Highly directional optical planar diffractive device

Abstract

Highly directional off-chip couplers comprise a periodic or quasi-periodic plurality of diffractive elements covered by a material with a high refractive index such that radiation is enabled toward the upper cladding and frustrated toward the substrate. The geometry of the diffractive elements is precisely chosen to control the radiated field profile. Thus, the device can be used as an ultra-efficient surface grating for coupling light between the chip and an optical fiber or photodetector, as an optical antenna arranged in a phased array configuration, or as an ultra-low-loss chip interconnecting system.

Description

[0001] HIGHLY DIRECTIONAL OPTICAL PLANAR DIFFRACTIVE DEVICE

[0002] FIELD OF INVENTION

[0003] The present disclosure generally relates to the field of integrated photonics, more in particular to the field of optical waveguide grating couplers and antennas for radiating light into optical fibers or free space from waveguide gratings.

[0004] BACKGROUND OF THE DISCLOSURE

[0005] An important challenge in integrated photonics is the coupling of light into and off planar waveguides. The problem arises from the fact that the mode size of conventional waveguides is typically orders of magnitude smaller than the mode field diameters of devices such as optical fibers and lasers.

[0006] Edge couplers are mode converters that adapt the mode size of the device to the waveguide mode. While these couplers can offer broad bandwidth and high coupling efficiency, they need to be positioned at the edge of the optical chip, which limits the flexibility of use. Alternatively, surface grating couplers are periodically or quasi-periodically patterned waveguides that resonantly radiate the supported mode vertically, with a resulting mode size that depends on the diffraction strength of the grating. The vertical radiation enables anywhere-on-chip positioning, which provides advantages for fiber-chip coupling, including wafer-scale testing and robustness to fiber misalignment, and allows the utilization of surface grating couplers as passive optical antennas for free-space coupling.

[0007] The power that is radiated by conventional surface grating couplers, particularly by those based on a silicon-on-insulator (SOI) platform, is not only directed upward (i.e., off-chip), but also toward the substrate, thereby reducing the directionality and hence limiting the coupling efficiency.

[0008] To overcome this limitation, one possibility is the introduction of bottom reflectors that recovers downward light, either metal mirrors or distributed Bragg reflectors as known in the art. However, this solution requires complex fabrication processes.

[0009] Another option is to utilize blazed grating profiles, to break the vertical symmetry of the structure, thereby benefiting constructive interference in the upward direction and destructive interference for the downward radiation as known in the art. Nevertheless, these designs need at least two etch steps, which introduces mask alignment tolerances and makes fabrication difficult.

[0010] Improved blazed surface grating couplers use two independently patterned guiding layers to optimize the grating coupler and maximize the amount of power radiated upward. In J. Notaros et al., Ultra-efficient CMOS fiber-to-chip grating couplers, in Optical Fiber Communications Conference and Exhibition (OFC), paper M2L5, 2016, bi-level surface grating couplers achieve a directionality of ~99%. More complex grating shapes (e.g., slanted) have been reported in Su et al., Fully-automated optimization of grating couplers, Optics Express, Vol. 26, No. 4, pp. 4023- 4034, February 2018. In all these cases, the use of non-standard grating profiles complicates fabrication.

[0011] Zero-order grating couplers utilize a prism to enable ~95% upward radiation from a subwavelength grating waveguide [see A. Sanchez-Postigo et al., Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency, Optics Letters, Vol. 41, No. 13, pp. 3013-3016, July 2016; A. Sanchez-Postigo et al., Breaking the coupling efficiency-bandwidth trade-off in surface grating couplers using zero-order radiation, Laser & Photonics Reviews, Vol. 15, No. 6, 2000542, June 2021], However, tilting the prism complicates the practical use of this device.

[0012] Surface grating couplers have been used to develop surface-emitting antennas that can be arranged in optical-phased-array (OPA) configurations to enable beam steering for LiDAR and free-space optical communications. While substantial efforts have been devoted to implementing antenna topologies and OPA architectures that maximize beam divergence and field of view, optimizing the emission efficiency has received little attention. Yet, in P. Ginel-Moreno et al., Highly efficient optical antenna with small beam divergence in silicon waveguides, Optics Letters, Vol. 45, No. 20, pp. 5668-5671, October 2020, optical antennas with L-shape segments fabricated using two etch steps are utilized to obtain emission efficiencies up to 72%.

[0013] Thus, for off-chip coupling, including fiber-chip coupling and OPA applications, surface grating couplers and optical antennas exhibiting near 100% emission efficiency or directionality and with ease of fabrication are desirable.

[0014] Any discussion of problems provided in this section has been included in this disclosure solely for the purposes of providing a background for the present invention, and should not be taken as an admission that any or all of the discussion was known at the time the invention was made.

[0015] SUMMARY OF THE INVENTION

[0016] The present invention relates to diffractive devices that can be used as a surface off-chip coupler for coupling light into and out of photonic integrated circuits, assemblies and methods including or involving such diffractive devices.

[0017] A first aspect relates to a diffractive device for coupling light into or out of a photonic integrated circuit. The diffractive device comprises: a substrate of a material having a refractive index ns; a waveguide grating comprising a plurality of radiative elements and having an effective refractive index nBfor optical diffraction of light of at least one wavelength A or light of a plurality of wavelengths (comprising at least one wavelength A) off the waveguide grating, said waveguide grating having a period A; and a cladding of a material having a refractive index nudisposed on a side of said waveguide grating. The cladding is, for example, an upper cladding disposed on the top of the waveguide grating, i.e. the side is the top side. Further, the diffractive device fulfills a single-beam condition. The single-beam condition is as follows: -ns< nB-A / / \ < -nu. A is the at least one wavelength, or a wavelength of the plurality of wavelengths, which can be the lowest wavelength thereof, the greatest wavelength thereof, and / or any wavelength thereof between the lowest and the greatest.

[0018] The diffractive device, which is preferably planar, is fabricated in e.g. a photonic substrate platform with a waveguide grating that is patterned such that a leaky mode is supported and the light that propagates through the grating is diffracted. On a side like e.g. the top side of the waveguide grating, the cladding is deposited and it has a refractive index that allows the fulfillment of the momentum-conservation law for only one diffraction order into the upper cladding and no diffraction order into the substrate. As the refractive index of the cladding material is higher than that of air, total internal reflection might occur at any parallel interface between both media, and therefore a slanted output surface, either in the form of an additionally deposited superstrate or of a prism, is provided in some embodiments, for example adjacent to the cladding. To maximize the radiation efficiency, an anti-reflection coating is, in some embodiments, deposited on the exit surface of the slanted output surface. In some embodiments, for fiber-chip coupling, the optical fiber is embedded in a high-refractive-index matching gel, which acts as the cladding, with a refractive index greater than the refractive index of the substrate. For example, if the substrate is made of silicon dioxide, the refractive index of the matching gel is greater than 1.444, and, if the substrate is undercut, the refractive index of the matching gel is greater than 1.

