Spatiotemporal Stabilization of Locally PT-symmetric Semiconductor Lasers

Abstract

We provide a feasible and compact scheme to control and stabilize the spatiotemporal dynamics of BAS lasers. The proposal is based on the ability of nonHermitian potentials with given local symmetries to manage the flow of light. A local PTsymmetric configuration allows to control, enhance and localize the generated light. We impose a pump modulation, with a central symmetry axis which induces in-phase gain and refractive index modulations due to the Henry factor. Both modulations are, in turn, spatially dephased by an appropriate index profile to yield to a local PT-symmetry within the modified BAS laser. Such local PT-symmetry potential induces an inward mode coupling, accumulating the light generated from the entire active layer at the central symmetry axis, which ensures spatial regularization and temporal stability. By an exhaustive exploration of the modulation parameters, we show a significant improvement of the intensity concentration, stability and brightness of the emitted beam. This approach produces a two-fold benefit: light localization into a narrow beam emission and the control over the spatiotemporal dynamics, improving the laser performance. Broad Area Semiconductor (BAS) amplifiers and lasers are prevalent and trustworthy light sources, used for many applications ranging from biomedicine [1] to telecommunications [2]. Their main advantage is the compactness and the high conversion efficiency, while their major drawback is the relatively low spatial and temporal quality of the emitted beam [3,4]. The fundamental phenomenon that induces spatiotemporal instabilities is Modulation instability (MI) [5]. This intrinsic instability and the nonlinear modal interaction lead to complex spatiotemporal dynamics and filamentation, a disruption of the field into multiple filaments, limiting possible applications [6,7]. The stabilization of these devices is achieved by considering different schemes, some of them by the introduction of spatial [8] or spatiotemporal modulations [9]. Besides, other studies introduced spatial non-Hermitian potentials in BAS amplifiers, with a double spatial modulation of refractive index and pump, leading to a substantial improvement of the spatial quality of the beam [10]. Also, verticalexternal-cavity surface-emitting lasers with external flat mirrors could be stabilized by applying a periodic spatiotemporal modulation of the pump current [11]. More recently, attention was paid on a specific kind of non-Hermitian systems, holding PT-symmetry [12]. In such materials, the complex refractive index fulfils: n(x) = n*(-x) i.e., the real part representing the refractive index is symmetric while the imaginary part representing gain-loss is antisymmetric in space. In periodic PT-symmetric media index and gain-loss modulations are dephased by a quarter of the wavenumber of the modulation. Such systems hold maximum asymmetric mode coupling which occurs at the PT-symmetry breaking point, or exceptional point, when the gain and loss modulation amplitudes are balanced [13,14]. In optics, global or local PT-symmetry lead to unconventional beam dynamics arising precisely from the asymmetric mode coupling, such as the unidirectional light transport following arbitrary vector fields [15,16]. In particular, it was also shown that local PT-symmetry could also be applied to stabilize the emission from BAS amplifiers [17,18]. Therefore, unidirectional mode coupling could be a scheme to regularizing the spatiotemporal dynamics of BAS lasers, while improving stability. In this letter, we propose to apply a local PT-symmetric potential to control the spatiotemporal dynamics of BAS lasers by localizing the light generated in the entire active layer into a narrow central beam. The typical complex emission from BAS sources is unstable both in space and in time domains, as shown on Fig. 1.a. The proposal is to regularize and control the emission by local PT-symmetry in modulated BAS, as shown in Fig. 1.b, leading to a narrow beam emission which is expected to be useful for a large variety of practical applications. Fig. 1. BAS emission, schematic illustration: (a) complex irregular spatial pattern emitted from a conventional BAS source, (b) bright and narrow beam emission from a modified BAS (PT-symmetric BAS) where \uf044p(x,z) is the pump modulation and \uf044n(x,z) the refractive index modulation. (c) Scheme of the transverse spatial distribution of the local PT-symmetric potential, when \uf044n(x,z) and \uf044p(x,z) induce balanced gain (in green) and effective refractive index (in purple) modulations, for different configurations denoted by the bellow defined central phase: Φ\uf020=\uf0200 (left), Φ = π/4 (center) and Φ = π/2 (right). BAS semiconductor sources, amplifiers and lasers, are generally described by stationary models including field and carriers [19] or, alternatively, by mean field models including temporal evolution [20]. A better approximation is given by the optical field propagation along the semiconductor, while carrier and field dynamics were neglected. Similarly, previous studies on local PT-symmetry were performed considering a strongly simplified and stationary models only considering a forward field propagation in a paraxial approximation. The present paper deals with the spatial regularization and temporal stabilization of BAS lasers requiring a spatiotemporal integration of field and carriers. A new integration scheme has been developed to include all, the temporal evolution and the spatial propagation of the electric field, and the temporal evolution of carriers. However, we do assume that the cavity round trip time is short as compared to the carrier’s relaxation time, and that the time evolution of the field in one roundtrip can be calculated by its propagation along the cavity assuming constant carriers. The second integration step is the temporal integration of the carrier spatial distribution considering an already stabilized field. Applying the slowly varying envelope approximation for the electric field, the BAS source may be represented by the following non-linear system of equations for the field amplitude envelope, A, and carriers, N: