Electro-optical modulator based on slow light effect

Abstract

The invention provides an electro-optical modulator based on a slow light effect. The electro-optical modulator comprises a substrate, a bottom electrode, an insulating layer, a slow light waveguide layer, an upper cladding and a signal electrode which are sequentially stacked from bottom to top. Wherein the slow light waveguide layer is a photonic crystal waveguide based on Z-cut film lithium niobate, the photonic crystal waveguide comprises a line defect waveguide and a plurality of air holes arranged in a triangular lattice structure, and the plurality of air holes are symmetrically arranged at two sides of the line defect waveguide. A photonic band gap is formed by a two-dimensional periodic optical medium structure formed by combining air holes arranged in a triangular lattice structure and Z-cut film lithium niobate, the slow light effect is achieved, and light waves in a specific frequency range can only be spread along a line defect waveguide by introducing the line defect waveguide. According to the invention, the interaction between the light field and the electric field is enhanced, the modulation efficiency and performance of the electro-optical modulator can be remarkably improved, and the development trend of miniaturization, integration and high speed of an existing communication network is met.

Description

Technical Field

[0001] The present application relates to the technical field of electro-optic modulators, and in particular to an electro-optic modulator based on the slow light effect. Background Art

[0002] As a key component in modern optical communications and optical signal processing systems, electro-optical modulators offer numerous significant advantages. They enable high-speed, efficient modulation of optical signals, thereby meeting the growing demand for high-capacity, high-speed data transmission. They are an essential core component in building modern fiber-optic communication networks and are widely used in a wide range of scenarios, including long-distance communications, metropolitan area networks, access networks, and data center interconnection.

[0003] In recent years, as the demand for information transmission rates within and / or between chips has gradually increased, high-speed interconnection within and / or between chips based on photons has become an important development direction for optical communications, and electro-optic modulators are the core components for achieving high-speed loading of electrical signals into optical signals. Among them, lithium niobate has a high electro-optic coefficient and a second-order nonlinear optical coefficient, so the modulators made from it are widely used in data centers, supercomputers and other scenarios where there is an urgent need for large-capacity, high-speed optoelectronic modulation. However, although traditional electro-optic modulators based on lithium niobate materials have been commercially mature, they still have the defects of large size and insufficient bandwidth, making it difficult to adapt to the development trend of miniaturization, integration and high speed of communication networks.

[0004] Therefore, how to provide an electro-optical modulator that can not only meet the development trend of miniaturization, integration and high speed of existing communication networks has become a technical problem that needs to be urgently solved by those skilled in the art. Summary of the Invention

[0005] The present application aims to solve one of the technical problems in the related art at least to a certain extent.

[0006] To achieve the above-mentioned objectives, an embodiment of the first aspect of the present application proposes an electro-optic modulator based on the slow-light effect, comprising a substrate, a bottom electrode, an insulating layer, a slow-light waveguide layer, an upper cladding layer and a signal electrode stacked in sequence from bottom to top; wherein the slow-light waveguide layer is a photonic crystal waveguide based on Z-cut thin film lithium niobate, the photonic crystal waveguide includes a linear defect waveguide extending along a first direction, and a plurality of air holes arranged in a triangular lattice structure, the plurality of air holes are symmetrically arranged on both sides of the linear defect waveguide along the second direction, and the upper cladding layer and the signal electrode are stacked in sequence on the linear defect waveguide.

[0007] Optionally, the distance a between the centers of adjacent air holes ranges from 350 nm to 500 nm.

[0008] Optionally, a width W of the line defect waveguide along the second direction ranges from 1.75a to 2.25a.

[0009] Optionally, the air hole includes a second air hole close to both side edges of the line defect waveguide along the second direction, and a first air hole away from both side edges of the line defect waveguide along the second direction, and an aperture R1 of the first air hole is larger than an aperture R2 of the second air hole.

[0010] Optionally, the aperture R1 of the first air hole ranges from 0.2a to 0.3a.

[0011] Optionally, the aperture R2 of the second air hole ranges from 0.7R1 to 0.8R1.

