A polarization-insensitive optical power coupler

By designing a polarization-insensitive optical power coupler, using silicon nitride vertical slit waveguide structure and low refractive index electrophotopolymer material, and applying voltage to adjust the waveguide refractive index, the polarization-independent power distribution in aligned TE and quasi-TM modes is achieved, solving the problem of wavelength and polarization sensitivity in the prior art, and is suitable for high-power systems and multi-dimensional multiplexing systems.

CN115826133BActive Publication Date: 2025-07-25XI AN JIAOTONG UNIV
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Patent Information

Application Number
CN202211625953.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-12-15
Publication Date
2025-07-25
Estimated Expiration
2042-12-15

AI Technical Summary

Technical Problem

Existing optical power couplers are highly sensitive to wavelength and polarization, making it difficult to achieve low loss and broadband polarization-insensitive power distribution in ultra-high bandwidth communications.

Method used

A polarization-insensitive optical power coupler is designed, and by controlling the coupling length ratio of quasi-TE and quasi-TM modes to 1, using a silicon nitride vertical slit waveguide structure and a low refractive index electrophotopolymer material, the refractive index of the waveguide structure is adjusted by applying an external voltage to achieve polarization-independent power distribution.

Benefits of technology

The polarization insensitive characteristics of aligned TE and quasi-TM modes are realized, and are suitable for power distribution in different proportions, with strong applicability and CMOS compatibility, and are suitable for high-power systems and multi-dimensional multiplexing systems.

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Abstract

The present invention discloses a polarization-insensitive optical power coupler, which includes two silicon nitride vertical slit waveguide structures. The waveguide structures are divided into a silicon nitride layer structure on the left and a silicon nitride layer structure on the right in the width direction, and the intermediate slit material is between the silicon nitride layer structures. The outer side of the waveguide structure is coated with a cladding material, and the intermediate slit material and the cladding material are silicon dioxide or a low-refractive-index electro-optic polymer. The present invention controls the coupling length ratio of the quasi-TE and quasi-TM modes to about 1, can achieve polarization-independent power distribution, and at the same time, the polarization insensitivity of the device has a certain applicability, that is, polarization insensitivity.
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Description

Technical Field

[0001] The present invention relates to the technical field of optical power couplers, and particularly to a polarization-insensitive optical power coupler. Background Art

[0002] An optical power coupler is one of the key components for separating and combining optical signals in an integrated optical circuit, and is also a basic building block for more complex optical devices and functions, such as Mach-Zehnder interferometers, optical phased arrays, mode multiplexers, etc. Although many implementations of beam splitters have been experimentally demonstrated on the SOI platform, low-loss, broadband, and polarization-insensitive optical power couplers are highly desirable for ultra-high bandwidth communications, e.g., multi-dimensional multiplexing systems. The directional coupler is one of the most popular methods for implementing a power splitter.

[0003] However, the performance of the power splitter of a traditional silicon directional coupler is highly sensitive to wavelength and polarization.

[0004] In the existing literature, H. Morino, T. Maruyama, and K. Iiyama, “Reduction of wavelength dependence of coupling characteristics using Si optical waveguide curved directional coupler,” J. Lightw. Technol., vol. 32, no. 12, pp. 2188–2192, Jun. 2014, can only effectively implement power splitting for a specific polarization state. Summary of the Invention

[0005] In order to overcome the above problems existing in the prior art, the present invention proposes a polarization-insensitive optical power coupler, which controls the coupling length ratio of the quasi-TE and quasi-TM modes to about 1, can achieve polarization-independent power splitting, and the device has polarization insensitivity.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A polarization-insensitive optical power coupler includes two waveguide structures with the same structural shape. The waveguide structures are strip-shaped and are arranged parallel to each other on the left and right. Each waveguide structure includes a left silicon nitride layer, a middle slit layer, and a right silicon nitride layer that are tightly arranged in sequence. The outside of the waveguide structure is coated with a cladding material. The material of the middle slit layer and the cladding material are both silicon dioxide or both low-refractive-index electro-optic polymers.

[0008] The low refractive index electro-optic polymer has a refractive index lower than that of silicon nitride and a relatively large electro-optic coefficient.

