Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers

Boudec, P. Le; Jaouen, C.; Francois, P.L.; Bayon, J.F.; Sanchez, François; Besnard, Pascal; Stéphan, G.

doi:10.1364/ol.18.001890

Cited by 63 publications

(21 citation statements)

References 8 publications

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“…Another example of AD is the 'winner-takes-all' dynamics in deeply modulated Fabry-Pérot lasers [5]. AD has also been reported in spontaneous self-pulsing [6,7], in the presence of an external modulation [8], in the noise spectrum at steady state [9], in the transient relaxation to steady state [10][11][12], in the chaotic regime [13][14][15][16] and in the routes to chaos [17]. If the dynamics is limited to the relaxation towards a steady state, AD implies that each modal intensity is characterized by a number of frequencies (smaller or equal to the mode number) while the total intensity is characterized by only one frequency, the largest of the modal intensity frequencies, the so-called relaxation oscillation frequency.…”

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confidence: 95%

Antiphase dynamics in pump-modulated multimode intracavity second-harmonic generation

Wang

Mandel

1996

Quantum Semiclass. Opt.

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Abstract. We determine numerically the response of a multimode laser with intracavity secondharmonic generation to a periodic modulation of the gain in the linear and nonlinear regimes.We show that resonances can appear either at the relaxation oscillation frequency or the low internal frequency and at its first subharmonic. Instabilities leading to period doubling occur at the low internal frequency and at its first harmonic.Multimode lasers have been shown to display diverse behaviours, regular and irregular. Because there can be a large number of modes that are coupled globally, these lasers may exhibit collective self-organization. One such self-organization is antiphase dynamics (AD). In its simplest form, AD is characterized by a cyclic periodic pulsing of the individual mode intensities. As a result, the N -mode laser is in a periodic state, with each mode having the same waveform but shifted from its neighbour by 1/N of the period. AD appears as a manifestation of the coherence properties associated with the phase of the mode intensities rather than with usual phase of the mode fields. The first experimental confirmation of AD in lasers was reported in [1] for a Nd:YAG laser cavity containing a KTP frequency doubling crystal. The theoretical analysis of this problem and an explanation of the mathematical mechanism through which antiphased solutions occur in this system was reported in [2] and [3]. More complex periodic AD states were found and analysed in [3] and [4]. Another example of AD is the 'winner-takes-all' dynamics in deeply modulated Fabry-Pérot lasers [5]. AD has also been reported in spontaneous self-pulsing [6,7], in the presence of an external modulation [8], in the noise spectrum at steady state [9], in the transient relaxation to steady state [10][11][12], in the chaotic regime [13][14][15][16] and in the routes to chaos [17]. If the dynamics is limited to the relaxation towards a steady state, AD implies that each modal intensity is characterized by a number of frequencies (smaller or equal to the mode number) while the total intensity is characterized by only one frequency, the largest of the modal intensity frequencies, the so-called relaxation oscillation frequency. In the chaotic domain, AD has the same characteristics as in the relaxation to steady state: each mode displays a number of frequencies with broadened peaks whereas the total intensity displays broad peaks around the largest of the modal intensity frequencies. In the present letter, we shall focus on multimode intracavity second-harmonic generation in the region of parameters where there is a stable steady state. Our primary aim is to study the influence of †

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confidence: 95%

Antiphase dynamics in pump-modulated multimode intracavity second-harmonic generation

Wang

Mandel

1996

Quantum Semiclass. Opt.

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“…It should not be confused with the electric field coherence of the single mode laser. AD has been reported in lasers in the case of spontaneous self-pulsing [1][2][3], in the presence of an external modulation [4,5], in the noise spectrum at steady state [6], in the transient relaxation to steady state [7,8], in the chaotic regime [9,10], and in the routes to chaos [11].A laser oscillating on N modes is characterized by N modal intensities I n ͑t͒, n 1, 2, . .…”

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confidence: 99%

Universal Properties of Multimode Laser Power Spectra

Mandel¹,

Wang²

1996

Phys. Rev. Lett.

