Method for operating optical device

Abstract

To provide a method for operating an optical device which can be easily manufactured.SOLUTION: There is provide a method for operating an optical device by propagating light with a frequency f, the optical device comprises a first optical waveguide and a second optical waveguide arranged on a substrate. The optical device has an optical coupling region in which an interval between the first optical waveguide and the second optical waveguide is smaller than that in other regions so that light is coupled between the first optical waveguide and the second optical waveguide. In the optical coupling region, there is provided a grating structure in which, first refractive index material and second refractive index material having a refraction index lower than that of the first refractive index material are alternately arranged at a frequency Λ in a light propagation direction, the grating structure is arranged around the first and second optical waveguides. When light speed in vacuum is denoted as c0, an effective refractive index corresponding to an optical waveguide mode in the optical coupling region is denoted as neff, the light with the frequency f in which the frequency Λ satisfies 11c0 / (20neff f)≤Λ≤3c0 / (4neff f) is propagated to the optical device for operating the optical device.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present disclosure relates to a method of operating an optical device. [Background technology]

[0002] In optical devices made of various materials such as silicon (Si), indium phosphide (InP), gallium arsenide (GaAs), gallium nitride (GaN), lithium niobate (LiNbO3), and compound semiconductors based on these materials, optical waveguides are widely used as a basic component of devices. These waveguides have the ability to confine light to a localized region by making the refractive index higher than the surrounding area, and by forming this region into a linear shape, they can propagate the light to the desired region.

[0003] In addition, various waveguide-type devices based on optical waveguides are also widely used as basic components of optical devices to realize various functions, such as directional couplers, which optically couple the optical propagation modes of two independent optical waveguides by bringing them close to each other at a distance equal to or less than the wavelength of the propagating light, thereby transferring any power of the propagating light; multi-mode interference (MMI), which forms a wide waveguide to make the eigenmode of the light propagating inside multi-mode, and then splits the propagating light into any number of waves or combines it by optical interference between the modes; polarization multiplexers / demultiplexers which split the input light into polarizations and output them to different locations, or vice versa; and grating couplers which have a diffraction grating structure in the direction of light propagation and diffract light of the desired wavelength or polarization up and down from the optical waveguide, thereby propagating light through space.

[0004] However, in general directional couplers or waveguide-type optical devices such as MMI, in order to transfer the optical power propagating in one optical waveguide to the other optical waveguide sufficiently, or to equally distribute the input optical power to multiple outputs, a long distance of several tens of times the wavelength of the propagating light is required, which leads to a problem of large device size. In addition, optical devices such as MMI, polarization multiplexer / demultiplexer, and grating coupler have a small range of operating wavelengths or polarizations, and in order to accommodate various wavelengths or polarizations, it is necessary to devise a method such as arranging devices corresponding to light with various attributes in parallel, which also leads to a large overall device size. For example, 3 dB couplers or 3 dB splitters, which are often used in directional couplers and split 50% of the optical power to the other side, have a problem that the tolerance range of the device length at which the desired transfer rate can be obtained is very narrow, about 1 micrometer. The fact that the device length within the tolerance range is small compared to the overall device length indicates that directional couplers are devices that are vulnerable to manufacturing errors.

[0005] As a technology to solve the above problems, a periodic structure with a period equal to or smaller than that of the propagating light, known as a sub-wavelength grating (SWG) structure, has been introduced into a Si-based optical device in a direction perpendicular to two optical waveguides. This has succeeded in realizing a smaller device size, polarization insensitivity, and wavelength independence (Non-Patent Documents 1 and 2). [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] C. Ye et al., “Ultra-Compact Broadband 2 x 23 dB Power Splitter Using a Subwavelength-Grating-Assisted Asymmetric Directional Coupler,” JLT, vol. 38, no. 8 (2020) [Non-Patent Document 2] P. Cheben, “Subwavelength integrated photonics,” Nature, vol. 560, pp. 565-572 (2018) Summary of the Invention [Problem to be solved by the invention]

[0007] Non-Patent Documents 1 and 2 disclose techniques for realizing a small directional coupler, but the SWG structure needs to have a periodic structure with a size equal to or smaller than the wavelength. In general, the refractive index of semiconductor optical materials such as Si and InP that constitute the waveguide exceeds 3, so a size of 1 / 3 or less of the wavelength is essentially required. For example, if the wavelength is 1.5 μm, a periodic structure of 0.5 μm or less is required, and if the filling rate of the optical waveguide core material is 50%, a fine structure of about 0.25 μm is required. It is difficult to form a structure of such a size with high precision in the optical semiconductor process, and a high-precision process such as electron beam (EB) lithography is required, which is a factor of high cost.

