Antiphased modulation of a laser array

Abstract

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:

Stability of two loss-coupled lasers

“…In figure 4 we display Re λ 5,6 and Im λ 3,4,5,6 as functions of w 2 for κ = 10 4 , β = 0.2/ √ κ and a fixed w 1 = 3 by using the analytical expressions (18), (15) is also in full agreement with the phase diagram depicted in figure 3. Outside that gap, i.e.…”

“…It is a simple matter to check that λ 5,6 are either real positive or complex conjugates with a positive real part. The steady state is thus also unstable for…”

“…Most theoretical works [1][2][3][4][5] consider lasers that are phase-locked via the complex amplitude coupling. Recently, a solid state laser array has been proposed [6] in which each laser can be pumped by an independent beam and the lasing intensities are coupled by cross-gain and cross-saturation. In this paper, we study an alternative mechanism of intensity coupling, based on cross-loss, which finds its origin in effects such as the thermal deformation.…”