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In a multimode laser operating near steady state, we determine analytically relations which connect the power spectrum density of each modal intensity and of the total intensity at the same frequency. We prove that, if the laser is in an antiphase regime, these relations become independent of the initial condition. This property rests on the existence of widely different time scales for the oscillation frequencies and their damping. Numerical simulations indicate that these relations remain true when a small amplitude modulation is applied to the control parameter.PACS numbers: 42.50. Ne, 42.55.Rz Recently, multimode lasers have been intensively studied as examples of spontaneous self-organized timeperiodic systems. This regime has been called antiphase dynamics (AD) in laser physics. It is a manifestation of the coherence property of nonsteady modal intensities that can be displayed by multimode lasers. It should not be confused with the electric field coherence of the single mode laser. AD has been reported in lasers in the case of spontaneous self-pulsing [1][2][3], in the presence of an external modulation [4,5], in the noise spectrum at steady state [6], in the transient relaxation to steady state [7,8], in the chaotic regime [9,10], and in the routes to chaos [11].A laser oscillating on N modes is characterized by N modal intensities I n ͑t͒, n 1, 2, . . . , N. The rate equation limit, where only model intensities and population inversion are coupled, applies to all the lasers in which AD has been reported up to now. For such lasers, the sum of the modal intensities SI͑t͒ P N n 1 I n ͑t͒ is the total intensity. In the case of self-pulsing, AD means that each modal intensity is periodic, though with different phases and/or frequencies, but the total intensity is also periodic. When the dynamics is characterized by the relaxation frequencies, AD means that each modal intensity is driven by a number of frequencies (smaller than or equal to the mode number) while the total intensity is driven by only one frequency, the one which is related to the single mode frequency. The purpose of this Letter is to put forward yet another signature of AD by deriving universal relations between the power spectra of I n ͑t͒ and SI͑t͒. Universality in this context means that the relations are independent of the initial condition, i.e., of the preparation of the system. We shall first show that, under rather weakly constraining conditions a general relation can be found between the power spectrum of the total intensity, the modal intensities, and the intensity phases. We shall then use the known phase properties of the AD regime in two specific examples to reduce these relations to closed relations between the power spectra of the modal and the total intensities.

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“…One might therefore expect the occurrence of perfect antiphase in this situation also, because of γ 2 = γ 3 . This is true but with the exception that here the perfect antiphase arises at the lowest frequency 3 and not at the middle frequency 2 . Concerning the dynamics at the other two frequencies, it is partially antiphased at 2 and, as in all cases, in-phased at 1 .…”

Section: Partial Versus Perfect Antiphase and Power Spectrum Relationsmentioning

confidence: 68%

“…Recently, intensity phase coherence in multimode lasers has attracted much attention centred around what is called antiphased dynamics [1][2][3][4][5][6][7][8][9][10][11][12]. In lasers built in ring cavities, mode competition allows only one mode to lase stably except if there is inhomogeneous line broadening.…”

Section: Introductionmentioning

confidence: 99%

Universal dynamical properties of three-mode Fabry - Perot lasers

Mandel

Otsuka

1997

Quantum Semiclass. Opt.

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Abstract. We present an asymptotic study of a three-mode Fabry-Perot laser with arbitrary relative modal gains in the rate equation limit. Dynamical modes are defined as the eigenvectors of the stability or Jacobian matrix. The associated eigenvalues are the decay rates and the relaxation oscillation frequencies. We show that if the modal gains are not equal, the ratio of the relaxation oscillation frequencies may display rational ratios which will lead to resonances. We classify the various states of the modal field intensities as in-phase, partial and perfect antiphase and find universal relations between the peak heights in the power spectra of the total and of the modal intensities at each of the relaxation oscillation frequencies. Our theoretical results are confirmed by numerical computation using the full rate equations. Experimental results obtained for the noise spectrum of an LNP microchip laser fully support our theoretical results. We also conjecture some properties of lasers operating in an arbitrary N-mode regime.

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Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers

Cited by 63 publications

References 8 publications

Antiphase dynamics in pump-modulated multimode intracavity second-harmonic generation

Antiphase dynamics in pump-modulated multimode intracavity second-harmonic generation

Universal Properties of Multimode Laser Power Spectra

Universal dynamical properties of three-mode Fabry - Perot lasers

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