[0008] The present disclosure has been made to solve the above-mentioned problems, and aims to provide an operating method for an optical device that requires less processing precision than before and can be easily manufactured. [Means for solving the problem]

[0009] A method for operating an optical device according to the present disclosure is a method for operating an optical device that propagates light of frequency f, the method comprising the steps of: The optical device includes a first optical waveguide and a second optical waveguide arranged side by side on a substrate, and has an optical coupling region in which the distance between the first optical waveguide and the second optical waveguide is narrower than in other regions such that the light is coupled between the first optical waveguide and the second optical waveguide; a grating structure is provided around the first optical waveguide and the second optical waveguide in the optical coupling region, in which a first refractive index material and a second refractive index material having a refractive index lower than that of the first refractive index material are alternately arranged with a period Λ in a propagation direction of the light, The speed of light in a vacuum is c0, and the effective refractive index corresponding to the guided mode in the optical coupling region is n eff Then, the period Λ is 11c0 / (20n eff f)≦Λ≦3c0 / (4n eff f) The light having the frequency f that satisfies the above is propagated to the optical device to operate it. Effect of the Invention

[0010] According to the method for operating an optical device disclosed herein, the processing precision required is relaxed compared to the conventional method, and the optical device can be easily manufactured. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a schematic top view showing a configuration of an optical device according to a first embodiment. [Diagram 2] 2 is a schematic enlarged perspective view showing a configuration of an optical coupling region of the optical device according to the first embodiment. FIG. [Diagram 3] 4 is a diagram illustrating the operating points of the optical device according to the first embodiment in comparison with the operating points of an optical device of the comparative example. [Figure 4] FIG. 4 is a schematic diagram for explaining the operation of the optical device according to the first embodiment in comparison with the operation of an optical device of the comparative example. [Diagram 5] 13 is a diagram showing the branching characteristics of optical power of an optical device of a comparative example. FIG. [Figure 6] 13 is a diagram showing the branching characteristics of optical power of an optical device of another comparative example. FIG. [Figure 7] 4 is a diagram showing the branching characteristics of optical power of the optical device according to the first embodiment. FIG. [Figure 8] FIG. 1 is a diagram showing a calculation model of the FDTD method. [Figure 9] FIG. 13 is a diagram showing characteristics of an optical device according to a comparative example. [Figure 10] 13 is a diagram showing the characteristics of the optical device according to the second embodiment in comparison with a comparative example. [Figure 11] 11 is a diagram illustrating the operation of the optical device according to the second embodiment in comparison with a comparative example. FIG. [Figure 12] FIG. 11 is a schematic top view showing the configuration of an optical device according to a third embodiment. [Figure 13] 13 is a schematic enlarged perspective view showing a configuration of an optical coupling region of an optical device according to a third embodiment. FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Embodiment 1 1 and 2 show the configuration of a directional coupler as an optical device according to the first embodiment. As shown in the plan view of FIG. 1, this directional coupler has an internal region with a higher refractive index than the surroundings, and two optical waveguides, a first optical waveguide 11 and a second optical waveguide 21, in which light is locally confined in this region and light is allowed to propagate only in a specific direction, are formed on a substrate 1. If this directional coupler is divided into regions in the light propagation direction, in the order of an input region A, a width shifting region B, a coupling region C, a width expansion region D, and an output region E, as shown in FIG. 1, the first optical waveguide 11 and the second optical waveguide 21 are configured as follows in each region. In the input region A, the first optical waveguide 11 and the second optical waveguide 21 are disposed with a sufficient interval of several times or more the wavelength of light. In the width shifting region B, the interval between the first optical waveguide 11 and the second optical waveguide 21 is changed so as to narrow from an interval of several times or more the wavelength of the propagating light in the input region A to about the size of the wavelength. In the width narrowing region B, the length of the region is about 10 times the wavelength or more, so that the first optical waveguide 11 and the second optical waveguide 21 are bent without optical loss, and both the first optical waveguide 11 and the second optical waveguide 21 are bent by drawing a curve such as a combination of arcs, a combination of sine waves or cosine waves, a cycloid curve, a clothoid curve, etc. In the optical coupling region C, the first optical waveguide 11 and the second optical waveguide 21 are arranged parallel and close to each other so that the interval is kept approximately constant at about the wavelength. Furthermore, in the width expansion region D, the interval between the first optical waveguide 11 and the second optical waveguide 21 is expanded to a sufficient interval of about the wavelength to several times the wavelength of light, in contrast to the width narrowing region B. The width expansion region D is about 10 times the wavelength or more, so that both the first optical waveguide 11 and the second optical waveguide 21 are bent by drawing a curve such as a combination of arcs, a combination of sine waves or cosine waves, or a cycloid curve, etc. Furthermore, in the output region E, the first optical waveguide 11 and the second optical waveguide 21 are disposed at a sufficient interval of at least several times the wavelength of light. This optical device constitutes a directional coupler in which the light of the first optical waveguide 11 and the second optical waveguide 21 are coupled in the optical coupling region C, which is the region where the first optical waveguide 11 and the second optical waveguide 21 are closest to each other.

