A simple model for optical pulse propagation in a nondegenerate two-level amplifying medium is considered, under the assumption of extreme Doppler broadening. Starting with a "Pade approximant" left reflection coefficient with N simple poles and N$\sb{\rm b}\leq$ N bound states, and employing Lamb's one-component inverse scattering method*, pulses whose initial area can be
>π are obtained. Then, employing the asymptotic behavior of the eigenvalues of the kernel of the right Marchenko equation, the asymptotic behavior of the pulses far into the medium is analyzed in detail when N
≤ 3. In addition to the expected portion of area
π near the light cone which undergoes amplification and compression, pulses with a continuous leading edge develop forward-moving oscillations, and some pulses trail behind one or more 2
π (or 0
π) solitons. Pulses whose final area is
π, 3
π, and 5
π are obtained. Interestingly, the number of trailed solitons is in general not equal to the number of bound states. These solitons are associated with a subset of the zeroes of the transmission coefficient rather than of its poles. Conditions for the appearance of a soliton are given in terms of the poles and residues of the left reflection coefficient. A connection is established between the values of the pulse profiles and their first 2N
− 1 derivatives at the light cone, and the residue and pole parameters of the left reflection coefficient. For N = 2 and the case in N = 3 where the pulse has a continuous leading edge, simple conditions for the appearance of a soliton are obtained in terms of the values of the pulse profiles and their first N
− 1 derivatives at the light cone, and the poles of the left reflection coefficient. It is established for N
≤ 3 that for each 2
π soliton there is a purely imaginary zero of the left reflection coefficient
Dissipative Kerr solitons in optical microresonators underpin chip-scale frequency combs with applications ranging from coherent telecommunications to precision spectroscopy. Yet the characterization of their intrinsic femtosecond temporal structure remains challenging, as the low pulse energy and broad spectral bandwidth necessitate optical amplification and careful dispersion compensation in conventional ultrafast diagnostics, both of which can significantly distort the waveform. Here we demonstrate a quantum-interference metrology of microcomb solitons based on Hong-Ou-Mandel interference. By attenuating the soliton stream to the single-photon level and measuring fourth-order interference, we directly retrieve near transform-limited pulse durations without amplification or dispersion management, remaining accurate even after propagation through 25 km of standard fiber. The same interferogram also provides direct access to the temporal separations in multi-soliton states by converting inter-soliton separations into additional interference dips at corresponding delays, enabling sub-picosecond characterization of their intracavity temporal structure. This quantum-inspired paradigm introduces a fundamentally new metrological approach that is immune to amplification and dispersion distortions, offering a powerful tool for the characterization of complex soliton physics.
The amplification of intense light pulses in resonance active media with an optical Stark effect and coherence effects is examined theoretically. In the course of the amplification, the pulse may go through a stage of an incoherent Stark quasisoliton. The envelope of this quasisoliton has an approximately constant, highly asymmetric shape. The energy of the quasisoliton is approximately constant. Upon further amplification, the Stark quasisoliton "breaks up" into a train of shorter pulses. Over a sufficiently long amplification distance, a true soliton may form in the active medium. In general, this true soliton is not the same as a standard π pulse in a medium without a Stark effect.