JP2012118384A - Optical modulator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an optical modulator exhibiting high performance in optical modulation characteristics and improved in optical insertion loss.SOLUTION: An optical modulator comprises an optical waveguide; a travelling-wave electrode to which a high frequency electric signal is applied; a bias electrode for applying a bias voltage to light; a high frequency electric signal interaction part for modulating a phase of the light by applying a high frequency electric signal to the travelling-wave electrode; and a biasing interaction part for adjusting the phase of the light by applying a bias voltage to the bias electrode, and both the high frequency electric signal interaction part and the biasing interaction part have ridge portions. A distance, on a top face of the ridge portion formed in the biasing interaction part, from an edge of an interaction optical waveguide to an edge of the top face is larger than a distance, on a top face of the ridge portion formed in the high frequency electric signal interaction part, from an edge of the interaction optical waveguide to an edge of the top face, and thus, propagation loss of light caused in the biasing interaction part is reduced.

Description

  The present invention relates to an optical modulator that uses an electro-optic effect to modulate light incident on an optical waveguide with a high-frequency electrical signal and emit it as an optical signal pulse, and has a small light insertion loss.

  In recent years, high-speed and large-capacity optical communication systems have been put into practical use. There is a demand for the development of a high-speed, small, low-cost, and highly stable optical modulator for incorporation into such a high-speed, large-capacity optical communication system.

As an optical modulator that meets such demands, a light modulator such as lithium niobate (LiNbO ₃ ) is used for a substrate having a so-called electro-optical effect (hereinafter abbreviated as an LN substrate) whose refractive index changes by applying an electric field. There is a traveling wave electrode type lithium niobate optical modulator (hereinafter abbreviated as an LN optical modulator) in which a waveguide and a traveling wave electrode are formed. This LN optical modulator is applied to a large capacity optical communication system of 2.5 Gbit / s and 10 Gbit / s because of its excellent chirping characteristics. Recently, application to a 40 Gbit / s ultra-high capacity optical communication system is also being studied.

  Hereinafter, an LN optical modulator using the electro-optic effect of lithium niobate that has been put to practical use or has been proposed will be described.

(First prior art)
FIG. 9 shows a schematic perspective view of a so-called ridge-type LN optical modulator disclosed in Patent Document 1, which is configured using a z-cut LN substrate, as a first conventional optical modulator. Here, FIG. 10 is a schematic top view of FIG. 9, and FIG. 11 is a schematic cross-sectional view taken along line AA ′ of FIGS. 9 and 10.

  An optical waveguide 3 is formed on the z-cut LN substrate 1. The optical waveguide 3 is an optical waveguide formed by thermally diffusing metal Ti at 1050 ° C. for about 10 hours, and constitutes a Mach-Zehnder interference system (or Mach-Zehnder optical waveguide). Accordingly, two interaction optical waveguides 3a and 3b, that is, two arms of the Mach-Zehnder optical waveguide are formed at a portion where the electrical signal and light of the optical waveguide 3 interact (referred to as an interaction portion).

A SiO ₂ buffer layer 2 is formed on the upper surface of the optical waveguide 3, and a traveling wave electrode 4 is formed on the upper surface of the SiO ₂ buffer layer 2 via a conductive layer 5. The conductive layer 5 is a conductive layer for suppressing a temperature drift caused by the pyroelectric effect peculiar to the LN optical modulator manufactured using the z-cut LN substrate 1, and usually a Si conductive layer is used. As the traveling wave electrode 4, a coplanar waveguide (CPW) having one central conductor 4a and two ground conductors 4b and 4c is used. Normally, the traveling wave electrode 4 is formed of Au, which is a noble metal material. The center conductor 4a takes various values, but in many cases is about 7 μm, and the gap between the center conductor 4a and the ground conductors 4b and 4c also takes various values, but is often about 15 μm. For simplification of explanation, the Si conductive layer 5 for suppressing temperature drift shown in FIG. 9 is omitted in FIGS. In the following, the Si conductive layer 5 is omitted and discussed. Reference numeral 6 denotes a high-frequency electric signal (or microwave) feeding line, which is a high-frequency connector or a microwave line. Reference numeral 7 denotes an output line for a high-frequency electric signal, which normally uses an electrical termination, but may be a high-frequency connector or a microwave line.

