Electro-optic modulator

Abstract

An electro-optical modulator for an integrated photonic circuit, including: a substrate having a thin film of lithium niobate disposed on an electrically insulating material; first and second optical waveguides disposed on the thin film of lithium niobate, the optical waveguides being mutually spaced and composed of silicon nitride; and a pair of plasmonic electrodes disposed on the thin film of lithium niobate and configured to define a plasmonic waveguide in a nanoscale gap there between; wherein the plasmonic waveguide is configured to communicatively interconnect the optical waveguides by photon-plasmon coupling so that a modulation voltage applied across the pair of plasmonic electrodes modulates a phase of an optical signal passing from either of the optical waveguides to the other of the optical waveguides via the plasmonic waveguide.

Description

[0001] ELECTRO-OPTIC MODULATOR

[0002] PRIORITY APPLICATION

[0003] This application claims priority from Australian Patent Application No. 2024902145, the entirety of which is hereby incorporated by reference.

[0004] TECHNICAL FIELD

[0005] The present invention relates to electro-optic modulation, and in particular to an electrooptic modulator, an electro-optical modulator assembly, and a method of producing an electro-optic modulator or electro-optical modulator assembly.

[0006] BACKGROUND

[0007] Electro-optic modulators are key components of photonic systems because they enable the conversion of electrical signals to optical signals. However, it remains challenging to develop electro-optic modulators capable of high-speed and low-energy operation, with minimal optical loss, deep modulation, compact dimensions, and seamless integration with other components.

[0008] It is desired to overcome or alleviate one or more difficulties of the prior art, or to at least provide a useful alternative.

[0009] SUMMARY

[0010] In accordance with some embodiments of the present invention, there is provided an electro-optical modulator for an integrated photonic circuit, including: a substrate having a thin film of lithium niobate disposed on an electrically insulating material; first and second optical waveguides disposed on the thin film of lithium niobate, the optical waveguides being mutually spaced and composed of silicon nitride; and a pair of plasmonic electrodes disposed on the thin film of lithium niobate and configured to define a plasmonic waveguide in a nanoscale gap there between; wherein the plasmonic waveguide is configured to communicatively interconnect the optical waveguides by photon-plasmon coupling so that a modulation voltage applied across the pair of plasmonic electrodes modulates a phase of an optical signal passing from either of the optical waveguides to the other of the optical waveguides via the plasmonic waveguide.

[0011] In some embodiments, the plasmonic electrodes are composed of gold, silver, copper, aluminium or platinum.

[0012] In some embodiments, the electrically insulating material is silicon dioxide.

[0013] In some embodiments, the nanoscale gap between the plasmonic electrodes is in a range of about 30 to 150 nm. In some embodiments, the nanoscale gap between the plasmonic electrodes is about 30 to 50 nm. In some embodiments, the nanoscale gap between the plasmonic electrodes is about 30 or 50 nm.

[0014] In some embodiments, in plan view the optical waveguides are mutually parallel but laterally offset from one another, the plasmonic electrodes are rectangular, orthogonal to the optical waveguides, and mutually parallel but partially offset with respect to one another along their longitudinal axes so that they have mutually opposing first portions that define the plasmonic waveguide, and second portions extending beyond the plasmonic waveguide, each of which opposes (and has the same length as) an end of the corresponding optical waveguide to define a gap therebetween for the photonplasmon coupling.

[0015] In some embodiments, in plan view the plasmonic electrodes are symmetrically arranged about the nanoscale gap and have a truncated triangular shape, the optical waveguides are co-linear and have ends with a truncated triangular shape, the flat tip of which is aligned with the nanoscale gap.

[0016] In some embodiments, the truncated triangular shape has a taper angle in the range of about 8-20°. In some embodiments, the truncated triangular shape has a taper angle of about 13°. In accordance with some embodiments of the present invention, there is provided an electro-optical modulator assembly, including: a Mach-Zender interferometer having:

[0017] (i) first and second electro-optical modulators in accordance with any one of the above embodiments;

[0018] (ii) a first directional coupler configured to distribute an input optical signal to the first and second electro-optical modulators;

[0019] (iii) a second directional coupler configured to merge outputs of the first and second electro-optical modulators; and a loopback component configured to receive the merged optical signals from the second directional coupler, and to return them to pass back through the first and second electro-optical modulators.