[0009] When the slit material and the cladding material of the optical power coupler are made of low refractive index electro-optic polymer, by applying an external voltage to the two waveguide structures to supply power to the two waveguide structures, the refractive index of the middle slit and the cladding of the waveguide structure is changed, and the tunable property of the present invention is extended; the refractive index of the middle slit layer will change with the adjustment of the voltage, thereby changing the refractive index of the whole two waveguides. At this time, the refractive indices of the X or Y polarization odd-symmetric mode and the even-symmetric mode change correspondingly. According to the mode coupling theory, a new coupling length of X or Y polarization is obtained. By adjusting the voltage, the ratio of the coupling lengths of the two polarization states is adjusted to about 1 again, and polarization-insensitive power distribution can be achieved.

[0010] The definitions of the parameters in the two waveguide structures are as follows: the distance between the geometric centers is d, the overall height of each waveguide structure is H, the overall width of the waveguide structure is W, and the thickness of the middle slit of the waveguide structure is W s , the thickness of the silicon nitride layer on the left side is W L , the thickness of the silicon nitride layer on the right side is W R ;

[0011] The distance d between the waveguide structures is between 100 - 900 nm, the height H is between 500 - 2000 nm, the width W is between 500 - 2000 nm, and the thickness of the middle slit layer W s is between 50 - 200 nm.

[0012] In the optical power coupler, the coupling length of the quasi-TE mode is L TE , the coupling length of the quasi-TM mode is L TM , when the ratio of the coupling lengths (L TE / L TM ) is 1, the optical power coupler has polarization-insensitive characteristics.

[0013] When the optical power coupler is applied to a wavelength of 1550 nm, W = 1700 nm, H = 1200 nm. When W L= W R = 775 nm, W s = 150 nm, the ratio of the coupling lengths corresponding to the two polarization states is closest to 1.

[0014] The parameters of the polarization-insensitive optical power coupler are adjusted through the following steps; Step 1:

[0015] Inject light of the quasi-TE or TM mode into the left or right waveguide structure, and the light will gradually couple into the adjacent waveguide structure. According to the simulation results, the effective refractive indices corresponding to the X polarization odd-symmetric mode, the X polarization even-symmetric mode, the Y polarization odd-symmetric mode, and the Y polarization even-symmetric mode of the two waveguides can be obtained respectively.

[0016] The coupling method is specifically as follows:

[0017] Based on the mode coupling theory, i.e., the following formula, the propagation behavior in the polarization-insensitive power splitter is regarded as the sum of the even-symmetric mode and the odd-symmetric mode along the waveguide structure. The coupling lengths of two mutually orthogonal polarization states are expressed as:

[0018] L TE = λ / [2 * (n e,TE - n o,TE )]

[0019] L TM = λ / [2 * (n e,TM - n o,TM )]

[0020] Where L TE is the coupling length, and L TM is the coupling length of the quasi-TM mode. n e,TE is the effective refractive index of the even-symmetric mode of the quasi-TE mode, n o,TE is the effective refractive index of the odd-symmetric mode of the quasi-TE mode, n e,TM is the effective refractive index of the even-symmetric mode of the quasi-TM mode, and n o,TM is the effective refractive index of the odd-symmetric mode of the quasi-TM mode;

[0021] Step 2:

[0022] Optimize the parameters of the cross-sectional structures of the two waveguides and the distance between the two waveguide structures, so that the ratio of the coupling lengths (L TE / L TM ) is set to 1. At this time, the cross-sectional structure parameters that can enable the device to achieve polarization-insensitive characteristics are obtained;

[0023] Step 3: As the transmission distance increases, the light will gradually couple from the incident waveguide to the adjacent waveguide until it is all coupled out from the adjacent waveguide structure. That is, when the waveguide length L is different values, different ratios of quasi-TE or TM mode light can be obtained in the two waveguides, so as to achieve different power distributions.

[0024] In the above Step 2, after obtaining the coupling lengths L TE and L TM of the two polarization states, calculate the ratio of the coupling length ratio (L TE / L TM ), compare it with 1, and measure whether its coupling length is too long (exceeding 100 μm). If the coupling length is too large, it will increase the overall device length, and adjust the waveguide structure.