[0019] In some embodiments, a prism of silicon nitride or a material, such as a material with a refractive index similar to that of silicon nitride (e.g., between 0.9 and 1.1 times the refractive index of the silicon nitride) is positioned on top of a silicon-on-insulator grating coupler using silicon-nitride cladding. The pitch and / or the duty cycle of the grating coupler is / are such that the single-beam radiation condition is met and radiation at an angle perpendicular to the output surface of the prism is possible, preferably at least at the nominal wavelength. A smooth variation of the pitch and the duty cycle is used to apodize the radiation strength and maximize the overlap between the radiated field and the mode field of the optical fiber when the latter is provided (including, for example but without limitation, an assembly according to the second aspect of the disclosure below), while the amount of power that is radiated upward, i.e. at said perpendicular angle, remains near 100%.

[0020] In some embodiments, the waveguide grating is between the substrate and the cladding. In some embodiments, the waveguide grating is adjacent to the cladding. In some embodiments, the waveguide grating is adjacent to the substrate.

[0021] In some embodiments, the diffractive device further comprises an insulator layer between the waveguide grating and the substrate. In some embodiments, the waveguide grating is adjacent to the insulator layer.

[0022] In some embodiments, the diffractive device further comprises an adaptation section for minimization of back-reflections due to the mismatch between an input waveguide and the grating structure. The adaptation section comprises a plurality of grating sections or waveguide segments with modified length.

[0023] In some cases the required radiation strength for maximum overlap may not be achievable because of fabrication limitations in the minimum size of the features. In this regard, in some other embodiments a subwavelength-grating metamaterial is introduced in the surface grating coupler to add a degree of freedom for apodization. Near 90% coupling efficiencies can be achieved for a structural minimum feature size of 80 nm.

[0024] In some cases, the minimum feature size of the waveguide grating is larger than 40 nm.

[0025] In some embodiments, segments of the waveguide grating that are configured to radiate a field are curved to form a focusing grating. The curving is preferably elliptical or substantially elliptical.

[0026] In some embodiments, a prism of silicon nitride or a material or metamaterial, such as a material or metamaterial with a refractive index similar to that of silicon nitride, is positioned on top of a silicon-on-insulator micro- or nano-antenna using a silicon-nitride cladding. The thickness of the silicon layer and the geometry of the grating structure are such that the single-beam condition is met and radiation strength is maximized, such that the diffractive elements radiate most of the incident power in the upward direction in a beam with a field diameter on the order of the wavelength. These micro- or nano-antennas can be densely packed to form a two-dimensional optical phased array like, for instance, in the fifth aspect of the disclosure below.

[0027] In some embodiments, a prism of silicon nitride or a material or metamaterial, such as a material or metamaterial with a refractive index similar to that of silicon nitride, is positioned on top of silicon-on-insulator millimeter-long optical antennas using a silicon-nitride cladding. The antennas comprise long waveguides with lateral perturbations that produce very low radiation strength. The geometry of the lateral perturbations is defined so that the single-beam condition is met and the radiated field is directed only upward, with near 100% emission efficiency. The high-refractive- index prism allows amplifying the wavelength sensitivity into the air, due to the refraction at the interface between the prism and the free space. By arranging the antennas together, a onedimensional array, like that of the sixth aspect of the disclosure below, can be formed with the radiation angle being tuned by wavelength scanning, thereby enabling beam steering applications.

[0028] In some embodiments, a prism of silicon nitride or a material or metamaterial, such as a material or metamaterial with a refractive index similar to that of silicon nitride, is positioned on top of a silicon-on-insulator surface comprising millimeter-long, millimeter-wide diffractive elements that radiate a non-divergent beam, that is, a beam that exhibits a radiation pattern with a narrow beamwidth for both principal planes of the antenna.

[0029] In some embodiments, the diffractive device is adapted to couple a field to be radiated into free space, generating a divergent beam in at least one of the principal planes of the antenna.

[0030] In some embodiments, the waveguide grating is a micro- or nano-antenna radiating a divergent beam with an aperture size between 0.5 and 1.5 times the wavelength (i.e., the at least one wavelength or a wavelength of the plurality of wavelengths).

[0031] In some embodiments, the waveguide grating has a length and a width each being at least 100 times greater than the at least one wavelength A or a wavelength of the plurality of wavelengths (optionally, the lowest and / or the greatest wavelength of the plurality of wavelength).

[0032] In some embodiments, the at least one operating wavelength A or the plurality of wavelengths is within any of the following ranges in which the single-beam condition is fulfilled: visible region (ranges from 380 nm to 700 nm) for applications such as quantum information processing, optical clocks or microscopy; short-range optical communications (ranges from 850 nm to 940 nm); optical communication region (ranges from 1260 nm to 1675 nm), which is subdivided in the different communication bands (O band, E band, S band, C band, L band, U band); mid-IR (MIR) (ranges from 2 pm to 20 pm) for absorption sensing and spectroscopy.

[0033] A second aspect relates to an assembly comprising: a diffractive device according to the first aspect of the disclosure, and an optical fiber. In the assembly, the optical fiber is coupled with the diffractive device. Further, the diffractive device is configured such that a profile of a field thereof to be radiated overlaps with a mode field of the optical fiber, thereby reducing coupling fiber-to- chip insertion losses; that is to say, the diffractive device has a radiated field profile, when there is radiation, overlapping the mode field of the optical fiber.

[0034] A third aspect relates to an assembly comprising: a diffractive device according to the first aspect of the disclosure, and a photodetector. In the assembly, the photodetector is couplable or coupled with the diffractive device. The diffractive device is preferably configured such that a profile of a field thereof to be radiated matches a size of the photodetector, thereby increasing a coupling efficiency; that is to say, the diffractive device has a radiated field profile, when there is radiation, matching the size of the photodetector.

[0035] A fourth aspect relates to an assembly at least comprising first and second diffractive devices according to the first aspect of the disclosure and at least comprising a superstrate. In the assembly, the superstrate of each diffractive device has a thickness of a material having a refractive index within a range of 0.9-nuand l.l-nu(i.e. equal to or greater than 90% of nuand equal to or smaller than 110% of nu); the thickness is, in some embodiments, homogeneous, i.e. constant. Further, the first and the second diffractive devices are arranged such that respective superstrates are in contact so that a field to be radiated field (when there is radiation) by one of the first and second diffractive devices is coupled to the other one of the first and second diffractive devices, thereby enabling chip interconnection.

[0036] To this end, for instance two silicon-on-insulator chips using a silicon-nitride cladding are bonded together, one of them positioned upside down, and the light radiated by a surface grating coupler is recovered by the other surface grating coupler, thereby enabling chip interconnects with nearly 100% efficiency.