[0013] FIG. 2 is an enlarged perspective view of the optical coupling region C. As shown in FIG. 2, the first optical waveguide 11 and the second optical waveguide 21 in the optical coupling region C have a substrate 1, a lower cladding layer 5 formed on the substrate 1, and core layers 11a and 21a, which are regions for confining light and are formed on the lower cladding layer 5 from a material having a higher refractive index than the lower cladding layer 5. Furthermore, the first optical waveguide 11 and the second optical waveguide 21 have a grating structure 3 in which protrusions (gratings) 31 are periodically and repeatedly arranged so as to be approximately perpendicular to the light propagation direction and to penetrate both the core layers 11a and 21a. Furthermore, the core layers 11a and 21a and the protrusions 31 are surrounded by a surrounding cladding 6 made of a material such as SiO2 or SiN having a lower refractive index than the material constituting the core layers. That is, the grating structure 3 has a configuration in which protrusions 31 made of a first refractive index material, which is the same material as the core layer, and surrounding cladding 6 made of a second refractive index material having a lower refractive index than the first refractive index material, are repeatedly arranged at a constant period, and the entire waveguide has a waveguide structure with a grating. The period Λ of the grating of the grating structure 3 is set so as to generally satisfy the following formula (1).

[0014]

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[0015] FIG. 3 shows a schematic diagram of the dispersion relationship of light propagating through an optical waveguide with a grating. The horizontal axis shows wave numbers, and the vertical axis shows frequency. Due to the action of the reciprocal lattice vectors of the grating, the dispersion characteristic is folded back at the so-called X point (=π / Λ), and the dispersion characteristic is curved near the X point, resulting in a Bragg reflection region where no propagation mode exists. The lower frequency side than the Bragg reflection region is the SWG region. In the optical waveguide with a grating shown in the prior art, the SWG region shown by the dashed arrow in the figure is the operating point. On the other hand, the higher frequency side than the Bragg reflection region is the radiation region, where the propagating light is radiated outside the waveguide, and the power is attenuated. The operating point of the optical device according to the first embodiment is the region shown by the solid arrow in FIG. 3. The period Λ of the grating is set so that the operating frequency f falls between f_min and f_max shown in FIG. 3, that is, so as to satisfy the formula (1). The optical device according to the first embodiment is characterized in that it operates at a frequency that is in the radiation region and shows the same wave number as the SWG device shown in the prior art. By setting Λ in this way, it is possible to make the grating period Λ longer than that of the prior art for the frequency f of light propagating through the same optical device, even though it is in the radiation region, which is an effect that the fineness of the pattern forming the grating can be relaxed.

[0016] The effect of the above structure will be described below. FIG. 4 shows a schematic diagram of the relationship between light propagating in a directional coupler based on a normal optical waveguide and a directional coupler based on an optical waveguide with a grating. In a structure based on a normal optical waveguide, the wave vector increases as the frequency of the propagating light increases, but in a structure based on an optical waveguide with a grating, the reciprocal lattice vector acts. When operating in a frequency range higher than the Bragg reflection range as in the technology of the present disclosure, the reciprocal lattice vector acts to fold back the wave vector of the propagating light, and as a result, the kz component of the wave vector can be set to a length similar to that of a conventional SWG. As a result, in the present disclosure, even with a long-period grating structure, the same effect as that of a conventional SWG structure can be obtained.

