (PIC), e.g. a silicon-based PIC (Si-PIC), coupled to a collimator and a mechanical beam scanner. The PIC provides a probing light beam at its output port. The collimator collimates the beam, and the beam scanner angularly scans the collimated beam. A reflection of the probing beam from a remote object or a feature of the external scenery may be received by the beam scanner and redirected back to the PIC through the collimator. The PIC may be configured to detect parameters of the reflection such as the reflection’s arrival time, optical modulation phase, optical frequency, signal strength, etc. A controller determines the distance to the remote feature based on the detected reflection parameters. As the beam scanner scans the collimated probing light beam, the controller builds a point cloud map of the external scenery.

[0028] The mechanical angular scanning of the collimated probing light beam about multiple axes may present reliability problems in addition to increasing size and weight of the scanner. It may therefore be desirable to replace the mechanical scanning, in at least one dimension, with light beam scanning or rendering not relying on moving parts. To that end, multiple output ports of a PIC may be coupled to a collimator providing a collimated output light beam propagating in a direction defined by the output port number or location. In one illustrative example of this approach, a single LiDAR channel may be equipped with an optical selector switch coupling the LiDAR channel to different optical ports. In another illustrative example, an array of LiDAR channels may be used instead of a single LiDAR channel, each channel having its own optical port, or several ports coupled to the channel through a dedicated optical switch. Multiple output beams propagating in a plurality of sensing directions may be provided simultaneously by multiple LiDAR channels on a same PIC chip, or on different PIC chips. The collimator directs the collimated beam to propagate in a direction defined by the emitting port location.

[0029] One challenge of such multiport beam scanning or rendering is that, at a sufficiently wide angular range of scanning or rendering, optical aberrations of the collimator begin to impact the degree of collimation of the probing light beam. The optical aberrations may include e.g. spherical aberration, coma, and / or astigmatism. The loss of collimation leads to a loss of signal strength due to poor beam directivity, and to loss of optical resolution of the LiDAR across at least a portion of the field of view.

[0030] In accordance with this disclosure, optical imperfections of a multiport beam scanner may be mitigated by disposing the multiple output ports on a curved portion of the PIC edge matching a field curvature of the collimator used to collimate the emitted beams. This reduces the cost and complexity of the collimator, which no longer needs to have a flat field and thus may be much simpler, lighter, and cheaper. The output ports (i.e. output waveguide or waveguide taper sections) may be oriented to direct the output light beam to a center of the collimator, allowing further size and weight reduction of the scanner due to using a beam collimator with a smaller clear aperture.

[0031] The field curvature matching and / or the engineered convergence of multiple beams on the collimator may allow more output ports to be accommodated while using a collimator of a given size and focal length. Furthermore, the diameter of the probing light beam may be increased to reduce the far field divergence of the probing light beam or beams, thus increasing range and / or spatial resolution.

[0032] In accordance with the present disclosure, there is provided a PIC comprising an edge and an array of output ports at the edge for providing a light beam in a port-specific out-coupling direction, such that out-coupling directions of different ports of the array converge at a common exit location downstream of the PIC edge. The PIC may include an optical switch operably coupled to the array of output ports for switching the light beam between the output ports of the array, and / or a plurality of LiDAR channels each coupled to an output port of the array. Each LiDAR channel may be equipped with its own optical switch if desired. The output ports of the array may be oriented non-parallel to one another to make sure that the out-coupling directions of different ports of the array converge to the common exit location. The curved portion may be concave spherical, aspherical, cylindrical, and / or acylindrical. The edge may further include a straight portion underneath or above the curved portion, forming a step in a thickness direction of the PIC.

[0033] In accordance with the present disclosure, there is provided a beam scanner comprising the PIC as defined above, coupled to a collimator disposed at the exit location for receiving the light beam from each out-coupling direction and collimating the light beam to propagate at a port-specific angle. In embodiments where the PIC has a curved portion of the edge, a curvature of the curved portion may be selected to match a field curvature of the collimator. In some embodiments, a first reflector, e.g. a tiltable mirror, a liquid crystal on silicon (LCoS) reflector, a galvo-motor based tiltable reflector, a servo-motor based tiltable reflector, etc., may be disposed downstream of the collimator for angularly scanning the collimated light beam about a first axis. A second reflector, e.g. a tiltable mirror or an LCoS reflector, may be disposed downstream of the collimator for angularly scanning the collimated light beam about a second axis. The first reflector may be configured to receive the light beam from a first output port of the array, and the second reflector may be configured to receive the light beam from a second, different output port of the array. The first and second axes may be non-parallel to one another.

[0034] In some embodiments, the beam scanner may include not one but a plurality of the PICs. The PICs may be disposed such that the exit locations of the PICs overlap. The collimator may be disposed at the overlap for receiving the light beam from each port-specific direction of each PIC and collimating the light beam to propagate at the port-specific angle. The PICs may be disposed in a fan configuration with the collimator at a center of the fan. A reflector may be disposed downstream of the collimator, for angularly scanning the collimated light beam. In some embodiments, a plurality of reflectors may be disposed each in an optical path between a corresponding PIC of the plurality of PICs and the collimator, for independently angularly scanning the light beams provided by individual PICs of the plurality of PICs.

