Design method of adiabatic coupler based on equation correction

Abstract

The invention belongs to the technical field of integrated photoelectronics, and particularly relates to a design method of an adiabatic coupler based on equation correction. The method comprises the following steps: step 1, obtaining effective refractive indexes of intrinsic modes in a coupled waveguide system and an uncoupled waveguide system through analogue simulation; step 2, the value of ne-no-n2-n1 is calculated; 3, correcting the effective refractive index of the intrinsic mode in the uncoupled waveguide system; 4, calculating a propagation constant beta; 5, calculating the coupling strength kappa between the first silicon core and the second silicon core; step 6, fragment length calculation; and 7, calculating the power transmission efficiency and determining the final device length. According to the design method, the device size of the thermal insulation coupler is greatly reduced, and the miniaturization design in a photonic integrated chip can be realized.

Description

Technical Field

[0001] The invention belongs to the technical field of integrated optoelectronics, and in particular relates to a design method of an adiabatic coupler based on equation correction. Background Art

[0002] Photonic integrated chips are the core components of modern optical communication devices. Multiple photonic chips can be integrated into one chip, thereby realizing the integration and coordination of multiple functions. In future large-scale photonic integrated chips, silicon photonic optical power couplers on silicon-on-insulator (SOI) platforms with high refractive index contrast are ideal candidate devices for large-scale photonic integration in optical communications, as reflected in the paper K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and Multimode Interference Couplers on Silicon-on-Insulator," IEEE Photon. Technol. Lett., vol. 18, no. 21, pp. 2287-2289, Nov. 2006.

[0003] Polarization-insensitive couplers are one of the basic components of photonic integrated chips. They can be realized by bent directional couplers, subwavelength grating structures, and adiabatic couplers. Adiabatic couplers are the preferred solution for realizing wide-bandwidth devices, as shown in the paper S. Zhao, J. Chen, D. Dai, and Y. Shi, “Polarization-insensitive silicon optical switch based on mode manipulated power splitters and phase shifters,” APL Photon., vol. 8, no. 1, Nov. 2023. Most traditional adiabatic couplers are connected in a linear manner, which requires a very large device size, which runs counter to the direction of higher integration in photonic integrated chips (miniaturization of devices). In complex photonic integrated chips, each component should occupy as little space as possible to reduce material, processing, and packaging costs. Therefore, it is necessary to propose a design method that can efficiently design compact adiabatic couplers. Summary of the invention

[0004] The object of the present invention is to provide a design method of an adiabatic coupler based on equation correction, aiming to design an adiabatic coupler with small size, low loss, high transmission efficiency and simple structure.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0006] A design method of an adiabatic coupler based on equation correction includes the following steps: Step 1, obtaining the effective refractive index of the eigenmode in the coupled waveguide system and the uncoupled waveguide system through simulation; Step 2, calculating |n e -n o |-|n2-n1|; Step 3, correction of the effective refractive index of the eigenmode in the uncoupled waveguide system; Step 4, calculation of the propagation constant β; Step 5, calculation of the coupling strength κ between the first silicon core and the second silicon core; Step 6, calculation of the segment length; Step 7, calculation of the power transmission efficiency and determination of the final device length.

[0007] Further, as a preferred technical solution of the present invention, the specific steps of step one include: sequentially changing the waveguide widths of the first silicon core and the second silicon core, taking the waveguide width w of the second silicon core as the horizontal coordinate, and obtaining the even eigenmode e in the coupled waveguide system through FDTD simulation e and odd eigenmodes e o The effective refractive index n e and n o , and the even eigenmodes e in the uncoupled waveguide system e and odd eigenmodes e o The effective refractive indices n1 and n2.

[0008] Further as a preferred technical solution of the present invention, in step 2, e -n o The value of |-|n2-n1| should be greater than 0.

[0009] Further, as a preferred technical solution of the present invention, it is assumed that e -n2=n1-n o , derive

[0010] n2=n e +n o -n1 (1)

[0011] n2 is corrected by equation (1).