[0017] 5 to 7 respectively show the results of calculations of the relationship between the length of the optical coupling region and the branching ratio of optical power when light with a wavelength of 1.55 μm is incident on a normal directional coupler without a grating structure, a directional coupler with a grating of an SWG structure, and a directional coupler with a grating structure according to the first embodiment. In each of the directional couplers, the first optical waveguide 11 and the second optical waveguide 21 in the optical coupling region are Si waveguides with a refractive index of 3.4, with widths of 0.4 μm and 0.5 μm, an interval of 0.2 μm, and a height of 0.25 μm, and are surrounded by a SiO2 cladding with a refractive index of 1.6 (n eff =2.38). FIG. 5 shows the calculation results for a normal directional coupler without a grating structure as a comparative example. FIG. 6 shows the calculation results for a normal directional coupler without a grating structure as a comparative example. eff 7 shows an example of the calculation results for the directional coupler according to the first embodiment, in which the grating structure 3 has a period of 0.39 μm (Λ=0.600c0 / (n eff ·f)) This is the calculation result when a grating structure with a filling rate of 50% is provided.

[0018] The reason why the widths of the first optical waveguide 11 and the second optical waveguide 21 are different is that by making the widths different, it is possible to shorten the distance required for optical branching. This effect becomes noticeable when the width ratio is about 1.2 times. The optimal ratio varies depending on the branching ratio to be designed. However, if the width ratio becomes too large, such as 2 times or more, the difference in effective refractive index between the respective guided modes of the first optical waveguide and the second optical waveguide becomes too large, and a coupling mode is not formed.

[0019] As shown in FIG. 5, a normal directional coupler without a grating cannot achieve 50% power splitting no matter how the length is set, but by adding an SWG structure as shown in FIG. 6, it is possible to achieve approximately 50% power splitting at a length of about 6 μm to 8 μm. In addition, in the configuration according to the first embodiment of FIG. 7, even if the grating has a period about 1.8 times longer than that of the SWG, it is possible to achieve approximately 50% power splitting at a length of about 6 μm to 8 μm, and it is found that characteristics equivalent to those of the conventional SWG structure are obtained. A directional coupler length that can achieve the same power splitting is long, which means that the required manufacturing accuracy of the directional coupler can be relaxed. At the same time, it also means that the optical length at which the desired characteristics are obtained is long, which has the effect of expanding the operating wavelength band.

[0020] The shape, material, and positional relationship of the directional coupler are not necessarily limited to those in the first embodiment. For example, the positions of the input-side optical waveguide and the output-side optical waveguide may be interchanged, the material of the substrate 1 may be other materials such as Si, GaAs, SiO2, SiN, LiNbO3, and the core layer does not have to be Si, but may be any material with a higher refractive index than the cladding layer, for example, SiO2 doped with Ge for SiO2 cladding. In this case, the refractive index of the device is generally small, which is disadvantageous in that the device size becomes large, but the optical loss of the propagating light is small, which is advantageous in that a low-loss device can be realized.

[0021] Embodiment 2 The second embodiment is a modification of the first embodiment, and is characterized in that in the directional coupler shown in FIGS. 1 and 2, the period of the grating 3 generally satisfies the following formula (2).

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[0022] In the first embodiment, it was confirmed that even with a long period grating, the same characteristics as those of a conventional SWG device can be obtained in terms of the branching ratio characteristics of optical power. However, since this operating region is the radiation region in the dispersion relationship of the optical waveguide, there is a problem that radiation loss is unavoidable in principle. In particular, there is a concern that the influence will be large when the period Λ of the grating is large, that is, when the operating frequency is located above the dispersion characteristics in FIG. 3. However, if Λ is in a range satisfying formula (2), it is possible to realize the effects shown in the first embodiment while suppressing the attenuation of propagating light due to the radiation mode, which is a disadvantage when introducing a long period grating.