[0012] Optionally, the substrate includes any one of a silicon dioxide substrate, a silicon substrate, a gallium nitride substrate, a silicon nitride substrate, and a lithium niobate substrate.

[0013] Optionally, the bottom electrode and the signal electrode are composed of conductive metal or metal oxide materials, and the conductive metal material includes an alloy or stack of any one or more of gold, aluminum, platinum, and titanium; the metal oxide includes any one of indium tin oxide, indium thallium oxide, and indium antimony oxide.

[0014] Optionally, the insulating layer and the upper cladding layer are composed of a low-refractive-index material, and the low-refractive-index material includes one of silicon dioxide, aluminum oxide, and silicon nitride.

[0015] Optionally, the thickness of the insulating layer ranges from 500 nm to 1500 nm.

[0016] Optionally, the thickness of the upper cladding layer ranges from 500 nm to 1500 nm.

[0017] Optionally, the thickness of the signal electrode ranges from 500 nm to 1000 nm.

[0018] The electro-optic modulator based on the slow light effect provided in this application has at least the following beneficial effects:

[0019] The present application provides an electro-optic modulator based on the slow-light effect, comprising a substrate, a bottom electrode, an insulating layer, a slow-light waveguide layer, an upper cladding layer and a signal electrode stacked in sequence from bottom to top. The slow-light waveguide layer is a photonic crystal waveguide based on a Z-cut thin film lithium niobate, and the photonic crystal waveguide includes a line defect waveguide and a plurality of air holes arranged in a triangular lattice structure, and the plurality of air holes are symmetrically arranged on both sides of the line defect waveguide. A two-dimensional periodic optical medium structure formed by combining the air holes arranged in a triangular lattice structure and the Z-cut thin film lithium niobate is used to form a photonic band gap to achieve the slow-light effect, and by introducing a line defect waveguide, light waves within a specific frequency range can only propagate along the line defect waveguide. The present application enhances the interaction between the optical field and the electric field, which can significantly improve the modulation efficiency and performance of the electro-optic modulator, and meet the development trend of miniaturization, integration and high speed of existing communication networks.

[0020] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0022] Figure 1 is a schematic diagram of a three-dimensional structure of an electro-optic modulator based on the slow light effect according to an embodiment of the present invention;

[0023] Figure 2 is a schematic diagram of a longitudinal cross-sectional structure of an electro-optic modulator based on the slow light effect according to an embodiment of the present invention;

[0024] Figure 3 FIG. 4 is a schematic diagram of the cross-sectional structure of a slow light waveguide layer according to an embodiment of the present invention.

[0025] Figure 4 Schematic diagram of the corresponding light field distribution in a photonic crystal unit cell of an electro-optic modulator based on the slow light effect according to an embodiment of the present invention.

[0026] Figure 5 Schematic diagram of light field distribution in a slow light waveguide layer of an electro-optic modulator based on the slow light effect according to an embodiment of the present invention.

[0027] Figure 6 1 is a diagram showing the corresponding relationship between the group refractive index of the transmitted light field and the operating frequency of the modulator in an electro-optic modulator based on the slow light effect according to an embodiment of the present invention.

[0028] 1 substrate; 2 bottom electrode; 3 insulating layer; 4 slow light waveguide layer; 41 line defect waveguide; 42 air hole; 421 first air hole; 422 second air hole; 5 upper cladding layer; 6 signal electrode. DETAILED DESCRIPTION

[0029] The following describes in detail embodiments of the present application, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0030] In the field of optical communications, electro-optic modulators are core components for high-speed loading of electrical signals into optical signals. Lithium niobate (LNbO) substrates, due to their high electro-optic coefficient and second-order nonlinear optical coefficient, are widely used in data centers, supercomputers, and other applications where high-capacity, high-speed electro-optical modulation is urgently needed. However, conventional LNbO3 bulk modulators suffer from large size and insufficient bandwidth, making them difficult to adapt to the current trend of miniaturization, integration, and high-speed communication networks.

