Antiphase dynamics and polarization effects in the Nd-doped fiber laser

Bielawski, S.; Derozier, D.; Glorieux, P.

doi:10.1103/physreva.46.2811

Cited by 164 publications

(45 citation statements)

References 41 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: 92%

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

Wang

Mandel

1996

Quantum Semiclass. Opt.

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“…First, a new term of cross-gain, which is absent in the usual ISHG equations: the intensity of element k, I k is amplified by its corresponding gain z k and also to a smaller extent by the gain of other elements. Second, a cross-saturation effect: the stimulated emission causes a saturation of gain of its corresponding intensity I k and also of the other element intensities [3]. When isolated from the others, each laser supports a single transverse and longitudinal mode assumed to be the same for all the lasers.…”

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confidence: 99%

Antiphased modulation of a laser array

Wang

Mandel

Otsuka

1996

Quantum Semiclass. Opt.

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Abstract. We propose a model for globally coupled lasers with intracavity second harmonic generation in which each laser gain is modulated separately. Suitable selection of the modulation phases can shift the resonance expected at the relaxation oscillation towards lower frequencies. This shift is accompanied by a reduction of the resonance width.In a recent paper [1], we analysed numerically the response of a multimode laser, with intracavity second harmonic generation (ISHG), to a periodic modulation of the gain in the linear and nonlinear regimes. We found that, depending on the relative phase of the modal gain modulation, the resonance which is expected at the relaxation oscillation frequency can appear to be or can be shifted to the lower internal frequency. However, the possibility of modulating the gain coefficient of each mode separately seems remote at this point. In this paper, we propose a globally coupled solid-state laser array with intracavity second harmonic generation in which such control is possible. The proposed laser array consists of a bulk laser crystal and a second harmonic generation crystal placed within the cavity mirrors. The bulk crystal is pumped by multiple parallel beams through one of the cavity mirrors and each lasing element forms an element of the array. Diffractive global coupling between all lasing elements can be achieved by the other cavity mirror which is a feedback mirror, onto which the doubling crystal is attached, using the Talbot effect for spatial arrays [2]. In the case of the usual ISHG scheme in multimode lasers, the pump power is applied to all lasing modes identically. Therefore, it is very difficult or even almost impossible to control the small signal gain of each mode independently. In contrast, in the scheme of laser arrays that we propose, each element is pumped by a different beam. As a result, it is now possible to control each pump power independently. In the scheme of the globally coupled ISHG lasers that we propose, the gain of each element is shared by the lasing fields from other elements by a Talbot diffractive coupling. Therefore, a small amount of crossgain appears in addition to cross-saturation. For the usual ISHG in multimode lasers, mode coupling occurs due to spatial hole burning. In this case, different lasing fields with different frequencies interact with population inversion gratings corresponding to different standingwave patterns in the crystal and stimulated emission follows accordingly. Therefore, no cross-gain appears in this situation. Hence the model can be described by the following rate equations:

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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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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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Antiphase dynamics and polarization effects in the Nd-doped fiber laser

Cited by 164 publications

References 41 publications

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

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

Antiphased modulation of a laser array

Universal Properties of Multimode Laser Power Spectra

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