Electro-optic modulator and operating method

Abstract

The present invention relates to an electro-optic modulator and a method for operating an electro-optic modulator. The electro-optic modulator comprises a substrate (Cd,S), an optical waveguide (C) arranged with the substrate, and a first graphene layer (Gb) arranged such that input light is absorbed by the operating electro-optic modulator. The electro-optic modulator is configured to operate at wavelengths of 8 micrometers to 15 micrometers.

Description

[Technical Field]

[0001] [Cross-reference of related applications] This application claims the benefits of European Patent Application No. 23382367.3, filed on April 20, 2023.

[0002] [Technical field] This disclosure relates to electro-optic modulators, and more particularly to graphene-based electro-optic modulators with waveguides. This disclosure further relates to a method for operating an electro-optic modulator with waveguides. [Background technology]

[0003] A modulator is a device that can be used to manipulate the properties of light, for example, the properties of a laser beam passing through the modulator. Depending on which properties of light are controlled or manipulated, the modulator may be referred to as, for example, an amplification modulator, a phase modulator, a polarization modulator, a frequency modulator, or the like.

[0004] An electro-optic modulator is a device that manipulates light using an electrical signal. Modulation can be applied, for example, to the phase, amplitude, or polarization of a beam. This electrical signal is typically applied to the electro-optic modulator by a drive circuit. This electrical signal may be an electric current, but is usually a voltage and is commonly referred to as the driving voltage, drive voltage, or applied voltage. The terms driving voltage, drive voltage, and applied voltage are used interchangeably throughout this disclosure.

[0005] Figure 1 shows an example of the absorption curve of a graphene electro-optic modulator, under a driving voltage V. DThe values ​​are schematically shown in normalized units as a function of (volts). Normalized absorbance refers to the light absorbed by the modulator at a given drive voltage divided by the modulator's maximum absorbance. The term normalized absorbance as defined herein is used throughout this disclosure. The curves are shown for an operating light wavelength (λ) of 1.55 micrometers. Wavelengths λ=1550 nm and λ=850 nm are commonly used in telecommunications and data communications (TeleCom and DataCom, respectively), but the behavior of the same trace is valid for other wavelengths, including all wavelengths supported by graphene. As seen in the example in this figure, not all drive voltages can modulate the light passing through the electro-optic modulator. The range of voltages that can do so is referred to as the operating range.

[0006] The offset voltage, also known as DC offset, represents the minimum voltage value required to reach the operating range and, therefore, the minimum voltage value required to modulate the light forming the input to the electro-optic modulator. A typical range for the offset voltage of modern electro-optic modulators can be 1V to 20V, but lower offset voltages (DC offsets close to 1V) can be achieved by electro-optic modulators that include a current amplifier, voltage amplifier, or transimpedance amplifier in either the modulator itself or the drive circuit.

[0007] Modulators with high DC offset operate at high drive voltages and therefore have further drawbacks. High offset voltage is associated with high power consumption. This generally negatively impacts all applications, but is particularly detrimental to server or battery-powered applications. High power consumption is generally associated with significant heat generation, which degrades the performance and stability of the electro-optic modulator, i.e., reduces static and dynamic modulation efficiency. This is particularly relevant to graphene-based modulators, where static modulation efficiency degrades as a function of temperature, as shown in Figure 16. Higher temperatures may narrow the temperature stability range, i.e., the temperature range in which the electro-optic modulator operates without significant performance degradation.

[0008] Reducing the effective DC offset voltage using current amplifiers, voltage amplifiers, or transimpedance amplifiers is complex and expensive. These amplifiers not only incur additional costs in the drive circuitry but also have speed limitations, potentially restricting the modulator speed. This is particularly relevant for high-speed modulators, such as graphene-based electro-optic modulators, where the modulator speed far exceeds the speed performance of state-of-the-art amplifiers.

[0009] Amplifiers, such as current amplifiers, voltage amplifiers, or transimpedance amplifiers, can introduce noise, offset, distortion, and timing jitter, which are understood as variations in the signal from its ideal temporal position. Noise, offset, distortion, and timing jitter can cause bit errors, further exacerbating the problem in high-speed data transmission.

[0010] Electro-optic modulators with high offset voltages require high voltage signals to operate, and therefore are more susceptible to stress and potentially less reliable. This is especially true for graphene-based modulators, which are more sensitive and prone to damage. Graphene electro-optic modulators are typically characterized by high DC offset voltages in the range of tens of volts. On the other hand, graphene-based electro-optic modulators can potentially support high modulation speeds up to several hundred GHz, thereby exacerbating the aforementioned drawbacks. [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] (See international survey report) [Overview of the Initiative] [Problems that the invention aims to solve]

[0012] This disclosure provides an electro-optic modulator, particularly a graphene electro-optic modulator, that mitigates or eliminates one or more of the above-mentioned drawbacks, in particular without impairing the speed of the electro-optic modulator (mitigating or eliminating the drawbacks), and further improves static and dynamic efficiency. [Means for solving the problem]

[0013] In one aspect of the present disclosure, an electro-optic modulator is provided. The electro-optic modulator comprises a substrate, an optical waveguide disposed with the substrate, and a first graphene layer and a second graphene layer arranged such that input light is absorbed by the electro-optic modulator during operation, the first and second graphene layers overlapping each other and separated from each other by one or more dielectric layers. The electro-optic modulator is configured to operate at wavelengths between 8 micrometers and 15 micrometers.

[0014] According to this embodiment, the graphene-based electro-optic modulator is configured to operate in the long-wavelength infrared range (LWIR), i.e., 8 micrometers to 15 micrometers. Operation in this range can significantly reduce the modulator's offset voltage. The offset voltage can be, for example, 1V, 0.5V, 0.2V, or less than 0.1V, e.g., about 0V, meaning that overcoming the offset voltage to initiate modulation can be avoided by operating the graphene-based electro-optic modulator in this wavelength range. Or, at the very least, the offset voltage may be very small.

[0015] Therefore, the drawbacks associated with high offset voltage can be avoided without compromising modulation speed, and the static and dynamic efficiency of the electro-optic modulator can be increased.

[0016] The LWIR range can be understood as a wavelength range of 8 micrometers to 15 micrometers. Below the LWIR range is the mid-wavelength infrared range (MWIR), which can be understood as a wavelength range of 3 micrometers to 8 micrometers. Further below the MWIR are the near-wavelength infrared range (NWIR) and the short-wavelength infrared (SWIR) range. Conventional electro-optical modulators operate in these last two ranges (NWIR and SWIR), for example, at 1550 nm and 850 nm, respectively.

