A directional coupler for terahertz applications

Abstract

This document describes a directional coupler for terahertz (THz) applications. The directional coupler comprises two waveguides that are disposed on an insulating substrate such that optical coupling occurs between the two waveguides at a coupling region of the directional coupler. Further, each of the two waveguides are formed with a longitudinal notch along a bottom edge of the waveguide at an interface between the waveguide and the insulating substrate such that the longitudinal notches of the two waveguides are disposed opposite one another across the coupling region.

Description

A DIRECTIONAL COUPLER FOR TERAHERTZ APPLICATIONSCROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority to Singapore patent application no. 10202402262P which was filed on 29 July 2024, the contents of which are hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] This application relates to a directional coupler for terahertz (THz) applications. The directional coupler comprises two waveguides that are disposed on an insulating substrate such that optical coupling occurs between the two waveguides at a coupling region of the directional coupler. Further, each of the two waveguides are formed with a longitudinal notch along a bottom edge of the waveguide at an interface between the waveguide and the insulating substrate such that the longitudinal notches of the two waveguides are disposed opposite one another across the coupling region.BACKGROUND

[0003] Fifth generation (5G) communication networks have become a cornerstone technology in enabling advancements such as the Internet of Things (loT), autonomous vehicles, and virtual reality. As technological demands continue to grow, the evolution toward sixth generation (6G) networks is widely anticipated. 6G networks are expected to support data transmission rates exceeding 1 terabit per second (Tbps), which will likely necessitate the use of carrier frequencies in the terahertz (THz) range due to the broad bandwidth available at those frequencies.

[0004] The shift to THz frequencies introduces new challenges in the design and implementation of communication systems. In particular, the increasing data rates and complexity of wired interconnections pose potential bottlenecks for high-speed signal transmission. As a result, in-plane platforms capable of efficiently manipulating THz waves are becoming increasingly desirable. However, at higher THz frequencies, traditional device materials and structures, such as free-standing silicon, often exhibit mechanical fragility and are difficult to integrate into stable, scalable systems. These limitations present obstacles to the reliable deployment of compact, high-frequency components for next-generation THz circuits.

[0005] As a result, those skilled in the art are constantly seeking a directional coupler that offers stable and efficient terahertz wave manipulation, while addressing challenges such as sensitivity to fabrication variations, mechanical fragility of device structures, and limitations in coupling efficiency at high frequencies.SUMMARY

[0006] In one aspect, the present application discloses a directional coupler for terahertz (THz) applications. The disclosed directional coupler comprises a first waveguide and a second waveguide disposed on an insulating substrate The two waveguides are laterally spaced and arranged in a directional coupler configuration such that optical coupling occurs between the first and second waveguides in a coupling region of the directional coupler. Further, each of the first and second waveguides comprises, within the coupling region, a longitudinal notch formed along a bottom edge of the waveguide at an interface between the waveguide and the insulating substrate, wherein each longitudinal notch extends continuously along a propagation length of a respective waveguide, corresponding to a length of the coupling region, and wherein the longitudinal notches of the first and second waveguides are formed on opposing inner edges of the respective waveguides such that the longitudinal notches of the first and second waveguides are disposed opposite one another across the coupling region.

[0007] In embodiments of this one aspect, the first and second waveguides comprise a material selected from a group consisting of silicon, germanium, aluminum nitride, silicon nitride, silicon-germanium, quartz, sapphire, a polymer and a compound semiconductor material including a III-V material. In embodiments, the insulating substrate may comprise borosilicate glass.

[0008] In embodiments of this one aspect, the directional coupler is configured to achieve an equal optical power split at output ports of the first and second waveguides.

[0009] In another aspect, the present application discloses a method for forming a directional coupler for terahertz (THz) applications. The disclosed method comprises the steps of forming a first waveguide and a second waveguide on an insulating substrate such that the first and second waveguides are laterally spaced and arranged in a directional coupler configuration such that optical coupling occurs between the first and second waveguides in acoupling region of the directional coupler configuration. The method then comprises the step of fonning, within the coupling region, a longitudinal notch along a bottom edge of each of the first and second waveguides at an interface between the waveguide and the insulating substrate, wherein each longitudinal notch extends continuously along a propagation length of a respective waveguide, corresponding to a length of the coupling region. In this embodiment, the longitudinal notches of the first and second waveguides are formed on opposing inner edges of the respective waveguides such that the longitudinal notches of the first and second waveguides are disposed opposite one another across the coupling region.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] 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 directional coupler for terahertz (THz) applications in accordance with embodiments of the present disclosure;Figure 2 illustrates a front view or cross-sectional view of the directional coupler in accordance with embodiments of the disclosure;Figure 3 illustrates a front view or cross-sectional view showing the formation of the directional coupler illustrated in Figure 2 using standard processing steps in accordance with embodiments of the present disclosure;Figure 4a illustrates the variation in output power difference at the outputs of the first and second waveguides as a function of waveguide thickness, for different step depths of the notches formed along the bottom edges of each of the waveguides;Figure 4b illustrates the variation in the insertion loss of the first and second waveguides as the waveguide thickness is varied, for different step depths of the notches formed along the bottom edges of each of the waveguides,Figure 4c illustrates the variation in the figure-of-merit of the directional coupler as a function of step depths of the notches formed along the bottom edges of each of the waveguides when the coupling gap between the two waveguides is set to be 30 pm;Figure 5a illustrates the variation in output power difference at the outputs of the first and second waveguides as a function of the coupling gap, for different step depths of the notches formed along the bottom edges of each of the waveguides;Figure 5b illustrates the variation in the insertion loss of the first and second waveguides as the coupling gap is varied, for different step depths of the notches formed along the bottom edges of each of the waveguides;Figure 5c illustrates the variation in the figure-of-merit of the directional coupler as a function of step depths of the notches formed along the bottom edges of each of the waveguides when the thickness of the two waveguides in the coupling region is set to be 175 pm;Figure 6a illustrates a simulated optical mode profile of a coupling region of a conventional directional coupler known in the art;Figure 6b illustrates a simulated optical mode profile of a coupling region of a directional coupler incorporating longitudinal notches formed along the bottom edges of each waveguide in accordance with embodiments of the present disclosure; andFigure 7 illustrates a flowchart that sets out the process or method for forming the directional coupler in accordance with embodiments of the disclosure.DETAILED DESCRIPTION

[0011] 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.

[0012] 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.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] 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.

[0017] 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.

[0018] 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.

[0019] 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.

[0020] 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.

[0021] Additionally, for the sake of brevity, extensive explanations of conventional techniques of fabricating semiconductor or photonic 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.

[0022] A directional coupler is a basic passive component that is commonly used in photonic and electromagnetic systems to split or combine signals between two or more waveguides based on the principle of evanescent field coupling. A typical directional coupler comprises of two parallel waveguides positioned in close proximity over a defined length, referred to as the coupling region. Within this coupling region, the optical modes of the waveguides interact through their overlapping evanescent fields, allowing power to transfer from one waveguide to the other. Such directional couplers are widely used in applications requiring power splitting, signal routing, or interference-based modulation.

[0023] In conventional directional coupler designs, the formation of notches, particularly at the sidewalls of the directional coupler’s waveguide sidewalls or waveguide-substrate interfaces, are typically avoided. Such detrimental features usually introduce surface roughness that may cause optical performance to degrade through increased scattering losses and fabrication variability. As a result, state-of-the-art directional couplers are commonly fabricated using processes that maintain straight sidewall profiles and employ precise end-point detection to prevent the formation of notches during etching

[0024] In embodiments of the disclosure, the directional coupled disclosed in Figure 1 includes the deliberate formation of a longitudinal notch along the bottom edge of each waveguide, at the interface between the waveguide and the insulating substrate on which the waveguides are formed on. This longitudinal notch is implemented as a step structure and in some embodiments, may be fabricated using a single etching step that simultaneously defines both the waveguides and the notch geometry.

[0025] By integrating the notch into the directional coupler design, as illustrated in Figure 1, the interaction between the optical modes in the coupling region is advantageously altered.As will be described in greater detail in later sections, simulation results demonstrate that this configuration leads to a significant improvement in the figure-of-merit (FOM) of the directional coupler, thereby enhancing performance robustness against process-induced variations in waveguide thickness and coupling gap.

[0026] Figure 1 illustrates a top view of directional coupler 100 configured in accordance with embodiments of the present disclosure. Directional coupler 100 comprises first waveguide 102 and second waveguide 104, both of which are disposed on substrate 101. As illustrated, first waveguide 102 and second waveguide 104 are laterally spaced and arranged in parallel within coupling region 110 to enable evanescent optical coupling to occur between these two waveguides. Within this coupling region 1 10, the waveguides are positioned in close proximity to one another to enable evanescent optical coupling. Coupling region 110 is defined as a region whereby the optical modes of the two waveguides interact to facilitate controlled power transfer from one waveguide to the other.

[0027] Tn operation, a terahertz (THz) optical signal 1 12 may be introduced into directional coupler 100 via an input port of first waveguide 102. This signal will propagate along the z- axis of directional coupler 100. By appropriately designing the length of first and second waveguides 102 and 104 respectively within coupling region 110, the optical signal 112 may be distributed between the two waveguides in a controlled manner to achieve a desired output ratio. In one example, the coupling length is selected to achieve an equal power split, such that the output power from first and second waveguides 102 and 104 is substantially equal (i.e., Ti = T ).

[0028] With reference to Figure 1, it can be seen that within coupling region 110, each of waveguides 102 and 104 include a corresponding longitudinal notch 103 and 105 (represented as dotted lines), respectively, formed along an inner bottom edge at the interface between each respective waveguide and substrate 101. These longitudinal notches are positioned such that the longitudinal notches laterally oppose each other across coupling region 110 and extends continuously along a propagation length of each respective waveguide, with the length of longitudinal notches 103 and 105 corresponding to a length of coupling region 110. In some embodiments, longitudinal notches 103 and 105 may be formed as step structures during the same etching process used to define the geometry of first and second waveguides 102 and 104.Additionally, as shown in Figure 1, coupling gap 106 may be defined as the distance between first waveguide 102 and second waveguide 104 within coupling region 110 and this gap directly influences the strength of the optical coupling between the two waveguides. It should be noted that the incorporation of longitudinal notches 103 and 105 within coupling region 110 improves the directional coupler’s resilience to process-induced variations, such as deviations in coupling gap and silicon thickness. In other embodiments of the disclosure, longitudinal notches 103 and 105 may extend beyond coupling region 110, along the propagation length of first and second waveguides 102 and 104, respectively.

[0029] In the embodiment shown in Figure 1, first waveguide 102 has a width Wi and second waveguide 104 has a width w2. These widths may be equal or different, depending on the desired coupling characteristics and power distribution. Each longitudinal notch is associated with a step structure having a step depth 108, which defines the lateral extent of the notch from the inner edge of the waveguide. The step depth 108 may be selected based on design considerations to optimize mode confinement and coupling behaviour. Section A- A7in Figure 1 indicates the cross-sectional plane along which the structural features of directional coupler 100 are further depicted in Figure 2.

[0030] Figure 2 illustrates a cross-sectional view of directional coupler 100 taken along the plane A- A' indicated in Figure 1. As shown, directional coupler 100 comprises first waveguide 102 and second waveguide 104 disposed on substrate 101. First waveguide 102 has width Wi and height hi, while second waveguide 104 has width iv2and height h2. These two waveguides are laterally separated by a coupling gap 106, which enables evanescent field interaction between the optical modes supported by the waveguides.

[0031] Within coupling region 110, each waveguide includes a corresponding longitudinal notch formed at the inner bottom edge of the waveguide at the interface with the substrate 101. These notches, i.e., longitudinal notches 103 and 105, may be implemented as step structures, characterized by a step depth 108 and a step height 202. Step depth 108 defines the lateral extent of the notch inward from the inner edge of each waveguide, while step height 202 defines the vertical displacement between the base of the waveguide and the recessed step surface. In embodiments of the disclosure, these dimensions may be selected based on design requirementsto influence modal confinement, substrate leakage, and coupling strength between the waveguides.