[0025] The specific method for adjusting the waveguide structure in the above Step 2 is:

[0026] First: Adjust the spacing d between the two waveguide structures so that the device length is less than 100 μm;

[0027] Second: Coarsely adjust the overall width W and height H of the waveguide structure. Calculate the ratio of the coupling lengths of the X and Y polarizations through step one, and continue to adjust the thickness of the middle slit, the thickness W of the silicon nitride layers on the left and right sides L 、W R 、the thickness W of the middle slit layer s , so that the output optical power has a similar response to the two polarization states, thus showing polarization-insensitive characteristics.

[0028] In step three above, the incident waveguide is defined as the BAR port, and the adjacent waveguide is defined as the CROSS port.

[0029] According to the power distribution ratio required by the target, the device length L can be further determined. For example, when the target distribution ratio is 50:50, when the waveguide structure length is L = 1 / 2L TE = 1 / 2L TM , then the device length is 34.76 μm. When different optical power coupler lengths are selected, equal splitting ratios including but not limited to 10:90, 20:80, 30:70, 40:60, 50:50 can be achieved. At the same time, the two polarization modes achieve almost the same state for these optical power coupling ratios and have polarization-insensitive characteristics.

[0030] Advantages of the present invention:

[0031] By designing a novel power splitter structure, the present invention is insensitive to two polarization modes, namely the TE and quasi-TM modes. Numerical calculation results show that by appropriately adjusting the structural parameters of the device, the present invention can achieve polarization-insensitive power distribution in large-scale integrated optical networks. Since this structure can simultaneously be applied to power splitters with different coupling ratios, it has strong applicability.

[0032] The optical power coupler of the present invention is applicable to power distribution with different ratios, making it have the same response to the TE and quasi-TM modes, that is, it has polarization insensitivity. The present invention is based on silicon nitride integrated waveguides. It has advantages such as CMOS compatibility and large manufacturing tolerances. At the same time, compared with silicon-based waveguides, it is not affected by two-photon absorption and is applicable to high-power systems, and is used in the technical field of multi-dimensional multiplexing systems. Description of the Drawings

[0033] Figure 1 is the basic structural schematic diagram of the present invention.

[0034] Figure 2 is the extended structural diagram of the present invention.

[0035] Figure 3 It is a representative diagram of the optimization process of the present invention.

[0036] Figure 4 It is a schematic diagram of the results between the present invention for two polarization states of quasi-TE and TM, different coupling lengths and normalized intensities.

[0037] Figure 5 It is a schematic diagram of the deviation shown by the two polarization states of quasi-TE and TM for different power distribution ratios under certain geometric parameter settings of the present invention.

[0038] Figure 6 It is the wavelength dependence shown by the normalized intensities of the two polarization states of quasi-TE and TM at the BAR port and the CROSS port in the wavelength range of 1500 - 1600 nm. Detailed implementation manners

[0039] The present invention will be further described in detail below with reference to the accompanying drawings.

[0040] The present invention is based on an integrated power divider with polarization-insensitive characteristics, such as Figure 1 As shown, it includes two silicon nitride vertical slit waveguides with a certain spacing. In the present invention, when the quasi-TE / TM modes are coupled to each other at both ports, they perform the same, that is, it shows polarization-insensitive power distribution.

[0041] Figure 1 For the power distribution mechanism in two polarization states, including two silicon nitride vertical slit waveguide structures, focusing on the parameter optimization process of the present invention, which includes optimizing and adjusting the geometric center spacing d between the two waveguides, the overall height H of each waveguide, the overall width W of the waveguide, and the thickness W of the middle slit s , the thickness W of the silicon nitride on the left layer L , the thickness W of the silicon nitride on the right layer R, It shows polarization-insensitive characteristics for the quasi-TE and quasi-TM modes. The material of the middle slit and the cladding material are silica or low-refractive-index electro-optic polymers.

[0042] The middle slit and cladding materials include but are not limited to silica, low-refractive-index electro-optic materials, etc.

[0043] When forming the slit layer based on the low-refractive-index electro-optic material, by applying an external voltage to the two waveguides, the refractive index of the middle slit layer will change with the adjustment of the voltage, thereby changing the overall refractive index of the two waveguides. At this time, the refractive indices of the X or Y polarization odd-symmetric mode and the even-symmetric mode change correspondingly. According to the mode coupling theory, a new coupling length of X or Y polarization can be obtained. At a certain voltage value, the ratio of the coupling lengths of the two polarization states is adjusted to about 1 again, and polarization-insensitive power distribution can be achieved.