  In the region shown as I in FIG. 10, the high-frequency electric signal propagating through the center conductor 4a and the ground conductors 4b and 4c interacts with the light propagating through the two interaction optical waveguides 3a and 3b. It is called an interaction part for high-frequency electric signals (or simply an interaction part).

  In the first prior art, the recesses 9a, 9b and 9c (or ridges 8a and 8b) are formed by digging the z-cut LN substrate 1 by etching or the like. Here, 12 is a side wall of the ridge portion (here, 8a).

  By adopting this ridge structure, it is possible to realize excellent characteristics in the effective refractive index (or microwave effective refractive index), characteristic impedance, modulation band, driving voltage, etc. of a high-frequency electric signal (or microwave). . In FIG. 11, the depth of the recesses 9a, 9b, and 9c (or the height of the ridges 8a, 8b) is emphasized, but in actuality, the depth is about several μm, and the central conductor 4a In comparison with the thickness of the ground conductors 4b and 4c of several tens of micrometers, the value is small.

  Next, the operation of the LN optical modulator according to the first prior art will be described. In order to operate this LN optical modulator, it is necessary to apply a DC bias voltage and a high-frequency electric signal between the center conductor 4a and the ground conductors 4b and 4c.

  The voltage-light output characteristics shown in FIG. 12 are the voltage-light output characteristics of the LN optical modulator, and Vb is the DC bias voltage at that time. As shown in FIG. 12, the DC bias voltage Vb is normally set at the midpoint between the peak and bottom of the light output characteristic. In the first prior art, a DC bias voltage is also applied to the interaction part I where the high-frequency electrical signal and light interact, so that a capacitor is provided at the electrical terminal (not shown) provided at the output part of the high-frequency electrical signal. Therefore, it is necessary to provide the function of the bias T, and the structure becomes complicated.

(Second prior art)
FIG. 13 shows the second prior art. In order to eliminate the bias T required in the first prior art, the electrical termination (not shown) is only a resistor and a DC bias is newly provided with a DC bias. This is an LN optical modulator having a so-called bias separation structure that is applied to the action part (or simply the DC bias part) II. This structure includes a high-frequency electrical signal interaction unit I in which a high-frequency electrical signal interacts with the interaction optical waveguides 3a and 3b, and a DC bias unit II in which a DC bias voltage is applied to the interaction optical waveguides 3a and 3b. It is called a bias separation type structure. An example thereof is disclosed in Patent Document 2.

  14A and 14B are sectional views taken along lines BB ′ and CC ′ in FIG. Here, 4a ′ is a central conductor, and 4b ′ and 4c ′ are ground conductors. Reference numerals 9a ', 9b', and 9c 'denote concave portions of the DC bias portion, and ridge portions 8a' and 8b 'are formed. 11a and 11b are DC bias electrodes.

Here, the problem of the second prior art shown in FIGS. 13 and 14 will be considered. FIGS. 15A and 15B show enlarged views of the region indicated by III in FIG. 14A and IV in FIG. 14B, respectively. However, in order to make the discussion easy to understand, the illustration of the SiO ₂ buffer layer 2, the central conductor 4a ′, and the bias electrodes 11a and 11b is saved. Reference numeral 12 denotes a sidewall of the ridge portion 8a in the high-frequency electrical signal interaction portion I through which the high-frequency electrical signal propagates. Reference numeral 12 'denotes a sidewall of the ridge portion 8a' in the DC bias portion II.

15A, U is the distance between the end of the interaction optical waveguide 3b in the interaction portion I and the side wall 12 of the ridge portion (from the end of the interaction optical waveguide 3b on the top surface 13 of the ridge portion 8a to the end of the top surface). V is the distance between the end of the interactive optical waveguide 3b and the side wall 12 'of the ridge portion (the top surface 13' of the ridge portion 8a ') in the DC bias portion II to which the DC bias voltage is applied. (Distance from the end of the working optical waveguide 3b to the end of the top surface). Further, _{W 1} and _{W 2} are each a width of 13 'and the ridge portion 8a 8a' and the top surface 13 of the. FIGS. 16A and 16B show the field distributions of light propagating through the interactive optical waveguide 3b as 14 and 14 ′ with respect to the ridge portion 8a and the ridge portion 8a ′, respectively (FIG. 15 and FIG. 15). Same cross section).

