CN113933933B - Preparation method and application of optimized curved waveguide - Google Patents
Preparation method and application of optimized curved waveguide Download PDFInfo
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- CN113933933B CN113933933B CN202111313016.4A CN202111313016A CN113933933B CN 113933933 B CN113933933 B CN 113933933B CN 202111313016 A CN202111313016 A CN 202111313016A CN 113933933 B CN113933933 B CN 113933933B
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- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
- G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
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- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
- G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
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- G—PHYSICS
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- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
- G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
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Abstract
The present disclosure provides a method of making optimized curved waveguides and applications thereof. The preparation method of the optimized curved waveguide comprises the following steps: obtaining a first part of a graph required by electron beam exposure by utilizing a preset nonlinear curvature bending relationship so as to obtain a first bending waveguide; obtaining a second part of a pattern required by electron beam exposure by utilizing a preset linear curvature bending relationship so as to obtain a second bending waveguide; taking a preset straight line as a symmetry axis, and obtaining a third part of the pattern required by the electron beam exposure, which is symmetrical to the first part of the pattern required by the electron beam exposure, so as to obtain a third curved waveguide; the first part, the second part and the third part are combined to form a pattern required by electron beam exposure, and an optimized curved waveguide is formed through an electron beam exposure process; wherein in the optimized curved waveguide, one end of the second curved waveguide is connected to the end of the first curved waveguide, and one end of the third curved waveguide is connected to the other end of the second curved waveguide.
Description
Technical Field
The present disclosure relates to the field of photonic integrated circuits, and in particular, to a method for preparing an optimized curved waveguide and applications thereof.
Background
Photonic Integrated Circuits (PICs) for optical interconnects have received attention in the fields of optical computing, communications, and the like. Silicon photonics has been widely used in photonic integrated circuit platforms and has demonstrated a variety of large-scale photonic integrated circuits. In these PICs, silicon waveguides are used for signal transmission, and there are many waveguides that bend and cross to form a circuit. Typical losses for a normal 90 deg. waveguide bend for a single mode silicon waveguide are about 0.01dB for a bend radius of a few microns. Although this value is already low, if there are hundreds of bends, the total bending loss will become several dB. Thus, future large-scale PICs need to further reduce bending losses, if possible.
BRIEF SUMMARY OF THE PRESENT DISCLOSURE
In view of this, the present disclosure provides a method for preparing an optimized curved waveguide and applications thereof, in order to at least partially solve the above-mentioned problems.
In order to achieve the above object, an aspect of the present disclosure provides a method of preparing an optimized curved waveguide, comprising:
obtaining a first part of a graph required by electron beam exposure by utilizing a preset nonlinear curvature bending relationship so as to obtain a first bending waveguide;
obtaining a second part of a pattern required by electron beam exposure by utilizing a preset linear curvature bending relationship so as to obtain a second bending waveguide;
taking a preset straight line as a symmetry axis, and obtaining a third part of the pattern required by the electron beam exposure, which is symmetrical to the first part of the pattern required by the electron beam exposure, so as to obtain a third curved waveguide;
the first part, the second part and the third part are combined to form a pattern required by electron beam exposure, and an optimized curved waveguide is formed through an electron beam exposure process;
wherein in the optimized curved waveguide, one end of the second curved waveguide is connected to the end of the first curved waveguide, and one end of the third curved waveguide is connected to the other end of the second curved waveguide.
According to an embodiment of the present disclosure, wherein the preset nonlinear curvature bending relationship is curvature
Increasing root with increasing curve length t, < >>
R is the radius of curvature.
According to the embodiment of the disclosure, the acute included angle formed by tangent lines at two ends of the first part of the pattern required by the electron beam exposure is theta,
a is the bending angle corresponding to the optimized bending waveguide, and p is the proportion of the bending angle a.
According to an embodiment of the present disclosure, wherein a=90°, p=10 to 100%.
According to an embodiment of the present disclosure, coordinates (x, y) corresponding to points on a first portion of a pattern required for electron beam exposure in plane coordinates x, y according to values of a and p specifically include:
wherein t is max The total length of the first part of the pattern required for electron beam exposure from the start point to the end point; r is R 0 Is defined by a reference radius R eff Size determination of R eff For reference radius, R 0 Is a constant; b=p×a/2.