[0020] In accordance with some embodiments of the present invention, there is provided a method of forming any one of the above electro-optical modulators, including the steps of: receiving a substrate having a thin film of lithium niobate disposed on an electrically insulating material; forming first and second optical waveguides on the thin film of lithium niobate, the optical waveguides being mutually spaced and composed of silicon nitride; and forming a pair of mutually opposing plasmonic electrodes on the thin film of lithium niobate and configured to define a plasmonic waveguide in a nanoscale gap there between; wherein the plasmonic waveguide is configured to communicatively interconnect the optical waveguides by photon-plasmon coupling so that a bias voltage applied across the pair of plasmonic electrodes modulates a phase of an optical signal passing from either of the optical waveguides to the other of the optical waveguides via the plasmonic waveguide.

[0021] In some embodiments, the step of forming the first and second optical waveguides includes depositing a layer of silicon nitride on the lithium niobate by plasma-enhanced chemical vapour deposition (PECVD). In accordance with some embodiments of the present invention, there is provided a method of forming the electro-optical modulator assembly, including the steps of: providing a pair of any one of the above electro-optical modulators; and configuring a first directional coupler to distribute an input optical signal to the first and second electro-optical modulators; configuring a second directional coupler to merge outputs of the first and second electro-optical modulators; and configuring a loopback component to receive the merged optical signals from the second directional coupler, and to return them to pass back through the first and second electro-optical modulators.

[0022] In some embodiments, the step of providing the pair of electro-optical modulators includes forming each of the electro-optical modulators in accordance with any of the above methods.

[0023] BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Some embodiments of the present invention are hereinafter described, by way of example only, with reference to the accompanying drawings, in which:

[0025] Figures 1 to 3 are schematic plan, side, and perspective views, respectively, of an electro-optical modulator in accordance with an embodiment of the present invention;

[0026] Figures 4 and 5 are schematic plan and perspective views, respectively, of an electro-optical modulator in accordance with an alternative embodiment of the present invention;

[0027] Figure 6 is a schematic plan view of a looped Mach-Zehnder interferometer in accordance with an embodiment of the present invention, incorporating two instances of a plasmonic optical modulator as described herein;

[0028] Figure 7 is a flow diagram of a method of producing an electro-optical modulator as described herein, in accordance with an embodiment of the present invention;

[0029] Figures 8 to 11 are plots representing respective simulated two-dimensional spatial distributions of electric fields within the plasmonic modulator of Figures 1 to Figure 12 is graph of normalised transmission by an electro-optic modulator in accordance with the embodiment of Figures 1 to 3 as a function of optical wavelength for bias voltages of 0 and 1.2V applied across the pair of electrodes; and

[0030] Figures 13 to 15 are plots representing respective simulated two-dimensional spatial distributions of electric fields within the plasmonic optical modulator of Figures 4 and 5.

[0031] DETAILED DESCRIPTION

[0032] Optical modulators made from materials such as semiconductors, liquid crystals, lithium niobate (LiNbOs), or polymers are generally large and suffer from integration issues due to the diffraction limit in dielectric materials. For example, conventional lithium niobate modulators require ~ 100 micron gaps between electrodes, making them undesirably large. Such difficulties have spurred the search for new optical technologies and materials that can overcome these limitations.

[0033] Plasmonic devices, which use materials with negative dielectric permittivities to confine light beyond the sub-diffraction limit, offer a promising solution, as they enable reduced energy consumption and smaller devices while facilitating tighter integration. Among potential materials, solid ferroelectric materials, known for their significant electro-optic effects and rapid response times, are particularly appealing for creating fast, integrated, and energy-efficient optical devices.