[0017] In some examples, the lower (i.e., first) and upper (i.e., second) graphene layers may overlap each other along at least a part of the width of the optical waveguide.

[0018] In some examples, the lower and upper graphene layers may overlap each other exactly along the width of the optical waveguide.

[0019] In some examples, the lower and upper graphene layers may overlap each other across and beyond the width of the waveguide.

[0020] In some examples, the first (lower) and second (upper) graphene layers may be disposed above the waveguide. In other examples, the first and second graphene layers may be disposed below the waveguide. In other examples, the first and second graphene layers may be disposed within the waveguide.

[0021] In some examples, the optical waveguide may include a Group IV semiconductor such as carbon (C), silicon (Si), germanium (Ge), tin (Sn), or lead (Pb). For example, the waveguide can include Ge, particularly SiGe. The waveguide can be, in particular, a germanium waveguide or a germanium-on-silicon waveguide. For an operating wavelength of 8 to 15 micrometers, the loss of the waveguide can be particularly low, for example, less than 4 dB / cm for a Ge waveguide and less than 5 dB / cm for a SiGe waveguide, so Ge and SiGe materials can be particularly beneficial for the waveguide. Generally, the transparency of Group IV semiconductors can be particularly high for an operating wavelength of 8 to 15 micrometers.

[0022] In these or other examples, the waveguide may include SiC, GeSn, GeC, SiGeSn, Si3N4 (e.g., Si3N4 polymer), sapphire, and / or chalcogenide (e.g., chalcogenide glass material). The waveguide can be, for example, a silicon-on-nitride (SON) waveguide, a silicon waveguide, a silicon-on-insulator (SOI) waveguide, a silicon-on-nitride-on-insulator (SONOI) waveguide, a silicon-on-sapphire (SOS) waveguide, a chalcogenide-on-silicon waveguide, a suspended silicon waveguide, a suspended germanium waveguide, an arsenic selenide waveguide, an arsenic sulfide waveguide, a hollow (air) waveguide, or a polymer-based waveguide. These waveguides can also be suitable for operating in the LWIR range.

[0023] In at least some cases of the aforementioned compounds, the loss of the waveguide can also be particularly low for an operating wavelength of 8 to 15 micrometers. For example, there may be strong optical confinement, and SiC waveguides, SiGeSn waveguides, GeC waveguides, and GeSn waveguides can have losses of less than 7 dB / cm, less than 8 dB / cm, less than 9 dB / cm, and less than 10 dB / cm, respectively, at an operating wavelength of 8 to 15 micrometers.

[0024] In some examples, the waveguide may include III-V semiconductors, as the transparency of these materials can also be particularly high for operating wavelengths of 8-15 micrometers.

[0025] Further aspects of the present disclosure provide a method for operating an electro-optic modulator as described throughout the disclosure. This method includes transmitting an optical input having a wavelength, for example, 8 to 15 micrometers, into an optical waveguide. This method further includes modulating the optical input.

[0026] Because the waveguide is specifically configured to operate in the wavelength range of 8 to 15 micrometers, graphene-based electro-optic modulators can operate at low drive voltages, as the offset voltage that needs to be overcome may be very small. Modulation can be performed with lower power consumption and higher reliability. Modulation can also be performed with increased static and dynamic efficiency without compromising the speed of the modulator.

[0027] In some examples, the offset voltage, i.e., the DC component of the drive voltage, may be lower than 1V, particularly lower than 0.5V, and more specifically lower than 0.2V. In some of these examples, the offset voltage may be lower than 0.1V, and could be, for example, about 0V or 0V. [Brief explanation of the drawing]

[0028] [Figure 1] An example of a normalized absorption curve for an electro-optic modulator is schematically shown as a function of the driving voltage at a wavelength of 1.55 micrometers.

[0029] [Figure 2] A schematic example of a graphene-based electro-optic modulator configured to operate at a wavelength of 1.55 micrometers is shown.

[0030] [Figure 3]A schematic cross-section of a second example of a graphene-based electro-optic modulator configured to operate at a wavelength of 1.55 micrometers is schematically shown, similar to the electro-optic modulator in Figure 2, but with a portion of the cladding layer above the waveguide, i.e., covering the waveguide, and the lower (Gb) and upper (Gu) graphene layers overlapping each other only across the entire width of the waveguide (C).

[0031] [Figure 4] A schematic example of a graphene-based electro-optic modulator configured to operate at a wavelength of 8 micrometers is shown.

[0032] [Figure 5] Figure 4 schematically shows a cross-section of the electro-optic modulator, where a portion of the cladding layer is located above the waveguide, i.e., it covers the waveguide.

[0033] [Figure 6] Figures 2 to 5 show an example of the normalized absorbance transition of graphene electro-optic modulators, as a function of the input light wavelength and driving voltage.

[0034] [Figure 7] The normalized absorbance progression is schematically shown in Figure 6 as a function of the drive voltage of four cutoffs measured at four operating wavelengths: 1.55 micrometers, 3 micrometers, 8 micrometers, and 15 micrometers, indicated by the vertical lines. The white dashed line indicates the operating voltage of the electro-optic modulator.

[0035] [Figure 8] A schematic diagram of the region up to a drive voltage of 2V is shown in Figure 7.

[0036] [Figure 9] The graphs show the transmittance curves as a function of the applied (driving) voltage for different thicknesses of the dielectric layer D2 of the electro-optic modulator in Figure 2, which operates with 1.55 micrometer light.

[0037] [Figure 10] Figure 2 shows graphs illustrating the bandwidth as a function of the thickness of the dielectric layer D2 for the electro-optic modulator operating with 1.55 micrometer light, for different graphene-metal contact resistivity.

[0038] [Figure 11] Figure 2 shows a graph illustrating the bandwidth curve as a function of the dielectric constant of the dielectric layer D2 of the electro-optic modulator operating with 1.55 micrometer light. The curve is shown for different graphene-metal contact resistivity.

[0039] [Figure 12] The graphs show the transmittance curves as a function of applied voltage for different dielectric constants of the dielectric layer D2 of the electro-optic modulator in Figure 2, which operates with 1.55 micrometer light.

[0040] [Figure 13] The graphs show the transmittance curves as a function of the applied voltage for different thicknesses of the dielectric layer D2 of the electro-optic modulator in Figure 4, which operates with 8 micrometer light.