[0035] In accordance with the present disclosure, there is further provided a method of manufacturing a PIC of this disclosure. The method may include forming, in the PIC, an array of output ports for outputting a light beam in a port-specific out-coupling direction, and forming an edge in the PIC. The edge comprises the array of output ports, and the out-coupling directions of different output ports of the array converge at a common exit location downstream of the PIC edge. Forming the edge may include forming a curved e.g. a concave portion of the edge, where the output ports of the array are coupled to the curved portion. Forming the curved edge portion edge may include determining a field curvature of a collimator for collimating the light beam, and matching the concave edge portion to the determined field curvature. The curved edge portion may be photolithographically defined and formed by etching. The etching may be performed to a thickness smaller than a thickness of the PIC

[0036] Referring now to FIG. 1, a beam scanner 150 includes a PIC 100 coupled to a collimator 106. An output port 104 of the PIC 100 emits a beam of light 103. The output port 104 is disposed at a focal plane of the collimator 106. Herein and throughout the specification, the term “port” is used to denote a terminal, a taper or coupler, or a waveguide end of a waveguide device, and may, but does not have to, mean an actual opening or a dedicated structure. The PIC may include a Si-PIC, for example. A 2D mechanical beam scanner 144 is optically coupled to the collimator 106. The 2D mechanical beam scanner 144 includes first 141 and second 142 tiltable mirrors having mutually perpendicular first 121 and second 122 axes of tilt, respectively.

[0037] A light source 101 may provide light to the PIC 100. In some embodiments, the light source 101 may be a part of, or mounted to, the PIC 100. For a LiDAR application, the PIC 100 may include circuitry for conveying the light received from the light source 101 to the output port 104, and for receiving a and processing a reflection of the ranging light beam from a remote object.

[0038] In operation, the collimator 106 collimates the light beam 103 emitted from the output port 104 as illustrated at 110, providing a collimated light beam 133. The collimated light beam 133 impinges onto the first tiltable mirror 141, which scans the collimated light beam 133 about the first axis 121, as indicated with an arrow next to the first axis 121. The first tiltable mirror 141 redirects the collimated light beam 133 to impinge onto the second tiltable mirror 142, which scans the collimated light beam 133 about the second axis 122 as indicated with an arrow next to the second axis 122, forming a ranging light beam 152. A reflection from a remote object illuminated with the ranging light beam 152 may be recovered by the scanner 144 and directed back to the output port 104, or to another dedicated port of the PIC 100 for further processing. In embodiment with dedicated receiver port(s), a dedicated beamsplitter or coupler may be used to separate the emitted light beam and the received reflection.

[0039] FIG. 2 illustrates cross-sectional areas scanned by the collimated light beam 133 at different locations along the optical path of the collimated light beam 133 in the LiDAR beam scanner 150 of FIG. 1. Plane A-A (FIGs. 1 and 2) corresponds to an optical path upstream of the beam scanner 144. A black dot 201 in FIG. 2 corresponds to the collimated light beam 133 prior to scanning. The first tiltable mirror 141 scans the collimated light beam 133 vertically, as denoted with a black vertical line 202 in FIG. 2 at a plane B-B (FIGs. 1 and 2) downstream of the first tiltable mirror 141 but upstream the second tiltable mirror 142. The second tiltable mirror 142 scans the (vertically scanned) collimated light beam 133 horizontally, resulting in a 2D scan represented by a black rectangle 203 in FIG. 2 at a plane C-C (FIGs. 1 and 2) downstream of the beam scanner 144. Together, the first 141 and second 142 tiltable mirrors scan the collimated light beam 133 in two dimensions (2D). A field of view corresponding to the 2D scanning is denoted in FIG. 2 with a dashed rectangle 210.

[0040] Turning to FIG. 3, a beam scanner 350 may scan a light beam in at least one dimension without having to rely on any moving parts. Instead of the mechanical scanner, the beam scanner 350 includes a PIC 300, e.g. a Si-PIC, comprising an optical switch 309 for switching light between first 304-1, second 304-2, third 304-3, and fourth 304-4 output ports of an array 304 of output ports. The output ports 304-1, 304-2, 304-3, and 304-4 are disposed at an edge 305 of the PIC 300. The output ports 304-1, 304-2, 304-3, and 304-4 may include waveguide tapers configured to provide a required mode field diameter and divergence of the output light beams.

[0041] The output ports 304-1, 304-2, 304-3, and 304-4 are optically coupled to a collimator 306, which is a common collimator for all of them. Switching light between the output ports 304-1, 304-2, 304-3, and 304-4 of the array 304 effectively redirects the output light beam to propagate at a port-specific angle, because the collimator 306 converts a beam coordinate upstream of the collimator 306 into a beam angle downstream of the collimator 306. For example, when the optical switch 309 switches the light to the first output port 304-1, a diverging first beam 303-1 is collimated by the collimator 306 to propagate downwards in FIG. 3 as a first output beam 360-1 shown in solid lines. When the optical switch 309 switches the light to e.g. the third output port 304-3, a diverging third beam 303-3 is collimated by the collimator 306 to propagate upwards in FIG. 3 as an output beam 360-3 shown in dashed lines. More than four output ports may be provided to cover all required scanning directions.

[0042] A light source 301 may provide light to the PIC 300. In some embodiments, the light source 301 may be a part of, or may be mounted to, the PIC 300. For a LiDAR application, the PIC 300 may include circuitry 311 for receiving and processing a reflection of the ranging light beam from a remote object. The collimator 306 may include e.g. a refractive lens, a diffractive lens, a metalens, a concave mirror, etc. The optical switch 309 may be implemented as a binary tree of Mach-Zehnder interferometer (MZI) based elementary switches 302 as illustrated, or may use another architecture for operation as a selector switch. Although 1x4 switch and accordingly four ports are illustrated in FIG. 3, the optical switch 309 may have any other practical number of ports. Larger switches provide more discrete directions of the ranging light beam, although larger switches may have a higher optical loss.