In the second prior art shown in FIG. 16, the width W ₁ of the top surface 13 of the interaction part I is equal to the width W ₂ of the top surface 13 ′ of the DC bias part II. V in the interaction part II is equal to each other. Generally, the closer the effective refractive index of the high frequency electric signal to the equivalent refractive index of the light, the width W ₁ of the top face 13 of the ridge portion 8a in the interaction section I is narrow is desirable. As described above, in the conventional technology so far, the W ₂ width of the ridge portion 8a ′ of the DC bias portion II is also narrowed (or U and V are substantially equal and small), and therefore the side wall 12 of the ridge portion 8a ′. Due to the surface roughness of ′, light is scattered, which is one of the factors that increase the insertion loss of light.

JP-A-4-288518 JP 2008-122786 A

  As described above, there is an urgent need to develop an optical modulator that reduces an increase in light insertion loss caused by the side wall of the ridge portion of the DC bias portion.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide an optical modulator that has high performance in light modulation characteristics and improved in light insertion loss.

  In order to solve the above problems, an optical modulator according to claim 1 of the present invention includes a substrate having an electro-optic effect, an optical waveguide for guiding light formed on the substrate, A traveling-wave electrode formed on one surface and made up of a high-frequency electric signal center conductor and a ground conductor for applying a high-frequency electric signal for modulating the light, and a central conductor for applying a bias voltage to the light And a bias electrode made of a ground conductor, and the optical waveguide has a high frequency electrical signal interaction unit for modulating the phase of the light by applying the high frequency electrical signal to the traveling wave electrode, and A bias interaction unit for adjusting the phase of the light by applying a bias voltage to the bias electrode, and both the high-frequency electrical signal interaction unit and the bias interaction unit In the optical modulator having a ridge portion formed by a recess formed by digging at least a part of the substrate, the interaction optical waveguide on the top surface of the ridge portion formed in the bias interaction portion. The distance from the end to the end of the top surface is greater than the distance from the end of the interactive optical waveguide to the end of the top surface at the top surface of the ridge portion formed in the high-frequency electrical signal interaction portion It is characterized by that.

  In order to solve the above problems, an optical modulator according to claim 2 of the present invention includes a substrate having an electro-optic effect, an optical waveguide for guiding light formed on the substrate, and the substrate. A traveling-wave electrode formed on one surface and made up of a high-frequency electric signal center conductor and a ground conductor for applying a high-frequency electric signal for modulating the light, and a central conductor for applying a bias voltage to the light And a bias electrode made of a ground conductor, and the optical waveguide has a high frequency electrical signal interaction unit for modulating the phase of the light by applying the high frequency electrical signal to the traveling wave electrode, and A bias interaction unit for adjusting the phase of the light by applying a bias voltage to the bias electrode, and both the high-frequency electrical signal interaction unit and the bias interaction unit In the optical modulator including a ridge portion formed by a recess formed by digging up at least a part of the substrate, an end of the top surface of the ridge portion formed in the bias interaction portion is the ridge portion. Of the top surface of the ridge portion formed in the high frequency electrical signal interaction portion is determined at a position where a surface extending the top surface of the ridge portion and a surface extending the side wall surface of the ridge portion in the vicinity of the top surface intersect. An end is determined at a position where a surface extending the top surface of the ridge portion and a surface extending the side wall surface of the ridge portion in the vicinity of the top surface intersect, and the ridge portion formed in the bias interaction portion The distance from the end of the interactive optical waveguide on the top surface to the end of the top surface is the end of the interactive optical waveguide on the top surface of the ridge portion formed in the high-frequency electrical signal interaction portion. It is characterized in greater than the distance to the edge of the top surface.

  In order to solve the above-described problem, an optical modulator according to a third aspect of the present invention is the optical modulator according to the first or second aspect, wherein all of the interactive optical waveguides are arranged in a light guiding direction. It is characterized in that it is formed in the ridge portion having the concave portions on both sides along the direction.

  In order to solve the above-mentioned problems, an optical modulator according to a fourth aspect of the present invention is the optical modulator according to the first or second aspect, wherein at least one of the interactive optical waveguides is a light guiding direction. Is formed in the ridge portion having the concave portion on one side in the direction along the line.

