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 $>\pi$ 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 $\leq$ 3. In addition to the expected portion of area $\pi$ 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$\pi$ (or 0$\pi$) solitons. Pulses whose final area is $\pi$, 3$\pi$, and 5$\pi$ 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 $\leq$ 3 that for each 2$\pi$ soliton there is a purely imaginary zero of the left reflection coefficient / in the lower half $\nu$ plane and that for a 0$\pi$ soliton there are a pair of zeroes of the left reflection coefficient lying symmetrically about the negative imaginary $\nu$ axis. ftn*G. L. Lamb, Jr., Phys. Rev. A 12, 2052 (1975). / Source: Dissertation Abstracts International, Volume: 49-03, Section: B, page: 0806. / Major Professor: J. Daniel Kimel. / Thesis (Ph.D.)--The Florida State University, 1987.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76257 |
| Contributors | Hochman, Richard David., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 203 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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