[0034] The development of thin film lithium niobate ("TFLN") on insulator waveguides represents a leap forward in the ability to make compact, on-chip opto-electronic devices. TFLN harnesses lithium niobate's excellent electro-optic properties in a more chip-friendly format. However, integrating TFLN into semiconductor chips is challenging due to its requirement for processing techniques that differ from standard CMOS processes.

[0035] To address these limitations, the inventors have developed electro-optical modulators that combine silicon nitride (Si3N4) with TFLN and plasmonics, and thus are also referred to herein as 'plasmonic modulators'. Silicon nitride is CMOS-compatible and provides a reliable platform for photonic circuits, enhancing TFLN's electro-optic benefits. When integrated with plasmonic structures, this enables the fabrication of next-generation optical modulators that exceed current performance metrics, heralding high-speed, energy-efficient, and densely integrated photonic circuits, including opto-electronic systems integrated on a single chip. The plasmonic modulators described herein provide on-chip modulation of light at extremely high frequencies, and with superior efficiency compared to traditional electro-optical modulators, and are suitable for incorporation into conventional semiconductor fabrication processes, especially within CMOS technology.

[0036] The electro-optical modulators described herein are fabricated on a substrate having a thin film of X-cut lithium niobate disposed on an electrically insulating material. This form of substrate is commercially available, and is often referred to as a "thin-film lithium niobate on insulator" (or simply "LNOI") substrate. In the described embodiments, the electro-optical modulators are fabricated on a LNOI substrate consisting of a thin (e.g., 300 nm) film of lithium niobate on an electrically insulating layer of silicon dioxide (SiOz) on a bulk silicon wafer substrate, although other LNOI substrate configurations may be used in other embodiments.

[0037] The electro-optical modulators are fabricated by forming on the LNOI substrate optical waveguides composed of silicon nitride (SisN4), interconnected by a plasmonic waveguide. Photon-plasmon coupling at the interface between each optical waveguide and the plasmonic waveguide allows an optical signal to travel from one optical waveguide to another via intermediate conversion to a surface plasmon polariton within the plasmonic waveguide. The plasmonic waveguide is formed by a nanoscale gap between a corresponding pair of mutually spaced plasmonic electrodes, enabling the phase of the optical signal to be controllably modulated by controlling a drive or modulation voltage applied across the pair of plasmonic electrodes. The electrodes are described herein as "plasmonic" because they are composed of at least one "plasmonic" material, meaning a metal or metal-like material having a negative real permittivity. In the described embodiments, the plasmonic material is gold, but other metals (e.g., copper, silver, aluminium or platinum) and / or other plasmonic materials may be used in other embodiments. Importantly, embodiments of the present invention do not require any patterning or etching of the lithium niobate layer, thereby maintaining compatibility with conventional semiconductor and CMOS manufacturing processes. The optical waveguides and the plasmonic waveguides can be formed in various configurations. Figures 1 to 3 are schematic plan, side, and perspective views, respectively, of an optical modulator 100 in accordance with one embodiment of the present invention. In plan view, the shown portions of the two optical waveguides 108, 110 are rectangular, and their respective longitudinal axes are parallel but laterally offset from one another, and orthogonal to the plasmonic waveguide that interconnects them.

[0038] The plasmonic electrodes 114 are rectangular, elongate, and mutually parallel, but partially offset with respect to one another along their longitudinal axes so that the plasmonic electrodes 114 have mutually opposing first portions that define the plasmonic waveguide 112, and second portions extending beyond the plasmonic waveguide 112, each of which opposes (and has the same length as) the end of the corresponding optical waveguide 108, 110. One end of each plasmonic electrode 114 abuts one side of the corresponding optical waveguide 108, 110. The photon-plasmon coupling between the plasmonic waveguide 112 and each of the optical waveguides 108, 110 occurs across the corresponding nanoscale 'coupling' gap 116 between the end of the optical waveguide 108, 110 and the second portion of the corresponding plasmonic electrode 114. The coupling gaps 116 and the gap 113 between the plasmonic electrodes are co-linear and have the same width.

