Dynamics of a Multimode Laser with Nonlinear, Birefringent Intracavity Elements

Roy, Rajarshi; Bracikowski, Christopher; James, Glenn E.

doi:10.1007/978-1-4615-2936-1_39

Cited by 5 publications

(7 citation statements)

References 19 publications

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“…We have assumed that a, b, and g are mode independent, in good agreement with the experimental results [1,14]. The parameter h equals t c ͞t f , where t c and t f are the cavity round trip time and fluorescence lifetime, respectively.…”

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confidence: 55%

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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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confidence: 55%

“…(ii) Intracavity second harmonic generation [14].-We shall consider only the case where all modes oscillate with the same polarization. The evolution equations for the modal intensities I n and the nonlinear gains G n are…”

mentioning

confidence: 99%

Universal Properties of Multimode Laser Power Spectra

Mandel¹,

Wang²

1996

Phys. Rev. Lett.

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“…The coupling coefficients, γ jk , describe the interaction between lasers j and k. In this paper we consider global coupling which occurs when a fraction of the field from one laser is mixed equally into all other lasers. For an array of identical lasers, global coupling can be modelled by taking γ jk = γ /N for all j and k. We take into account the birefringence of the optical elements in the cavity and the harmonic conversion efficiency of the fundamental intensity, following the treatment given in [4], as shown in the last term of the right-hand side of (1). The laser mode can oscillate in one of two orthogonal polarizations.…”

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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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“…The value of varies from 0 to 1 [21]. Each cavity mode can be polarized only in one of the two orthogonal directions ( or ).…”

Section: The Modelmentioning

confidence: 99%

“…In this paper we report the results of our numerical studies on the effect of coupling of two multimode Nd:YAG lasers with intracavity KTP crystal for frequency doubling. The chaotic behavior of such a laser has been studied extensively by many authors both experimentally and theoretically [14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal

Kuruvilla

Nandakumaran

2000

Pramana - J Phys

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Abstract. The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.

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Dynamics of a Multimode Laser with Nonlinear, Birefringent Intracavity Elements

Cited by 5 publications

References 19 publications

Universal Properties of Multimode Laser Power Spectra

Universal Properties of Multimode Laser Power Spectra

Antiphased modulation of a laser array

Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal

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