Simple mathematical model describing multitransversal solid-state lasers

Hollinger, F.; Jung, Christoph; Weber, Horst

doi:10.1364/josab.7.001013

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…Although the phase shift between adjacent transverse modes in one round trip is irrational multiples of and lies close to 2/3, the laser output can become chaotic in a good cavity under Gaussian pumping. This result is different from the results of Hollinger et al 5,19 We believe that, as the cavity is tuned toward 1/3 degeneration, the beam-propagationdominant laser dynamics is transformed into an interplay of beam propagation and gain dynamics. Thus the route to chaos close to the degenerate configuration involves the mixing effect of quasi-period-and period-multiplying bifurcation.…”

Section: Discussioncontrasting

confidence: 91%

“…We believe that the cavity loss 1 Ϫ 2 is the key factor that differentiates the results of Melnikov et al 1 and Hollinger et al 5,19 from ours. The V-shaped threshold becomes as smooth as Melnikov's result [ Fig.…”

Section: Interplay Of Beam Propagation and Gain Dynamic Bifurcationsupporting

confidence: 53%

“…6 of Ref. 19 where chaos exists within small ranges of phase difference (which corresponds to R in our case) and round trip loss (or 1 Ϫ 2 ).…”

Section: Interplay Of Beam Propagation and Gain Dynamic Bifurcationmentioning

confidence: 71%

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Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations

2001

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Propagation-dominant instabilities and chaos were found under so-called good-cavity conditions in an axially pumped solid-state laser operated near the 1/3-degenerate cavity configuration that had not previously been studied numerically. By using the generalized Huygens integral together with rate equations, we obtained a V-shaped configuration that depends on a quasi-periodic threshold. We call the propagation dominant because the laser behaves as a conservative system governed by beam propagation. Although it had previously been predicted that chaos would be impossible under nearly degenerate conditions, we have recognized that the laser is transformed into chaos as a result of the interplay of beam propagation and gain dynamics as the cavity is tuned close to degeneracy.

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Section: Discussioncontrasting

confidence: 91%

Section: Interplay Of Beam Propagation and Gain Dynamic Bifurcationsupporting

confidence: 53%

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Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations

2001

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“…, the square vortex lattices were obtained numerically [21]. The additional term with the square of transverse laplacian is responsible for transverse mode selection due to finite gain linewidth.An alternative model with discrete time step equal to τ = 2L r /c (time of bouncing of radiation between mirrors) utilizes the standard rate equations of class-B laser written at n-th step for electric field [5,22]:…”

Section: Square Vortex Latticesmentioning

confidence: 99%

3D-vortex labyrinths in the near field of solid-state microchip laser

Okulov

2008

Journal of Modern Optics

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The spatiotemporal vortex lattices generated in high Fresnel number solid-state microchip lasers are studied in connection with Talbot phenomenon generic to spatially periodic electromagnetic fields. The spatial layout of light field is obtained via dynamical model based on Maxwell-Bloch equations for class-B laser, discrete Fox-Lee map with relaxation of inversion and static model based on superposition of copropagating Gaussian beams. The spatial patterns observed experimentally and obtained numerically are interpreted as nonlinear superposition of vortices with helicoidal phase dislocations. The usage of vortex labyrinths and Talbot lattices as optical dipole traps for neutral atoms is considered for the wavelength of trapping radiation in the range 0.98 $\div$ 2.79 $\mu m$. The separable optical trapping potential is mounted as a sum of array of vortex lines and additional parabolic subtrap. The factorization of macroscopic wavefunction have led to analytical solution of Gross-Pitaevski equation for ground state of ensemble of quantum particles trapped in vortex labyrinth and in spatially - periodic array of Gaussian beams.Comment: 10 pages 7 figure

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Symbolic Description of Irregular Behaviour in a Laser Model

Jung

Hollinger

1992

NATO ASI Series

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Simple mathematical model describing multitransversal solid-state lasers

Cited by 10 publications

References 12 publications

Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations

Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations

3D-vortex labyrinths in the near field of solid-state microchip laser

Symbolic Description of Irregular Behaviour in a Laser Model

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