Optical modulator

Abstract

The present invention reduces Vπ⋅L. An optical modulator (1) comprises an optical waveguide (2), a first cladding layer (3), a first electrode (4), a second electrode (5), and a second cladding layer (7). The first cladding layer (3) covers the optical waveguide (2). The first electrode (4) is spaced apart in the width direction from a first end (21) of the optical waveguide (2) in the width direction. The second electrode (5) is spaced apart in the width direction from a second end (22) of the optical waveguide (2) in the width direction, and a voltage is applied between the first electrode (4) and the second electrode (5). The second cladding layer (7) covers the first cladding layer (3). The refractive index of the first cladding layer (3) is lower than the refractive index of the optical waveguide (2). The relative permittivity of the second cladding layer (7) is higher than the relative permittivity of the first cladding layer (3). The second cladding layer (7) has a slit (72) overlapping the optical waveguide (2). The relative permittivity inside the slit (72) is lower than the relative permittivity of the second cladding layer (7).

Description

Optical modulator

[0001] The present invention generally relates to an optical modulator, and more particularly to an optical modulator including an optical waveguide.

[0002] Non-Patent Document 1 discloses an electro-optic modulator as an optical modulator, which includes an optical waveguide, signal electrodes and ground electrodes disposed on both sides in the width direction of the optical waveguide, and SiO ２ layer (SiO ２ cladding), and a high dielectric constant material layer (high dielectric constant cladding) covering the SiO ２ layer.

[0003] Non-Patent Document 1 reports that in an optical modulator including a high dielectric constant cladding, the electric field strength in the optical waveguide becomes higher than that in an optical modulator including only a SiO ２ cladding, and Vπ·L representing the performance index of the optical modulator is reduced.

[0004] Nuo Chen et al., High-efficiency electro-optic modulator on thin-film lithium niobate with high-permittivity cladding, Laser Photonics Rev. 2023, 17, 2200927

[0005] In an optical modulator, further reduction of Vπ·L may be desired.

[0006] An object of the present invention is to provide an optical modulator capable of reducing Vπ·L.

[0007] An optical modulator according to one aspect of the present invention comprises an optical waveguide, a first cladding layer, a first electrode, a second electrode, and a second cladding layer. The first cladding layer covers the optical waveguide. The first electrode is spaced in the width direction from a first end in the width direction of the optical waveguide and is arranged along the optical propagation direction of the optical waveguide. The second electrode is spaced in the width direction from a second end in the width direction of the optical waveguide and is arranged along the optical propagation direction of the optical waveguide. A voltage is applied between the second electrode and the first electrode. The second cladding layer covers the first cladding layer. The refractive index of the first cladding layer is smaller than the refractive index of the optical waveguide. The relative permittivity of the second cladding layer is larger than the relative permittivity of the first cladding layer. The second cladding layer has a slit formed on its main surface that overlaps the optical waveguide. The relative permittivity inside the slit is smaller than the relative permittivity of the second cladding layer. The relative permittivity inside the slit and the relative permittivity of the first cladding layer are both greater than 0. The relative permittivity inside the slit is 2.25 times or less the relative permittivity of the first cladding layer.

[0008] The optical modulator according to the above embodiment of the present invention is capable of reducing Vπ·L.

[0009] Figure 1 is a partially broken perspective view showing an optical modulator according to Embodiment 1. Figure 2 is a partially broken plan view of the same optical modulator. Figure 3 is a cross-sectional view of the same optical modulator taken along line III-III in Figure 2. Figure 4 is a plan view of the main part of the same optical modulator. Figure 5 is a schematic diagram of electric field lines generated in the same optical modulator. Figure 6 is a distribution diagram showing the distribution of electric field lines generated in the same optical modulator. Figure 7 is an explanatory diagram of the dimensions of the same optical modulator. Figure 8 is an explanatory diagram showing the relationship between t1 / t2 and normalized Vπ・L. Figure 9 is a graph showing the relationship between t1 / g1 and normalized Vπ・L. Figure 10 is an explanatory diagram showing the relationship between ε2 / ε1 and normalized Vπ・L. Figure 11 is an explanatory diagram of the thickness of the second cladding layer in an optical modulator according to Modification 1 of Embodiment 1. Figure 12 is a cross-sectional view of the main part of an optical modulator according to Modification 2 of Embodiment 1. Figure 13 is a graph showing the relationship between the normalized slit width and the normalized Vπ·L. Figure 14 is a partially broken cross-sectional view of an optical modulator according to Modification 3 of Embodiment 1. Figure 15 is a partially broken cross-sectional view of an optical modulator according to Modification 4 of Embodiment 1. Figure 16 is a partially broken cross-sectional view of an optical modulator according to Modification 5 of Embodiment 1. Figure 17 is a partially broken cross-sectional view of an optical modulator according to Modification 6 of Embodiment 1. Figure 18 is a partially broken cross-sectional view of an optical modulator according to Modification 7 of Embodiment 1. Figure 19 is a partially broken perspective view of an optical modulator according to Embodiment 2. Figure 20 is a partially broken cross-sectional view of the same optical modulator. Figure 21 is a dimensional diagram of the same optical modulator. Figure 22 is a graph showing the relationship between t0 / t1 and the normalized Vπ·L. Figure 23 is a graph showing the relationship between the normalized slit width and the normalized Vπ·L. Figure 24 is a partially broken cross-sectional view of an optical modulator according to Modification 1 of Embodiment 2. Figure 25 is a partially broken cross-sectional view of an optical modulator according to a modified example 2 of Embodiment 2. Figure 26 is a partially broken cross-sectional view of an optical modulator according to Embodiment 3. Figure 27 is a graph showing the relationship between ε3 / ε2 and the normalized Vπ·L. Figure 28 is a graph showing the relationship between ε3 / ε1 and the normalized Vπ·L. Figure 29 is a partially broken cross-sectional view of an optical modulator according to Embodiment 4. Figure 30 is a partially broken cross-sectional view of an optical modulator according to Embodiment 5.Figure 31 is a partially broken cross-sectional view of an optical modulator according to Embodiment 6. Figure 32 is a partially broken cross-sectional view of an optical modulator according to Embodiment 7. Figure 33 is a partially broken cross-sectional view of an optical modulator according to Embodiment 8. Figure 34 is a partially broken cross-sectional view of an optical modulator according to Embodiment 9. Figure 35 is a partially broken cross-sectional view of an optical modulator according to Embodiment 10. Figure 36 is a partially broken plan view of an optical modulator according to Embodiment 11. Figure 37 shows the same optical modulator and is a cross-sectional view taken along the line XXXVII-XXXVII in Figure 36. Figure 38 shows the same optical modulator and is a cross-sectional view taken along the line XXXVIII-XXXVIII in Figure 36. Figure 39 is a partially broken plan view of an optical modulator according to a modified example of Embodiment 11. Figure 40 is a partially broken plan view of an optical modulator according to Embodiment 12. Figure 41 shows the same optical modulator and is a cross-sectional view taken along the line XXXXI-XXXXI in Figure 40. Figure 42 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXII-XXXXII in Figure 40. Figure 43 is a partially broken plan view of the optical modulator according to Embodiment 13. Figure 44 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXIV-XXXXIV in Figure 43. Figure 45 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXV-XXXXV in Figure 43. Figure 46 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXVI-XXXXVI in Figure 43. Figure 47 is a partially broken plan view of the optical modulator according to Embodiment 14. Figure 48 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXVIII-XXXXVIII in Figure 47. Figure 49 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXIX-XXXXIX in Figure 47. Figure 50 shows the optical modulator described above, and is a cross-sectional view taken along the line XXXXX-XXXXX in Figure 47.

[0010] Embodiments 1 to 14 will be described below with reference to the drawings. The drawings referenced in Embodiments 1 to 14 below are schematic diagrams, and the size and thickness of the components shown in the drawings do not necessarily reflect the actual dimensions, nor do the ratios of size and thickness between components necessarily reflect the actual dimensional ratios. In addition, each drawing defines and represents a Cartesian coordinate system with three mutually orthogonal axes: the X, Y, and Z axes. The X, Y, and Z axes are all virtual axes, and the arrows indicating "X," "Y," and "Z" in the drawings are for illustrative purposes only and do not have any actual physical counterparts. Furthermore, the "slits" in the cladding layers (first cladding layer 3, second cladding layer 7) do not necessarily penetrate the cladding layer in the thickness direction, and may not penetrate the cladding layer at all.

[0011] (Embodiment 1) The optical modulator 1 according to Embodiment 1 will be described with reference to Figures 1 to 7.

[0012] (1) As shown in the configuration diagram 1, the optical modulator 1 comprises two optical waveguides 2, a first cladding layer 3, two first electrodes 4, a second electrode 5, and a second cladding layer 7. The first cladding layer 3 covers the two optical waveguides 2. The two first electrodes 4 correspond one-to-one with the two optical waveguides 2. Each of the two first electrodes 4 is spaced in the width direction from the first end 21 in the width direction (parallel to the X-axis) of the corresponding optical waveguide 2 and is arranged along the optical propagation direction (parallel to the Y-axis) of the optical waveguide 2. The second electrodes 5 are spaced in the width direction from the second end 22 in the width direction of the two optical waveguides 2 and are arranged along the optical propagation direction of each of the two optical waveguides 2. The second cladding layer 7 covers the first cladding layer 3. The relative permittivity of the second cladding layer 7 is greater than that of the first cladding layer 3. The second cladding layer 7 has two slits 72 that overlap each of the two optical waveguides 2.

[0013] In the following explanation, for the sake of clarity, when distinguishing between the two optical waveguides 2, the optical waveguide 2 on the left in Figure 1 may be referred to as the first optical waveguide 2, and the optical waveguide 2 on the right may be referred to as the second optical waveguide 2. Similarly, when distinguishing between the two first electrodes 4, the first electrode 4 on the left in Figure 1 may be referred to as the first signal electrode 4, and the first electrode 4 on the right may be referred to as the second signal electrode 4. In the optical modulator 1, in a plan view from the Z-axis direction, the first signal electrode 4, the first optical waveguide 2, the second electrode 5, the second optical waveguide 2, and the second signal electrode 4 are arranged in the order of first signal electrode 4, first optical waveguide 2, second electrode 5, second optical waveguide 2, and second signal electrode 4.

[0014] Furthermore, the optical modulator 1 further comprises a substrate 10 and a cladding layer 9. The optical modulator 1 of this embodiment includes an optical waveguide material layer 20 containing two optical waveguides 2. In the optical modulator 1, the optical waveguide material layer 20 containing the two optical waveguides 2 is supported on the substrate 10 via the cladding layer 9. In addition, as shown in Figure 4, the optical modulator 1 further includes, in addition to the two optical waveguides 2, a Y-shaped input optical waveguide 25 connected to the first end of the two optical waveguides 2 in the optical propagation direction, and a Y-shaped output optical waveguide 26 connected to the second end of the two optical waveguides 2 in the optical propagation direction. Note that the first cladding layer 3 and the second cladding layer 7 are omitted from the illustration in Figure 4.

