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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theory of a self-induced transparency in crystals

V. N. Lisin

Published Nov 18, 2003• 0 citations
Publisher

Abstract

We take into account that both the local symmetry and the crystal symmetry determine the directions of the dipole matrix element vectors of the optically excited ions. We have shown on an example of the model system LaF3:Pr3+, that the new type of soliton (2π - 4π soliton) may exist in crystals and that the Vector Area Theorem Mapping of the pulse time evolution during propagation is effective method to analyze the soliton properties.

DOI
10.1117/12.526969

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Vector area theorem mapping in crystals and polarization stability of SIT solitons

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The stability of polarization, areas, and the number of self-induced transparency (SIT) solitons at the output of the LaF 3 : Pr 3+ crystal is theoretically studied versus the polarization direction and the area of the input linearly polarized laser pulse. For this purpose, the Vector Area Theorem is rederived and the two-dimensional Vector Area Theorem map is obtained. The map is governed by the crystal symmetry and takes into account directions of the dipole matrix element vectors of the different site subgroups of optically excited ions. The Vector Area Theorem mapping of the time evolution of the laser pulse allows one to highlight soliton polarization properties.

arXiv:physics/0110017•Journal of Experimental and Theoretical Physics Letters•Sep 1, 2001•0 citations
We take into account that both the local symmetry and the crystal symmetry determine the directions of the dipole matrix element vectors of the optically excited ions. We have shown on an example of the model system LaF3:Pr3+, that the new type of soliton (2π - 4π soliton) may exist in crystals and that the Vector Area Theorem Mapping of the pulse time evolution during propagation is effective method to analyze the soliton properties.
The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum consists of the propagation through the crystal of solitary wave packets of coherent excitons and photons with anomalous small losses. In the running frame of reference at the site occupied by the soliton a single aperiodic transformation of photons into excitons and a reverse motion of the energy into the field takes place. The solutions of the SIT equations have been received in the slowly-varying amplitude approximation. Taking into account the phase modulation, the authors have shown the appearance of the branch of the carrier wave frequency with anomalous dispersion not only at the given pulse width but at the given pulse amplitude. They have also found the exact solution of the above mentioned equations taking into account the effect of saturation of the dipole momentum transition from the crystal ground state to the exciton state. It leads to the increasing of the soliton time width, to the decreasing of its amplitude and worsens the SIT observation.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
The propagation of a step-function light pulse in a nondamping resonant medium is studied. Numerical analysis and conservation laws show that the asymptotic solution cannot be described by a single solition-lattice-type solution. As the pulses propagate in space they become narrower and with larger amplitude, but the time separation between pulses remains constant. This result is explained by an asymptotic area theorem which restricts the time average of the electric field to be equal to that of the imput field.
Propagation of a pulse of self-induced transparency in a resonance medium is discussed for the case when it is necessary to take into account the direct electric dipole-dipole interaction between atoms. An equation for the envelope of a wave packet—the sine-Gordon equation—is obtained for the case of durations short compared to ω 0 −1 (ω0 is the transition frequency). The dependence of the velocity and the amplitude of the soliton on the magnitude of the dipole-dipole interaction of atoms is examined in the adiabatic approximation.
The stability of polarization, areas, and the number of self-induced transparency (SIT) solitons at the output of the LaF 3 : Pr 3+ crystal is theoretically studied versus the polarization direction and the area of the input linearly polarized laser pulse. For this purpose, the Vector Area Theorem is rederived and the two-dimensional Vector Area Theorem map is obtained. The map is governed by the crystal symmetry and takes into account directions of the dipole matrix element vectors of the different site subgroups of optically excited ions. The Vector Area Theorem mapping of the time evolution of the laser pulse allows one to highlight soliton polarization properties.