[0012] Further, as a preferred technical solution of the present invention, in step 4, for the coupled waveguide system, the even eigenmode e e and odd eigenmodes e o The propagation constants are and For an uncoupled waveguide system, the even eigenmodes e e and odd eigenmodes e o The propagation constants are and

[0013] In coupled waveguide systems, even eigenmodes e e and odd eigenmodes e o The difference in propagation constants is defined as

[0014] 2S=β e -β o (3)

[0015] In an uncoupled waveguide system, the even eigenmode e e and odd eigenmodes e o The mismatch coefficient of the propagation constant is defined as

[0016]

[0017] Further, as a preferred technical solution of the present invention, in step 5, the relationship between the coupling strength κ between the first silicon core and the second silicon core, the difference S of the propagation constant in the coupled waveguide system, and the mismatch coefficient δ of the propagation constant in the uncoupled waveguide system is:

[0018] S 2 =δ 2 +κ 2 (5)

[0019] Substituting equation (3) and equation (4) into equation (5), we obtain the coupling strength κ:

[0020]

[0021] In equation (6), the coupling strength κ>0, that is, |β e -β o |-|β2-β1|>0, also |n e -n o |-|n2-n1|>0; Taking the square root of both sides of equation (6), we get

[0022]

[0023] To simplify the equation, define γ = δ / κ and substitute it into equation (5), we can derive

[0024] S 2 =κ 2 (1+γ 2 ) (8).

[0025] Further, as a preferred technical solution of the present invention, in step 6, the beam propagation direction is assumed to be the z direction. In order to realize adiabatic mode evolution transmission in the coupler, the power loss cannot be greater than the value ε. The adiabatic criterion in the coupled waveguide system is:

[0026]

[0027] Formula (9) takes the maximum value of power loss ε, that is, equation (9) takes the equal sign;

[0028] Use central difference instead of differentiation of spatial coordinates

[0029]

[0030] Substituting equation (10) into equation (9), we obtain

[0031]

[0032] where κ mid and γ mid is the definition of the central mean, that is

[0033]

[0034] The right side of equation (11) defines the length L of the i-th segment i =z i+1 -z i , so from equation (11) we can deduce L i for:

[0035]

[0036] Where ε is a constant, which represents the maximum power loss value that needs to be met in practical applications.

[0037] The design method of an adiabatic coupler based on equation correction described in the present invention adopts the above technical solution and has the following technical effects compared with the prior art:

[0038] (1) The present invention theoretically derives a design method for an adiabatic coupler based on equation correction and provides detailed design steps for use by those skilled in the art.

[0039] (2) The design method of the present invention is far superior to the traditional linear connection scheme in terms of efficiency. When achieving a transmission efficiency of 99%, the design method of the present invention only requires a length of 45.895 μm, while the traditional linear connection scheme requires a length of 203 μm, which is 4.4 times the length of the design method of the present invention. The design method of the present invention greatly reduces the device size of the adiabatic coupler and can realize the miniaturization design in the photonic integrated chip. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of the input end of the adiabatic mode coupler of the present invention;

[0041] Figure 2 It is a schematic diagram of the output end of the adiabatic mode coupler of the present invention;

[0042] Figure 3 Schematic diagram of the steps of the method of the present invention;

[0043] Figure 4 A schematic diagram of the effective refractive index obtained by simulation in the present invention;

[0044] Figure 5 The present invention obtains the |n through simulation parameters e -n o Schematic diagram of |-|n2-n1|;

[0045] Figure 6 is a schematic diagram of the corrected effective refractive index of the present invention;

[0046] Figure 7 is the value after the sixth function correction by the method of the present invention. e -n o Schematic diagram of |-|n2-n1|;

[0047] Figure 8 Schematic diagram of power transmission efficiency of the method of the present invention;

[0048] The reference numerals are: 1, cladding; 2, first silicon core; 3, second silicon core. DETAILED DESCRIPTION

[0049] The present invention is further explained below in detail with reference to the accompanying drawings so that those skilled in the art can more deeply understand the present invention and be able to implement it. However, the following reference examples are only used to explain the present invention and are not intended to limit the present invention.

