Polarization switching of light interacting with a degenerate two-level optical medium

Byrne, Julie A.; Gabitov, Ildar R.; Kovačič, Gregor

doi:10.1016/s0167-2789(03)00245-8

Cited by 29 publications

(46 citation statements)

References 19 publications

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“…polarisation precessing VS with a spiral structure quite similar to the double scroll polarisation attractors demonstrated theoretically for dye laser, vertical-cavity semiconductor laser and degenerate two-level optical medium. [27][28][29] The double-scroll attractor is sensitive to the external perturbations caused by small fluctuations of the lasing field due to spontaneous emission and fluctuating fibre birefringence. In the same way as for spiral chaotic attractors, [27][28][29][30] this sensitivity can lead to completely unpredictable behaviour with large variations of output dynamics (red and blue lines in Figure 2a).…”

Section: Experiments Detailsmentioning

confidence: 99%

Spiral attractor created by vector solitons

et al. 2014

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Mode-locked lasers emitting a train of femtosecond pulses called dissipative solitons are an enabling technology for metrology, high-resolution spectroscopy, fibre optic communications, nano-optics and many other fields of science and applications. Recently, the vector nature of dissipative solitons has been exploited to demonstrate mode locked lasing with both locked and rapidly evolving states of polarisation. Here, for an erbium-doped fibre laser mode locked with carbon nanotubes, we demonstrate the first experimental and theoretical evidence of a new class of slowly evolving vector solitons characterized by a double-scroll chaotic polarisation attractor substantially different from Lorenz, Rö ssler and Ikeda strange attractors. The underlying physics comprises a long time scale coherent coupling of two polarisation modes. The observed phenomena, apart from the fundamental interest, provide a base for advances in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetisation in data storage devices and many other areas. Light: Science & Applications (2014) 3, e131; doi:10.1038/lsa.2014.12; published online 17 January 2014Keywords: chaos; mode-locked laser; polarisation phenomena; vector soliton INTRODUCTION Vector solitons (VSs) in mode-locked lasers comprise a train of stabilized short pulses (dissipative solitons 1-13 ) with the specific shape defined by a complex interplay and balance between the effects of gain/ loss, dispersion and nonlinearity. The state of polarisation (SOP) of the solitons either rotates with a period of a few round trips or is locked. [4][5][6][7][8][9][10][11][12][13] The stability of VSs at the different time scales from femtosecond to microseconds is an important issue to be addressed for increased resolution in metrology, 14 spectroscopy 15 and suppressed phase noise in high speed fibre optic communication. 16 In addition, there is considerable interest in achieving high flexibility in the generation and control of dynamic SOPs in the context of trapping and manipulation of atoms and nanoparticles, 17-19 control of magnetisation 20 and secure communications. 21 The stability and evolution of VSs at a time interval from a few to thousands of cavity round trips is defined by asymptotic states (attractors) which the laser SOP approaches at a long time scale, viz. fixed point, periodic, quasiperiodic and chaotic dynamics. Soto-Crespo and Akhmediev 1,2 predicted theoretically based on the Ginzburg-Landau scalar model that dissipative solitons can generate strange attractors at the time scale of thousands of cavity round trips. Quantitative characterisation of strange attractors is usually based on the determination of geometric properties such as the fractal dimensionality, entropy and Lyapunov exponents. [22][23][24][25][26] For experimental data obtained in the form of a one-dimensional waveform (output power vs. time), such analysis requires the accumulation of a large amount of low noise data that is very difficult to achieve in systems where...

