An edge coupler

Abstract

This document describes an edge coupler that comprises a semiconductor structure embedded within a dielectric layer that is formed on a substrate. The semiconductor structure comprises two sections: a first section that has a moth-eye structure formed of a plurality of tapered elements having a constant pitch and varying lengths with the tapered elements being arranged along an in-plane axicon topology; and a second section that comprises a tapered coupling structure.

Description

AN EDGE COUPLERCROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority to Singapore patent application no. 10202401952V which was filed on 3 July 2024, the contents of which are hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] This application relates to an edge coupler that comprises a semiconductor structure embedded within a dielectric layer that is formed on a substrate. The semiconductor structure comprises two sections: a first section that has a moth-eye structure formed of a plurality of tapered elements having a constant pitch and varying lengths with the tapered elements being arranged along an in-plane axicon topology; and a second section that comprises a tapered coupling structure.BACKGROUND

[0003] The rapid expansion of data centers worldwide has driven a growing demand for high-density data communications. Silicon photonics, which is compatible with CMOS fabrication processes, has emerged as an effective platform for processing both incoming and outgoing optical signals within complex on-chip networks. However, a key challenge in interfacing photonic integrated circuits (PICs) with optical fibers lies in the mismatch between optical fibers and on-chip waveguides, particularly with respect to their mode field diameters and effective refractive indices.

[0004] Standard optical fiber modes, such as SMF-28, exhibit a circular Gaussian mode with a mode field diameter (MFD) of approximately 10 pm. In contrast, edge-emitting lasers, such as distributed feedback (DFB) lasers, produce non-circular (e g. rectangular) Gaussian modes with lateral dimensions of only a few microns. This mismatch is further compounded by the significantly smaller mode sizes of typical silicon waveguides, which are often in the sub-micron range Edge couplers address this issue by enabling efficient optical coupling between fibers and silicon waveguides, making them a critical component in photonic transceiver circuits.

[0005] Edge coupler designs span a wide spectrum in terms of geometric complexity and fabrication methods, ranging from simple to highly intricate configurations. Among the main considerations in edge coupler design include insertion loss (or coupling efficiency), device footprint, operational bandwidth, polarization dependence, and alignment tolerance One of the most basic and widely adopted designs by those skilled in the art is the edge coupler design that incorporates an inverse taper structure, wherein the width of the waveguide is gradually reduced along the direction of light propagation down to the lithographic limit.

[0006] The inverse taper operates based on the principle of adiabatic mode transition, wherein the optical mode of the propagating signal gradually evolves from a free-space radiation mode into a guided mode confined within the waveguide core. As the width of the waveguide narrows along the taper, the effective refractive index of the guided mode decreases, causing the optical field to become increasingly delocalized into the surrounding cladding material. If the waveguide width becomes too narrow, the confinement weakens to the extent that the mode is no longer supported and begins to radiate outward where this critical width is referred to as the cutoff width. The narrow part of the taper serves to minimize Fresnel reflection at the fiber-waveguide interface by improving mode matching, while the taper length ensures a gradual transformation of the optical mode, thereby minimizing scattering loss The overall coupling efficiency of the inverse taper is primarily determined by the tip width and taper length.

[0007] For example, when an inverse taper is optically coupled to an optical fiber with approximately 5 pm mode field diameter (MFD), the typical insertion loss introduced at the interface, commonly referred to as the facet, ranges between 3 dB and 6 dB. In this context, the term facet refers to the cleaved or polished end surface of the photonic chip where light is coupled into or out of the waveguide. This coupling efficiency can be further improved through the use of fibers with smaller MFDs, such as a lensed SMF-28 fiber with an MFD of 3 pm, which provides better spatial overlap between the fiber and waveguide modes. Nevertheless, in practical applications, it is often preferable to design edge couplers that can interface effectively with standard single-mode fibers such as SMF-28 (MFD = 10 pm), due to their greater alignment tolerance which is a critical factor in scalable and robust photonic packaging.

[0008] As a result, those skilled in the art are constantly seeking an edge coupler that offers high coupling efficiency with minimal polarization dependence, while being compatible with standard single-mode fibers for ease of integration in photonic packaging.SUMMARY

[0009] In one aspect, the present application discloses an edge coupler for coupling an optical signal from an optical fiber to an optical waveguide. The disclosed edge coupler comprises a first dielectric layer disposed on a substrate and a semiconductor structure embedded within the first dielectric layer along a horizontal plane of the first dielectric Tn embodiments of the disclosure, the semiconductor structure comprises a first section having a moth-eye structure formed of a plurality of tapered elements having a constant pitch and varying lengths, the tapered elements being arranged along an in-plane axicon topology, such that tip ends of the tapered elements define a contour of an axicon for receiving the optical signal from the optical fiber and base ends of the tapered elements are coupled to a second section. The semiconductor structure also comprises a second section that has a tapered coupling structure with a coupling base end coupled to the base ends of the tapered elements and a coupling tip end coupled to the optical waveguide, the tapered coupling structure having a width that decreases from the coupling base end to the coupling tip end.

[0010] In embodiments of the one aspect, the in-plane axicon topology of the tapered elements of the edge coupler has an axicon angle, a, defined as:where an axicon length Laxiconis defined as a lateral distance along the horizontal plane of the semiconductor structure between a tip end of a shortest tapered element and a tip end of a longest tapered element, and an axicon width W is defined as a width of the coupling base end of the second section at a widest part of the coupling-based end.

[0011] In embodiments of the one aspect, the constant pitch of the plurality of tapered elements is less than a wavelength of the optical signal and / or each of the plurality of tapered elements may have a constant width that is equal or less than the constant pitch of the plurality of tapered elements.

[0012] In embodiments of the one aspect, the respective base-ends of the tapered elements of the edge coupler are uniformly distributed across the axicon width, W of the coupling base end of the second section, such that the base ends span the axicon width, W of the coupling base end of the second section. In further embodiments, the axicon length L_axicon is between 0.5pm and 3pm and / or the axicon angle, a is between 1° and 11°. In further embodiments, a tip length Ltipof the shortest tapered element is between 20 pm and 40 pm.

[0013] In embodiments of the one aspect, the edge coupler further comprises a cavity formed between the substrate and the first dielectric layer, the cavity being disposed vertically below the semiconductor structure or further comprises a second dielectric layer disposed on the first dielectric layer and positioned vertically above the first section of the semiconductor structure. In other embodiments, the substrate of the edge coupler comprises silicon, the dielectric layer comprises silicon dioxide and the semiconductor structure comprises silicon nitride or silicon.