[0037] A fifth aspect relates to an assembly at least comprising first and second diffractive devices, with at least the first diffractive device being according to the first aspect of the disclosure and at least comprising a superstrate. In the assembly, the superstrate of the first diffractive device has a thickness of a material having a refractive index within a range of 0.9-nuand l.l-nu(i.e. equal to or greater than 90% of nuand equal to or smaller than 110% of nu); the thickness is, in some embodiments, homogeneous, i.e. constant. Further, the first and the second diffractive devices being arranged such that second diffractive device is in contact with the superstrate of the first diffractive device so that a field to be radiated field by one of the first and second diffractive devices is coupled to the other one of the first and second diffractive devices, thereby enabling chip interconnection.

[0038] A sixth aspect relates to a bi-dimensional array of micro-antennas or nano-antennas comprising a plurality of diffractive devices according to the first aspect of the disclosure.

[0039] The diffractive devices may have an aperture size between 0.5 and 1.5 times the at least one operating wavelength or a wavelength of the plurality of wavelengths. Further, in some embodiments, the antennas are grouped either in the form of a rectangular grid, a radial arrangement or a sparse distribution.

[0040] A seventh aspect relates to an array of millimeter-long waveguide antennas comprising a plurality of diffractive devices according to the first aspect of the disclosure.

[0041] An eighth aspect relates to a method comprising: arranging a diffractive device according to the first aspect of the disclosure; and coupling light of at least one wavelength X or a plurality of wavelengths into the diffractive device.

[0042] In some embodiments, the light is coupled out of a photonic integrated circuit. In some other embodiments, the method further comprises coupling at least part of the coupled light into a photonic integrated circuit.

[0043] In some embodiments, the method further comprises radiating field by the waveguide grating of the diffractive device.

[0044] In some embodiments, the method further comprises engineering a field to be radiated by the waveguide grating of the diffractive device by selecting a geometrical parameter of the waveguide grating prior to arranging the diffractive device.

[0045] In some embodiments, the method further comprises coupling the diffractive device with an optical fiber. The field is engineered such that the field to be radiated overlaps with a mode field of the optical fiber, thereby reducing coupling fiber-to-chip insertion losses.

[0046] In some embodiments, the method further comprises coupling the diffractive device with a photodetector. The field is engineered such that the field to be radiated matches a size of the photodetector, thereby increasing a coupling efficiency.

[0047] In some embodiments, arranging the diffractive device comprises manufacturing the diffractive device.

[0048] In some embodiments, the method further comprises coupling the diffractive device with the photonic integrated circuit for coupling light into or out of the photonic integrated circuit.

[0049] A ninth aspect relates to a method comprising: manufacturing a diffractive device according to the first aspect of the disclosure.

[0050] In some embodiments, the method further comprises coupling light of at least one wavelength X or a plurality of wavelengths into the manufactured diffractive device. BRIEF DESCRIPTION OF THE DRAWING FIGURES

[0051] The subject matter of the present disclosure is particularly pointed out and distinctly claimed in the concluding portion of the specification. A more complete understanding of the present disclosure, however, may best be obtained by referring to the detailed description and claims when considered in connection with the drawing figures, wherein like numerals denote like elements and wherein:

[0052] Figs, la and lb show schematic perspective and lateral views, respectively, of an apodized surface grating coupler for chip-to-fiber or chip-to-photodetector coupling according to e.g. a first embodiment.

[0053] Fig. lc and Id show schematic perspective and lateral views, respectively, of an apodized surface grating coupler for chip-to-fiber o chip-to-photodetector coupling with a minimum feature size greater than 80 nm and an adaptation section comprising a silicon segment and a trench, according to e.g. a second embodiment.

[0054] Fig. le and If show schematic perspective and top views, respectively, of an apodized surface grating coupler for chip-to-fiber o chip-to-photodetector coupling with a minimum feature size > 80 nm and transverse subwavelength gratings between the silicon segments of the waveguide grating, according to e.g. a third embodiment.

[0055] Fig. lg shows a schematic representation (lateral view) of two chips interconnected through off- chip couplers, according to e.g. a fourth embodiment;

[0056] Fig. lh and li show schematic perspective and top views of a millimeter-long optical antenna, according to e.g. a fifth embodiment.

[0057] Fig. lj shows a schematic perspective of an electrically long antenna in both longitudinal and transverse directions, according to e.g. a sixth embodiment.

[0058] Fig. Ik shows a lateral view of an apodized surface grating coupler for chip-to-fiber or chip-to- photodetector coupling in which the cladding material is replaced by a metamaterial formed by stacked layers of silicon and silicon dioxide.

[0059] Fig. 2 shows a wave-vector (k) diagram graphically representing the single-beam phase-matching condition for a surface grating coupler using a high-refractive-index upper cladding and prism. The horizontal and vertical axes of the figure represent the module of the z- and / -components of the wave-vector normalized to ko = 2n / A, i.e., kz / ko and k / ko, respectively. The shaded area indicates the (kz,ky) range that guarantees only-upward radiation. Fig. 3 shows the target mode field of an SMF-28 optical fiber positioned above the chip at 559with respect to the vertical and the radiation strength profile to radiate 95%, 99%, and 99.9% of the input power and maximize the coupling efficiency to the optical fiber.

[0060] Fig. 4 schematizes the design procedure of surface grating couplers and micro-antennas.

[0061] Fig. 5a shows the radiation angles (at a wavelength of e.g. 1550 nm and for the TE polarization) that meet the single-beam condition as a function of the pitch (A) and the duty cycle (DC) of a slab waveguide grating comprising silicon strips and silicon-nitride-filled trenches, according a first embodiment. The dashed line indicates the pairs (A, DC) that guarantee radiation at an angle of e.g. 559into a silicon nitride upper cladding.

[0062] Fig. 5b shows the radiation strength or leakage factor of the slab waveguide grating of Fig. 5a as a function of the pitch (A) and the duty cycle (DC). The dashed line indicates the pairs (A, DC) that guarantee radiation at an angle of e.g. 559into a silicon nitride upper cladding.

[0063] Fig. 5c shows the radiation strength as a function of the pitch of the slab waveguide grating of Fig. 5a.

[0064] Fig. 5d shows the radiation strength as a function of the duty cycle of the slab waveguide grating of Fig. 5a.

[0065] Fig. 5e shows the required radiation strength as a function of the propagation direction (z axis) to radiate a near Gaussian field at an angle of e.g. 559and yield a high coupling efficiency to an SMF- 28 optical fiber using a fiber-chip surface grating coupler of Figs, la - lb.

[0066] Figs. 5f shows the pitch and duty cycle apodization profiles to achieve the target radiation strength of Fig. 5e.