[0032] The inclusion of longitudinal notches 103 and 105 within coupling region 110 alters the effective geometry of coupling region 110 and may be used to tune the directional coupler’ s performance. As described in later sections, these features contribute to enhanced resilience against fabrication-induced variations in waveguide thickness and coupling gap, while also improving mode symmetry and reducing substrate leakage.

[0033] Figure 3 illustrates a fabrication process flow for forming directional coupler 100 in accordance with embodiments of the disclosure, with emphasis on the coupling region of the directional coupler 100. The process begins at step 301, where an insulating substrate 101, such as borosilicate glass is provided. At step 302, a high-resistivity silicon wafer 306 is bonded onto substrate 101 to form a bonded wafer stack

[0034] Following bonding step 302, the process proceeds to step 303, in which the bonded silicon layer 306 is thinned to a desired thickness using a grinding process, resulting in a planarized silicon layer 307. This grinding step defines the thickness of the final waveguides and contributes to the vertical confinement of the optical modes.

[0035] At step 304, the photonic structures are defined through a single etching step. This step simultaneously patterns first waveguide 102 and second waveguide 104 on the thinned silicon layer, as well as the corresponding longitudinal notches 103 and 105 formed at the bottom inner edges of each waveguide within the coupling region. These notches are implemented as step structures that extend laterally inwards from the inner edge of each waveguide, as previously described with respect to Figures 1 and 2. The use of a single etching step to define both the waveguide geometries and the associated step structures within the coupling region simplifies fabrication, reduces alignment complexity, and ensures consistent profile definition.

[0036] Figures 4a and 4b illustrate the simulated impact of varying silicon thickness on the performance of the directional coupler for various step depths or widths of the longitudinal notches formed at the base of the w aveguides within the coupling region.

[0037] Figure 4a illustrates the simulated variation in power difference between the outputs of the first and second waveguides as a function of silicon thickness, for step depths of 0 pm, 10 pm, 30 pm, and 50 pm. As shown, it was found that the power difference is minimized when the thickness of the silicon layer was 175 pm. Notably, the results show that the inclusion of a 10 pm step depth yields the lowest power imbalance within the process window as indicated by boundary 402, demonstrating the effectiveness of the longitudinal notches in improving output symmetry.

[0038] Figure 4b illustrates the corresponding insertion loss for the same set of step depths and silicon thickness variations. While the simulated results show that insertion loss generally increases with greater step depths, particularly when the waveguide is thinner, the 10 pm step depth offers a favourable balance, maintaining low insertion loss across the process window.

[0039] Figure 4c illustrates the trade-off in performance through a computed figure-of-merit (FOM), defined as the product of average insertion loss and average power difference within the process window (as indicated by boundary box 402 in Figures 4a, and 4b and boundary box 502 in Figures 5a and 5b). Specifically, within this process window, the FOM is determined by averaging the insertion loss and power difference values across the range of silicon thicknesses (i.e., Figures 4a and 4b) or coupling gaps (i.e., Figures 5a and 5b) represented in the window. The step depth that yields the lowest FOM is identified as the optimal configuration, representing the best trade-off between minimizing insertion loss and achieving balanced power distribution at the coupler outputs. Hence, the FOM may be defined as:FOM = average insertion loss X average power difference where the insertion loss is defined as Insertion loss = 1 — (7^ + 712) , and the power difference is defined as Power difference = 17 — T21.

[0040] The graph in Figure 4c plots the FOM as a function of step depth when the coupling gap is fixed at 30 pm. The plot reveals that a step depth of 10 pm achieves the minimum FOM value (0.00077), as highlighted in the accompanying table. In other words, this plot shows that a 10 pm step depth provides the optimal trade-off between minimizing insertion loss and powerimbalance, thereby improving the overall robustness of the directional coupler to variations in silicon thickness.

[0041] Figures 5a and 5b illustrate the effect of coupling gap variation on the performance of the directional coupler for different step depths introduced at the base of the waveguides.