[0014] In another aspect, the present application discloses a method for forming an edge coupler for coupling an optical signal from an optical fiber to an optical waveguide. The disclosed method comprises the steps of forming a first dielectric layer on a substrate and forming a semiconductor structure embedded within the first dielectric layer along a horizontal plane of the first dielectric. In embodiments, the forming of the semiconductor structure comprises the steps of forming a first section comprising a moth-eye structure comprising a plurality of tapered elements having a constant pitch and varying lengths, the tapered elements being arranged along an in-plane axicon topology, such that tip ends of the tapered elements define a contour of an axicon for receiving the optical signal from the optical fiber and base ends of the tapered elements are coupled to a second section, and forming the second section comprising a tapered coupling structure having a coupling base end coupled to the base ends of the tapered elements and a coupling tip end coupled to the optical waveguide, the tapered coupling structure having a width that decreases from the coupling base end to the coupling tip end.BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Various embodiments of the present disclosure are described below with reference to the following drawings:Figure 1 illustrates a top view of an embodiment of a semiconductor structure of an edge coupler in accordance with embodiments of the present disclosure where the semiconductor structure is configured as a waveguide;Figure 2 illustrates a top view of an in-plane axicon topology as known in the art;Figure 3 illustrates a perspective view of an embodiment of the edge coupler shown in Figure 1 in accordance with embodiments of the present disclosure;Figure 4 illustrates a front view or cross-sectional view showing the formation of the edge coupler illustrated in Figure 3 using standard photonic processing steps in accordance with embodiments of the present disclosure;Figure 5 illustrates a perspective view of another embodiment of the edge coupler shown in Figure 1 in accordance with embodiments of the present disclosure;Figure 6 illustrates a front view or cross-sectional view showing the formation of the edge coupler illustrated in Figure 5 using standard photonic processing steps in accordance with embodiments of the present disclosure;Figure 7 illustrates a perspective view of yet another embodiment of the edge coupler shown in Figure 1 in accordance with embodiments of the present disclosure;Figure 8 illustrates a front view or cross-sectional view showing the formation of the edge coupler illustrated in Figure 7 using standard photonic processing steps in accordance with embodiments of the present disclosure;Figure 9 illustrates a perspective view of still yet another embodiment of the edge coupler shown in Figure 1 in accordance with embodiments of the present disclosure;Figure 10 illustrates a front view or cross-sectional view showing the formation of the edge coupler illustrated in Figure 9 using standard photonic processing steps in accordance with embodiments of the present disclosure;Figure 11 illustrates the simulated optical coupling efficiency as a function of axicon length of the edge coupler design in accordance with embodiments of the disclosure;Figure 12 illustrates the simulated optical coupling efficiency as a function of the thickness of the semiconductor structure and as a function of the thickness of the bottom cladding of the edge coupler design in accordance with embodiments of the disclosure;Figure 13a illustrates the simulated optical coupling from a standard single mode 10pm MFD to a 0.2pm thick silicon nitride (SiN) waveguide via the edge coupler illustrated in Figure 1 whereby the edge coupler has a bottom cladding thickness of 1 pm;Figure 13b illustrates the simulated optical coupling performance along the z-axis of the edge coupler when the thickness of the bottom cladding is varied;Figure 14 illustrates the simulated optical coupling performance for silicon nitride and silicon based edge couplers;Figure 15 illustrates the simulated optical coupling efficiency for the silicon nitride and silicon based edge couplers illustrated in Figure 14;Figure 16 illustrates the simulated optical performance of the edge coupler illustrated in Figure 1 when the axicon angle of the in-plane axicon topology is varied;Figure 17 illustrates the simulated coupling efficiency of the edge coupler illustrated in Figure 1 as a function of the tip length of the shortest tapered element and the thickness of the semiconductor structure;Figure 18 illustrates a flowchart that sets out the process or method for forming the edge coupler in accordance with embodiments of the disclosure;Figure 19 illustrates a perspective view of still yet another embodiment of the edge coupler shown in Figure 1 in accordance with embodiments of the present disclosure whereby trenches are formed on either side of the semiconductor structure of the edge coupler,Figure 20 illustrates a front view or cross-sectional view showing the formation of the edge coupler illustrated in Figure 19 using standard photonic processing steps in accordance with embodiments of the present disclosure; andFigure 21 illustrates a top view of another embodiment of a semiconductor structure of an edge coupler in accordance with embodiments of the present disclosure where the semiconductor structure is configured as a waveguide.DETAILED DESCRIPTION

[0016] The following detailed description is made with reference to the accompanying drawings, showing details and embodiments of the present disclosure for the purposes of illustration. Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments, even if not explicitly described in these other embodiments Additions and / or combinations and / or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0017] In the context of various embodiments, the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements. The term “and / or” includes any and all combinations of one or more of the associated listed items.

[0018] In the context of various embodiments, the term “about” or “approximately” as applied to a numeric value encompasses the exact value and a reasonable variance as generally understood in the relevant technical field, e g., within 10% of the specified value.

[0019] As used herein, “comprising” means including, but not limited to, whatever follows the word “comprising”. Thus, use of the term “comprising” indicates that the listed elements are required or mandatory, but that other elements are optional and may or may not be present.

[0020] As used herein, “consisting of’ means including, and limited to, whatever follows the phrase “consisting of’. Thus, use of the phrase “consisting of’ indicates that the listed elements are required or mandatory, and that no other elements may be present.

[0021] It should be noted that although the terms first, second and third are used herein to describe various elements, these elements should not be limited by these terms as these terms are meant to only distinguish one element from another element. Thus, the first element described herein could be termed as a second element without departing from this disclosure.

[0022] In the context of various embodiments, the term “surround” means to enclose something completely to form a barrier around it. Thus, the use of the term “surround” indicates that something is on all sides of another thing.

[0023] In the context of various embodiments, the term “disposed on" relates to the placement or deposition of one material or layer onto the surface of another and may involve one or more types of deposition techniques.

[0024] In the context of various embodiments, the term “around” or “adjacent” means to be in the proximity or location of something and does not necessarily mean that two objects have to be in contact.

[0025] In the context of various embodiments, the directional terms mentioned herein, such as “above” and “below” or “upper” and “lower” refer to directions as described with reference to the drawings. Therefore, the directional terms are only used for illustration and are not meant to limit the present disclosure.

[0026] As used herein, a “layer” refers to a material portion including a region having a particular thickness. The layer may extend over the entirety of the structure or may cover only part of the structure as defined in the description. For example, a layer may be located between two horizontal planes; may be located between, or at, a top surface and a bottom surface of the structure. The layer may also extend horizontally, vertically, and / or along the surface of the structure.

[0027] As used herein, “embedded” refers to a semiconductor layer or structure that is physically positioned within a dielectric layer such that it is at least partially enclosed by the dielectric material. The embedded layer or structure is located between opposing portions of the dielectric layer, rather than being situated entirely on top of or beneath it.

[0028] As used herein, “in-plane axicon topology” refers to a geometric arrangement in which structural features such as tapered elements of varying lengths and constant pitch are positioned along a contour that approximates the profile of an axicon within a horizontal plane of the structure. In this configuration, the tip ends of the elements define a lateral boundary that resembles the base of a conical or axicon-shaped surface.

[0029] Additionally, for the sake of brevity, extensive explanations of conventional techniques of fabricating semiconductor devices and integrated circuits are not described in detail herein. The tasks and processes described herein may also be integrated into a more comprehensive procedure with extra steps of features that are not elaborated upon in this document. Specifically, certain processes of fabricating semiconductor devices are well known to one skilled in the art hence, such processes will be omitted entirely.