[0041] [Figure 14] The graphs show the transmittance curves as a function of the applied voltage for different dielectric constants of the dielectric layer D2 of the electro-optic modulator in Figure 4, which operates with 8-micrometer light.

[0042] [Figure 15] Figure 4 shows graphs illustrating the transmittance curves as a function of the applied voltage for different lengths of the electro-optic modulator operating with 8 micrometer light.

[0043] [Figure 16] Figure 4 shows a graph illustrating the transmittance curve as a function of the applied voltage for the electro-optic modulator operating with 8-micrometer light at different operating temperatures.

[0044] [Figure 17]This section outlines how to operate an electro-optic modulator. [Modes for carrying out the invention]

[0045] [Detailed description of the embodiment] Hereinafter, embodiments of the present disclosure are given in detail, and one or more examples thereof are shown in the drawings. Each example is provided merely for illustrative purposes and not as an limitation. Indeed, it will be apparent to those skilled in the art that various modifications and variations can be made in the present disclosure. For example, features illustrated or described as part of one embodiment can be used in conjunction with another embodiment to obtain yet another embodiment. Thus, the present disclosure is intended to encompass such modifications and variations that fall within the scope of the appended claims and their equivalents.

[0046] According to one aspect of the present disclosure, an electro-optic modulator is provided. The electro-optic modulator comprises a substrate, an optical waveguide disposed with the substrate, and a first graphene layer and a second graphene layer arranged such that input light is absorbed by the electro-optic modulator during operation, the first and second graphene layers overlapping each other and separated from each other by one or more dielectric layers. The electro-optic modulator is configured to operate at wavelengths of 8 micrometers to 15 micrometers.

[0047] Schematic examples of electro-optic modulators are shown in Figures 2 to 5. The electro-optic modulators in Figures 2 and 3 are configured to operate in the NWIR range, for example, at 1.55 micrometers. The electro-optic modulators in Figures 4 and 5 are configured to operate in the LWIR range, for example, at 8 micrometers. As shown in the figures, the dimensions of the different components of the electro-optic modulators, such as the optical waveguide and the graphene and dielectric layers, differ in both examples, and each electro-optic modulator can operate in its corresponding wavelength range.

[0048] The electro-optic modulators in these examples include a substrate. The substrate typically comprises a lower or underlayer S, which is a semiconductor, and an upper or upper layer Cd, which is typically an oxide material. In the examples in Figures 2 to 5, the upper layer Cd of the substrate, also called the cladding, is located on top of the lower layer S of the substrate.

[0049] The lower substrate S may, in some examples, be made of a group IV semiconductor. In other examples, it may be made of group III-V semiconductors, group II-VI semiconductors, chalcogenide materials, polymer materials, nitride materials, oxide materials, crystalline materials, organic or hybrid materials, metals, glass, air, vacuum, or other materials. For example, the lower substrate S may be made of Si (silicon). In other examples, it may be made of silicon dioxide, glass, or other materials. The bottom of the substrate S may act only as a support for the layer above it and therefore may not be strictly necessary for the electro-optic modulator to operate. The lower substrate S may, in some cases, be omitted, and the upper Cd of the substrate acts as a support for the rest of the layer above. In some other cases, the lower substrate S may be part of the optical waveguide.

[0050] The upper part of the Cd substrate may include oxide materials, nitride materials, polymer materials, fluoride glass, chalcogenide glass materials, chalcogenide materials, semiconductor materials, air, or vacuum, and may be made of these materials, for example. For example, in the case of oxides, some examples include the layer material Cd, which may include SiO2 (silicon dioxide), or aluminum oxide (Al2O3), or phosphorus pentoxide (P2O5), or boron oxide (B2O3), or magnesium oxide (MgO), or calcium oxide (CaO), or tantalum oxide (V) (Ta2O5), or HfO2 (hafnium oxide), or titanium dioxide (TiO2), or zirconium dioxide (ZrO2), and may be made of these materials, for example.

[0051] In other examples, for instance, in the case of nitrides, to give a few examples, the layer material Cd is silicon nitride (Si x N x), or aluminum nitride (AIN), or gallium nitride (GaN), or boron nitride (BN), or titanium nitride (TiN), or indium nitride (InN), or tantalum nitride (TaN), or tungsten nitride (WN), or may be made of these, for example.

[0052] In the case of polymers, to give a few examples, the layer material Cd may include, for example, polymethyl methacrylate (PMMA), or polytetrafluoroethylene (PTFE), or perfluoropolymer, or polystyrene (PS), or polyethylene (PE), or polypropylene (PP), or polyvinyl chloride (PVC), or polycarbonate (PC), or SU-8, or may be made of these materials.

[0053] For example, in the case of fluoride glass, to give a few examples, the layer material Cd may include, for instance, indium fluoride (InF3) glass, gallium fluoride (GaF3) glass, aluminum fluoride (AlF3) glass, or ZBLAN (Zr-Ba-La-Al-Na fluoride) glass, or may be made of these materials.

[0054] For example, in the case of chalcogenides, to give a few examples, the layer material Cd may contain, or be made of, arsenic trisulfide (As2S3), or arsenic selenide (As2Se3), or germanium-antimony-sulfur (Ge-Sb-S) systems, or germanium-antimony-selenium (Ge-Sb-Se) systems, or tellurium-based chalcogenides, or indium-based chalcogenides.

[0055] For example, in the case of semiconductors, to give a few examples, the layer material Cd may contain silicon germanium (SiGe), or indium gallium arsenide phosphate (InGaAsP), or indium aluminum arsenide (InAlAs), or indium gallium arsenide (InGaAs), or may be made of these materials. The cladding layer, also known as cladding, can optionally cover the waveguide C (as shown in Figures 3 and 5), separating the waveguide C from the Gb layer and / or dielectric layer D1 and / or dielectric layer D2. The portion of the cladding layer that separates the waveguide C from the rest of the upper layers may be, if present, for example, 1 to 10 nm thick.

[0056] The electro-optic modulator further comprises an optical waveguide C disposed together with the substrate, for example, on top of the substrate Cd. The optical waveguide C may be made of a different material. The waveguide C may include, for example, a group IV semiconductor, a group III-V semiconductor, a group II-VI semiconductor, a chalcogenide glass material, a chalcogenide material, a polymer material, an oxide material, a nitride material, a crystalline material, an organic or hybrid material, a two-dimensional (2D) material, a nanostructured material, a suspension material, a metal, air (hollow), or a vacuum, and may be made of these materials.