[0042] Figure 5a illustrates the simulated variation in power difference between the first and second output ports as a function of coupling gap, for step depths of 0 pm, 10 pm, 30 pm, and 50 pm. When the coupling gap is 30 ± 5 pm, as indicated by boundary 502, the presence of the notch (step depth > 0) significantly reduces the power imbalance between outputs. Among the various step depths, the 10 pm configuration exhibits the lowest power difference within the target coupling gap range.

[0043] Figure 5b illustrates the corresponding simulated insertion loss values for the same step depths across the same range of coupling gaps. A general trend of increasing insertion loss is observed as the step depth increases; however, the insertion loss associated with the 10 pm step depth remains relatively low.

[0044] Figure 5c illustrates the trade-offs between power difference and insertion loss through the calculated FOM, defined as a product of the two quantities. Among the simulated step depths with a silicon thickness of 175 pm, it was found that when the step depth is at 10 pm, the configuration was able to achieve the lowest FOM value (0.00481), as shown in the embedded table. This result confirms that a step depth of 10 pm provides the optimal balance between performance and robustness when the coupling gap is subject to fabrication-induced variation.

[0045] Based on the simulation results, it can be seen that by incorporating the notch structure into the directional coupler design, the effects of process-induced variations, particularly in coupling gap and silicon thickness were able to be mitigated. These variations can significantly impact the coupling efficiency and output balance of the device. Table 1 below summarizes the typical ranges of coupling gap, silicon thickness, and waveguide width considered in the design, expressed as fractions of the terahertz wavelength ( ).TABLE 1TABLE 2

[0046] In a preferred embodiment of the disclosure, the step depth and step height associated with the notches may be limited to values below 60 pm and 40 pm, respectively.Step geometries within these bounds ensure that the performance of the directional coupler remains stable and within acceptable limits, avoiding excessive insertion loss or power imbalance across the expected fabrication tolerances.

[0047] Figure 6a illustrates a simulated optical model profile of a directional coupler that was fabricated using standard processing steps. Based on the simulated profile, it can be seen that the optical mode of the directional coupler in the coupling region exhibits significant leakage 602 from the waveguides into the substrate, as indicated by the downward spread of mode intensity. As a result of this leakage, the directional coupler suffers from coupling loss and a reduction in overall coupling efficiency.

[0048] Figure 6b illustrates a simulated optical model profile of a directional coupler formed in accordance with embodiments of the present disclosure, whereby a longitudinal notch is formed along the bottom edge of each of the waveguides Based on the simulated profile, it can be seen that the optical mode of the directional coupler in the coupling region remains well- confined within the waveguide with visibly less leakage into the substrate This improvement is due to the longitudinal notch formed at the base of the waveguides which alters the optical model distribution and improves the overall vertical confinement of the optical modes.

[0049] A process for forming a directional coupler for THz applications is disclosed in Figure 7 in accordance with embodiments of the disclosure. Process 700 begins at step 702 with process 700 forming a first waveguide and a second waveguide on an insulating substrate such that the first and second waveguides are laterally spaced and arranged in a directional coupler configuration. Due to this arrangement, optical coupling occurs between the first and second waveguides in a coupling region of the directional coupler configuration. At step 704, process 700 then forms, within the coupling region, a longitudinal notch along a bottom edge of each of the first and second waveguides at an interface between the waveguide and the insulating substrate. In embodiments of the disclosure, the longitudinal notch extends continuously along the propagation length of the respective waveguide corresponding to a length of the coupling region, and the longitudinal notches of the first and second waveguides are formed on opposing inner edges of the respective waveguides such that the longitudinal notches of the first and second waveguides are disposed opposite one another across thecoupling region. In other embodiments of the disclosure, process 700 may form the longitudinal notch beyond the length of the coupling region.

[0050] In embodiments of the disclosure, the first and second waveguides are formed from a material selected from a group consisting of silicon, germanium, aluminum nitride, silicon nitride, silicon-germanium, quartz, sapphire, a polymer and a compound semiconductor material including a III-V material.