[0030] Edge coupler designs vary widely in both geometric complexity and fabrication approaches. Key design considerations typically include the insertion loss (or coupling efficiency) of the edge coupler, the edge coupler’s device footprint, and alignment tolerance. One of the most basic and widely used edge coupler designs is the inverse taper design. In this design, the width of the waveguide gradually narrows along the direction of light propagation, down to the lithographic limit.

[0031] To improve the coupling with smaller mode field diameter (MFD) fibers and to achieve lower insertion loss, inverse tapers can be paired with lensed fibers. However, for practical photonic packaging, it is generally preferred that edge couplers be able to efficiently interface with standard single-mode fibers such as SMF-28, which have an MFD of approximately 10 pm, due to their superior alignment tolerance. Coupling efficiency can also be improved by adding a dielectric structure over the inverse taper, forming an intermediate waveguide, often referred to as a spot size converter (SSC). This additional waveguide helps improve spatial mode matching with the fiber. Materials used for this dielectric layer may include, but are not limited to, polymer, silicon nitride (SiN), or silicon oxynitride (SiON), all of which are compatible with CMOS processes. In a typical configuration using SiN with a silicon dioxide (SiO2) cladding, the SSC may have a cross-sectional dimension of approximately 3 pm by 3 pm. However, increasing the thickness of SiN or SiON films can lead to mechanical stress and cracking issues on the substrate. While polymer-based films offer a simpler alternative, they suffer from higher absorption losses in the near-infrared range and reduced environmental durability compared to Si-based materials.

[0032] Another approach to improve coupling efficiency involves reducing substrate leakage, which can be achieved either by increasing the thickness of the bottom cladding layer or by removing the substrate entirely. Substrate removal, though effective in lowering insertion loss, typically requires complex fabrication processes such as deep etching and selective wet removal of the substrate material, and can compromise mechanical stability during the dicing process. Further enhancements to the inverse taper design may involve the introduction of taper dimensionality in the vertical direction, effectively forming a three-dimensional taper. Although ideal vertical tapers could be fabricated using grayscale lithography, this method is not well-suited for scalable or CMOS -compatible manufacturing. A practical alternativeinvolves cascading multiple inverse tapers fabricated in successive etch steps, resulting in a 3D profile that supports efficient mode transformation. Simulations of such cascaded taper structures have demonstrated significant reductions in insertion loss for both transverse electric (TE) and transverse magnetic (TM) modes.

[0033] In addition to the introduction of taper dimensionality in the vertical direction, coupling performance can be enhanced by introducing multiple taper tips arranged laterally along the waveguide facet. These multi-tip or “trident” coupler designs function analogously to optical antennas, where each tip captures part of the incident free-space optical mode. By increasing the number of tips, the effective capture cross-section is expanded, improving spatial overlap with the fiber mode. Multi-tip edge couplers also offer greater design flexibility, such as enabling efficient interfacing with non-circular optical beams emitted by edge-emitting lasers.

[0034] A top view of a semiconductor structure of an edge coupler designed in accordance with embodiments of the disclosure is illustrated in Figure 1. Semiconductor structure 100 acts as an edge coupler and is configured to couple an incoming optical signal 102 from an optical fiber (not shown in Figure 1) into optical waveguide 108 As shown, semiconductor structure 100 comprises two primary sections: a first section 104 that receives and shapes incoming optical signal 102, and a second section 106 that transitions the shaped optical signal from first section 104 into waveguide 108. Specifically, Figure 1 illustrates the top view of semiconductor structure 100 in the X-Z plane, and this view illustrates the overall geometry of semiconductor structure 100, with light propagating along the Z-axis, from the interface of an optical fiber towards optical waveguide 108.

[0035] First section 104 comprises a moth-eye structure that is formed from a plurality of tapered elements 110, each having constant pitch p and varying lateral lengths along the Z-axis of semiconductor structure 100, forming a subwavelength-periodic interface. These tapered elements 110 are arranged along an in-plane axicon topology, such that their tip ends 112 collectively define the geometric arrangement of axicon contour 114. This axicon contour 114 serves as the incident surface of semiconductor structure 100 through which optical signal 102 is received and coupled into semiconductor structure 100 for subsequent propagation to waveguide 108. In embodiments of the disclosure, a moth-eye structure is understood tocomprise a periodic array of subwavelength-scale tapered elements (e.g., cones or pyramids) arranged on a substrate surface to form a gradient refractive index interface that minimizes Fresnel reflection. The tapered elements 110 may typically be fabricated in silicon or silicon nitride using lithography and etching techniques compatible with CMOS processes and may be arranged along a linear or axicon contour to facilitate free-space-to-waveguide mode coupling.

[0036] Specifically, the axicon topology is realized by arranging a plurality of tapered elements 1 10 such that their tip ends collectively define a conical or axi con-like convex surface within the horizontal plane of semiconductor structure 100. This geometric arrangement emulates the profile of an axicon and forms the light-receiving interface of the edge coupler. Analogous to its application in solar cells, where moth-eye structures are used to reduce surface reflection and improve energy conversion efficiency, the moth-eye structure in this context is intended to function as an effective anti-reflection interface. To suppress or to reduce the occurrence of grating-induced diffraction effects, the pitch p of tapered elements 110 is selected to be smaller than the free-space wavelength A satisfying the condition p < X.

[0037] In embodiments, axicon contour 114 may be characterized by an axicon length ^•axicon, which extends laterally between the tip of the shortest and longest tapered elements. The base ends of each of tapered elements 110 have a width of w0, which when combined defines a width IV of the coupling base end of second section 106 It should be noted that a tip length Ltipis defined as the length of the shortest tapered element of the plurality of tapered elements 110.

[0038] In one embodiment, the pitch p of the moth-eye structure is selected based on the material composition of semiconductor structure 100 and its cladding. For example, when semiconductor structure 100 comprises a silicon nitride (SiN) waveguide cladded with silicon dioxide (SiCh), the pitch p is preferably no greater than 1 pm. When semiconductor structure 100 comprises a silicon (Si) waveguide similarly cladded with SiO?, the pitch is more tightly constrained, preferably no greater than 0.7 pm. Ideally, the width iv0of each tapered element in the moth-eye structure is equal to the pitch p, such that w0= p. However, in practical fabrication environments, lithographic constraints impose a minimum printable line widthwmin , which may necessitate a narrower effective width of each tapered element, as defined by w0= p - wmin.

[0039] In embodiments of the disclosure, the number of tapered elements N in the motheye structure is selected such that the elements are uniformly distributed across width W of the coupling base end of second section 106, ensuring consistent coverage along axicon contour 114. The tip length Ltipof the shortest tapered element is chosen to minimize surface reflection loss. Preferably, the tip length Ltipof the shortest tapered element may be selected to be greater than or equal to 30 pm to minimize reflection loss.

[0040] Further, in operation, upon traversing the axicon-shaped moth-eye structure, the incident optical signal transitions into a narrower region in second section 106 which is also referred to as the “focusing area,” where the optical signal is directed towards an input of waveguide 108. This focusing area is characterized by a taper length L[aper. In embodiments of the disclosure, the taper length Ltapermay be approximately 60 pm and this may be sufficient for efficient adiabatic mode conversion. Accordingly, in this embodiment, the total length of semiconductor structure 100 of the edge coupler along the horizontal plane (i . e. , along the Z-axis), including the axicon region, tip length, and taper section can be maintained under 100 pm, resulting in a compact footprint well suited for dense photonic integration.