[0057] For example, in the case of a group IV semiconductor, the waveguide C may include, for example, carbon (C), silicon (Si), germanium (Ge), tin (Sn), or lead (Pb), which are used individually or in combination thereof.

[0058] For example, in the case of III-V compound semiconductors, to give a few examples, the waveguide C may include, in some cases, gallium arsenide (GaAs), or indium phosphide (InP), or indium gallium arsenide (InGaAs), or indium gallium arsenide phosphide (InGaAsP), or may be made of these materials.

[0059] For example, in the case of group II-VI compound semiconductors, to give a few examples, the waveguide C may include, in some cases, zinc selenide (ZnSe), zinc sulfide (ZnS), or cadmium telluride (CdTe), or may be made of these materials.

[0060] For example, in the case of chalcogenides, to give a few examples, the waveguide C may include, in some cases, arsenic trisulfide (AS2S3) or a germanium-antimony-sulfur (Ge-Sb-S) system, or may be made of such materials.

[0061] For example, in the case of 2D materials, to give a few examples, the waveguide C may include, in some cases, a transition metal dichalcogenide (for example, molybdenum disulfide (MoS2) or tungsten disulfide (WS2)) or graphene, or may be made of them.

[0062] For example, in the case of oxides, to give a few examples, the waveguide C may include, in some cases, silica (SiO2), or doped silica, or sapphire, or may be made of these materials.

[0063] For example, in the case of polymers, to give a few examples, waveguide C may include, in some cases, polymethyl methacrylate (PMMA), or polystyrene, or polyimide, or fluorinated polymer, or may be made of these materials.

[0064] For example, in the case of nitrides, to give a few examples, the waveguide C may include silicon nitride (Si3N4) or gallium nitride (GaN) in some cases, or may be made of such materials.

[0065] For example, in the case of crystals, the waveguide C may, in some cases, include lithium niobate (LiNbO3), potassium titanyl phosphate (KTP), or barium beta borate (BBO), or may be made of these materials.

[0066] For example, in the case of organic or hybrid materials, to give a few examples, the waveguide C may include, in some cases, an organic material or an organic-inorganic hybrid material having nonlinear optical properties, and may be made of such materials.

[0067] For example, in the case of nanostructured materials, the waveguide C may include, in some examples, a photonic crystal, or may be made of it, for example.

[0068] The optical waveguide C may include Ge. Such a waveguide may provide particularly low loss, for example less than 4 dB / cm. The Ge layer may have a thickness of 1 to 6 micrometers, for example about 2 or 4 micrometers, in some of these examples. In some examples, the optical waveguide C may include SiGe. Such a waveguide may provide particularly low loss, for example less than 5 dB / cm. The SiGe layer may have a thickness of 1 to 6 micrometers, for example about 2 or 4 micrometers, in some of these examples.

[0069] In other examples, the optical waveguide may include an upper SiGe layer on an intermediate graded SiGe layer (in composition) on a lower Si layer. For example, Si 0.2 Ge 0.8 layers may be provided on Si 1-x Ge x layers, and Si 1-x Ge x layers may be provided on Si layers. The exponent "x" may vary from 0.8 at the top surface of the graded SiGe layer to 0 at the bottom surface of the graded SiGe layer. The Si 0.2 Ge 0.8 layer may have a thickness of about 2 micrometers, and the graded SiGe layer may have a thickness of about 11 micrometers. Other examples where the ratios of Si and Ge in the upper layer (and thus the compositional gradient of the intermediate layer) are different may be possible. Other examples where the thicknesses of Si and Ge are different may be possible.

[0070] In the examples shown in Figures 2 and 4, the optical waveguide C is embedded in the upper part of the substrate Cd such that the upper surface of the waveguide is coplanar with the upper surface of the substrate Cd. In other examples, the upper surface of the waveguide does not need to be coplanar with the upper surface of the substrate Cd; for example, the upper surface of waveguide C may be located above or below the upper surface of the substrate Cd. In some examples, the bottom surface of the optical waveguide may be in contact with the upper surface of the bottom of the substrate S. In Figures 2 to 5, waveguide C is shown to have a rectangular cross-section, but other shapes are also possible. In some examples, waveguide C may have a triangular, elliptical, circular, or any other suitable cross-sectional shape.

[0071] The electro-optic modulators in Figures 2–5 further comprise a first (lower in these examples) graphene layer Gb positioned such that the input light L is absorbed by the electro-optic modulator during operation. In the examples shown, the graphene layer Gb extends over at least a portion of the optical waveguide C, and in particular over the entire optical waveguide. The graphene layer Gb may also be provided, for example, over the waveguide and a portion of the upper part of the substrate Cd. Extending the graphene layer Gb beyond the optical waveguide C, i.e., over at least a portion of the cladding layer Cd, can improve the performance of the electro-optic modulator. In some examples, the graphene layer may extend beyond the optical waveguide by up to approximately 25% of the waveguide width. Extending beyond 25% of the waveguide width does not further significantly improve performance.

[0072] In other examples, the graphene layer Gb may be provided directly on the waveguide C, for example, i.e., part of the dielectric layer D1 and the cladding Cd above the optical waveguide C may be absent. In other examples, the graphene layer Gb may be provided in another preferred location, for example, below the optical waveguide C.

[0073] The electro-optic modulators in the examples shown in Figures 2 to 5 further comprise a dielectric layer D2 on top of a graphene layer Gb. The dielectric layer D2 may include, for example, one or more of the following materials: HfO2, SiO2, Si3N4, Al2O3, ZrO2, TiO2, TiN, HfSiO4, ZrSiO4, calcium copper titanate, barium titanate, strontium titanate, barium strontium titanate, polystyrene, polypropylene, polyamide, polyethylene, polytetrafluoroethylene, and transition metal dichalcogenides (TMD or TMDC). The dielectric layer D2 may include one or more two-dimensional (2D) materials. The dielectric layer D2 may include any suitable 2D (electrical) insulator. The dielectric layer D2 may include a combination of a suitable 2D (electrical) insulator and a 3D oxide material.

[0074] The electro-optic modulators in Figures 2 to 5 further include a second (upper in these examples) graphene layer Gu, particularly above the (first) graphene layer Gb, so that the input light L is absorbed by the electro-optic modulator during operation. In these examples in particular, the second graphene layer Gu may absorb less light than the first graphene layer Gb. Also, like the first graphene layer, the second graphene layer may extend over at least a portion of the optical waveguide C, for example, over only a portion of the optical waveguide, over the entire optical waveguide (without extending beyond it), or over the entire optical waveguide and over at least a portion of the cladding layer Cd. The performance of the electro-optic modulator can be improved by providing the graphene layer Gu to extend beyond the optical waveguide C, i.e., over at least a portion of the cladding layer Cd.