[0031] Therefore, the present application provides an LNOI (Lithium Niobate On Insulator) electro-optic modulator based on the slow-light effect, comprising an isolation layer composed of an insulating material such as silicon dioxide, a slow-light waveguide layer formed on the isolation layer and based on thin-film lithium niobate, and an upper confinement layer formed on the slow-light waveguide layer. Due to the high refractive index contrast between the upper confinement layer and the isolation layer and the slow-light waveguide layer, the excellent optical field confinement capabilities of the upper confinement layer and the isolation layer, and the advantages of on-chip integration, the overall performance of the electro-optic modulator is significantly improved compared with traditional lithium niobate materials, and meets the development trend of miniaturization, integration, and high-speed of existing communication networks. As a result, the electro-optic modulator provided by the present application can be more widely used in optical interconnection, especially in the field of integrated optics.

[0032] According to one aspect of this application, Figures 1 to 3 As shown, an electro-optic modulator based on the slow-light effect is provided, comprising a substrate 1, a bottom electrode 2, an insulating layer 3, a slow-light waveguide layer 4, an upper cladding layer 5, and a signal electrode 6, stacked in order from bottom to top. The slow-light waveguide layer 4 is a photonic crystal waveguide based on a Z-cut lithium niobate thin film, and the photonic crystal waveguide includes a linear defect waveguide 41 extending along a first direction and a plurality of air holes 42 arranged in a triangular lattice structure. The plurality of air holes 42 are symmetrically arranged on both sides of the linear defect waveguide 41 along a second direction.

[0033] For ease of description, the X direction in the figure can be set as the first direction, which is also the direction in which the linear defect waveguide 41 extends; the Y direction in the figure can be set as the second direction, which is also the direction perpendicular to the direction in which the linear defect waveguide 41 extends; the Z direction in the figure can be set as the third direction, which is also the direction perpendicular to the surface of the slow light waveguide layer 4; and both the first direction and the second direction are parallel to the surface of the slow light waveguide layer 4, and the Z tangent direction of the thin film lithium niobate is in the same direction as the third direction.

[0034] It is understood that a photonic crystal is a periodically arranged optical medium structure whose periodically varying refractive index can significantly affect the propagation of light waves, forming a so-called "photonic band gap," which prevents light waves within a specific frequency range from propagating within the photonic crystal. Photonic crystal waveguides, based on photonic crystals, introduce defects or modify the structure of certain regions to enable light waves of specific frequencies to propagate along specific paths within the photonic crystal waveguide, freeing them from the constraints of the surrounding periodic structure of the photonic crystal.

[0035] Because the photonic crystal waveguide includes a linear defect waveguide 41 extending in a first direction and multiple air holes 42 arranged in a triangular lattice structure, with the multiple air holes 42 symmetrically arranged on either side of the linear defect waveguide 41 along a second direction, the linear defect waveguide 41 extending in the first direction can disrupt the lattice periodicity of the photonic crystal waveguide, generating a guided mode frequency band within the photonic band gap (PBG), allowing light waves to propagate along the defect path (the linear defect waveguide 41). Furthermore, the multiple air holes 42 periodically arranged in a triangular lattice structure, combined with the Z-cut lithium niobate thin film, form a two-dimensional periodic optical dielectric structure that forms the PBG and further regulates the optical field, prohibiting light waves within a specific frequency range from propagating within it.

[0036] Therefore, the existence of the photonic bandgap in the photonic crystal waveguide enables strong control over the propagation of the light field. Compared with the traditional ridge waveguide, the photonic crystal waveguide can confine a larger transmission optical mode field, has lower transmission loss and a wider transmission window, and therefore it is easy to achieve lower waveguide end face coupling loss and reduce the insertion loss of the electro-optic modulator.

[0037] like Figures 4 to 6As shown, by symmetrically arranging the air holes 42 on both sides of the linear defect waveguide 41, the light field constraint can be further optimized, and the light field can be more concentrated in the area corresponding to the linear defect waveguide 41, so that when the light wave propagates in the slow light waveguide layer 4, the lattice constant (the distance between the centers of adjacent air holes 42) and the aperture of the air holes 42 can be adjusted, so that the refractive index change of the air holes 42 and the band gap effect of the photonic crystal can work synergistically, thereby increasing the group refractive index corresponding to the light field and significantly reducing the group velocity at the edge of the band gap, realizing the slow light effect, extending the interaction time between the light field and the waveguide, and enhancing the interaction between the light field and the electric field, thereby significantly improving the modulation efficiency of the electro-optical modulator, and thus achieving a higher modulation depth.