[0015] In the optical modulator 1, the first electrode 4 and the second electrode 5, which are positioned on both sides in the width direction of the optical waveguide 2, are two electrodes for controlling the light guiding the optical waveguide 2 located between the first electrode 4 and the second electrode 5. In the optical modulator 1 of this embodiment, the first electrode 4 is the signal electrode and the second electrode 5 is the ground electrode. In the optical modulator 1, a first voltage signal consisting of a digital signal is supplied from an external control device (not shown) to the first electrode 4 and the second electrode 5 on both sides of the first optical waveguide 2. In addition, in the optical modulator 1, a second voltage signal consisting of a digital signal is supplied from the control device to the first electrode 4 and the second electrode 5 on both sides of the second optical waveguide 2. If V0 is the voltage applied when there is no phase difference between the light passing through the first optical waveguide 2 and the light passing through the second optical waveguide 2, and V1 is the voltage when the phase difference is 180 degrees, then Vπ is Vπ = V1 - V0. In the optical modulator 1, if L (see Figure 4) is the length of the first electrode 4 and the second electrode 5 in the direction along the optical propagation direction of the optical waveguide 2, then the smaller the value of Vπ・L, the more it becomes possible to improve performance while miniaturizing the device.

[0016] (1.1) Substrate As shown in Figure 3, the substrate 10 has a main surface 101. The substrate 10 is, for example, a semiconductor substrate. The semiconductor substrate is, for example, a silicon substrate. The silicon substrate constituting the semiconductor substrate may be a silicon substrate doped with impurities or an undoped silicon substrate. The semiconductor substrate is not limited to a silicon substrate, but may also be an SOI (Silicon On Insulator) substrate or a CSOI (Cavity-SOI) substrate. Furthermore, the semiconductor substrate is not limited to a silicon substrate, but may also be, for example, a germanium substrate or a compound semiconductor substrate (for example, a GaAs substrate). Furthermore, the substrate 10 is not limited to a semiconductor substrate, but may also be, for example, a sapphire substrate, a glass substrate or a quartz substrate.

[0017] (1.2) Cladding layer As shown in Figure 3, the cladding layer 9 is arranged on the main surface 101 of the substrate 10. The cladding layer 9 is arranged, for example, to cover the entire surface of the main surface 101 of the substrate 10.

[0018] The refractive index of the cladding layer 9 is smaller than the refractive index of each of the two optical waveguides 2. The material of the cladding layer 9 is, for example, SiO ２ or the like. The materials of the first cladding layer 3 and the cladding layer 9 are not limited to SiO ２ and may be oxides such as Al ２ O ３ , LaAlO ３ , LaYO ３ , ZnO, HfO ２ , MgO, Y ２ O ３ or polymers such as BCB (benzocyclobutene), PI (polyimide). In the optical modulator 1, the cladding layer 9 may be an air layer.

[0019] (1.3) First optical waveguide, second optical waveguide, input optical waveguide, output optical waveguide, and optical waveguide material layer As shown in FIG. 1, in the present embodiment, each of the two optical waveguides 2 is a ridge-type optical waveguide. In each of the two optical waveguides 2, the width W0 (see FIG. 2) of the optical waveguide 2 is larger than the thickness of the optical waveguide 2 (thickness in the direction along the Z axis). Each of the two optical waveguides 2 has an elongated shape with the width direction (direction parallel to the X axis) as the short side direction. In the optical modulator 1 of the present embodiment, in a cross-sectional view perpendicular to the optical propagation direction of the two optical waveguides 2, the two optical waveguides 2 are symmetrically arranged around the second electrode 5. As shown in FIG. 4, in the present embodiment, the input optical waveguide 25, the second electrode 5, and the output optical waveguide 26 are arranged in this order: the input optical waveguide 25, the second electrode 5, and the output optical waveguide 26. Each of the input optical waveguide 25 and the output optical waveguide 26 is a ridge-type optical waveguide.

[0020] As shown in FIG. 3, the optical waveguide material layer 20 is disposed on the main surface 91 of the cladding layer 9. In the present embodiment, the optical waveguide material layer 20 covers the entire main surface 91 of the cladding layer 9. The optical waveguide material layer 20 has a first main surface 201 and a second main surface 202 opposite to the first main surface 201. In the optical waveguide material layer 20, the second main surface 202 is in contact with the main surface 91 of the cladding layer 9.

[0021] The material of the optical waveguide material layer 20 is, for example, lithium niobate (LiNbO ３In this embodiment, the optical waveguide material layer 20 is a lithium niobate substrate. The material of the optical waveguide material layer 20 is not limited to lithium niobate, but can also be LiTaO ３ (Lithium tantalate), PLT (lead lanthanum titanate), PZT (lead titanium zirconate), PLZT (lead lanthanum zirconate titanate), KNbO ３ (Potassium niobate), BaTiO ３ (Barium titanate), KTN (Potassium niobate tantalate), SrTiO ３ (Strontium titanate), Bi ４ Ti ３ O １２ The material may be selected from the group consisting of bismuth titanate and electro-optic polymers (EO polymers).

[0022] (1.4) First Cladding Layer As shown in Figures 1 and 3, the first cladding layer 3 is arranged on the first main surface 201 of the optical waveguide material layer 20 so as to cover the two optical waveguides 2 (only one optical waveguide 2 is shown in Figure 3). The first cladding layer 3 is formed in a predetermined pattern on the first main surface 201 of the optical waveguide material layer 20. More specifically, the first cladding layer 3 is arranged at a distance from each of the two first electrodes 4 (only the two first electrodes 4 are shown in Figure 3) and the second electrode 5.

[0023] The refractive index of the first cladding layer 3 is smaller than the refractive index of each of the two optical waveguides 2. The refractive index of the first cladding layer 3 is smaller than the refractive index of the optical waveguide material layer 20. The material of the first cladding layer 3 is, for example, SiO ２ The material of the first cladding layer 3 is SiO ２ Not limited to Al ２ O ３ , LaAlO ３ LaYO ３ ZnO, HfO ２ , MgO, Y ２ O ３ These may be oxides, polymers such as BCB (benzocyclobutene) and PI (polyimide). In this embodiment, the material of the first cladding layer 3 is the same as the material of the cladding layer 9, but the material of the first cladding layer 3 may be different from the material of the cladding layer 9.

[0024] (1.5) Two First and Second Electrodes In this embodiment, as shown in Figure 1, the two first electrodes 4 and the second electrode 5 are arranged on the first main surface 201 of the optical waveguide material layer 20. The two first electrodes 4 and the second electrode 5 are formed in predetermined patterns on the first main surface 201 of the optical waveguide material layer 20. In the optical modulator 1 of this embodiment, in a cross-sectional view perpendicular to the optical propagation direction of the two optical waveguides 2, the two first electrodes 4 are arranged symmetrically with respect to the second electrode 5. Each of the two first electrodes 4 and the second electrode 5 is elongated with the width direction of the optical waveguide 2 as its shorter side. In the optical propagation direction of the optical waveguide 2 (direction parallel to the Y-axis), the lengths of the two first electrodes 4 and the second electrode 5 are the same. "The lengths of the two first electrodes 4 and the second electrode 5 are the same" means that the lengths of each of the two electrodes (the two first electrodes 4 and the second electrode 5) do not necessarily have to be exactly the same as the length of the remaining electrode, but rather the lengths of the two electrodes do not necessarily have to be within the range of 90% to 110% of the length of the remaining electrode. In this embodiment, the thicknesses of the two first electrodes 4 and the second electrode 5 are the same. "The thicknesses of the two first electrodes 4 and the second electrode 5 are the same" means that the thicknesses of each of the two electrodes (the two first electrodes 4 and the second electrode 5) do not necessarily have to be exactly the same as the thickness of the remaining electrode, but rather the thicknesses of the two electrodes do not necessarily have to be within the range of 90% to 110% of the thickness of the remaining electrode. In this embodiment, the thickness of each of the two first electrodes 4 and the second electrode 5 is greater than the thickness of each of the two optical waveguides 2. In the optical modulator 1 of this embodiment, in a cross-sectional view perpendicular to the optical propagation direction of the two optical waveguides 2, the two first electrodes 4 are separated from the first cladding layer 3, and the second electrode 5 is also separated from the first cladding layer 3.

[0025] The two first electrodes 4 and the second electrode 5 are electrically conductive. The materials of the two first electrodes 4 and the second electrode 5 are, for example, aluminum, copper, platinum, gold, silver, titanium, nickel, chromium, molybdenum, tungsten, tantalum, magnesium, iron, or alloys mainly composed of any of these metals. The two first electrodes 4 and the second electrode 5 may also have a structure in which multiple metal films made of these metals or alloys are laminated.

[0026] (1.6) Second Cladding Layer In this embodiment, as shown in Figure 1, the second cladding layer 7 is arranged to cover the first cladding layer 3, the two first electrodes 4, the second electrode 5, and the region on the first main surface 201 of the optical waveguide material layer 20 that is not in contact with the first cladding layer 3, the two first electrodes 4, and the second electrode 5. In this embodiment, the second cladding layer 7 is in contact with the first cladding layer 3, the two first electrodes 4, the second electrode 5, and the region on the first main surface 201 of the optical waveguide material layer 20 that is not in contact with the first cladding layer 3, the two first electrodes 4, and the second electrode 5.

[0027] The material of the second cladding layer 7 is SrTiO ３ (Strontium titanate), BaTiO ３ (Barium titanate), PbLaTiO ３ (Lead lanthanum titanate), PZT (Lead titanium zirconate), PLZT (Lead titanium lanthanum zirconate), LiNbO ３ (Lithium niobate), LiTaO ３ (Lithium tantalate), KNbO ３ (Potassium niobate), PbTiO ３ (Lead titanate), PKNO (lead potassium niobate), PMN (lead magnesium niobate), Bi ４ Ti ３ O １２ (Bismuth titanate), BST (Barium strontium titanate), KLN (Potassium lanthanum niobate), Al ２ O ３ , LaAlO ３ LaYO ３ ZnO, HfO ２ , MgO, Y ２ O ３ , TiO２ Ta ２ O ５ The material is selected from the group consisting of SiN and AlN. The material of the second cladding layer 7 may be any material having a higher dielectric constant than the material of the first cladding layer 3.

