Methods for generating non-reciprocal topological mode conversion, dynamic optical waveguide structures and devices

Abstract

This invention belongs to the field of optical communication and discloses a method for generating non-reciprocal topological mode conversion, a dynamic optical waveguide structure, and a device. The method includes: adjusting the real and imaginary parts of the waveguide refractive index in a sinusoidal manner in space and time, satisfying the wave vector matching condition in the positive direction and not satisfying it in the negative direction; obtaining the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch from the coupling equation, and selecting the real and imaginary modulation amplitudes as the parameter space to determine the singularity position in the negative direction; constructing a closed loop around the singularity in the waveguide parameter space; and applying the closed-loop parameter values ​​to waveguide modulation. This invention creatively combines dynamic modulation with topological properties around the singularity, resulting in mode transmission and conversion results that possess both non-reciprocity and topological properties. The former is caused by dynamic modulation, while the latter originates from the topological properties generated around the singularity. This method can be applied to broadband optical isolators and mode converters.

Description

Technical Field

[0001] This invention relates to the field of optical communication technology, and in particular to a method for generating non-reciprocal topology mode conversion, a dynamic optical waveguide structure, and a device. Background Technology

[0002] Similar to diodes in electronic devices, optical isolators allow forward-propagating light to pass through while isolating reverse-propagating light, thus preventing reflected light from affecting system stability. Optical isolators have a wide range of applications in optical systems. On-chip integrated optical isolators are often fabricated from optical waveguides. Ordinary optical waveguide structures cannot break the reciprocity principle (Tmn = T′nm), thus failing to produce the optical isolator effect. There are three main methods to break the reciprocity principle: using magnetic materials, introducing nonlinear effects, and using dynamic modulation. Using magnetic materials is costly and incompatible with traditional integrated circuits, while producing nonlinear effects requires very high light intensity. Therefore, thanks to the rapid development of photolithography technology, dynamic modulation technology has been widely used in silicon photonics experiments.

[0003] Dynamic modulation technology refers to altering the distribution of the real or imaginary part of the waveguide's dielectric constant in space or time through methods such as optical pumping or voltage control. The frequency and wave vector of the dielectric constant modulation must satisfy the wave vector matching condition, causing the light field propagating in one direction to be converted while remaining unchanged in the other, thus achieving the function of an optical isolator. However, while existing research has produced an optical isolator effect through modulation, its stability and operating bandwidth cannot be guaranteed.

[0004] Achieving broadband and stable optical isolation is a crucial issue in practical applications. Singularities in non-Hermitian optical systems possess characteristics different from Dirac points, known as topological properties. In short, a chiral mode transition can occur by circling a single singularity in parameter space. Regardless of whether the incident mode is odd or even, the outgoing mode is always even in one direction and odd in the other. This transition is highly robust; as long as the singularity is surrounded by a circling path, the outgoing results are identical.

[0005] Therefore, by leveraging the topological characteristics of singular points and existing dynamic modulation techniques, broadband optical isolators with strong anti-interference capabilities can be designed. Summary of the Invention

[0006] The purpose of this invention is to creatively combine the topological characteristics around singular points with dynamic modulation technology to provide a method, dynamic optical waveguide structure and device for generating non-reciprocal topological mode conversion. This conversion method can effectively improve the anti-interference capability of broadband optical isolators and mode converters.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] The first aspect of the present invention is to provide a method for generating a non-reciprocal topology mode transformation, comprising the following steps:

[0009] S1, construct the parameter space of the waveguide structure parameters, adjust the real and imaginary parts of the waveguide refractive index in a sinusoidal form in space and time, and make the wave vector matching condition satisfied in the positive direction, while not satisfying the wave vector matching condition in the negative direction.

[0010] S2, the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch is obtained from the coupling equation, and the real modulation amplitude and imaginary modulation amplitude are selected as the parameter space to determine the singular point parameters in the opposite direction;

[0011] S3, make a closed loop in the waveguide parameter space around the singular point in the opposite direction;

[0012] S4 applies the closed-loop parameter values ​​to waveguide modulation to obtain a dynamic optical waveguide structure that combines non-reciprocity and topology.

