Implementation method for periodic resonance mode conversion of symmetric light waves in dual-channel waveguide

Abstract

The invention relates to a method for realizing periodic resonance mode conversion of symmetric light waves in a dual-channel waveguide. The method is proposed based on the distributed Fourier algorithm to transmit the light waves, and in the symmetrical dual-channel potential well, the mode with the same space can be converted in the two waveguides at the same time, so that the number of light wave transmission in the waveguides is doubled, and the information transmission quantity is increased. And due to the symmetry of the dual-channel waveguide, the transmission loss can be obviously inhibited compared with that of a single-channel waveguide. When the two waveguides are asymmetric, a novel phenomenon can be observed. When the dual-channel potential well is asymmetric, even space-scale conversion and odd space-scale conversion can be respectively realized in the two waveguides, so that not only is the information transmission quantity increased, but also the information transmission types are increased. Due to the existence of the nonlinear effect, the resonance condition shifts, the conversion efficiency is reduced, and the conversion efficiency under the nonlinear effect can be obviously improved by introducing the frequency offset for correction.

Description

Technical Field

[0001] The invention relates to the field of optical technology, and in particular to a method for realizing periodic conversion of symmetrical light waves in a dual-channel waveguide. Background Art

[0002] Rabi oscillation is one of the basic concepts of quantum mechanics. It refers to the resonant transition that can excite electrons from one energy level to another and back under the drive of an external field or radio frequency wave, and the periodic conversion and recovery of the two energy levels. This phenomenon is universal and can be observed in many different physical systems, such as atoms, semiconductors, magnetic fields, Bose-Einstein condensates (BECs), condensed matter, etc., and has important applications in quantum computing and quantum information processing. In experiments, due to the strong controllability of light waves, many phenomena in quantum mechanics can be observed in optical systems through the analogy between quantum mechanics and wave optics, so that optical instruments can be used for better observation and measurement. For example, optical analogy phenomena such as Bloch oscillations, Zener tunneling, and dynamic localization can be observed using engineered photonic devices. Extending the concept of Rabi oscillation to the field of optics, the longitudinal periodic modulation of the refractive index plays the role of an external field, promoting the realization of parametric amplification, optical tunneling suppression, and optical isolation. Rabi oscillations are manifested in optics as periodic resonant mode conversion. By setting the appropriate modulation frequency, optical resonant mode conversion can be achieved. In 2007, Kartashov et al. proposed for the first time a theoretical model for applying resonant mode conversion to multimode waveguides, and subsequently demonstrated experiments on the optical analogy of Rabi oscillations in different optical waveguides. Since then, resonant mode conversion under different optical waveguide structures has been widely studied, and many novel phenomena have been observed. For example, optical transitions and Rabi oscillations in waveguide arrays, Rabi oscillations and stimulated mode conversion on a subwavelength scale, conversion of resonant modes in PT-symmetric waveguides, resonant mode conversion under nonlinear modulated waveguides, and in more complex spiral structures, coupling of vortex modes with different topological charges can be achieved. Considering the nonlinear effects in waveguides, the concept of mode conversion can be further extended to the research field of optical solitons. For example, the mode conversion of azimuth-modulated vortex solitons in nonlinear waveguides has been studied.

[0003] The present invention is based on the transmission of light waves by the distributed Fourier algorithm, and proposes a method for periodic conversion of symmetrical light waves in a dual-channel waveguide. In a symmetrical dual-channel potential well, modes with the same parity can be converted in two waveguides at the same time, which doubles the number of light waves transmitted in the waveguide and increases the amount of information transmitted. And due to the symmetry of the dual-channel waveguide, the transmission loss can be significantly suppressed compared with the single-channel waveguide. When the two waveguides are asymmetric, novel phenomena can be observed. When the dual-channel potential well is asymmetric, even parity conversion and odd parity conversion can be realized in the two waveguides respectively, which not only increases the amount of information transmitted, but also increases the types of information transmission. In addition, the influence of nonlinear effects on the conversion process is also studied. The results show that the existence of nonlinear effects will cause the resonance conditions to shift and the conversion efficiency to decrease. By introducing frequency deviation correction, the conversion efficiency under nonlinear effects can be significantly improved. Summary of the invention

