Towards a Cavity Soliton Semiconductor Laser
L. A. Lugiato1, G. Tissoni1, F. Prati1, P. Caccia1, M. Brambilla2, M. Bache3, R.
Kheradmand4, I. Protsenko5, S. Barbay6, R. Kuszelewicz6
1CNISM,
INFM-CNR e Dipartimento di Fisica e Matematica, Università dell'Insubria,
Como, Italy
2CNISM, INFM-CNR e Dipartimento di Fisica, Università e Politecnico di Bari, Italy
3COM.DTU, Technical University of Denmark, DK-2800 Lyngby, Denmark
4Research Institute for Applied Physics and Astronomy, University of Tabriz, Iran
5Lebedev Physics Institute, Moscow, Russia Scientific Center of Applied Research,
JINR, Dubna, Russia
6LPN, Laboratoire de Photonique et Nanostructures, Marcoussis, France
Summary
An absorptive element in a Vertical Cavity Surface Emitting Laser (VCSEL) can
originate bistability between the trivial non-lasing solution and a patterned state.
Cavity Solitons can therefore exist over a zero intensity background, originating a
Cavity Soliton Laser [1].
Introduction
Cavity solitons (CSs) are bright intensity peaks over a dark homogeneous
background. They arise in the coherent field transmitted by nonlinear optical
resonators, and are generated through diffraction-mediated light–matter interaction
which leads to field self-localization within the cavity [2]. CSs have been recently
experimentally demonstrated in broad area, driven vertical cavity surface emitting
laser (VCSELs) operated as amplifiers, i.e. biased slightly below the lasing threshold
[3]. In a laser with a saturable absorber (LSA) it is possible to achieve the optimal
condition where a patterned stationary state coexists with a dark state of pure
spontaneous emission corresponding to a laser below threshold. Under this condition
the contrast between the CSs and the homogeneous background is maximum. On
the other hand, since such a device will be able to generate CSs without an external
holding beam, it is the realization of a Cavity Soliton Laser (CSL).
Discussion
A theoretical prediction of dissipative optical localized structures (autosolitons) in a
laser with a saturable absorber was proposed by Rosanov and co-workers [4,5]. For
semiconductor materials, the existence of propagating spatial solitons (different from
the CSs) has been demonstrated in an optical amplifier [6]. Here, instead, we
considered a VCSEL with an absorbing medium integrated in the cavity.
We considered a rate equation model which consists in one equation for the electric
field and two equations for the carrier densities in the amplifier and in the absorber.
With an appropriate choice of the operating parameters, the steady state curve of the
homogeneous stationary solutions exhibits bistability between the lasing state and
the off state. When the linewidth enhancement factor in the amplifier is larger than in
the absorber, as it is normally, the whole branch of the lasing state is unstable due to
a Turing instability as it is necessary to allow the formation of CSs. It may be also
affected by an oscillatory Hopf instability which, fortunately, can be avoided by
assuming that the material is the same in the two parts of the medium. This is
precisely the case for the monolithic device realized at LPN.
Numerical simulations show the existence of an extended range of values for the
pump parameter of the amplifier, where stationary and stable cavity solitons exist.
A crucial point for CSLs is the mechanism for switching CSs on and off,
independently of one another and of the boundary. In the experiments on CS
generation, performed up to now in presence of a holding beam, the switching was
achieved using a writing/erasing address beam coherent with respect to the holding
beam, with the same phase for writing and in opposition of phase for erasing.
In absence of a holding beam, as it happens for CSLs, there is no reference phase
and the switching can only be incoherent, which is an important advantage because
it does not require phase control. Our numerical calculations predict that incoherent
switching is indeed possible.
In a first set of simulations we used a coherent address beam slightly mistuned with
respect to the laser field, and verified that writing and erasing can be achieved by
controlling the power of the beam. In order to write a CS the power must be larger
than a lower level and smaller than an upper threshold. To erase, the power must be
larger than the upper threshold for writing.
Subsequently we analysed the possibility of obtaining the on/off switching by a
localized injection of carriers. In an optically pumped device this can be achieved by
replacing the coherent address beam with a beam oscillating in the frequency range
of the pump, as it is done in the experiments of LPN. The simulations showed that
the same pulse can be used both to write and erase the CSs, and erasing is much
faster (~1 ns) than writing (~100 ns).
We have verified that the results do not change significantly if the model is completed
by including dynamical equations for the macroscopic material polarizations.
From the experimental viewpoint, LPN has designed, grown and characterised a
cavity in which the gain section, composed of two InAs/GaAs quantum wells, is at the
anti-node of the intra-cavity field at cavity resonance and at the anti-node of the
pump field between 795 and 805 nm. The saturable absorber section, composed of
one quantum well of InAs/AlGaAs, is at the anti-node of the resonant intra-cavity field
while being at a node of the pump field. This experimental configuration seems to be
perfectly suitable for reproducing the theoretical predictions in this system.
Conclusions
In this work we theoretically predicted and numerically demonstrated the existence
and stability of cavity solitons in a VCSEL with saturable absorber. A monolithic
cavity has been especially designed and grown to verify the theoretical predictions,
paving the way to the realization of a Cavity Soliton Laser.
Acknowledgements
This research is performed in the framework of the FET Open Project FunFACS.
References
[1] M. Bache, et al., Applied Physics B: Lasers and Optics 81, 913 (2005).
[2] L. A. Lugiato, IEEE J. Quantum Electron., QE-39, 193 (2003).
[3] S. Barland, et al., Nature, 419, 699 (2002).
[4] A. G. Vladimirov, et al., J. Opt. B: Quantum Semiclass. Opt., 1, 101 (1999).
[5] S. V. Fedorov, et al., Phys. Rev. E, 61, 5814 (2000).
[6] E. A. Ultanir, et al., Phys. Rev. Lett., 90, 253 903 (2003).