[0028] The second cladding layer 7 has two slits 72 that overlap each of the two optical waveguides 2. The two slits 72 are formed on the main surface 70 of the second cladding layer 7 and penetrate the second cladding layer 7 in the thickness direction. In the optical modulator 1 of this embodiment, each of the two slits 72 in the second cladding layer 7 exposes a different portion of the first cladding layer 3, which is in contact with the air. In this embodiment, the relative permittivity inside each of the two slits 72 is smaller than the relative permittivity of the second cladding layer 7. In the optical modulator 1, since the second cladding layer 7 has slits 72, as shown in Figures 5 and 6, electric field lines (electric field lines e1 in Figure 5) passing through the second cladding layer 7 are more likely to bend and enter the optical waveguide 2, making it possible to increase the electric field strength in the optical waveguide 2.

[0029] (2) Performance of the optical modulator In the optical modulator 1 of this embodiment, as shown in Figure 7, when the thickness of the first cladding layer 3 is t2 and the reference thickness of the second cladding layer 7 is t1, it is preferable that t1 / t2 is 1 or more when viewed in a cross-sectional view perpendicular to the optical propagation direction of the optical waveguide 2 (first optical waveguide 2). In this embodiment, the reference thickness t1 is the maximum value of the difference between the length from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region between the first electrode 4 and the second electrode 5 in a plan view from the Z-axis direction where the second cladding layer 7 overlaps the first cladding layer 3.

[0030] Figure 8 is an explanatory diagram showing the relationship between t1 / t2 and the normalized Vπ・L. Figures 8(b) and 8(a) are shown in enlarged view. In Figure 8(a), the horizontal axis is t1 / t2 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. Vπ・L0 is the value of Vπ・L when the second cladding layer 7 is absent and t1=0 and t1 / t2=0. Therefore, the vertical axis in Figure 8(a) is Vπ・L normalized by setting the value of Vπ・L0 at t1=0 to 100.

[0031] From Figure 8(a), it can be seen that Vπ·L can be reduced by making t1 / t2 greater than 0. Also from Figure 8(a), it can be seen that when t1 / t2 is 1 or greater, Vπ·L becomes approximately constant. Furthermore, from Figure 8(b), when t1 / t2 is greater than 5, Vπ·L increases slightly compared to the case where t1 / t2 is 5 or less.

[0032] Furthermore, in the optical modulator 1 of this embodiment, as shown in Figure 7, when viewed in a cross-sectional view perpendicular to the optical propagation direction of the optical waveguide 2 (first optical waveguide 2), the shortest distance between the first cladding layer 3 and the first electrode 4 is g1, the shortest distance between the first cladding layer 3 and the second electrode 5 is g2 (= g1), and the reference thickness of the second cladding layer 7 is t1, it is preferable that t1 / g1 is 0.5 or more.

[0033] Figure 9 is a graph showing the relationship between t1 / g1 and the normalized Vπ・L. In Figure 9, the horizontal axis is t1 / g1 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. Vπ・L0 is the value of Vπ・L when the second cladding layer 7 is absent and t1=0 and t1 / g1=0. Therefore, the vertical axis in Figure 9 is Vπ・L normalized by setting the value of Vπ・L0 at t1=0 to 100. From Figure 9, it can be seen that Vπ・L can be reduced by making t1 / g1 greater than 0. Also from Figure 9, it can be seen that when t1 / g1 is 0.5 or greater, Vπ・L becomes approximately constant.

[0034] Figure 10 is an explanatory diagram showing the relationship between ε2 / ε1 and the normalized Vπ・L, where ε2 is the relative permittivity of the second cladding layer 7 and ε1 is the relative permittivity of the first cladding layer 3. Figure 10(b) is an enlarged view of a part of Figure 10(a). In Figure 10(a), the horizontal axis is ε2 / ε1 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. Vπ・L0 is the value of Vπ・L when the relative permittivity of the second cladding layer is the same as that of the first cladding layer, i.e., ε2 / ε1 = 1. From Figure 10(a), it can be seen that when ε2 / ε1 is 5 or more, Vπ・L can be reduced by 20% or more, and when ε2 / ε1 is 50 or more, Vπ・L can be reduced by 40% or more. From Figure 10(b), it can be seen that when ε2 / ε1 is 1500 or more, Vπ・L becomes approximately constant. Therefore, in the optical modulator 1 of this embodiment, the relative permittivity of the second cladding layer 7 is preferably 5 times or more, and more preferably 50 times or more, than the relative permittivity of the first cladding layer 3. Furthermore, if the relative permittivity of the second cladding layer 7 becomes too large, it becomes difficult to match the characteristic impedance and the effective refractive index with respect to high frequencies. Therefore, in the optical modulator 1 of this embodiment, it is desirable that the relative permittivity of the second cladding layer 7 is 1500 times or less than the relative permittivity of the first cladding layer 3.

[0035] (3) The optical modulator 1 according to the first embodiment comprises an optical waveguide 2, a first cladding layer 3, a first electrode 4, a second electrode 5, and a second cladding layer 7. The first cladding layer 3 covers the optical waveguide 2. The first electrode 4 is spaced in the width direction away from the first end 21 in the width direction of the optical waveguide 2 and is arranged along the optical propagation direction of the optical waveguide 2. The second electrode 5 is spaced in the width direction away from the second end 22 in the width direction of the optical waveguide 2 and is arranged along the optical propagation direction of the optical waveguide 2. The second cladding layer 7 covers the first cladding layer 3. In the optical modulator 1, a voltage is applied between the first electrode 4 and the second electrode 5. The refractive index of the first cladding layer 3 is smaller than the refractive index of the optical waveguide 2. The relative permittivity of the second cladding layer 7 is larger than the relative permittivity of the first cladding layer 3. The second cladding layer 7 has a slit 72 formed on the main surface 70 of the second cladding layer 7 that overlaps the optical waveguide 2. The relative permittivity inside the slit 72 is smaller than the relative permittivity of the second cladding layer 7. In the optical modulator 1 according to Embodiment 1, the inside of the slit 72 is air, and the relative permittivity inside the slit 72 is approximately 1. The relative permittivity inside the slit 72 and the relative permittivity of the first cladding layer 3 are greater than 0. The relative permittivity inside the slit 72 is less than 1 times the relative permittivity of the first cladding layer 3. In the optical modulator 1 according to Embodiment 1, the relative permittivity inside the slit 72 is smaller than the relative permittivity of the second cladding layer 7 and also smaller than the relative permittivity of the first cladding layer 3.

[0036] The above configuration makes it possible to reduce Vπ·L. More specifically, with the above configuration, when a voltage is applied between the first electrode 4 and the second electrode 5 on both sides of the optical waveguide 2, the electric field lines passing through the second cladding layer 7 between the first electrode 4 and the second electrode 5 are more likely to bend near the slit 72 to pass through the optical waveguide 2, and the electric field strength of the optical waveguide 2 becomes higher than the electric field strength inside the slit 72 of the second cladding layer 7. As a result, the electric field strength in the optical waveguide 2 is greater than when the slit 72 is not formed in the second cladding layer 7, making it possible to reduce Vπ·L.

[0037] Furthermore, in the optical modulator 1 according to Embodiment 1, the slit 72 in the second cladding layer 7 penetrates the second cladding layer 7 in the thickness direction of the second cladding layer 7. Also, when the width of the optical waveguide 2 (first optical waveguide 2) is W0 (see Figure 7) and the width of the slit 72 (slit width) is W1 (see Figure 7), W1 / W0 is 1.

[0038] With the above configuration, the electric field strength in the optical waveguide 2 can be increased, and Vπ・L can be further reduced.

[0039] Furthermore, in the optical modulator 1 according to Embodiment 1, when the thickness of the first cladding layer 3 is t2 in a cross-sectional view perpendicular to the optical propagation direction of the two optical waveguides 2 (first optical waveguide 2), and the thickness of the second region 73 (see Figure 7) which overlaps the first cladding layer 3 and differs from the first region in which the slit 72 is formed in the second cladding layer 7 is t1, then t1 / t2 is 1 or greater.

[0040] The above configuration makes it possible to suppress variations in Vπ・L. In the optical modulator 1 according to Embodiment 1, it is preferable that t1 / t2 is 1 or more and 5 or less.

[0041] Furthermore, in the optical modulator 1 according to Embodiment 1, when the shortest distance between the first cladding layer 3 and the first electrode 4 is defined as g1 and the reference thickness of the second cladding layer 7 is defined as t1 in a cross-sectional view perpendicular to the optical propagation direction of the optical waveguide 2 (first optical waveguide 2), t1 / g1 is 0.5 or greater.

[0042] The above configuration makes it possible to suppress variations in Vπ・L.

[0043] (4) Modifications of Embodiment 1 (4.1) Modification 1 The optical modulator 1 according to Modification 1 of Embodiment 1 will be described with reference to Figure 11. With respect to the optical modulator 1 according to Modification 1 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0044] The optical modulator 1 according to Modification 1 differs from the optical modulator 1 according to Embodiment 1 in that a first recess 74 is formed in the second cladding layer 7 between the first cladding layer 3 and the first electrode 4, and a second recess 75 is formed in the second cladding layer 7 between the first cladding layer 3 and the second electrode 5. The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5 where the second cladding layer 7 overlaps the first cladding layer 3 when viewed in plan from the Z-axis direction. The above-mentioned lengths ta, tb, and difference tc are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1 with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM (Scanning Electron Microscope). In the second cladding layer 7, the thickness of the region where the slit 72 is formed (first region) (0 in modified example 1) is thinner than the reference thickness.

[0045] The optical modulator 1 according to Modification 1, like the optical modulator 1 according to Embodiment 1, has a slit 72 in the second cladding layer 7 that overlaps the optical waveguide 2 (first optical waveguide 2), making it possible to reduce Vπ・L.

[0046] (4.2) Modification 2 The optical modulator 1 according to Modification 2 of Embodiment 1 will be described with reference to Figure 12. With respect to the optical modulator 1 according to Modification 2 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0047] In the optical modulator 1 according to the modified example 2, as shown in Figure 12, the width W1 of the slit 72 in the second cladding layer 7 is wider than the width W0 of the optical waveguide 2 (first optical waveguide 2), which is different from the optical modulator 1 according to embodiment 1.

[0048] Figure 13 is a graph showing the relationship between W1 / W0 and the normalized Vπ・L. In Figure 13, the horizontal axis is W1 / W0, and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. In Figure 13, Vπ・L0 is the value of Vπ・L when W1 / W0 = 0. Therefore, the vertical axis in Figure 13 is Vπ・L normalized by setting the value of Vπ・L0 when W1 = 0 to 100.

[0049] As can be seen from Figure 13, when W1 / W0 is between 0.15 and 2.1, Vπ・L can be reduced by 20% or more. Embodiment 1 is the case where W1 / W0 = 1, and Modification 2 is the case where 1 < (W1 / W0) ≤ 2.1.