[0043] One drawback of the beam scanner 350 of FIG. 3 is that the collimator 306 needs to have a large enough clear aperture to be able to receive and collimate diverging beams from all output ports of the array, which may extend over the entire width of the PIC 300. Larger collimators are usually heavier and more costly. Another drawback of the beam scanner 350 is that highly off-axis light beams may not get collimated very well, causing a loss of power density and directivity of the ranging beam at ranging angles corresponding to highly off-axis beams. This is illustrated in FIG. 3 by the first output beam 360-1 being slightly converging, especially in comparison with the third output beam 360-3, which is closer to an optical axis 380 of the collimator 306 than the first output beam 360-1, and accordingly is less aberrated. The poor directivity may cause a loss of signal strength at a distance, and / or the loss of spatial resolution in a LiDAR application of the beam scanner 350, in particular at extreme angles of scanning and associated portions of the field of view.

[0044] In accordance with this disclosure, the collimator size and / or the collimating imperfections may be reduced by orienting the output couplers of a PIC chip at such angles that the out-coupling directions represented by chief rays, or central rays, of light beams emitted by different output ports converge or overlap on the collimator. Referring for a non-limiting illustrative example of this to FIG. 4A, a beam scanner 450A is similar to the beam scanner 350 of FIG. 3, includes similar elements, and operates in a similar manner. Specifically, the beam scanner 450A may include the light source 301 coupled to a PIC 400A having the circuitry 311 and the switch 309 that switches the light between different output ports including first 404-1, second 404-2, third 404-3, and fourth 404-4 output ports of an array 404. A collimator 406, e.g. a refractive lens, a diffractive lens, a metalens, a concave mirror, etc., may be used to collimate light beams emitted by the PIC 400A.

[0045] The optical switch 309 of the PIC 400A of the beam scanner 450A of FIG. 4 A may be implemented as a binary tree of the MZI switches 302, and may include a required number of individual MZI switches, and a required number of output ports. Switching light between the output ports 404-1, 404-2, 404-3, and f404-4 effectively redirects the output light beam to propagate at a port-specific angle. For example, when the optical switch 309 switches the light to the first output port 404-1, a diverging first beam 403-1 is collimated by the collimator 306 to propagate as a first output beam 460-1 shown in solid lines, and when the optical switch 309 switches the light to the third output port 404-3, a diverging third beam 403-3 is collimated by the collimator 406 to propagate as an output beam 460-3 shown in dashed lines.

[0046] One distinction of the beam scanner 450A of FIG. 4A from the beam scanner 350 of FIG. 3 is that the output ports 404-1, 404-2, 404-3, and 404-4 of the array 404 of output ports in FIG. 4A are oriented non-parallel to one another, such that the light beam is out-coupled in a port-specific out-coupling direction. Different out-coupling directions of the array 404 converge at a common location downstream of a PIC 400A edge 405. This location is termed herein “exit location”. Thus, the output ports 404-1, 404-2, 404-3, and 404-4 of the array 404 are oriented such that chief rays of emitted light beam converge to the exit location. The collimator 406 may be suitably disposed at the exit location, allowing the clear aperture of the collimator 406 to be considerably reduced. This provides significant size, weight, and cost reduction of the scanner 450A, and furthermore may provide better collimated output light beams. To attain required directivity and divergence of the out-coupled light, the output ports 404-1, 404-2, 404-3, and 404-4 may include taper structures that expand the guided light mode for out-coupling from the PIC 400A at its edge 405.

[0047] Turning to FIG. 4B, a beam scanner 450B is similar to the beam scanner 450A of FIG. 4A, includes similar elements, and operates in a similar manner. One difference of the beam scanner 450B of FIG. 4B from the beam scanner 450A of FIG. 4A is that, instead of the switch 309 being coupled to a single LiDAR channel represented by the circuitry 311 in FIG. 4A, a PIC 400B of the beam scanner 450B of FIG. 4B includes a plurality of LiDAR channels 311-1, 311-2, 311-3, and 311-4 coupled to the first 404-1, second 404-2, third 404-3, and fourth 404-4 output ports, respectively. The LiDAR channels 311-1, 311-2, 311-3, and 311-4 receive their light input from a splitter 415 coupled to the light source 301, and may operate independently of one another for transmission and reception. Optically, the beam scanner 450B has the same advantages resulting from the chief ray engineering as the beam scanner 450A of FIG. 4A. One further advantage of the beam scanner 450B of FIG. 4B is that all output beams including the first output beam 460-1 and the third output beam 460-3 may be provided simultaneously, or in any desired temporal order. In some embodiments, at least some of the LiDAR channels 311-1, 311-2, 311-3, and 311-4 may be equipped with their respective switches or switching trees, for further increasing the overall number of output ports and accordingly the overall number of sensing directions. All output ports may be coupled to the edge 405. It is to be understood that the term “beam scanner” as used herein encompasses such instances of simultaneous presence of ranging light beams propagating in different directions. The term “beam scanner” as used herein also encompasses combination configurations of FIGs. 4A and 4B and other similar configurations where a PIC chip includes a plurality of LiDAR channels, each channel being equipped with its own optical selector switch or a corresponding switching tree.

[0048] It is to be further noted that, even when the chief rays of the light beams emitted by output port structures are engineered to converge or combine together at the collimator, beam collimation imperfections may still remain. The collimation imperfections may remain at least due to a so-called Petzval field curvature of the collimator, herein termed merely “field curvature” for brevity. An image field is defined as a geometrical area where a sharp image may be obtained by an imaging system. Although one can construct a collimator lens to have a flat image field to match generally flat image sensors or flat extended light sources, many types of collimators, especially simpler and cheaper ones such as a singlet spherical lens, usually have a curved image field. When such a collimator is coupled to a flat source of light beams such as the PIC 300 of FIG. 3, the PIC 400A of FIG. 4A, or the PIC 400B of FIG. 4B, the degree of collimation of the light beams will depend on the proximity of the output ports to the optical axis of the collimator, generally being worse for off-axis output ports as compared to on-axis sources / ports.