[0044] The present invention is based on a silicon nitride vertical slot waveguide. The waveguide core is composed of three materials, namely silicon nitride, silicon dioxide, and silicon nitride materials from left to right, combined with a silicon dioxide cladding. The two lines respectively represent the coupling states of the quasi-TE and quasi-TM modes in the present invention. Among them, the middle slot and the cladding material can also be filled with a low-refractive-index electro-optic polymer material, and the refractive index of the middle polymer is changed by applying an external voltage. Under the action of an external electric field, the electro-optic coefficient of the electro-optic polymer itself and the intensity of the external electric field determine the refractive index of the polymer and the refractive index contrast of the entire waveguide.

[0045] As Figure 2 shown, the materials of the cladding and the middle slot can both be replaced with low-refractive-index polymer materials. At the same time, electrodes are made on both sides of the two waveguide structures to supply power to the two slot waveguides, thereby changing the refractive indices of the middle slot and the cladding, and expanding the tunable properties of the present invention.

[0046] As Figure 3 shown: L TE 、L TM are the coupling lengths of the power divider for the quasi-TE and TM modes. Figure 3 is the change of the coupling length of the quasi-TE mode and the ratio of the coupling lengths of the two polarization states (L TE / L TM ) with different waveguide spacings.

[0047] According to Figure 1 the conceptual diagram shown, the implementation method and process of the present invention are described:

[0048] Step 1:

[0049] The quasi-TE / TM mode is incident in the left / right waveguide. After a certain transmission distance L, the light is gradually coupled into the adjacent waveguide structure until all of it is coupled out from the adjacent waveguide, and a certain proportion of the quasi-TE / TM mode light is obtained in the right / left waveguide structure.

[0050] Step 2:

[0051] Optimize the parameters of the two waveguide structures and the spacing between the two waveguide structures, and set the coupling length ratio (L TE / L TM ) to be close to 1.

[0052] According to Figure 3 Adjust the spacing between the two silicon nitride vertical waveguides and the coupling length ratio (L TE / L TM ) and the coupling length of the quasi-TE mode of the present invention. According to Figure 2 the shown trend, the larger the spacing between the two waveguides, the coupling length of the quasi-TE mode first increases and then decreases. In order to achieve the effect of polarization insensitivity, select L TE / LTM Geometric parameters close to 1.

[0053] Step 3: Select a certain device length according to a certain power splitting ratio requirement.

[0054] When light in the quasi-TE and TM modes is incident from one port, after propagating a certain distance, it will be fully coupled into the adjacent waveguide structure. During this process, other optical power splitting ratios will be experienced. If a certain optical power splitting ratio is desired, only a specific transmission length needs to be selected. At the same time, the two polarization states have non-similar responses at this length.

[0055] After the present invention selects certain structural parameters, according to Figure 4 the shown result graph, coupling ratios including but not limited to 10:90, 20:80, 50:50, 70:30, etc. can be achieved for the TE mode. At this time, the deviation of the coupling ratio between the TE mode and the TM mode is only 0.22%. Under this condition, the coupling length ratios of the two polarization states are close to 1. Therefore, the two orthogonally polarized states can be effectively in the same coupling state at 1550 nm.

[0056] According to Figure 5 it can be known that the present invention takes the power splitting ratio of the TE mode as the standard, and the deviation of the power splitting ratio of the TM mode is shown. It is shown that for different power splitting ratios of the present invention, the deviation between the two polarization modes is less than 1.6%, which shows the insensitivity of the present invention to the polarization state.

[0057] Step 4: Take the 50:50 splitting ratio as an example to illustrate the wavelength dependence of the present invention.

[0058] According to Figure 6 it can be known that the present invention includes but is not limited to taking 1550 nm as the design center, and the wavelength dependence of the normalized intensities of the quasi-TE / and TM modes at the BAR port and the CROSS port is small.