[0067] Fig. 6a shows the field distribution, simulated using 2D FDTD method, of a silicon fiber-chip surface grating coupler using a silicon-nitride upper cladding and prism for an SMF-28 optical fiber, operating at a wavelength of 1550 nm and TE polarization, according to a first embodiment of Figs, la - lb. The waveguide grating follows the apodization profiles of Fig. 5f.

[0068] Fig. 6b shows the coupling efficiency as a function of the wavelength for the TE polarization for the fiber-chip surface grating coupler of Fig. 6a.

[0069] Fig. 7a shows the pitch and duty cycle apodization profiles of a fiber-chip surface grating coupler to radiate a near Gaussian field with high coupling efficiency to an SMF-28 optical fiber at a nominal wavelength of 1550 nm and TE polarization, for a minimum feature size of 80 nm.

[0070] Fig. 7b shows the back-reflection as a function of the lengths of the silicon segment and silicon- nitride-filled trench of an adaptation section, according to a second embodiment of Figs, lc - Id.

[0071] Fig. 7c shows the field distribution, simulated using 2D FDTD method, of a silicon fiber-chip surface grating coupler using a silicon-nitride upper cladding and prism for an SMF-28 optical fiber, operating at a wavelength of e.g. 1550 nm and TE polarization, for a minimum feature size of 80 nm, according to e.g. the second embodiment of Figs, lc - Id. The waveguide grating follows the apodization profiles of Fig. 7a.

[0072] Fig. 7d shows the coupling efficiency as a function of the wavelength for the TE polarization for the fiber-chip surface grating coupler of Fig. 7c.

[0073] Fig. 8a shows the radiation angles (at a wavelength of e.g. 1550 nm and for the TE polarization) that meet the single-beam condition as a function of the pitch (A) and the equivalent refractive index (nswc) synthesized via subwavelength-grating (SWG) metamaterial engineering of a slab waveguide grating comprising silicon strips and SWG-synthesized trenches, for a duty cycle in the propagation direction of 50%, according to e.g. the third embodiment. The dashed line indicates the pairs (A, nswc) that guarantee radiation at an angle of e.g. 559into a silicon nitride upper cladding.

[0074] Fig. 8b shows the radiation strength or leakage factor of the slab waveguide grating of Fig. 8a as a function of the pitch (A) and the equivalent refractive index of the SWG-synthesized trenches (nswc). The dashed line indicates the pairs (A, nswc) that guarantee radiation at an angle of 559into a silicon nitride upper cladding.

[0075] Fig. 8c shows the radiation strength as a function of the pitch of the slab waveguide grating of Fig. 8a.

[0076] Fig. 8d shows the radiation strength as a function of the equivalent refractive index nswc of the slab waveguide grating of Fig. 8a.

[0077] Fig. 8e shows the required radiation strength as a function of the propagation direction (z axis) to radiate a near Gaussian field at an angle of e.g. 559and yield a high coupling efficiency to an SMF- 28 optical fiber using a fiber-chip surface grating coupler of Figs, le - If.

[0078] Figs. 8f shows the pitch and nswc apodization profiles to achieve the target radiation strength of Fig. 8e.

[0079] Fig. 8g shows the field distribution, simulated using 2D FDTD method, of a silicon fiber-chip surface grating coupler using a silicon-nitride upper cladding and prism for an SMF-28 optical fiber, operating at a wavelength of e.g. 1550 nm and TE polarization, according to a third embodiment of Figs, le - If. The waveguide grating follows the apodization profiles of Fig. 5f. Fig. 8h shows the coupling efficiency as a function of the wavelength for the TE polarization for the fiber-chip surface grating coupler of Fig. 8g.

[0080] Fig. 8i shows the duty cycle in the transverse direction (DCX) as a function of the equivalent refractive index nswc for a transverse pitch of 450 nm, calculated following the procedure reported in in J. M. Luque-Gonzalez et al., "A review of silicon subwavelength gratings: building breakthrough devices with anisotropic metamaterials," Nanophotonics, Vol. 10, No. 11, pp. 2765-2797 (2021).

[0081] Figs. 8j shows the DCXapodization profile to achieve the target radiation strength of Fig. 8e for a transverse pitch of 450 nm.

[0082] Fig. 9 shows the prism with the angle convention for a millimeter-long antenna with silicon-nitride upper cladding according to the fifth embodiment of Fig. lh.

[0083] Fig. 10 shows a two-dimensional optical phased array of micro-antennas.

[0084] Figs. 11a and lib show the radiation efficiency and the radiation strength, respectively, of the antenna of Figs, lh and li as a function of the length of the gap (g) and the width of the lateral segments (W / s).

[0085] Figs. 12a shows the beamwidth of the far-field of the antenna of Figs, lh and li in the prism and when it is diffracted to the air, and Fig. 12b shows the far-field spot in the air in vertical direction (0) at e.g. the wavelength A = 1550 nm. Fig. 12c shows a distribution of the near field radiated by the first 100 periods of the antenna, where only an upward beam is radiated.

[0086] Fig. 13 shows the simulated wavelength sensitivity in the air of the grating antenna of Figs, lh and li. The inset shows the radiation angle in the air.

[0087] Fig. 14 shows a one-dimensional optical phased array of millimeter-long antennas according to the fifth embodiment of Figs, lh and li.

[0088] It will be appreciated that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help improve understanding of illustrated embodiments of the present disclosure.

[0089] DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0090] The description of exemplary embodiments of the present disclosure provided below is merely exemplary and is intended for purposes of illustration only; the following description is not intended to limit the scope of the invention disclosed herein. Moreover, recitation of multiple embodiments having stated features is not intended to exclude other embodiments having additional features or other embodiments incorporating different combinations of the stated features. In this sense, for example, it will be noted that values of parameters indicated below (of, for example, wavelength, refractive indices, etc.) are exemplary and are intended to ease the comprehension of the present disclosure, such values and other values fall within the scope of the present disclosure.

[0091] As discussed in greater detail below, a diffractive device, preferably a planar or flat diffractive device, is provided with a cladding 105 that, in the following, will be referred to as upper cladding 105 due to its position on the diffractive device. The upper cladding 105 makes the diffractive device meet a single-beam radiation condition for light of at least some wavelength or wavelengths, and preferably has a high refractive index, i.e. above 1.5.

[0092] In some embodiments, the device comprises a waveguide grating 103 formed by a plurality of diffractive elements, with a pitch A and duty cycle DC = o / A to engineer the radiation angle and strength profile of the grating along the propagation direction. Subwavelength grating structures 109 can be introduced transversely in the gaps between the diffractive segments to achieve lower radiation strengths with larger feature sizes. In some embodiments, the planar device comprises a solid waveguide core 110 that is loaded with a series, i.e. a plurality, of lateral diffractive segments 111 placed aside. The propagating Bloch-Floquet mode evanescently overlaps with the lateral diffractive segments which are physically separated from the waveguide core. This allows precise control of the overlap and hence the radiation strength of the antenna, resulting in a planar device with a millimeter-scale length, preferably a length between 1 mm and 10 mm.