[0051] 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. A directional coupler for terahertz (THz) applications comprising: a first waveguide and a second waveguide disposed on an insulating substrate and laterally spaced and arranged in a directional coupler configuration such that optical coupling occurs between the first and second waveguides in a coupling region of the directional coupler configuration, wherein each of the first and second waveguides comprises within the coupling region a longitudinal notch formed along a bottom edge of the waveguide at an interface between the waveguide and the insulating substrate, wherein each longitudinal notch extends continuously along a propagation length of a respective waveguide, corresponding to a length of the coupling region, and wherein the longitudinal notches of the first and second waveguides are formed on opposing inner edges of the respective waveguides such that the longitudinal notches of the first and second waveguides are disposed opposite one another across the coupling region.

2. The directional coupler according to claim 1, wherein the first and second waveguides comprise a material selected from a group consisting of silicon, germanium, aluminum nitride, silicon nitride, silicon -germanium, quartz, sapphire, a polymer and a compound semiconductor material including a III-V material.

3. The directional coupler according to claim 1 or 2, wherein the insulating substrate comprises borosilicate glass.

4. The directional coupler according to any one of claims 1 to 3, wherein a thickness of the first and second waveguides is between 165pm and 185pm when the first and second waveguides comprise silicon.

5. The directional coupler according to claim 4, wherein a step-depth of the longitudinal notches of the first and second waveguides is between 5pm and 15pm.

6. The directional coupler according to claim 4, wherein a step-height of the longitudinal notches of the first and second waveguides is between 20pm and 40pm.

7. The directional coupler according to claim 4, wherein a step-depth of the longitudinal notches of the first and second waveguides is 10pm and a step-height of the longitudinal notches of the first and second waveguides is 30pm.

8. The directional coupler according to any one of claims 1 to 7, wherein a coupling gap of the coupling region between the first and second waveguides is between 25pm and 35pm.

9. The directional coupler according to any one of claims 1 to 8, wherein the coupling region has a length between 2000pm and 3000pm.

10. The directional coupler according to any one of claims 1 to 9, wherein the directional coupler is configured to achieve an equal optical power split at output ports of the first and second waveguides.

11. A method for forming a directional coupler for terahertz (THz) applications comprising: forming a first waveguide and a second waveguide on an insulating substrate such that the first and second waveguides are laterally spaced and arranged in a directional coupler configuration such that optical coupling occurs between the first and second waveguides in a coupling region of the directional coupler configuration, forming, within the coupling region, a longitudinal notch along a bottom edge of each of the first and second waveguides at an interface between the waveguide and the insulating substrate, wherein each longitudinal notch extends continuously along a propagation length of a respective waveguide corresponding to a length of the coupling region, and wherein the longitudinal notches of the first and second waveguides are formed on opposing inner edges of the respective waveguides such that the longitudinal notches of the first and second waveguides are disposed opposite one another across the coupling region.

12. The method according to claim 11, wherein the forming of the first and second waveguides comprise using a material selected from a group consisting of silicon, germanium, aluminum nitride, silicon nitride, silicon-germanium, quartz, sapphire, a polymer and a compound semiconductor material including a IH-V material.

13. The method according to claim 11 or 12, wherein the insulating substrate comprises borosilicate glass.

14. The method according to any one of claims 11 to 13, wherein a thickness of the first and second waveguides is between 165pm and 185pm when the first and second waveguides are formed using silicon.

15. The method according to claim 14, wherein the longitudinal notches of the first and second waveguides are formed with a step-depth between 5pm and 15pm.

16. The method according to claim 14, wherein the longitudinal notches of the first and second waveguides are formed with a step-height between 20pm and 40pm.

17. The method according to claim 14, wherein the longitudinal notches of the first and second waveguides are formed with a step-depth of 10pm and a step-height of 30pm.

18. The method according to any one of claims 11 to 17, wherein a coupling gap of the coupling region between the first and second waveguides is formed to be between 25 pm and 35pm.

19. The method according to any one of claims 11 to 18, wherein the coupling region is formed with a length between 2000pm and 3000pm.

20. The method according to any one of claims 11 to 19, wherein the formed directional coupler is configured to achieve an equal optical power split at output ports of the first and second waveguides.

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