[0050] Furthermore, as can be seen from Figure 13, when W1 / W0 is between 0.5 and 1.4, Vπ・L can be reduced by 30% or more.

[0051] (4.3) Modification 3 The optical modulator 1 according to Modification 3 of Embodiment 1 will be described with reference to Figure 14. With respect to the optical modulator 1 according to Modification 3 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0052] In the optical modulator 1 according to Modification 3, as shown in Figure 14, the width W1 (see Figure 2) of the slit 72 in the second cladding layer 7 is narrower than the width W0 (see Figure 2) of the optical waveguide 2 (first optical waveguide 2), which is the same as the optical modulator 1 according to Embodiment 1. The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5, viewed in a plan view from the Z-axis direction, where the second cladding layer 7 overlaps with the first cladding layer 3. The lengths ta, tb, and difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1 with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM.

[0053] As can be seen from Figure 13, Modification 3 can reduce Vπ・L by 20% or more when 0.15 ≤ (W1 / W0) < 1. Furthermore, Modification 3 can reduce Vπ・L by 30% or more when W1 / W0 is 0.5 or more and less than 1.

[0054] (4.4) Modification 4 The optical modulator 1 according to Modification 4 of Embodiment 1 will be described with reference to Figure 15. With respect to the optical modulator 1 according to Modification 4 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0055] The optical modulator 1 in modified example 4 differs from the optical modulator 1 in embodiment 1 in that the end face of the first cladding layer 3 and the end face of the first electrode 4 are in contact. The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5, viewed in plan from the Z-axis direction, where the second cladding layer 7 overlaps the first cladding layer 3. The lengths ta, tb, and difference tc described above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1 with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM. In the second cladding layer 7, the thickness (0 in modified example 4) of the region where the slit 72 is formed (first region) is thinner than the reference thickness.

[0056] The optical modulator 1 according to Modification 4, like the optical modulator 1 according to Embodiment 1, has a slit 72 in the second cladding layer 7 that overlaps the optical waveguide 2 (first optical waveguide 2), making it possible to reduce Vπ·L.

[0057] (4.5) Modification 5 The optical modulator 1 according to Modification 5 of Embodiment 1 will be described with reference to Figure 16. With respect to the optical modulator 1 according to Modification 5 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0058] In Modification 5, the second cladding layer 7 does not overlap with the first cladding layer 3 in the thickness direction. The first cladding layer 3 has a first main surface 31 that is in contact with the first main surface 201 of the optical waveguide material layer 20, and a second main surface 32 that is opposite to the first main surface 31. Modification 5 differs from Embodiment 1 in that the second cladding layer 7 does not cover the second main surface 32 of the first cladding layer 3, but covers two side surfaces 36 of the first cladding layer 3.

[0059] The optical modulator 1 according to Modification 5, like the optical modulator 1 according to Embodiment 1, has a slit 72 in the second cladding layer 7 that overlaps the optical waveguide 2 (first optical waveguide 2), making it possible to reduce Vπ・L.

[0060] (4.6) Modification 6 The optical modulator 1 according to Modification 6 of Embodiment 1 will be described with reference to Figure 17. With respect to the optical modulator 1 according to Modification 6 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0061] In modified example 6, the second cladding layer 7 does not overlap with the first electrode 4 in the thickness direction of the first electrode 4. Also, in modified example 6, the second cladding layer 7 does not overlap with the second electrode 5 in the thickness direction of the second electrode 5.

[0062] The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3, in the region A1 between the first electrode 4 and the second electrode 5 where the second cladding layer 7 overlaps with the first cladding layer 3 when viewed in plan from the Z-axis direction. The lengths ta, tb, and difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1 with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM. In the second cladding layer 7, the thickness of the region where the slit 72 is formed (first region) (0 in modified example 6) is thinner than the reference thickness.

[0063] The optical modulator 1 according to Modification 6, like the optical modulator 1 according to Embodiment 1, has a slit 72 in the second cladding layer 7 that overlaps the optical waveguide 2 (first optical waveguide 2), making it possible to reduce Vπ・L.

[0064] (4.7) Modification 7 The optical modulator 1 according to Modification 7 of Embodiment 1 will be described with reference to Figure 18. With respect to the optical modulator 1 according to Modification 7 of Embodiment 1, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 4) are denoted by the same reference numerals and their description is omitted.

[0065] The optical modulator 1 according to the modified example 7 differs from the optical modulator 1 according to the first embodiment in that the first cladding layer 3 includes a first portion 34 interposed between the second cladding layer 7 and the first electrode 4, and a second portion 35 interposed between the second cladding layer 7 and the second electrode 5, so that the second cladding layer 7 does not come into contact with the first electrode 4 and the second electrode 5.

[0066] In Modification 7, the reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5, viewed in plan from the Z-axis direction, where the second cladding layer 7 overlaps with the first cladding layer 3. The lengths ta, tb, and difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1 with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM. In the second cladding layer 7, the thickness (0 in Modification 7) of the region where the slit 72 is formed (first region) is thinner than the reference thickness.

[0067] The optical modulator 1 according to Modification 7, like the optical modulator 1 according to Embodiment 1, has a slit 72 in the second cladding layer 7 that overlaps the optical waveguide 2 (first optical waveguide 2), making it possible to reduce Vπ・L.

[0068] (Embodiment 2) The optical modulator 1A according to Embodiment 2 will be described with reference to Figures 19 to 21. With respect to the optical modulator 1A according to Embodiment 2, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted.

[0069] (1) In the optical modulator 1A according to the second embodiment of the configuration, the second cladding layer 7 has two slits 72A that overlap each of the two optical waveguides 2 in a cross-sectional view perpendicular to the optical propagation direction of the two optical waveguides 2. The two slits 72A are formed on the main surface 70 of the second cladding layer 7 and do not penetrate the second cladding layer 7 in the thickness direction of the second cladding layer 7.

[0070] As shown in Figure 21, in a cross-sectional view perpendicular to the optical propagation direction of the optical waveguide 2 (first optical waveguide 2), when the thickness of the first region 71 in the second cladding layer 7 where the slit 72A is formed is t0, and the reference thickness of the second cladding layer 7 is t1, then t0 / t1 is less than 0.8. The reference thickness t1 of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5 in a plan view from the Z-axis direction, as shown in Figure 20. The lengths ta, tb, and difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1A in a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM. Therefore, the reference thickness of the second cladding layer 7 is the maximum value of the difference tc in the second region 73 that overlaps with the first cladding layer 3 and differs from the first region 71 in the second cladding layer 7.

[0071] Figure 22 is a graph showing the relationship between normalized t0 and normalized Vπ・L. In Figure 22, the horizontal axis is t0 / t1 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. When t0 / t1 = 1, it is a comparative example in which the slit 72A is not formed. When t0 = 0 and t0 / t1 = 0, it is Embodiment 1. In Figure 22, Vπ・L0 is the value of Vπ・L when t0 / t1 = 1. Therefore, the vertical axis of Figure 22 is Vπ・L normalized with the value of Vπ・L0 when t0 / t1 = 1 set to 100.

[0072] Figure 22 shows that when t0 / t1 is less than 0.8, Vπ·L can be reduced compared to the comparative example. Also, Figure 22 shows that when t0 / t1 is 0.2 or less, Vπ·L can be reduced by more than 20% compared to the comparative example.

[0073] (2) The optical modulator 1A according to the second embodiment comprises an optical waveguide 2, a first cladding layer 3, a first electrode 4, a second electrode 5, and a second cladding layer 7. The first cladding layer 3 covers the optical waveguide 2. The first electrode 4 is spaced in the width direction away from the first end 21 in the width direction of the optical waveguide 2 and is arranged along the optical propagation direction of the optical waveguide 2. The second electrode 5 is spaced in the width direction away from the second end 22 in the width direction of the optical waveguide 2 and is arranged along the optical propagation direction of the optical waveguide 2. A voltage is applied between the second electrode 5 and the first electrode 4. The second cladding layer 7 covers the first cladding layer 3. The refractive index of the first cladding layer 3 is smaller than the refractive index of the optical waveguide 2. The relative permittivity of the second cladding layer 7 is larger than the relative permittivity of the first cladding layer 3. The second cladding layer 7 has a slit 72A formed on the main surface 70 of the second cladding layer 7 that overlaps the optical waveguide 2. The relative permittivity inside the slit 72A is smaller than the relative permittivity of the second cladding layer 7. In the optical modulator 1A according to Embodiment 2, the inside of the slit 72A is air, and the relative permittivity inside the slit 72A is approximately 1. In the optical modulator 1A according to Embodiment 2, the relative permittivity inside the slit 72A is smaller than the relative permittivity of the second cladding layer 7 and also smaller than the relative permittivity of the first cladding layer 3.

[0074] The above configuration makes it possible to improve Vπ·L. More specifically, with the above configuration, when a voltage is applied between the first electrode 4 and the second electrode 5 on both sides of the optical waveguide 2 (first optical waveguide 2), the electric field lines passing through the second cladding layer 7 between the first electrode 4 and the second electrode 5 are more likely to bend near the slit 72A to pass through the optical waveguide 2, and the electric field strength of the optical waveguide 2 becomes higher than the electric field strength inside the slit 72A of the second cladding layer 7. As a result, the electric field strength in the optical waveguide 2 is greater compared to the case where the slit 72A is not formed in the second cladding layer 7, making it possible to improve Vπ·L.

[0075] (3) Modifications of Embodiment 2 (3.1) Modification 1 The optical modulator 1A according to Modification 1 of Embodiment 2 will be described with reference to Figure 24. With respect to the optical modulator 1A according to Modification 1 of Embodiment 2, components that are the same as those in the optical modulator 1A according to Embodiment 2 (see Figures 19 to 21) are denoted by the same reference numerals and their description is omitted.

[0076] The optical modulator 1A according to the modified example 1 differs from the optical modulator 1A according to embodiment 2 in that, as shown in Figure 24, the width W1 of the slit 72A in the second cladding layer 7 is wider than the width W0 of the optical waveguide 2.

[0077] Figure 23 is a graph showing the relationship between normalized W1 and normalized Vπ・L, where W0 is the width of the optical waveguide 2, W1 is the width of the slit 72A in the second cladding layer 7, and t0 / t1 is a parameter. In Figure 23, the horizontal axis is W1 / W0 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100.

[0078] Figure 23 shows that if t0 / t1 is 0.2 or less, Vπ・L can be reduced by 20% or more when W1 / W0 is in the range of 0.9 to 1.6. Embodiment 2 is the case where W1 / W0 = 1, and Modification 1 is the case where 1 < (W1 / W0) ≤ 1.6.

