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  • Received: May. 29, 2020

    Accepted: Jul. 6, 2020

    Posted: Aug. 6, 2020

    Published Online: Aug. 6, 2020

    The Author Email: Jin Kaichao (1370887198@qq.com), Li Yongdong (leyond@mail.xjtu.edu.cn), Li Feng (felix831204@xjtu.edu.cn), Belić Milivoj R. (milivoj.belic@qatar.tamu.edu), Zhang Yanpeng (ypzhang@mail.xjtu.edu.cn), Zhang Yiqi (zhangyiqi@mail.xjtu.edu.cn)

    DOI: 10.1117/1.AP.2.4.046002

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    Kaichao Jin, Yongdong Li, Feng Li, Milivoj R. Belić, Yanpeng Zhang, Yiqi Zhang. Rabi oscillations of azimuthons in weakly nonlinear waveguides[J]. Advanced Photonics, 2020, 2(4): 046002

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(a) Basic modes, (b) degenerate dipole modes, (c) degenerate quadrupole modes, (d) degenerate hexapole modes, and (e) degenerate octopole modes. First row: first-order modes, second row: second-order modes, and third row: third-order modes. The panels are shown in the window −2≤x≤2 and −2≤y≤2. Other parameters: V0=500 and w=1.

Fig. 1. (a) Basic modes, (b) degenerate dipole modes, (c) degenerate quadrupole modes, (d) degenerate hexapole modes, and (e) degenerate octopole modes. First row: first-order modes, second row: second-order modes, and third row: third-order modes. The panels are shown in the window 2x2 and 2y2. Other parameters: V0=500 and w=1.

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Amplitude and phase of (a)–(d) the first-order and (e)–(h) the second-order azimuthons constructed from (a) and (e) the degenerate dipoles, (b) and (f) the quadrupoles, (c) and (g) the hexapoles, and (d) and (h) the octopoles. The panels are shown in the window −2≤x≤2 and −2≤y≤2. Other parameters: A=0.4 and B=0.5.

Fig. 2. Amplitude and phase of (a)–(d) the first-order and (e)–(h) the second-order azimuthons constructed from (a) and (e) the degenerate dipoles, (b) and (f) the quadrupoles, (c) and (g) the hexapoles, and (d) and (h) the octopoles. The panels are shown in the window 2x2 and 2y2. Other parameters: A=0.4 and B=0.5.

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Rabi transition of (a) a dipole and (b) a hexapole. In each case, the propagation is shown by the isosurface plot above which amplitude distributions at selected distances are shown. In both cases, the weak longitudinally periodic modulation exists in the region 30≤z≤90, with d≈25.2 and μ≈0.031 in (a) and d≈36.36 and μ≈0.014 in (b). (c) The Rabi oscillation period zR versus the frequency detuning ℓ.

Fig. 3. Rabi transition of (a) a dipole and (b) a hexapole. In each case, the propagation is shown by the isosurface plot above which amplitude distributions at selected distances are shown. In both cases, the weak longitudinally periodic modulation exists in the region 30z90, with d25.2 and μ0.031 in (a) and d36.36 and μ0.014 in (b). (c) The Rabi oscillation period zR versus the frequency detuning .

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(a) Rabi transition of a deformed dipole. (b) The amplitude and phase of the azimuthon based on the dipole in (a). (c) The transition of a deformed hexapole. (d) The amplitude and phase of the azimuthon based on the hexapole in (c). (e) The transition of a deformed higher-order dipole. (f) The amplitude and phase of the azimuthon based on the higher-order dipole in (e). The panels are shown in the window −2≤x≤2 and −2≤y≤2. Other parameters: A=0.4 and B=0.5.

Fig. 4. (a) Rabi transition of a deformed dipole. (b) The amplitude and phase of the azimuthon based on the dipole in (a). (c) The transition of a deformed hexapole. (d) The amplitude and phase of the azimuthon based on the hexapole in (c). (e) The transition of a deformed higher-order dipole. (f) The amplitude and phase of the azimuthon based on the higher-order dipole in (e). The panels are shown in the window 2x2 and 2y2. Other parameters: A=0.4 and B=0.5.

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(a) Transition between dipole and hexapole azimuthons with d≈25.2 and μ≈0.085. (b) Transition between dipole and hexapole azimuthons with d≈22.1 and μ≈0.034. The weak longitudinally periodic modulation has to always exist during propagation.

Fig. 5. (a) Transition between dipole and hexapole azimuthons with d25.2 and μ0.085. (b) Transition between dipole and hexapole azimuthons with d22.1 and μ0.034. The weak longitudinally periodic modulation has to always exist during propagation.

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