According to an embodiment of the disclosure, wherein R eff ＝4；R 0 ＝2.929。
According to an embodiment of the present disclosure, wherein the preset linear curvature bending relationship is a curvature of
R is as follows min Is determined by the position of the end coordinates of the third part of the pattern required by the electron beam exposure and the angle corresponding to the normal bending.
According to an embodiment of the present disclosure, wherein the angle corresponding to normal bending is a (1-p).
According to an embodiment of the disclosure, wherein the preset straight line is y= -x+r eff 。
Another aspect of the present disclosure provides for the use of a method of preparing an optimized curved waveguide in the preparation of an optical component.
From the above technical solution, the present disclosure provides the following technical effects:
(1) The preparation method of the optimized curved waveguide provided by the embodiment of the disclosure starts from the design of a curved path, and reduces the loss problem caused by larger radiation loss of the bending in the prior Euler bending;
(2) According to the preparation method of the optimized bending waveguide, the input/output position and the occupied area are the same as those of normal bending, so that the optimized bending can be used as conventional bending in PICs, and bending loss of the PICs in a large scale in the future is reduced;
(3) The preparation method of the 90-degree optimized bent waveguide reduces the transmission loss of the 90-degree bent waveguide, and when the reference radius is 4 mu m, the 90-degree bent waveguide loss is 36.5% of the minimum loss in the prior art;
(4) The optimized bending provided by the embodiment of the disclosure can be directly applied to 90-degree bending waveguides and also can be used for low-loss optimization of optical components such as micro-ring resonators and Y-branches.
Drawings
FIG. 1 schematically illustrates a 90 ° curved waveguide curve diagram consisting of Euler curves and normal curves in the prior art;
FIG. 2 schematically illustrates a flow chart of a method of preparing an optimized curved waveguide according to an embodiment of the present disclosure;
FIG. 3 schematically illustrates a graph obtained by matlab simulation when embodiments of the present disclosure are in different relationships according to curvature and bending length;
FIG. 4 schematically illustrates a schematic diagram of an optimized curved waveguide curve obtained by matlab simulation when the ratio of the optimized curved waveguide curve is different according to another embodiment of the present disclosure;
FIG. 5 schematically illustrates a mode field transmission diagram obtained by FDTD software simulation for an input light wavelength of 1550nm according to a further embodiment of the present disclosure with a 90 optimized curved waveguide curve at 100%;
fig. 6 schematically illustrates a side view (a), a cross-slope view (b), and a top view (c) of an SEM image of an optimized curved waveguide obtained when a 90 ° optimized curved waveguide curve accounts for 50% after processing according to the method of optimizing a curved waveguide curve according to another embodiment of the present disclosure.
[ reference numerals description ]
1-a first curved waveguide; 2-a second curved waveguide; 3-a third curved waveguide.
Detailed Description
For the purposes of promoting an understanding of the principles and advantages of the disclosure, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same.
Studies have shown that several approaches have been proposed in order to reduce bending losses. For example, spline curves and normal bend stitching are used to facilitate smooth connection of input/output ends to curved waveguides. Normal bending means that the input and output straight waveguides are connected by a curved waveguide with a constant curvature. The waveguide loss decreases as the spline increases in length because the input-output waveguide and curved waveguide junction is smoother and the transition is smoother. However, the use of spline curves makes the 90 ° bend not of a fixed size and larger than a curved waveguide of constant curvature, which is undesirable. As another example, TIR mirrors and external grooves are proposed theoretically, which reduce bending losses by reducing field leakage outside the waveguide. However, these methods require additional manufacturing processes in addition to forming the silicon waveguide.