[0049] In accordance with this disclosure, the field curvature of the collimator may be taken into account and compensated for by curving an end facet, or at least a portion of the end facet containing the light-emitting output light ports, of the PIC to match the field curvature of the collimator. Referring for a non-limiting illustrative example of this to FIG. 5 A, a beam scanner 550A is similar to the beam scanner 350 of FIG. 3 and the beam scanner 450A of FIG. 4 A, includes similar elements, and operates in a similar manner. Specifically, the beam scanner 550A of FIG. 5A may include the light source 301 coupled to the LiDAR channel circuitry 311, the switch 309 for switching the light between different output ports, and the collimator 406. The optical switch 309 of FIG. 5 A and the LiDAR channel circuitry 311 are implemented in a PIC 500A. The optical switch 309 may include a required number of the individual MZI switches 302, e.g. thermally tuned MZI switches, and an array of output ports 504. Output ports 504-1, 504-2, 504-3, and 504-4 of the array 504 are oriented non-parallel to one another, such that the light beam is out-coupled in a portspecific out-coupling direction, and different out-coupling directions of the array 504 converge at a common exit location. In other words, the output ports 504-1, 504-2, 504-3, and 504-4 of the array 504 are oriented such that chief rays i.e. central rays of emitted diverging light beams converge to the exit location.

[0050] The collimator 406 is disposed at the exit location. Switching light between the output ports 504-1, 504-2, 504-3, and 504-4 of the array 504 effectively redirects an output light beam 560 to propagate at a port-specific angle. When the optical switch 309 switches the light e.g. to the first output port 504-1, a diverging first beam 503-1 is collimated by the collimator 406 to propagate as a first output beam 560-1, and when the optical switch 309 switches the light e.g. to the third output port 504-3, a diverging third beam 503-3 is collimated by the collimator 406 to propagate as a third output beam 560-3. To provide required directivity / divergence of the out-coupled light, the output ports 504-1, 504-2, 504-3, and 504-4 may include taper structures that expand the guided light mode for out-coupling from the PIC 500A with the required mode field diameter and divergence.

[0051] One distinction of the beam scanner 550A of FIG. 5A from the beam scanner 450A of FIG. 4A is that the edge of the PIC 500A of FIG. 5 A includes a curved portion 505. The curved edge portion 505 is shown with a thick black line. The output ports 504-1, 504-2, 504-3, and 504-4 of the array 504 are coupled to the curved portion 505. To reduce or eliminate optical aberrations related to the field curvature of the collimator 406, the profile of the curved portion 505 may be selected to match a field curvature 416 of the collimator 406, which may be determined with high accuracy by using optical design software, and / or by direct measurements. The matching of the edge and field curvatures effectively reduces or eliminates optical aberrations and output beam collimation imperfections related to the non-flat field of the collimator 406.

[0052] The curved portion 505 of the PIC 500A edge may be concave, spherical / cylindrical, or aspherical / acylindrical, depending on the specific profile of the field curvature 416 of the collimator 406. The optical design degree of freedom related to the ability to match the field curvature of the collimator allows inexpensive and lightweight collimators based on refractive and / or diffractive lenses, metalenses, curved mirror, etc., to be used. The curved edge portion 505 of the PIC 500A may be formed using various techniques, including without limitation laser dicing, straight cutting followed by bulk polishing e.g. with a cylindrical polisher, and / or deep trench etching, with the etching profile defined by photolithography.

[0053] Turning to FIG. 5B, a beam scanner 550B is similar to the beam scanner 550A of FIG. 5A, includes similar elements, and operates in a similar manner. One difference of the beam scanner 550B of FIG. 5B from the beam scanner 550A of FIG. 5A is that, instead of the switch 309 coupled to a single LiDAR channel represented by the circuitry 311 in FIG. 5 A, the beam scanner 5 5 0B of FIG. 5B includes the plurality of LiDAR channels 311-1, 311-2, 311-3, and 311-4 coupled to the first 504-1, second 504-2, third 454-3, and fourth 504-4 output ports, respectively. The LiDAR channels 311-1, 311-2, 311-3, and 311-4 may operate independently of one another for transmission and reception. Optically, the beam scanner 550B has the same advantages resulting from the chief ray engineering as the beam scanner 550A of FIG. 5 A. One further advantage of the beam scanner 550B of FIG. 5B is that all output beams including the first output beam 560-1 and the third output beam 560-3 may be provided simultaneously, or in any required temporal order, similarly to the beam scanner 450B of FIG. 4B. Similarly to the configurations of FIGs. 4A and 4B, the configurations of FIGs. 5 A and 5B may be combined to create a beam scanner with a PIC chip including a plurality of LiDAR channels, each channel being equipped with its own optical switch or optical switching tree, with the output ports the individual switching trees coupled to the curved edge portion 505.

[0054] Referring now to FIGs. 6A, 6B, and 6C, a PIC 600 is an example implementation of the PIC 500A of FIG. 5A or the PIC 500B of FIG. 5B. The PIC 600 of FIGs. 6A, 6B, and 6C is a Si-PIC having a photolithographically defined and etched curved edge portion 605. The Si-PIC 600 includes a silicon substrate 670 supporting an oxide layer 672 with waveguide structures 674 formed therein, including an array of output ports or couplers 604. The output ports may utilize adiabatic taper structures or other mode converters for converting a mode field diameter of a guided mode to provide a required spot size and divergence of the out-coupled light beam. The output ports 604 terminate at the curved edge portion 605 of the Si-PIC 600. A straight portion 605’ of the Si-PIC 600 is disposed underneath (or above if flipped) the curved portion 605 in the view of FIG. 6B and 6C, forming a step 680 of a depth D in a thickness direction 682 of the Si-PIC 600 (View A-A in FIG. 6B taken along lines A - A in FIG. 6A).