[0075] The second graphene layer Gu may be referred to as the upper graphene layer, and the (first) graphene layer Gb may be referred to as the lower graphene layer. The graphene layer Gu may be provided, for example, on top of the dielectric layers D2 and Cd. In other examples, the first Gb graphene layer and the second Gu graphene layer may be provided in other suitable locations, for example, below the optical waveguide C. The dielectric layer D2 may be provided between the first graphene layer Gb and the second graphene layer Gu.

[0076] One or more additional dielectric layers may be provided between the upper graphene layer and the lower graphene layer. In the example, the graphene layers, e.g., the upper and / or lower graphene layers, may be placed ("sandwiched") between dielectric layers. By sandwiching the upper and / or lower graphene layers with dielectrics, the quality of the upper and / or lower graphene layers can be improved.

[0077] In the examples shown in Figures 2 to 5, the electro-optic modulator comprises a dielectric layer D1 above the substrate Cd and above the optical waveguide C, and below the lower graphene layer Gb. In this example, the bottom surface of dielectric layer D1 is in contact with the top surface of the substrate Cd and the top surface of the optical waveguide C, and the top surface of dielectric layer D1 is in contact with the bottom surface of the (lower) graphene layer Gb. In this example, the electro-optic modulator also comprises a dielectric layer D3 on top of a second graphene layer Gu. The bottom surface of dielectric layer D3 is in contact with the top surface of the (upper) graphene layer Gb in this example. Dielectric layer D1 may be a 3D dielectric layer or a 2D material, and may contain oxides or nitrates. The base dielectric layer D1 may contain, for example, SiO2. The base dielectric layer D1 may contain, for example, at least one of the following 2D layered materials: hBN, MoTez, WSez, WS2, MoS2, MoSez, WS, WSez, black phosphorus, or SnSz. This layer D1 may be omitted in other examples. The dielectric layer D3 may be a 3D dielectric layer or a 2D material, and may contain an oxide or nitrate. This layer D3 may be omitted in other examples.

[0078] Optionally, one or more additional dielectric layers can be placed above and / or below the upper and / or lower graphene layers.

[0079] All layers in this specification are in contact, that is, they are in contact with adjacent layers. For example, the upper surface of dielectric layer D2 is in contact with the bottom surface of graphene layer Gu, and the bottom surface of dielectric layer D2 is in contact with the upper surface of graphene layer Gb. Also, the bottom surface of dielectric layer D3 is in contact with the upper surface of the second graphene layer Gu.

[0080] Where present, in some examples, one or more of the dielectric layers D1, D2, and D3 may include one or more of the following 2D layered materials: hBN, MoTe2, WSe2, WS2, graphene, MoS2, MoSe2, WS2, WSe2, black phosphorus, and SnS2. Throughout this disclosure, the terms 2D material or 2D layered material may be used to refer to nanomaterials defined by their property of being one or two or several atoms thick. They are referred to herein as 2D (layered) materials because they are substantially two-dimensional.

[0081] The thickness of the dielectric layer D2 may be 5nm to 2000nm, or for example, 5nm to 500nm or 9nm to 30nm in some cases.

[0082] In some examples, one or more of the dielectric layers D1, D2, and D3 may be omitted. For example, dielectric layers D1 and D3 may be omitted.

[0083] An electro-optic modulator may comprise two electrodes M1 and M2. A drive voltage is applied between electrodes M1 and M2 to operate the electro-optic modulator. The terms “drive voltage” and “applied voltage” are used interchangeably herein. The two electrodes may be optionally partially positioned on top of the substrate Cd. In some examples, the electrodes may be on dielectric layers D1, D2, or D3. The optical waveguide C and the aforementioned layers D1, Gb, D2, Gu, and D3 may be provided between electrodes M1 and M2 (laterally), for example, as shown in Figures 2 to 5. In some examples, the longitudinal directions of the waveguide C and the first and second electrodes M1 and M2 may be substantially parallel. The first and second electrodes M1 and M2 may be separated along a direction perpendicular to the length of the waveguide. This direction may be referred to as the lateral direction.

[0084] The first graphene layer Gb may extend laterally from the first electrode M1 toward the second electrode M2, and the second graphene layer Gu may extend laterally from the second electrode M2 ​​facing the first electrode M1 toward the first electrode M1. The first graphene layer Gb may be placed on the waveguide and may not reach the second electrode M2, and the second graphene layer Gu may be placed on the optical waveguide and may not reach the first electrode M1.

[0085] As mentioned above, Figures 3 and 5 schematically show cross-sections of the electro-optic devices of Figures 2 and 4, respectively, but these further include a portion of the substrate layer Cd above the waveguide C. In Figure 3, the Gu and Gb layers also extend beyond the optical waveguide C along the width direction of the waveguide (and modulator).

[0086] In the examples of Figures 2, 3, 4, and 5, the dielectric layer D2 extends (along the transverse direction) between the first electrode M1 and the second electrode M2 ​​and is in contact with them. In cross-section, the first graphene layer Gb and the dielectric layer D1 are in contact with the first electrode M1 and extend (along the transverse direction) over the substrate Cd and the optical waveguide C, but do not reach the second electrode M2. One end of the first graphene layer Gb is configured to be electrically connected to the first electrode M1. Extensions of other layers in cross-section are also possible.

[0087] In cross-sectional view, the second graphene layer Gu and dielectric layer D3 are in contact with the second electrode M2 ​​and extend (along the transverse direction) over the substrate Cd and the optical waveguide C, but do not reach the first electrode M1. One end of the second graphene layer Gu is configured to be electrically connected to the second electrode M2. Extensions of other layers in the cross-section are also possible.

[0088] In some examples, the electro-optic modulators described herein can implement interferometer configurations, such as those based on a Mach-Zehnder interferometer. The interferometer may comprise two or more optical waveguide bifurcations that are separated from each other but connected to each other. At least one of the bifurcations may include an electro-optic modulator as described herein.

[0089] In some examples, an electro-optic modulator, i.e., a Mach-Zehnder interferometer, may comprise a first optical waveguide bifurcation or arm and a second optical waveguide bifurcation or arm. The first optical waveguide bifurcation may include an electro-optic modulator as described above, and the second optical waveguide bifurcation may or may not include an additional electro-optic modulator. The first and second optical waveguide bifurcations may be separated in a direction perpendicular to the longitudinal direction of the first and second optical waveguide bifurcations (the longitudinal direction of the waveguide is the direction of light transmission). In some examples, the interferometer base configuration may have more than two bifurcations.