[0041] Figure 2 illustrates a conceptual diagram of the optical behaviour of an in-plane axicon contour 202 of an in-plane axicon topology 200 as known to one skilled in the art. As can be seen, axicon contour 202 forms a tapering geometry that introduces a lateral linear phase profile to incoming optical signal 201. This geometry is analogous to a Fresnel biprism with lateral linear phase and is designed to refract an incident free-space beam (e g., optical signal 201) at a refraction angle ft, thereby directing the optical energy inward toward a central focal region. The refraction of light from the biprism is illustrated as rays 204 and 205, while the diffraction of light is illustrated as rays 203 and 206.

[0042] The refraction angle ft is governed by Snell’s law and is a function of both the refractive index of the axicon material and the axicon angle a. The axicon angle a corresponds to the slope of the axicon contour relative to the horizontal propagation axis, along the Z-axis(in the X-Z plane). With reference to the geometrical layout of semiconductor structure 100 shown in Figure 1, the axicon angle a may be defined as: ...equation (1)where axicon length ha.YiConis defined as a lateral distance along the horizontal plane of the semiconductor structure between the tips of the shortest and longest tapered elements, and axicon width PF is defined as a width of the coupling base end of the second section at a widest part of the coupling-based end.

[0043] Based on Snell’s law, the refraction angle / ? may be defined as: ...equation (2)where naxcis defined as the refractive index of the in-plane axicon topology 200, nais defined as the refractive index of the surrounding and a is defined as the axicon angle.

[0044] The interaction between the focused and diffracted components of optical signal 201 gives rise to a non-diffracting focal region, the length of which is characterized by: ... equation (3)where W is defined as the width of axicon topology 200.

[0045] It may be appreciated from the foregoing that axicon contour 202 as illustrated in Figure 2 corresponds to, and may geometrically overlap with, axicon contour 114 as defined by the arrangement of the tips of tapered elements 1 10 in semiconductor structure 100 as illustrated in Figure 1. While Figure 2 presents a conceptual diagram of optical signal 201 propagating through an axicon profile (from the right to the left), Figure 1 illustrates a physical realization of this concept using the moth-eye structure described above with optical signal 102 being incident on the tips of the tapered elements 110 of the moth-eye structure (i.e., in an opposite direction from optical signal 201 as shown in Figure 2). In particular, the plurality of tapered elements 110 are arranged such that the tip ends 112 of these tapered elements 110emulate the shape of axicon contour 114, mimicking the function of an anti-reflection interface or coating while focusing the coupled optical signal 102 to waveguide 108. In particular, the use of the moth-eye patterned axicon topology in the semiconductor structure minimizes reflection and improves coupling efficiency of the edge coupler design.

[0046] Figure 3 illustrates a perspective view of edge coupler 300 configured to receive optical signal 102 from optical fiber 302 and direct it into semiconductor structure 301 in accordance with embodiments of the disclosure. As shown, edge coupler 300 comprises semiconductor structure 301 embedded within dielectric layer 304, which is itself formed on substrate 306. As depicted, optical fiber 302 is aligned with the input side of semiconductor structure 301 to enable efficient coupling of optical signal 102 into semiconductor structure 301 through the moth-eye structure of semiconductor structure 301. In this illustration, optical signal 102 is shown to propagate along the Z-axis of edge coupler 300.

[0047] Semiconductor structure 301 includes a first section formed with a plurality of tapered elements arranged as a moth-eye structure as described in the previous sections. These tapered elements are configured in an in-plane axicon topology to form an anti-reflective interface that matches the mode field diameter of optical fiber 302. As shown in Figure 3, this interface is aligned to directly receive optical signal 102 from optical fiber 302 and guide it toward the waveguide section of semiconductor structure 301. Dielectric layer 304 encapsulates semiconductor structure 301 and provides optical confinement by surrounding semiconductor structure 301 with a material having a lower-refractive-index.

[0048] Figure 4 illustrates a cross-sectional process flow for fabricating edge coupler 300 in accordance with embodiments of the disclosure. The sequence of steps proceeds from the left to right across process steps 401, 402 and 403. In step 401, substrate 306 is provided with a bottom cladding layer comprising dielectric material 304, upon which semiconductor structure 301 is deposited. Patterned hard mask 407 is formed over semiconductor structure 301 to define the geometry of semiconductor structure 301 during subsequent etching steps with optional chemical mechanical polishing (CMP) being applied as required. Hard mask 407 acts as an etch-resistant barrier during the patterning process of the semiconductor structure 301.

[0049] In step 402, semiconductor structure 301 is etched using the hard mask 407 as a protective pattern. The etching step selectively removes the exposed portions (not shown) of semiconductor structure 301, resulting in a defined semiconductor structure aligned with the mask geometry.

[0050] In step 403, dielectric cladding layer comprising dielectric material 304 is deposited over the entire structure, encapsulating the patterned semiconductor structure 301 and providing optical confinement and environmental protection for semiconductor structure 301. In embodiments of the disclosure, dielectric material 304 may comprise silicon dioxide, substrate 306 may comprise silicon substrate and semiconductor structure 301 may comprise silicon or silicon nitride. Additionally, the thickness of the bottom cladding layer may be set to be at least 3 pm to minimize substrate leakage loss.

[0051] Figure 5 illustrates a perspective view of edge coupler 500 configured to receive optical signal 102 from optical fiber 302 and direct it into semiconductor structure 301 in accordance with embodiments of the disclosure. Edge coupler 500 shares a similar geometry and layout as the embodiment illustrated in Figure 3 with the addition of deep etched holes 504 patterned around semiconductor structure 301. These holes act as access points for a wet etch process, wherein a chemical etchant is introduced through holes 504 to selectively remove portions of substrate 306 located beneath semiconductor structure 301, thereby forming cavity 502 beneath semiconductor structure 301. This cavity 502 serves to reduce substrate leakage loss by eliminating high-index substrate material below the optical mode, thus enhancing overall coupling efficiency between the optical fiber and the semiconductor structure

[0052] Figure 6 illustrates a cross-sectional process flow for fabricating edge coupler 500 in accordance with embodiments of the disclosure. The sequence of steps proceeds from the left to right across process steps 601, 602, 603, 604 and 605. In step 601, substrate 306 is provided with a bottom cladding layer comprising dielectric material 304, upon which semiconductor structure 301 is deposited. Patterned hard mask 407 is formed over semiconductor structure 301 to define the geometry of semiconductor structure 301 during subsequent etching steps.

[0053] In step 602, semiconductor structure 301 is etched using the hard mask 407 as a protective pattern. The etching step selectively removes the exposed portions (not shown) of semiconductor structure 301, resulting in a defined semiconductor structure aligned with the mask geometry.

[0054] In step 603, dielectric cladding layer comprising dielectric material 304 is deposited over the entire structure, encapsulating the patterned semiconductor structure 301. In embodiments of the disclosure, dielectric material 304 may comprise silicon dioxide, substrate 306 may comprise silicon substrate and semiconductor structure 301 may comprise silicon or silicon nitride.