[0079] Furthermore, Figure 23 shows that if t0 / t1 is 0.1 or less, Vπ・L can be reduced by 20% or more when W1 / W0 is in the range of 0.4 to 2.6.

[0080] (3.2) Modification 2 The optical modulator 1A according to Modification 2 of Embodiment 2 will be described with reference to Figure 25. With respect to the optical modulator 1A according to Modification 2 of Embodiment 2, components that are the same as those in the optical modulator 1A according to Embodiment 2 (see Figures 19 to 21) are denoted by the same reference numerals and their description is omitted.

[0081] In the optical modulator 1A according to the modified example 2, as shown in Figure 25, the width W1 of the slit 72A of the second cladding layer 7 is wider than the width W0 of the optical waveguide 2, and the two inner surfaces in the width direction of the slit 72A each coincide with the two surfaces of the first cladding layer 3, thus differing from the optical modulator 1A according to embodiment 2.

[0082] The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 (which is 0 at points where the inner surface in the width direction of the slit 72A coincides with the side surface of the first cladding layer 3, as shown in Figure 25) in the region A1 between the first electrode 4 and the second electrode 5 where the second cladding layer 7 overlaps with the first cladding layer 3 in a plan view from the Z-axis direction.

[0083] In the modified example 2, W1 / W0 is, for example, 3, but it can be seen that Vπ・L can be reduced if t0 / t1 (see Figures 21 and 23) is 0.7 or less.

[0084] (3.3) Modification 3 The optical modulator 1A according to Modification 2 of Embodiment 3 differs from the optical modulator 1A according to Embodiment 2 in that the width W1 of the slit 72A of the second cladding layer 7 is narrower than the width W0 of the optical waveguide 2.

[0085] In Modification 3, Figure 23 shows that if t0 / t1 is 0.2 or less, Vπ・L can be reduced by 20% or more when W1 / W0 is in the range of 0.9 or more and less than 1. Also in Modification 3, if t0 / t1 is 0.1 or less, Vπ・L can be reduced by 20% or more when W1 / W0 is in the range of 0.4 or more and less than 1.

[0086] (Embodiment 3) The optical modulator 1B according to Embodiment 3 will be described with reference to Figure 26. With respect to the optical modulator 1B according to Embodiment 3, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 26, the illustration of one of the two optical waveguides 2 described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0087] (1) The optical modulator 1B according to Embodiment 3 differs from the optical modulator 1 according to Embodiment 1 in that it further comprises a third cladding layer 8. The third cladding layer 8 covers the first cladding layer 3 and the second cladding layer 7. In this embodiment, a part of the third cladding layer 8 is located within the slit 72 of the second cladding layer 7, and the third cladding layer 8 is in contact with the first cladding layer 3. The third cladding layer 8 is also in contact with the second cladding layer 7.

[0088] The relative permittivity of the third cladding layer 8 is smaller than that of the second cladding layer 7. The refractive index of the third cladding layer 8 is smaller than the refractive index of each of the two optical waveguides 2. The refractive index of the third cladding layer 8 is smaller than the refractive index of the optical waveguide material layer 20.

[0089] The material of the third cladding layer 8 is, for example, SiO ２ The material of the third cladding layer 8 is SiO ２ Not limited to Al ２ O ３ , LaAlO ３ LaYO ３ ZnO, HfO ２ , MgO, Y ２ O ３ These may be oxides, polymers such as BCB (benzocyclobutene) and PI (polyimide). In this embodiment, the material of the third cladding layer 8 is the same as the material of the first cladding layer 3, but the material of the third cladding layer 8 may be different from the material of the first cladding layer 3.

[0090] Figure 27 is a graph showing the relationship between ε3 / ε2 and the normalized Vπ・L, where ε3 is the relative permittivity of the third cladding layer 8 and ε2 is the relative permittivity of the second cladding layer 7. In Figure 27, the horizontal axis is ε3 / ε2 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. Vπ・L0 is the value of Vπ・L when the relative permittivity of the third cladding layer is the same as that of the second cladding layer, i.e., ε3 / ε2 = 1. From Figure 27, it can be seen that when ε3 / ε2 is 0.6 or less, Vπ・L can be reduced by 10% or more, and when ε3 / ε2 is 0.3 or less, Vπ・L can be reduced by 20% or more. Therefore, in the optical modulator 1B of this embodiment, the relative permittivity of the third cladding layer 8 is preferably 0.6 times or less, and more preferably 0.3 times or less, than the relative permittivity of the second cladding layer 7.

[0091] Figure 28 is a graph showing the relationship between ε3 / ε1 and the normalized Vπ・L, where ε3 is the relative permittivity of the third cladding layer 8 and ε1 is the relative permittivity of the first cladding layer 3. In Figure 28, the horizontal axis is ε3 / ε1 and the vertical axis is {(Vπ・L) / (Vπ・L0)} × 100. Vπ・L0 is the value of Vπ・L when ε3 / ε1 = 3.6. From Figure 28, it can be seen that if ε3 / ε1 is greater than 0 and less than 3.6, Vπ・L can be reduced; if ε3 / ε1 is greater than 0 and 2.25 or less, Vπ・L can be reduced by 10% or more; and if ε3 / ε1 is greater than 0 and 1.3 or less, Vπ・L can be reduced by 20% or more. Therefore, in the optical modulator 1B of this embodiment, from the viewpoint of reducing Vπ・L by 10% or more, it is preferable that ε3 / ε1 is greater than 0 and 2.25 or less, and from the viewpoint of reducing Vπ・L by 20% or more, it is desirable that ε3 / ε1 is greater than 0 and 1.3 or less.

[0092] (2) Effects The optical modulator 1B according to Embodiment 3 includes a second cladding layer 7 covering the first cladding layer 3. The relative permittivity of the second cladding layer 7 is greater than that of the first cladding layer 3. The second cladding layer 7 has a slit 72 that overlaps the optical waveguide 2. In the optical modulator 1B according to Embodiment 3, the relative permittivity inside the slit 72 is smaller than that of the second cladding layer 7. The relative permittivity inside the slit 72 and the relative permittivity of the first cladding layer 3 are greater than 0. The relative permittivity inside the slit 72 is 2.25 times or less the relative permittivity of the first cladding layer 3.

[0093] The above configuration makes it possible to improve Vπ·L. More specifically, with the above configuration, when a voltage is applied between the first electrode 4 and the second electrode 5 on both sides of the optical waveguide 2 (first optical waveguide 2), the electric field concentration in the region overlapping the optical waveguide 2 in the second cladding layer 7 can be mitigated, the electric field strength in the optical waveguide 2 increases, and it becomes possible to improve Vπ·L.

[0094] Furthermore, the optical modulator 1B according to Embodiment 3 further comprises a third cladding layer 8 covering the first cladding layer 3 and the second cladding layer 7. The relative permittivity of the third cladding layer 8 is smaller than that of the second cladding layer 7.

[0095] According to the above configuration, it is possible to stabilize the impedance of the optical waveguide 2 and the optical confinement performance, thereby improving reliability. In the above configuration, the relative permittivity of the third cladding layer 8 is preferably 0.6 times or less of the relative permittivity of the second cladding layer 7, and more preferably 0.3 times or less. Also, in the above configuration, the relative permittivity of the third cladding layer 8 is greater than 0 times the relative permittivity of the second cladding layer 7.

[0096] (Embodiment 4) An optical modulator 1C according to Embodiment 4 will be described with reference to Figure 29. With respect to the optical modulator 1C according to Embodiment 4, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 29, the illustration of one of the two optical waveguides 2 (second optical waveguide 2) described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0097] (1) The optical modulator 1C according to Embodiment 4 differs from the optical modulator 1 according to Embodiment 1 in that the first cladding layer 3 has two second slits 33 formed therein that communicate with the two slits 72 (hereinafter also referred to as the first slits 72) of the second cladding layer 7. Note that in Figure 29, only one of the two first slits 72 is shown, and only one of the two second slits 33 is shown.

[0098] The first cladding layer 3 has a first main surface 31 that is in contact with the first main surface 201 of the optical waveguide material layer 20, and a second main surface 32 that is opposite to the first main surface 31. The first main surface 31 of the first cladding layer 3 is in contact with the two optical waveguides 2. In this embodiment, the two second slits 33 of the first cladding layer 3 are formed on the second main surface 32 of the first cladding layer 3 and do not penetrate the first cladding layer 3. Each of the two second slits 33 overlaps the optical waveguide 2 in the thickness direction of the corresponding optical waveguide 2 of the two optical waveguides 2. Also, each of the two second slits 33 overlaps the corresponding first slit 72 of the two first slits 72. In a direction parallel to the width direction of the optical waveguide 2, the opening width of the second slit 33 is the same as the opening width of the first slit 72. The statement "the opening width of the second slit 33 is the same as the opening width of the first slit 72" is not limited to the case where the opening width of the second slit 33 perfectly matches the opening width of the first slit 72, but is sufficient if the opening width of the second slit 33 is within the range of 90% to 110% of the opening width of the first slit 72. Furthermore, in the direction parallel to the width direction of the optical waveguide 2, the opening width of the second slit 33 is not limited to the same as the opening width of the first slit 72, but may be different from the opening width of the first slit 72. The opening width of the first slit 72 is the same as the slit width of slit 72 described in Embodiment 1.

[0099] (2) The optical modulator 1C according to the effect embodiment 4 includes a second cladding layer 7 covering the first cladding layer 3. The relative permittivity of the second cladding layer 7 is greater than that of the first cladding layer 3. The second cladding layer 7 has a slit 72 that overlaps the optical waveguide 2 (first optical waveguide 2).

[0100] The above configuration makes it possible to improve Vπ·L. More specifically, with the above configuration, when a voltage is applied between the first electrode 4 and the second electrode 5 on both sides of the optical waveguide 2, the electric field concentration in the region overlapping the optical waveguide 2 in the second cladding layer 7 can be mitigated, the electric field strength in the optical waveguide 2 increases, and it becomes possible to improve Vπ·L.

[0101] Furthermore, the optical modulator 1C has a second slit 33 formed in the first cladding layer 3 that communicates with the first slit 72 of the second cladding layer 7.

[0102] With the above configuration, the electric field strength in the optical waveguide 2 can be further increased, making it possible to further improve Vπ・L. In the optical modulator 1C, the deeper the second slit 33 of the first cladding layer 3, the thinner the first cladding layer 3 becomes on the optical waveguide 2. This makes it easier for electric field lines passing through the second cladding layer 7 to bend and enter the optical waveguide 2, making it possible to further increase the electric field strength in the optical waveguide 2. The second slit 33 may penetrate the first cladding layer 3. In this case, the main surface 23 of the optical waveguide 2 (see Figure 29) may be in contact with air (air cladding layer).