[0090] In some examples, additional waveguides of additional electro-optic modulators may be configured to operate at wavelengths of 8 to 15 micrometers. That is, in some examples, all optical waveguides may be configured to operate at wavelengths of 8 to 15 micrometers, while in other examples, only one or not all of the optical waveguides may be configured to operate at wavelengths of 8 to 15 micrometers.

[0091] In some examples, a third electrode may be provided, and a second optical waveguide branch may be located between the second electrode and the third electrode. The Mach-Zehnder interferometer can have several configurations, as described, for example, with reference to Figures 10A to 10E of U.S. Patent Application No. 2021 / 0173281 A1.

[0092] In some cases, the arms of a Mach-Zehnder interferometer may be driven in a push-pull configuration.

[0093] Figure 6 shows an example of the normalized absorbance progression of graphene electro-optic modulators, such as those in Figures 2-5 (modulators), as a function of input light wavelength and drive voltage. The graph in Figure 6 is common to all graphene-based electro-optic modulators, such as those in Figures 2-5, which include one or two layers of graphene separated by one or more dielectric layers, with waveguides positioned above or below them, for example. Note that when the graphene layer and dielectric layer are positioned below the optical waveguide, they are also positioned above the bottom of the substrate S.

[0094] Figure 6 shows four vertical lines. From left to right, the following applies: The vertical line on the left represents 1.55 micrometers, indicating the typical operating wavelength of a graphene-based electro-optic modulator. The next vertical line represents 3 micrometers, indicating the lower limit of the MWIR wavelength range. The following vertical line represents 8 micrometers, indicating the lower limit of the LWIR wavelength range. The vertical line on the right of this figure represents 15 micrometers, indicating the upper limit of the LWIR wavelength range. As shown in Figure 6, the absorbance of a graphene-based electro-optic modulator depends on the driving voltage and operating wavelength.

[0095] Figure 7 schematically shows the normalized absorbance progression of a graphene-based electro-optic modulator as a function of the drive voltage for the four operating wavelengths shown in Figure 6: 1.55 micrometers, 3 micrometers, 8 micrometers, and 15 micrometers. Figure 8 schematically shows the region up to a drive voltage of 2V in Figure 7. Figures 7 and 8 show that the offset voltage is approximately 3 volts at the 1.55 micrometer operating wavelength, approximately 0.5 volts at the 3 micrometer operating wavelength, 0 volts at the 8 micrometer operating wavelength, and 0 volts at the 15 micrometer operating wavelength. Therefore, by operating at wavelengths of 8 micrometers or higher, the offset voltage of the graphene-based electro-optic modulator can be reduced to less than 0.1V, and even to approximately 0V. The modulator can be set quickly or immediately within the operating window. Thus, one or more of the following can be achieved: reduced power consumption, reduced heat generation, improved reliability, reduced errors due to nonlinearity and reduced cost, reduced complexity of the drive circuit, and the elimination of the need for amplifiers, such as current, voltage, or transconductance amplifiers. This could enable low timing jitter and high-speed performance.

[0096] Furthermore, the slopes of the operating curves at wavelengths of 8 and 15 micrometers are steeper than those at wavelengths of 1.55 and 3 micrometers. Therefore, by operating at wavelengths of 8–15 micrometers, the static modulation efficiency, and thus the dynamic modulation efficiency, of the electro-optic modulator is also increased.

[0097] Static modulation efficiency is generally defined as the ratio of the change in optical output power, usually expressed in dB, to the change in the drive voltage, usually expressed in volts. Therefore, static modulation efficiency can usually be determined as the slope of the optical output power as a function of the drive voltage curve, and has units of dB / V. An example of such a slope is shown in Figure 1, from which it can be seen that the static modulation efficiency in this example (i.e., at 1.55 micrometers) is -0.62 dB / V.

[0098] The concept of dynamic modulation efficiency is similar to that of static modulation efficiency, but instead of being measured in DC, it is measured by applying an AC voltage. To determine dynamic modulation efficiency, the AC voltage is typically applied in the GHz range. Dynamic modulation efficiency is calculated as the extinction ratio (ER) extracted from the eye diagram, separated from the applied AC voltage (Vpp).

[0099] Dynamic modulation efficiency and static modulation efficiency are related. Generally, improved static modulation efficiency is expected to lead to higher dynamic modulation efficiency. However, bandwidth can be a limiting factor that reduces dynamic modulation efficiency relative to static modulation efficiency.

[0100] As shown in Figures 7 and 8, the modulation index of the 15-micrometer trace is lower compared to the modulation index of the 8-micrometer trace. The modulation index of an electro-optic modulator can be understood as the difference between the maximum and minimum power absorbed by the electro-optic modulator. This is usually measured in dB. An example of modulation index is shown in the graph in Figure 1.

[0101] Therefore, by operating at a wavelength of 8 micrometers, very low or even zero offset voltages can be obtained with increased static and dynamic modulation efficiency, without any reduction in speed or modulation depth. Furthermore, the increase in static and dynamic modulation efficiency can generally be achieved in the LWIR range.

[0102] The offset voltage tends to be temperature-dependent and may be slightly dependent on the quality of the graphene, but as shown below with respect to Figure 16, even if the temperature changes from, for example, 150K to 300K, a zero offset voltage is maintained when operating within the LWIR range.

[0103] It should be noted that if the electro-optic modulator is not configured to operate at wavelengths of 8 to 15 micrometers, but instead at, for example, 1.55 micrometers, the offset voltage may be reduced in other ways. For example, to reduce the offset voltage, the thickness of the dielectric material between the first graphene layer Gb and the second graphene layer Gu, for example, the thickness of the dielectric layer D2, may be reduced. However, leakage and dielectric breakdown may occur, as described below. Also, the bandwidth and modulation speed may be reduced, as shown in Figure 9 described below.

[0104] Figure 9 shows graphs of transmittance curves (dB) as a function of applied voltage (V) for different thicknesses of the dielectric layer D2 of the electro-optic modulator of Figure 2 operating at a wavelength of 1.55 micrometers. Figure 10 shows graphs of bandwidth (GHz) as a function of dielectric thickness of the dielectric layer D2 of the electro-optic modulator of Figure 2. The lines are shown for graphene-metal contact resistivity of 100, 200, 350, 550, and 800 Ωμm.