[0013] Preferably, in step S2, the method for deriving the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch is as follows:

[0014] The conversion between even mode Ψ1 and odd mode Ψ2 is achieved by modulating the waveguide dielectric constant. The modulation function includes real and imaginary parts, and the coupling equation is:

[0015] ε(z,t)=ε0+sgn(x)[δε1cos(qz-Ωt+φ1)+iδε2cos(qz-Ωt+φ2)],

[0016] Where ε0 is the dielectric constant of the waveguide, δε1 and δε2 represent the modulation amplitude, Ω represents the modulation frequency, q represents the wave vector, z represents the direction of light propagation in the waveguide, t represents time, sgn(x) is the step function, and φ 1,2 It is the initial phase of modulation; let Ω = Ω2 – Ω1, q = k2 – k1, which satisfies the positive phase matching condition.

[0017] Preferably, in step S3, the wave vector mismatch is zero in the positive direction, Δk f =0, there are no singularities;

[0018] In the opposite direction, the wave vector mismatch is not zero, Δk b = 2(k1-k2), a singularity exists, and the singularity parameter is (E + =E – c1 = 0, c2 = Δk / 2.

[0019] More preferably, the method for creating a closed loop around the singular point in the opposite direction in the waveguide parameter space is as follows:

[0020] In the parameter space, an endpoint is determined. Starting from this endpoint, the two parameters are continuously varied based on the closed-loop parametric equation to form a closed loop path. When the loop ends, the two parameters return to the endpoint and the closed loop path surrounds the singular point.

[0021] Preferably, in step S3, the closed-loop parametric equation is:

[0022] c1(z)=c 10 ±Δc1sin(2πz / L0) and c2(z)=c 20 +Δc2sin(πz / L0),

[0023] When the parameters evolve along the closed-loop adiabatic equation described above, quasi-energy exchange occurs in the reverse direction; however, no energy exchange occurs in the forward direction.

[0024] Preferably, in step S4, the equation of motion for the modulated waveguide is derived as follows:

[0025]

[0026] Where c 1,2 =1 / 2δε 1,2 (ω1ω2) 1 / 2 Solve the equation ε0∫sgn(x)E1(x)E2(x)dx to obtain [a1(z),a2(z)]. T =M(z,0)[a1(0),a2(0)] T M(z,0) is the transfer matrix:

[0027]

[0028] Where C′=[–Δk 2 / 4+(–c1 2 +c2 2 –2ic1c2)] 1 / 2 ;

[0029] The quasi-energy E of the system is given by exp(–iEζ)[a1(0),a2(0)]. T =M(ζ,0)[a1(0),a2(0)] T Find that ζ = 2π / Δk; find that E is:

[0030]

[0031] Preferably, the waveguide has a dielectric constant of ε0 = 12.75 and a width of d = 1 μm, and the dielectric constant is based on but not limited to silicon dielectric.

[0032] A second aspect of the present invention is to provide a dynamic optical waveguide structure, which is fabricated using a method for generating non-reciprocal topological mode conversion as described in any of the preceding claims, wherein the mode transmission and conversion results possess both non-reciprocity and topological properties.

[0033] Preferably, the parameters of the dynamic optical waveguide structure include ε0 = 12.75, δε1(z) = sin(2πz / L0), and δε2(z) = 0.2 + 2sin(πz / L0).

[0034] A third aspect of the present invention is to provide a broadband optical isolator, which is fabricated using the dynamic optical waveguide structure described above.

[0035] A fourth aspect of the present invention is to provide a mode converter, which is fabricated using the dynamic optical waveguide structure described above.

[0036] The present invention adopts the above technical solution and has the following technical effects compared with the prior art:

[0037] This invention sinusoidally adjusts the real and imaginary parts of the waveguide refractive index in space and time, ensuring that the wave vector matching condition is satisfied in the positive direction but not in the negative direction. The relationship between quasi-energy, modulation amplitude, and wave vector mismatch is obtained from the coupling equation. The real and imaginary modulation amplitudes are selected as the parameter space, with no singularities in the positive direction but singularities in the negative direction. A closed-loop parameter around the singularity is designed and applied to waveguide modulation. The parameter rotates clockwise or counterclockwise around the closed loop, equivalent to the mode being excited from the left or right side of the waveguide and propagating to the other end. This invention creatively combines dynamic modulation with a dynamic optical waveguide structure around the singularity. Its mode transmission and conversion results possess both non-reciprocity and topological properties; the former is caused by dynamic modulation, and the latter originates from the topological characteristics generated around the singularity. This structure can be applied to broadband optical isolators and mode converters. Attached Figure Description

[0038] Figure 1 A schematic diagram of the framework for generating non-reciprocal topology mode transformations;

[0039] Figure 2 This is a schematic diagram of topological or non-reciprocal mode conversion in a dielectric waveguide.