[0103] (Embodiment 5) An optical modulator 1D according to Embodiment 5 will be described with reference to Figure 30. With respect to the optical modulator 1D according to Embodiment 5, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 30, the illustration of one of the two optical waveguides 2 (second optical waveguide 2) described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0104] (1) The optical modulator 1D according to the 5th embodiment differs from the optical modulator 1 according to the 1st embodiment in that the first cladding layer 3 has a multilayer structure and the second cladding layer 7 has a multilayer structure.

[0105] In this embodiment, the first cladding layer 3 includes a first layer 301 and a second layer 302 laminated on the first layer 301. The refractive index of each of the first layer 301 and the second layer 302 is smaller than the refractive index of the optical waveguide material layer 20.

[0106] The material of the second layer 302 is different from, but may be the same as, the material of the first layer 301. The materials of the first layer 301 and the second layer 302 are, for example, SiO ２ Al ２ O ３ , LaAlO ３ LaYO ３ ZnO, HfO ２ , MgO, Y ２ O ３ The material is selected from the group consisting of BCB (benzocyclobutene) and PI (polyimide).

[0107] In this embodiment, the second cladding layer 7 includes a third layer 701 and a fourth layer 702 laminated on the third layer 701.

[0108] The material of the fourth layer 702 is different from, but may be the same as, the material of the third layer 701. The materials of the third layer 701 and the fourth layer 702 are, for example, SrTiO ３ (Strontium titanate), BaTiO ３ (Barium titanate), PbLaTiO ３ (Lead lanthanum titanate), PZT (lead titanium zirconate), PLZT (lead titanium lanthanum zirconate), LiNbO ３ (Lithium niobate), LiTaO ３ (Lithium tantalate), KNbO ３ (Potassium niobate), PbTiO ３ (Lead titanate), PKNO (lead potassium niobate), PMN (lead magnesium niobate), Bi ４ Ti ３ O １２ (Bismuth titanate), BST (Barium strontium titanate), KLN (Potassium lanthanum niobate), Al ２ O ３ , LaAlO ３ LaYO ３ ZnO, HfO ２ , MgO, Y ２ O ３ , TiO ２ Ta ２ O ５ The material is selected from the group consisting of SiN and AlN.

[0109] The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region where the second cladding layer 7 overlaps the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5 in a plan view from the Z-axis direction. The above lengths ta, length tb, and difference tc are values measured from a cross-sectional SEM image obtained by observing a cross-section by cutting the optical modulator 1D with a plane orthogonal to the optical propagation direction of the optical waveguide 2 using SEM. In the second cladding layer 7, the thickness (0 in this embodiment) of the region (the first region) where the slit 72 is formed is thinner than the reference thickness.

[0110] (2) Effect Similar to the optical modulator 1 according to Embodiment 1, the optical modulator 1D according to Embodiment 5 has a slit 72 where the second cladding layer 7 overlaps the optical waveguide 2 (the first optical waveguide 2), so it is possible to improve Vπ·L.

[0111] (Embodiment 6) The optical modulator 1E according to Embodiment 6 will be described with reference to FIG. 31. Regarding the optical modulator 1E according to Embodiment 6, the same components as those of the optical modulator 1D (see FIG. 30) according to Embodiment 5 are denoted by the same reference numerals and the description thereof is omitted. In FIG. 31, illustration of one of the two optical waveguides 2 described in Embodiment 1 and illustration of one of the two first electrodes 4 are omitted.

[0112] (1) Configuration The optical modulator 1E according to Embodiment 6 is different from the optical modulator 1D according to Embodiment in that it further includes a fourth cladding layer 38 interposed between a part of the third layer 701 and a part of the fourth layer 702 of the second cladding layer 7.

[0113] The material of the fourth cladding layer 38 is, for example, SiO ２ etc. The material of the fourth cladding layer 38 is not limited to SiO ２ and may be Al ２ O ３ , LaAlO ３ , LaYO ３ , ZnO, HfO ２ , MgO, Y ２ O ３These may be oxides, polymers such as BCB (benzocyclobutene) and PI (polyimide).

[0114] The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between {(length tb2 from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3) + (length tb1 of the fourth cladding layer 38 in the Z-axis direction)} in the region A1 between the first electrode 4 and the second electrode 5 where the second cladding layer 7 overlaps with the first cladding layer 3 when viewed in plan from the Z-axis direction. The difference tc is tc1 + tc2 shown in Figure 31. The lengths ta, tb2, tb1 and the difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1E with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM. In the second cladding layer 7, the thickness (0 in this embodiment) of the region where the slit 72 is formed (first region) is thinner than the reference thickness.

[0115] (2) Effects The optical modulator 1E according to Embodiment 6, like the optical modulator 1D according to Embodiment 5, has a slit 72 in the second cladding layer 7 that overlaps the optical waveguide 2 (first optical waveguide 2), so that Vπ・L can be reduced.

[0116] (Embodiment 7) The optical modulator 1F according to Embodiment 7 will be described with reference to Figure 32. With respect to the optical modulator 1F according to Embodiment 7, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 32, the illustration of one of the two optical waveguides 2 described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0117] (1) The optical modulator 1F according to the 7th embodiment differs from the optical modulator 1 according to the 1st embodiment in that the first electrode 4 and the second electrode 5 are arranged on the second main surface 202 of the optical waveguide material layer 20.

[0118] The first electrode 4 is spaced apart in the width direction of the optical waveguide 2 from the first end 21 in the width direction of the optical waveguide 2 and is arranged along the optical propagation direction of the optical waveguide 2. The second electrode 5 is spaced apart in the width direction of the optical waveguide 2 from the second end 22 in the width direction of the optical waveguide 2 and is arranged along the optical propagation direction of the optical waveguide 2. In this embodiment, the first electrode 4 and the second electrode 5 are covered with a cladding layer 9. The reference thickness t1 of the second cladding layer 7 (see Figure 7) is the maximum value of the difference between the length from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5 in a plan view from the Z-axis direction, where the second cladding layer 7 overlaps with the first cladding layer 3.

[0119] (2) Effects The optical modulator 1F according to Embodiment 7, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ・L.

[0120] (3) Modification of Embodiment 7 In the modified embodiment, one of the first electrode 4 and the second electrode 5 may be placed on the second main surface 202 of the optical waveguide material layer 20, and the other may be placed on the first main surface 201 of the optical waveguide material layer 20.

[0121] (Embodiment 8) The optical modulator 1G according to Embodiment 8 will be described with reference to Figure 33. With respect to the optical modulator 1G according to Embodiment 8, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 33, the illustration of one of the two optical waveguides 2 described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0122] (1) The optical modulator 1G according to the configuration embodiment 8 differs from the optical modulator 1 according to embodiment 1 in that the first electrode 4 and the second electrode 5 are arranged across the first main surface 201 and the second main surface 202 of the optical waveguide material layer 20.

[0123] In this embodiment, the first electrode 4 and the second electrode 5 are U-shaped in a cross-sectional view perpendicular to the optical propagation direction (parallel to the Y-axis) of the optical waveguide 2, and are in contact with both the first main surface 201 and the second main surface 202 of the optical waveguide material layer 20. Furthermore, in each of the first electrode 4 and the second electrode 5, the portion located on the second main surface 202 of the optical waveguide material layer 20 is covered by the cladding layer 9. The reference thickness t1 of the second cladding layer 7 (see Figure 7) is the maximum difference between the length from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 in the region A1 between the first electrode 4 and the second electrode 5 in a plan view from the Z-axis direction, where the second cladding layer 7 overlaps with the first cladding layer 3.

[0124] (2) Effects The optical modulator 1G according to Embodiment 8, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ・L.

[0125] (Embodiment 9) The optical modulator 1H according to Embodiment 9 will be described with reference to Figure 34. With respect to the optical modulator 1H according to Embodiment 9, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 34, the illustration of one of the two optical waveguides 2 described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0126] (1) The optical modulator 1H according to the 9th embodiment differs from the optical modulator 1 according to the 1st embodiment in that it is equipped with a first electrode 4H and a second electrode 5H instead of the first electrode 4 and second electrode 5 of the optical modulator 1 according to the 1st embodiment, and further includes a third electrode 14H and a fourth electrode 15H.

[0127] The materials of the first electrode 4H, the second electrode 5H, the third electrode 14H, and the fourth electrode 15H are, for example, the same as the materials of the first electrode 4 and the second electrode 5 of the optical modulator 1 according to Embodiment 1.

[0128] In this embodiment, the third electrode 14H, the first electrode 4H, the optical waveguide 2, the second electrode 5H, and the fourth electrode 15H are arranged in the direction along the width direction of the optical waveguide 2 (parallel to the X-axis), in the order of third electrode 14H, first electrode 4H, optical waveguide 2, second electrode 5H, and fourth electrode 15H. In the optical modulator 1H of this embodiment, the third electrode 14H is the ground electrode, the first electrode 4H is the first signal electrode, the second electrode 5H is the second signal electrode, and the fourth electrode 15H is the ground electrode. In the optical modulator 1H of this embodiment, a differential signal voltage is applied between the first electrode 4H and the second electrode 5H.

[0129] The second cladding layer 7 covers the first cladding layer 3, the first electrode 4H, the second electrode 5H, the third electrode 14H, and the fourth electrode 15H, and has a slit 72 in the region that overlaps with the optical waveguide 2 in the thickness direction of the optical waveguide 2.

[0130] The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3, in the region A1 between the first electrode 4H and the second electrode 5H, viewed in a plan view from the Z-axis direction, where the second cladding layer 7 overlaps with the first cladding layer 3. The lengths ta, tb, and difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1H with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM.

[0131] (2) Effect The optical modulator 1H according to Embodiment 9, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ・L.

[0132] (Embodiment 10) An optical modulator 1I according to Embodiment 10 will be described with reference to Figure 35. With respect to the optical modulator 1I according to Embodiment 10, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figure 35, the illustration of one of the two optical waveguides 2 described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted.

[0133] (1) The optical modulator 1I according to Embodiment 10 differs from the optical modulator 1 according to Embodiment 1 in that the first electrode 4 and the second electrode 5 are arranged across the first main surface 201 of the optical waveguide material layer 20 and a part of the second cladding layer 7. In Embodiment 10, the second cladding layer 7 has a first main surface 711 that is in contact with the first main surface 201 of the optical waveguide material layer 20, and a second main surface 712 that is opposite to the first main surface 711. In Embodiment 10, the first electrode 4 and the second electrode 5 cover a part of the second main surface 712 of the second cladding layer 7. The reference thickness of the second cladding layer 7 is the maximum value of the difference tc between the length ta from the top surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3 and the length tb from the bottom surface of the second cladding layer 7 to the bottom surface of the first cladding layer 3, in the region A1 between the first electrode 4 and the second electrode 5 where the second cladding layer 7 overlaps with the first cladding layer 3 when viewed in a plan view from the Z-axis direction. The lengths ta, tb, and difference tc mentioned above are values ​​measured from the cross-sectional SEM image obtained by cutting the optical modulator 1I with a plane perpendicular to the optical propagation direction of the optical waveguide 2 and observing the cross-section with an SEM.