[0055] The depth D of etching of the step 680 may satisfy the following condition (1) which ensures that a diverging light beam 603 emitted by each output port 604 clears the straight edge portion 605’ of the PIC 600:

[0056] D / L> tan (0 / 2) (1)

[0057] where L is a maximum length of the step in the direction of propagation of a diverging light beam 603 emitted by any of the output ports 604, and ^is the divergence angle of the diverging light beam 603 (View A-A in FIG. 6C). When the depth D satisfies the condition (1), the system efficiency is improved.

[0058] Referring to FIG. 7, a 2D beam scanner 750 includes the beam scanner 550A of FIG. 5A for providing solid-state beam scanning or rastering in a first direction, and a mechanical ID scanner for providing mechanical beam scanning in a second, different direction e.g. a perpendicular direction, as illustrated. The mechanical scanner includes a tiltable reflector 740 downstream of the collimator 406 for scanning the output light beam 560 emitted by any of the output ports 504 and collimated by the collimator 406. The output light beam 560 is scanned by tilting the tiltable reflector 740 about a first axis 721. The tiltable reflector 740 may include e.g. a galvo-motor based tiltable reflector, a step- or servo-motor based tiltable reflector, a microelectromechanical system (MEMS) mirror, etc. In some embodiments, a liquid crystal on silicon (LCoS) reflector, which can angularly scan or redirect an impinging beam, may be used in place of the tiltable reflector 740.

[0059] The switching-based scanning provided by the PIC 500A, in combination with the mechanical scanning provided by the tiltable reflector 740, allows the beam scanner 750 to scan the ranging light beam in two dimensions. The 2D beam scanner 750 may include any beam scanner disclosed herein, e.g. the beam scanner 350 of FIG. 3, the beam scanner 450A of FIG. 4A, the beam scanner 450B of FIG. 4B, and / or the beam scanner 550B of FIG. 5B. The two latter beam scanner variants, 450B and 550B, may provide several or all beams at different angles simultaneously, as has been explained above with reference to FIGs. 4B and 5B respectively, and are also considered beam scanners in the terminology used herein.

[0060] Turning to FIG. 8, a 2D beam scanner 850 is similar to the 2D beam scanner 750 of FIG. 7, and includes similar elements. The 2D beam scanner 850 of FIG. 8 includes the beam scanner 550A of FIG. 5A for providing solid-state beam scanning or rastering in a first direction, and a couple of coaxial tiltable reflectors for providing mechanical beam scanning in a second, perpendicular direction. A first reflector 840A tiltable about a first axis 820A is configured to receive a light beam from first output ports 504A of the array 504 disposed above an optical axis 480 of the collimator 406. A second reflector 840B tiltable about a second axis 820B parallel to the first axis 820A is configured to receive a light beam from second output ports 504B of the array 504 below the optical axis 480 of the collimator 406. This allows light emitted from the first 504A and second 504B output ports to be redirected in an independent manner, expanding available modes of scanning along the second direction, e.g. allowing simultaneous independent scanning with different scanning rates, scanning directions, and / or scanning ranges if required. Furthermore, having separate first 840A and second 840B reflectors allows one to reduce the size of individual reflectors. More than two tiltable reflectors may be provided, e.g. an array of MEMS tiltable reflectors and / or LCoS reflectors may be used, potentially down to a single reflector per single output port. Multi-channel PICs 400B of FIG. 4B and 500B of FIG. 5B, and their variants, may be used in place of the PIC 500A.

[0061] Referring now to FIG. 9, a beam scanner 950 is similar to the beam scanner 850 of FIG. 8, and includes similar elements. The beam scanner 950 of FIG. 9 includes a PIC 900, first 906A and second 906B collimators coupled to the PIC 900, and first 940A and second 940B tiltable reflectors coupled to the first 906A and second 906B collimators respectively. One difference of the beam scanner 950 of FIG. 9 from the beam scanner 850 of FIG. 8 is that the PIC 900 of the beam scanner 950 of FIG. 9 has not one but two curved edge portions, a first curved portion 905A and a second curved portion 905B. First output ports 904A are disposed above a symmetry axis 990 of the PIC 900 and are coupled to the first curved edge portion 905A. Only two of the first ports 904A, labeled 1 and 2, are illustrated in FIG. 9 for brevity. These are outer ports of the array of first ports 904A.

[0062] Similarly, second output ports 904B are disposed below the symmetry axis 990 and are coupled to the second curved edge portion 905B. Only two of the second ports 904B, labeled 3 and 4, are shown as the outer ports of the array of second ports 904B. The first ports 904A are coupled to the first collimator 906A, which is coupled to the first tiltable reflector 940A. The second ports 904B are coupled to the second collimator 906B, which is coupled to the second tiltable reflector 940B. First 920A and second 920B tilt axes of the first 940A and second 940B tiltable reflectors, respectively, are non-parallel to one another.

[0063] More than two sets of collimators and tiltable reflectors may be provided. An array of collimators coupled to an array of reflectors may be used, to provide sequential or simultaneous independent scanning in a multitude of directions. The reflectors may include galvo- or servo-motor driven mirrors, MEMS tiltable mirrors, LCoS reflectors, etc.