  In order to solve the above problems, an optical modulator according to claim 5 of the present invention is the optical modulator according to any one of claims 1 to 4, wherein the substrate is made of lithium niobate. It is a feature.

  In the optical modulator according to the present invention, the distance between the optical waveguide in the DC bias portion and the side wall of the ridge portion is wider than the distance between the optical waveguide in the high frequency electrical signal interaction portion and the side wall of the ridge portion, or DC By making the width of the top surface of the ridge portion in the bias portion wider than the width of the top surface of the ridge portion in the high frequency electrical signal interaction portion where the high frequency electrical signal and light interact, light propagation loss in the DC bias portion There is an excellent advantage of reducing the insertion loss of light as an optical modulator.

1 is a top view showing a schematic configuration of an optical modulator according to a first embodiment of the present invention. (A) Cross-sectional view taken along the line DD ′ of FIG. 1, (b) Cross-sectional view taken along the line EE ′ of FIG. (A) The figure which added the field distribution of the propagating light to Fig.2 (a), (b) The figure which added the field distribution of the propagating light to FIG.2 (b) The figure explaining the principle of this invention Partial enlarged view of the ridge Sectional drawing of DC bias part of the optical modulator concerning the 1st Embodiment of this invention Sectional drawing of DC bias part of the optical modulator concerning the 2nd Embodiment of this invention Sectional drawing of DC bias part of the optical modulator concerning the 3rd Embodiment of this invention The perspective view which shows schematic structure about the optical modulator of 1st prior art The top view which shows schematic structure about the optical modulator of 1st prior art Sectional view in AA 'of FIG. The figure explaining the principle of operation of an optical modulator The top view which shows schematic structure about the optical modulator of 2nd prior art (A) Sectional view taken along line BB 'in FIG. 13, (b) Sectional view taken along line CC' in FIG. (A) Enlarged view of III in FIG. 14, (b) Enlarged view of IV in FIG. (A) The figure which added the field distribution of the propagating light to Fig.15 (a), (b) The figure which added the field distribution of the propagating light to FIG.15 (b),

  Hereinafter, embodiments of the present invention will be described. However, since the same reference numerals as those in the related art shown in FIGS. 9 to 16 correspond to the same functional units, description of the functional units having the same reference numerals is omitted here. To do.

(First embodiment)
FIG. 1 is a top view of a first embodiment of the present invention. 2A and 2B are sectional views taken along line DD 'and EE' in FIG. 1, respectively. 2A and 2B are sectional views of the interactive optical waveguide 3b as in FIGS. 15A and 15B. As can be seen from FIG. 2A corresponding to the high-frequency electrical signal interaction section I, as in the first and second prior arts, the center conductor 4a ′ and the ground conductors 4b ′ and 4c ′ are formed. The width W ₁ of the top surface 13 of the ridge portion 8a is narrowed so that the effective refractive index of the high-frequency electric signal propagating through the traveling wave electrode is close to the equivalent refractive index of the light propagating through the high-frequency electric signal interaction optical waveguide 3b. is doing. As a result, high-speed optical modulation is possible as in the prior art.

On the other hand, the distance V ′ between the interaction optical waveguide 3b of FIG. 2B corresponding to the DC bias portion II and the side wall 12 ′ of the ridge portion 8a ′ is shown in FIG. The distance U is sufficiently larger than the distance U between the interaction optical waveguide 3b and the side wall 12 of the ridge portion 8a. Alternatively, the width W ₂ ′ of the top surface 13 ′ of the ridge portion 8 a ′ in the DC bias portion II is made sufficiently wider than the width W ₁ of the top surface 13 of the ridge portion 8 a in the interaction portion I (W ₁ <W ₂ ').

FIGS. 3A and 3B correspond to FIGS. 2A and 2B, respectively, and show the field distributions 14 and 14 'of the propagating light. As can be seen from FIG. 3B, in this embodiment, the width W ₂ ′ of the top surface 13 ′ of the ridge portion 8 a ′ is sufficiently wider than the field distribution 14 ′ of light propagating through the optical waveguide 3 b in the DC bias portion.