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A method for realizing periodic resonance mode conversion of symmetrical light waves in a dual-channel waveguide comprises the following steps:

[0006] A method for realizing periodic resonance mode conversion of symmetrical light waves in a dual-channel waveguide is characterized by comprising the following steps:

[0007] S1, according to model (1) and set σ = 0, Ω z =0, the single-channel potential well depth parameter is set to p=6, and the energy level distribution characteristics of the eigenmodes u1 to u4 and the corresponding intrinsic values ​​β1 to β4 of the unmodulated light beam in the single-channel multimode waveguide expressed by equations (2) and (3) can be obtained. u1 and u3 have the same symmetry even parity, and u2 and u4 have the same symmetry odd parity.

[0008] S2, superimpose the eigenmodes with the same symmetry obtained above and introduce longitudinal periodic modulation Ω z ,satisfy Select m = 1, n = 3 or m = 2, n = 4, bring it into model (1) and set σ = 0; use the orthogonality of the eigenmode to obtain the weight evolution process in the eigenmode conversion process represented by equation (4); set the resonant frequency Ω z =β1-β3, the light waves u1 and u3 with even parity can achieve periodic resonance mode conversion when transmitted in a single-channel waveguide; setting the resonance frequency Ω z =β2-β4, light waves u2 and u4 with odd parity can achieve periodic resonance mode conversion when transmitted in a single-channel waveguide; the conversion periods of odd parity and even parity are different;

[0009] S3, change the depth of the waveguide potential well and the spacing of the potential wells; increase the depth p of the potential well, and the number of eigenmodes in the potential well increases accordingly; increase the value of the potential well spacing w, and the single-channel waveguide gradually becomes a dual-channel waveguide; set p1=p2=12, the eigenmodes in the two channels increase to 8, u1 to u8 and are symmetrically distributed in the two channels; in the process of increasing the potential well spacing, two adjacent modes with the same symmetry gradually approach each other and have the same eigenvalue; set w=4, the two-channel potential wells are completely independent and become two symmetrical dual-channel potential wells, and the 8 eigenmodes in the potential wells are close to each other to become 4 modes, u1 to u4;

[0010] S4, superimpose the four eigenmodes with the same symmetry obtained above and transmit them in the symmetrical dual-channel waveguide; set the resonant frequency Ω z =β1-β3, the even-parity light waves u1 and u3 can simultaneously realize periodic resonance mode conversion in the two-channel waveguide; set the resonance frequency Ω z =β2-β4, odd-parity light waves u2 and u4 can simultaneously realize periodic resonant mode conversion in two-channel waveguides, and the conversion rate is doubled; the conversion periods of odd parity and even parity are different;

[0011] S5, change the structure of the dual-channel waveguide; increase the depth of one of the waveguide channel potential wells, the two waveguide potential wells show asymmetry, and the eigenmodes in the two potential wells show asymmetric distribution; set p1=20, p2=14, the adjacent modes with different symmetric structures in the two channel potential wells gradually approach each other and have the same eigenvalue; u2 in the left channel and u1 in the right channel have the same eigenvalue β1, and u4 in the left channel and u3 in the right channel have the same eigenvalue β2;

[0012] S6, superimpose the four modes u1 to u4 according to equation (5) and set the resonant frequency Ω z =β1-β2, and transmit in an asymmetric dual-channel waveguide; Substitute (5) into (1) and set σ = 0; Using the orthogonality of the eigenmode, the weight evolution process in the eigenmode conversion process represented by (6) is obtained; The conversion periods of odd-parity and even-parity light waves are different, and they need to be modulated separately; Satisfying the modulation relationship given by (7), odd-parity and even-symmetric light waves can simultaneously realize the periodic conversion of the resonant mode in the asymmetric dual-channel waveguide under different modulations (μ1 = 0.055, μ2 = 0.1);