[0134] (2) Effects The optical modulator 1I according to Embodiment 10, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ・L.

[0135] (Embodiment 11) The optical modulator 1J according to Embodiment 11 will be described with reference to Figures 36 to 38. With respect to the optical modulator 1J according to Embodiment 11, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figures 36 to 38, the illustration of one of the two optical waveguides 2 described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 is omitted. In Figures 37 and 38, the region A1 of the second cladding layer 7 is the region between the first electrode 4 and the second electrode 5 in a plan view from the Z-axis direction.

[0136] (1) The optical modulator 1J according to Embodiment 11 differs from the optical modulator 1 according to Embodiment 1 in that a part of the second cladding layer 7 is removed in order to adjust the impedance or the effective refractive index for high-frequency signals. Therefore, in this embodiment, as shown in Figures 37 and 38, the cross-sectional shape perpendicular to the optical propagation direction (Y-axis direction) of the optical waveguide 2 is not constant. Furthermore, in an optical modulator where the cross-sectional shape perpendicular to the optical propagation direction of the optical waveguide is constant and there is no second cladding layer, the impedance and the effective refractive index for high-frequency signals depend greatly on the distance between the first electrode and the second electrode, thus limiting the adjustment range. In contrast, the optical modulator 1J according to Embodiment 11 allows for adjustment of the impedance and the effective refractive index for high-frequency signals regardless of whether the relative permittivity of the second cladding layer 7, the shape of the second cladding layer 7, or the shape of the slit 72 in the second cladding layer 7 is changed, thus providing a high degree of design freedom and a wide adjustment range for impedance and the effective refractive index for high-frequency signals.

[0137] (2) Effects The optical modulator 1J according to Embodiment 11, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7. By devising the shape of the second cladding layer 7 and the slit 72, the electric field strength of the optical waveguide 2 can be increased, Vπ・L can be reduced, and the driving voltage of the optical modulator 1J can be reduced.

[0138] (3) Modified Example of Embodiment 11 The optical modulator 1J according to a modified example of Embodiment 11 will be described with reference to Figure 39. With respect to the optical modulator 1J according to a modified example of Embodiment 11, components that are the same as those in the optical modulator 1J according to Embodiment 11 (see Figures 36 to 38) are denoted by the same reference numerals and their description is omitted.

[0139] In the modified optical modulator 1J, as shown in Figure 39, the shape of the removed portion of the second cladding layer 7 differs from that of the optical modulator 1J in Embodiment 11. The cross-sectional view along line XXXVII-XXXXVII in Figure 39 is the same as that in Figure 37. Also, the cross-sectional view along line XXXVIII-XXXXVIII in Figure 39 is the same as that in Figure 38.

[0140] The optical modulator 1J according to a modified example of Embodiment 11, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which allows the electric field strength of the optical waveguide 2 to be increased and reduces Vπ・L.

[0141] (Embodiment 12) The optical modulator 1K according to Embodiment 12 will be described with reference to Figures 40 to 42. With respect to the optical modulator 1K according to Embodiment 12, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figures 40 to 42, the illustration of one of the two optical waveguides 2 (see Figure 1) described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 (see Figure 1) is omitted.

[0142] (1) The optical modulator 1K according to the configuration embodiment 12 differs from the optical modulator 1 according to embodiment 1 in that, as shown in Figures 40 and 42, a portion of the second cladding layer 7 other than the slit 72 is removed in order to adjust the impedance or the effective refractive index for high-frequency signals. Therefore, in the optical modulator 1K of this embodiment, as shown in Figures 40 to 42, the shape of the second cladding layer 7 is not constant in the cross section perpendicular to the optical propagation direction (direction parallel to the Y axis) of the optical waveguide 2. At the position of the cross section in Figure 41, the slit 72 is formed in the second cladding layer 7, whereas at the position of the cross section in Figure 42, the second cladding layer 7 is removed along the entire length in the X-axis direction. The optical modulator 1K according to Embodiment 12 allows for adjustment of impedance and effective refractive index for high-frequency signals regardless of whether the dielectric constant of the second cladding layer 7, the shape of the second cladding layer 7, the shape of the slits 72 in the second cladding layer 7, or the arrangement range of the second cladding layer 7 is changed. Therefore, it offers a high degree of design flexibility and a wide adjustment range for impedance and effective refractive index for high-frequency signals.

[0143] Furthermore, the optical modulator 1K according to Embodiment 12 differs from the optical modulator 1 according to Embodiment 1 in that, as shown in Figures 40 to 42, the shapes of the first electrode 4 and the second electrode 5 are different from the shapes of the first electrode 4 and the second electrode 5 (elongated shape) in the optical modulator 1 according to Embodiment 1, in order to adjust the impedance or the effective refractive index for high-frequency signals. Alternatively, the optical modulator 1K according to Embodiment 12 differs from the optical modulator 1 according to Embodiment 1 in that a part of each of the first electrode 4 and the second electrode 5 is removed. In the optical modulator 1K of this embodiment, as shown in Figures 41 and 42, the shapes of the first electrode 4 and the second electrode 5 are not constant in the cross section perpendicular to the optical propagation direction (direction parallel to the Y-axis) of the optical waveguide 2. In this embodiment, the distance between the first electrode 4 and the first end 21 of the optical waveguide 2 is different between the cross section in Figure 41 and the cross section in Figure 42. Furthermore, in this embodiment, the distance between the second electrode 5 and the second end 22 of the optical waveguide 2 differs between the cross-sectional position in Figure 41 and the cross-sectional position in Figure 42. Also, in this embodiment, the distance between the first electrode 4 and the second electrode 5 differs between the cross-sectional position in Figure 41 and the cross-sectional position in Figure 42. The optical modulator 1K according to Embodiment 12 allows for adjustment of the impedance and the effective refractive index for high-frequency signals even when the shapes of the two first electrodes 4 and the second electrode 5 are changed, thus providing a high degree of design freedom and a wide adjustment range for impedance and the effective refractive index for high-frequency signals.

[0144] (2) Effects The optical modulator 1K according to Embodiment 12, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ・L.

[0145] (Embodiment 13) The optical modulator 1L according to Embodiment 13 will be described with reference to Figures 43 to 46. With respect to the optical modulator 1L according to Embodiment 13, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figures 43 to 46, the illustration of one of the two optical waveguides 2 (see Figure 1) described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 (see Figure 1) is omitted.

[0146] (1) The optical modulator 1L according to the configuration embodiment 13 differs from the optical modulator 1 according to embodiment 1 in that, as shown in Figures 43 to 46, a portion of the second cladding layer 7 other than the slit 72 is removed in order to adjust the impedance or the effective refractive index for high-frequency signals. Therefore, in the optical modulator 1L of this embodiment, the shape of the second cladding layer 7 is not constant in the cross section perpendicular to the optical propagation direction (direction parallel to the Y axis) of the optical waveguide 2. At the cross section positions in Figure 44 and Figure 45, a portion of the second cladding layer 7 is removed, and the second cladding layer 7 is arranged over the first cladding layer 3, a portion of the first main surface 201 of the optical waveguide material layer 20, a portion of the first electrode 4, and a portion of the second electrode 5, whereas at the cross section position in Figure 46, the second cladding layer 7 is removed over the entire length in the X-axis direction. The optical modulator 1L according to Embodiment 13 allows for adjustment of the impedance and the effective refractive index for high-frequency signals regardless of whether the dielectric constant of the second cladding layer 7, the shape of the second cladding layer 7, the shape of the slits 72 in the second cladding layer 7, or the arrangement range of the second cladding layer 7 is changed. Therefore, it offers a high degree of design flexibility and a wide adjustment range for impedance and the effective refractive index for high-frequency signals.

[0147] Furthermore, the optical modulator 1L according to Embodiment 13 differs from the optical modulator 1 according to Embodiment 1 in that, as shown in Figures 43 to 46, the shapes of the first electrode 4 and the second electrode 5 are different from the shapes of the first electrode 4 and the second electrode 5 (elongated shape) in the optical modulator 1 according to Embodiment 1, in order to adjust the impedance or the effective refractive index for high-frequency signals. Alternatively, the optical modulator 1L according to Embodiment 13 differs from the optical modulator 1 according to Embodiment 1 in that a part of each of the first electrode 4 and the second electrode 5 is removed. In the optical modulator 1L of this embodiment, as shown in Figures 44 to 46, the shapes of the first electrode 4 and the second electrode 5 are not constant in the cross-section perpendicular to the optical propagation direction (direction parallel to the Y-axis) of the optical waveguide 2. In this embodiment, the shape of the first electrode 4 differs from that of the cross-section in Figure 44, Figure 45, and Figure 46. Furthermore, in this embodiment, the shape of the second electrode 5 differs from that of the cross-sectional position in Figure 44, Figure 45, and Figure 46. In this embodiment, the distance between the first electrode 4 and the first end 21 of the optical waveguide 2 differs from that of the cross-sectional position in Figure 44 and Figure 46. Furthermore, in this embodiment, the distance between the second electrode 5 and the second end 22 of the optical waveguide 2 differs from that of the cross-sectional position in Figure 44 and Figure 46. Furthermore, in this embodiment, the distance between the first electrode 4 and the second electrode 5 differs from that of the cross-sectional position in Figure 44 and Figure 46. The optical modulator 1L according to Embodiment 13 has a high degree of design freedom and a wide adjustment range for impedance and effective refractive index for high-frequency signals, as it can adjust the impedance and effective refractive index for high-frequency signals even if the shapes of the two first electrodes 4 and second electrodes 5 are changed.

[0148] (2) Effects The optical modulator 1L according to Embodiment 13, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ·L.

[0149] (Embodiment 14) The optical modulator 1M according to Embodiment 14 will be described with reference to Figures 47 to 50. With respect to the optical modulator 1M according to Embodiment 14, components that are the same as those in the optical modulator 1 according to Embodiment 1 (see Figures 1 to 7) are denoted by the same reference numerals and their description is omitted. Note that in Figures 47 to 50, the illustration of one of the two optical waveguides 2 (see Figure 1) described in Embodiment 1 is omitted, and the illustration of one of the two first electrodes 4 (see Figure 1) is omitted.