[0039] With this geometry, the coupling gaps 116 and the plasmonic gap 113 are equal and can be any distance from about 30 nm to 150 nm to provide the plasmonic waveguide 112 and the photon-plasmon coupling between the plasmonic waveguide 112 and each optical waveguide 108, 110. However, the performance of the modulator improves with decreasing gap size, as a smaller gap enhances surface plasmon polariton confinement, and reduces the required driving voltage. The plasmonic electrodes 114 have a common length between about 3.5 zm and 30 zm, and a common width between about 1 zm and 1.5 zm. The optical waveguides 108, 110 have a common width between about 1 zm and 1.5 zm.

[0040] As described above, an input optical signal entering the modulator 100 from one of the optical waveguides 108 is converted across the corresponding coupling gap 116 to a surface plasmon polariton in the plasmonic waveguide 112. This surface wave travels along the plasmonic waveguide 112 towards the other optical waveguide 110, and is then converted back to an (output) optical signal across the corresponding coupling gap 116 to the other optical waveguide 110. The phase of the output optical signal can thus be controlled by controlling a modulation voltage applied across the plasmonic electrodes 114.

[0041] In an alternative embodiment, as shown in Figures 4 and 5, the plasmonic waveguide 112 and the optical waveguides 108, 110 of the electro-optical modulator 400 are all co-linear. In this embodiment, the plasmonic electrodes 114 are not mutually offset as they are in the first embodiment, and the ends of the plasmonic electrodes 114 and the optical waveguides 108, 110 are not orthogonal to their sides but are configured to enhance the photon-plasmon coupling relative to the first embodiment described above. Specifically, in the illustrated embodiment, the ends of the optical waveguides 108, 110 that couple to the plasmonic waveguide 112 are not flat as they are in the first embodiment, but are tapered like the end of a pencil, being generally triangular, but more accurately are shaped like a slightly truncated triangle or "V"-shape to define a tip (albeit a blunt tip with a square end due to the truncation). This tapered geometry enables the electric field to be concentrated at the blunt tip, improving the conversion of the photonic mode in the photonic waveguide 108, 110 to the plasmonic mode in the plasmonic gap 112. In the described embodiment, the coupling ends of the optical waveguides 108, 110 have a taper angle of 13°, but other taper angles may be used in other embodiments. In work leading up to the invention, the inventors found that taper angles less than about 8° may not provide sufficient coupling, and taper angles greater than about 20° can lead to excessive losses and / or reflections. Accordingly, taper angles in the range of 8-20° are found to provide the best performance.

[0042] Similarly, the ends of the plasmonic electrodes 114 are correspondingly shaped so that the pair of plasmonic electrodes 114 defines an approximately complementary and funnel-shaped portion at each end of the plasmonic waveguide 112, in which the tapered ends of the optical waveguides 108, 110 are located, with the flat tips of the optical waveguides 108, 110 being the same size as, and aligned with, the plasmonic waveguide gap 113 between the plasmonic electrodes 114. To put it another way, the pair of plasmonic electrodes 114 are shaped like a symmetrical pair of truncated triangles with their truncated ends mutually spaced and opposing. However, as shown in Figures 4 and 5, the inclined edges of each funnel are not parallel to the inclined edges of the V-shaped ends of the corresponding optical waveguide 108, 110 such that the gap therebetween decreases towards the tip of the corresponding optical waveguide 108, 110, and the size of the squared-off end of the truncated V- shape is equal to the width of the gap 113 between the plasmonic electrodes 114. It should be understood that the specific configurations of the illustrated embodiments are only examples of possible electro-optical modulator configurations, and many other configurations of the plasmonic waveguide and optical waveguides will be apparent to those skilled in the art in light of this disclosure.