[0055] In step 604, deep etched holes 504 are etched around patterned semiconductor structure 301 with the locations of these holes being provided sufficiently far from semiconductor structure 301 so that that their presence may not affect the overall performance of edge coupler 500. In step 605, a wet chemical etch process is applied via holes 504 to selectively etch away parts of substrate 306 beneath patterned semiconductor structure 301 to form cavity 502.

[0056] Figure 7 illustrates a perspective view of edge coupler 700 configured to receive optical signal 102 from optical fiber 302 and direct it into semiconductor structure 301 in accordance with embodiments of the disclosure. Edge coupler 700 has a similar geometry and layout as the embodiment illustrated in Figure 3 with the addition of dielectric top 702 patterned above the moth-eye structure of semiconductor structure 301. Dielectric top 702 acts as an intermediate waveguide for edge coupler 700, and functions to improve mode matching and coupling efficiency between optical fiber 302 and semiconductor structure 301. In embodiments of the disclosure, dielectric top 702 may comprise silicon dioxide or any other dielectric material that may provide excellent refractive index contrast with semiconductor structure 301.

[0057] Figure 8 illustrates a cross-sectional process flow for fabricating edge coupler 700 in accordance with embodiments of the disclosure. The sequence of steps proceeds from the left to right across process steps 801, 802, 803 and 804. In step 801, substrate 306 is provided with a bottom cladding layer comprising dielectric material 304, upon which semiconductorstructure 301 is deposited. Patterned hard mask 407 is similarly formed over semiconductor structure 301 to define the geometry of semiconductor structure 301 during subsequent etching steps.

[0058] At step 802, semiconductor structure 301 is etched using the hard mask 407 as a protective pattern. The etching step selectively removes the exposed portions (not shown) of semiconductor structure 301, resulting in a defined semiconductor structure aligned with the mask geometry.

[0059] In step 803, dielectric cladding layer comprising dielectric material 304 is deposited over the entire structure, encapsulating the patterned semiconductor structure 301. At step 804, dielectric top 806 may be formed above the moth-eye region of the patterned semiconductor structure 301. This may be achieved through polymer spin coating followed by lithographic patterning. Alternatively, dielectric top 806 may be formed by depositing a dielectric film, followed by photolithographic patterning and etching using a photoresist mask. The choice of fabrication method is left to one skilled in the art and may depend on the properties of the dielectric top and the desired patterning resolution.

[0060] Figure 9 illustrates a perspective view of edge coupler 900 configured to receive optical signal 102 from optical fiber 302 and direct it into semiconductor structure 301 in accordance with embodiments of the disclosure. As can be seen, edge coupler 900 incorporates the deep etched holes 504 and cavity 502 of edge coupler 500 together with the dielectric top 702 of edge coupler 700 while maintaining the common features of these embodiments.

[0061] Figure 10 illustrates a cross-sectional process flow for fabricating edge coupler 900 in accordance with embodiments of the disclosure The sequence of steps proceeds from the left to right across process steps 1001, 1002, 1003, 1004, 1005 and 1006. In step 1001, substrate 306 is provided with a bottom cladding layer comprising dielectric material 304, upon which semiconductor structure 301 is deposited. Patterned hard mask 407 is formed over semiconductor structure 301 to define the geometry of semiconductor structure 301 during subsequent etching steps.

[0062] In step 1002, semiconductor structure 301 is etched using the hard mask 407 as a protective pattern. The etching step selectively removes the exposed portions (not shown) of semiconductor structure 301, resulting in a defined semiconductor structure aligned with the mask geometry.

[0063] In step 1003, dielectric cladding layer comprising dielectric material 304 is deposited over the entire structure, encapsulating the patterned semiconductor structure 301. In embodiments of the disclosure, dielectric material 304 may comprise silicon dioxide, substrate 306 may comprise silicon substrate and semiconductor structure 301 may comprise silicon or silicon nitride.

[0064] In step 1004, dielectric top 806 may be formed above the moth-eye region of the patterned semiconductor structure 301. At the subsequent step 1004, deep etched holes 504 may then be etched around patterned semiconductor structure 301 with the locations of these holes being provided sufficiently far from semiconductor structure 301 so that that their presence may not affect the overall performance of edge coupler 900. In step 1006, a wet chemical etch process is applied via holes 504 to etch away substrate 306 beneath patterned semiconductor structure 301 to form cavity 502.

[0065] Simulation Results

[0066] Concrete physical dimensions for the proposed edge coupler design may be derived based on realistic fabrication parameters for SiN and Si photonic platforms. These parameters may include, but are not limited to, a minimum feature width of approximately 0.1 - 0.2 gm, waveguide thicknesses of 0.2 - 0.4 pm for SiN and 0.09 - 0.22 pm for Si, and a bottom cladding layer of SiCh having a thickness of 2-3 pm. The scope of the optical simulations is limited to the fabrication process flow illustrated in Figure 4 and based on empirical refractive index data from established sources for SiN, Si and SiCh fabrication processes.

[0067] Figure 11 illustrates the simulated impact of axicon length Laxiconin a SiN-based multi-tip edge coupler when the edge coupler is interfaced with a standard single-mode optical fiber having a mode field diameter (MFD) of 10 pm and when an optical signal in the C-band, e g., — 1.55 / zm, is incident on the edge coupler. In the simulated configuration, the SiNwaveguide was configured to have a thickness of 0.4 gm and a waveguide width of 1 gm, with a 2 gm thick SiCf bottom cladding. The width of the semiconductor structure of the edge coupler was set to 10 gm to match the fiber MFD. The tip elements forming the moth-eye structure was formed with a length of 30 gm, a tip width of 0.2 gm, and a pitch of 1 gm The taper of the coupler was set to 60 gm in length to facilitate adiabatic mode conversion.

[0068] Plots 1101, 1102, 1103, 1104, 1105 and 1106 show that the axicon length Laxicon, which corresponds to the lateral extent of the axicon topography, significantly influences the focusing behaviour of the edge coupler. When no axicon structure was employed in the edge coupler design (i.e., Laxicon— 0), it can be seen from plot 1101 that the optical field exhibits interference patterns resembling those seen in multimode interferometers (MMIs) and has a coupling efficiency of 70.5%. As the axicon topography is incrementally introduced, i.e., as the axicon length Laxtconis gradually increased, these interference patterns diminish, and the coupling efficiency of the edge coupler gradually increases, i.e., the coupling efficiency is 74.6% in plot 1102 (Laxicon— 0.5pm) and 75.6% in plot 1103 (Laxicon— 1pm). Specifically, at an axicon length« 2pm, the optical field exhibits characteristics of a non-diffracting mode (from the perspective of axicon optics) and has a coupling efficiency of 75.3%. This can be seen in plot 1 104. Beyond this optimal length, excessive focusing occurs, leading to beam divergence and reflection at the taper sidewalls, accompanied by renewed interference effects, and these effects can be seen in plots 1105 and 1106 which have coupling efficiencies of 71.5% and 70.4%, respectively.