[0093] According to an aspect of this description, there is provided a (planar) diffractive device for radiating light with near 100% emission efficiency to e.g. an optical fiber, a photodetector, an interconnected optical chip, or free space for beam steering and lidar applications.

[0094] In the embodiments of Figs, la and lb, a fiber-chip surface grating coupler is shown in a silicon- on-insulator (SOI) platform with a silicon substrate 101, a silicon dioxide insulator layer or buried oxide (BOX) 102, a silicon waveguide grating core 104, and a silicon nitride upper cladding with a slanted output surface. Alternatively, a flat silicon nitride upper cladding 105 is used and a superstrate or a prism of a material with a refractive index npequal or similar to that of silicon nitride, within a range of ±10%, is positioned on top 106. In all cases, an anti-reflection coating 107 is deposited on the output surface. From now on, for simplicity, the utilization of a prism will be assumed. Optionally, the BOX 102 can be undercut to increase the range of effective refractive indices that meet said single-beam condition. The materials of the cladding and the prism may be selected from the group consisting of silicon nitride, zirconium dioxide, yttria-stabilized zirconium dioxide, lithium niobate, titanium dioxide, silicon carbide, tantalum pentoxide, strontium titanate, zinc oxide, zinc selenide, high-index optical glasses, or material with a refractive index higher than the refractive index of the insulator substrate and lower than the refractive index of silicon.

[0095] At least in the embodiments of Figs, lc and Id, a few features 108, i.e. waveguide segments, are introduced at the beginning of the grating as an adaptation section to reduce back-reflections caused by the mode mismatch between the input waveguide and the grating waveguide.

[0096] At least in the embodiments of Figs, le and If, transverse subwavelength grating structures 109 are introduced in the gaps between silicon segments of the waveguide grating core.

[0097] Fig. lg shows two chips interconnected by means of surface couplers as those of Figs, la - If.

[0098] Turning to Figs, lh and li, an embodiment of a SOI waveguide antenna is shown that comprises a silicon-nitride upper cladding 105 and an antireflection-coated 107 prism 106 of silicon nitride or similar material, with a solid waveguide core 110 loaded with lateral silicon diffractive segments 111.

[0099] As for the embodiments of Fig. lj, a grating antenna 112 is electrically long (length higher than 500 times the operating wavelength) in both transverse and longitudinal directions to generate a highly collimated free-space beam with a small divergence angle in both azimuthal and elevation directions.

[0100] In the embodiment of Fig. Ik, the upper cladding of silicon nitride of the embodiment of Figs, la and lb is substituted with a stack of silicon and silicon dioxide layers 113 that synthesizes a metamaterial with a refractive index similar to that of silicon nitride.

[0101] Unlike other prism-assisted devices, in these designs the prism can be positioned in direct contact with the chip surface, which remarkably simplifies the manipulation of the structure. Furthermore, the fabrication of the device relies on simple, one-step lithography.

[0102] To minimize reflections at the discontinuity between the prism and the air (refractive index nair) or the optical fiber (refractive index nt), an antireflection (AR) coating 107 is deposited on the output surface of the former. This AR coating acts as a quarter-wavelength adapter, with a refractive index r / 4 = ^ / np^air (prism-air) or r / 4 = (prism-fiber) and thickness of 0.25A / r) / 4.

[0103] A planar diffractive device of embodiments of Figs, la - lk supports a leaky Bloch-Floquet mode with an effective refractive index where nuis the (equivalent) refractive index of the upper cladding, 0Uis the radiation angle into the upper cladding, nsis the refractive index of the substrate, 6Sis the radiation angle into the substrate, nBis the effective refractive index of the Bloch-Floquet mode, m is the diffraction order, A is the wavelength, A is the period, and a is the radiation strength or leakage factor. The real part of the effective index determines the radiation angle of the light toward the upper cladding and substrate. The supported mode is radiated only upward, thus enabling a directionality of 100%, when the single-beam condition is met (Fig. 2): which implies that the radiation angle is arcsin and 6Sis not real.

[0104] In some embodiments, such as in those of Figs, la - lg, the width (l / l / ) of the waveguide grating is configured to provide a specific radiated field diameter in the transverse direction. The pitch (A) and duty cycle (DC = a / ), or the properties of the transverse SWG features (Ax, DCX= a / Ax) can be varied along the propagation direction to control the effective index of the Bloch-Floquet mode and hence the radiation angle for meeting the single-beam condition and the radiation strength.

[0105] For the exemplary embodiments of e.g. Figs, la - lg, the effective index of the Bloch-Floquet mode of a periodic waveguide is calculated as a function of the geometry of the diffractive elements (e.g., pitch and the duty cycle). For this computation, if the grating waveguide is wide (l / l / » A), the structure can be considered x-invariant, and 2D finite-difference time-domain (FDTD) or 2D eigenmode-expansion-method (EME) simulations of a single period can be used. For microantennas (1 / 1 / ~ A), 3D FDTD simulations are employed as known in the art.

[0106] In the embodiments of Figs, la - lg, an SOI platform is formed by a layer of silicon nitride (nu= 2, thickness Hu= 2 pm) 105 on top of a core layer of silicon (refractive index nc= 3.476, thickness H = 220 nm) 104 on top of a buried oxide (ns= 1.444, thickness HBOX = 2 pm) 102 on top of a silicon substrate 101. A prism of Ohara S-NPH3 (np= 1.89) 106 is positioned on top of the upper cladding. All values are considered for a wavelength of 1550 nm. These refractive indices produce a range of radiation angles for single-beam operation of 46.29< 0U< 909, which, due to the slightly smaller refractive index of the prism, translates into 49.89< 0air < 909in the air. A maximum range of single-beam-enabled angles can be obtained by undercutting the substrate, therefore replaced by air (ns= 1). Then, the range of radiation angles is 309< 0U< 909(31.99< 0air < 909).

[0107] In the embodiments of Figs, la - If, a silicon-nitride-cladding surface grating coupler can be designed to maximize the coupling efficiency to an SMF-28 optical fiber. For simplicity, the optical fiber will be assumed to be in physical contact with the prism through the corresponding antireflection coating 107. The coupling efficiency (CE), defined as the fraction of input guided power that is radiated into the optical fiber, can be calculated as the product of two factors: the amount of power that is radiated upward (Prad), whether coupled or not into the optical fiber, and the overlap integral (OL) between the radiated field and the mode field of the optical fiber, i.e., CE = Prad - OL. Operating in the single-beam regime, the former is theoretically 100% of the input power.