[0043] Regardless of the specific geometry of the electro-optical modulators, a pair of the electro-optical modulators 602, 604 can be combined to form an electro-optic amplitude modulator incorporating a looped Mach-Zehnder interferometer structure, as shown in Figure 6. The optical amplitude modulator employs a push-pull configuration for efficient operation, and can be formed on a single substrate or chip. If the input optical signal is not generated on the same chip, it can be coupled onto the chip through edge couplers (not shown) known to those skilled in the art. This optical signal is then equally distributed between both arms 606, 608 of the Mach-Zehnder interferometer by a first directional coupler 610.

[0044] To achieve modulation, one arm 606 of the interferometer is biased by applying a drive or modulation voltage across the plasmonic electrodes 114 of the corresponding electro- optical modulator 602, creating a corresponding phase shift (e.g., of radians for digital switching). After modulation, the light from both arms 606, 608 of the interferometer is merged at a second directional coupler 612, but unlike a conventional Mach-Zehnder interferometer, the combined light is then ingeniously looped back through the second directional coupler 612 using a 180-degree arc waveguide 614, divided between the two arms of the second directional coupler 612, and reintroduced into the plasmonic waveguides of the respective plasmonic modulators 602, 604. Finally, the two light paths are merged by the first directional coupler 610 to produce the output optical signal. By passing the light through the modulators 602, 604 twice, the half-wave voltage (Vpi) is thus halved. Thus this configuration enhances modulation efficiency by reducing the energy required for modulation, and in a compact footprint. The drive / modulation voltage (Vpi) and device length are critical parameters in the design of optical modulators. For example, a conventional prior art optical modulator with an optical waveguide but without plasmonics may have a source / ground electrode gap of 4.5 pm, a device length of 7.8 mm, and a Vpi of 2.9V. In contrast, the electrooptic modulators described above can have an electrode gap as small as 30 nm, approximately 150 times smaller. Moreover, by passing the light through the modulators 602, 604 twice, the looped Mach-Zehnder interferometer structure described above effectively halves the device length compared with a conventional Mach-Zehnder interferometer, making it ~300 times shorter overall. These small dimensions enable switching speeds surpassing 500 GHz, limited by the (terahertz) plasma frequency of the plasmonic electrodes 114.

[0045] As described above, the electro-optical modulators described herein can be fabricated on commercially available LNOI substrates by processing steps that are compatible with standard semiconductor and CMOS processing. Figure 7 is a flow diagram of a simplified process for producing an electro-optical modulator in accordance with some embodiments of the present invention. Starting with a LNOI substrate 702, a silicon nitride layer is deposited onto the thin film of lithium niobate at step 704, using a standard deposition process such as plasma-enhanced chemical vapour deposition (PECVD). At step 706, the deposited nitride layer is then patterned to form the optical waveguides, using a standard patterning process having nanometer scale resolution, such as electron-beam lithography and selected area Deep Reactive Ion Etching (DRIE) through a photoresist mask.

[0046] At steps 708 and 710, a plasmonic material is deposited onto the substrate and then patterned to form the plasmonic electrodes, again using standard processing steps such as electron-beam lithography, electron-beam deposition of the plasmonic material, followed by a lift-off step. The result is an electro-optical or plasmonic modulator as described herein.

[0047] While plasmonic modulators are already available, they rely on organic polymers and necessitate the integration of electro-optic materials during device fabrication, making them incompatible with standard semiconductor and CMOS processing. Moreover, the electro-optic polymers necessitate high-temperature poling processes, and suffer from limited lifetimes. The electro-optic modulators described herein can be fabricated using processes compatible with standard semiconductor and CMOS manufacturing, thereby reducing manufacturing costs and improving scalability. The modulators require lower operating voltages and less energy than prior art modulators, and are capable of extremely high modulation frequencies exceeding 600GHz due to the very small RC time constants and the ultra-fast response of lithium niobate. The incorporation of a plasmonic waveguide allows confinement below the diffraction limit, and consequently reduces the footprint of the modulators, allowing high density on-chip integration.