[0013] S7, nonlinear effect is introduced into the asymmetric dual-channel waveguide, σ=1 is set in the self-focusing nonlinear medium, and σ=-1 is set in the self-defocusing nonlinear medium; the four modes u1 to u4 are superimposed and then transmitted and evolved in the asymmetric dual-channel waveguide, and the weight evolution process in the eigenmode conversion process is obtained according to equation (6); at this time, the resonance condition is destroyed, and the light beam no longer undergoes periodic conversion;

[0014] S8, introduce frequency deviation β′ to correct the resonance frequency, and set the resonance frequency to Ω z =β1-β2+β′, β′=0.1 and β′=-0.07 are set in the self-focusing and defocusing nonlinear media respectively; the four modes u1 to u4 are superimposed and then transmitted and evolved in the asymmetric dual-channel waveguide, and the weight evolution process in the eigenmode conversion process is obtained according to formula (6); the odd-parity periodic resonance mode conversion is realized in the left channel waveguide, and the even-parity periodic resonance mode conversion is realized in the right channel waveguide.

[0015] The propagation of the light beam is described by the following nonlinear Schrödinger equation:

[0016]

[0017] Here q(x, z) is the dimensionless amplitude, the longitudinal coordinate z and the transverse coordinate x are the transmission distance and the input beam width respectively; the potential well distribution is represented by R(x)=V1+V2, where V1=p1 sech(x+w) 2 ,V2=p2 sech(xw) 2 , p 1，2 is the potential well depth, w is the distance between the two waveguides; the parameter μ represents the spatial frequency of the longitudinal periodic modulation Ω z Depth; σ=1(σ=-1) Kerr nonlinear self-focusing (defocusing) effect;

[0018] Nonlinear effects and longitudinal periodic modulation are not considered, that is, σ=0 and μ=0;

[0019] q(x, z) = u(x) × e iβz (2)

[0020] where β is the transmission constant and u(x) describes the distribution of the transverse mode; substituting it into equation (1), we obtain the linear eigenvalue equation:

[0021]

[0022] According to equation (3), a series of eigenvalues ​​and eigenmodes are obtained. The eigenmodes with the same symmetry are superimposed to satisfy Introduce longitudinal periodic modulation, substitute q(x, z) into equation (1) and set σ = 0, and multiply by and And integrating x, we can get the coupling conversion equation of the resonant mode:

[0023]

[0024]

[0025] Adjust the potential well parameters p1 = 20, p2 = 14, w = 4, and the dual-channel waveguide presents an asymmetric distribution; and let

[0026]

[0027] Substituting equation (5) into equation (1) and using the orthogonality condition, we can obtain:

[0028]

[0029]

[0030]

[0031]

[0032] Here,

[0033]

[0034] Use |ρ1(z)| 2 =|c1(z)| 2 +|c2(z)| 2 represents the superposition weight of the two initial modes, |ρ2(z)| 2 =|c3(z)| 2 +|c4(z)| 2 Represents the superposition weight of the converted mode. The conversion period of even parity and odd parity is different, so the two channels should be modulated separately, and the modulation depth μ1 and μ2 need to satisfy the following proportional relationship to achieve simultaneous conversion:

[0035] Ω R2 =μ1H′ L24 =μ2H′ R13 (7)

[0036] The beneficial effects of the present invention are:

[0037] The present invention transmits light waves based on the distributed Fourier algorithm, and proposes a method for realizing periodic conversion of symmetrical light waves in a dual-channel waveguide. In the symmetrical dual-channel potential well, the number of light waves transmitted in the waveguide is doubled, and the amount of information transmitted is increased. And due to the symmetry of the dual-channel waveguide, the transmission loss can be significantly suppressed compared with the single-channel waveguide. Even parity conversion and odd parity conversion can be realized in the two waveguides respectively, which not only increases the amount of information transmitted, but also increases the types of information transmission. In addition, the existence of nonlinear effects will cause the resonance conditions to shift and the conversion efficiency to decrease. By introducing frequency deviation correction, the conversion efficiency under nonlinear effects can be significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the distribution of eigenmodes in a single-channel potential well.