  FIG. 4 shows the propagation loss of light in the interactive optical waveguide 3b when the distance V ′ between the interactive optical waveguide 3b and the side wall 12 ′ of the ridge 8a ′ is a variable (the point is the second prior art). The same characteristics). As can be seen from this figure, in the first embodiment, the distance V ′ between the interaction optical waveguide 3b and the side wall 12 ′ of the ridge 8a ′ can be made sufficiently large. An increase in light insertion loss due to the roughness can be reduced. Preferably, 1 μm is required as V ′, and if it is 2 μm or more, the characteristics are remarkably improved, and if it is 3 μm or more, it is most preferable.

  FIG. 6 is a cross-sectional view (cross-section EE ′ of FIG. 1) of the DC bias portion in the first embodiment of the present invention. Although the above description has been given using the ridge portion 8a ', it goes without saying that the present configuration can also be applied to the ridge portion 8b', and FIG. 6 shows an embodiment thereof.

  In the above description, the side wall and the top surface of the ridge portion have been described as intersecting at a flat surface, but the present invention is not limited to this. As shown in the partially enlarged view of the ridge portion in FIG. 5, the intersection of the side wall and the top surface may be R-shaped. In this case, the end of the top surface is determined at a position where a surface obtained by extending the top surface and a surface obtained by extending the side wall near the top surface intersect.

(Second Embodiment)
FIG. 7 is a cross-sectional view of the DC bias portion according to the second embodiment of the present invention (corresponding to the EE ′ cross section of FIG. 1). In this embodiment, the interaction optical waveguide 3b has a complete ridge structure in which recesses are formed on both sides like 8a '. However, the interaction optical waveguide 3a has a recess only on one side like 8b''. It is not a complete ridge structure.

  Even if the ridge structure is not perfect as described above, the present invention can be applied by setting the distance V ′ (on the concave portion 9b ′ side) in the ridge portion 8b ″.

(Third embodiment)
FIG. 8 is a cross-sectional view of the DC bias portion according to the third embodiment of the present invention (corresponding to the EE ′ cross-section of FIG. 1). In the present embodiment, the ridge portions 8a ″ and 8b ″ in which the interactive optical waveguides 3a and 3b are formed do not have a complete ridge structure.

  Also in the present embodiment, the present invention can be applied by setting the distance V ′ (on the concave portion 9b ′ side) as in the second embodiment.

(Each embodiment)
The feature of the present invention is that the distance from the optical waveguide to the side wall of the ridge (in other words, the distance from the light propagating through the optical waveguide to the side wall of the ridge) in the high frequency electrical signal interaction unit and the DC bias unit is made different. It is a characteristic, and a structure in which the width of the top surface of the ridge portion is different in each of the high frequency electrical signal interaction portion and the DC bias portion is preferable.

  In practice, the increase in insertion loss due to the roughness of the side wall of the ridge portion is determined by the distance between the edge of the field distribution of light propagating through the interactive optical waveguide and the side wall of the ridge portion. In order to achieve this, “the magnitude relation about the distance between the end of the interaction optical waveguide in the interaction part I and the DC bias part II and the side wall of the ridge” and “the edge of the field distribution of light propagating through the interaction optical waveguide; The discussion has been made on the assumption that “the magnitude relationship regarding the distance from the side wall of the ridge portion” is the same. Therefore, in the present invention, the distance between the edge of the light field distribution propagating through the interaction optical waveguide and the side wall of the ridge portion is determined by the distance between the edge of the light field distribution propagating through the interaction optical waveguide and the side wall of the ridge portion. It may be replaced with a distance.

  Further, although the discussion has been made on the assumption that the widths of the optical waveguides in the interaction part I and the DC bias part II are equal to each other, they may be different from each other, and in that case, the interaction optical waveguide and the ridge side wall may be different. The present invention can be applied by setting the distance or the width of the top surface of the ridge portion to a predetermined value.

Although the Mach-Zehnder optical waveguide is used as an example of the branched optical waveguide, it goes without saying that the present invention can be applied to other branched / multiplexed optical waveguides such as a directional coupler. The present invention can also be applied to other optical waveguides. As a method for forming the optical waveguide, various methods for forming the optical waveguide such as a proton exchange method can be applied in addition to the Ti thermal diffusion method, and various materials other than SiO ₂ such as Al ₂ O ₃ can be applied as the buffer layer.

  In addition, the present invention does not depend on the electrode structure of the DC bias unit, and it goes without saying that the present invention can be applied to various electrode structures such as a CPW structure, an asymmetric coplanar strip (ACPS) structure, and a symmetric coplanar strip (CPS) structure.