[0048] EXAMPLE I

[0049] In one example, the spatial distribution of electric field intensity in an electro-optical modulator 100 with the configuration shown in Figures 1 to 3 was simulated using the ANSYS™ Lumerical suite of simulation software. The plasmonic electrodes 114 of the modulator were composed of gold, and were 3.5 zm long and 1 zm wide. The width of the optical waveguides 108, 110 was 1.5 zm, and the gap 113 between the plasmonic electrodes 114 and the gap 116 between each plasmonic electrode 114 and the corresponding optical waveguide 108, 110 were 30 nm. The lithium niobate layer 104 of the LNOI substrate had a thickness of 300 nm, and the thickness of both the silicon nitride layer (and thus the waveguides 108, 110) and the plasmonic electrodes 114 was 300 nm.

[0050] Figures 8 to 11 are different views of the resulting simulated spatial distribution of electric field intensity in the electro-optical modulator 100.

[0051] Figure 8 is a cross-sectional end view of the electric field resulting from the fundamental Transverse Electric (TE) mode excitation of one of the optical waveguides 108, 110 . The electric field is predominantly localized within the Lithium Niobate (LN) layer 104 just under the silicon nitride waveguide 108, 110.

[0052] Figure 9 is a cross-sectional end view of the electric field distribution of the plasmonic waveguide 112. The electric field is largely confined to the interface between the lithium niobate 104, the plasmonic electrodes 114, and the air gap therebetween, along the inner lower corner edge each plasmonic electrode 114, highlighting the critical interaction between plasmons on the electrode surface and the electro-optic effect of lithium niobate. Figure 10 is a plan view of the electric field for the entire modulator 100, demonstrating efficient photon-plasmon coupling between the plasmonic waveguide 112 and the input and output optical waveguides 108, 110.

[0053] Figure 11 is a cross-sectional end view of the electric field distribution at the output waveguide, confirming the modulator's effective transmission and modulation capabilities of the modulator 100.

[0054] Finally, Figure 12 shows the simulated normalised transmission through the modulator 100 for bias voltages of 0 V and 1.2 V applied across the plasmonic electrodes 114, 1.2 V corresponding to a phase shift of radians.

[0055] EXAMPLE II

[0056] For comparison, the spatial distribution of electric field intensity in an electro-optical modulator with the configuration shown in Figures 4 & 5 was also simulated, as described above. The simulation parameters were as described above for Example I, except that the width of the optical waveguides 108, 110 was 1.1 um, and the gap 113 between the plasmonic electrodes 114 was 50 nm.

[0057] Figure 13 is a plan view of the electric field intensity of the modulator 400, demonstrating efficient photon-plasmon coupling at the input (left) 108 and output (right) 110 optical waveguides. The photon-to-plasmon coupling is enhanced by the tapered geometries of the plasmonic waveguide electrodes 114 and the optical waveguides 108, 110, achieving strong coupling despite the photonic mode being strongly confined in the lithium niobate (LN) layer 104 below the electrodes 114.

[0058] Figure 14 is a cross-sectional end view of the fundamental Transverse Electric (TE) mode excitation of one optical waveguide 108, 110, the electric field being predominantly localized within the lithium niobate layer 104 under the waveguide 108, 110.

[0059] Finally, Figure 15 is a cross-sectional end view of the plasmonic waveguide, revealing electric field confinement at the lithium niobate 104 and plasmonic waveguide 112 interface, again highlighting the critical interaction between plasmons and the electrooptic effect of lithium niobate.

[0060] Many modifications will be apparent to those skilled in the art without departing from the scope of the present invention.

Claims

CLAIMS:

1. An electro-optical modulator for an integrated photonic circuit, including: a substrate having a thin film of lithium niobate disposed on an electrically insulating material; first and second optical waveguides disposed on the thin film of lithium niobate, the optical waveguides being mutually spaced and composed of silicon nitride; and a pair of plasmonic electrodes disposed on the thin film of lithium niobate and configured to define a plasmonic waveguide in a nanoscale gap there between; wherein the plasmonic waveguide is configured to communicatively interconnect the optical waveguides by photon-plasmon coupling so that a modulation voltage applied across the pair of plasmonic electrodes modulates a phase of an optical signal passing from either of the optical waveguides to the other of the optical waveguides via the plasmonic waveguide.