[0039] Figure 2 It is a transmission diagram and weight evolution diagram of odd-parity and even-parity modes in a single-channel potential well.

[0040] Figure 3 is the distribution of eigenmodes under the symmetric double-channel potential well.

[0041] Figure 4 It is a transmission diagram and weight evolution diagram of odd-parity and even-parity modes under a symmetric dual-channel potential well.

[0042] Figure 5 The distribution of eigenmodes in asymmetric double-channel potential wells

[0043] Figure 6 It is a transmission diagram of odd-parity and even-parity modes and a weight evolution diagram under an asymmetric dual-channel potential well.

[0044] Figure 7 Schematic diagram of mode conversion transmission and weight evolution in self-focusing medium (σ=1) and defocusing medium (σ=-1) under an asymmetric dual-channel potential well.

[0045] Figure 8 The relationship between frequency deviation and conversion distance, the schematic diagram of mode conversion transmission under asymmetric dual-channel potential well and the weight evolution diagram. DETAILED DESCRIPTION

[0046] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0047] The method for realizing periodic conversion of a symmetrical light wave in a dual-channel waveguide described in this embodiment includes the following steps:

[0048] S1, according to model (1) and set σ = 0, Ω z =0, the single-channel potential well depth parameter is set to p=6, and the energy level distribution characteristics of the four eigenmodes u1 to u4 and the corresponding intrinsic values ​​β1 to β4 of the unmodulated light beam in the single-channel multimode waveguide expressed by equations (2) and (3) can be obtained. u1 and u3 have the same symmetry even parity, and u2 and u4 have the same symmetry odd parity;

[0049] S2, superimpose the eigenmodes with the same symmetry obtained above and introduce longitudinal periodic modulation Ω z , satisfying q(x,z)=c m (z)u m (x)e iβmz +cn (z)u n (x)e iβnz ; Select m = 1, n = 3 or m = 2, n = 4, bring it into model (1) and set σ = 0; use the orthogonality of the eigenmode to obtain the weight evolution process in the eigenmode conversion process represented by equation (4); set the resonant frequency Ω z =β1-β3, the light waves u1 and u3 with even parity can achieve periodic resonance mode conversion when transmitted in a single-channel waveguide; setting the resonance frequency Ω z =β2-β4, the light waves u2 and u4 with odd parity can realize periodic resonance mode conversion when transmitted in a single-channel waveguide; the conversion periods of odd parity and even parity are different and there is a certain transmission loss in the conversion process.

[0050] S3, change the depth of the waveguide potential well and the spacing of the potential wells; increase the depth p of the potential well, and the number of eigenmodes in the potential well increases accordingly; increase the value of the potential well spacing w, and the single-channel waveguide gradually becomes a dual-channel waveguide; set p1=p2=12, the number of eigenmodes in the two channels doubles to 8, u1 to u8, and are symmetrically distributed in the two channels; in the process of increasing the potential well spacing, two adjacent modes with the same symmetry gradually approach each other and have the same eigenvalue; set w=4, the two-channel potential wells are completely independent and become two symmetrical dual-channel potential wells, and the 8 eigenmodes in the potential wells approach each other to become 4 modes, u1 to u4;

[0051] S4, (4) shows that the modes with the same parity structure can also be converted periodically in the symmetric dual-channel waveguide, and this idea can be verified by the transmission of light waves through the Fourier algorithm. The four eigenmodes with the same symmetry obtained above are superimposed to satisfy q(x,z)=c m (z)u m (x)e iβmz +c n (z)u n (x)e iβnz , transmitted in a symmetrical dual-channel waveguide. Set the resonant frequency Ω z =β1-β3, the even-parity light waves u1 and u3 can simultaneously realize periodic conversion in the two-channel potential wells; set the resonance frequency Ω z =β2-β4, odd-parity light waves u2 and u4 can realize period conversion in the two-channel potential wells at the same time, and the conversion rate is doubled; the conversion periods of odd parity and even parity are different; compared with the single-channel potential well, the number of light waves transmitted is increased, and the transmission loss is effectively suppressed.

