Determination method and method for manufacturing an optical control element

Abstract

This optical control element has an optical waveguide formed using an electro-optic material. This determination unit involves a step for selecting, on the basis of required characteristics of the optical control element, formula (I) and / or formula (II) as the expression for calculating a performance index of an EO material at a wavelength λ; a step for calculating a performance index FOM1 and / or a performance index FOM2 using the expression selected in the selection step; and a step for determining, on the basis of the performance index of the EO material calculated in the calculation step, a wavelength band suitable for use of the optical control element. [In the formula, n is the index of refraction of the electro-optic material, r is the electro-optic coefficient of the electro-optic material, α is the propagation loss per unit length in a phase modulation region of the optical waveguide, and λ is the wavelength.]

Description

[Technical Field]

[0001] The present invention relates to a determination method for determining a suitable wavelength band when an electro-optic material is used in an optical control element, based on a novel figure of merit; a method for manufacturing an optical control element using this determination method; and an optical control element. [Background technology]

[0002] Inorganic ferroelectric materials such as lithium niobate (LiNbO3) are known to be used as electro-optical materials (EO materials) applicable to optical control elements such as optical modulators, optical switches, optical interconnects, optoelectronic circuits, wavelength converters, field sensors, THz wave generators / detectors, and optical phased arrays. However, inorganic ferroelectric materials have limitations in terms of high speed, miniaturization, and integration of optical control elements, and hybridization with semiconductor materials, which are advantageous for miniaturization and integration, is also difficult.

[0003] On the other hand, organic electro-optic polymers (organic EO polymers) exhibit a greater electro-optic effect compared to inorganic ferroelectric materials. Furthermore, organic EO polymers can operate at high speeds and are easily hybridized with semiconductors, ferroelectrics, and their microstructures. Thus, in addition to their high speed and low power consumption, organic EO polymers are expected to be materials that will play a key role in next-generation optical communications due to their miniaturization and integration capabilities. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] "Organic Materials for Nonlinear Optics," edited by The Chemical Society of Japan, Quarterly Review of Chemistry No. 15 (1992) [Non-Patent Document 2] "Organic Nonlinear Optical Materials", Ch. Bosshard, et al., Gordon and Breach Publishers(1995) [Non-Patent Document 3] "Latest Technologies in Opto-Organic Materials for Information and Communication," supervised by Toshikuni Kainō, CMC Publishing, 2007. [Non-Patent Document 4] "Organic Electro-Optics and Photonics", Larry R. Dalton, et. al., Cambridge University Press(2015) [Overview of the project] [Problems that the invention aims to solve]

[0005] The development of organic EO polymers to date has been based on the premise of use in the C-band, which is a long-range communication wavelength band. Therefore, the evaluation of organic EO polymers used in optical control elements has been based on the electro-optic coefficient r or n 3 The value of r(n: refractive index), and / or α(α: propagation loss per unit length) or n 3 This is done by comparing r / α, and r or n 3 It was considered that the larger the value of r and / or the smaller the α, the more suitable the device was for use in the C band.

[0006] In recent years, there has been a demand for the development of optical control elements that are useful (highly efficient) in wavelength bands shorter than the C band. Organic EO polymers that are transparent in the short wavelength band have small electro-optic coefficients r and n 3 r, α, or n 3 When evaluated using the r / α value, it received a low rating, and it had not attracted attention as a material capable of realizing highly efficient optical control elements in wavelengths shorter than the C band.

[0007] The present invention provides a determination method that can appropriately evaluate the performance of electro-optical materials in each wavelength band, a method for manufacturing an optical control element using the same, and an optical control element. [Means for solving the problem]

[0008] The present invention provides the following determination method, a method for manufacturing an optical control element, and an optical control element. 〔1〕 A determination method including a step of determining a wavelength band suitable for use of an optical control element, where the optical control element has an optical waveguide formed using an electro-optic material, and the determination method includes: a step of selecting the following formula (I) and / or formula (II) as a formula for calculating a performance index of the electro-optic material at wavelength λ based on the required characteristics of the optical control element; a step of calculating a performance index FOM1 and / or a performance index FOM2 using the formula selected in the selecting step; and the determining step determines a wavelength band suitable for use of the optical control element based on the performance index of the electro-optic material calculated in the calculating step.

Equation

number

[0009] According to the present invention, a determination method is available that can appropriately evaluate the performance of electro-optical materials in each wavelength band, and an optical control element can be manufactured using this determination method. [Brief explanation of the drawing]

[0010] [Figure 1]This is a schematic diagram of a Mach-Zehnder interferometer type waveguide that can be equipped with an optical control element. [Figure 2] This is a schematic diagram of the x-x' section in Figure 1. [Figure 3] Figure 2 is a graph showing the electric field Ey of light propagating through the optical waveguide at each position in the direction of the distance d between the electrodes (y-direction). [Figure 4] This graph plots the minimum distance dmin between electrodes against the wavelength propagating through an optical waveguide. [Figure 5] This graph shows the figure of merit FOM1 against wavelength for the electro-optic polymers obtained in the examples. [Figure 6] This graph shows the figure of merit (FOM2) against wavelength for the electro-optic polymers obtained in the examples. [Figure 7] This graph shows the conventional index n3r with respect to wavelength for the electro-optic polymers obtained in the examples. [Figure 8] This graph shows the conventional exponent α with respect to wavelength for the electro-optic polymers obtained in the examples. [Figure 9] This image shows a cross-section of the optical incident end face of the optical modulator obtained in the example. [Figure 10] This graph shows the time waveform of the optical modulation of the optical modulator obtained in the example. [Figure 11] This image shows a cross-section of the optical incident end face of the optical modulator obtained in the example. [Figure 12] This graph shows the time waveform of the optical modulation of the optical modulator obtained in the example. [Modes for carrying out the invention]

[0011] The embodiments of the present invention will be described below with reference to the drawings, but the present invention is not limited to the following embodiments.

[0012] <Judgment method> The determination method of this embodiment aims to determine the wavelength band suitable for use in an optical control element in which an optical waveguide is formed using an electro-optical material (hereinafter sometimes referred to as "EO material") by evaluating the performance of the EO material for each wavelength band. The determination method is as follows: The process involves selecting the following equations (I) and / or (II) as formulas for calculating the figure of merit of the EO material at wavelength λ, based on the required characteristics of the optical control element. A step of calculating performance index FOM1 and / or performance index FOM2 using the formula selected in the selection step, The process includes determining a wavelength band suitable for use with an optical control element based on the performance index of the EO material calculated in the calculation process.

number

[0013] The determination method may further involve selecting at least formula (II) as the step to be selected. In this case, the calculation step is: In the phase modulation region of an optical waveguide, the acceptable propagation loss is max And the allowable length L of the phase modulation region. max The ratio (Loss max / L max ) is the acceptable propagation loss α per unit length in the phase modulation domain. c In that case, At each wavelength λ, α≦α c If the relationship is such that α = α c Let α > α c When the relationship is such that α is used, it is preferable to calculate the performance index FOM2.

[0014] In this embodiment, the unit of the performance index FOM1 is (V·cm). -1 The unit of the performance index FOM2 is (V·dB). -1These units shall be expressed as follows. As described later, when the unit of the electro-optic coefficient r is expressed as pm / V, the unit of the propagation loss per unit length α is expressed as dB / cm, and the unit of the wavelength λ is expressed as nm, the order of magnitude of the lengths among these units shall be adjusted to make the performance indices FOM1 and FOM2 conform to the above units.

[0015] In the above determination method, the wavelength band suitable for use of the optical control element is determined based on the performance index FOM1 and / or performance index FOM2 of the EO material newly discovered by the present inventors. The performance indices FOM1 and FOM2 are given by λ as shown in equations (I) and (II) respectively. 2 It differs from conventionally used indices in that it includes λ. Conventional indices were used to evaluate optical control elements used at specific wavelengths such as the C band, and therefore did not include the wavelength λ (the r or n mentioned above). 3 The value of r, and / or α or n 3 The value of r / α was used. In contrast, the performance indices FOM1 and FOM2 used in this embodiment are indices that include the wavelength λ in order to evaluate the performance at each wavelength when the optical control element is used at different wavelengths, taking into account the effect of wavelength.

[0016] In other words, because the conventionally used index does not include the wavelength λ factor, even if an EO material having such an index is used, it may be determined that it is unsuitable for use in optical control elements depending on the wavelength band used. In contrast, according to the determination method of this embodiment, the merit index of the EO material can be calculated by considering the wavelength λ (used wavelength band) in which the optical control element is used, using the merit index FOM1 and / or FOM2. Therefore, when an optical waveguide is formed using an EO material having a merit index calculated based on equation (I) and / or equation (II), it is possible to determine the wavelength band suitable for use of the optical control element having said optical waveguide.

[0017] (Derivation of performance indices FOM1 and FOM2) The performance indices FOM1 and FOM2, represented by equations (I) and (II), are derived based on the technical details described below. The following explanation will show that by using performance indices FOM1 and FOM2, the wavelength band suitable for the use of optical control elements can be appropriately determined.

[0018] In the following explanation, we will use the case where the optical control element is an optical modulator and the optical waveguide provided by the optical control element is a single-arm driven Mach-Zehnder interferometer type waveguide (hereinafter sometimes referred to as "MZ-type waveguide") as an example. Figure 1 is a schematic diagram of an MZ-type waveguide that can be provided by an optical control element. Figure 2 is a schematic diagram of the x-x' cross section of Figure 1. In an MZ-type waveguide, light input from the left side in Figure 1 propagates within the optical waveguide. As shown in Figure 2, an optical waveguide generally consists of a core 11 through which light mainly propagates and a cladding 12 provided around it, with the core 11 containing EO material. Light input to the optical waveguide of an MZ-type waveguide propagates through the two branched arm sections 10a and 10b as shown in Figure 1, and then rejoins and is interfered with before being output. An upper electrode 15 for phase modulation is placed on the cladding 12 in one of the two arm sections 10a and 10b. In this specification, phase modulation refers to shifting the phase of input light. In phase modulation in an MZ-type waveguide, it refers to shifting the phase of light propagating along one of the arm sections 10a, and the phase shift is performed by applying an electric field using the upper electrode 15 located on the arm section 10a.