[0069] These findings underscore the non-trivial contribution of the axicon structure to the optical performance of the edge coupler designed in accordance with embodiments of the disclosure. Notably, an axicon length of approximately 2 pm, corresponding to an axicon angle of approximately 21.8°, yields the highest coupling efficiency of about 75%. This optimal focusing condition is a function of the axicon geometry of the moth-eye structure of the semiconductor structure and its refractive index.

[0070] The influence of bottom cladding thickness tbo[on coupling efficiency is illustrated in Figure 12. For clarity, the bottom cladding refers to the dielectric layer sandwiched between the semiconductor structure and the substrate. Plots 1202 and 1204 show that the coupling performance increases as the thickness of the bottom cladding increases, and the performancesaturates when the thickness of the bottom cladding tbot> 3[im. In these simulations, the axicon length is fixed at Laxicon=while all other geometric parameters of the edge coupler remain consistent with those described above.

[0071] As can be seen from plots 1202 and 1204, the coupling efficiency of the edge coupler improves from a coupling efficiency of approximately 75% when a 2 pm thick bottom cladding is used, to a coupling efficiency of around 83% when the thickness of the bottom cladding is increased to 3 pm. Additionally, when the thickness of the SiN-semiconductor structure is reduced from 0.4 pm (as shown in plot 1204) to 0.2 pm (as shown in plot 1202), while simultaneously adjusting the width of the semiconductor structure from 1 pm to 1.5 pm to maintain mode confinement, this yields a further increase in coupling efficiency to approximately 87%.

[0072] However, it should be noted that when the thickness of the SiN was reduced further to 0.1 pm, the simulation results show that no additional gains were produced. This is attributed to the increasingly delocalized optical mode in thinner semiconductor structures, which demands a proportionally thicker bottom cladding to avoid substrate leakage. Given that standard Si photonic fabrication processes typically support bottom SiOa cladding thicknesses in the 2-3 pm range, reducing the thickness of the SiN-semiconductor substrate below 0.2 pm is not practical.

[0073] Figure 1 a illustrates the coupling process between a standard single-mode optical fiber (MFD = 10 pm) and a 0.2 pm-thick SiN waveguide using the edge coupler designed in accordance with embodiments of the disclosure, with the bottom SiCh cladding layer of the edge coupler having a thickness of 1 pm. Plot 1306 illustrates the intensity of the optical field distribution in the single-mode optical fiber, plot 1304a illustrates the intensity of the optical field distribution in the edge coupler when the thickness of the bottom cladding is 1pm, and plot 1302 illustrates the intensity of the optical field distribution in the SiN waveguide.

[0074] In this simulation, the incident optical signal is assumed to exhibit transverse electric (TE) polarization. The mode profiles of the input optical fiber (source) and the silicon nitride (SiN) waveguide (target) are presented in the cross-sectional YZ-plane to illustrate their respective spatial intensity distributions. Additionally, a side-view along the XZ-plane isshown to visualize the optical coupling transition from the fiber to the waveguide. In this configuration, substrate leakage is observed in plot 1304a, as indicated by dashed arrow that represents downward propagation of optical energy into the substrate, arising from insufficient vertical confinement by the bottom cladding layer.

[0075] Figure 13b further illustrates the effect of increasing the thickness of the bottom cladding of the edge coupler on coupling behaviour, as viewed from the side-view of the edge coupler (XZ-plane). As the bottom cladding thickness increases, the extent of substrate leakage is visibly reduced and this is shown in the optical field distributions as plotted in plots 1304b, 1304c, 1304d and 1304e. The simulation results show diminishing changes when the bottom cladding thickness tb0[is increased beyond 3 pm, which is consistent with the saturation trend observed in Figure 12 for a semiconductor structure with a thickness of 0.2 pm and 0.4 pm.

[0076] SiN-based and Si-based edge couplers were designed based on the foregoing, and their respective simulated optical field distributions are illustrated in Figure 14, with their geometrical parameters set out in Table 1 below. Additionally, the thickness of the bottom claddings for these edge couplers is tbot= 3 / im and the tip length Ltip= 30pm.TABLE 1

[0077] Specifically, the top-view of an optical field distribution of a semiconductor structure (of the edge coupler) comprising SiN clad with SiOz is illustrated in plot 1402, while its corresponding side-view distribution is shown in plot 1406. For comparison, the top-view of the optical field distribution of a semiconductor structure formed from Si and similarly clad with SiO? is illustrated in plot 1404, with the associated side-view shown in plot 1408. In plots 1402 and 1404, the geometric outlines of the moth-eye structures of the semiconductorstructures (of the respective edge couplers) are included for illustrative purposes. The corresponding spectral coupling performance for each edge coupler is shown in Figure 15, where plot 1502 represents the performance of the SiN-based edge coupler and plot 1504 represents the performance of the Si-based edge coupler. These results indicate that the SiN- based edge coupler achieves a coupling efficiency of approximately 87. 1%, while the Si-based edge coupler demonstrates a slightly lower efficiency of approximately 80.5%, both measured at an operating wavelength of A = 1.55pm.

[0078] Figure 16 illustrates the effect of the axicon angle a on the focusing characteristics of an axicon, in accordance with embodiments of the disclosure. In this simulation, the axicon is modelled using germanium (Ge), selected for its relatively high refractive index (-3.9), which exceeds that of both silicon (Si -3.5) and silicon nitride (SiN -2). This higher refractive index enables more pronounced beam focusing behaviour in response to variations in the axicon angle. The width of the axicon is fixed at 100 pm, and the operating wavelength is selected from the infrared spectrum, within the transparency window of Ge. The results demonstrate that the depth-of-focus, which may also be referred to as the non-diffracting region, can be continuously tuned from a few tens of microns to the sub -millimetre range by adjusting the axicon angle a from approximately 11° to 1. 1° as illustrated in plots 1602, 1604, 1606, 1608, 1610 and 1612.

[0079] Figure 17 illustrates the effect of tip length Ltipon the reduction of the effect of Fresnel reflection at the axicon surface of the semiconductor structure in accordance with embodiments of the disclosure. Similar to the moth-eye structure, which functions as a subwavelength-patterned anti-reflection interface by mimicking a graded refractive index profile, increasing the tip length Ltlpresults in a more gradual transition in the effective refractive index experienced by the incident light. This gradual transition reduces reflection at the interface. Simulation results show that as the tip length Ltipincrease from 5 pm to 50 pm, this leads to a progressive reduction in Fresnel reflection, i.e., the coupling efficiency increases, with diminishing returns observed when the tip length Ltipincrease beyond approximately 30 pm. Plot 1702 illustrates the coupling efficiency of the semiconductor structure when the semiconductor structure comprises SiN and has a thickness of 0.2 pm while plot 1704 illustrates the coupling efficiency of the semiconductor structure when the semiconductor structure comprises SiN and has a thickness of 0.4 pm

[0080] A process for forming an edge coupler in accordance with embodiments of the disclosure is illustrated in Figure 18. Process 1800 begins at step 1802 with process 1800 forming a first dielectric layer on a substrate. At step 1804, process 1800 then proceeds to form a semiconductor structure that is embedded within the first dielectric layer along a horizontal plane of the first dielectric. Process 1800 then forms a first section comprising a moth-eye structure. The moth-eye structure has a plurality of tapered elements having a constant pitch and varying lengths with the tapered elements being arranged along an in-plane axicon topology, such that tip ends of the tapered elements define a contour of an axicon for receiving the optical signal from the optical fiber and base ends of the tapered elements are coupled to a second section. This takes place at step 1806. At step 1808, process 1800 then forms the second section comprising a tapered coupling structure having a coupling base end coupled to the base ends of the tapered elements and a coupling tip end coupled to an optical waveguide. The tapered coupling structure has a width that decreases from the coupling base end to the coupling tip end.