[0040] Figure 3 This is a schematic diagram illustrating the conversion between even mode Ψ1 and odd mode Ψ2 by modulating the waveguide dielectric constant.

[0041] Figure 4 and Figure 5 The Riemann surface of the quasi-energy E±real part is defined by taking c1 and c2 as bivariate parameter spaces.

[0042] Figure 6 For pattern Ψ 1,2 Intensity | a 1,2 (z)| 2 Distribution along the propagation direction: Schematic diagrams showing that modes Ψ1 and Ψ2 are excited in 6(a) and 6(b), respectively;

[0043] Figure 7 Let E be the electric field in the xz plane. z Distribution: Among them, Figure 7 (a)-(b) and Figure 7 (c)-(d) respectively draw the electric field E for reverse and forward incident directions. z Distribution of;

[0044] Figure 8 The power ratio varies with waveguide length: where, Figure 8 (a) shows the power ratio as a function of waveguide length L0 under the three closed loops; Figure 8 (b) is the case where the closed loop does not enclose the singular point; Figure 8 (c) shows the effect of the longitudinal dimension of the closed loop controlled by Δc1 on the power ratio; Figure 8 (d) The power ratios under two different closed-loop conditions are plotted. Detailed Implementation

[0045] The present invention will now be described in detail and specifically through specific embodiments to enable a better understanding of the invention. However, the following embodiments do not limit the scope of the invention.

[0046] This embodiment provides a method for generating non-reciprocal topology mode conversion. The main technical solution is to design a dynamic optical waveguide structure with strong anti-interference capability by utilizing the topological characteristics of singular points and existing dynamic modulation technology. This structure can be applied to broadband optical isolators and mode converters.

[0047] like Figure 1 The diagram shown illustrates the framework of a method for generating non-reciprocal topology mode transformations, which mainly includes the following steps:

[0048] S1, construct the parameter space of the waveguide structure parameters, adjust the real and imaginary parts of the waveguide refractive index in a sinusoidal form in space and time, and make the wave vector matching condition satisfied in the positive direction, while not satisfying the wave vector matching condition in the negative direction.

[0049] S2, the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch is obtained from the coupling equation, and the real modulation amplitude and imaginary modulation amplitude are selected as the parameter space; in the positive direction, the wave vector mismatch is zero, so there are no singular points; in the opposite direction, the wave vector mismatch is not zero, there are singular points, and the location of the singular points in the opposite direction is determined.

[0050] S3. In the waveguide parameter space, construct a closed loop around the singular point in the opposite direction, and design a closed loop parameter around the singular point based on the closed loop parameter equation.

[0051] S4 applies the closed-loop parameter values ​​to waveguide modulation. The parameters rotate clockwise or counterclockwise around the closed loop, which is equivalent to the mode being excited from the left or right side of the waveguide and propagating to the other end, thus obtaining a dynamic optical waveguide structure that combines non-reciprocity and topology.

[0052] By combining dynamic modulation with the transformation around a singularity, a non-reciprocal topological transformation is achieved. The dynamic optical waveguide structure modulated using this method exhibits both non-reciprocity and topological properties in its mode transmission and transformation results; the former is caused by dynamic modulation, while the latter stems from the topological characteristics generated around the singularity.

[0053] Based on this method for generating non-reciprocal topological mode conversion, a dynamic optical waveguide structure is provided. This dynamic optical waveguide structure is fabricated using this method, and its mode transmission and conversion results exhibit both non-reciprocity and topological properties. The former is caused by dynamic modulation, while the latter originates from the topological characteristics generated around singular points. This dynamic optical waveguide structure can be applied to on-chip integrated broadband optical isolators, or it can be used to fabricate mode converters.