1: z-cut LN substrate (LN substrate)
2: SiO ₂ buffer layer (buffer layer)
3: Mach-Zehnder optical waveguide (optical waveguide)
3a, 3b: interaction optical waveguide constituting Mach-Zehnder optical waveguide 4: traveling wave electrode 4a, 4a ′: central conductor 4b, 4b ′, 4c, 4c ′: ground conductor 5: Si conductive layer 6: high-frequency electric signal feeder 7: High-frequency electric signal output lines 8a, 8b: Ridge portions in the interaction portion I 8a ′, 8a ″, 8b ′, 8b ″: Ridge portions in the DC bias portion II 9a, 9b, 9c: In the interaction portion I Concave part 9a ', 9b', 9c ': Concave part 11a, 11b: DC bias electrode 12, 12': Side wall of ridge part 13, 13 ': Top surface of ridge part 14, 14': Electric field of light Distribution I: High-frequency electrical signal interaction part (interaction part)
II: DC bias interaction section (DC bias section)
U, U ′, V, V ′: Distance between the interaction optical waveguide and the ridge side wall

Claims (5)

A substrate having an electro-optic effect, an optical waveguide for guiding light formed on the substrate, and a high-frequency electric signal formed on one surface side of the substrate for applying a high-frequency electric signal for modulating the light A traveling wave electrode composed of a center conductor and a ground conductor for electrical signals, and a bias electrode composed of a center conductor and a ground conductor for applying a bias voltage to the light,
The optical waveguide has a high frequency electrical signal interaction unit for modulating the phase of the light by applying the high frequency electrical signal to the traveling wave electrode, and a bias voltage to the bias electrode to apply the light. And a bias interaction unit for adjusting the phase of
In an optical modulator comprising a ridge formed by a recess formed by digging at least a part of the substrate into both the high-frequency electrical signal interaction unit and the bias interaction unit,
The distance from the end of the interaction optical waveguide to the end of the top surface on the top surface of the ridge portion formed in the bias interaction portion is the ridge portion formed in the high-frequency electrical signal interaction portion. An optical modulator characterized by being larger than the distance from the end of the interactive optical waveguide to the end of the top surface on the top surface of the optical modulator. A substrate having an electro-optic effect, an optical waveguide for guiding light formed on the substrate, and a high-frequency electric signal formed on one surface side of the substrate for applying a high-frequency electric signal for modulating the light A traveling wave electrode composed of a center conductor and a ground conductor for electrical signals, and a bias electrode composed of a center conductor and a ground conductor for applying a bias voltage to the light,
The optical waveguide has a high frequency electrical signal interaction unit for modulating the phase of the light by applying the high frequency electrical signal to the traveling wave electrode, and a bias voltage to the bias electrode to apply the light. And a bias interaction unit for adjusting the phase of
In an optical modulator comprising a ridge formed by a recess formed by digging at least a part of the substrate into both the high-frequency electrical signal interaction unit and the bias interaction unit,
At the end of the top surface of the ridge portion formed in the bias interaction portion, a surface obtained by extending the top surface of the ridge portion and a surface obtained by extending the side wall surface of the ridge portion in the vicinity of the top surface intersect. Determined by the position,
The end of the top surface of the ridge portion formed in the high frequency electrical signal interaction portion includes a surface extending the top surface of the ridge portion and a surface extending the side wall surface of the ridge portion in the vicinity of the top surface. Is determined at the position where
The distance from the end of the interactive optical waveguide to the end of the top surface of the top surface of the ridge portion formed in the bias interaction portion is the ridge formed in the high frequency electrical signal interaction portion. An optical modulator characterized by being larger than the distance from the end of the interactive optical waveguide to the end of the top surface on the top surface of the part.   3. The optical modulator according to claim 1, wherein all of the interactive optical waveguides are formed in the ridge portion having the concave portions on both sides in a direction along a light guiding direction. 4.   3. The optical modulator according to claim 1, wherein at least one of the interactive optical waveguides is formed in the ridge portion having the concave portion on one side in a direction along a light guiding direction. 4. .   The optical modulator according to any one of claims 1 to 4, wherein the substrate is made of lithium niobate.

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