[0081] Figure 19 illustrates a perspective view of edge coupler 1900 configured to receive optical signal 102 from optical fiber 302 and direct it into semiconductor structure 301 in accordance with embodiments of the disclosure. It should be noted that the labels used in Figures 19 and 20 are consistent with those employed in Figures 3 through 10 to maintain continuity and facilitate comparison.

[0082] As shown, edge coupler 1900 comprises semiconductor structure 301 embedded within dielectric layer 304, which is itself formed on substrate 306. As depicted, optical fiber 302 is aligned with the input side of semiconductor structure 301 to enable efficient coupling of optical signal 102 into semiconductor structure 301 through the moth-eye structure of semiconductor structure 301. In this illustration, optical signal 102 is shown to propagate along the Z-axis of edge coupler 1900.

[0083] Semiconductor structure 301 includes a first section formed with a plurality of tapered elements arranged as a moth-eye structure as described in the previous sections. These tapered elements are configured in an in-plane axicon topology to form an anti-reflective interface that matches the mode field diameter of optical fiber 302. As shown in Figure 19, thisinterface is aligned to directly receive optical signal 102 from optical fiber 302 and guide it toward the waveguide section of semiconductor structure 301.

[0084] Edge coupler 1900 further includes a pair of deep trenches, first trench 1905a and second trench 1905b, formed within dielectric layer 304 along opposite longitudinal sides of semiconductor structure 301. These trenches are aligned parallel to the Z-axis (direction of optical propagation) and are configured to extend vertically (along the Y-axis) through the dielectric layer. Semiconductor structure 301 is laterally positioned between these trenches, along the X-axis. Functionally, trenches 1905a and 1905b are configured to suppress lateral dispersion and minimize radiation loss of the optical signal 102 as it couples into and propagates through the semiconductor structure 301 , thereby improving overall coupling efficiency.

[0085] Figure 20 illustrates a cross-sectional process flow for fabricating edge coupler 1900 in accordance with embodiments of the disclosure. The sequence of steps proceeds from the left to right across process steps 2001 , 2002, 2003 and 2004.

[0086] In step 2001, substrate 306 is provided with a bottom cladding layer comprising dielectric material 304, upon which semiconductor structure 301 is deposited. Patterned hard mask 407 is formed over semiconductor structure 301 to define the geometry of semiconductor structure 301 during subsequent etching steps.

[0087] In step 2002, semiconductor structure 301 is etched using the hard mask 407 as a protective pattern. The etching step selectively removes the exposed portions (not shown) of semiconductor structure 301, resulting in a defined semiconductor structure aligned with the mask geometry.

[0088] In step 2003, dielectric cladding layer comprising dielectric material 304 is deposited over the entire structure, encapsulating the patterned semiconductor structure 301. In embodiments of the disclosure, dielectric material 304 may comprise silicon dioxide, substrate 306 may comprise silicon substrate and semiconductor structure 301 may comprise silicon or silicon nitride.

[0089] In step 2004, a first trench is etched along a longitudinal side (along the direction of the z-axis) of semiconductor structure 301 to form trench 1905a and a second trench is etched along an opposite longitudinal side of semiconductor structure 301 to form trench 1905b such that semiconductor structure 301 is positioned laterally (along the direction of the X-axis) between trenches 1905a and 1905b. As shown, trenches 1905a and 1905b extend vertically (along the direction of the Y-axis) through dielectric material 304. In embodiments of the disclosure, dielectric material 304 may be either partially etched (not shown) or completely etched down to the underlying substrate 306 during the formation of trenches 1905a and 1905b. The etching of these trenches may be performed using a wet or dry etching process to selectively etch away parts of dielectric material 304. Trenches 1905a and 1905b are configured such that they reduce lateral dispersion of optical signal 102 that is coupled from optical fiber 302 into semiconductor structure 301. Specifically, the width and depth of trenches 1905a and 1905b may be selected based on desired modal confinement parameters, as determined through electromagnetic simulation, as well as fabrication tolerances. Moreover, the placement of trenches 1905a and 1905b relative to semiconductor structure 301 is optimized to reduce lateral leakage and radiation losses, thereby enhancing optical coupling efficiency of edge coupler 1900.

[0090] Figure 21 illustrates a top view of another embodiment of the edge coupler wherein the semiconductor structure of the edge coupler is designed as a metamaterial-based structure. As shown, the semiconductor structure of edge coupler 2100 is made up of subwavelength features arranged to form a graded optical interface for efficient fiber-to-chip coupling. As can be seen from Figure 21, edge coupler 2100 comprises a semiconductor structure having first section 2104 and second section 2106. First section 2104 includes an array of subwavelength features arranged in an in-plane axicon topology. These features are periodically distributed along the optical propagation direction (Z-axis), with each feature having a pitch denoted by A and a width denoted by a

[0091] In this embodiment, the subwavelength features are configured such that the pitch A is less than half the operating wavelength of the incident optical signal (A < A / 2), and the fill factor a / A is less than 0.5 where the fill factor is defined as a parameter that is used to describe the proportion of a periodic structure that is occupied by the high-index material (i.e , the feature width) relative to the total period or pitch of the structure. This configuration enablesthe effective refractive index of the semiconductor structure to emulate that of a thinner core waveguide, thereby improving mode matching with the incident optical signal. As a result, the design supports simplified fabrication through a single step etching process while maintaining high optical coupling efficiency.

[0092] Waveguide 2108 includes a tapered coupling region 2109 having a taper length Lt0, which provides a smooth mode transition from the metamaterial-based structure into waveguide 2108. Tapered coupling region 2109 may be integrated directly with some of the periodic subwavelength features at a coupling tip end of second section 2106 and facilitates adiabatic mode conversion into the guided mode of waveguide 2108. Simulations conducted using a 400 nm thick SiN waveguide have demonstrated coupling efficiencies comparable to designs based on a 200 nm thick SiN core, confirming the performance benefits of this metamaterial-based implementation. It should also be noted that this edge coupler configuration, i.e., edge coupler 2100, may be integrated into any of the embodiments previously described in the present disclosure.

[0093] Numerous other changes, substitutions, variations, and modifications may be ascertained by the skilled in the art and it is intended that the present application encompass all such changes, substitutions, variations, and modifications as falling within the scope of the appended claims.