[0059] Example: This example is carried out for 1550 nm;

[0060] After obtaining the coupling lengths of the two polarization states, calculate the ratio of their coupling lengths, compare it with 1, and measure whether the coupling length is too long. If the coupling length L is too large, it will increase the overall device length. At this time, the distance d between the two waveguides can be preferentially adjusted so that the device length is within the ideal range (less than 100 μm), and then the overall width W and height H of the waveguide are roughly adjusted to about W = 1700 nm and H = 1200 nm. By calculating the ratio of the coupling lengths of the X and Y polarizations, continue to adjust the thickness of the middle slit, the thickness W L of the left and right silicon nitride layers, W R and the thickness W . of the middle slit layer. When Wl= W r = 775 nm, W s = 150 nm, the ratio of the coupling lengths corresponding to the two polarization states at a wavelength of 1550 nm is closest to 1. There is a similar response for the two polarization states, thus exhibiting polarization-insensitive characteristics.

[0061] The present invention controls the coupling length ratio (L TE / L TM ) of the quasi-TE and quasi-TM modes to around 1, enabling polarization-independent power splitting, and its coupling length is several tens of micrometers. At the same time, the polarization insensitivity of this device has a certain applicability. When the length of the device is different, the power splitting ratios at the BAR port and the CROSS port are different, but the same response is exhibited for both the quasi-TE and quasi-TM polarization modes, that is, polarization insensitivity.

[0062] When light is incident from one waveguide, after a period of time, part of the light is coupled to the CROSS port and the other part passes through the BAR port, thereby achieving a certain coupling ratio. When different device lengths are selected, splitting ratios including but not limited to 10:90, 20:80, 30:70, 40:60, 50:50, etc. can be achieved.

[0063] When the waveguide length is L = 1 / 2L TE = 1 / 2L TM= = 34.76 μm, a splitting ratio of 50:50 can be achieved. Both polarization modes achieve an almost identical state for these optical power coupling ratios, having polarization-insensitive characteristics.

[0064] For the silicon nitride slit vertical waveguide structure, based on the mode coupling theory, a structure using two vertical slit waveguides simultaneously is proposed, including but not limited to the wavelength-dependent characteristics of the quasi-TE and quasi-TM modes with a design center of 1550 nm in the present invention.

[0065] The present invention can realize a polarization-insensitive optical power coupler. For the waveguide structure parameters, there are various selection and combination methods for the distance between the two waveguides and the device length. The refractive index material of the middle slit can also be further extended to an electro-optic polymer, and the overall refractive index contrast of the waveguide can be adjusted by applying an electric field to this material. Therefore, any further extension containing the present invention also falls within the protection scope of the present invention.

[0066] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. The accompanying drawings here are used to provide a further understanding of the present invention. However, the protection scope of the present invention is not limited to the disclosed embodiments, and is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Therefore, any obvious changes to the technical solutions that belong to the technical concept of the present invention should fall within the protection scope of the present invention.

Claims

1. A polarization-insensitive optical power coupler, characterized in that It includes two waveguide structures with the same structural shape. The waveguide structures are strip-shaped, and the two waveguide structures are arranged parallel to each other left and right. Each waveguide structure includes a left silicon nitride layer, a middle slit layer, and a right silicon nitride layer that are sequentially and tightly arranged; a cladding material is coated outside the waveguide structure, and the material of the middle slit layer and the cladding material are both silicon dioxide or both low-refractive-index electro-optic polymers; The distance d between the waveguide structures is between 100 - 900 nm, the height H is between 500 - 2000 nm, the width W is between 500 - 2000 nm, and the thickness W of the middle slit layer s is between 50 - 200 nm; In the optical power coupler, the coupling length of the quasi-TE mode is L TE , and the coupling length of the quasi-TM mode is L TM , when the ratio of the coupling lengths (L TE / L TM ) is 1, the optical power coupler has polarization-insensitive characteristics.

2. The polarization-insensitive optical power coupler according to claim 1, wherein The low-refractive-index electro-optic polymer has a refractive index lower than that of silicon nitride and a large electro-optic coefficient.

3. A polarization-insensitive optical power coupler according to claim 1, wherein When the slit material and the cladding material of the optical power coupler are low-refractive-index electro-optic polymers, by applying an external voltage to the two waveguide structures to supply power to the two waveguide structures, the refractive indices of the middle slit and the cladding of the waveguide structure are changed to expand the tunable properties of the present invention; the refractive index of the middle slit layer will change with the adjustment of the voltage, thereby changing the overall refractive index of the two waveguides. At this time, the refractive indices of the X or Y polarization odd-symmetric mode and the even-symmetric mode correspondingly change. According to the mode coupling theory, a new coupling length of X or Y polarization is obtained. By adjusting the voltage, the ratio of the coupling lengths of the two polarization states is adjusted to about 1 again, and polarization-insensitive power distribution can be achieved.