In recent years, euler curves have been used to reduce coupling losses between straight waveguides and normally curved waveguides. The use of euler curves in silicon waveguide bending has also been demonstrated, as the curvature of euler curves increases linearly from zero, enabling a smooth connection between a straight waveguide and a normally curved waveguide. Studies have shown that S-bend waveguides using Euler curves in optical delay lines; also a relatively large bending radius (20 μm) silicon waveguide L-bend consisting of a 100% euler curve was incorporated into the Si-PIC for measuring waveguide losses. As shown in fig. 1, a novel 90 ° curved waveguide curve consisting of euler curves and normal curves, ultimately reduces the bending losses. In fig. 1, a is a constant, which is called euler parameter. The end point of the Euler curve has a minimum radius of curvature R min The length of the curve is L max . Euler curve passing curvature at input is 1/R min Is connected to a symmetrical euler curve at the output of the 90 ° bend waveguide curve. Thus, the start and end points of the bend are (0, 0) and (R eff ，R eff ). The ratio of the euler curves can be varied from 0 to 100% by varying a. In other words, a curved waveguide consisting of 100% euler curves is not optimal, and the euler curves used in combination with normal bending are critical to ultimately reduce bending losses. The bends they propose are fabricated on Complementary Metal Oxide Semiconductor (CMOS) platforms, with r=4μm bending losses of 0.002dB/90 °, being 1/10 of the fixed curvature.
The losses of a curved waveguide are mainly three aspects, namely losses due to curved optical mode distribution (and its mismatch with the straight waveguide mode at the input and output connection), curved radiation losses (i.e. the imaginary part of the propagation constant) and scattering losses due to sidewall roughness, the former two depending on the radius of curvature, the latter depending on the shape of the waveguide cross section and the waveguide material, etc.
Therefore, in order to solve the problem of curvature radius in a centralized way, starting from the design of a bending path, the preparation method of the optimized bending waveguide reduces the loss problem caused by larger radiation loss of bending in the prior Euler bending; and a curved waveguide with lower loss and the same input/output position and footprint as a normal curve is called an optimized curved waveguide.
The following schematically illustrates a method of preparing an optimized curved waveguide. It should be noted that the examples are only specific embodiments of the disclosure and are not intended to limit the scope of the disclosure.
Fig. 2 schematically illustrates a flow chart of a method of preparing an optimized curved waveguide according to an embodiment of the present disclosure.
As shown in fig. 2, the preparation method includes operations S201 to S204.
In operation S201, a first portion of a pattern required for electron beam exposure is obtained using a preset nonlinear curvature bending relationship to obtain a first curved waveguide.
In accordance with an embodiment of the present disclosure,the preset nonlinear curvature bending relation is curvature
Increasing root with increasing curve length t, < >>
R is the radius of curvature.
It should be noted that, the curve length t represents the length of the first portion of the curve of the pattern required by the electron beam exposure; the radius of curvature R is expressed from a reference radius R eff Change to R min Is a variable value of (a).
According to the embodiment of the disclosure, the acute included angle formed by tangent lines at two ends of the first part of the pattern required by the electron beam exposure is theta,
a is the bending angle corresponding to the optimized bending waveguide, and p is the proportion of the bending angle a.
According to embodiments of the present disclosure, for example, a may be a=90°, p=10 to 100%, where p may be, for example, but not limited to: 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%.
According to an embodiment of the present disclosure, coordinates (x, y) corresponding to each point on a first portion of a pattern required for electron beam exposure in plane coordinates x, y according to values of a, p specifically include:
wherein t is max The total length of the first part of the pattern required for electron beam exposure from the start point to the end point; r is R 0 Is defined by a reference radius R eff Is determined by the size of (2); b=p×a/2.
According to embodiments of the present disclosure, for example, R may be eff ＝4；R 0 ＝2.929。
In operation S202, a second portion of the pattern required for the electron beam exposure is obtained using a preset linear curvature bending relationship to obtain a second curved waveguide.
According to an embodiment of the present disclosure, the preset linear curvature bending relationship is a curvature of
R is as follows min Is determined by the position of the end coordinates of the third part of the pattern required by the electron beam exposure and the angle corresponding to the normal bending.
According to embodiments of the present disclosure, the angle corresponding to normal bending is a (1-p).
The normal bending means that the radius is a constant value R min Is a circular arc of (a).