Claims

CLAIMS1. An edge coupler for coupling an optical signal from an optical fiber to an optical waveguide, the edge coupler comprising: a first dielectric layer disposed on a substrate; a semiconductor structure embedded within the first dielectric layer along a horizontal plane of the first dielectric, the semiconductor structure comprising: a first section comprising a moth-eye structure formed of a plurality of tapered elements having a constant pitch and varying lengths, the tapered elements being arranged along an in-plane axicon topology, such that tip ends of the tapered elements define a contour of an axicon for receiving the optical signal from the optical fiber and base ends of the tapered elements are coupled to a second section; and the second section comprising a tapered coupling structure having a coupling base end coupled to the base ends of the tapered elements and a coupling tip end coupled to the optical waveguide, the tapered coupling structure having a width that decreases from the coupling base end to the coupling tip end.

2. The edge coupler according to claim 1, wherein the in-plane axicon topology of the tapered elements has an axicon angle, a, defined as:where an axicon length Laxiconis defined as a lateral distance along the horizontal plane of the semiconductor structure between a tip end of a shortest tapered element and a tip end of a longest tapered element, and an axicon width tFis defined as a width of the coupling base end of the second section at a widest part of the coupling-based end.

3. The edge coupler according to claims 1 or 2, wherein the constant pitch of the plurality of tapered elements is less than a wavelength of the optical signal.

4. The edge coupler according to any one of claims 1 to 3, wherein each of the plurality of tapered elements have a constant width that is equal or less than the constant pitch of the plurality of tapered elements.The edge coupler according to claim 2, wherein respective base-ends of the tapered elements are uniformly distributed across the axicon width, ffl of the coupling base end of the second section, such that the base ends span the axicon width, ffl of the coupling base end of the second section The edge coupler according to claim 2, wherein the axicon length Laxiconis between 0.5pm and 3pm. The edge coupler according to claims 2, 5 or 6, wherein the axicon angle, a is between 1° and 11°. The edge coupler according to claims 2, 5, 6 or 7, wherein a tip length L[ipof the shortest tapered element is between 20 pm and 40 pm. The edge coupler according to any one of claims 1 to 8 further comprising a cavity formed between the substrate and the first dielectric layer, the cavity being disposed vertically below the semiconductor structure. The edge coupler according to any one of claims 1 to 9 further comprising a second dielectric layer disposed on the first dielectric layer and positioned vertically above the first section of the semiconductor structure. The edge coupler according to any one of claims 1 to 10, wherein the substrate comprises silicon, the dielectric layer comprises silicon dioxide and the semiconductor structure comprises silicon nitride or silicon. The edge coupler according to any one of claims 1 to 8, or 10, wherein the first dielectric layer further comprises: a first trench defined along a longitudinal side of the semiconductor structure; a second trench defined along an opposite longitudinal side of the semiconductor structure such that the semiconductor structure is laterally positioned between the first and second trenches, wherein the first and second trenches extend vertically through the first dielectric layer and are configured to reduce lateral dispersion of an optical signal coupled from the optical fiber into the semiconductor structure.

13. The edge coupler according to claim 1, wherein the semiconductor structure comprises a metamaterial structure fonned from a plurality of periodic subwavelength features arranged in a repeating pattern along an optical propagation direction of the optical signal through the semiconductor structure, and wherein the optical waveguide comprises a tapered coupling region that is integrated with the periodic subwavelength features at the coupling tip end of the second section of the semiconductor structure.

14. The edge coupler according to claim 13, wherein a pitch of the subwavelength features is less than half of an operating wavelength of the optical signal, and wherein a fill ratio of the subwavelength features is less than 50% of the pitch of the subwavelength features.

15. A method for forming an edge coupler for coupling an optical signal from an optical fiber to an optical waveguide, the method comprising: forming a first dielectric layer on a substrate; forming a semiconductor structure embedded within the first dielectric layer along a horizontal plane of the first dielectric, the forming of the semiconductor structure comprising the steps of: forming a first section comprising a moth-eye structure comprising a plurality of tapered elements having a constant pitch and varying lengths, the tapered elements being arranged along an in-plane axicon topology, such that tip ends of the tapered elements define a contour of an axicon for receiving the optical signal from the optical fiber and base ends of the tapered elements are coupled to a second section; and forming the second section comprising a tapered coupling structure having a coupling base end coupled to the base ends of the tapered elements and a coupling tip end coupled to the optical waveguide, the tapered coupling structure having a width that decreases from the coupling base end to the coupling tip end.

16. The method according to claim 15, wherein the in-plane axicon topology of the tapered elements has an axicon angle, a, defined as:where an axicon length Lax[conis defined as a lateral distance along the horizontal plane of the semiconductor structure between a tip end of a shortest tapered element and a tip end of a longest tapered element, and an axicon width IFis defined as a width of the coupling base end of the second section at a widest part of the coupling-based end.

17. The method according to claims 15 or 16, wherein the constant pitch of the plurality of tapered elements is less than a wavelength of the optical signal.

18. The method according to any one of claims 15 to 17, wherein each of the plurality of tapered elements have a constant width that is equal or less than the constant pitch of the plurality of tapered elements.

19. The method according to claim 16, wherein respective base-ends of the tapered elements are uniformly formed across the axicon width, W of the coupling base end of the second section, such that the base ends span the axicon width, W of the coupling base end of the second section.

20. The method according to claim 16, wherein the axicon length Laxiconis between 0.5pm and 3 pm.

21. The method according to claims 16, 19 or 20, wherein the axicon angle, a is between 1° and 11°.

22. The method according to claims 16, 19, 20 or 21, wherein a tip length Ltipof the shortest tapered element is between 20 pm and 40 pm.

23. The method according to any one of claims 15 to 22 further comprising the step of etching a cavity between the substrate and the first dielectric layer, the cavity being disposed vertically below the semiconductor structure.

24. The method according to any one of claims 15 to 23 further comprising the step of forming a second dielectric layer on the first dielectric layer and positioned vertically above the first section of the semiconductor structure.

25. The method according to any one of claims 15 to 24, wherein the substrate comprises silicon, the dielectric layer comprises silicon dioxide and the semiconductor structure comprises silicon nitride or silicon.

26. The method according to any one of claims 15 to 22, or 25, wherein the step of forming the first dielectric layer further comprises the steps of: forming a first trench defined along a longitudinal side of the semiconductor structure; forming a second trench defined along an opposite longitudinal side of the semiconductor structure such that the semiconductor structure is laterally positioned between the first and second trenches, wherein the first and second trenches extend vertically through the first dielectric layer and are configured to reduce lateral dispersion of an optical signal coupled from the optical fiber into the semiconductor structure.

27. The method according to claim 15, wherein the step of forming the semiconductor structure further comprises the steps of: forming the semiconductor structure as a metamaterial structure having a plurality of periodic subwavelength features arranged in a repeating pattern along an optical propagation direction of the optical signal through the semiconductor structure, and forming a tapered coupling region in the optical waveguide such that the tapered coupling region is integrated with the periodic subwavelength features at the coupling tip end of the second section of the semiconductor structure.

28. The method according to claim 27, wherein a pitch of the subwavelength features is less than half of an operating wavelength of the optical signal, and wherein a fill ratio of the subwavelength features is less than 50% of the pitch of the subwavelength features.

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