4. A polarization-insensitive optical power coupler according to claim 1, wherein The parameters in the two waveguide structures are defined as follows: the distance between the geometric centers is d, the overall height of each waveguide structure is H, the overall width of the waveguide structure is W, and the thickness of the middle slit of the waveguide structure is W s , the thickness of the left-side silicon nitride layer is W L , the thickness of the right-side silicon nitride layer is W R .

5. A polarization-insensitive optical power coupler according to claim 4, characterized in that When the optical power coupler is applied at a wavelength of 1550 nm, W = 1700 nm and H = 1200 nm. When W L = W R = 775 nm, and W s = 150 nm, the ratio of the coupling lengths corresponding to the two polarization states is closest to 1.

6. A polarization-insensitive optical power coupler according to claim 4, wherein The parameters of the polarization-insensitive optical power coupler are adjusted through the following steps; Step 1: Light in the quasi-TE or TM mode is incident on the left or right waveguide structure, and the light will gradually couple into the adjacent waveguide structure. According to the simulation results, the effective refractive indices corresponding to the X polarization odd-symmetric mode, the X polarization even-symmetric mode, the Y polarization odd-symmetric mode, and the Y polarization even-symmetric mode of the two waveguides can be obtained respectively; The specific coupling method is: Based on the mode coupling theory, that is, the following formula, the propagation behavior in the polarization-insensitive power splitter is regarded as the sum of the even-symmetric mode and the odd-symmetric mode along the waveguide structure. The coupling lengths of two mutually orthogonal polarization states are expressed as: L TE = λ / [2 * (n e,TE - n o,TE )] L TM = λ / [2 * (n e,TM - n o,TM )] where L TE is the coupling length, L TM is the coupling length of the quasi-TM mode, n e,TE is the effective refractive index of the even-symmetric mode of the quasi-TE mode, n o,TE is the effective refractive index of the odd-symmetric mode of the quasi-TE mode, n e,TM is the effective refractive index of the even-symmetric mode of the quasi-TM mode, n o,TM is the effective refractive index of the odd-symmetric mode of the quasi-TM mode; Step 2: Optimize the parameters of the cross-sectional structures of the two waveguides and the distance between the two waveguide structures so that the ratio of the coupling lengths (L TE / L TM ) is set to 1, and at this time, the cross-sectional structure parameters that enable the device to achieve polarization-insensitive characteristics are obtained; Step 3: As the transmission distance increases, the light will gradually couple from the incident waveguide into the adjacent waveguide until all of it is coupled out from the adjacent waveguide structure. That is, when the waveguide length L is different values, different ratios of quasi-TE or TM mode light can be obtained in the two waveguides, thereby achieving different power distributions.

7. A polarization-insensitive optical power coupler according to claim 6, characterized in that, In the second step, the coupling lengths L TE and L TM are obtained, and then the ratio of the coupling length ratios (L TE / L TM ) is calculated, compared with 1, and it is measured whether the coupling length is too long. If the coupling length is too large, it will increase the overall device length, and the waveguide structure is adjusted.

8. A polarization-insensitive optical power coupler according to claim 6, wherein The specific method for adjusting the waveguide structure in Step 2 is: First: Adjust the distance d between the two waveguide structures so that the device length is less than 100 μm; Second: Coarsely adjust the overall width W and height H of the waveguide structure. Calculate the ratio of the coupling lengths of the X and Y polarizations through Step 1, and continue to adjust the thickness of the middle slit and the thicknesses W L , W R , and the thickness W of the middle slit layer s . The output optical power has a similar response for the two polarization states, thus exhibiting polarization-insensitive characteristics.

9. A polarization-insensitive optical power coupler according to claim 6, wherein In Step 3, the incident waveguide is defined as the BAR port, and the adjacent waveguide is defined as the CROSS port; According to the power distribution ratio required by the target, the device length L can be further determined. For example, when the target distribution ratio is 50:50 and the waveguide structure length is L = 1 / 2L TE = 1 / 2L TM then the device length is 34.76 μm.