[0019] In optical control elements, the index used to evaluate high speed is V, where V is the half-wavelength voltage (the voltage at which the output light intensity becomes zero) in the MZ-type waveguide. π Let [V] be the half-wavelength voltage, and let L be the length of the phase modulation region of the MZ-type waveguide (Figure 1). πIt is expressed as the product of and length L (Equation (i-1)). The phase modulation region is the region where the above-mentioned phase modulation is performed, and in the MZ-type waveguide shown in Figure 1, it is the region where the upper electrode 15 of one arm portion 10a is located. Therefore, the length L of the phase modulation region is the length of the upper electrode 15 (length in the direction of light propagation). In addition, in the optical control element, the index for evaluating power saving is the half-wavelength voltage V π Let V be the half-wavelength voltage, and let Loss[dB] be the propagation loss in the phase modulation region. π It is expressed as the product of and the propagation loss (Equation (ii-1)).

number

[0020] V in equation (i-1) π The value of L, and V in equation (ii-1) π A smaller Loss value indicates that the optical control element has superior speed and power efficiency. Therefore, to obtain an optical control element with superior speed, it is preferable to reduce the distance d in equation (i-1). Also, to obtain an optical control element with superior power efficiency, it is preferable to reduce the distance d (Figures 1 and 2) in equation (ii-1). On the other hand, most of the light propagating through the optical waveguide propagates through the core 11, but some seeps into the cladding 12. Therefore, in the phase modulation region, if the distance d becomes small, the light seeping from the core 11 is more easily absorbed by the upper electrode 15 and the lower electrode 16, thus reducing the amount of light propagating through the optical waveguide.

[0021] From these perspectives, the inventors have determined that the distance d is such that the loss of light of wavelength λ propagating through the optical waveguide is within an acceptable range (hereinafter referred to as "minimum distance d"). minIt is preferable to set it to ), and in the procedure described below, the minimum distance d at a specific wavelength λ min We made that decision.

[0022] First, the minimum distance d min To determine this, the spread (mode) of light propagating through the optical waveguide was calculated. Specifically, the refractive index of the core (EO polymer) was set to 1.64, the refractive index of the cladding (organic silica) to 1.48, and the size of the core was set to a length h in the direction of distance d (y direction) of 1.5 μm and a length w in the direction perpendicular to the y direction of 1.5 μm. Figure 3 shows the results of calculating the modes of light when light with a wavelength of 1.55 μm was propagated in this optical waveguide. The calculation of the light propagation modes was performed using optical waveguide simulation software (BeamPROP: RSoft) based on the beam propagation method. Figure 3 is a graph showing the electric field Ey (intensity of the light mode) of light propagating through the optical waveguide at each position in the direction of distance d between electrodes (y direction) shown in Figure 2. In Figure 3, the horizontal axis represents the position y at a distance d from the center of the core (y-direction), with 0 representing the center of the core. The vertical axis represents the electric field Ey of light at a distance y, with the electric field Ey at the center of the core (y=0) set to 1. From the results shown in Figure 3, it can be read that the position y at which the electric field Ey of light becomes sufficiently small compared to the center of the core, for example, when the electric field Ey of light is -23 dB, corresponds to a position y of ±2.81 μm.

[0023] Next, the propagation loss when electrodes were placed at positions y = ±2.81 in the phase modulation region of the MZ-type waveguide (with a distance d = 5.62 μm) was calculated using the simulation software described above. The simulation results showed that the propagation loss per unit length was 0.4 dB / cm, confirming that the loss of light propagating through the optical waveguide was within an acceptable range. The distance d of 5.62 μm at this time was then determined to be the minimum distance d when the wavelength used was 1.55 μm. min (See Table 1 below.)

[0024] For other wavelengths propagating through the optical waveguide of the MZ-type waveguide (wavelengths shown in Table 1 below), the above calculation of the optical propagation mode was performed, and the minimum distance d from position y when the electric field Ey of the light is -23 dB was also calculated. min The following was determined. The results are shown in Table 1 and Figure 4 below. Figure 4 shows the values ​​shown in Table 1 plotted (each point in Figure 4), and the plotted points fitted using the least squares method (dashed line in Figure 4), with respect to the wavelength propagating through the optical waveguide, the minimum distance d min This is a graph plotting the values. [Table 1]

[0025] The inventors of this invention, from the graph shown in Figure 4, found that the minimum distance d min It is proportional to the wavelength λ (approximately d min We found that the relationship is d = 3.62 × λ, and using this relationship, we derived the performance index FOM1 and performance index FOM2 expressed by equations (I) and (II) above. Specifically, in equations (i-1) and (ii-1) above, the relationship d = d was found from the graph shown in Figure 4. min By using =3.62×λ, we derived the relationship that is equal in equations (i-2) and (ii-2) below. Since Γ in these equations is a constant (Γ≈0.85 in the optical waveguides for which the results in Figures 3 and 4 were calculated), the exponents expressed in equations (i-1) and (ii-1) above are λ, as shown on the right-hand side of equations (i-2) and (ii-2) below. 2 / n 3 r and αλ 2 / n 3 It can be seen that it is proportional to r.

number

[0026] Based on this relationship, the reciprocals of the right-hand sides in equations (i-2) and (ii-2) are defined as the performance indices FOM1 and FOM2, respectively, as expressed in equations (I) and (II) above.

[0027] From the above, it can be understood that by using the merit indices of performance FOM1 and FOM2, the performance of the EO material can be evaluated for each wavelength, and the wavelength band suitable for use in the optical control element obtained using the EO material can be appropriately determined. V in equation (i-1) π The value of L, and V in equation (ii-1). π The smaller the Loss value, the better the optical control element's high speed and power efficiency. Therefore, optical control elements obtained using EO materials with a large value of the figure of merit FOM1 (Equation (I)) are superior in high speed, and optical control elements obtained using EO materials with a large value of the figure of merit FOM2 (Equation (II)) are superior in power efficiency.

[0028] Next, each step of the determination method of this embodiment will be described. (Selection process) In the selection step, at least one of the above equations (I) and (II) is selected based on the required characteristics of the optical control element to calculate the figure of merit of the EO material for forming the optical waveguide of the optical control element. Required characteristics of the optical control element include high speed and low power consumption. For example, when evaluating the material performance of an EO material suitable for obtaining an optical control element that requires high speed, equation (I) should be selected in the selection step. For example, when evaluating the material performance of an EO material suitable for obtaining an optical control element that requires low power consumption, equation (II) should be selected in the selection step. Depending on the characteristics required of the optical control element, such as when achieving both high speed and low power consumption, both equations (I) and (II) may be selected.

[0029] (Calculation process) In the calculation process, the performance index is calculated using the formula selected in the selection process. If formula (I) is selected in the selection process, performance index FOM1 is calculated; if formula (II) is selected in the selection process, performance index FOM2 is calculated. Both performance indexes FOM1 and FOM2 may be calculated in the calculation process.

[0030] When calculating the figure of performance FOM2 in the calculation process, the value of propagation loss α per unit length may be used in equation (II), but depending on the value of α, the acceptable propagation loss α per unit length in the phase modulation region may vary. c You may use this. Specifically, at wavelength λ, α ≤ α c If so, then α is α c Change to α>α c In this case, the figure of merit FOM2 at wavelength λ may be calculated using equation (II) with respect to α. Propagation loss per unit length α c This is the acceptable propagation loss in the phase modulation region. max [dB] and the allowable length L of the phase modulation region. max The ratio (Loss max / L max )

[0031] Acceptable propagation loss α per unit length in the phase modulation region c , acceptable propagation loss in the phase modulation region max , and the allowable length L of the phase modulation region max These can all be set according to the type or application of the optical control element in which the optical waveguide is formed using EO material. Propagation loss α per unit length c , propagation loss max , and length L max In all cases, these can be the maximum value within the acceptable range.

[0032] From the relationship shown in equation (II), the n in the numerator 3 As r decreases, the value of the performance index FOM2 decreases, while as the denominator α decreases, the numerator n decreases. 3 Even if r is small, the value of the figure of performance FOM2 becomes large. Therefore, the propagation loss α and α per unit length c α≦α c If the relationship is satisfied, then in equation (II) α = α c By calculating the performance index FOM2 as follows, n 3 The contribution of r can be appropriately evaluated.

[0033] (The process of making a determination) In the determination step, based on the performance index of the EO material calculated in the calculation step, the wavelength band suitable for use of the optical control element, which has an optical waveguide formed using the EO material, is determined. In the determination step, for example, as described in the embodiments below, the performance index may be determined using homogeneous variance analysis (Lorentz-type dispersion formula), or the performance index may be determined using heterogeneous variance analysis (Gauss-type dispersion formula).

[0034] Next, we will describe each component used in the determination method of this embodiment. (Optical control element) The optical control element has an optical waveguide formed using EO material as described above. As shown in Figure 2, the optical waveguide has a core 11 and a cladding 12 that surrounds the core 11, and the core 11 contains EO material. The shape (structure) of the optical waveguide may be a channel-type waveguide as shown in Figure 2, or it may be a ridge-type waveguide, an inverse ridge-type waveguide, a photonic crystal waveguide, etc.

