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arXiv:physics/0110017 · Journal of Experimental and Theoretical Physics Letters

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

V. N. Lisin

Published Sep 1, 2001• 0 citations
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Abstract

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.

DOI
10.1134/1.1417167

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Polarization stability of SIT solitons

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The stability of polarization, areas and number of self- induced transparency (SIT)-solitons on an output the LaF3: Pr3+ sample is theoretically researched versus of the polarization direction and the area of the input linearly polarized laser pulse. For this purpose the Vector Area Theorem is rederived taking into account directions of the dipole matrix element vectors of the six different subgroups of Pr3+ ions. It is shown that there are SIT solitons, which polarizations are directed so between as along the crystallographic axes in the LaF3:Pr3+. For an absorbing medium the interference of these ion's subgroups reduces that SIT-solitons are stable if its polarization is directed between the crystallographic axes. Solitons are nonstable, if its polarization are directed along one of the crystallographic axes: a small change of an input pulse polarization reduces to a soliton splitting up into two separate solitons, which polarizations are directed between the crystallographic axes under an angle +30 and accordingly -30 degrees to the given axis. For an amplifying medium it is just on the contrary.

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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.
The stability of polarization, areas and number of self- induced transparency (SIT)-solitons on an output the LaF3: Pr3+ sample is theoretically researched versus of the polarization direction and the area of the input linearly polarized laser pulse. For this purpose the Vector Area Theorem is rederived taking into account directions of the dipole matrix element vectors of the six different subgroups of Pr3+ ions. It is shown that there are SIT solitons, which polarizations are directed so between as along the crystallographic axes in the LaF3:Pr3+. For an absorbing medium the interference of these ion's subgroups reduces that SIT-solitons are stable if its polarization is directed between the crystallographic axes. Solitons are nonstable, if its polarization are directed along one of the crystallographic axes: a small change of an input pulse polarization reduces to a soliton splitting up into two separate solitons, which polarizations are directed between the crystallographic axes under an angle +30 and accordingly -30 degrees to the given axis. For an amplifying medium it is just on the contrary.
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.
Self-induced transparency (SIT) is a kind of coherent transient phenomena in two-level atomic system. The optical pulse with an area that is an integer multiple of 2π, which causes SIT in an absorber, is stable and a kind of soliton. Thus SIT is expected to be useful in pulse compression and pulse shaping. In this paper, we discuss some problems in experiments of SIT and surveys the experimental results of SIT. It is also described the recent experimental results of coherent nonlinear pulse propagation in BiI3 crystal using tunable sub-picosecond pulses.
The behavior of the photon-echo polarization in solids is discussed. The photon echo in La F3: Pr3+ is considered in some details as a typical example. The echo is induced by linearly polarized pulses propagating along the c axis of the crystal, with an angle between their electric vectors. The polarization direction and the intensity of the echo in the case of small-area exciting pulses are calculated both for the twopulse echo and the three-pulse echo. An experiment on La F3: Pr3+ is also performed and the result is well interpreted by the calculation.
By solving the two-level Maxwell-Bloch equations for resonant pulses numerically, we observe precursors in a regime where the area theorem is fulfilled. The precursors are $0\ensuremath{\pi}$ pulses traveling at a velocity close to the speed of light, and the main signal is a self-induced transparency (SIT) $2\ensuremath{\pi}$ soliton traveling at a much lower velocity. The manifestation of the precursors is strongest when the input pulse duration is on the same order as the inhomogeneous lifetime and the input area is close to $\ensuremath{\pi}$. Depending on the relationship between the input pulse duration and the inhomogeneous lifetime, the precursors can interact linearly or nonlinearly with the material. Experimental confirmation of these results should offer a direct and reasonably straightforward way of measuring optical precursors.