[0064] The beam scanner 950 may provide two simultaneous independent 2D scans of collimated ranging beams, both ranging beams being emitted out of plane of FIG. 9, towards the viewer. For example, when the beam scanner 950 is used in an automotive LiDAR application, the beam scanner 950 may be oriented to simultaneously scan to the left and right of a moving vehicle. Referring for a nonlimiting illustrative example of such configuration to FIG. 10 with further reference to FIG. 9, the beam scanner 950 of FIG. 9 may be placed at a front of a vehicle 1002 (FIG. 10) to provide a left 2D angular range 1000A to the left of the vehicle 1002, and a right 2D angular range 1000B to the right of the vehicle 1002. The left- and rightside scanning may be performed independently.

[0065] The left 2D angular range 1000A (FIG. 10) corresponds to the first tiltable reflector 940A (FIG. 9), which redirects a light beam emitted from one of the first output ports 904A and collimated by the first collimator 906A. Accordingly, the right 2D angular range 1000B (FIG. 10) corresponds to the second tiltable reflector 904B (FIG. 9) redirecting light beams emitted from one of the second output ports 940B and collimated by the second collimator 906B. Dots 1060A in the left 2D angular range 1000A correspond to specific angles of collimated ranging beams scanned by the first tiltable reflector 940A, and dots 1060B in the right 2D angular range 1000B correspond to specific angles of collimated ranging beams scanned by the second tiltable reflector 940B. For a LiDAR application, each dot 1060A and 1060B corresponds to a distance and / or velocity measurement performed by detecting a reflection of a corresponding ranging beam from a remote object, or a part thereof. It is to be understood that only three vertical dots shown in each angular range 1000A and 1000B are shown for brevity. More dots per vertical / horizontal direction may be provided.

[0066] The usage of multiple independently operable reflectors in PIC-based beam scanners of FIGs. 8 and 9 to redirect collimated ranging beams provides the flexibility of selecting a direction and timing of the scanning; furthermore, the usage of multiple independently operable reflectors provides the flexibility of selecting an amplitude or angular range of the scanning. Referring for a non-limiting illustrative example to FIG. 11 with further reference to FIG. 9, a first 2D angular range 1100A (FIG. 11) corresponds to the first tiltable reflector 940A (FIG. 9) redirecting a light beam emitted from one of the first output ports 904A and collimated by the first collimator 906A. Accordingly, a second 2D angular range 1100B (FIG. 11) corresponds to the second tiltable reflector 904B (FIG. 9) redirecting light beams emitted from one of the second output ports 940B and collimated by the second collimator 906B. Dots 1160A in the first 2D angular range 1100A correspond to the angles of collimated ranging beams scanned by the first tiltable reflector 940A, and dots 1160B in the second 2D angular range 1100B correspond to the angles of collimated ranging beams scanned by the second tiltable reflector 940B. For a LiDAR application, each dot 1160A and 1160B corresponds to a distance and / or velocity measurement performed by detecting a reflection of a corresponding ranging beam from a remote object or a part thereof. It is to be understood that only three vertical dots shown in each angular range 1100A and 1100B are only intended for illustration. The actual number of dots (discrete measurement directions) is likely to be much higher.

[0067] Although the total number of dots in the first 1100A and second 1100B 2D scanning ranges is the same, the density of dots 1160A in the first 2D angular range 1100A is lower than the density of dots 1160B in the second 2D angular range 1100B. The difference of the dots density corresponds to the difference of the scanning range of the first 940A and second 940B tiltable reflectors. In this example, the first tiltable reflector 940A is scanned over a larger scanning range, resulting in the larger first 2D angular range 1100 A and a lesser density of the dots 1160A than the second 2D angular range 1100B having higher density of the dots 1160B. Thus, the configuration of the scanner 950 of FIG. 9, and the scanner 850 of FIG. 8 forthat matter, allows varying pixel densities across different rows and different portions of the field of view.

[0068] In some LiDAR applications, different sensitivity zones or angular scanning ranges may have a same pixel density but different measurement time cycles. One example of this is shown in FIG. 12 where a vehicle 1202 has two areas of LiDAR scanning, a near-distance area 1200A termed “low-beam area”, and a far-distance area 1200B termed “high-beam area”. Similarly to a low-beam road illumination in vehicles, the low-beam area 1200A is intended to access surroundings near the vehicle 1202 but in a wider area, and the high-beam area 1200B is intended for sensing farther away from the vehicle 1202, to track road conditions further ahead, but in a comparatively narrower area. In the low-beam area 1200A, the return signal is generally accumulated faster due to the comparatively high strength of the reflected signal, which allows for a shorter measurement in each individual measurement point 1260A and, accordingly, more points can be measured per unit time. Conversely, in the high-beam area 1200B, the return signal in each individual measuring point 1260B is accumulated slower due to the larger distance and the smaller signal magnitude, which requires a longer signal accumulation time. Due to this, the pixel density in the low-beam 1200A and high-beam 1200B areas may be same or similar, as shown in FIG. 12.

[0069] FIG. 13 illustrates the LiDAR scanning ranges in a more traditional angular format. A low-beam scanning range 1300A corresponding to the low-beam area 1200A in FIG. 12 is wider than a high-beam scanning range 1300B corresponding to the high-beam area 1200B in FIG. 12.

