Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell–Bloch laser

Louvergneaux

et al. 2004

Phys. Rev. E

Self Cite

Using a realistic model of wide aperture, weakly astigmatic lasers we develop a framework to analyze experimental average intensity patterns. We use the model to explain the appearance of patterns in terms of the modes of the cavity and to show that the breaking of the symmetry of the average intensity patterns is caused by overlaps in the frequency spectra of nonvanishing of modes with different parity. This result can be used even in systems with very fast dynamics to detect experimentally overlaps of frequency spectra of modes.

Section: Symmetry and Average Amplitude Productsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Average patterns and coherent phenomena in wide aperture lasers

D’Alessandro¹,

Louvergneaux

et al. 2004

Phys. Rev. E

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“…This is the situation corresponding to the regular patterns of [5,6,7], but also of irregular nonsymmetric patterns that do not fit in the classification scheme devised in [5]. Moreover, this behavior is very similar to what happens when only two cavity modes are active [1]: the solution with lowest threshold is the single-mode solution (low complexity); this loses stability to a periodic solution that involves both cavity modes (high complexity), which is replaced, as the pump is increased further, by a stationary mode-locked solution (low complexity).…”

Section: Introductionmentioning

confidence: 86%

“…1 If one uses this procedure with topos obtained for a given set of control parameter values to another set, the temporal functions obtained will not be, in general, orthogonal in time. We will use this property later to discuss the nature of the bifurcations of the system.…”

Section: ͑14͒mentioning

confidence: 99%

“…It is possible to study in detail the case of few-mode dynamics or modes with some degeneracies (see, for example, [1] for a review of the twomode case or [2] for a study of the antiphase dynamics of N identical modes). However, when the number of modes increases analytical treatments become scarce and one is forced to revert to average methods.…”

Section: Introductionmentioning

confidence: 99%

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Spontaneous improvement of spatial coherence and frequency locking in high-pump-power multimode lasers

D’Alessandro

2004

Phys. Rev. A

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By using the time average of amplitude products we are able to identify changes in the dynamical complexity and the spatial coherence of a multimode laser. We find that there are cases in which as the pump increases, the dynamical complexity decreases and the spatial coherence improves. In some limiting cases the complexity is reduced to zero and the beam is completely coherent spatially. We show that these phenomena are caused by phase synchronization of the mode amplitudes and that they can be observed using slow detectors

Symmetry breaking and bifurcations in lasers

Chillingworth

D’Alessandro

2003 European Quantum Electronics Conference. EQEC 2003 (IEEE Cat No.03TH8665)

2003

The standard Fabry-P6rot cavity laser is assumed to have axial symmetry, i.e. to have geometrical symmetry O(2). While it is true that this is a very reasonable assumption in many circumstances, it is also true that there are many physical phenomena that reduce this symmetry (forced syimetry breaking). For example, astigmatism reduces the geometrical symmetry of a laser from O(2) to Dz. The breaking of the axial symmetry may alter significantly the bifurcation structure of a laser, at least in some regimes. It is therefore important to develop a coherent and rigorous approach to model generic symmetry breaking in laser models in order to compare their predictions with experimental results.The approach to this problem taken in this paper is to derive the normal form equations for a two level laser in the presence of symmetry breaking, i.e. under the assumption that there are terms in the laser equations that represent the breaking of the symmetry and that are small [I]. We pose restrictions neither on the type of symmetry that is broken nor on the mechanism that lifts the degeneracy and obtain a set of ordinary differential equations whose coefficients can be put in direct relationship to experimentally accessible parameters.As an example, we apply the equations to the case of a two mode laser whose axial symmetry is broken by astigmatism.In this case there are three fundamental solutions to the laser equations: a single mode sofutioii, when one mode is active and the other is dormant, a mode-beating solution, with both modes active, but at slightly different frequencies, and a frequency locked solution. with both modes active and oscillating at the same frequency. Using the normal forms we can predict the range of stability of each of these solutions and draw the corresponding bifurcation diagrams for the laser equations. Moreover, using the expression of the equation coefficients in terms of the laser parameters we can directly compare the results of the predictions of the normal forms with numerical simulations (and, eventually, experimental results). 1 Frequency beating I I , I I I '1 I I Frequency locked , Single _ _ _ _ _ _ -------Pump parameter [a.u.] 1 mode Figure I: Cottiparison of a typical b@rcation diagrani of CI two mode laser coriipiited using the normal fornis with rirrnierical solutioiu of the fir11 laser equations. The solid (dashed) lines indicate (un)srcrble solutioris as computed using the nornial fornis. The circles, diailiorids arid sqirases represent the resiilts of riuniericnl integration of the complete laser eqirations. The circles corsesporid to stationan single iiiode solutions, the diairioiids to periodic frequency beating solittioris arid the square rcpreseiits LI stationary two inode fre queticy locked soliition. The iriiages it1 the inserts show the stationagl j e l d in the ccise of the single mode arid the freqirency locked solution arid the two oscillating patterns in the case of the periodic solutioti.