[0035] The optical control element may be an MZ-type optical modulator in which a Mach-Zehnder (MZ) interferometer is constructed with an optical waveguide as shown in Figure 1, or it may be a nested MZ-type optical modulator in which an MZ interferometer is further integrated on two branch paths of an MZ interferometer, a single phase modulator without a branch structure, or an optical phased array composed of multiple branches and phase modulators.

[0036] The electro-optic material can be a known material, and may be an inorganic or organic material. Examples of inorganic materials include inorganic dielectric materials such as lithium niobate, GaAs semiconductors, InP semiconductors, and glass. Examples of organic materials include electro-optic crystal materials such as DAST, and electro-optic polymers (hereinafter sometimes referred to as "EO polymers").

[0037] EO polymers are polymers that exhibit a second-order nonlinear optical effect and include electro-optic molecules and a base polymer (matrix polymer). The electro-optic molecules may be bonded to the base polymer or dispersed in the base polymer. The electro-optic molecules are compounds that exhibit a second-order nonlinear optical effect. Known compounds may be used as the electro-optic molecules, or compounds having structures represented by the chemical formulas shown in formulas (E-1) to (E-5) and (E-1a) below may be used. The EO material is preferably an organic material, and more preferably an EO polymer. The EO material may be an EO polymer containing a compound having a structure represented by the chemical formulas shown in formulas (E-1) to (E-5) and (E-1a) below, or it may be an EO polymer in which the compound is bonded to a base polymer. The EO polymer may be an EO polymer in which the reactive groups of the electro-optic molecules and the reactive groups of the base polymer react to form linking groups.

[0038] [ka]

[0039] The base polymer (matrix polymer) is the polymer that forms the basis of the EO polymer. Known polymers can be used as the base polymer, including (meth)acrylic polymers such as PMMA, polyimides, polycarbonates, olefin polymers, cycloolefin polymers, vinyl polymers, polyesters, polyalkylsiloxanes, epoxy resins, and the like.

[0040] The cladding 12 is not particularly limited as long as it is formed from a material having a refractive index lower than that of the core 11, and known materials can be used. Examples of materials constituting the cladding 12 include glass such as quartz glass and multi-component glass, fluororesins, silicone resins, organic silica (inorganic silica bonded with organic components), (meth)acrylic polymers such as PMMA, polyimide, polycarbonate, olefin polymers, cycloolefin polymers, and the like.

[0041] As shown in Figures 1 and 2, when an upper electrode 15 and a lower electrode 16 are provided in the phase modulation region, the upper electrode 15 and the lower electrode 16 can be formed from a known conductive material such as a metal material.

[0042] Specific examples of optical control elements to which the determination method of this embodiment is applied include, for example, optical modulators, optical switches, optical transceivers, optical phased arrays, LiDAR, smart glasses, optical interconnects, optoelectronic circuits, wavelength converters, electric field sensors, THz wave generators and detectors, and the like.

[0043] <Manufacturing method for optical control elements> The manufacturing method for the optical control element of this embodiment includes the steps of determining a wavelength band suitable for use of the optical control element using the determination method described above, and forming an optical waveguide using the EO material whose performance index was determined in the calculation step. This makes it possible to manufacture an optical control element suitable for use in the wavelength band determined in the determination step.

[0044] Specific examples of optical control elements include those described above. The optical waveguide preferably includes a core 11 and a cladding 12, as described above. The EO material used in the process of forming the optical waveguide can be used to form the core 11 of the optical waveguide. Examples of EO materials include those described above, and an EO polymer is preferred. The optical waveguide may be formed by a known formation method.

[0045] <Optical control elements used in wavelength bands below 1259nm> The optical control element used in the wavelength band of 1259 nm or less in this embodiment (hereinafter sometimes referred to as "specific optical control element") is an optical control element having an optical waveguide formed of EO material, and having a figure of merit FOM1 of 1.2 (V·cm) in the wavelength band of 1259 nm or less. -1 Wavelength bands greater than or equal to 1259 nm, and / or wavelength bands less than or equal to 1259 nm with a figure of merit FOM2 of 0.20 (V·dB) -1These are used in the wavelength band specified above (hereinafter, the wavelength band that satisfies these conditions may be referred to as the "specific wavelength band"). The specific optical control element satisfies the following [A] and / or [B]. [A] The figure of merit FOM1 calculated based on the above formula (I) for the EO material contained in a specific optical control element is 1.2 (V·cm) in any wavelength band below 1259 nm. -1 The above is true, and the specific optical control element has a wavelength band of 1259 nm or less and an index of merit FOM1 of 1.2 (V·cm). -1 It is used in the wavelength bands mentioned above. [B] The figure of merit FOM2 calculated based on the above formula (II) for the EO material contained in a specific optical control element is 0.2 (V·dB) in any wavelength band below 1259 nm. -1 The above applies to a specific optical control element with a wavelength band of 1259 nm or less and an index of merit FOM2 of 0.2 (V·dB). -1 It is used in the wavelength bands mentioned above.

[0046] In this specification, the performance indices FOM1 and FOM2 of a particular optical control element are values ​​determined using heterogeneous analysis of variance (Gaussian dispersion formula), as described in the examples below.

[0047] Depending on the specific optical control element, a useful (highly efficient) optical control element can be provided in the short wavelength band of 1259 nm or less.

[0048] Specific examples of a particular optical control element include those described above. The optical waveguide preferably includes a core 11 and a cladding 12 as described above. An EO material can be used to form the core 11 of the optical waveguide. Examples of EO materials include those described above, and an EO polymer is preferred. Examples of EO materials for forming the core 11 in a particular optical control element include compounds having a structure represented by the chemical formulas shown in formulas (E-2) and (E-3) above. When an upper electrode 15 and a lower electrode 16 are provided in the phase modulation region of the optical waveguide as described above, known conductive materials such as metallic materials can be used to form the upper electrode 15 and the lower electrode 16.

[0049] The specific wavelength band is a wavelength band of 1259 nm or less, and in which the figures of merit FOM1 and / or FOM2 are greater than or equal to the above range. The wavelength band of 1259 nm or less may be 1140 nm or less, usually 200 nm or more, may be 300 nm or more, may be 400 nm or more, may be 500 nm or more, or may be 600 nm or more. Also, the figure of merit FOM1 is 1.2 (V·cm). -1 The wavelength range exceeding this is 1.4 (V·cm). -1 The wavelength band may also be greater than or equal to 1.5(V·cm) -1 The wavelength band may also be greater than or equal to 1.8(V·cm) -1 The wavelength range may also be greater than or equal to 48 (V·cm). -1 The wavelength range is as follows: The figure of merit FOM2 of the EO material is 0.20 (V·dB). -1 The wavelength band exceeding this is 0.25 (V·dB). -1 The wavelength band may also be greater than or equal to 0.30 (V·dB) -1 The wavelength range may be greater than or equal to 8 (V·dB). -1 The wavelength ranges are as follows. The numerical ranges of the above-mentioned wavelength ranges, performance index FOM1, and performance index FOM2 can be combined arbitrarily.

[0050] If the specific wavelength range is the range exemplified above, the wavelength range of the performance index FOM1 and FOM2 in the wavelength band below 1259 nm, and the values ​​of the performance index FOM1 and FOM2, will also change in conjunction with the range exemplified above for the specific wavelength range. [Examples]

[0051] The present invention will be described in more detail below with reference to examples, but the present invention is not limited to these examples.

[0052] [Examples 1-5] EO polymers (EO materials) were prepared by bonding compounds represented by the chemical formulas (E-1) to (E-5) shown above (hereinafter sometimes referred to as "compound (E-1)," etc.) to a base polymer using the following procedure.

[0053] (Preparation of compound (E-1)) Compound (E-1) was prepared according to the procedure described in Example 57 of International Publication No. 2011 / 024774.

[0054] (Preparation of compound (E-2)) Compound (E-2) was prepared according to the procedure described in Synthesis Example 13 of International Publication No. 2019 / 151318.

[0055] (Preparation of compound (E-3)) The compound (E-3)(2-[4-[(E)-2-(benzyloxy)-4-[butyl(4-hydroxybutyl)amino]styryl]3-cyano-5-(trifluoromethyl)-5-phenylfuran-2(5H)-ylidene]malononitrile) was synthesized using the following procedure.

[0056] <Synthesis of 4-t-butyldiphenylsilyloxybutylbutylamine (E3-1)> [ka] Under an Ar stream, a solution obtained by mixing 4-butylaminobutanol (22.2 g (0.156 mol)), triethylamine (37.3 g (0.366 mol)), and Dry DMF (230 mL) was cooled with water, and TBDPSCl (40.6 g (0.153 mol)) was added dropwise thereto over 10 minutes under the condition of a temperature of 4 to 10 °C. Then, the temperature was raised to room temperature and stirred for 3 hours. The reaction solution was dispersed in 1.2 L of water and extracted twice with ethyl acetate. The organic layer obtained by extraction was washed successively with water (twice) and saturated brine, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain 55.3 g of the compound represented by the formula (E3-1) (hereinafter sometimes referred to as "compound (E3-1)") (yield: 92.3%).

[0057] <Synthesis of N,N-4-t-butyldiphenylsilyloxybutylbutyl)3-benzyloxyaminobenzene (E3-2)>

Chemical formula

[0058] <Synthesis of (N,N-4-hydroxybutylbutyl)3-benzyloxyaminobenzene (E3-3)>

Chemical formula

[0059] <Synthesis of (N,N-4-acetoxybutylbutyl)3-benzyloxyaminobenzene (E3-4)> [ka] Under an Ar gas stream, a solution of compound (E3-3) (9.65 g (29.5 mmol)), triethylamine (4.60 g (45.5 mmol)), and dry methylene chloride (100 mL) was mixed and cooled on ice. Acetyl chloride (3.2 g (40.8 mol)) was added dropwise over 20 minutes at a temperature of 3-15°C, and the mixture was stirred at room temperature for 1 hour. The reaction mixture was dispersed in ice water (200 mL) with hydrochloric acid (5 mL (60 mmol)) and quenched. The organic layer was washed twice with water (200 mL), then washed again with 5% sodium bicarbonate solution (100 mL), dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain 10.9 g (29.5 mmol) of the compound represented by formula (E3-4) (hereinafter sometimes referred to as "compound (E3-4)") (yield: 100%).