[0038] Here, the distance between the centers of adjacent air holes 42 can be set to the lattice constant a of the triangular lattice structure. For a photonic crystal waveguide with Z and alternating periods of thin-film lithium niobate and air holes 42, the wavelength of the electromagnetic wave at the corresponding frequency is approximately 2.2 to 2.6 times the period constant, and the duty cycle (i.e., the ratio between the aperture R of the air hole 42 and the lattice constant a) affects the width of the photonic band gap, which is the band gap characteristic of the photonic crystal. Therefore, the present application sets the lattice constant a to between 350nm and 500nm. At the same time, by adjusting the duty cycle, optimizing the lattice constant a and the aperture R of the air hole 42, the light field can be regulated, and light waves within a specific frequency range are prohibited from propagating inside the photonic crystal waveguide, thereby increasing the band gap width.

[0039] Since the line defect waveguide 41 can destroy the lattice periodicity of the photonic crystal waveguide and generate a guided mode frequency band in the photonic bandgap, the light wave can propagate along the defect path (line defect waveguide 41). Therefore, by limiting the width of the line defect waveguide 41 along the second direction, the number of modes that the line defect waveguide 41 can support can be limited, and the electro-optical modulation efficiency and device performance can be optimized in multiple dimensions. Here, the width of the line defect waveguide 41 along the second direction can be set to W, and the range of W can be between 1.75a and 2.25a, ​​so that the TM mode corresponding to the line defect waveguide 41 includes the fundamental mode and / or the higher-order mode.

[0040] Furthermore, because the slow-light waveguide layer 4 is a photonic crystal waveguide based on Z-cut lithium niobate thin film, with its optical axis perpendicular to the film surface, the high electro-optic coefficient of Z-cut lithium niobate significantly responds to TM mode light fields, making it a suitable material for electro-optic modulation. Furthermore, compared to conventional X / Y-cut lithium niobate thin film, an electro-optic modulator based on a photonic crystal waveguide based on Z-cut lithium niobate, combined with a vertical electrode distribution to achieve a high overlap between the modulating electric field and the waveguide-transmitted light field, can further enhance the interaction between the light field and the modulating electric field, thereby improving the modulation efficiency and performance of the electro-optic modulator.

[0041] Furthermore, since the upper cladding layer 5 and the signal electrode 6 are stacked in sequence on the line defect waveguide 41 and form a ridge structure to effectively limit the light field in the slow light waveguide layer 4, the light field can be more concentrated in the area corresponding to the line defect waveguide 41, thereby enhancing the light field intensity. At the same time, the bottom electrode 2 and the signal electrode 6 cooperate with each other in the third direction, so that the modulated electric field can act more accurately on the area where the light field is concentrated, forming a high degree of overlap between the modulated electric field and the light field distribution, thereby improving the electro-optical modulation efficiency, reducing the half-wave voltage, and reducing the energy consumption of the device.

[0042] Furthermore, the ridge structure helps optimize light field distribution, reduce mode distortion during light propagation, and improve optical signal quality. This compact stacked design also helps reduce the overall device size, facilitating the miniaturization and integration of optoelectronic devices, meeting the high-integration requirements of modern optical communication systems. Furthermore, the upper cladding layer 5 provides stable support for the signal electrode 6, ensuring good contact between the electrode and the waveguide, enhancing the stability and reliability of the device in various environments, and extending its service life.

[0043] Furthermore, since the control of the light field requires the optimization of the size parameters of the lattice constant a and the aperture R of the air hole 42, and the optimization process of these parameters has high requirements for structural design and process, and the matching between the parameters and process is relatively difficult, in order to reduce the difficulty of controlling the light field, the air hole 42 can be divided into a second air hole 422 close to the edge of the linear defect waveguide 41 in the second direction, and a first air hole 421 away from the edge of the linear defect waveguide 41. Thus, by only adaptively adjusting the aperture of the second air hole 422 so that the aperture of the second air hole 422 is smaller than the aperture of the first air hole 421, the control of the light field can be achieved, and then the intensity of the slow light effect in the slow light waveguide and the operating frequency band of the electro-optical modulator can be controlled, thereby reducing the difficulty of controlling the light field of the electro-optical modulator, making the preparation process of the electro-optical modulator provided in this application compatible with existing integrated optical processes, and achieving large-scale integration.