[0054] like Figure 2 The diagram illustrates topological or non-reciprocal mode conversion in a dielectric waveguide. Odd and even modes, whether incident in the forward or reverse direction, are represented by symmetric and antisymmetric electric field distributions, respectively. mn (T' mn ) represents the forward (reverse) transmittance from the n-mode to the m-mode, where m,n = 1 or 2 indicates an even or odd mode. Figure 2 The left waveguide shows the waveguide structure around the singularity point. In this case, the mode output depends only on the propagation direction and is independent of the incident direction. Specifically, for forward propagation, assume T... 21 >T 11 ≈T 22 >T 12 Then, odd modulo predominates at the right output. Typically, topology transformations follow T... mn =T' nm The reciprocity of T' is satisfied during reverse transmission. 12 >T' 11 ≈T' 22 >T'21 This results in the output of an even mode on the left side. Figure 2 The waveguide on the right shows a dynamically modulated waveguide structure. The transmittance of the normally incident even mode converted to an odd mode is T. 21 However, the transmittance of the odd mode converted to the even mode by the reverse-incident incidence is T'. 12 =0≠T 21 Therefore, it is a non-reciprocal schema transformation. Below, we will discuss the results of non-reciprocal topological transformations by combining the two.

[0055] like Figure 3 The diagram illustrates the conversion between even mode Ψ1 and odd mode Ψ2 achieved by modulating the waveguide dielectric constant. In step S2, the method for deriving the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch is as follows: the conversion between even mode Ψ1 and odd mode Ψ2 is achieved by modulating the waveguide dielectric constant. The modulation function includes a real part and an imaginary part, and the coupling equation is:

[0056] ε(z,t)=ε0+sgn(x)[δε1cos(qz-Ωt+φ1)+iδε2cos(qz-Ωt+φ2)] (1)

[0057] Where ε0 is the dielectric constant of the waveguide, δε1 and δε2 represent the modulation amplitude, Ω represents the modulation frequency, q represents the wave vector, z represents the direction of light propagation in the waveguide, t represents time, sgn(x) is the step function, and φ 1,2 It is the initial phase of modulation; let Ω = Ω2 and q = k2 - k1, which satisfy the positive phase matching condition.

[0058] In step S3, the wave vector mismatch is zero in the positive direction, Δk f =0, no singularity exists; in the opposite direction, the wave vector mismatch is not zero, Δk b = 2(k1-k2), a singularity exists, and the singularity parameter is (E + =E – c1 = 0, c2 = Δk / 2.

[0059] In step S3, the specific method for forming a closed loop around the singular point in the opposite direction in the waveguide parameter space is as follows: determine an endpoint in the parameter space, take the endpoint as the starting point, continuously change the two parameters based on the closed loop parameter equation to form a closed loop path, and the two parameters return to the endpoint at the end of the loop and the closed loop path surrounds the singular point.

[0060] Specifically, the closed-loop parametric equation is: c1(z) = c 10 ±Δc1sin(2πz / L0) and c2(z)=c 20+Δc2sin(πz / L0), when the parameter changes along the closed-loop parameter equation above, quasi-energy exchange occurs in the opposite direction; while in the positive direction, there is no energy exchange.

[0061] Furthermore, in the above-mentioned genetic scheme, the equation of motion for the modulated waveguide in step S4 is derived as follows:

[0062]

[0063] Where c 1,2 =1 / 2δε 1,2 (ω1ω2) 1 / 2 Solve the equation ε0∫sgn(x)E1(x)E2(x)dx to obtain [a1(z),a2(z)]. T =M(z,0)[a1(0),a2(0)] T M(z,0) is the transfer matrix:

[0064]

[0065] Where C′=[–Δk 2 / 4+(–c1 2 +c2 2 –2ic1c2)] 1 / 2 ;

[0066] The quasi-energy E of the system is given by exp(–iEζ)[a1(0),a2(0)]. T =M(ζ,0)[a1(0),a2(0)] T Find that ζ = 2π / Δk; find that E is:

[0067]

[0068] In the opposite direction, a singularity (E) is generated due to the mismatch of the wave vectors. + =E – ): c1 = 0, c2 = Δk / 2. Conversely, there are no singularities in the positive direction. Taking c1 and c2 as a bivariate parameter space, the quasi-energy E ± The real part is like Figure 4 and Figure 5 As shown.