[0060] <Synthesis of (N,N-4-acetoxybutylbutyl)3-benzyloxy-4-formylaminobenzene (E3-5)> [ka] Dry DMF (40 mL) was cooled with ice under an Ar gas stream, and phosphorus oxychloride (5.4 g (35 mmol)) was added dropwise over 15 minutes at a temperature of 5-7°C. The mixture was then heated to room temperature and stirred for 30 minutes. Next, under ice cooling, a solution of compound (E3-4) (10.8 g (29.2 mmol) and DryDMF (15 mL) was added dropwise at a temperature of 5-8°C, stirred at room temperature for 30 minutes, heated to approximately 70°C, stirred for 1 hour, then cooled on ice, and 20% NaOAc water (70 mL) was added dropwise. After stirring at room temperature for 1 hour, it was extracted twice with ethyl acetate (100 mL). The organic layer obtained by extraction was washed with water (twice) and saturated brine in that order, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain a residue (11.2 g). This residue was purified by silica gel chromatography (350 g silica gel, CHCl3 / AcOEt:4 / 1) to obtain 9.27 g (23.3 mmol) of the compound represented by formula (E3-5) (hereinafter sometimes referred to as "compound (E3-5)") (yield: 80%).

[0061] Compound (E3-5) 1 1H-NMR analysis was performed. 1 H-NMR CDCl3 0.94(t 3H), 1.35(m 2H), 1.59(m 2H), 1.63(m 2H), 2.05(s 3H), 3.26(t 2H), 3.30(t 2H), 4.07(t 2H), 5.18(s 2H), 6.01(d 1H), 6.26(t 1H), 7.33(t 1H), 7.36-7.45(m 4H), 7.72(d 1H), 10.25(s 1H)

[0062] <Synthesis of (N,N-4-hydroxybutylbutyl)3-benzyloxy-4-formylaminobenzene (E3-6)> [ka] Under an Ar stream, 2N-NaOH aqueous solution (60 mL (120 mmol)) was added dropwise to a mixed solution of compound (E3-5) (9.10 g (22.9 mmol)) and EtOH (70 mL) over 30 minutes under the condition of 21 - 28 °C, and then stirred for 1 hour. The reaction solution was dispersed in water (210 mL) and extracted twice with chloroform (200 mL). The organic layer obtained by extraction was washed twice with 10% brine (100 mL), dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain a residue (8.55 g). This residue was purified by silica gel chromatography (350 g of silica gel, CHCl3 / AcOEt: 3 / 1 → 1 / 1) to obtain 7.62 g (21.4 mmol) of the compound represented by formula (E3-6) (hereinafter sometimes referred to as "compound (E3-6)"). (Yield: 93%)

[0063] For compound (E3-6), 1 1H-NMR analysis was performed. 1 1H-NMR CDCl3 0.94 (t, 3H), 1.32 (m, 2H), 1.50 - 1.62 (m, 4H), 1.63 - 1.71 (m, 2H), 3.27 (t,​​​​​​​​​​​​​​​​1 1H-NMR analysis and 13 13C-NMR analysis were performed. 1 1H-NMR DMSO-d6 0.90 (t, 3H), 1.27 - 1.35 (m, 2H), 1.42 - 1.53 (m, 2H), 1.53 - 1.62 (m, 2H), 3.42 (m, 2H), 3.47 - 3.59 (m, 4H), 5.21 (m, 2H), 6.26 (bs, 1H), 6.59 (dd, 1H), 6.78 (bd, 1H), 7.20 - 8.20 (m, 12H) 13 13C-NMR analysis DMSO-d6 13.61, 19.35, 23.90, 29.21, 29.31, 50.65, 50.80, 60.16, 69.87, 98.10, 109.22, 112.26, 112.94, 114.20, 121.85, 126.23, 127.88, 128.22, 128.47, 129.43, 130.45, 130.88, 135.80, 156.36, 161.80, 176.39

[0066] (Preparation of compound (E-4)) Compound (E-4) ((E)-2-(4-(4-(butyl(4-hydroxybutyl)amino)styryl)-3-cyano-5-methyl-5-(perfluorophenyl)furan-2(5H)-ylidene)malononitrile) was synthesized according to the following procedure.

[0067] (Synthesis of N-butyl-N-(4-(tert-butyldiphenylsilyl)oxy)butylaniline (E4-2))

Chemical formula

[0068] <Synthesis of 4-(butyl(phenyl)amino)butan-1-ol (E4-3)> [ka] Under an Ar gas stream, compound (E4-2) (54.7 g (0.12 mmol)) and THF (500 mL) were mixed to a solution, to which 1.0 M-TBAF-THF (151 mL (0.15 mol)) was added, and the mixture was stirred at a temperature of 22-23°C for 1 hour. The reaction mixture was dispersed in water (1 L) and extracted with ethyl acetate. The mixture was washed with water (twice) and saturated saline solution in that order, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain 56.5 g of residue. This residue was purified by silica gel chromatography (600 g silica gel, n-Hex / AcOEt: 3 / 1, 1 / 2) to obtain 26.5 g of the compound represented by formula (E4-3) (hereinafter sometimes referred to as "compound (E4-3)") (yield: 100%).

[0069] <Synthesis of 4-(butyl(phenyl)amino)butylacetate (E4-4)> [ka] Under an Ar gas stream, a solution of compound (E4-3) (26.5 g (0.12 mol)), triethylamine (24.2 g (0.24 mol)), and dry methylene chloride (200 mL) was mixed and cooled on ice. Acetyl chloride (12.3 g (0.16 mol)) was added dropwise over 25 minutes at a temperature of 3-8°C. After stirring at the same temperature for 1 hour, water (200 mL) was added dropwise to quench the reaction mixture. After liquid-liquid extraction, the mixture was washed with water and then saturated saline solution, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain 31 g of residue. This residue was purified by silica gel chromatography (230 g silica gel, n-Hex / AcOEt: 10 / 1, 9 / 1) to obtain 28.2 g of the compound represented by formula (E4-4) (hereinafter sometimes referred to as "compound (E4-4)") (yield: 89%).

[0070] <Synthesis of (N,N-4-acetoxybutylbutyl)-4-formylaminobenzene (E4-5)> [ka] Dry DMF (160 mL) was cooled with ice under an Ar gas stream, and phosphorus oxychloride (19.8 g (128.8 mol)) was added dropwise over 15 minutes at a temperature of 5-7°C. The mixture was then heated to room temperature and stirred for 30 minutes. Next, compound (E4-4) (28.2 g (107.1 mol) and DryDMF (85 mL) were added dropwise over 15 minutes at a temperature of 18-30°C, then heated to 85-90°C and stirred for 2.5 hours. After cooling on ice, 20% NaOAc water (240 mL) was added dropwise. This was stirred at room temperature for 1 hour, and then extracted with ethyl acetate. The organic layer obtained by extraction was washed twice with water and then with saturated brine, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain a residue (29.4 g). This residue was purified by silica gel chromatography (250 g silica gel, n-Hex / AcOEt: 5 / 1, 1 / 1) to obtain 26.4 g of the compound represented by formula (E4-5) (hereinafter sometimes referred to as "compound (E4-5)") (yield: 85%).

[0071] <Synthesis of (N,N-4-hydroxybutylbutyl)-4-formylaminobenzene (E4-6)> [Chemistry] Under an Ar stream, 2N-NaOH aqueous solution (152 mL (304 mmol)) was added dropwise to a solution of compound (E4-5) (26.4 g (90.6 mmol)) and EtOH (165 mL) over 30 minutes under the condition of a temperature of 21 - 25 °C, and then stirred for 1 hour. The reaction solution was dispersed in water (1 L) and extracted with ethyl acetate. The organic layer obtained by extraction was washed twice with water and then with saturated brine, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain a residue (21.8 g). This residue was purified by silica gel chromatography (220 g of silica gel, n-Hex / AcOEt: 1 / 1 → 1 / 2) to obtain 20.8 g of the compound represented by the formula (E4-6) (hereinafter sometimes referred to as "compound (E4-6)") (yield: 92%).

[0072] <Preparation of 2-[3-cyano-4,5-dimethyl-5-(perfluorophenyl)furan-2(5H)-ylidene]malononitrile (E4-7)> The compound represented by the formula (E4-7) (hereinafter sometimes referred to as "compound (E4-7)") was prepared according to the procedure described in Synthesis Example 1 of EO molecules in International Publication No. 2019 / 151318.

[0073] <Synthesis of compound (E-4)> [Chemistry] <( Under an Ar stream, a solution of compound (E4-6) (3.24 g (13.0 mmol)), compound (E4-7) (3.51 g (10.0 mmol)), and EtOH (100 mL) was heated to 37 - 45 °C and stirred for 5 hours, and then ice-cooled. The precipitated crystals were filtered off, washed with IPE, and dried under reduced pressure at 50 °C to obtain 3.51 g of compound (E-4) (yield: 93%).

