Functional Segmentation Method for the Design of Compact Adiabatic Devices

Round 1

Reviewer 1 Report

In this paper, the authors report two algorithms based on quadratic function and cubic function segmentation which can be applied to calculate a compact taper waveguide. However, there are some issues that the authors are suggested to consider:

1.       The research status is insufficient in introduction.

2.       The coordinates of section 2 and section 3 should be consistent with each other for easier understand.

3.     Both in section 2 and section 3, the authors have a short discussion according to Fig.3 and Fig.7. Why the difference assumptions about power transfer of 95% and 90% is proposed? What is the author's reference basis?

4.       In section 3, the thickness of core is lost.

5.       The Effective index varies with the changes of thickness and width in nature, it is insufficient for estimating the mode conversion. The authors should reinforce other results to explain.

6.       Why the quadratic function segmentation design for the adiabatic taper waveguide and the cubic function design for the adiabatic mode coupler? Could the cubic function segmentation can be used to design taper waveguide? The main reason should be provided to detail the difference of two method for different application.

7.       In Fig.7, the conventional linear-shape connection result should be given.

no comments

Author Response

Response to Reviewer 1

Dear Reviewer 1,

Thank you for your suggestions. We do appreciate the time you have spent and we are working to close this paper with you so that it can be utilized by the Photonics community. We have addressed your points below and incorporated the various suggestions you have given. Reviewing paper is not the most rewarding job, and our thanks to you for spending the time to provide us with valuable feedbacks.  

Comments and Suggestions for Authors

In this paper, the authors report two algorithms based on quadratic function and cubic function segmentation which can be applied to calculate a compact taper waveguide. However, there are some issues that the authors are suggested to consider: 

Q1. The research status is insufficient in introduction. 

A1. Thanks for the advice. We have enriched the Introduction Section. The introduction is reproduced below.

In photonic integrated circuits, energy is transferred in different structures, and even when it is transferred in the same structure, the structural parameters will change, and at this time it is necessary to design a connection structure to transfer energy from one module to another [1-5]. In order to realize the design of connection structure, adiabatic devices based on the adiabatic mode evolution play an increasingly important role [6-8]. In adiabatic devices, the designated mode at the input slowly evolves to the designated mode at the output. The output mode can be the same or different from the input mode, which is referred to as transfer efficiency when the modes are the same and conversion efficiency when the modes are different. No other unwanted modes are significantly excited during this evolution, and the power transfer/conversion efficiency from the designated input mode to the designated output mode is very high.

One way to achieve adiabatic mode evolution transfer is to connect different functional units linearly, but the resulting device structure has a long size [9], which runs counter to the direction of optical integration towards higher integration. The analytical method can reduce the size of the adiabatic device. However, the analytical method design for adiabatic devices is only suitable for simple device structures, and the analytical method is not universal [6-14]. The methods proposed in Ref. [6-8] are only suitable for the design of adiabatic couplers, and are not suitable for the design of adiabatic tapered waveguides and adiabatic mode couplers in this study. Ref. [10-14] are all analytical designs of adiabatic tapered waveguides, in which Ref [10] describes mode propagation by using a ray model, thus perfecting the analytical design rules for tapered waveguides proposed by Milton and Burns. In Ref [14], an equivalent waveguide concept, which converts a straight waveguide into an equivalent conformal structure by means of conformal mapping, was proposed and applied to the design and analysis of a fully adiabatic tapered waveguide. These analytical methods are only suitable for the design of specific types of adiabatic devices, and are not suitable for the design of other types of adiabatic devices, which greatly limits the wide range of applications of these analytical methods. In the last three years, in order to design adiabatic devices with complicated three-dimensional (3D) geometries, numerical design methods [15-17] have been proposed. Numerical methods can handle various types of adiabatic devices and can also be used to design device structures with geometric shapes, which is convenient for applications. The numerical design methods for the adiabatic device [15-17] are calculated accurately, and the methods are universal, but for each section needs to be simulated, how many sections are divided, how many simulations are required, and the length of the device is selected from the simulation results, which increases the complexity of the design of adiabatic device.

Therefore, in order to eliminate the need for simulations for each section, this study proposes a functional segmentation design method for the design of adiabatic taper waveguides and adiabatic mode converters. For the design of adiabatic taper waveguides, the device size of the quadratic function design is much smaller than that of the conventional linear-shape connection design (see Section 2). And for the design of adiabatic mode converters, the cubic function segmentation design method in this study is better than the analytical method in Ref. [9] (see Section 3).