In operation S203, a third portion of the electron beam exposure desired pattern symmetrical to the first portion of the electron beam exposure desired pattern is obtained with the predetermined straight line as the symmetry axis to obtain a third curved waveguide.
According to an embodiment of the present disclosure, the preset straight line is y= -x+r eff 。
In operation S204, the first portion, the second portion, and the third portion are combined to form a pattern required for electron beam exposure, and an optimized curved waveguide is formed through an electron beam exposure process.
According to the embodiment of the disclosure, for example, the preset nonlinear curvature bending relationship, the preset linear curvature bending relationship and the preset straight line are y= -x+r eff Programming, inputting matlab software, then obtaining a bending graph after running the programming, deriving a coordinate file corresponding to the graph, processing to obtain a graph required by electron beam exposure, and forming the graph into an optimized bending waveguide through an electron beam exposure process.
According toAccording to the embodiments of the present disclosure, according to the above formulas (1) to (3), a curve of the proportion p of the bending angle corresponding to the optimized bending waveguide within the angle of 45 ° can be obtained. The intention to achieve a 90 ° bend is only to relate this curve to y= -x+r eff The curve is symmetrical, and the middle part is connected by an arc, thus obtaining a completely connected 90-degree bent waveguide.
In the optimized curved waveguide, one end of the second curved waveguide is connected to the end of the first curved waveguide, and one end of the third curved waveguide is connected to the other end of the second curved waveguide.
According to the embodiment of the disclosure, compared with the fact that the core of the Euler bending is that the curvature of the curve linearly increases along with the increase of the length of the curve, the first bending waveguide and the third bending waveguide are not completely adopted, but are combined with the normal bending second bending waveguide, so that the loss problem caused by the fact that the radiation loss of the bending is large in the Euler bending in the past is reduced.
Fig. 3 schematically shows a schematic graph obtained by matlab simulation when the embodiments of the present disclosure are in different relations according to curvature and bending length.
As shown in fig. 3, the normal bending is indicated by a dash-dot line, wherein the curvature of the curve represented by the dash-dot line is fixed and does not change with the change of the bending length; the optimized curve is represented by a solid line, wherein the curve represented by the solid line has a curvature that is the square root of the curve length; euler bending is indicated by a dashed line, wherein the dashed line represents a curve whose curvature varies linearly with the length of the curve. The solid line is between the dotted line and the dashed line. For the three curves, coordinates (0, 0) and coordinates (4, 4) are turning points joining a straight line (straight waveguide) and a curved portion. The curvature of the normal curve (dash-dot line) suddenly transitions from 0 (linear curvature of 0) before the coordinates (0, 0) to 1/4 of the fixed curvature, and from 1/4 at (4, 4) to 0 (linear curvature of 0) after, where a large mode conversion loss occurs. The curvature of the euler curve (dashed line) varies linearly with the length of the curve, i.e. gradually increases from 0 at (0, 0) and then gradually decreases until the curvature at coordinates (4, 4) will be 0. This variation reduces the mode switching losses at the splice, but it also concentrates the task of achieving a 90 ° turn of the mode at the mid-point of the euler curve, increasing the radiation losses of the bend. The optimized bending (solid line) does not directly change the curvature step by step, and the task of focusing 90 DEG turning to the middle point of bending like Euler bending, so that larger bending radiation loss is caused, and the two main losses existing in normal bending and Euler bending are balanced.
Fig. 4 schematically illustrates a schematic diagram of an optimized curved waveguide curve obtained by matlab simulation when the ratio of the optimized curved waveguide curve is different according to another embodiment of the present disclosure.
As shown in fig. 4, when p=50%, a first portion of a pattern required for electron beam exposure is obtained using a preset nonlinear curvature bending relationship to obtain a first curved waveguide 1; obtaining a second part of the pattern required by the electron beam exposure by utilizing a preset linear curvature bending relationship to obtain a second bending waveguide 2; taking a preset straight line as a symmetry axis, obtaining a third part of the pattern required by the electron beam exposure, which is symmetrical to the first part of the pattern required by the electron beam exposure, so as to obtain a third curved waveguide 3; the first part, the second part and the third part are combined to form a pattern required by electron beam exposure, and an optimized curved waveguide is formed through an electron beam exposure process; wherein in the optimized curved waveguide, one end of the second curved waveguide 2 is connected to the end of the first curved waveguide 1, and one end of the third curved waveguide 3 is connected to the other end of the second curved waveguide 2. When p is 0, the obviously bent waveguide curve bends slowly, and the loss is reduced.