[0050] The cross sections of the input and output ends of the adiabatic coupler of the present invention are respectively as follows: Figure 1 and 2 As shown, the structure includes a cladding 1, a first silicon core 2 and a second silicon core 3, wherein the material of the cladding 1 is SiO2 with a refractive index n SiO2 =1.445, width W0, thickness h0. The refractive index n of the first silicon core 2 and the second silicon core 3 Si =3.455, thickness h = 220nm. The wavelength of the incident light beam is 1.55μm. The width of the first silicon core 2 is W I =560nm, the width of the second silicon core 3 is w I =380nm. The width of the first silicon core 2 is W O =380nm, the width of the second silicon core 3 is w O=560nm. The gap width between the first silicon core 2 and the second silicon core 3 is set to g=150nm. The distance between the left boundary of the first silicon core 2 and the left boundary of the cladding 1 is set to 705nm, and the distance between the right boundary of the second silicon core 3 and the right boundary of the cladding 1 is set to 705nm. The width and height of the cladding 1 are W0=2500nm and h0=1250nm respectively.

[0051] The waveguide width W of the first silicon core 2 is W I =560nm reduced to W O =380nm, the waveguide width w of the second silicon core 3 is from w I =380nm increases to w O =560nm. Although the waveguide widths of the first silicon core 2 and the second silicon core 3 change in the beam propagation direction, the sum of the waveguide widths of the first silicon core 2 and the second silicon core 3 plus the gap width remains unchanged, that is, W+w+g=W TOT , where W TOT =1090nm.

[0052] The coupled waveguide system is defined as a structure comprising a first silicon core 2 and a second silicon core 3, such as Figure 1 and Figure 2 As shown. In the present invention, an uncoupled waveguide system is defined as one in which the boundary of one of the two silicon cores is flush with the cladding, which can be the same as the first silicon core 2 in the coupled waveguide system, and the right boundary of the second silicon core 3 is flush with the right boundary of the cladding (it can also be the same as the second silicon core 3 in the coupled waveguide system, and the left boundary of the first silicon core 2 is flush with the left boundary of the cladding). In this way, the mode in one of the silicon cores can be guided to the boundary, and only one silicon core has a mode, which is called an uncoupled waveguide system.

[0053] The design steps of the design method of the present invention are shown in Table 1.

[0054] Table 1 Design steps of this method

[0055]

[0056]

[0057] like Figure 3 As shown, a design method of an adiabatic coupler based on equation correction includes the following steps:

[0058] Step 1: Calculate the effective refractive index of the eigenmode in the coupled waveguide system and the uncoupled waveguide system by simulation; change the waveguide width of the first silicon core 2 and the second silicon core 3 in turn, take the waveguide width w of the second silicon core 3 as the horizontal coordinate, and obtain the even eigenmode e in the coupled waveguide system by FDTD simulation. e and odd eigenmodes e oThe effective refractive index n e and n o , and the even eigenmodes e in the uncoupled waveguide system e and odd eigenmodes e o The effective refractive indices n1 and n2 are plotted on Figure 4 It is easy to understand the changing trend of the effective refractive index.

[0059] Step 2: Calculate |n e -n o |-|n2-n1| value;

[0060] In theory | e -n o The value of |-|n2-n1| should be greater than 0, but Figure 5 The results in show negative values ​​from 0.38μm to 0.42μm and from 0.52μm to 0.56μm. It is speculated that the main reason is that in the uncoupled waveguide system, the values ​​of n1 and n2 may be affected by the second silicon core reaching the boundary, so the values ​​of n1 and n2 need to be corrected.