 

Q2. The coordinates of Section 2 and Section 3 should be consistent with each other for easier understand. 

A2. Thanks for the suggestion. We have uniformly defined the horizontal direction as the x-axis and the vertical direction as the y-axis in the revised version.  

 

Q3. Both in Section 2 and Section 3, the authors have a short discussion according to Fig. 3 and Fig. 7. Why the difference assumptions about power transfer of 95% and 90% is proposed? What is the author’s reference basis?

A3. Thanks. Our reference basis is as follows. Ref. [15] defines the adiabatic regime. When the power loss is greater than 10%, the adiabatic performance is poor. We can say that we are in an acceptable adiabatic regime when the power loss is less than or equal to 10%. Therefore, we choose a minimum power transfer efficiency of 90%, and we can choose a power transfer efficiency of 95% when we need a better adiabatic regime. Of course, if one wishes to pursue a better adiabatic regime, one can also choose a higher power transfer efficiency, say 99% or even higher. 

[15]  T. L. Liang, Y. Tu, X. Chen, Y. Huang, Q. Bai, Y. Zhao, J. Zhang, Y. Yuan, J. Li, F. Yi, W. Shao, and S.-T. Ho, “A Fully Numerical Method for Designing Efficient Adiabatic Mode Evolution Structures (Adiabatic Taper, Coupler, Splitter, Mode Converter) Applicable to Complex Geometries,” J. Lightw. Technol. 39(17), 5531–5547 (2021).

 

Q4. In Section 3, the thickness of core is lost. 

A4. Thanks very much. The thickness of the silicon core is h₂ = 220 nm. This information has also been added in the revised version.  

 

Q5. The effective index varies with the changes of thickness and width in nature, it is insufficient for estimating the mode conversion. The authors should reinforce other results to explain. 

A5. Thanks very much for the suggestion. The variation of the effective refractive index with the width of the waveguide is one way in which we can determine the existence of a mode hybridization region. In this way, it is determined that there is mode conversion in some areas, for example, it is determined that there is mode conversion near W₀ = 0.75 μm in Figure 6. To achieve mode conversion, the input width W_I and output width W_O of the waveguide need to meet the conditions: W_I < W₀ < W_F. After some simulation, the Eigenmode Expansion (EME) simulator from Lumerical is used to determine whether mode conversion really exists. Finally, it is determined that when the input waveguide width is W_I = 0.69 μm and the output waveguide width is W_F = 0.83 μm, the mode conversion can indeed be realized, and the conversion efficiency is shown in Figure 7. It is proved that there is indeed a mode conversion from width W_I = 0.69 μm to width W_F = 0.83 μm.

 

Q6. Why the quadratic function segmentation design for the adiabatic taper waveguide and the cubic function design for the adiabatic mode coupler? Could the cubic function segmentation can be used to design taper waveguide? The main reason should be provided to detail the difference of two method for different application. 

A6. Thanks for the question. Through various works [1, 2], it has been shown that quadratic function shapes generally give more efficient adiabatic taper waveguides compared to linear-shape design. Ref. [9] shows that cubic function shapes can often give efficient adiabatic mode converters. Therefore, a quadratic function segmentation method is developed for the design of adiabatic taper waveguides and a cubic function segmentation method for the design of adiabatic mode converters. Of course, the cubic function segmentation method can also be used in the design of adiabatic taper waveguides, but the results are poor, as shown in the Figure 3. It can be seen from Figure 3 that the transfer efficiency of the adiabatic taper waveguide designed with cubic function segmentation is much worse than that of the adiabatic taper waveguide designed with quadratic function segmentation, and even worse than that of the linear-shape connection.

[1]  W. K. Burns, A. F. Milton, and A. B. Lee, “Optical waveguide parabolic coupling horns,” Appl. Phys. Lett. 30(1), 28–30 (1977).

[2]  A. F. Milton and W. K. Burns, “Mode coupling in optical waveguide horns,” IEEE J. Quantum Electron. 13(10), 828–835 (1977).

[9]  J. Guo, and Y. Zhao, “Analysis of mode hybridization in tapered waveguides,” IEEE Photon. Tech. Lett., 27(23), 2441-2444 (2015).

 

Q7. In Fig.7, the conventional linear-shape connection result should be given. 

