Fig 2 - uploaded by Stephan Pachnicke
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Exemplary eigenvalue decomposition after superposition of four eigenvalues as a function of Δí µí±. (a) Real value and (b) imaginary value.
Source publication
We investigate the transmission of densely multiplexed solitons using a photonic integrated chip and the nonlinear Fourier-transform and analyze required launch conditions, the effect of (de-)multiplexing and noise on the nonlinear spectrum, and equalization techniques that can be used to enhance the transmission performance.
Contexts in source publication
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... more than two eigenvalues are linearly superimposed, channels further interfere with each other, leading to combinations of the effects described in Subsection III.A. However, for a large number of soliton channels, channels far from each other asymptotically reach condition (2.2). For the example shown in Fig. 2, a fixed channel spacing of Δí µí± = 1.2 was chosen in order to comply with the frequency spacing used in the following sections of this paper. The remaining free parameters are thus Δí µí± and Δí µí¼. However, since we will apply QPSK modulation to the eigenvalues' NFT coefficients, Δí µí¼ ∈ [0, ±90°, 180°] was used. The ...
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... was chosen in order to comply with the frequency spacing used in the following sections of this paper. The remaining free parameters are thus Δí µí± and Δí µí¼. However, since we will apply QPSK modulation to the eigenvalues' NFT coefficients, Δí µí¼ ∈ [0, ±90°, 180°] was used. The post-superposition values of the four eigenvalues are shown in Fig. 2 as a function Δí µí±, applied to each of the pulse pairs, i.e., the pulses are assumed to be equidistant in their transmission window. Here, the real parts of the eigenvalues were set to Re{í µí¼} = [−1.8, −0.6, 0.6, 1.8] and Δí µí¼ set to 0 between all neighboring ...
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... can be seen in Fig. 2(a), a fusion of all four eigenvalues into one high energy eigenvalue occurs for 0 ≤ Δí µí± í µí± ~•€• ⁄ < 0.135. Besides, a noticeable decrease of the eigenvalues' imaginary value (or, equivalently, a shift of the energy into the continuous spectrum) is shown in Fig. ...
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... can be seen in Fig. 2(a), a fusion of all four eigenvalues into one high energy eigenvalue occurs for 0 ≤ Δí µí± í µí± ~•€• ⁄ < 0.135. Besides, a noticeable decrease of the eigenvalues' imaginary value (or, equivalently, a shift of the energy into the continuous spectrum) is shown in Fig. ...
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... From here on, pure merging occurs, with the conservation of four eigenvalues with four different real parts. However, one can see that the eigenvalues are not on their desired, initial spectral positions until Δí µí± í µí± pqrs ⁄ is roughly set to 1, i.e., Δí µí± ≈ 1.76 in the dimensionless system of units defined above. The simulation from Fig. 2 has been repeated for the evaluation of post-superposition eigenvalue positions, as a function of Δí µí±, for all 256 possible combinations of the four QPSKmodulated NFT coefficients (Δí µí¼ ∈ [0, ±90°, 180°]). This is shown in Fig. 3 as a color-coded histogram. It makes apparent that a longer Δí µí± above 2.7 (Δí µí± í µí± pqrs ⁄ ...
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... more than two eigenvalues are linearly superimposed, channels further interfere with each other, leading to combinations of the effects described in Subsection III.A. However, for a large number of soliton channels, channels far from each other asymptotically reach condition (2.2). For the example shown in Fig. 2, a fixed channel spacing of Δí µí± = 1.2 was chosen in order to comply with the frequency spacing used in the following sections of this paper. The remaining free parameters are thus Δí µí± and Δí µí¼. However, since we will apply QPSK modulation to the eigenvalues' NFT coefficients, Δí µí¼ ∈ [0, ±90°, 180°] was used. The ...
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... was chosen in order to comply with the frequency spacing used in the following sections of this paper. The remaining free parameters are thus Δí µí± and Δí µí¼. However, since we will apply QPSK modulation to the eigenvalues' NFT coefficients, Δí µí¼ ∈ [0, ±90°, 180°] was used. The post-superposition values of the four eigenvalues are shown in Fig. 2 as a function Δí µí±, applied to each of the pulse pairs, i.e., the pulses are assumed to be equidistant in their transmission window. Here, the real parts of the eigenvalues were set to Re{í µí¼} = [−1.8, −0.6, 0.6, 1.8] and Δí µí¼ set to 0 between all neighboring ...
Context 8
... can be seen in Fig. 2(a), a fusion of all four eigenvalues into one high energy eigenvalue occurs for 0 ≤ Δí µí± í µí± ~•€• ⁄ < 0.135. Besides, a noticeable decrease of the eigenvalues' imaginary value (or, equivalently, a shift of the energy into the continuous spectrum) is shown in Fig. ...
Context 9
... can be seen in Fig. 2(a), a fusion of all four eigenvalues into one high energy eigenvalue occurs for 0 ≤ Δí µí± í µí± ~•€• ⁄ < 0.135. Besides, a noticeable decrease of the eigenvalues' imaginary value (or, equivalently, a shift of the energy into the continuous spectrum) is shown in Fig. ...
Context 10
... From here on, pure merging occurs, with the conservation of four eigenvalues with four different real parts. However, one can see that the eigenvalues are not on their desired, initial spectral positions until Δí µí± í µí± pqrs ⁄ is roughly set to 1, i.e., Δí µí± ≈ 1.76 in the dimensionless system of units defined above. The simulation from Fig. 2 has been repeated for the evaluation of post-superposition eigenvalue positions, as a function of Δí µí±, for all 256 possible combinations of the four QPSKmodulated NFT coefficients (Δí µí¼ ∈ [0, ±90°, 180°]). This is shown in Fig. 3 as a color-coded histogram. It makes apparent that a longer Δí µí± above 2.7 (Δí µí± í µí± pqrs ⁄ ...