[0052] S5, change the structure of the dual-channel waveguide, increase the depth of one of the waveguide channel potential wells, the two waveguide potential wells show asymmetry, and new characteristics can be obtained from equation (3), the eigenmodes in the two potential wells show asymmetric distribution. Set p1 = 20, p2 = 14, the adjacent modes with different symmetric structures in the two channel potential wells gradually approach each other and have the same eigenvalue; u2 in the left channel and u1 in the right channel have the same eigenvalue β1, and u4 in the left channel and u3 in the right channel have the same eigenvalue β2; due to the different conversion periods of odd parity and even parity structures under different symmetric structures, they need to be modulated separately.

[0053] S6, superimpose the four modes u1 to u4 according to formula (5) and set the resonant frequency Ω z =β1-β2, and transmit in an asymmetric dual-channel waveguide; substitute formula (5) into formula (1) and set σ=0; use the orthogonality of the eigenmode to obtain the weight evolution process in the eigenmode conversion process represented by formula (6); due to the different conversion periods of odd-parity and even-parity light waves, they need to be modulated separately; satisfying the modulation relationship given by formula (7), odd-parity and even-symmetric modes can simultaneously realize the periodic conversion of the resonant mode in the asymmetric dual-channel waveguide under different modulations (μ1=0.055, μ2=0.1). Not only the number of light wave transmissions is increased, but also the types of light wave transmissions are increased.

[0054] S7, nonlinear effect is introduced into the asymmetric dual-channel waveguide, σ=1 is set in the self-focusing nonlinear medium, and σ=-1 is set in the self-defocusing nonlinear medium. The four modes u1 to u4 are superimposed according to equation (5) and then transmitted and evolved in the asymmetric dual-channel waveguide. The weight evolution process during the eigenmode conversion is obtained according to equation (6). It can be seen that the resonance condition will be destroyed at this time, and the light beam will no longer undergo periodic conversion.

[0055] S8, introduce frequency deviation β′ to correct the resonance frequency, and set the conversion frequency to Ω z =β1-β2+β′, β′=0.1 and β′=-0.07 are set in the self-focusing and defocusing nonlinear media respectively by numerical matching; the four modes u1 to u4 are superimposed and then transmitted and evolved in the asymmetric dual-channel waveguide, and the weight evolution process in the eigenmode conversion process is obtained according to formula (6); at this time, the periodic conversion of odd-parity and even-parity resonance modes is realized in the two channels and the conversion efficiency is significantly improved.

[0056] The propagation of the light beam is described by the following nonlinear Schrödinger equation:

[0057]

[0058] Here q(x, z) is the dimensionless amplitude, and the longitudinal coordinate z and transverse coordinate x are the transmission distance and input beam width, respectively. The potential well distribution is represented by R(x)=V1+V2, where V1=p1 sech(x+w) 2 , V2=p2sech(xw) 2 , p 1，2 is the potential well depth, w is the distance between the two waveguides. The parameter μ represents the spatial frequency of the longitudinal periodic modulation Ω z Depth. σ=1(σ=-1) Kerr nonlinear self-focusing (defocusing) effect.

[0059] Nonlinear effects and longitudinal periodic modulation are not considered, that is, σ=0 and μ=0.