[0074] For compound (E-4) 1 1H-NMR analysis and 13 13C-NMR analysis were performed. 1 H-NMR DMSO-d6 0.97(t 3H), 1.34-1.42(m 3H), 1.57-1.65(m 4H), 1.70-1.77(m 2H), 2.19(s 3H), 3.36-3.43(m 2H), 3.43-3.49(m 2H), 3.71(d 2H), 6.65(d 2H), 6.68(d 1H), 7.25(d 1H), 7.41(d 2H) 13 C-NMR analysis DMSO-d6 13.67, 19.40, 23.72, 26.12, 29.09, 29.40, 50.11, 50.30, 51.58, 60.27, 89.82, 94.17, 107.05, 109.87, 111.80, 112.19, 112.46, 112.93, 121.49, 134.30, 137.58, 141.80, 145.47, 149.74, 152.92, 171.44, 176.74

[0075] (Preparation of compound (E-5)) The compound (E-5)(4-[4-(N,N-butyl4-hydroxybutyl)aminophenyl]3-cyano-5,5-dimethylfuran-2(5H)-ylidene]malononitrile) was synthesized using the following procedure.

[0076] <Synthesis of 2-methyltrimethylsilyloxypropionitrile (E5-1)> [ka] 1,5,7-Triazabicyclo[4,4,0]5-Decempolystyrene (PS-TBD) (100 mg (0.121 mmol)) was added to acetone (100 mL), and trimethylsilyl cyanide (10.0 g (101 mmol)) was added dropwise while stirring at room temperature. After stirring at room temperature for 3 hours, PS-TBD was filtered off, and the acetone was concentrated under reduced pressure to obtain 14.4 g of the compound represented by formula (E5-1) (hereinafter sometimes referred to as "compound (E5-1)") (yield: 100%).

[0077] Compound (E5-1)1 H-NMR analysis and 13 1C-NMR analysis was performed. 1 H-NMR CDCl3:0.24(s 9H), 1.60(s 6H) 13 C-NMR CDCl3:1.32, 30.89, 66.17, 122.79

[0078] <Synthesis of 1-(4-fluorophenyl)-2-hydroxy-2-methylpropan-1-one (E5-2)> [ka] Magnesium (3.22 g (132 mmol)) was mixed with THF (18 mL), a few drops of 1,2-dibromoethane were added, and then a solution of 4-bromofluorobenzene (20.1 g (115 mmol)) diluted with THF (10 mL) was added dropwise under water-cooled stirring. After stirring at room temperature for 3 hours, compound (E5-1) (14.4 g (101 mmol)) diluted with 20 mL of THF was added dropwise under water-cooled stirring. After stirring at room temperature for 16 hours, the mixture was cooled to below 10°C, and 110 mL of 6 mol / L hydrochloric acid aqueous solution was slowly added dropwise. After stirring at room temperature for 2.5 hours, sodium bicarbonate (40 g) was dispersed and added to neutralize the mixture. Ethyl acetate (300 mL) and 10% saline solution (300 mL) were added for extraction. The ethyl acetate extract was washed with 10% saline solution, dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain the crude compound (E5-2) represented by formula (E5-2) (hereinafter sometimes referred to as "compound (E5-2)"). 10.6 g of compound (E5-2) was obtained by silica gel column chromatography (chloroform / ethyl acetate: 10 / 1) (yield: 58%).

[0079] <Synthesis of 3-cyano-2-dicyanomethylene-4-(4-fluorophenyl)-5,5-dimethyl-2,5-dihydrofuran (E5-3)> [ka] Compound (E5-2) (10.6 g (58.1 mmol)) and malononitrile (11.5 g (174 mmol)) were dissolved in pyridine (45 mL), acetic acid (0.2 g) was added, and the mixture was stirred at room temperature for 5 days. The reaction mixture was dispersed in water (900 mL), and the precipitated crystals were collected by filtration. The obtained crystals were washed with water, then methanol, and dried under reduced pressure at 70°C to obtain the compound represented by formula (E5-3) (hereinafter sometimes referred to as "compound (E5-3)") (12.0 g (43.0 mmol)).

[0080] Compound (E5-3) 1 H-NMR analysis, 13 13C-NMR analysis and differential scanning calorimetry were performed to measure the melting point. 1 H-NMR DMSO-d6:1.75(s 6H), 7.53(dd 2H), 7.91(dd 2H) 13 C-NMR DMSO-d6: 24.50, 55.61, 100.60, 103.24, 110.99, 111.32, 112.19, 116.87, 123.91, 131.32, 163.69, 165.37, 177.01 DSC:mp 273℃

[0081] <(E-5) synthesis> [ka] Compound (E5-3) (7.20 g (25.8 mmol)) and N,N-butyl-4-hydroxybutylamine (11.3 g (77.8 mmol)) were added to a mixture of pyridine (130 mL) and acetonitrile (90 mL), and the mixture was heated and stirred at an oil bath temperature of 50°C for 22 hours. The solvent was concentrated under reduced pressure at 50°C. THF (450 mL) and ethyl acetate (450 mL) were added to the concentrate and dissolved. This was washed with 10% saline solution (600 mL) in which potassium carbonate (60 g) was dissolved, then dried over anhydrous sodium sulfate, and the solvent was concentrated under reduced pressure to obtain crude compound (E-5). The crude product was purified by silica gel short column chromatography to obtain red crystals. These were washed with ethyl acetate and then methanol, and then heated and dried under reduced pressure at 70°C to obtain compound (E-5) (6.01 g (14.8 mmol)) (yield 57%).

[0082] Compound (E-5) 1 H-NMR analysis, 13 ¹³C-NMR analysis, melting point measurement using differential scanning calorimeter, and mass spectrometry were performed. 1 H-NMR DMSO-d6 0.93(t 3H), 1.35(m 2H), 1.48(m 2H), 1.53-1.65(m 4H), 1.81(s 6H), 3.43-3.49(m 6H), 4.49(t 1H), 6.92(d 2H), 8.05(d 2H) 13 C-NMR DMSO-d6 13.67, 19.41, 23.61, 26.60, 28.95, 29.41, 50.04, 50.21, 50.38, 60.27, 88.90, 98.12, 112.12, 112.35, 112.57, 113.63, 113.69, 132.60, 152.77, 173.98, 177.81 DSC:mp 249.8℃ ESI-MS:M+1=405.2

[0083] (Synthesis of base polymer (A-1)) 24.15 g (241.2 mmol) of methyl methacrylate (MMA), 10.65 g (68.64 mmol) of 2-(isocyanatoethyl) methacrylate (MOI), and 1.53 g (9.32 mmol) of azobisisobutyronitrile (AIBN) were dissolved in 57 mL of anhydrous toluene. After sealing with argon, the mixture was stirred in an oil bath at 60°C for 2 hours. After cooling the reaction mixture to room temperature, it was added dropwise to 1420 mL of anhydrous diisopropyl ether (IPE), and the precipitate was filtered off. After washing with anhydrous IPE, the mixture was dried under reduced pressure at 70°C to obtain 24.1 g of base polymer (A-1).

[0084] (Derivatization of base polymer (A-1) (methyl carbamate derivative)) Under Ar gas conditions, 7.0 g of base polymer (A-1) was dissolved in 245 mL of anhydrous tetrahydrofuran, and 15 mL of anhydrous methanol and 280 μL of dibutyltin dilaurate (DBTDL) were added. The mixture was stirred in an oil bath at 60°C for 2 hours. After cooling the reaction mixture, it was poured into 2.8 L of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed with IPE, and then dried under reduced pressure at 70°C to obtain a derivative of base polymer (A-1).

[0085] The obtained derivatives were measured using a differential scanning calorimetry system (Rigaku Thermo plus DSC 8230, Rigaku Corporation) with 10 mg of the sample and a reference sample in an empty Al container under a nitrogen atmosphere and a heating rate of 10°C / min. The glass transition temperature (Tg) was found to be 97°C. Furthermore, the molecular weight was determined by GPC using Alliance e2695 (Waters Japan Co., Ltd.) (column: Shodex GPC KF-804L (8 mmφ × 300 mm), developing solvent: THF, column temperature: 40°C). The weight-average molecular weight (Mw) was 76,300 and the number-average molecular weight (Mn) was 35,500.

[0086] (Synthesis of base polymer (A-2)) 7.90 g (78.9 mmol) of methyl methacrylate (MMA), 3.32 g (21.4 mmol) of 2-(isocyanatoethyl) methacrylate (MOI), and 0.497 g (3.03 mmol) of azobisisobutyronitrile (AIBN) were dissolved in 15 mL of anhydrous toluene. After sealing with argon, the mixture was stirred in an oil bath at 60°C for 2 hours. After cooling the reaction mixture to room temperature, it was diluted with 5 mL of anhydrous toluene and added dropwise to 450 mL of anhydrous diisopropyl ether (IPE). The precipitate was filtered off. After washing with anhydrous IPE, the mixture was dried under reduced pressure at 70°C to obtain 10.68 g of base polymer (A-2).

[0087] A derivative of base polymer (A-2) was obtained and analyzed using the same procedure as for the derivatization of base polymer (A-1) described above. The glass transition temperature Tg was 97°C, the weight-average molecular weight Mw was 75,500, and the number-average molecular weight Mn was 30,200.

[0088] (Synthesis of base polymer (A-3)) 3.95 g (39.5 mmol) of methyl methacrylate (MMA), 1.66 g (10.7 mmol) of 2-(isocyanatoethyl) methacrylate (MOI), and 0.247 g (1.50 mmol) of azobisisobutyronitrile (AIBN) were dissolved in 10 mL of anhydrous toluene. After sealing with argon, the mixture was stirred in an oil bath at 60°C for 2.5 hours. After cooling the reaction mixture to room temperature, it was diluted with 10 mL of anhydrous toluene and added dropwise to 250 mL of anhydrous diisopropyl ether (IPE). The precipitate was filtered off. After washing with anhydrous IPE, the mixture was dried under reduced pressure at 70°C to obtain 3.70 g of base polymer (A-3).