[0069] As a preferred embodiment, the waveguide structure is made of silicon, with a dielectric constant ε0 = 12.75 and a width d = 1 μm. This dielectric constant is based on dielectric silicon. Using the above-described modulation scheme combined with the singularity, the frequencies of modes Ψ1 and Ψ2 are ω1 = 0.112 × 2πc / d and ω2 = 0.188 × 2πc / d, respectively, with wave vectors k1 = 0.303 × 2π / d and k2 = 0.284 × 2π / d, and a wave vector mismatch Δk in the opposite direction. b =0.234μm -1 .

[0070] It should be noted that the method for generating non-reciprocal topological mode conversion provided by the present invention is also applicable to other dielectric materials, such as dielectric materials including but not limited to silicon dioxide.

[0071] Therefore, the positive singularity is located at c. 1,EP =0 and c 2,EP =0.117μm -1 The figure shows a star-shaped representation. When the parameter moves along c1(z) = c 10 ±Δc1sin(2πz / L0) and c2(z)=c 20 When the closed-loop change is +Δc2sin(πz / L0), the solid line in the figure describes the instantaneous evolution of the quasi-energy. Here, c1=c 10 and c2 = c 20 The sign indicates the starting point, and the plus or minus sign defines the clockwise and counterclockwise directions of rotation. Forward (counter-clockwise) propagation represents clockwise (counter-clockwise) rotation around the singularity.

[0072] First consider the reverse direction, from... Figure 4 and Figure 5 We can clearly see that a quasi-energy exchange occurs at the end of the loop; secondly, considering the positive direction, the two states at the starting point have the same real part of the quasi-energy and different imaginary parts. After one closed-loop parameter evolution, the quasi-energy returns to its initial value, with no energy exchange.

[0073] Based on the above-described method for generating non-reciprocal topological mode conversion, this invention also provides a dynamic optical waveguide structure, which is fabricated using the method described above. Its mode transmission and conversion results possess both non-reciprocity and topological properties. Furthermore, the parameters of the dynamic optical waveguide structure include ε0 = 12.75, δε1(z) = sin(2πz / L0), and δε2(z) = 0.2 + 2sin(πz / L0).

[0074] Furthermore, this invention also provides a device fabricated using the topological properties of singularities and existing dynamic modulation techniques. For example, a broadband optical isolator with strong anti-interference capabilities can be designed, which is fabricated using the aforementioned dynamic optical waveguide structure. Additionally, depending on the requirements, a corresponding mode converter can also be fabricated using the dynamic optical waveguide structure.

[0075] To further illustrate the effect of the conversion method of the present invention on the distribution of mode intensity along the propagation direction, such as... Figure 6 As shown, we have drawn the pattern Ψ 1,2 Intensity | a 1,2 (z)| 2 The distribution along the propagation direction, where modes Ψ1 and Ψ2 are excited in 6(a) and 6(b), respectively.

[0076] In the opposite direction, as mode Ψ1 is incident, the intensity of the conversion to generate Ψ2 continuously increases, while Ψ1 first increases and then decreases. Ψ2(|a2(0)| 2 The output strength of ) is much greater than that of Ψ1(|a1(0)| 2 As Ψ2 is incident, the intensity of the transformation generating Ψ1 first increases and then decreases, while the change in Ψ2 is not significant. In summary, regardless of the input mode, backpropagation will produce a specific mode output, which is consistent with existing topological transformations.

[0077] In the positive direction, the intensity of the incident mode remains essentially constant, while the intensity of the converted mode increases rapidly. Then, at a certain location, the intensities of the two modes intersect and simultaneously increase with increasing propagation distance. Output intensity |a 1,2 (50)| 2 The transmittance T of the even mode converted to the odd mode by normal incidence is significantly amplified compared to the incident intensity. This topological transformation is also non-reciprocal. 21 equal Figure 6 The output intensity of Ψ2 in (a), i.e., T 21 =|a2(50)| 2 ≈700. Similarly, we get T. 12 ≈700,T' 12 ≈0,T' 21 ≈30. Therefore, T 21 ≠T' 12 And T 12 ≠T' 21 The non-reciprocal condition is met.