[0044] Here, the aperture of the first air hole 421 can be set to R1, and the aperture of the second air hole 422 can be set to R2. According to the intensity of the slow light effect, the range of the aperture R1 of the first air hole 421 is set to be between 0.2a and 0.3a, and according to the intensity of the slow light effect and the operating frequency band of the electro-optic modulator, the range of the aperture R2 of the second air hole 422 is set to be between 0.7R1 and 0.8R1.

[0045] As an example, the period constant a of the triangular lattice structure in the photonic crystal waveguide is 450 nm; the diameter R1 of the first air hole 421 is 0.25a; the width W of the linear defect waveguide 41 is 2a; and the aperture R2 of the second air hole 422 is 0.75R1.

[0046] In some embodiments, the substrate 1 includes any one of commonly used integrated optical substrates such as a silicon dioxide substrate, a silicon substrate, a gallium nitride substrate, a silicon nitride substrate, and lithium niobate, so as to facilitate further integration and application of the electro-optic modulator.

[0047] As an example, the substrate 1 is a quartz substrate.

[0048] Bottom electrode 2 is disposed on substrate 1 and may have a thickness ranging from 500 nm to 1000 nm. Signal electrode 6 may be composed of a conductive metal or metal oxide material. The conductive metal material may include an alloy or laminate of one or more of gold, aluminum, platinum, and titanium. The metal oxide may include indium tin oxide, indium thallium oxide, or indium antimony oxide.

[0049] As an example, the bottom electrode 2 is composed of a gold metal thin film with a thickness of 600 nm.

[0050] An insulating layer 3 is disposed on the bottom electrode 2 and can have a thickness ranging from 500 nm to 1500 nm. The insulating layer 3 can be composed of low-refractive-index insulating materials commonly used in integrated optics, such as silicon dioxide, aluminum oxide, or silicon nitride. This layer isolates the bottom electrode 2 from direct contact with the slow-light waveguide layer 4. Furthermore, it creates a refractive index difference with the slow-light waveguide layer 4, thereby cooperating with the subsequent upper cladding layer 5 to limit the longitudinal distribution of the light field, confining the light field primarily within the slow-light waveguide layer 4.

[0051] As an example, the insulating layer 3 is composed of a silicon dioxide thin film with a thickness of 500 nm.

[0052] The upper cladding layer 5 is disposed on the linear defect waveguide 41 and can have a thickness between 500 nm and 1500 nm. The upper cladding layer 5 can be composed of low-refractive-index insulating materials commonly used in integrated optics, such as silicon dioxide, aluminum oxide, or silicon nitride. The upper cladding layer 5 not only provides direct contact between the subsequent signal electrode 6 and the slow-light waveguide layer 4, but also creates a refractive index difference with the slow-light waveguide layer 4, thereby cooperating with the insulating layer 3 to limit the longitudinal distribution of the light field, ensuring that the light field is primarily distributed within the slow-light waveguide layer 4.

[0053] As an example, the upper cladding layer 5 is composed of a silicon dioxide thin film with a thickness of 500 nm.

[0054] The signal electrode 6 is disposed on the upper cladding layer 5 and can have a thickness between 500 nm and 1000 nm. The signal electrode 6 can be composed of a conductive metal or metal oxide material. Examples of the signal electrode 6 include alloys or stacks of one or more of gold, aluminum, platinum, and titanium. Metal oxides include indium tin oxide, indium thallium oxide, and indium antimony oxide. The signal electrode 6 is used to apply an electrical signal and form an electric field with the bottom electrode 2 to modulate the light field transmitted in the slow light waveguide layer 4.

[0055] As an example, the signal electrode 6 is composed of a gold metal thin film with a thickness of 400 nm.