According to another embodiment of the present disclosure, the input light wavelength is 1550nm, the reference radius R, according to the proportion of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100% in the bend angles corresponding to the optimized bend waveguides eff When a is 4 μm and a is 90 °, a corresponding bending loss table is obtained by FDTD simulation, and when the proportion of the bending angle corresponding to the optimized bending waveguide reaches 50%, as shown in the following table 1, the obtained value of 90 ° bending loss is the minimum 0.00073dB, i.e., 0.00073dB/90 °.
TABLE 1
| Proportion p | Transmittance of light | Transmission loss (dB) |
| 0 | 0.99743 | 0.01118 |
| 0.1 | 0.998876 | 0.00488 |
| 0.2 | 0.999324 | 0.00294 |
| 0.3 | 0.995587 | 0.01921 |
| 0.4 | 0.99689 | 0.01353 |
| 0.5 | 0.999833 | 0.00073 |
| 0.6 | 0.999654 | 0.0015 |
| 0.7 | 0.999455 | 0.00237 |
| 0.8 | 0.999327 | 0.00292 |
| 0.9 | 0.999374 | 0.00272 |
| 1 | 0.99939 | 0.00265 |
According to another embodiment of the present disclosure, a method for preparing a 90 ° optimized curved waveguide is provided, which reduces transmission loss of the 90 ° curved waveguide, with reference to radius R eff At 4 μm, the 90 ° bend waveguide loss is 36.5% of the minimum loss of the current state of the art.
When the curvature of the curve is proportional to the square of the path length of the curve, a 90 ° bend having a square relationship of 100% gives a waveguide having a bending loss of 0.02801dB, namely 0.02801dB/90 °, and a transmittance of 0.993571. Compared with the proportion of the bending angle corresponding to the optimized bending waveguide, which is 100 percent, the 90-degree bending loss is large, and the transmittance is relatively low.
According to an embodiment of the present disclosure, the optimized curved waveguide obtained by the method for preparing an optimized curved waveguide is processed, for example, the processing steps may be the following steps:
(1) The SOI wafer was diced into squares with an area of 20mm x 19mm, and concentrated sulfuric acid was added: the volume ratio of the hydrogen peroxide is 3:1 (the SOI sheet can be 210nm top silicon, the middle silicon dioxide layer can be 2 mu m, the bottom silicon substrate can be 725 mu m), and the organic matters and metal particles on the surface of the sheet are removed by washing with deionized water;
(2) Placing hydrofluoric acid: the water is 1:19, washing the natural oxide layer by deionized water for 30 s;
(3) Ammonia water is put in: hydrogen peroxide: water was 0.2:1:6, in the solution, carrying out water bath at 86 ℃ for 10min, and removing organic matters and particles;
(4) Placing hydrochloric acid: hydrogen peroxide: the water is 1:1:5, in the solution, carrying out water bath at 86 ℃ for 10min, and removing metals;
(5) Washing with deionized water and drying with nitrogen;
(6) Performing Reactive Ion Etching (RIE) on the top silicon, and etching an interface between the top silicon layer and the silicon dioxide layer to a depth of 210nm;
(7) Placing in acetone solution for 20min, and removing the electron beam glue mask;
(8) Putting the mixture into ethanol solution and deionized water for cleaning, and drying by nitrogen;
(9) Cutting, grinding and polishing the end face of the sample wafer;
(10) The transmission loss of silicon optical waveguides connected by a plurality of 90 ° bends was tested.
According to an embodiment of the present disclosure, after the optimized curved waveguide obtained by the method for preparing an optimized curved waveguide is processed, a side view (a), a transverse bevel view (b) and a top view (c) of the obtained SEM image of the optimized curved waveguide are obtained when the proportion of the 90 ° optimized curved waveguide curve shown in fig. 6 is 50%.