[0108] To radiate a power Prad with a specific field profile that maximizes the overlap with a field G(z), the radiation strength must be where the input power at the beginning of the grating (z = 0) is assumed to be 1. For an optical fiber positioned at an angle 6 with respect to the vertical, the target field can be approximated as where C is a normalization constant such that ^ G2(z)dz = 1 and MFD is the mode field diameter of the optical fiber. Figure 3 shows the target field G(z) for an SMF-28 optical fiber with a mode field diameter MFD = 10.4 pm and a tilt angle 6 = 559, as well as the leakage factor a(z) to radiate 90%, 95%, and 99.9% of the input power. In this figure, zmaxdenotes the position of the grating waveguide at which the maximum a is achieved. It is apparent that the higher Prad is, the higher a is needed.

[0109] According to Eq. (4), to radiate all of the incident power (Prad = 100%) an infinite a should be synthesized. Thus, for a fixed fiber angle (e.g., 559), the achievable range of a values using feasible grating geometries may not be sufficient to produce the required a(z) profile. By reducing Prad, synthesizable a values can be attained, but this solution reduces the directionality. All power can be radiated, however, by setting the a(z) profile constant to its maximum value for z > zmax. By optimizing the resulting a(z), it is possible to maximize the coupling efficiency to the optical fiber.

[0110] The design procedure of the embodiments of Figs, la - lb is schematized in Fig. 4. First, the effective index of the grating waveguide is calculated as a function of A and DC for the TE polarization at a nominal wavelength of 1550 nm. Then, radiation angles are obtained from the real part of the effective index using Eq. (1). In Fig. 5a, real radiation angles that meet the singlebeam condition are represented. For low / \ values (A < 0.5A / nB), the structure enters the Bragg and subwavelength regimes, while substrate radiation is enabled for large A values. From this map, the relationship between A and DC to keep the angle 0Uconstant is found. The white dashed curve indicates the pairs (A, DC) for which the radiation angle is fixed to 559, which enables singlebeam radiation. Figure 5b shows the radiation strength, calculated from the imaginary part of the effective index, as a function of A and DC. For 0U= 559, the attainable leakage factor is shown as a function of A and DC in Figs. 5c and 5d, respectively. By combining the required a(z) profile of Fig. 5e with the a(A) and a(DC) profiles of Figs. 5c and 5d, it is possible to obtain the apodization functions A(z) and DC(z), shown in Fig. 5f, that lead to the target radiated field at a constant angle 0Uof 559. Since the chosen angle ensures upward, single-beam radiation, the directionality is "'100%. Together with the ~100% overlap integral due to the apodization, a coupling efficiency of ~100% to the optical fiber can be achieved.

[0111] Finally, the full grating structure is simulated, monitoring the amount of power that is coupled into a conveniently positioned optical fiber with the right inclination angle of 58.79. The electric field distribution (TE polarization) and the coupling efficiency of the designed fiber-chip grating coupler are shown in Figs. 6a and 6b, respectively. It is apparent that all power is radiated upward, with downward radiation being naturally frustrated, thereby achieving an unprecedented coupling efficiency of 98% (-0.09 dB). Back-reflections are negligible because of the smooth transition, caused by the apodization profile, from the homogeneous input waveguide and the grating waveguide.

[0112] The length of the first features of the grating waveguides cannot be smaller than a minimum size imposed by fabrication constraints. Consequently, the beginning of the grating cannot be apodized in practical realizations of the device, which thus would reduce the coupling efficiency and introduce undesired scattering and reflections. In the exemplary embodiment of Figs, lc - Id, a minimum feature size of 80 nm, which is typical in currently available deep-ultra-violet (DUV) lithography techniques, is considered; notwithstanding, other minimum feature sizes, smaller and larger, are possible and also fall within the scope of the present disclosure. For the embodiment of Figs, lc - Id, new apodization functions A(z) and DC(z), shown in Fig. 7a, are computed to optimize the coupling efficiency when 7\(z)-DC(z) and 7\(z)-[l-DC(z)] are greater than 80 nm. Then, an adaptation section 108 is included before the first grating tooth. This adaptation section comprises a silicon segment of length LL and a trench of length Lz. Figure 7b shows the back- reflection as a function of L-L and Lz, showing that a minimum back-reflection of 1.2% (-19 dB) is achieved for Li = 320 nm and Lz = 80 nm. Figure 7c and 7d show, respectively, the electric field distribution and the achieved coupling efficiency, with a peak value of 85% (-0.71 dB).

[0113] In the embodiment of Figs, le - If, the apodization is performed using subwavelength grating (SWG) metamaterial engineering instead of DC variations, in order to provide an alternative degree of freedom. This apodization allows to fix a duty cycle of 50% in the propagation direction to increase the minimum feature size of the grating and avoid the use of adaptation sections. A periodic structure comprising a series of segments of refractive indices ni and nz with a period that suppresses diffraction and reflection effects (A < 0.5A / nB) can behave as a homogeneous anisotropic waveguide of artificial material with an equivalent refractive index nswc (ni < nswc < nz). Subwavelength grating metamaterials, since their first demonstration in silicon waveguides at NRC Canada, have fueled the development of high-performance devices in areas as diverse as waveguiding, power splitting, edge coupling, polarization handling, and biosensing, to name a few. The design procedure follows Fig. 4, using A and nswc as the apodization parameters. Figures 8a and 8b show the radiation angle and the radiation strength, respectively, as a function of pitch and the equivalent refractive index nswc for a fixed duty cycle in the propagation direction of 50%, which guarantees fabricable feature sizes. The dashed line represents pairs (A, nswc) that lead to 0U= 559. Figures 8c and 8d show a(A) and a(nswG), respectively. By mapping these functions into the target a(z) profile (Fig. 8e), the apodization profiles A(z) and neq(z) are obtained, as shown in Fig. 8f. The simulated field distribution and coupling efficiency as a function of the wavelength are shown in Figs. 8g and 8h, respectively. Finally, for the practical implementation of the structure, using the procedure reported in J. M. Luque-Gonzalez et al., "A review of silicon subwavelength gratings: building break-through devices with anisotropic metamaterials," Nanophotonics, Vol. 10, No. 11, pp. 2765-2797 (2021), neq(z) is mapped into actual SWG structures with a constant transverse pitch A, of 450 nm and a variable duty cycle DCx(z), as shown in Figs. 8i and 8j.

[0114] The silicon-nitride-cladding surface grating coupler that is shown in Figs, la - If can be designed to operate as a micro-antenna. The design is identical to that described for chip-to-fiber coupling except for the reduced mode field diameter that is required to radiate a beam with a field diameter of less than 5 pm in both longitudinal and transverse directions. To achieve high radiation strengths, it might be necessary to radiate with angles that are far away from the vertical or to use thicker SOI substrates.

[0115] The micro-antennas 113 can be arranged to form a two-dimensional optical phased array (OPA). Figure 9 shows an exemplary schematic of a 11 x 5 array.