[0089] A derivative of base polymer (A-3) was obtained and analyzed using the same procedure as for the derivatization of base polymer (A-1) described above. The glass transition temperature (Tg) was 98°C, the weight-average molecular weight (Mw) was 64800, and the number-average molecular weight (Mn) was 31400.

[0090] (Synthesis of base polymer (A-4)) 7.50 g (74.9 mmol) of methyl methacrylate (MMA), 3.00 g (19.3 mmol) of 2-(isocyanatoethyl) methacrylate (MOI), and 0.464 g (2.83 mmol) of azobisisobutyronitrile (AIBN) were dissolved in 15 mL of anhydrous toluene. After sealing with argon, the mixture was stirred in an oil bath at 60-61°C for 3 hours. After cooling the reaction mixture to room temperature, it was added dropwise to 450 mL of anhydrous diisopropyl ether (IPE), and the precipitate was filtered off. After washing with anhydrous IPE, the mixture was dried under reduced pressure at 50°C to obtain 8.48 g of base polymer (A-4).

[0091] A derivative of base polymer (A-4) was obtained and analyzed using the same procedure as for the derivatization of base polymer (A-1) described above. The glass transition temperature Tg was 99°C, the weight-average molecular weight Mw was 76,900, and the number-average molecular weight Mn was 32,100.

[0092] (Synthesis of base polymer (A-5)) 7.90 g (78.9 mmol) of methyl methacrylate (MMA), 3.32 g (21.4 mmol) of 2-(isocyanatoethyl) methacrylate (MOI), and 0.497 g (3.03 mmol) of azobisisobutyronitrile (AIBN) were dissolved in 15 mL of anhydrous toluene. After sealing with argon, the mixture was stirred in an oil bath at 60°C for 2 hours. After cooling the reaction mixture to room temperature, it was diluted with anhydrous toluene (8 mL) and added dropwise to 450 mL of anhydrous diisopropyl ether (IPE). The precipitate was filtered off. After washing with anhydrous IPE, the mixture was dried under reduced pressure at 70°C to obtain 8.325 g of base polymer (A-5).

[0093] A derivative of base polymer (A-5) was obtained and analyzed using the same procedure as for the derivatization of base polymer (A-1) described above. The glass transition temperature (Tg) was 99°C, the weight-average molecular weight (Mw) was 83400, and the number-average molecular weight (Mn) was 36900.

[0094] (Manufacturing of EO polymer (EO-1)) 4.70 g of the base polymer (A-1) obtained above was dissolved in 190 mL of anhydrous tetrahydrofuran (THF). To this, 2.10 g (3.04 mmol) of compound (E-1) and 150 μL of dibutyltin dilaurate (DBTDL) were added, and the mixture was stirred in an oil bath at 60°C for 2 hours. Next, 10 mL of anhydrous methanol and 60 μL of DBTDL were added, and the mixture was stirred at 60°C for 30 minutes. After cooling the reaction mixture, it was poured into 1500 mL of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed with IPE (1 L), and then dried under reduced pressure at 70°C. 2.83 g of EO polymer (EO-1) was obtained as a black powder (glass transition temperature Tg: 131°C).

[0095] (Manufacturing of EO polymer (EO-2)) 1.75 g of the base polymer (A-2) obtained above was dissolved in 105 mL of anhydrous tetrahydrofuran (THF). To this, 0.7505 g (0.969 mmol) of compound (E-2) and 100 μL of dibutyltin dilaurate (DBTDL) were added and the mixture was stirred in an oil bath at 60°C for 2 hours. Next, 5 mL of anhydrous methanol was added and the mixture was stirred at 60°C for 30 minutes. After the reaction mixture was cooled, it was poured into 1050 mL of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed with IPE (300 mL), and then dried under reduced pressure at 70°C. 1.746 g of EO polymer (EO-2) was obtained as a black powder (glass transition temperature Tg: 127°C).

[0096] (Manufacturing of EO polymer (E-3)) 2.00 g of the base polymer (A-3) obtained above was dissolved in 80 mL of anhydrous tetrahydrofuran (THF). To this, 2.00 g (3.06 mmol) of compound (E-3) and 40 μL of dibutyltin dilaurate (DBTDL) were added and the mixture was stirred in an oil bath at 60°C for 3 hours. Next, 4 mL of anhydrous methanol was added and the mixture was stirred at 60°C for 30 minutes. After the reaction mixture was cooled, it was poured into 900 mL of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed twice with IPE (100 mL), and then dried under reduced pressure at 70°C. 2.83 g of EO polymer (EO-3) was obtained as a blue-violet powder (glass transition temperature Tg: 126°C).

[0097] (Manufacturing of EO polymer (EO-4)) 1.05 g of the base polymer (A-4) obtained above was dissolved in 65 mL of anhydrous tetrahydrofuran (THF). To this, 0.90 g (0.77 mmol) of compound (E-4) and 30 μL of dibutyltin dilaurate (DBTDL) were added, and the mixture was stirred in an oil bath at 60°C for 2 hours. Next, 3 mL of anhydrous methanol was added, and the mixture was stirred at 60°C for 45 minutes. After cooling the reaction mixture, it was poured into 650 mL of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed twice with IPE (100 mL), and then dried under reduced pressure at 50°C. 1.29 g of EO polymer (EO-4) was obtained as a black powder (glass transition temperature Tg: 146°C).

[0098] (Manufacturing of EO polymer (EO-5)) 1.754 g (3.35 mmol) of the base polymer (A-5) obtained above was dissolved in 105 mL of anhydrous tetrahydrofuran (THF). To this, 0.754 g (1.86 mmol) of compound (E-5) and 100 μL of dibutyltin dilaurate (DBTDL) were added, and the mixture was stirred in an oil bath at 55°C for 2 hours. Next, 5 mL of anhydrous methanol was added, and the mixture was stirred at 60°C for 120 minutes. After cooling the reaction mixture, it was poured into 1050 mL of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed three times with IPE (100 mL), and then dried under reduced pressure at 70°C. 1.66 g of EO polymer (EO-5) was obtained as an orange-red powder (glass transition temperature Tg: 120°C).

[0099] (Determination of performance indices FOM1 and FOM2) To calculate the performance indices FOM1 and FOM2, EO polymers were deposited using the following procedure, and the propagation loss α, refractive index n, and electro-optic coefficient r per unit length of EO polymers (EO-1) to (EO-5) were measured.

[0100] [Method for forming EO polymer films] Each EO polymer (EO-1) to (EO-5) was added to cyclohexanone to adjust the concentration to 1-20% by weight. The solution was then applied to a cleaned substrate (quartz glass) using a Mikasa 1H-DX2 spin coater at a speed of 500-6000 rpm, and subsequently vacuum-dried for 1 hour near the glass transition temperature (Tg). The polymer solution concentration and spin coater rotation speed were appropriately selected to achieve the desired film thickness.

[0101] [Absorbance spectrum of an EO polymer thin film] The absorbance spectra of thin films of each EO polymer (EO-1) to (EO-5), with a thickness of approximately 0.15 μm, deposited on quartz glass using the above deposition method, were measured using a Hitachi High-Tech Science UH-4150 spectrophotometer. The absorption coefficient a(ω) per unit length was calculated by dividing the absorbance by the film thickness.

[0102] [Absorbance spectrum of thick film of EO polymer] Three different thicknesses of EO polymer were fabricated for each EO polymer (EO-1) to (EO-5) by forming depressions of three different depths, ranging from 40 to 350 μm, on quartz glass, filling them with EO polymer, and polishing the surface. The absorbance spectra of the EO polymer thick films of each thickness were measured using a Hitachi High-Tech Science UH-4150 spectrophotometer. The graph plotting the absorbance for each thickness at each wavelength (frequency ω) was approximated by a linear function, and the absorption coefficient a(ω) per unit length at frequency ω was calculated from its slope.

[0103] [Propagation loss α per unit length of EO polymer] The propagation loss per unit length of the optical waveguide, 0.4 dB / cm, calculated by simulation, was added to the absorption coefficient a(ω) to obtain the propagation loss per unit length α(ω). For the absorption coefficient a(ω), 1 × 10⁻⁶ measurements of the absorbance spectrum of the thin film were used. -3 Values ​​less than 1 × 10⁻¹ indicate that the absorbance of the thin film is less than 1 × 10⁻¹ due to the large error caused by the limitations of the measuring instrument. -3 For the above wavelengths (frequency ω), the value of the absorption coefficient a(ω) calculated from the absorbance of the thin film is used, and the absorbance of the thin film is 1 × 10⁻⁶ -3 For wavelengths (frequency ω) less than 1, the absorption coefficient a(ω) value calculated from the absorbance of the thick film was used.

[0104] [Refractive index of EO polymers] The refractive index n of each EO polymer (EO-1) to (EO-5) was measured using a Metricon 2010 / M prism coupler on EO polymer films with a thickness of approximately 3 μm deposited on quartz glass.

[0105] [Electro-optic coefficient r of EO polymer] The EO coefficient was measured using the same method as described in the reference paper ("Transmission ellipsometric method without an aperture for simple and reliable evaluation of electro-optic properties", Toshiki Yamada and Akira Otomo, Optics Express, vol.21, pages 29240-48 (2013)). The laser light sources used were Agilent Technologies' DFB laser 81663A (wavelengths 1308 nm and 1550 nm), Toptica Photonics' DFBpro laser (wavelength 976 nm), and Coherent's OBIS LX laser (wavelength 640 nm).