[0023] The effects of this embodiment will be described below. The radiation loss in each structure was calculated using electromagnetic field simulation (Finite Difference Time Domain Method, FDTD method). Figure 8 shows a calculation model for the FDTD method. An optical waveguide with a grating of 0.22 μm in height is installed in the cladding from 10 μm to 100 μm, and a normal optical waveguide of the same height is used from 0 μm to 10 μm. The refractive index n is 3.4 for the protrusion 31 of the grating structure, 1.6 for the surrounding cladding 6, and 3.4 for the optical waveguide. In this model, the fundamental mode of the optical waveguide is excited at the position X = 0 μm and propagated toward the right in the drawing. The relationship between the propagation distance and the power of the propagating light was calculated when the period of the grating was changed in various ways.

[0024] Figure 9 shows the calculation results of the radiation loss in the SWG region and the Bragg reflection region in Figure 3. eff f)~0.491c0 / (n eff It can be seen that in the SWG region with a grating period of 0.34 μm (Λ=0.522c0 / (n eff In the Bragg reflection region of f), since there is no propagation mode within the optical waveguide with a grating, it can be seen that the power attenuates while oscillating greatly according to the propagation distance.

[0025] Figure 10 shows the calculation results of the radiation loss in the radiation region in Figure 3. The period Λ is 0.36μm to 0.38μm (Λ is 0.553c0 / (n eff f)~0.583c0 / (n eff In the structure of the second embodiment, since the structure is in the radiation region, there is a slight loss, but it is understood that the loss is suppressed to approximately the same level as the loss characteristic of the SWG region in FIG. 9. On the other hand, when the period Λ is increased to 0.40 μm to 0.60 μm (Λ is 0.614c0 / (n eff f)~0.922c0 / (n eff In the region f), radiation loss is large and the optical power of the propagating light is significantly attenuated.

[0026] In Fig. 11, the period Λ is 0.20 μm (Λ = 0.307c0 / (n eff ·f)) (Fig. 11D), 0.34μm (Λ=0.522c0 / (n eff ·f))(Fig. 11C), 0.38μm(Λ=0.583c0 / (n eff ·f))(Fig. 11B), 0.60μm(Λ=0.922c0 / (n eff The calculation results of the electromagnetic field distribution of the propagating light in the structure with large radiation loss shown in Fig. 9 and Fig. 10 are shown. In Fig. 11, an upward arrow (↑) indicates a positive electric field, and a downward arrow (↓) indicates a negative electric field, with the darker the arrow, the larger the absolute value. It can be seen that in the structure with large radiation loss shown in Fig. 9 and Fig. 10, the intensity of the propagating light decreases as it moves to the right.

[0027] Embodiment 3 12 and 13 show the configuration of an optical device according to the third embodiment. This optical device is an optical device in which the optical coupling region is a multi-mode interference (MMI) waveguide. As shown in the plan view of FIG. 12, this optical device has a region inside which the refractive index is higher than the surroundings, and two optical waveguides, a first optical waveguide 11 and a second optical waveguide 21, in which light is locally confined in the region and light is allowed to propagate only in a specific direction, are formed on a substrate 1. If this optical device is divided into regions in the light propagation direction in the order of an input region A, a width adjustment region B, a coupling region C, a width expansion region D, and an output region E as shown in FIG. 12, the first optical waveguide 11 and the second optical waveguide 21 in each region have the following configuration. In the input region A, the first optical waveguide 11 and the second optical waveguide 21 are arranged at a sufficient interval of several times or more the wavelength of light. In the width shifting region B, the interval between the first optical waveguide 11 and the second optical waveguide 21 is changed from an interval of several times or more of the wavelength of the propagating light in the input region to be narrowed to about the wavelength size. In this width shifting region B, the length of the region is about 10 times or more of the wavelength so that the first optical waveguide 11 and the second optical waveguide 21 are bent without optical loss, and both the first optical waveguide 11 and the second optical waveguide 21 are configured to bend by drawing a curve such as a combination of circular arcs, a combination of sine waves or cosine waves, or a cycloid curve or a clothoid curve. In the optical coupling region C, a grating structure 30 is formed to configure an MMI section, and light is configured to be incident on this grating structure 30 from the first optical waveguide 11 and the second optical waveguide 21. Also, light from the grating structure 30 in the optical coupling region C is configured to be coupled again to the first optical waveguide 11 and the second optical waveguide 21 in the width expansion region D. In the width expansion region D, the distance between the first optical waveguide 11 and the second optical waveguide 21 is expanded from about the wavelength, which is the distance on the optical coupling region C side, to a sufficient distance of several times the wavelength of light or more, in contrast to the width narrowing region B. The width expansion region D has a length of about 10 times the wavelength or more, and both the first optical waveguide 11 and the second optical waveguide 21 are configured to bend in a curve such as a combination of circular arcs, a combination of sine waves or cosine waves, or a cycloid curve.Furthermore, in the output region E, the first optical waveguide 11 and the second optical waveguide 21 are disposed at a sufficient interval that is at least several times the wavelength of the light.