According to embodiments of the present disclosure, since the input/output locations and footprints are the same as normal bends, optimized bends may be used as conventional bends in PICs, reducing bending losses in future large-scale PICs.
The disclosure also provides applications of the preparation method of the optimized curved waveguide in preparation of optical components.
According to the embodiment of the disclosure, the optimized bending can be directly applied to 90-degree bending waveguides, and can also be used for low-loss optimization of optical components such as micro-ring resonators, Y-branches and the like.
While the foregoing is directed to embodiments of the present disclosure, other and further details of the invention may be had by the present application, it is to be understood that the foregoing description is merely exemplary of the present disclosure and that no limitations are intended to the scope of the disclosure, except insofar as modifications, equivalents, improvements or modifications may be made without departing from the spirit and principles of the present disclosure.
Claims (6)
1. A method of preparing an optimized curved waveguide comprising:
obtaining a first part of a graph required by electron beam exposure by utilizing a preset nonlinear curvature bending relationship so as to obtain a first bending waveguide;
obtaining a second part of a pattern required by electron beam exposure by utilizing a preset linear curvature bending relationship so as to obtain a second bending waveguide;
taking a preset straight line as a symmetry axis, and obtaining a third part of the pattern required by the electron beam exposure, which is symmetrical to the first part of the pattern required by the electron beam exposure, so as to obtain a third curved waveguide;
the first part, the second part and the third part are combined to form a pattern required by the electron beam exposure, and the optimized curved waveguide is formed through an electron beam exposure process;
wherein, in the optimized curved waveguide, one end of the second curved waveguide is connected with the end of the first curved waveguide, and one end of the third curved waveguide is connected with the other end of the second curved waveguide;
wherein the preset nonlinear curvature bending relationship is curvature
As the curve length t increases it grows in root,
r is the radius of curvature;
wherein the electron beam exposes the first pattern of the required patternThe acute included angle formed by the tangent lines at two ends of the part is theta,
a is the bending angle corresponding to the optimized bending waveguide, and p is the proportion of the bending angle a;
and obtaining corresponding coordinates (x, y) of each point on the first part of the graph required by the electron beam exposure in plane coordinates x and y according to the values of the a and the p, wherein the method specifically comprises the following steps:
wherein t is max The total length of the first part of the pattern required for electron beam exposure from the start point to the end point; r is R 0 The size of (2) is R eff Size determination of R eff For reference radius, R 0 Is a constant; b=p×a/2;
the preset linear curvature bending relation is that the curvature is
R is as follows min Is determined by the position of the end coordinates of the third part of the pattern required by the electron beam exposure and the angle corresponding to the normal bending.
2. The preparation method according to claim 1, wherein a=90°, and p=10 to 100%.
3. The preparation method according to claim 1, wherein R eff ＝4；R 0 ＝2.929。
4. The preparation method according to claim 1, wherein the angle corresponding to the normal bending is a (1-p).
5. The preparation method according to claim 1, wherein the preset straight line is y= -x+r eff 。
6. Use of the method for producing optimized curved waveguides according to any of claims 1-5 for producing optical components.
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| US20030095771A1 (en) * | 2001-11-13 | 2003-05-22 | Heu-Gon Kim | Planar lightwave circuit with polynominal-curve waveguide |
| CN111796360A (en) * | 2019-04-01 | 2020-10-20 | 朗美通经营有限责任公司 | Curved waveguide structure |
| CN113253450A (en) * | 2021-05-18 | 2021-08-13 | 浙江大学 | Low-loss integrated curved optical waveguide and design method thereof |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030095771A1 (en) * | 2001-11-13 | 2003-05-22 | Heu-Gon Kim | Planar lightwave circuit with polynominal-curve waveguide |
| CN111796360A (en) * | 2019-04-01 | 2020-10-20 | 朗美通经营有限责任公司 | Curved waveguide structure |
| CN113253450A (en) * | 2021-05-18 | 2021-08-13 | 浙江大学 | Low-loss integrated curved optical waveguide and design method thereof |
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| 弯曲波导研究进展及其应用;高峰 等;中国光学;全文 * |
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