A7. Thanks for the advice. In the design of the adiabatic taper waveguide in Section 2, it has been demonstrated that the functional segmentation design in this study leads to better results than the conventional linear-shape connection. Therefore, in Figure 7 of Section 3, we added the analytical method design in Ref. [9] as a comparison (instead of the result of the conventional linear-shape connection), which can better reflect the advantages of the functional segmentation design in this study. It can be seen from Figure 7 that the method in Ref. [9] has obvious oscillation, indicating a large energy loss. Therefore, the effect of functional segmentation design is better than that of the design in Ref. [9].

[9]  J. Guo, and Y. Zhao, “Analysis of mode hybridization in tapered waveguides,” IEEE Photon. Tech. Lett., 27(23), 2441-2444 (2015).  

 

Our thanksWe thank you for all the inquisitions and suggestions that make this a better paper. We sincerely thank you for the time you have spent. Hope we have addressed all the suggestions you brought up, and the paper can be published soon so that others can use the method. Your recommendation and support for the publication of this paper would be greatly appreciated.

Author Response File: Author Response.docx

Reviewer 2 Report

This manuscript presented a simulation work on the adiabatic device design. I am not expert on this topic. So the following comments can only be taken as a reference for the further revision. 

1. Does a waveguide need to be treated as a power device?  This could be not a critical factor.

2.  A waveguide working at a specific wavelength should be identified, but this manuscript there is no wavelength information.

3. Is there any experimental information to confirm the conclusion?

 

no comments!

Author Response

Response to Reviewer 2

Dear Reviewer 2,

Thank you for your suggestions. We do appreciate the time you have spent and we are working to close this paper with you so that it can be utilized by the Photonics community. We have addressed your points below and incorporated the various suggestions you have given. Reviewing paper is not the most rewarding job, and our thanks to you for spending the time to provide us with valuable feedbacks.  

Comments and Suggestions for Authors

This manuscript presented a simulation work on the adiabatic device design. I am not expert on this topic. So the following comments can only be taken as a reference for the further revision.

 

Q1. Does a waveguide need to be treated as a power device? This could be not a critical factor. 

A1. Thanks for the question. The main purpose of this study is to propose algorithms for the design of adiabatic waveguide devices. For the designed adiabatic device structure, it is necessary to simulate and calculate the power transfer/conversion efficiency of the designed device structure. Thus, from this point of view, a waveguide can be treated as a power device. In addition, we also refer to the definition of power devices in Ref. [1-4], and the range of the “power devices” covers a very wide range of devices and technology, from the massive 4 in, 3000-A thyristor to the high-voltage integrated circuit and the power MOSFET, also including Si power devices, silicon carbide (SiC) power devices and so on. Therefore, from this point of view, a waveguide can also be treated as a power device. 

[1]  M. S. Adler, K. W. Owyang, B. J. Baliga and R. A. Kokosa, "The evolution of power device technology," IEEE Transactions on Electron Devices, vol. 31, no. 11, pp. 1570-1591, Nov. 1984.

[2]  X. She, A. Q. Huang, Ó. Lucía and B. Ozpineci, "Review of silicon carbide power devices and their applications," IEEE Transactions on Industrial Electronics, vol. 64, no. 10, pp. 8193-8205, Oct. 2017.

[3]  M. Bhatnagar and B. J. Baliga, "Comparison of 6H-SiC, 3C-SiC, and Si for power devices," IEEE Transactions on Electron Devices, vol. 40, no. 3, pp. 645-655, Mar. 1993.

[4]  H. Wang, F. Wang and J. Zhang, "Power semiconductor device figure of merit for high-power-density converter design applications," IEEE Transactions on Electron Devices, vol. 55, no. 1, pp. 466-470, Jan. 2008.

 

Q2. A waveguide working at a specific wavelength should be identified, but this manuscript there is no wavelength information. 

A2. Thanks very much. The wavelength of the light beam is set to 1.55 μm in this work. This information has also been added in the revised version.  

 

Q3. Is there any experimental information to confirm the conclusion?

A3. Thanks for the question. The purpose of this paper is to develop functional segmentation methods for the design of compact adiabatic devices. Based on our previous research on the numerical design algorithms, we will focus on the experimental information in the near future.  

 

Our thanks

We thank you for all the inquisitions and suggestions that make this a better paper. We sincerely thank you for the time you have spent. Hope we have addressed all the suggestions you brought up, and the paper can be published soon so that others can use the method. Your recommendation and support for the publication of this paper would be greatly appreciated.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed the comments. I recommended to accept in present form.