[0106] [Calculation of performance indices FOM1 and FOM2 based on homogeneous analysis of variance (Lorentz variance formula)] When calculating the performance indices FOM1 and FOM2 based on homogeneous analysis of variance (Lorentz variance formula), the linear sensitivity χ (1) (ω) and second-order nonlinear susceptibility χ (2) The following equations (Q1) and (Q2) were used as model equations for (ω,ω,0). In the equations, ω is the frequency, ω0 is the resonance frequency, Γ0 is the uniform dispersion width, and χ0 (1) χ0 is the linear susceptibility at zero frequency. (2) This is the zero-frequency second-order nonlinear susceptibility.

number

[0107] The values ​​measured in the above [absorbance spectrum of EO polymer thin film] were fitted using the following equations (Q3) and (Q4) to obtain the zero-frequency linear sensitivity χ0 (1) The resonance frequency ω0 and uniform dispersion width Γ0 were determined. In equations (Q3) and (Q4), ε r (ω) is the relative permittivity at frequency ω, c is the speed of light, and a(ω) is the absorption coefficient at frequency ω.

number

[0108] Next, the values ​​measured at wavelengths of 1308 nm and 1532 nm using the above [refractive index of EO polymer] are fitted using the following formula (Q5), and the background term χ of the linear sensitivity is calculated. b (1) The following equation was determined. In the equation below, n(ω) is the refractive index at frequency ω.

number

[0109] The absorption spectrum fitting and the refractive index fitting are performed using χ. b (1) The change is 1 × 10 -6 Repeat until the following is true: χ0 (1) ,ω0,Γ0,χ b (1) This was the final decision.

[0110] Next, the values ​​measured in the above [Electro-optic coefficient r of EO polymer] at wavelengths of 1308 nm and 1550 nm for EO polymer (EO-1) and (EO-2) are fitted using the above formula (Q2) and the following formula (Q6), respectively, for EO polymer (EO-3) the values ​​at wavelengths of 976 nm, 1308 nm, and 1550 nm, for EO polymer (EO-4) the values ​​at wavelengths of 976 nm, 1308 nm, and 1550 nm, and for EO polymer (EO-5) the values ​​at wavelengths of 640 nm, 976 nm, 1308 nm, and 1550 nm, respectively, using the above formula (Q2) and the following formula (Q6), and the zero-frequency second-order nonlinear susceptibility χ0 (2) The solution was determined. Fitting was performed using the nonlinear least squares method (Levenberg-Marquardt method).

number

[0111] For the EO polymers (EO-1) to (EO-5) obtained above, the refractive index n and electro-optic coefficient r were determined from the relationship obtained above, and the propagation loss α per unit length was calculated using the measured values ​​to determine the performance index FOM1 and FOM2. Note that in calculating the performance index FOM2, α ≤ α c If so, then α is α c Using α > α c In this case, α was used. The results are shown in Table 2, Figure 5, and Figure 6. Also, in Figures 7 and 8, the conventionally used exponent n is shown for EO materials (E-1) to (E-5). 3 The results of calculating r and α are shown.

[0112] [Table 2]

[0113] [Calculation of performance indices FOM1 and FOM2 based on heterogeneous analysis of variance (Gaussian variance formula)] When calculating the performance indices FOM1 and FOM2 based on heterogeneous analysis of variance (Gaussian variance formula), the linear sensitivity χ is used. (1) (ω), and second-order nonlinear susceptibility χ (2) The following equation was used as the model equation for (ω,ω,0). In the equation, ω is the frequency, m is the ordinal number of the resonance, and ω m0 Γ is the resonance frequency, m0 is the uniform dispersion width, and Δω m0 is the heterogeneous dispersion width, and χ m (1) χ is the magnitude of the linear sensitivity, m (2) is the magnitude of the second-order nonlinear susceptibility. The ordinal number m of the resonance can be appropriately selected depending on the degree of reproducibility of the absorbance spectrum (difference between measured and calculated values), but in this example, m=4 was used for analysis.

number

[0114] The values ​​measured in the above [absorbance spectrum of EO polymer thin film] are fitted using the above equations (Q3) and (Q4) to obtain the magnitude of the linear sensitivity χ. m (1) , resonance frequency ω m0 , uniform dispersion width Γ m0 , non-uniform dispersion width Δω m0 We made that decision.

[0115] Next, the values ​​measured at wavelengths of 1308 nm and 1532 nm using the above [refractive index of EO polymer] are fitted to the above formula (Q5), and the background term χ of the linear sensitivity is obtained. b (1) We made that decision.

[0116] The absorption spectrum fitting and the refractive index fitting are performed using χ. b (1) The change is 1 × 10 -6 Repeat until the following is achieved: m (1) , ω m0 , Γ m0 , Δω m0 , χ b (1) This was the final decision.

[0117] Next, the values ​​measured in the above [Electro-optic coefficient r of EO polymer] at wavelengths of 1308 nm and 1550 nm for EO polymer (EO-1) and (EO-2) are fitted using the above formula (Q6), the values ​​measured at wavelengths of 976 nm, 1308 nm, and 1550 nm for EO polymer (EO-3), the values ​​measured at wavelengths of 976 nm, 1308 nm, and 1550 nm for EO polymer (EO-4), and the values ​​measured at wavelengths of 640 nm, 976 nm, 1308 nm, and 1550 nm for EO polymer (EO-5) are fitted using the above formula (Q6), and the magnitude of the second-order nonlinear susceptibility χ is determined. m (2) The solution was determined. Fitting was performed using the nonlinear least squares method (Levenberg-Marquardt method).

[0118] For the EO polymers (EO-1) to (EO-5) obtained above, the refractive index n and electro-optic coefficient r were determined from the relationship obtained above, and the propagation loss α per unit length was calculated using the measured values ​​to determine the performance index FOM1 and FOM2. Note that in calculating the performance index FOM2, α ≤ α c If so, then α is α c Using α > α c In this case, α was used. The results are shown in Table 3. Table 4 shows the performance index FOM1 calculated above as 1.2 (V·cm). -1 The maximum (λmax) and minimum (λmin) wavelengths exceeding this value, and the figure of merit FOM2 of 0.20 (V·dB) -1 The maximum (λmax) and minimum (λmin) wavelengths for which the above values ​​occur are shown.

[0119] [Table 3]

[0120] [Table 4]

[0121] [Example 6] An optical modulator for a wavelength of 1550 nm was fabricated using the following procedure, and the performance index of the optical modulation was evaluated.

[0122] (Preparation of EO polymer (E-1a)) The EO polymer (E-1a), represented by the following formula, was prepared according to the procedure described in Example 2 of International Publication No. 2018 / 003842. Based on heterogeneous dispersion analysis (Gaussian dispersion formula), the figure of merit of the EO polymer (E-1a) at a wavelength of 1550 nm was calculated to be 1.33 (V·cm) for the figure of merit FOM1. -1 The performance index FOM2 is 0.22 (V·dB). -1 That was the case. [ka] [In the formula, k, p, q, and r represent integers greater than or equal to 1.]

[0123] (Preparation of cladding material composition) 0.67 g of 3-methacryloyloxypropyltrimethoxysilane (manufactured by Tokyo Chemical Industry Co., Ltd.) and 0.06 g of zirconium propoxide (manufactured by Tokyo Chemical Industry Co., Ltd.) were added to a mixed solution of 0.41 g of ethanol and 0.05 g of 0.1 N hydrochloric acid aqueous solution and stirred. This mixture was stored at a temperature of 5°C or below for 12 hours or more, and then 0.071 g of Omnirad 819 (manufactured by IGM Resins) was added and stirred for 30 minutes to obtain a cladding material composition.

[0124] (Fabrication of the lower electrode) A lower electrode was fabricated by sputtering an IZO (100 nm) film onto a silicon substrate with a 2 μm thick thermal oxide film.

[0125] (Fabrication of the lower cladding) The cladding material composition prepared above was spin-coated onto the lower electrode (3,500 rpm for 30 seconds), heated at 95°C for 30 minutes, then at 120°C for 15 minutes, irradiated with LED light of 365 nm wavelength at 100°C, and finally heated at 190°C for 16 hours. The thickness of the fabricated lower cladding was 2.21 μm.

[0126] (Core layer fabrication) A 15% by mass cyclohexanone solution of EO polymer (E-1a) was spin-coated (1,300 rpm × 30 seconds) onto the lower cladding prepared above, and then heated in a vacuum at 180°C for 1 hour. The thickness of the prepared core layer was 1.40 μm.

[0127] (Fabrication of electrodes for polling, and polling process) On the core layer fabricated above, IZO (100 nm) was deposited by sputtering to fabricate a poling electrode, and a structure for poling treatment was obtained. After heating this structure to a temperature of 176°C, a voltage of 420 V was applied between the lower electrode and the poling electrode for 3 minutes to perform poling treatment. After cooling to room temperature while the voltage was applied, the voltage was turned off. Then, the poling electrode was removed with an etching solution (manufactured by Kanto Chemical Co., Inc., ITO-06N).

[0128] (Formation of optical waveguide) On the core layer of the structure that had undergone poling treatment, IZO (50 nm) was deposited by sputtering as a processing mask. Then, a mask pattern was fabricated by photolithography, and the core layer was processed into a rectangular structure (1.32 μm × 1.40 μm) by dry etching using a reactive ion etching apparatus, and this was used as an optical waveguide (core). The optical waveguide had a Mach-Zehnder (MZ) type optical modulator structure.

[0129] (Fabrication of upper cladding) On the optical waveguide formed above, the cladding material composition prepared above was spin-coated (3,500 rpm × 30 seconds), heated at 90°C for 10 minutes, and then irradiated with LED light having a wavelength of 365 nm at 100°C for 5 minutes. The film thickness of the fabricated upper cladding was 1.65 μm from the upper surface of the optical waveguide (core).