[0116] In the embodiment of Figs, lh - li, a surface grating coupler is designed to operate as a millimeter- long optical antenna, which can be embedded in an optical-phased-array configuration and used for beam steering applications such as lidar or satcom. The antenna is formed by a waveguide core 110 that is loaded with an arrangement of diffractive lateral segments 111. The width of the waveguide core (W) is selected to minimize leakage losses to the silicon substrate and to delocalize the guided mode, which allows enlarged, easily fabricable gaps (g) between the waveguide core 110 and the lateral diffractive blocks 111. The evanescent field interacts with the lateral segments 111, with a pitch (A) and duty cycle (DC = a / A) that enable single-beam radiation with a specific radiation strength.

[0117] The millimeter-long antenna is based on an SOI platform with a silicon core (nc= 3.476, H = 220 nm) 110 and a buried oxide layer (ns= 1.444, HBOX = 2 pm) 102 on top of a silicon substrate 101. An upper cladding of silicon nitride (nu= 2) 105 is used with a thickness of 2 pm, on top of which an Ohara S-NHP3 prism (np= 1.89) 106 with an angle of = 55° is positioned. Schematic representation (lateral view) together with the angle convention is shown in Fig. 10.

[0118] In this example, a core width of 500 nm is chosen to guarantee single-mode operation for the waveguides. The corresponding effective index for a TM polarized mode is 2.146. The period of the lateral diffractive blocks is 410 nm to radiate towards the top SiN cladding with an angle 0U= 55°, which is within the single-beam condition range (-46.29< 0U< -909).

[0119] The use of the high-refractive-index prism also benefits the wavelength sensitivity of the antenna, an essential parameter for beam steering in the elevation direction (0). Specifically, the wavelength sensitivity in the prism is

[0120] By applying the Snell's law at the interface between the air and the output surface of the prism, the wavelength sensitivity becomes

[0121] In the case of using an Ohara S-NHP3 prism, the factor K > np= 1.89, which denotes an angular amplification in the air.

[0122] By assuming that the effective index of the antenna remains unaffected after the introduction of the loading segments, from Eq. (1) a pitch of 410 nm is calculated to radiate into the air at an angle 0o = 65° using an Ohara prism with an angle ip = 55°.

[0123] To design the antenna, Bloch-Floquet analysis of a single period, including the waveguide core and lateral segments, is performed. By considering the attenuation constant of the propagating mode, a, the mode field of a single-period is then concatenated, thereby forming the near field of a millimeter-long antenna without carrying out the computationally demanding simulation of the full structure. This method allows to efficiently calculate the radiated near field, from which the far-field can be obtained by computing the two-dimensional Fourier transform (Fraunhofer diffraction integral). This information allows to estimate the form of the far-field radiated beam and its angular divergence with high accuracy.

[0124] Once the grating period and core are designed to radiate at a specific angle, the geometry of the loading segments (Ls, g, W / s) is chosen to achieve the desired attenuation constant (a) of the propagating mode. This is possible because the lateral diffractive elements are physically separated from the waveguide core, which has a negligible effect on the Bloch-Floquet effective index but a considerable effect on radiation strength. For simplicity, the length Lsis set to a constant value. Then, the length of the gap (g) and the width of the lateral segments (W / s) is scanned to compute the radiation efficiency and radiation strength, as shown in Figs. 11a and lib, respectively. As expected, provided the single-beam condition is satisfied, the radiation efficiency is near 100% and virtually independent of g and W / s. Both parameters are then utilized to control the radiation strength. For g = 240 nm, Ls= 120 nm and W / s= 120 nm, a = 0.0005 pm-1, for which the antenna length is 2.5 mm and the resulting beamwidth of the far-field is 0.0679, as shown in Fig. 12a and Fig. 12b. The 3D-FDTD propagation of the near field through the first 100 periods of the antenna is shown in Fig. 12c, showing a 100% directionality.

[0125] For this exemplary antenna, the wavelength sensitivity in the air is 0.35? / nm around the design central wavelength, shown in Fig. 13, which is more than twice the wavelength sensitivity of similar antennas in SOI.

[0126] The millimeter-long optical antennas can be arranged to form a one-dimensional optical OPA. Figure 14 shows an exemplary schematic comprising 10 antennas sharing lateral diffractive elements. Depending on the amplitude with which each antenna is fed, the far-field spot will have a specific shape and angular divergence in azimuthal direction ( ). Furthermore by controlling the phase difference between the antennas, the far-field spot can vary its pointing angle in azimuth ( ).

[0127] In virtue of the reciprocity principle in optics, the behavior of the waveguide gratings of all embodiments is reciprocal. Therefore, not only do the off-chip couplers radiate from the chip into the air, but also from the optical fiber, laser, or free space into the chip.

[0128] Applications of the described embodiments include fiber-chip coupling for telecom, datacom, and quantum technologies; chip interconnects; beam steering for secure free-space optical communications and satellite communications, light detection and ranging (lidar), remote sensing, three-dimensional imaging and mapping, or environmental monitoring, to name a few.

[0129] The present invention has been described above with reference to a number of exemplary embodiments and examples. It should be appreciated that the particular embodiments shown and described herein are illustrative of the invention and its best mode and are not intended to limit in any way the scope of the invention as set forth in the claims. The features of the various embodiments may stand alone or be combined in any combination. The terms "includes", "comprises" and derivations thereof (such as "including", "comprising", etc.) should not be understood in an excluding sense, that is, these terms should not be interpreted as excluding the possibility that what is described and defined may include further elements, steps, etc. Further, unless otherwise noted, various illustrated steps of a method can be performed sequentially or at the same time, and not necessarily be performed in the order illustrated. It will be recognized that changes and modifications may be made to the exemplary embodiments without departing from the scope of the present invention. These and other changes or modifications are intended to be included within the scope of the present invention, as expressed in the following claims.

Claims

CLAIMS1. A diffractive device for coupling light into or out of a photonic integrated circuit, comprising: a substrate of a material having a refractive index ns; a waveguide grating having an effective refractive index nBfor optical diffraction of light off the waveguide grating of at least one wavelength A or a plurality of wavelengths comprising at least one wavelength A, said waveguide grating having a period A; a cladding of a material having a refractive index nudisposed on a side of said waveguide grating, wherein the diffractive device fulfills a single-beam condition, the single-beam condition being: -ns< nB-A / / \ < -nu.

2. The diffractive device according to claim 1, wherein radiation of light for at least one wavelength X or a plurality of wavelengths is allowed toward the upper cladding and frustrated toward the substrate.

3. The diffractive device according to any of the preceding claims, wherein the diffractive device is planar.

4. The diffractive device according to any of the preceding claims, wherein the cladding is made out of a metamaterial with an equivalent refractive index nu.

5. The diffractive device according to any of the preceding claims, wherein said cladding has a slanted output surface perpendicular to a direction along which light of the at least one wavelength or the plurality of wavelengths is to be diffracted.