[0078] The non-reciprocal topological transformation implemented above can be verified through numerical simulation using the COMSOL Multiphysics finite element solver. The specific verification method is as follows:

[0079] like Figure 7As shown, the electric field E in the xz plane is... z Distribution. Among them, Figure 7 (a)-(b) and Figure 7 (c)-(d) respectively draw the electric field E for reverse and forward incident directions. z The field distribution is as follows: the modulation region is z = 0–50 μm, and the remaining region is unmodulated with a dielectric constant of 12.75. To distinguish the incident modes, the inset shows an enlarged field pattern at the incident end.

[0080] For backpropagation, when Ψ1 is excited, the output electric field distribution is antisymmetric, meaning the output mode is Ψ2. The intensity of Ψ2 is significantly amplified compared to the intensity of the incident Ψ1. When Ψ2 is excited in the reverse direction, the output field distribution is also almost antisymmetric, meaning the incident mode is not converted, but merely amplified.

[0081] Magnification and Figure 6 The inconsistency in the calculation results of (b) is mainly due to a flaw in the gain-loss setting of the time-domain model used, leading to inconsistent gain-loss modulation between modes Ψ1 and Ψ2. For forward transmission, regardless of whether the injected symmetric or antisymmetric mode is used, the output is a mixture of Ψ1 and Ψ2, with significant intensity amplification, which is consistent with... Figure 6 The results were consistent.

[0082] Finally, we discuss the impact of waveguide length and closed-loop configuration on conversion efficiency. For example... Figure 8 As shown, the power ratio varies with waveguide length, η 11 and η 12 Represented by solid and dashed lines respectively. η 11 and η 12 Let η be the power ratio of the output terminal Ψ1 when Ψ1 and Ψ2 are incident, respectively. Then, for the positive direction, η... 11 =T 11 / (T 11 +T 21 ) and η 12 =T 12 / (T 12 +T 22 ), and in the opposite direction there is η 11 =T' 11 / (T' 11 +T' 21 ) and η 12 =T' 12 / (T' 12 +T' 22 ).

[0083] in Figure 8(a) The power ratio varies with waveguide length L0 for three closed loops. The inset shows the relative positions of the singularities and the closed loops. All closed loops contain singularities, but the distance from the singularity to the start point of each closed loop is different. For the leftmost closed loop, if the waveguide length is less than 50 μm, the parameters change too rapidly, and adiabatic evolution cannot be guaranteed. When L0 > 130 μm, η 11 and η 12 Both are close to 0, resulting in stable output. Regardless of whether Ψ1 or Ψ2 is incident in reverse, the output mode is almost always Ψ2. If the closed-loop starting point is closer to the singularity, the power ratio increases slightly after stabilization. Nevertheless, the output mode is still mainly Ψ2, accounting for nearly 90%.

[0084] For comparison, Figure 8 (b) The case where closed loops do not enclose singular points was further investigated. For example... Figure 8 As shown in (b), the left loop is far from the singularity, while the right loop is close to it. For the left loop, even with a sufficiently long waveguide, the power ratio cannot be stable. η 11 and η 12 Both oscillate and change as L0 increases. Regardless of whether Ψ1 or Ψ2 is incident, the output is almost always the incident mode. For the right-loop case, due to η... 11 =η 12 ≈0.06, although this ring does not contain singularities, the output is still mainly Ψ2. This is consistent with... Figure 8 The result of (a) is similar because even if the instantaneous eigenvalues ​​do not intersect, the nonadiabatic transitions near the singular point are still very strong.

[0085] The longitudinal dimension of the closed loop controlled by Δc1 has little effect on the power ratio, such as Figure 8 As shown in (c).

[0086] In a positive direction, pattern propagation is entirely different. Figure 8 (d) The power ratios under two different closed-loop conditions are plotted. η 11 and η 12 The values ​​quickly stabilized at 0.5, almost unrelated to the choice of the closed loop.

[0087] Based on the above design, by adding an additional ordinary lossy waveguide region at both ends of the waveguide, a robust optical isolator can be constructed, and its operating wavelength is not limited by the selected frequency. Although the position of the singular point moves in the parameter space with the change of frequency, the mode output remains essentially unchanged as long as the singular point is surrounded by a closed loop. The robustness of this topology transformation is beneficial to the production and manufacturing of non-reciprocal devices.

