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Technically speaking, ADFT works for any pulse width, even less than 1 ps, because ADFT does not require transform-limited pulses. An ultrashort pulse with less than 1 ps pulse width can be prechirped with prisms or diffraction gratings in free space before entering the dispersive fiber such that the pulse width is broadened to be longer than 1 ps and hence the slowly varying envelope approximation can still be used to solve the nonlinear Schrödinger equation analytically.
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Technically speaking, ADFT works for any pulse width, even less than 1 ps, because ADFT does not require transform-limited pulses. An ultrashort pulse with less than 1 ps pulse width can be prechirped with prisms or diffraction gratings in free space before entering the dispersive fiber such that the pulse width is broadened to be longer than 1 ps and hence the slowly varying envelope approximation can still be used to solve the nonlinear Schrödinger equation analytically.
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In most cases of Raman amplification, cw or quasi-cw pumping configurations are used to avoid the pulse walk-off between the Stokes and pump fields. Therefore, the assumptions made on short pulses are only relevant to the Stokes field as they are not necessary for the pump fields.
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In most cases of Raman amplification, cw or quasi-cw pumping configurations are used to avoid the pulse walk-off between the Stokes and pump fields. Therefore, the assumptions made on short pulses are only relevant to the Stokes field as they are not necessary for the pump fields.
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This assumption does not hold when the Stokes field is significantly amplified and its intensity becomes comparable to that of the pumps. In this case, the pump intensity is no longer independent of the propagation distance and is a function of the intensity of the Stokes field. Then, we cannot solve Eq. (1) analytically and hence need to rely on numerical calculations.
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This assumption does not hold when the Stokes field is significantly amplified and its intensity becomes comparable to that of the pumps. In this case, the pump intensity is no longer independent of the propagation distance and is a function of the intensity of the Stokes field. Then, we cannot solve Eq. (1) analytically and hence need to rely on numerical calculations.
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