[0060] q(x, z) = u(x) × e iβz (2)

[0061] Where β is the transmission constant and u(x) describes the distribution of the transverse mode. Substituting it into equation (1), we get the linear eigenvalue equation:

[0062]

[0063] Set w = 0, p1 = p2 = 6, and use the plane wave expansion method to obtain the energy level and essential mode distribution of the mode in the waveguide from equation (3), as follows: Figure 1 As shown. Figure 1 It can be seen that under the selected parameters, the single-channel waveguide exhibits four eigenmodes u1 to u4, among which u1 and u3 have the same parity structure, i.e., even parity symmetry, and u2 and u4 have the same parity structure, i.e., odd parity symmetry.

[0064] The eigenmodes with the same symmetry obtained above are superimposed to satisfy Introduce longitudinal periodic modulation, substitute q(x,z) into equation (1) and set σ=0, and multiply by and And integrating x, we can get the coupling conversion equation of the resonant mode:

[0065]

[0066]

[0067] Setting the resonant frequency Ω z =β m -β n By analyzing equation (4) using the Runge-Kutta method and bringing (2) into (1) to perform numerical simulation of the evolutionary beam transmission, we can obtain the transmission diagram of the mode conversion and the weight evolution diagram, as shown in Figure 2 shown. Figure 2 It can be seen that the modes with the same parity structure can be converted periodically, and the conversion periods of odd parity and even parity are different. And there is a certain transmission loss in the conversion process.

[0068] Change the depth of the waveguide potential well and the spacing of the potential wells. Increasing the depth of the potential well p increases the number of eigenmodes in the potential well. Increasing the value of the potential well spacing w, the single-channel waveguide gradually becomes a dual-channel waveguide. Set p1 = p2 = 12, w = 1.55, and according to formula (3), the energy level and eigenmode distribution of the mode in the waveguide can be obtained, as follows: Figure 3 As shown. Under the selected parameters, the eigenmodes in the two channels increase to 8, u1 to u8, and are symmetrically distributed in the two channels. As the potential well spacing increases, two adjacent modes with the same symmetry gradually approach each other and have the same eigenvalue. When the potential well depth increases to w = 4, the two-channel potential wells become completely independent and become two symmetrical dual-channel potential wells. The 8 eigenmodes in the potential wells approach each other to become 4 modes, recorded as u1 to u4, as shown in Figure 3 shown.

[0069] Superimpose the four eigenmodes with the same symmetry to satisfy Substituting q(x,z) into equation (1) and setting σ = 0, the resonant frequency Ω z =β1-β3, and according to formula (4), the periodic conversion and weight evolution diagram of the resonance mode of even parity u1 and u3 in the symmetric double-channel potential well can be obtained. Set the resonance frequency Ω z =β2-β4, and we get the periodic conversion and weight evolution diagram of the resonant modes of odd parity u2 and u4 in the symmetric double-channel potential well, as shown in Figure 4 As shown. Figure 4 It can be seen that the periodic conversion of the resonance mode of odd parity or even parity can be realized simultaneously in the waveguides of the two channels, and the conversion rate is doubled. Similarly, the conversion period of odd parity and even parity is different. At this time, compared with the single-channel potential well, not only the number of light waves transmitted is increased, but also the transmission loss is effectively suppressed.

[0070] Adjust the potential well parameters p1 = 12, p2 = 10, the dual-channel waveguide presents an asymmetric distribution, and the eigenmodes with the same parity present an asymmetric distribution in the two channels. With the increase of potential depth, new characteristics emerge, that is, adjacent modes with different parity structures gradually degenerate. Adjust the potential well depth to p1 = 20, p2 = 14, u2 in the left channel and u1 in the right channel have the same eigenvalue β1, and u4 in the left channel and u3 in the right channel have the same eigenvalue β2, as shown in Figure 5 shown.