[0056] It should be noted that the above-mentioned electro-optical modulator includes but is not limited to modulators such as phase modulator, Mach-Zehnder intensity modulator, dual Mach-Zehnder intensity modulator, and pulse modulator.

[0057] In summary, the present application provides an electro-optic modulator based on the slow-light effect, comprising a substrate 1, a bottom electrode 2, an insulating layer 3, a slow-light waveguide layer 4, an upper cladding layer 5, and a signal electrode 6 stacked in sequence from bottom to top. The slow-light waveguide layer 4 is a photonic crystal waveguide based on a Z-cut thin-film lithium niobate, and the photonic crystal waveguide includes a linear defect waveguide 41 and a plurality of air holes 42 arranged in a triangular lattice structure. The plurality of air holes 42 are symmetrically arranged on both sides of the linear defect waveguide 41. A two-dimensional periodic optical medium structure formed by combining the air holes 42 arranged in a triangular lattice structure with the Z-cut thin-film lithium niobate forms a photonic band gap, realizing the slow-light effect, and by introducing the linear defect waveguide 41, light waves within a specific frequency range can only propagate along the linear defect waveguide 41. The present application enhances the interaction between the optical field and the electric field, which can significantly improve the modulation efficiency and performance of the electro-optic modulator and meet the development trend of miniaturization, integration, and high speed of existing communication networks.

[0058] In the descriptions of the foregoing embodiments, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are mutually inconsistent.

[0059] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

Claims

1. An electro-optic modulator based on slow light effect, characterized in that: The invention comprises a substrate, a bottom electrode, an insulating layer, a slow light waveguide layer, an upper cladding layer and a signal electrode stacked in sequence from bottom to top; wherein the slow light waveguide layer is a photonic crystal waveguide based on Z-cut lithium niobate thin film, the photonic crystal waveguide comprises a line defect waveguide extending along a first direction, and a plurality of air holes arranged in a triangular lattice structure, the plurality of air holes are symmetrically arranged on both sides of the line defect waveguide along a second direction, the upper cladding layer and the signal electrode are stacked in sequence on the line defect waveguide.

2. The electro-optic modulator according to claim 1, wherein The air holes include second air holes close to both side edges of the line defect waveguide along the second direction, and first air holes away from both side edges of the line defect waveguide along the second direction, and an aperture R1 of the first air hole is larger than an aperture R2 of the second air hole.

3. The electro-optic modulator according to claim 2, wherein: The distance a between the centers of adjacent air holes ranges from 350 nm to 500 nm.

4. The electro-optic modulator according to claim 2, wherein: The width W of the linear defect waveguide along the second direction ranges from 1.75a to 2.25a.

5. The electro-optic modulator according to claim 2, wherein: The aperture R1 of the first air hole ranges from 0.2a to 0.3a.

6. The electro-optic modulator according to claim 2, wherein: The diameter R2 of the second air hole ranges from 0.7R1 to 0.8R1.

7. The electro-optic modulator according to claim 1, wherein The substrate includes any one of a silicon dioxide substrate, a silicon substrate, a gallium nitride substrate, a silicon nitride substrate, and a lithium niobate substrate.

8. The electro-optic modulator according to claim 1, wherein The bottom electrode and the signal electrode are composed of conductive metal or metal oxide materials, wherein the conductive metal material includes any one or more alloys or stacks of gold, aluminum, platinum, and titanium; and the metal oxide includes any one of indium tin oxide, indium thallium oxide, and indium antimony oxide.

9. The electro-optic modulator according to claim 1, wherein: The insulating layer and the upper cladding layer are composed of a low-refractive-index material, and the low-refractive-index material includes one of silicon dioxide, aluminum oxide, and silicon nitride.

10. The electro-optic modulator according to claim 1, wherein The thickness of the insulating layer ranges from 500 nm to 1500 nm.

11. The electro-optic modulator according to claim 1, wherein: The thickness of the upper cladding layer ranges from 500 nm to 1500 nm.

12. The electro-optic modulator according to claim 1, wherein The thickness of the signal electrode ranges from 500 nm to 1000 nm.

Images