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7The 30th International Conference on Advanced Laser Technologies ALT'23
LS-I-15
Transverse instabilities in wide-aperture semiconductor lasers with a vertical cavity and method for their suppression
A. A. Krents12, N.E. Molevich12, E.A. Yarunova12
1- Department of Theoretical Physics, Lebedev Physical Institute, Novo-Sadovaya Str. 221, Samara, Russia
2- Department of Physics, Samara National Research University, Moskovskoye Shosse 34, Samara, Russia
krenz86@mail.ru
Wide-aperture lasers are subject to various spatiotemporal instabilities. Modulation instability is characteristic of wide-aperture semiconductor surface-emitting lasers with a vertical cavity (VCSEL) [1]. In optics, this instability can lead to filamentation and beam quality degradation [2]. In this regard, it is relevant to investigate methods to improve the spatial and temporal quality of the radiation of such devices. This paper proposes to use coherent external optical injection to suppress the modulation instability arising in the VCSEL.
The dynamics of VCSEL can be described by a model that takes into account generation in a single longitudinal mode, presented in the [1]:
BE
— = -[1 + id + 2C(ia -1)(N - 1)]E +1 A±E + Einj,
Bt
dN___ dt ~ -
N -1 +2(N -1) +7d A±N.
where E, N are dimensionless envelopes of the electric field and population inversion, respectively. The parameter Einj is the normalized injected field. d represents the detuning between the cavity and the injected
field frequencies, a is the linewidth enhancement factor. As the basic parameters of the system, we chose the parameters given in the paper [1]: d = -1.5 , a-1.5, С = 0.6 , d = 0.052 , I = 1.85 , y = 0.1.
A standard linear analysis was performed to investigate the stability of VCSEL generation. The aperture sizes at which the spatially homogeneous generation mode becomes unstable were determined ( Zmin «115ym ). The method of external optical injection was proposed to stabilize the generation. It is shown that coherent optical injection can suppress all unstable transverse modes. The stabilization effect has a threshold nature. The threshold value of injection can be calculated by the formula:
\Emj\ = ^-1 + p/2 + ^/y(/p2 -4(p-1))12, where / = 2C(I-1) and P = V 1 + a2.
An implicit Crank-Nicholson scheme with periodic boundary conditions, which is unconditionally stable, was used to numerically solve the system of equations (1). The spatially homogeneous laser generation regime with addition of Gaussian noise of small amplitude was chosen as initial conditions. As a result of numerical calculations, it was obtained that the system dynamics depends on the size of the spatial domain L. Simulation of spatiotemporal dynamics at L < Lmin, showed that the regime of spatiotemporal uniform generation is stable, despite the presence of unstable modes. Unstable modes arise only in the case of L > Lmin . Without injection, the instability of the homogeneous generation mode leads to spatiotemporal chaos and filamentation of the laser radiation. It is shown that for chosen parameters the injected amplitude is sufficient for stabilization to be of the order of 1% of the stationary field amplitude modulus. The proposed method of optical injection to suppress modulation instability is effective and can be used in this system. It was found that external optical radiation of low amplitude can completely suppress the modulation instability.
This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the state assignment (project No. 0023-2019-0003, FSSS-2023-0009).
[1] W. Ahmed, S. Kumar, R. Herrero, M. Botey, M .Radziunas, K. Staliunas, Stabilization of flat-mirror vertical-external-cavity surface-emitting lasers by spatiotemporal modulation of the pump profile, Physical Review A, vol.92(4), p. 043829 (2015)
[2] W. Ahmed , S. Kumar, J. Medina, M. Botey, R. Herrero, K. Staliunas, Stabilization of broad-area semiconductor laser sources by simultaneous index and pump modulation, Optics Letters, vol. 43(11), pp. 2511-2514 (2018).