[0071] Based on the above results, consider the following form of superposition:

[0072]

[0073] Substituting equation (5) into equation (1) and using the orthogonality condition, we can obtain:

[0074]

[0075]

[0076]

[0077]

[0078] Here,

[0079]

[0080] Because the odd-parity and even-parity conversion periods are different, in the asymmetric dual-channel potential well, the two channels should be modulated separately, and the modulation depths μ1 and μ2 need to satisfy the following proportional relationship to achieve simultaneous conversion:

[0081] Ω R2 =μ1H′ L24 =μ2H′ R13 (7)

[0082] Setting the resonant frequency Ω z =β1-β2, and the Runge-Kutta method is also used to analyze equation (7) and substitute equation (5) into equation (1) and set σ = 0 to perform numerical simulation of the evolution beam transmission. The transmission diagram of mode conversion and the weight evolution diagram can be obtained, as shown in Figure 6 As shown. Figure 6 It can be seen that the odd-parity and even-parity modes can simultaneously realize periodic conversion in the asymmetric dual-channel potential well under different modulations (μ1=0.055, μ2=0.1), which not only increases the number of light wave transmissions, but also increases the types of light wave transmissions.

[0083] Introducing nonlinear effects in the asymmetric dual-channel waveguide, setting σ = 1 in the self-focusing nonlinear medium and σ = -1 in the self-defocusing nonlinear medium, superimposing modes u1 to u4 according to formula (5), substituting them into formula (1) and using the distributed Fourier algorithm to perform the transmission evolution of the beam, it can be seen that the resonance condition will be destroyed at this time, and the beam will no longer undergo periodic conversion, such as Figure 7 shown.