[0150] (1) The optical modulator 1M according to the configuration embodiment 14 differs from the optical modulator 1 according to embodiment 1 in that, as shown in Figures 47 to 50, a portion of the second cladding layer 7 other than the slit 72 is removed in order to adjust the impedance or the effective refractive index for high-frequency signals. Therefore, in the optical modulator 1L of this embodiment, the shape of the second cladding layer 7 is not constant in a cross section perpendicular to the optical propagation direction (direction parallel to the Y axis) of the optical waveguide 2. At the position of the cross section in Figure 48, a portion of the second cladding layer 7 is removed, and the second cladding layer 7 is arranged over the first cladding layer 3, a portion of the first main surface 201 of the optical waveguide material layer 20, a portion of the first electrode 4, and a portion of the second electrode 5. At the position of the cross section in Figure 49, compared to the cross section in Figure 48, a portion of the second cladding layer 7 that overlaps with the first cladding layer 3 is removed. More specifically, at the cross-sectional position shown in Figure 49, the second cladding layer 7 has a third slit 77 that exposes a portion of the first cladding layer 3 in the region between the optical waveguide 2 and the first electrode 4 in a plan view from the thickness direction of the optical waveguide material layer 20. The length of the third slit 77 in the optical propagation direction of the optical waveguide 2 (parallel to the Y-axis) is shorter than the length of slit 72. Also at the cross-sectional position shown in Figure 49, the second cladding layer 7 has a fourth slit 78 that exposes a portion of the first cladding layer 3 in the region between the optical waveguide 2 and the second electrode 5 in a plan view from the thickness direction of the optical waveguide material layer 20. The length of the fourth slit 78 in the optical propagation direction of the optical waveguide 2 (parallel to the Y-axis) is shorter than the length of slit 72. At the cross-sectional position shown in Figure 50, the second cladding layer 7 is removed along its entire length in the X-axis direction. The optical modulator 1M according to Embodiment 14 allows for adjustment of impedance and effective refractive index for high-frequency signals regardless of whether the dielectric constant of the second cladding layer 7, the shape of the second cladding layer 7, the shape of the slits 72 in the second cladding layer 7, or the arrangement range of the second cladding layer 7 is changed. Therefore, it offers a high degree of design flexibility and a wide adjustment range for impedance and effective refractive index for high-frequency signals.

[0151] Furthermore, the optical modulator 1M according to Embodiment 14 differs from the optical modulator 1 according to Embodiment 1 in that, as shown in Figures 47 to 50, the shapes of the first electrode 4 and the second electrode 5 are different from the shapes of the first electrode 4 and the second electrode 5 (elongated shape) in the optical modulator 1 according to Embodiment 1, in order to adjust the impedance or the effective refractive index for high-frequency signals. Alternatively, the optical modulator 1M according to Embodiment 14 differs from the optical modulator 1 according to Embodiment 1 in that a part of each of the first electrode 4 and the second electrode 5 is removed. In the optical modulator 1M of this embodiment, as shown in Figures 48 to 50, the shapes of the first electrode 4 and the second electrode 5 are not constant in the cross-section perpendicular to the optical propagation direction (direction parallel to the Y-axis) of the optical waveguide 2. In this embodiment, the shape of the first electrode 4 differs from that of the cross-section in Figure 48, Figure 49, and Figure 50. Furthermore, in this embodiment, the shape of the second electrode 5 differs from that of the cross-sectional position in Figure 48, Figure 49, and Figure 50. In this embodiment, the distance between the first electrode 4 and the first end 21 of the optical waveguide 2 differs from that of the cross-sectional position in Figure 48 and Figure 50. Furthermore, in this embodiment, the distance between the second electrode 5 and the second end 22 of the optical waveguide 2 differs from that of the cross-sectional position in Figure 48 and Figure 50. Furthermore, in this embodiment, the distance between the first electrode 4 and the second electrode 5 differs from that of the cross-sectional position in Figure 48 and Figure 50. The optical modulator 1M according to Embodiment 14 has a high degree of design freedom and a wide adjustment range for impedance and effective refractive index for high-frequency signals, as it can adjust the impedance and effective refractive index for high-frequency signals even if the shapes of the two first electrodes 4 and second electrodes 5 are changed.

[0152] (2) Effect The optical modulator 1M according to Embodiment 14, like the optical modulator 1 according to Embodiment 1, has a slit 72 formed in the second cladding layer 7, which makes it possible to increase the electric field strength of the optical waveguide 2 and reduce Vπ・L.

[0153] (Other examples) Embodiments 1 to 14 described above are merely one of many embodiments of the present invention. Embodiments 1 to 14 described above can be modified in various ways depending on the design, etc., as long as the objective of the present invention is achieved, and may be combined as appropriate.

[0154] Optical modulators 1, 1B to 1M have two slits 72 in the second cladding layer 7 that overlap with two optical waveguides 2 (first optical waveguide 2, second optical waveguide 2), but it is sufficient to have at least one slit 72 that overlaps with the first optical waveguide 2. Optical modulators 1, 1B to 1M have one slit 72 formed for each of the multiple optical waveguides 2 in the second cladding layer 7, but two or more slits 72 may be formed for each of the multiple optical waveguides 2 so as to be aligned in the direction of optical propagation of the optical waveguide 2. Optical modulator 1A has two slits 72A in the second cladding layer 7 that overlap with two optical waveguides 2 (first optical waveguide 2, second optical waveguide 2), but it is sufficient to have at least one slit 72A that overlaps with the first optical waveguide 2. In the optical modulator 1A, one slit 72A is formed for each of the multiple optical waveguides 2 in the second cladding layer 7, but two or more slits 72A may be formed for each of the multiple optical waveguides 2 so as to be aligned in the direction of optical propagation of the optical waveguide 2.

[0155] Optical modulators 1A, 1C to 1M may further include the third cladding layer 8 of optical modulator 1B.

[0156] Optical modulators 1, 1A to 1M may have a configuration that does not include a cladding layer 9 and a substrate 10.

[0157] Optical modulators 1, 1A to 1M may have a cavity in the substrate 10 that overlaps the optical waveguide 2 in the thickness direction of the substrate 10. In this case, optical modulators 1, 1A to 1M can improve high-frequency characteristics. The cavity in the substrate 10 may penetrate through the substrate 10 in the thickness direction, or it may be formed from the main surface 101 of the substrate 10 to a predetermined depth position.

[0158] If the material of the optical waveguide material layer 20 is lithium niobate, each of the two optical waveguides 2 may be a Ti-diffusing type optical waveguide.

[0159] 1, 1A, 1B, 1C, 1D, 1E, 1F, 1G, 1H, 1I, 1J, 1K, 1L, 1M Optical modulator 2 Optical waveguide 21 First end 22 Second end 20 Optical waveguide material layer 3 First cladding layer 33 Second slit 4, 4H First electrode 5, 5H Second electrode 7 Second cladding layer 70 Main surface 71 First region 72 Slit (First slit) 72A Slit 73 Second region 8 Third cladding layer

Claims

1. The optical waveguide comprises: an optical waveguide; a first cladding layer covering the optical waveguide; a first electrode spaced in the width direction from a first end of the optical waveguide in the width direction and arranged along the optical propagation direction of the optical waveguide; a second electrode spaced in the width direction from a second end of the optical waveguide in the width direction and arranged along the optical propagation direction of the optical waveguide, to which a voltage is applied between the electrode and the first electrode; and a second cladding layer covering the first cladding layer, wherein the refractive index of the first cladding layer is smaller than that of the optical waveguide; the relative permittivity of the second cladding layer is larger than that of the first cladding layer; the second cladding layer has a slit formed on its main surface that overlaps the optical waveguide; the relative permittivity inside the slit is smaller than that of the second cladding layer; and the relative permittivity inside the slit and the relative permittivity of the first cladding layer are both greater than 0. An optical modulator in which the relative permittivity inside the slit is 2.25 times or less the relative permittivity of the first cladding layer.

2. The optical modulator according to claim 1, wherein the relative permittivity inside the slit is smaller than the relative permittivity of the first cladding layer.

3. The optical modulator according to claim 1 or 2, wherein the slit penetrates the second cladding layer in the thickness direction of the second cladding layer.

4. The optical modulator according to claim 3, wherein when the width of the optical waveguide is W0 and the width of the slit is W1, W1 / W0 is 0.15 or more and 2.1 or less.

5. The optical modulator according to claim 3, wherein when the width of the optical waveguide is W0 and the width of the slit is W1, W1 / W0 is 0.5 or more and 1.4 or less.

6. The optical modulator according to claim 1 or 2, wherein the slit does not penetrate the second cladding layer in the thickness direction of the second cladding layer.

7. The optical modulator according to claim 6, wherein when the thickness of the region in the second cladding layer in which the slit is formed is t0, and the reference thickness of the second cladding layer is t1, t0 / t1 is less than 0.

8.

8. The optical modulator according to claim 6, wherein when the thickness of the region in the second cladding layer in which the slit is formed is t0, and the reference thickness of the second cladding layer is t1, t0 / t1 is greater than 0 and 0.2 or less.

9. The optical modulator according to claim 7 or 8, wherein when the width of the optical waveguide is W0 and the width of the slit is W1, W1 / W0 is 0.4 or more and 2.6 or less.

10. The optical modulator according to claim 7 or 8, wherein when the width of the optical waveguide is W0 and the width of the slit is W1, W1 / W0 is 0.9 or more and 1.6 or less.

11. The optical modulator according to any one of claims 1 to 10, wherein when the thickness of the first cladding layer is t2 and the reference thickness of the second cladding layer is t1, t1 / t2 is 1 or more.

12. The optical modulator according to claim 11, wherein t1 / t2 is 5 or less.

13. An optical modulator according to any one of claims 1 to 12, wherein when the shortest distance between the first cladding layer and the first electrode is g1, and the reference thickness of the second cladding layer is t1, t1 / g1 is 0.5 or more.

14. The optical modulator according to any one of claims 7 to 13, wherein the reference thickness is the thickness of the second region that overlaps the first cladding layer, unlike the first region in which the slit is formed.

15. The optical modulator according to any one of claims 1 to 14, wherein the relative permittivity of the material of the second cladding layer is equal to or greater than the relative permittivity of the material of the optical waveguide.

16. The optical modulator according to any one of claims 1 to 5, wherein the first cladding layer has a second slit that overlaps with the optical waveguide and overlaps with the first slit, which is the slit of the second cladding layer.

17. The optical modulator according to any one of claims 1 to 16, further comprising a third cladding layer covering the first cladding layer and the second cladding layer, wherein the relative permittivity of the third cladding layer is smaller than that of the second cladding layer.

18. The optical modulator according to claim 17, wherein the relative permittivity of the third cladding layer is 0.6 times or less the relative permittivity of the second cladding layer.

19. The optical modulator according to claim 17, wherein the relative permittivity of the third cladding layer is 0.3 times or less the relative permittivity of the second cladding layer.

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