[0130] (Fabrication of upper electrode) On the upper cladding layer fabricated above, IZO (100 nm) was deposited by sputtering. Then, a mask pattern was fabricated by photolithography, and patterning was performed with an etching solution (manufactured by Kanto Chemical Co., Inc., ITO-06N) to form an upper electrode. The length L of the upper electrode was set to 1 cm.

[0131] (Fabrication of optical modulator) By cutting both end faces of the optical waveguide with a dicing saw, the optical input / output end faces were formed, and an optical modulator with a structure corresponding to FIG. 1 was completed. FIG. 9 is an image showing a cross section of the optical input end face of the fabricated optical modulator. FIG. 10 is a graph showing the time waveform of the optical modulation of the fabricated optical modulator. As shown in FIG. 10, Channel Ch2 is the applied voltage, and Channel Ch1 is the output optical intensity of 1550 nm of the MZ optical modulator. The optical output waveform of a typical MZ optical modulator for a triangular waveform voltage change is shown, and the above-mentioned V π was 4.4 V, and the above-mentioned V π L was 4.4 V·cm.

[0132] [Example 7] An optical modulator for wavelength 640 nm as an optical control element was fabricated by the following procedure, and the performance index of the optical modulation was evaluated.

[0133] (Preparation of EO polymer (E-5a)) The EO polymer (E-5a) represented by the following formula was prepared by the following procedure. The performance index of the EO polymer (E-5a) at a wavelength of 640 nm calculated based on the inhomogeneous dispersion analysis (Gaussian dispersion type) was such that the performance index FOM1 was 3.61 (V·cm) -1 and the performance index FOM2 was 0.60 (V·dB) -1 . [Chemical formula] [In the formula, k, p, and r represent integers of 1 or more.]

[0134] (Synthesis of base polymer (A-5a)) 7.00 g (31.8 mmol) of adamantyl methacrylate (AdMA), 2.60 g (16.8 mmol) of 2-(isocyanatoethyl) methacrylate (MOI), and 0.266 g (1.62 mmol) of azobisisobutyronitrile (AIBN) were dissolved in 18 mL of anhydrous toluene. After sealing with argon, the mixture was stirred in an oil bath at 70°C for 2 hours. After cooling the reaction mixture to room temperature, it was diluted with 15 mL of anhydrous toluene and added dropwise to a mixture of 450 mL of anhydrous diisopropyl ether (IPE) and 15 mL of anhydrous toluene. The precipitate was filtered off. After sequential washing with anhydrous IPE and anhydrous hexane, the mixture was dried under reduced pressure at 45°C to obtain 8.70 g of base polymer (A-5a).

[0135] (Derivatization of base polymer (A-5a) (methyl carbamate derivative)) Under Ar gas conditions, 1.0 g of base polymer (A-5a) was dissolved in 35 mL of anhydrous tetrahydrofuran, and 3 mL of anhydrous methanol and 40 μL of dibutyltin dilaurate (DBTDL) were added. The mixture was stirred in an oil bath at 55°C for 2 hours. After cooling the reaction mixture, it was poured into 350 mL of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed with 100 mL of IPE and 100 mL of hexane, and then dried under reduced pressure at 65°C to obtain a derivative of base polymer (A-1).

[0136] In the same manner as the analysis of the derivative of base polymer (A-1) described above, the derivative of base polymer (A-5a) was analyzed, and its glass transition temperature Tg was 155°C, its weight-average molecular weight Mw was 78600, and its number-average molecular weight Mn was 31300.

[0137] (Manufacturing of EO polymer (EO-5a)) 6.842 g (11.2 mmol) of the base polymer (A-5a) obtained above was dissolved in 300 mL of anhydrous tetrahydrofuran (THF). To this, 3.430 g (8.48 mmol) of compound (E-5) and 100 μL of dibutyltin dilaurate (DBTDL) were added, and the mixture was stirred in an oil bath at 55°C for 2 hours. Next, 40 mL of anhydrous methanol was added, and the mixture was stirred at 55°C for 1 hour. After cooling the reaction mixture, it was poured into 3.6 L of diisopropyl ether (IPE) and stirred. The precipitated powder was filtered, washed twice with IPE (100 mL), washed twice with methanol (100 mL), and then dried under reduced pressure at 70°C. 9.10 g of EO polymer (EO-5a) was obtained as an orange-red powder (glass transition temperature Tg: 164°C).

[0138] (Fabrication of the lower cladding) The cladding material composition prepared according to the procedure described in Example 6 was spin-coated (3,000 rpm × 30 seconds) onto the lower electrode prepared according to the procedure described in Example 6, heated at 95°C for 30 minutes, 120°C for 15 minutes, and 190°C for 16 hours, and then irradiated with 365 nm LED light at 100°C. The thickness of the prepared lower cladding was 1.27 μm.

[0139] (Core layer fabrication) A 12% by mass cyclohexanone solution of EO polymer (E-5a) was spin-coated (3,200 rpm × 30 seconds) onto the lower cladding prepared above, and then heated at 170°C in a vacuum for 1 hour. The thickness of the prepared core layer was 0.52 μm.

[0140] (Fabrication of electrodes for polling, and polling process) A 100nm IZO film was deposited on the core layer prepared as described above by sputtering to create a poling electrode and obtain a structure for poling. After raising the temperature of this structure to 164°C, a voltage of 240V was applied between the lower electrode and the poling electrode for 1 minute to perform the poling process. After cooling to room temperature while the voltage was still applied, the voltage was turned off. Subsequently, the poling electrode was removed with an etching solution (ITO-06N, manufactured by Kanto Chemical Co., Ltd.).

[0141] (Formation of optical waveguides) IZO (50 nm) was deposited on the core layer of the poling-treated structure by sputtering as a processing mask. Subsequently, a mask pattern was fabricated by photolithography, and the core layer was processed into a ridge structure (with a convex portion width of 0.99 μm and a height of 0.27 μm) by dry etching using a reactive ion etching apparatus, which served as the optical waveguide (core). The optical waveguide formed a Mach-Zehnder (MZ) type optical modulator structure.

[0142] (Preparation of the upper cladding) The cladding material composition prepared according to the procedure described in Example 6 was spin-coated (2,000 rpm × 30 seconds) onto the optical waveguide formed above, heated at 90°C for 10 minutes, and then irradiated with LED light of 365 nm wavelength at 100°C for 5 minutes. The thickness of the fabricated upper cladding was 1.55 μm from the top surface of the optical waveguide (core).

[0143] IZO (100 nm) was deposited on the upper cladding layer prepared as described above by sputtering. Subsequently, a mask pattern was created by photolithography, and the upper electrode was formed by patterning with an etching solution (ITO-06N, manufactured by Kanto Chemical Co., Ltd.). The length L of the upper electrode was set to 0.5 cm.

[0144] (Fabrication of optical modulators) The ends of the waveguide were cut with a dicing saw to create the optical input and output end faces, completing an optical modulator with a structure corresponding to Figure 1. Figure 11 is a cross-sectional image of the optical input end face of the fabricated optical modulator. Figure 12 is a graph showing the time waveform of the optical modulation of the fabricated optical modulator. In Figure 12, channel Ch1 is the output light intensity of the MZ optical modulator at 640 nm, and channel Ch2 is the applied voltage. A typical optical output waveform of an MZ optical modulator is shown for voltage changes of a triangular waveform, and the above V π This is 2.48V, the above V π L was 1.24 V·cm.

[0145] V calculated in Example 6 π Since the value of V π L calculated in Example 7 is smaller than the value of V

Industrial Applicability

[0146] The present invention can determine a wavelength band suitable for use in optical control elements such as optical modulators, optical switches, optical transceivers, optical phased arrays, LiDAR, smart glasses, optical interconnections, optoelectronic circuits, wavelength converters, electric field sensors, THz wave generators / detectors, etc. In particular, using an electro-optic material such as an electro-optic polymer that has not been conventionally focused on, a highly efficient optical control element can be realized in a wavelength band shorter than the C band.

Explanation of Signs

[0147] 10a, 10b Arm portions, 11 Core, 12 Clad, 15 Upper electrode, 16 Lower electrode.

Claims

1. A determination method that includes a step of determining a wavelength band suitable for use with an optical control element, The optical control element has an optical waveguide formed using an electro-optical material, The aforementioned determination method is, A step of selecting the following equation (I) and / or equation (II) as the formula for calculating the figure of merit of the electro-optic material at wavelength λ, based on the required characteristics of the optical control element, The process includes a step of calculating performance index FOM1 and / or performance index FOM2 using the formula selected in the above selection step, The determination step is a determination method that determines a wavelength band suitable for use of the optical control element based on the performance index of the electro-optic material calculated in the calculation step. [Math 1] [In the formula, n is the refractive index of the electro-optic material, r is the electro-optic coefficient of the electro-optic material, α is the propagation loss per unit length in the phase modulation region of the optical waveguide, and λ is the wavelength.]

2. The aforementioned selection step involves selecting at least formula (II), The calculation process described above is: The acceptable propagation loss in the phase modulation region. ｍａｘ And the allowable length L of the phase modulation region. ｍａｘ The ratio (Loss ｍａｘ / L ｍａｘ ) is the allowable propagation loss α per unit length in the phase modulation region. ｃ In that case, At each wavelength λ, α≦α ｃ If the relationship is such that α = α ｃ Let α > α ｃ The determination method according to claim 1, wherein if the relationship is such that α is used to calculate the performance index FOM2.

3. The determination method according to claim 1 or 2, wherein the electro-optic material is an electro-optic polymer.

4. A step of determining the wavelength band by the determination method described in any one of claims 1 to 3, A method for manufacturing an optical control element suitable for use in the wavelength band, comprising the step of forming the optical waveguide using the electro-optic material.

Images