Claims

1. A method for realizing periodic resonance mode conversion of symmetrical light waves in a dual-channel waveguide, characterized in that: The following steps are involved: S1, according to model (1) and set σ = 0, Ω z =0, the single-channel potential well depth parameter is set to p=6, and the energy level distribution characteristics of the eigenmodes u1 to u4 and the corresponding intrinsic values ​​β1 to β4 of the unmodulated light beam in the single-channel multimode waveguide expressed by equations (2) and (3) can be obtained. u1 and u3 have the same symmetry even parity, and u2 and u4 have the same symmetry odd parity. S2, superimpose the eigenmodes with the same symmetry obtained above and introduce longitudinal periodic modulation Ω z ,satisfy Select m = 1, n = 3 or m = 2, n = 4, bring it into model (1) and set σ = 0; use the orthogonality of the eigenmode to obtain the weight evolution process in the eigenmode conversion process represented by equation (4); set the resonant frequency Ω z =β1-β3, the light waves u1 and u3 with even parity can achieve periodic resonance mode conversion when transmitted in a single-channel waveguide; setting the resonance frequency Ω z =β2-β4, light waves u2 and u4 with odd parity can achieve periodic resonance mode conversion when transmitted in a single-channel waveguide; the conversion periods of odd parity and even parity are different; S3, change the depth of the waveguide potential well and the spacing of the potential wells; increase the depth p of the potential well, and the number of eigenmodes in the potential well increases accordingly; increase the value of the potential well spacing w, and the single-channel waveguide gradually becomes a dual-channel waveguide; set p1=p2=12, the eigenmodes in the two channels increase to 8, u1 to u8 and are symmetrically distributed in the two channels; in the process of increasing the potential well spacing, two adjacent modes with the same symmetry gradually approach each other and have the same eigenvalue; set w=4, the two-channel potential wells are completely independent and become two symmetrical dual-channel potential wells, and the 8 eigenmodes in the potential wells are close to each other to become 4 modes, u1 to u4; S4, superimposing the four eigenmodes with the same symmetry obtained above and transmitting them in a symmetrical dual-channel waveguide; Setting the resonant frequency Ω z =β1-β3, the even-parity light waves u1 and u3 can simultaneously realize periodic resonance mode conversion in the two-channel waveguide; set the resonance frequency Ω z =β2-β4, odd-parity light waves u2 and u4 can simultaneously realize periodic resonant mode conversion in two-channel waveguides, and the conversion rate is doubled; the conversion periods of odd parity and even parity are different; S5, change the structure of the dual-channel waveguide; increase the depth of one of the waveguide channel potential wells, the two waveguide potential wells show asymmetry, and the eigenmodes in the two potential wells show asymmetric distribution; set p1=20, p2=14, the adjacent modes with different symmetric structures in the two channel potential wells gradually approach each other and have the same eigenvalue; u2 in the left channel and u1 in the right channel have the same eigenvalue β1, and u4 in the left channel and u3 in the right channel have the same eigenvalue β2; S6, superimpose the four modes u1 to u4 according to equation (5) and set the resonant frequency Ω z =β1-β2, and transmit in an asymmetric dual-channel waveguide; Substitute (5) into (1) and set σ = 0; Using the orthogonality of the eigenmode, the weight evolution process in the eigenmode conversion process represented by (6) is obtained; The conversion periods of odd-parity and even-parity light waves are different and need to be modulated separately; Satisfying the modulation relationship given by (7), odd-parity and even-parity light waves can simultaneously realize the periodic conversion of the resonant mode in the asymmetric dual-channel waveguide under different modulations (μ1 = 0.055, μ2 = 0.1); S7, nonlinear effect is introduced into the asymmetric dual-channel waveguide, σ=1 is set in the self-focusing nonlinear medium, and σ=-1 is set in the self-defocusing nonlinear medium; the four modes u1 to u4 are superimposed and then propagated and evolved in the asymmetric dual-channel waveguide, and the weight evolution process in the eigenmode conversion process is obtained according to formula (6); At this point, the resonance condition is destroyed and the light beam no longer undergoes periodic conversion; S8, introduce frequency deviation β′ to correct the resonance frequency, and set the resonance frequency to Ω z =β1-β2+β′, β′=0.1 and β′=-0.07 are set in the self-focusing and defocusing nonlinear media respectively; the four modes u1 to u4 are superimposed and then transmitted and evolved in the asymmetric dual-channel waveguide, and the weight evolution process in the eigenmode conversion process is obtained according to formula (6); the odd-parity periodic resonance mode conversion is realized in the left channel waveguide, and the even-parity periodic resonance mode conversion is realized in the right channel waveguide. The propagation of the light beam is described by the following nonlinear Schrödinger equation: Here q(x,z) is the dimensionless amplitude, the longitudinal coordinate z and the transverse coordinate x are the transmission distance and the input beam width respectively; the potential well distribution is represented by R(x)=V1+V2, where V1=p1sech(x+w) 2 , V2=p2sech(xw) 2 , p 1,2 is the potential well depth, w is the distance between the two waveguides; the parameter μ represents the spatial frequency of the longitudinal periodic modulation Ω z Depth; σ=1(σ=-1) Kerr nonlinear self-focusing (defocusing) effect; Nonlinear effects and longitudinal periodic modulation are not considered, that is, σ=0 and μ=0; q(x,z)=u(x)×e iβz (2) where β is the transmission constant and u(x) describes the distribution of the transverse mode; substituting it into equation (1), we obtain the linear eigenvalue equation: According to equation (3), a series of eigenvalues ​​and eigenmodes are obtained. The eigenmodes with the same symmetry are superimposed to satisfy Introduce longitudinal periodic modulation, substitute q(x,z) into equation (1) and set σ = 0, and multiply by and And integrating x, we can get the coupling conversion equation of the resonant mode: Adjust the potential well parameters p1 = 20, p2 = 14, w = 4, and the dual-channel waveguide presents an asymmetric distribution; and let Substituting equation (5) into equation (1) and using the orthogonality condition, we can obtain: Here, Use |ρ1(z)| 2 =|c1(z)| 2 +|c2(z)| 2 represents the superposition weight of the two initial modes, |ρ2(z)| 2 =|c3(z)| 2 +|c4(z)| 2 Represents the superposition weight of the converted mode. The conversion period of even parity and odd parity is different, so the two channels should be modulated separately, and the modulation depth μ1 and μ2 need to satisfy the following proportional relationship to achieve simultaneous conversion: Oh R2 =μ1H′ L24 =μ2H′ R13 (7)。

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