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Register a new userSome fundamental considerations on the dynamics of class B laser threshold crossing
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With the help of a simple rate equation model, we analyze the intrinsic dynamics of threshold crossing for Class B lasers. A thorough discussion of the characteristics and the limitations of this very commonly employed model, which provides excellent qualitative predictions on the laser behaviour, is offered. Approximate solutions for the population inversion and for the field intensity, up to the point where the latter reaches macroscopic levels, are found and discussed, together with the associated characteristic times. Numerical verifications test the accuracy of these solutions and confirm their validity. A discussion of the implications on threshold dynamics is presented, together with the motivation for focussing on this -- nowadays most common -- class of lasers.
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The threshold properties of very small lasers (down to the nanoscale) are a topic of active research in light of continuous progress in nanofabrication. With the help of a simple rate equation model we analyze the intrinsic, macroscopic dynamics of threshold crossing for Class B lasers. We use the deterministic aspects of the basic rate equations to extract some fundamental time constants from an approximate analysis of laser dynamics in the threshold region. Approximate solutions for the population inversion and for the field intensity, up to the point where the latter reaches macroscopic levels, are found and discussed. The resulting timescales characterize the lasers ability to respond to perturbations (external modulation or intrinsic fluctuations in the lasing transition region). Numerical verifications test the accuracy of these solutions and confirm their validity. The predictions are used to interpret experimental results obtained in mesoscale lasers and to speculated about their extension to nanolasers.
Chaos in semiconductor lasers or other optical systems have been intensively studied in past two decades. However, the route from period doubling to chaos is still not sufficiently visible, in particular, in gain-modulated semiconductor lasers. In this article we perform a careful investigation of the route to chaos exhibited by directly modulated semiconductor lasers near the threshold region with various values of modulation frequency and amplitude. Gain nonlinearity is included in the simulation of pulse train generation through gain switching, and a new form of phase space representation is introduced to distinctly display period doubling, tripling, quadrupling and chaos. The irregular behaviour is examined at various modulation frequencies and amplitudes, highlighting the possible route to chaos for very large amplitude modulation in the near-threshold region. The existence of deterministic trajectories below the laser threshold is rendered possible by the presence of the (average component of the) spontaneous emission, a point which has not often been explicitly considered. Furthermore, we report on the existence of a transition between similar attractors characterized by a temporal transient which depends on the amplitude of the modulation driving the pump.
We address the problem of achieving a random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. In this system, the elastic scattering cross-section is related to the complex atomic polarizability. As a consequence, the random laser threshold is expressed as a function of this polarizability, which can be fully determined by spectroscopic measurements. We apply this idea to experimentally evaluate the threshold of a random laser based on Raman gain between non-degenerate Zeeman states and find a critical optical thickness on the order of 200, which is within reach of state-of-the-art cold-atom experiments.
We experimentally study the coherence time of a below-threshold Raman laser in which the gain medium is a gas of magneto-optically trapped atoms. The second-order optical coherence exhibits photon bunching with a correlation time which is varied by two orders of magnitude by controlling the gain. Results are in good agreement with a simple analytic model which suggests the effect is dominated by gain, rather than dispersion, in this system. Cavity ring-down measurements show the photon lifetime, related to the first-order coherence time, is also increased.
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical point of view, for instance games obtained via transformations such as duplications of strategies or positive affine mappings of of payoffs. We show the need to define classes of decompositions to achieve commutativity of game transformations and decompositions.
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