2. The electro-optical modulator of claim 1, wherein the plasmonic electrodes are composed of gold, silver, copper, aluminium or platinum.

3. The electro-optical modulator of claim 1 or 2, wherein the electrically insulating material is silicon dioxide.

4. The electro-optical modulator of any one of claims 1 to 3, wherein the nanoscale gap between the plasmonic electrodes is in a range of about 30 to 150 nm.

5. The electro-optical modulator of claim 4, wherein the nanoscale gap between the plasmonic electrodes is about 30 to 50 nm.

6. The electro-optical modulator of claim 4, wherein the nanoscale gap between the plasmonic electrodes is about 30 or 50 nm.

7. The electro-optical modulator of any one of claims 1 to 6, wherein in plan view the optical waveguides are mutually parallel but laterally offset from one another, the plasmonic electrodes are rectangular, orthogonal to the optical waveguides, and mutually parallel but partially offset with respect to one another along their longitudinal axes so that they have mutually opposing first portions that define the plasmonic waveguide, and second portions extending beyond theplasmonic waveguide, each of which opposes (and has the same length as) an end of the corresponding optical waveguide to define a gap therebetween for the photon-plasmon coupling.

8. The electro-optical modulator of any one of claims 1 to 6, wherein in plan view the plasmonic electrodes are symmetrically arranged about the nanoscale gap and have a truncated triangular shape, the optical waveguides are co-linear and have ends with a truncated triangular shape, the flat tip of which is aligned with the nanoscale gap.

9. The electro-optical modulator of claim 8, wherein the truncated triangular shape has a taper angle in the range of about 8-20°.

10. The electro-optical modulator of claim 8, wherein the truncated triangular shape has a taper angle of about 13°.

11. An electro-optical modulator assembly, including: a Mach-Zender interferometer having:(i) first and second electro-optical modulators in accordance with any one of claims 1 to 10;(ii) a first directional coupler configured to distribute an input optical signal to the first and second electro-optical modulators;(iii) a second directional coupler configured to merge outputs of the first and second electro-optical modulators; and a loopback component configured to receive the merged optical signals from the second directional coupler, and to return them to pass back through the first and second electro-optical modulators.

12. A method of forming the electro-optical modulator of any one of claims 1 to 10, including the steps of: receiving a substrate having a thin film of lithium niobate disposed on an electrically insulating material; forming first and second optical waveguides on the thin film of lithium niobate, the optical waveguides being mutually spaced and composed of silicon nitride; and forming a pair of mutually opposing plasmonic electrodes on the thin film oflithium niobate and configured to define a plasmonic waveguide in a nanoscale gap therebetween; wherein the plasmonic waveguide is configured to communicatively interconnect the optical waveguides by photon-plasmon coupling so that a bias voltage applied across the pair of plasmonic electrodes modulates a phase of an optical signal passing from either of the optical waveguides to the other of the optical waveguides via the plasmonic waveguide.

13. The method of claim 12, wherein the step of forming the first and second optical waveguides includes depositing a layer of silicon nitride on the lithium niobate by plasma-enhanced chemical vapour deposition (PECVD).

14. A method of forming the electro-optical modulator assembly of claim 11, including the steps of: providing a pair of electro-optical modulators in accordance with any one of claims 1 to 10; and configuring a first directional coupler to distribute an input optical signal to the first and second electro-optical modulators; configuring a second directional coupler to merge outputs of the first and second electro-optical modulators; and configuring a loopback component to receive the merged optical signals from the second directional coupler, and to return them to pass back through the first and second electro-optical modulators.

15. The method of claim 14, wherein the step of providing the pair of electro-optical modulators includes forming each of the electro-optical modulators in accordance with the method of claim 12 or 13.

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