[0061] Step 3: Correction of the effective refractive index of the eigenmode in the uncoupled waveguide system;

[0062] By assuming that n e -n2=n1-n o , derive

[0063] n2=n e +n o -n1 (1)

[0064] By using equation (1), n2 is corrected as follows: Figure 6 shown.

[0065] At this time, calculate |n e -n o |-|n2-n1|, such as Figure 7 As shown in the figure, after correction, |n e -n o |-|n2-n1| is consistent with the theoretical change trend and meets the design requirements.

[0066] Step 4: Calculation of the propagation constant β;

[0067] For coupled waveguide systems, the even eigenmodes e e and odd eigenmodes e o The propagation constants are and For an uncoupled waveguide system, the even eigenmodes e e and odd eigenmodes e oThe propagation constants are and

[0068] In coupled waveguide systems, even eigenmodes e e and odd eigenmodes e o The difference in propagation constants is defined as

[0069] 2S=β e -β o (3)

[0070] In an uncoupled waveguide system, the even eigenmode e e and odd eigenmodes e o The mismatch coefficient of the propagation constant is defined as

[0071]

[0072] Step 5: Calculation of coupling strength κ between the first silicon core 2 and the second silicon core 3;

[0073] The relationship between the coupling strength κ between the first silicon core 2 and the second silicon core 3, the difference S in the propagation constant in the coupled waveguide system, and the mismatch coefficient δ of the propagation constant in the uncoupled waveguide system is:

[0074] S 2 =δ 2 +κ 2 (5)

[0075] Substituting equation (3) and equation (4) into equation (5), we can obtain the coupling strength κ as

[0076]

[0077] It can be seen from equation (6) that the coupling strength κ>0, that is, |β e -β o |-|β2-β1|>0, also |n e -n o Principle analysis of |-|n2-n1|>0.

[0078] Taking the square root of both sides of equation (6), we can get

[0079]

[0080] To simplify the equation, define γ = δ / κ and substitute it into equation (5), we can derive

[0081] S 2 =κ 2 (1+γ 2 ) (8)

[0082] Equation (8) is formally irrelevant to the parameters in the uncoupled waveguide system, which serves as a simplification.

[0083] Step 6: Calculate the fragment length;

[0084] Assuming that the beam propagates in the z direction, in order to achieve adiabatic mode evolution transmission in the coupler, the power loss cannot be greater than a certain value ε. The adiabatic criterion in the coupled waveguide system is

[0085]

[0086] In order to improve the robustness of the proposed design method, the maximum value of the power loss ε is taken in the above formula, that is, equation (9) takes an equal sign.

[0087] Use central difference instead of differentiation of spatial coordinates

[0088]

[0089] Substituting equation (10) into equation (9), we can obtain

[0090]

[0091] where κ mid and γ mid is the definition of the central mean, that is

[0092]

[0093]

[0094] The right side of equation (11) defines the length L of the i-th segment i =z i+1 -z i , so from equation (11) we can deduce that L i for:

[0095]

[0096] Where ε is a constant, which represents the maximum power loss value that needs to be met in practical applications.

[0097] In this embodiment, assuming that the maximum power loss value ε=0.001 that needs to be satisfied in actual applications, the calculated lengths are shown in Table 2.

[0098] Table 2 Design parameters calculated according to equation (14)

[0099]

[0100] Step 7: Calculation of power transmission efficiency and determination of final device length;

[0101] The transmission efficiency of the adiabatic coupler designed by the design method of the present invention and the traditional linear connection scheme is as follows: Figure 8 As shown in the figure, it can be seen that when a transmission efficiency of 99% is to be achieved, the design method of the present invention only requires a length of 45.895 μm, while the traditional linear connection solution requires a length of 203 μm, which is 4.4 times the length of the design method of the present invention. Therefore, the design method proposed in the present invention realizes the design of ultra-compact devices, which can be used for cascading between different functional units in a photonic integrated chip, and realizes the design goal of higher integration in a photonic integrated chip.