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Section: Experiments Detailsmentioning

confidence: 99%

Spiral attractor created by vector solitons

et al. 2014

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“…(11b), and the electric field envelopes E ± (x, t) can then be recovered using a set of two Marchenko-type equations [51]. The evolution equations for the scattering data corresponding to the most general asymptotic initial state are listed in [48]; their derivation proceeds along the lines of the treatment given in [35] for the singlepolarization, two-level Maxwell-Bloch equations.…”

Section: Polarization Dynamics In a λ-Configuration Mediummentioning

confidence: 99%

“…(11a)-the N -soliton solutions [48,51]. In fact, in the integrable Maxwell-Bloch-type equations, if the spectral line is not infinitely narrow (i.e., g(λ) = δ(λ), the Dirac delta function) the continuous radiation not only disperses away, but also becomes absorbed in the medium via Landau damping [29].…”

Section: Polarization Dynamics In a λ-Configuration Mediummentioning

confidence: 99%

“…The constants d + and d − determine the phase and position of the soliton. If the cumulative initial population difference diverges with increasing distance into the medium, A(x) → ±∞ as x → ∞, one electric-field amplitude saturates while the other decays, which is the one-soliton case of the polarization switching [47,48].…”

Section: Polarization Dynamics In a λ-Configuration Mediummentioning

confidence: 99%

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Stochastic pulse switching in a degenerate resonant optical medium

et al. 2012

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Using the idealized integrable Maxwell-Bloch model, we describe random optical-pulse polarization switching along an active optical medium in the Λ-configuration with disordered occupation numbers of its lower energy sub-level pair. The description combines complete integrability and stochastic dynamics. For the single-soliton pulse, we derive the statistics of the electric-field polarization ellipse at a given point along the medium in closed form. If the average initial population difference of the two lower sub-levels vanishes, we show that the pulse polarization will switch intermittently between the two circular polarizations as it travels along the medium. If this difference does not vanish, the pulse will eventually forever remain in the circular polarization determined by which sub-level is more occupied on average. We also derive the exact expressions for the statistics of the polarization-switching dynamics, such as the probability distribution of the distance between two consecutive switches and the percentage of the distance along the medium the pulse spends in the elliptical polarization of a given orientation in the case of vanishing average initial population difference. We find that the latter distribution is given in terms of the well-known arcsine law.

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“…The system of equations (1.5) and (1.6) is exactly solvable in the framework of the IS method [25][26][27][28]. This system of equations thus constitutes a compatibility condition for a certain linear system, namely…”

Section: A Rybin and J Timoneṅmentioning

confidence: 99%

Nonlinear theory of slow light

Rybin

Timonen

2011

Phil. Trans. R. Soc. A.

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In the framework of the nonlinear L model, propagation of solitons was analysed in atomic vapours and Bose-Einstein condensates. The complicated nonlinear interplay between fast and slow-light solitons in a L-type medium was shown to facilitate control of its optical transparency and formation of optical gates. An exact analytical description was given for the deceleration, stopping and revival of slow-light solitons in the experimentally relevant non-adiabatic regime. A stopping slow-light soliton imprints a localized immobile polarization pattern in the medium, which, as explicitly demonstrated here, can be used as a bit of readable optical memory. The whole process can be controlled with the background field and an auxiliary laser field. The latter regulates the signal velocity, while the slow-light soliton can be stopped by switching off the former. The location and shape of the imprinted memory bit were also determined. With few assumptions characteristic of slow light, the L model was reduced to a simpler nonlinear model that also describes two-dimensional dilatonic gravity. Exact solutions could now be derived also in the presence of relaxation. Spontaneous decay of the upper atomic level was found to be strongly suppressed, and the spatial form of the decelerating slow-light soliton was preserved, even if the optical relaxation time was much shorter than the typical time scale of the soliton. The effective relaxation coefficient of the slow-light soliton was significantly smaller than that of an arbitrary optical pulse. Such features are obviously of great importance when this kind of system is applied, in practice, to information processing. A number of experimentally observable properties of the solutions reported were found to be in good agreement with recent experimental results, and a few suggestions are also made for future experiments.

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Polarization switching of light interacting with a degenerate two-level optical medium

Cited by 29 publications

References 19 publications

Spiral attractor created by vector solitons

Spiral attractor created by vector solitons

Stochastic pulse switching in a degenerate resonant optical medium

Nonlinear theory of slow light

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