[0105] The simulation was performed for an electro-optic modulator with a length of 60 μm (Y direction, see Figure 22). The lower part of the substrate S is silicon, and the upper part of the substrate Cd is SiO2. Dielectric layers D1 and D3 each have a thickness of 10 nm. The thickness of dielectric layer D2 is varied, and the dielectric constant of dielectric layer D2 is maintained at 10. The transmittance curves for dielectric layer D2 thicknesses of 5, 7, 10, 15, and 20 nm are shown in Figure 9.

[0106] In the simulation, waveguide C is a silicon waveguide with a height of 220 nm and a width of 450 nm. Electrodes M1 and M2 have a thickness of 80 nm (vertically in Figure 2) and are separated by a distance of 2000 nm. The thickness of the SiO2 portion of the cladding layer Cd between waveguide C and the bottom of dielectric layer D1 (not shown in Figure 2, but shown in Figure 3) is 10 nm. In these simulations, the dielectric constant ε r The value is 10. The temperature was set to 300K.

[0107] As shown in Figure 9, reducing the thickness of the dielectric layer D2, and generally the amount of dielectric material between the first graphene layer Gb and the second Gu graphene layer, reduces the offset voltage. The DC offset voltage is at least 1.5V. However, a thickness of 5nm is already the limit; that is, at a dielectric thickness of 5nm, the risk of dielectric breakdown may be excessive. However, as will be explained below, reducing the thickness of the D2 dielectric can lead to leakage and dielectric breakdown, and more importantly, as shown in Figure 10, it can reduce the bandwidth and modulation speed. As shown in Figure 10, reducing the thickness of D2 can significantly reduce the bandwidth of the electro-optic modulator for all graphene-metal contact resistivity considered.

[0108] As can be seen, the parameters of an electro-optic modulator are interrelated, and the effect of modifying one parameter is not apparent in others. As shown in Figures 9 and 10, reducing the dielectric thickness reduces the offset voltage, but at the cost of reducing the modulation speed and bandwidth. Furthermore, it also increases the risk of dielectric leakage and dielectric breakdown.

[0109] Another method to reduce the offset voltage may be by increasing the dielectric constant of the dielectric layer between the first Gb graphene layer and the second Gu graphene layer. Simulations were performed for the electro-optic modulator shown in Figure 2 operating at a wavelength of 1.55 micrometers, and the data are shown above. In this case, the thickness of the dielectric layer D2 is maintained at 10 nm, but the dielectric constant is varied to values ​​of 7, 10, 13, 16, 19, and 30.

[0110] Figure 11 shows a graph illustrating the curve of the bandwidth (GHz) as a function of the dielectric constant of the dielectric layer D2 of the electro-optic modulator of Figure 2 operating with 1.55 micrometer light. The curve is shown for different graphene-metal contact resistivity, namely 100, 200, 350, 550, and 800 Ωμm.

[0111] Figure 12 shows graphs illustrating the transmittance curves (dB) as a function of applied voltage (V) for different dielectric constants of the dielectric layer D2 of the electro-optic modulator shown in Figure 2.

[0112] As shown in Figure 12, increasing the dielectric constant of the dielectric layer D2, and generally increasing the dielectric constant of the amount of dielectric material between the first Gb graphene layer and the second Gu graphene layer, reduces the offset voltage. The DC offset voltage is at least 1V. However, increasing the dielectric constant of the dielectric material can reduce the bandwidth and modulation speed, as shown in Figure 11.

[0113] Figures 11 and 12 show the dielectric constant ε. r This shows that increasing the dielectric constant (ε) reduces the offset voltage. However, the DC offset voltage is high. r Even at 30), the voltage remains above 1V. See Figure 12. Also, as can be seen from these figures, increasing the dielectric constant reduces the modulation speed and bandwidth.

[0114] Figure 13 shows graphs illustrating the transmittance curves (dB) as a function of applied voltage (V) for different thicknesses of the dielectric layer D2 of the electro-optic modulator of Figure 4 operating with 8 micrometer light. The offset voltage is zero for all curves. This figure demonstrates that the DC offset voltage is always zero regardless of the thickness of the D2 dielectric, and therefore does not impair the bandwidth and speed of the electro-optic modulator.

[0115] Figure 14 shows graphs of transmittance curves (dB) as a function of applied voltage (V) for different dielectric constants of the dielectric layer D2 of the electro-optic modulator of Figure 4 operating with 8 micrometer light. The DC offset voltage is zero for all curves. This figure shows that the DC offset voltage is always zero regardless of the dielectric constant of the D2 dielectric, and therefore does not impair the bandwidth and speed of the electro-optic modulator.

[0116] The dimensions of the electro-optic modulator, for example, its components, are adapted to operate within the LWIR range. The simulations in Figures 13 and 14 were performed for an electro-optic modulator with a length of 250 μm (Y direction, see Figure 4). The lower part of the substrate layer S is silicon, and the upper part of the substrate layer Cd is SiO2. Dielectric layer D1 has a thickness of 2 nm, and dielectric layer D3 has a thickness of 1000 nm. The transmittance curves for dielectric layer D2 thicknesses of 5, 7, 10, 15, 20, 25, and 30 nm are shown in Figure 13. The dielectric constant of dielectric layer D2 is 3.6. In Figure 14, the dielectric constant is varied to values ​​of 3, 5, 7, 9, and 11. In the same figure, dielectric layer D2 has a thickness of 10 nm.

[0117] In the simulations in Figures 13 and 14, waveguide C is a Ge waveguide with a height of 1550 nm and a width of 4650 nm. Electrodes M1 and M2 have a thickness of 80 nm (in the vertical direction in Figure 4) and are separated by a distance of 2000 nm. The SiO2 cladding layer (not shown in Figure 4 but shown in Figure 5) has a thickness of 2 nm. The temperature was set to 300 K.

[0118] Considering at least Figures 13 and 14, providing an electro-optic modulator configured to operate at wavelengths of 8 to 15 micrometers is an effective way to reduce offset voltage and further improve static and dynamic modulation efficiency while avoiding the aforementioned drawbacks (reduced bandwidth and modulation speed).