6. The diffractive device according to any of claims 1-4, further comprising a superstrate or a prism arranged on said cladding, said superstrate or said prism being of a material having a refractive index within a range of 0.9-nuand l.l-nu, said superstrate or said prism having a slanted output surface perpendicular to a direction along which light of the at least one wavelength or the plurality of wavelengths is to be diffracted.

7. The diffractive device according to claim 6, wherein the diffractive device comprises the superstrate.

8. The diffractive device according to any of claims 5-7, wherein the slanted output surface comprises antireflection coating adapted to avoid total internal reflection at the output surface.

9. The diffractive device according to any of the preceding claims, wherein the substrate is undercut.

10. The diffractive device according to any of the preceding claims, wherein said cladding is made out of a gel or resin with a high refractive index in which an optical fiber can be embedded.

11. The diffractive device according to any of the preceding claims, wherein the waveguide grating has a width adapted to provide a mode field diameter of a field to be radiated in a transverse direction.

12. The diffractive device according to any of the preceding claims, wherein at least one of a pitch and a duty cycle of the waveguide grating is adapted to gradually modify a field to be radiated along a propagation direction.

13. The diffractive device according to any of the preceding claims, wherein the waveguide grating is segmented at a subwavelength scale for gradually modifying a field to be radiated.

14. The diffractive device according to any of the preceding claims, further comprising an adaptation section comprising a plurality of waveguide segments with a length that produces a destructive interference of back-reflections, the plurality of waveguide segments being positioned between the input waveguide and the first radiative segment of said waveguide grating.

15. The diffractive device according to any of the preceding claims, wherein segments of said waveguide grating that are configured to radiate a field are curved to form a focusing grating, the curving being preferably elliptical or substantially elliptical.

16. The diffractive device according to any of claims 11-15, wherein the diffractive device is adapted to couple a field to be radiated into free space, generating a divergent beam in at least one of the principal planes of the antenna.

17. The diffractive device according to claim 16, wherein the waveguide grating is a micro- or nano-antenna radiating a divergent beam with an aperture size between 0.5 and 1.5 times the wavelength.

18. The diffractive device according to claim 16, wherein the waveguide grating is a millimeter-long optical antenna.

19. The diffractive device according to claim 16, wherein the waveguide grating has a length and a width each being at least 100 times greater than the at least one wavelength A or the plurality of wavelengths.

20. The diffractive device according to any of the preceding claims, wherein the substrate comprises a silicon-on-insulator substrate.

21. The diffractive device according to claim 20 when directly or indirectly depending upon claim 6, wherein the materials of the cladding and the prism are selected from the group consisting of silicon nitride, zirconium dioxide, yttria-stabilized zirconium dioxide, lithium niobate, titanium dioxide, silicon carbide, tantalum pentoxide, strontium titanate, zinc oxide, zinc selenide, high-index optical glasses, or material with a refractive index higher than the refractive index of the insulator substrate and lower than the refractive index of silicon.

22. The diffractive device according to any of the preceding claims, wherein a minimum feature size of the waveguide grating is larger than 40 nm.

23. The diffractive device according to claim 22, wherein the minimum feature size is 80 nm.

24. The diffractive device according to any of the preceding claims, wherein the at least one wavelength A or the plurality of wavelengths is within any of the following ranges in which the single-beam condition is fulfilled: from 380 nm to 700 nm; from 850 nm to 940 nm; from 1260 nm to 1675 nm; and / or from 2 pm to 20 pm.

25. An assembly comprising a diffractive device according to any of the preceding claims and an optical fiber, the optical fiber being coupled with the diffractive device; wherein the diffractive device is configured such that a profile of a field thereof to be radiated overlaps with a mode field of the optical fiber, thereby reducing coupling fiber-to-chip insertion losses.

26. An assembly comprising a diffractive device according to any of claims 1-24 and a photodetector, the photodetector being coupled with the diffractive device; wherein the diffractive device is configured such that a profile of a field thereof to be radiated matches a size of the photodetector, thereby increasing a coupling efficiency.

27. A bi-dimensional array of micro- or nano-antennas comprising a plurality of diffractive devices with an aperture size between 0.5 and 1.5 times the at least one operating wavelength according to claim 17.

28. The bi-dimensional array of micro- or nano-antennas according to claim 27, wherein the antennas are grouped either in the form of a rectangular grid, a radial arrangement or a sparse distribution.

29. An array of millimeter-long waveguide antennas comprising a plurality of diffractive devices according to claim 18.

30. An assembly at least comprising first and second diffractive devices, wherein at least the first diffractive device is according to claim 7 or according to any of claims 8-24 when directly or indirectly depending upon claim 7, wherein: the superstrate of the first diffractive device has a thickness of a material having a refractive index within a range of 0.9-nuand l.l-nu, the thickness preferably being homogeneous; the first and the second diffractive devices being arranged such that second diffractive device is in contact with the superstrate of the first diffractive device so that a field to be radiated field by one of the first and second diffractive devices is coupled to the other one of the first and second diffractive devices, thereby enabling chip interconnection.

31. An assembly at least comprising first and second diffractive devices, each of the first and second diffractive devices being according to claim 7 or according to any of claims 8-24 when directly or indirectly depending upon claim 7, wherein:the superstrate of each diffractive device has a thickness of a material having a refractive index within a range of 0.9-nuand l.l-nu, the thickness preferably being homogeneous; the first and the second diffractive devices being arranged such that respective superstrates are in contact so that a field to be radiated by one of the first and second diffractive devices is coupled to the other one of the first and second diffractive devices, thereby enabling chip interconnection.

32. A method comprising: arranging a diffractive device according to any of claims 1-24; and coupling light of at least one wavelength A or a plurality of wavelengths into the diffractive device.

33. The method according to claim 32, wherein the light is coupled out of a photonic integrated circuit.

34. The method according to claim 32, further comprising coupling at least part of the coupled light into a photonic integrated circuit.

35. The method according to any of claims 32-34, further comprising radiating field by the waveguide grating of the diffractive device.

36. The method according to any of claims 32-35, further comprising engineering a field to be radiated by the waveguide grating of the diffractive device by selecting a geometrical parameter of the waveguide grating prior to arranging the diffractive device.

37. The method according to claim 36, further comprising coupling the diffractive device with an optical fiber; wherein the field is engineered such that the field to be radiated overlaps with a mode field of the optical fiber, thereby reducing coupling fiber-to-chip insertion losses.

38. The method according to claim 36, further comprising coupling the diffractive device with a photodetector; wherein the field is engineered such that the field to be radiated matches a size of the photodetector, thereby increasing a coupling efficiency.

39. The method according to any of claims 32-38, wherein arranging the diffractive device comprises manufacturing the diffractive device.

40. The method according to any of claims 32-36, further comprising coupling the diffractive device with the photonic integrated circuit for coupling light into or out of the photonic integrated circuit.

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