[0028] 13, the MMI portion of the optical coupling region C includes a substrate 1, a lower cladding layer 5 formed on the substrate 1, a grating structure 30 made of a material having a higher refractive index than the lower cladding layer 5 and having gratings 33 arranged periodically and repeatedly on the lower cladding layer 5 so as to be approximately perpendicular to the direction of light propagation, and a surrounding cladding 6 made of a material such as SiO2 or SiN having a lower refractive index than the material constituting the core layer arranged so as to surround the grating 33. The period of the grating 33 is set to approximately satisfy the following formula (3) (same as formula (1) in the first embodiment). In order to function as an MMI with sufficiently small optical loss, the width of the grating structure 30 in the x direction, i.e., the direction perpendicular to the direction of light propagation and parallel to the substrate 1, needs to be three times the wavelength of light or more.

[0029]

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[0030] By adopting the third embodiment, it is possible to realize power splitting operation in a wide wavelength range, similar to the SWG structure MMI disclosed in the prior art, with a long-period grating that requires lower manufacturing accuracy, which provides the advantage of reducing manufacturing costs.

[0031] Although various exemplary embodiments and examples are described in this disclosure, various features, aspects, and functions described in one or more embodiments are not limited to the application of a specific embodiment, but can be applied to the embodiments alone or in various combinations. Therefore, countless modifications not illustrated are expected within the scope of the technology of this disclosure. For example, the following are included: modifying, adding, or omitting at least one component; and extracting at least one component and combining it with components of other embodiments. [Explanation of symbols]

[0032] 1 Substrate, 3, 30 Grating structure, 11 First optical waveguide, 21 Second optical waveguide, C Optical coupling region, 31, 33 Grating

Claims

1. A method of operating an optical device that propagates and operates light of frequency f, comprising the steps of: The optical device includes a first optical waveguide and a second optical waveguide arranged side by side on a substrate, and has an optical coupling region in which the distance between the first optical waveguide and the second optical waveguide is narrower than in other regions such that the light is coupled between the first optical waveguide and the second optical waveguide; a grating structure is provided around the first optical waveguide and the second optical waveguide in the optical coupling region, in which a first refractive index material and a second refractive index material having a refractive index lower than that of the first refractive index material are alternately arranged with a period Λ in a propagation direction of the light, The speed of light in a vacuum is c 0 , the effective refractive index corresponding to the guided mode in the optical coupling region is n eff Then, the period Λ is 11c 0 / (20n eff ・f)≦Λ≦3c 0 / (4n eff ・f) A method for operating an optical device, comprising: propagating light of the frequency f that satisfies the above formula through the optical device and operating the optical device.

2. The period Λ is 11c 0 / (20n eff ・f)≦Λ≦3c 0 / (5n eff ・f) 2. The method of claim 1, further comprising propagating light of the frequency f that satisfies the above formula through the optical device to operate it.

3. 3. The method for operating an optical device according to claim 1, wherein the width of the first optical waveguide in the optical device is 1.2 to 2 times the width of the second optical waveguide.

4. A method of operating an optical device that propagates and operates light of frequency f, comprising the steps of: the optical device comprises a first optical waveguide and a second optical waveguide arranged side by side on a substrate, and a grating structure in which a first refractive index material and a second refractive index material having a refractive index lower than that of the first refractive index material are alternately arranged with a period Λ in the propagation direction of the light, The light is configured to be incident on the grating structure from the first optical waveguide and the second optical waveguide, a width of the grating structure in a direction perpendicular to the propagation direction of the light and parallel to the substrate is three times or more the wavelength of the light; The speed of light in a vacuum is c 0 , the effective refractive index corresponding to the guided mode in the grating structure is n eff Then, the period Λ is 11c 0 / (20n eff ・f)≦Λ≦3c 0 / (4n eff ・f) A method for operating an optical device, comprising: propagating light of the frequency f that satisfies the above formula through the optical device and operating the optical device.

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