[0088] The specific embodiments of the present invention have been described in detail above, but they are merely examples, and the present invention is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications and substitutions to the present invention are also within the scope of the present invention. Therefore, all equivalent transformations and modifications made without departing from the spirit and scope of the present invention should be covered within the scope of the present invention.

Claims

1. A method for generating non-reciprocal topological mode transformations, characterized in that, Includes the following steps: S1, construct the parameter space of the waveguide structure parameters, adjust the real and imaginary parts of the waveguide refractive index in a sinusoidal form in space and time, and make the wave vector matching condition satisfied in the positive direction, while not satisfying the wave vector matching condition in the negative direction. S2, the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch is obtained from the coupling equation, and the real modulation amplitude and imaginary modulation amplitude are selected as the parameter space to determine the location of the singular point in the opposite direction; S3, make a closed loop in the waveguide parameter space around the singular point in the opposite direction; S4. The closed-loop parameter values ​​are applied to waveguide modulation to obtain a dynamic optical waveguide structure that combines non-reciprocity and topology. In step S2, the method for deriving the relationship between the quasi-energy of the Floquet state and the modulation amplitude and wave vector mismatch is as follows: The conversion between even mode Ψ1 and odd mode Ψ2 is achieved by modulating the waveguide dielectric constant. The modulation function includes real and imaginary parts, and the coupling equation is: ， in Let be the dielectric constant of the waveguide. and Ω represents the modulation amplitude, and Ω represents the modulation frequency. q represents wave vector, z Indicates the direction of light propagation in the waveguide. t To represent time, sgn( x ) is a step function. This is the initial phase of modulation; let Ω = Ω2 – Ω1, q = k 2– k 1. The positive phase matching condition is met; In step S3, the wave vector mismatch is zero in the positive direction, Δ k f = 0, there are no singularities; In the opposite direction, the wave vector mismatch is not zero, Δ k b = 2( k 1 - k 2) There are singular points, and the parameters of the singular points are ( E + = E – ): c 1 = 0, c 2 = Δ k / 2.

2. The method for generating non-reciprocal topology mode transformations according to claim 1, characterized in that, The specific method for constructing a closed loop around the singular point in the opposite direction in the waveguide parameter space is as follows: In the parameter space, an endpoint is determined. Starting from this endpoint, the two parameters are continuously varied based on the closed-loop parametric equation to form a closed loop path. When the loop ends, the two parameters return to the endpoint and the closed loop path surrounds the singular point.

3. The method for generating non-reciprocal topology mode transformations according to claim 2, characterized in that, In step S3, the closed-loop parameter equation is: ， When the parameters evolve along the closed-loop adiabatic equation described above, quasi-energy exchange occurs in the reverse direction; however, no energy exchange occurs in the forward direction.

4. The method for generating non-reciprocal topology mode transformations according to claim 3, characterized in that, In step S4, the equation of motion for the modulated waveguide is derived as follows: ， in Solve this equation to obtain [ a 1( z ), a 2( z )] T = M( z , 0)[ a 1(0), a 2(0)] T M( z (0) represents the transfer matrix: ， in ; The quasi-energy of the system E Depend on Find out, Find E for: 。 5. The method for generating non-reciprocal topology mode transformations according to claim 4, characterized in that, The dielectric constant of the waveguide is = 12.75, width is d = 1µm; Mode Ψ1 and Ψ2 frequencies ω 1 = 0.112 × 2πc / d , ω 2 = 0.188 × 2πc / d wave vector is k 1 = 0.303 × 2π / d , k 2 = 0.284 × 2π / d Wave vector mismatch Δ in the opposite direction k b = 0.234µm -1 .

6. A dynamic optical waveguide structure, characterized in that, The method for generating non-reciprocal topology mode conversion as described in any one of claims 1 to 5 is used, and the mode transmission and conversion results are both non-reciprocal and topological.

7. The dynamic optical waveguide structure according to claim 6, characterized in that, The parameters of the dynamic optical waveguide structure include and .

8. A broadband optical isolator or mode converter, characterized in that, The structure is fabricated using the dynamic optical waveguide structure as described in any one of claims 6 to 7.

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