[0070] Referring to FIG. 14, a beam scanner 1450 is similar to the beam scanner 750 of FIG. 7, and includes similar elements. The beam scanner 1450 of FIG. 14 includes not one but a plurality of PICs 500, such as the PIC 500A of FIG. 5 A or the PICs 500B of FIG. 5B. The PICs 500 provide beam scanning or rastering in a first direction, by switching ranging beams between output ports (as in PIC 500A of FIG. 5 A) or by providing simultaneous ranging beams (as in PIC 500B of FIG. 5B). The PICs 500 (FIG. 14) are coupled to a common collimator 1406. The PICs 500 are disposed in a fan configuration, i.e. disposed such that the exit locations to which the out-coupling directions of output ports of the individual PICs 500 converge overlap with one another. The exit locations overlap proximate to the common collimator 1406, allowing a clear aperture of the latter to be reduced, in a similar manner as for the reduced-aperture collimators of FIGs. 4A-B and 5A-B. The collimator 1406 may be disposed at the center of the fan formed by the PICs 500.

[0071] In the beam scanner 1450 of FIG. 14, the multidirectional sensing due to PICs 500 is complemented by mechanical ID scanning of the out-coupled light beams collimated by the common collimator 1406 to propagate at port-specific angles. This mechanical scanning occurs in a second direction, which is typically perpendicular to the first direction. In the embodiment shown, the mechanical scanning is provided by a reflector 1440 tiltable about an axis 1120 and disposed downstream of the common collimator 1406.

[0072] In operation, beams 1403 (FIG. 14) are emitted by the PICs 500 from their respective output ports. The beams 1403 are collimated by the collimator 1406 and scanned by tilting the tiltable reflector 1440 about its tilt axis 1420. The tiltable reflector 1140 may include e.g. a galvo mirror, a microelectromechanical system (MEMS) mirror, a stepper motor driven mirror, a rotating mirror, etc. The solid-state (switching-based) scanning in the first direction, in combination with the mechanical scanning in the second direction, allows the beam scanner 1450 to scan the ranging light beam(s) in two directions, or in other words in two dimensions. In some embodiments, a Liquid Crystal on Silicon (LCoS) based reflective beam steerer / metasurface mirror may be used for scanning in the second direction.

[0073] Using more than one PIC 500 allows the scanning range in the first direction to be increased several times. For example, if one PIC 500 allows scanning over the range of 30 degrees, three PICs 500, as illustrated in FIG. 14, allow the scanning over the range of about 90 degrees; four PICs 500 would accordingly allow the scanning range of approximately 120 degrees; and so on. The number of PICs is determined by the overall scanning range and a switching-enabled scanning by each individual PIC. For generality, the 2D beam scanner 1450 may use any other solidstate beam scanner disclosed herein, e.g. the beam scanner 350 of FIG. 3, the beam scanner 450A of FIG. 4 A, and / or the beam scanner 450B of FIG. 4B. In addition to increasing the scanning range, or instead of increasing the scanning range, the density of the scanning directions may be increased.

[0074] Another benefit of several PIC chips sharing a same beam scanner is the ability to scale the product to a very large number of ports, or the number of lines in a Li DAR. image. For some applications, the number of ports or lines may need to be increased e.g. from 64 to 128, 256, 512, or 1024 ports or lines. The high number of ports may exceed the number of ports afforded by a widest chip that may be processed using available photolithography equipment, e.g. the width of chip may exceed the available reticle size. Furthermore, the number of electrodes that can be connected to a single Si-PIC is also limited by the width of edge of Si-PIC. Smaller Si-PIC chips have the benefit of smaller total area and therefore a lower cost, shorter optical path and therefore a lower optical loss, and a more compact overall size of the packaged scanner.

[0075] Turning to FIGs. 15A and 15B, a beam scanner 1550 is similar to the beam scanner 1450 of FIG. 14, and includes similar elements. The beam scanner 1550 of FIGs. 15A and 15B includes not one but a plurality of reflectors 1540 tiltable about respective non-parallel axes 1520. Each tiltable reflector 1540 is disposed in an optical path between the corresponding PIC 500 of the plurality of PICs and a common collimator 1506 disposed to receive light beams 1503 from all PICs 500 as they are being scanned by the corresponding tiltable reflectors 1540. The function of the tiltable reflectors 1540 is to independently scan the diverging light beams 1503 provided by individual PICs 500. For each PIC 500 - tiltable reflector 1540 pair, the scanning is performed in two dimensions / directions, one dimension / direction due to switching of output light beams in the PIC 500, and the other dimension / direction due to scanning by the corresponding tiltable reflector 1540. If required, the number of the PIC 500 - tiltable reflector 1540 pairs may be increased to make the full 360 degrees circle, with the common collimator 1506, e.g. a refractive lens and / or a metalens, disposed at the center of the circle.

[0076] Referring now to FIG. 16 with further reference to FIGs. 4A-4B, 5A-5B, and FIGs. 6A-6C, a method 1600 for manufacturing a PIC of this disclosure includes forming (FIG. 16; 1602), in the PIC, an array of output ports for outputting a light beam in a port-specific out-coupling direction. For example, the array 504 of output ports may be formed in the PIC 500A of FIG. 5 A or the PIC 500B of FIG. 5B, for outputting e.g. the light beam 503-1 or 503-3 in a direction depending on what port the light beam is our-coupled from.

[0077] The method 1600 (FIG. 16) includes forming (1604) an edge in the PIC, the edge comprising the array of output ports. The edge / output ports are configured such that the out-coupling directions of different output ports of the array converge at a common exit location downstream of the PIC edge. By way of a non-limiting example, the output ports of the array 504 (FIG. 5A) are coupled to the curved edge portion 505 of the PIC 500A and oriented for the out-coupling directions (i.e. chief rays of the diverging beams 503-1 and 503-3) to converge at the collimator 406. The forming may include forming a curved portion of the edge (FIG. 16; a group 1606) e.g. the curved portion 505 in FIG. 5A. In some embodiments, the edge may remain straight as e.g. the straight edge 405A in the PIC 400A of FIG. 4A. In the PIC 400A of FIG. 4A, the output couplers or ports 404 are oriented for the out-coupling directions to converge at the collimator 406, allowing a size reduction of the latter.

