64 research outputs found
Two-Pulse Propagation in Media with Quantum-Mixed Ground States
We examine fully coherent two-pulse propagation in a lambda-type medium,
under two-photon resonance conditions and including inhomogeneous broadening.
We examine both the effects of short pulse preparation and the effects of
medium preparation. We contrast cases in which the two pulses have matched
envelopes or not, and contrast cases in which ground state coherence is present
or not. We find that an extended interpretation of the Area Theorem for
single-pulse self-induced transparency (SIT) is able to unify two-pulse
propagation scenarios, including some aspects of electromagnetically-induced
transparency (EIT) and stimulated Raman scattering (SRS). We present numerical
solutions of both three-level and adiabatically reduced two-level density
matrix equations and Maxwell's equations, and show that many features of the
solutions are quickly interpreted with the aid of analytic solutions that we
also provide for restricted cases of pulse shapes and preparation of the
medium. In the limit of large one-photon detuning, we show that the two-level
equations commonly used are not reliable for pulse Areas in the 2 range,
which allows puzzling features of previous numerical work to be understood.Comment: 28 pages, 7 figures. Replaced with version accepted in PR
Existence of superposition solutions for pulse propagation in nonlinear resonant media
Existence of self-similar, superposed pulse-train solutions of the nonlinear,
coupled Maxwell-Schr\"odinger equations, with the frequencies controlled by the
oscillator strengths of the transitions, is established. Some of these
excitations are specific to the resonant media, with energy levels in the
configurations of and and arise because of the interference
effects of cnoidal waves, as evidenced from some recently discovered identities
involving the Jacobian elliptic functions. Interestingly, these excitations
also admit a dual interpretation as single pulse-trains, with widely different
amplitudes, which can lead to substantially different field intensities and
population densities in different atomic levels.Comment: 11 Pages, 6 Figures, presentation changed and 3 figures adde
Matched Pulse Propagation in a Three-Level System
The B\"{a}cklund transformation for the three-level Maxwell-Bloch equation is
presented in the matrix potential formalism. By applying the B\"{a}cklund
transformation to a constant electric field background, we obtain a general
solution for matched pulses (a pair of solitary waves) which can emit or absorb
a light velocity solitary pulse but otherwise propagate with their shapes
invariant. In the special case, this solution describes a steady state pulse
without emission or absorption, and becomes the matched pulse solution recently
obtained by Hioe and Grobe. A nonlinear superposition rule is derived from the
B\"{a}cklund transformation and used for the explicit construction of two
solitons as well as nonabelian breathers. Various new features of these
solutions are addressed. In particular, we analyze in detail the scattering of
"invertons", a specific pair of different wavelength solitons one of which
moving with the velocity of light. Unlike the usual case of soliton scattering,
the broader inverton changes its sign through the scattering. Surprisingly, the
light velocity inverton receives time advance through the scattering thereby
moving faster than light, which however does not violate causality.Comment: 20 pages, Latex, 12 eps figure files some comments and references are
added. postscript file with 12 figures can be obtained at
http://photon.kyunghee.ac.kr/~qhpark
Magnetothermal instability in laser plasmas including hydrodynamic effects
The impact of both density gradients and hydrodynamics on the evolution of the field compressing magnetothermal instability is considered [J. J. Bissell et al., Phys. Rev. Lett. 105, 175001 (2010)]. Hydrodynamic motion is found to have a limited effect on overall growth-rates; however, density gradients are shown to introduce an additional source term corresponding to a generalised description of the field generating thermal instability [D. Tidman and R. Shanny, Phys. Fluids 17, 1207 (1974)]. The field compressing and field generating source terms are contrasted, and the former is found to represent either the primary or sole instability mechanism for a range of conditions, especially those with Hall parameter v > 101. The generalised theory is compared to numerical simulation in the context of a recent nano-second gas-jet experiment [D. H. Froula et al., Phys. Rev. Lett. 98, 135001 (2007)] and shown to be in good agreement: exhibiting peak growth-rates and wavelengths of order 10 ns1 and 50 lm, respectively. The instability’s relevance to other experimental conditions, including those in inertial confinement fusion (I.C.F.) hohlraums, is also discussed
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