[0102] The specific implementation scheme described above further describes in detail the purpose, technical scheme and beneficial effects of the present invention. It should be understood that the above is only a specific implementation scheme of the present invention and is not intended to limit the scope of the present invention. Any equivalent changes and modifications made by any technician in the field without departing from the concept and principle of the present invention should fall within the scope of protection of the present invention.

Claims

1. A design method of an adiabatic coupler based on equation correction, characterized in that: The following steps are involved: Step 1, obtaining the effective refractive index of the eigenmode in the coupled waveguide system and the uncoupled waveguide system through simulation; Step 2: Calculate |n e -n o |-|n2-n1| value; Step 3: Correction of the effective refractive index of the eigenmode in the uncoupled waveguide system; Step 4: Calculation of the propagation constant β; Step 5: Calculate the coupling strength κ between the first silicon core and the second silicon core; Step 6: Calculate the fragment length; Step 7: Calculate the power transmission efficiency and determine the final device length.

2. The design method of the adiabatic coupler based on equation correction according to claim 1 is characterized in that: The specific steps of step 1 include: changing the waveguide widths of the first silicon core and the second silicon core in sequence, taking the waveguide width w of the second silicon core as the horizontal coordinate, and obtaining the even eigenmode e in the coupled waveguide system through FDTD simulation e and odd eigenmodes e o The effective refractive index n e and n o , and the even eigenmodes e in the uncoupled waveguide system e and odd eigenmodes e o The effective refractive indices n1 and n2.

3. The design method of the adiabatic coupler based on equation correction according to claim 2 is characterized in that: In step 2, e -n o The value of |-|n2-n1| should be greater than 0.

4. The design method of the adiabatic coupler based on equation correction according to claim 3 is characterized in that n e -n2=n1-n o , derive n2=n e +n o -n1 (1) n2 is corrected by equation (1).

5. The design method of an adiabatic coupler based on equation correction according to claim 4, characterized in that: In step 4, for the coupled waveguide system, the even eigenmode e e and odd eigenmodes e o The propagation constants are and For an uncoupled waveguide system, the even eigenmodes e e and odd eigenmodes e o The propagation constants are and In coupled waveguide systems, even eigenmodes e e and odd eigenmodes e o The difference in propagation constants is defined as 2S＝β e -β o (3) In an uncoupled waveguide system, the even eigenmode e e and odd eigenmodes e o The mismatch coefficient of the propagation constant is defined as 6. The design method of an adiabatic coupler based on equation correction according to claim 5, characterized in that: In step 5, the relationship between the coupling strength κ between the first silicon core and the second silicon core, the difference S in the propagation constant in the coupled waveguide system, and the mismatch coefficient δ of the propagation constant in the uncoupled waveguide system is: S 2 =d 2 +k 2 (5) Substituting equation (3) and equation (4) into equation (5), we obtain the coupling strength κ: In equation (6), the coupling strength κ>0, that is, |β e -β o |-|β2-β1|>0, also |n e -n o Principle analysis of |-|n2-n1|>0; Taking the square root of both sides of equation (6), we get To simplify the equation, define γ = δ / κ and substitute it into equation (5), we can derive S 2 =k 2 (1+c 2 ) (8).

7. The design method of an adiabatic coupler based on equation correction according to claim 6, characterized in that: In step 6, the beam propagation direction is assumed to be the z direction. In order to realize adiabatic mode evolution transmission in the coupler, the power loss cannot be greater than the value ε. The adiabatic criterion in the coupled waveguide system is Formula (9) takes the maximum value of power loss ε, that is, equation (9) takes the equal sign; Use central difference instead of differentiation of spatial coordinates Substituting equation (10) into equation (9), we obtain where κ mid and γ mid is the definition of the central mean, that is The right side of equation (11) defines the length L of the i-th segment i =z i+1 -z i , so from equation (11) we can deduce L i for: Where ε is a constant, which represents the maximum power loss value that needs to be met in practical applications.

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