[0119] Figure 15 shows graphs of the transmittance curves (dB) as a function of applied voltage (V) for different lengths of the electro-optic modulator shown in Figure 4, operating with 8 micrometers of light. Unless otherwise indicated, the parameters described above for Figures 13 and 14 apply to this figure. In this figure, the thickness of the dielectric layer D2 is 20 nm, the dielectric constant of the dielectric layer D2 is 9, and the length is varied between 200 micrometers and 400 micrometers. Figure 15 shows that the length of the electro-optic modulator changes the modulation amplitude, but the DC offset voltage is zero for all curves.

[0120] Figure 16 shows graphs of the transmittance curves (dB) as a function of applied voltage (V) for the electro-optic modulator of Figure 4 operating with 8-micrometer light at different operating temperatures. Unless otherwise indicated, the parameters described above for Figures 13 and 14 apply to this figure. In this figure, the thickness of the dielectric layer D2 is 10 nm, the dielectric constant of the dielectric layer D2 is 3.6, and the temperature was varied from 50 K to 300 K. The DC offset voltage is zero for all curves.

[0121] Therefore, Figures 15 and 16 show that the results with very low or zero offset voltages in Figures 7 and 8 still hold true even when the length and / or operating temperature of the electro-optic modulator are varied.

[0122] A further aspect of this disclosure provides a method 100 for operating the electro-optic modulator described herein, particularly to reduce the offset voltage. This method is shown in the flowchart of Figure 17. The method includes, in block 110 (step 110), transmitting an optical input having a wavelength of 8 to 15 micrometers to an optical waveguide. For example, a laser beam may be transmitted toward waveguide C. The method includes, in block 120 (step 120), modulating the optical input.

[0123] The waveguide C of the graphene-based electro-optic modulator is configured to operate in the wavelength range of 8 micrometers to 15 micrometers, so that the input light can be modulated with a very low offset voltage, or even without an offset voltage. Therefore, the modulator can operate in a low-power and reliable manner. Static and dynamic efficiencies can be increased without compromising the speed of the modulator and without requiring current, voltage, or transimpedance amplifiers.

[0124] In some examples, the offset voltage, i.e., the DC component of the drive voltage, may be lower than 1V, particularly lower than 0.5V, and more specifically lower than 0.2V. In some of these examples, the offset voltage may be lower than 0.1V, and could be, for example, about 0V or 0V.

[0125] The method may further include applying a drive voltage lower than 1V, particularly lower than 0.5V, and more specifically lower than 0.2V. In some of these examples, a drive voltage lower than 0.1V may be applied.

[0126] Different types of modulation can be performed using electro-optic modulators. For example, modulation may include modifying the amplitude, phase, or polarization of the optical input.

[0127] This specification uses examples to disclose teachings, including preferred embodiments, and to enable a person skilled in the art to translate such teachings into practice, including fabricating and using any device or system, and performing any incorporated methods. The patentable scope is defined by the claims and may include other examples that a person skilled in the art may conceive. Such other examples are intended to be within the claims if they have structural elements that are not different from the language of the claims, or if they include equivalent structural elements that are substantially different from the language of the claims. A person skilled in the art may combine and adapt aspects from the various embodiments described, as well as other known equivalents of each such embodiment, to construct further embodiments and technologies in accordance with the principles of this application. Where reference numerals related to the drawings are placed in parentheses in the claims, they are merely for the purpose of increasing the clarity of the claims and should not be construed as limiting the claims. [Explanation of Symbols]

[0128] C optical waveguide Cd substrate upper layer (top) / cladding S Substrate lower layer (bottom) D1, D2, D3 dielectric layers Gb First graphene layer (lower graphene layer) Gu Second graphene layer (upper graphene layer) L Input light M1,M2 electrode

Claims

1. An electro-optic modulator, circuit board and An optical waveguide arranged together with the aforementioned substrate, The device comprises a first graphene layer and a second graphene layer arranged such that the input light is absorbed by the electro-optic modulator during operation, The first and second graphene layers overlap each other and are separated from each other by one or more dielectric layers. The electro-optic modulator is configured to operate at wavelengths of 8 micrometers to 15 micrometers.

2. The electro-optic modulator according to claim 1, wherein the optical waveguide includes a group IV semiconductor, a hollow waveguide, or a polymer-based waveguide.

3. The electro-optic modulator according to claim 2, wherein the optical waveguide includes Ge.

4. The electro-optic modulator according to claim 3, wherein the optical waveguide includes SiGe.

5. The electro-optic modulator according to any one of claims 1 to 4, wherein the first and second graphene layers overlap each other over at least a portion of the width of the optical waveguide.

6. The electro-optic modulator according to any one of claims 1 to 5, wherein the first and second graphene layers overlap each other over the entire width of the optical waveguide.

7. The electro-optic modulator according to any one of claims 1 to 6, wherein the first and second graphene layers overlap each other, at least one of the first and second graphene layers extends along and beyond the entire width of the optical waveguide, and at least one of the first and second graphene layers extends beyond the optical waveguide by up to about 25% of the width of the optical waveguide, particularly by 0 to 10% of the width of the optical waveguide.

8. The electro-optic modulator according to any one of claims 1 to 7, wherein the first graphene layer extends from a first electrode, and the second graphene layer extends from a second electrode facing the first electrode.

9. The electro-optic modulator according to claim 8, wherein the first graphene layer reaches the second electrode, and the second graphene layer reaches the first electrode.

10. The electro-optic modulator according to any one of claims 1 to 9, further comprising a cladding, wherein at least a portion of the optical waveguide is embedded within the cladding.

11. The electro-optic modulator according to claim 10, wherein the upper surface of the optical waveguide is on the same plane as the upper surface of the cladding.

12. The aforementioned electro-optic modulator is an interferometer, particularly a Mach-Zehnder interferometer, An electro-optic modulator according to any one of claims 1 to 11, comprising two or more optical waveguide branch sections that are separated from each other but connected to each other, wherein at least one of the branch sections includes an electro-optic modulator according to any one of claims 1 to 11.

13. A method for operating an electro-optic modulator according to any one of claims 1 to 12, Transmitting an optical input having a wavelength of 8 micrometers to 15 micrometers into an optical waveguide, and A method comprising modulating the aforementioned optical input.

14. The method according to claim 13, further comprising applying a drive voltage lower than 1V.

15. The method according to claim 14, wherein the applied drive voltage is lower than 0.5V, and more particularly lower than 0.2V.

16. The method according to any one of claims 13 to 15, wherein the offset voltage is lower than 0.5V, particularly lower than 0.2V, and particularly lower than 0.1V.

17. The method according to any one of claims 13 to 16, wherein modulation includes modifying the amplitude, phase, or polarization of the optical input.

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