[0078] For embodiments of the method 1600 including forming the curved edge portion, the forming may include determining (1608) a field curvature of a collimator for collimating the emitted light beam, followed by matching (1610) the concave edge portion to the determined field curvature. Herein, the term “matching” means providing a substantially same, or similar enough a shape, for the collimation of the light beams emitted from any of the output ports to be suitable for an intended application of the beam scanner. For example, in FIG. 5 A, the curved edge portion 505 is shaped to match the field curvature 416 of the collimator 406, allowing efficient collimation of a light beam emitted from any output port.

[0079] Forming the curved edge portion may include e g. bulk polishing of a PIC chip to a desired edge curvature. The bulk polishing may be performed using a cylindrical polishing counterpart of a proper diameter. The bulk polishing may be suitable for cylindrical shapes, as well as for acylindrical shapes by using computer-controlled polishing methods. Alternatively, the curved edge portion may be formed by laser dicing provided that the laser dicing produces a sufficiently high optical quality of the edge.

[0080] Deep etching (1612) of the required curved shape allows any desired shape, e.g. concave, cylindrical or acylindrical, to be produced. As illustrated in FIG. 6C, the etching may be performed to a thickness smaller than the PIC thickness. The minimal thickness D of the etching may be defined by the condition (1) above. The condition represented by the condition (1) allows the emitted diverging light beam 603 to clear the PIC chip straight edge portion 605’ (FIG. 7C).

[0081] The present disclosure is not to be limited in scope by the specific embodiments described herein. Other various embodiments and modifications, in addition to those described herein, may be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure.

[0082] Although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth of the present disclosure as described herein.

Claims

1. A photonic integrated circuit (PIC) comprising:an edge; andan array of output ports at the edge for providing a light beam in a port-specific out-coupling direction;wherein out-coupling directions of different ports of the array converge at a common exit location downstream of the PIC edge.

2. The PIC of claim 1, further comprising an optical switch operably coupled to the array of output ports for switching the light beam between the output ports of the array.

3. The PIC of claim 1 or claim 2, further comprising a plurality of light detection and ranging (LiDAR) channels each coupled to an output port of the array.

4. The PIC of any one of claim 1 to claim 3, wherein the output ports of the array are oriented non-parallel to one another, whereby the out-coupling directions of different ports of the array converge to the common exit location.

5. The PIC of any one of claim 1 to claim 4, wherein the edge comprises a curved portion, wherein the output ports of the array are coupled to the curved portion of the edge.

6. The PIC of claim 5, wherein the curved portion is concave.

7. The PIC of claim 5, wherein the curved portion is acylindrical.

8. The PIC of claim 5, wherein the edge further comprises a straight portion underneath or above the curved portion, forming a step in a thickness direction of the PIC.

9. A beam scanner comprising the PIC of claim 1 and a collimator disposed at the exit location for receiving the light beam from each out-coupling direction and collimating the light beam to propagate at a port-specific angle.

10. The beam scanner of claim 9, wherein the edge of the PIC comprises a curved portion having a curvature matching a field curvature of the collimator.

11. The beam scanner of claim 9 or claim 10, further comprising a first reflector downstream of the collimator, for angularly scanning the collimated light beam about a first axis.

12. The beam scanner of claim 11, wherein the first reflector comprises at least one of: a galvo-motor based tiltable reflector, a servo-motor based tiltable reflector, a microelectromechanical system (MEMS) mirror, or a liquid crystal on silicon (LCoS) reflector.

13. The beam scanner of claim 11, further comprising a second reflector downstream of the collimator, for angularly scanning the collimated light beam about a second axis, wherein:the first reflector is configured to receive the light beam from a first output port of the array; andthe second reflector is configured to receive the light beam from a second, different output port of the array.

14. The beam scanner of claim 13, wherein the first and second axes are non-parallel to one another.

15. The beam scanner of claim 9, comprising a plurality of the PICs disposed such that the exit locations of the PICs overlap, wherein the collimator is disposed at the overlapfor receiving the light beam from each port-specific direction of each PIC and collimating the light beam to propagate at the port-specific angle.

16. The beam scanner of claim 15, wherein the PICs are disposed in a fan configuration with the collimator at a center of the fan.

17. The beam scanner of claim 15 or claim 16, further comprising a reflector downstream of the collimator, for angularly scanning the collimated light beam.

18. The beam scanner of claim 15, further comprising a plurality of reflectors each in an optical path between a corresponding PIC of the plurality of PICs and the collimator, for independently angularly scanning the light beams provided by individual PICs of the plurality of PICs.

19. A method of manufacturing a photonic integrated circuit (PIC), the method comprising:forming, in the PIC, an array of output ports for outputting a light beam in a port-specific out-coupling direction; andforming, in the PIC, an edge, wherein:the edge comprises the array of output ports; andthe out-coupling directions of different output ports of the array converge at a common exit location downstream of the PIC edge.

20. The method of claim 19, wherein forming the edge comprises forming a curved portion of the edge, wherein the output ports of the array are coupled to the curved portion.

21. The method of claim 20 wherein forming the curved edge portion comprises: determining a field curvature of a collimator for collimating the light beam; andmatching the concave edge portion to the determined field curvature.

22. The method of claim 20, wherein forming the curved edge portion comprises etching the PIC.

23. The method of claim 22, wherein the etching is performed to a thickness smaller than a thickness of the PIC.

24. The method of claim 20, wherein forming the curved edge portion comprises forming a concave edge portion.

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