We report a first experimental study of the nonlinear dynamics appearing in a 1550 nm single-mode VCSEL subject to parallel and to orthogonal optical injection. For the first time to our knowledge we ...report experimentally measured stability maps identifying the boundaries between regions of different nonlinear dynamics for both cases of polarized injection. A rich variety of nonlinear behaviours, including periodic (limit cycle, period doubling) and chaotic dynamics have been experimentally observed.
In this paper, we report an experimental and theoretical study of the random excitation of the linearly polarized modes of a gain-switched VCSEL characterized by having polarization switching under ...continuous wave operation. We show that equal probability of excitation of both linearly polarized modes can be achieved by adjusting the modulation conditions and the sampling time. Our VCSEL is such that the bistable region associated to the polarization switching is very narrow, indicating that the random process of excitation of the polarizations works independently of the existence of those bistable regions. A characterization of the random polarization switching is performed by analyzing the dependence of the probability of excitation, autocorrelation, and histograms of both polarized signals on the modulation conditions and sampling times. We finally present preliminar results on random number generation using the analyzed system.
In this paper, we report a theoretical and experimental study of the phase diffusion in a gain-switched single-mode semiconductor laser. Our modelling includes nonlinear dependencies of the carrier ...recombination rate and the semiconductor material gain on the carrier number. Also a comparison with the results obtained with linear models is performed. We focus on the below threshold operation, that is, the regime where most of the phase diffusion occurs in quantum random number generators based on the above mentioned system. Using the extracted parameters for our laser and simple analytical expressions for the laser linewidth, we show that logarithmic material gain and cubic carrier recombination dependence on the carrier number must be considered for a good agreement between experiments and theory. In this way we show that consideration of these nonlinearities is essential for obtaining a good quantitative description of the phase diffusion when using rate equations modelling.
We present experiments and numerical simulations of optical frequency combs generated by gain-switching a single mode laser diode when subject to optical injection. Our analysis focuses on the combs ...with a frequency separation <inline-formula><tex-math notation="LaTeX">f_R</tex-math></inline-formula> in the GHz range. We present experimental maps in the parameter space spanned by the detuning and the strength of the optical injection that identify the boundaries between regions with different dynamical states. A rich variety of nonlinear behaviors including injection-locked, unlocked and irregular combs are observed and analyzed. The dynamical state corresponding to an injection locked comb, P<inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>, is characterized by an optical phase oscillation with a well defined amplitude in such a way that repeats or changes in 2<inline-formula><tex-math notation="LaTeX">\pi</tex-math></inline-formula> with an <inline-formula><tex-math notation="LaTeX">N/f_R</tex-math></inline-formula> period, where <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> is a natural number. Different regions of locked combs with a tongue shape around detuning values given by multiples of <inline-formula><tex-math notation="LaTeX">f_R</tex-math></inline-formula> appear in the maps. P1 and P2 are the most widespread locked states for large values of the modulation amplitude. As this amplitude decreases a much larger variety of P<inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> states with large values of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> appear in small area regions of the map. Our numerical simulations are in very good agreement with experimental results.
We present experimental and theoretical results of bistable polarization switching in a single transverse mode 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical ...injection. We focus our analysis on the bistability induced by power variation of the master laser found on the recently observed state of simultaneous injection locking of the parallel polarization mode and excitation of the orthogonal polarization mode, IL+PS. Experimental stability maps identifying, in the injected power-frequency detuning plane, where this state is observed, and corresponding bistable regions are reported for several bias currents. We find bistability between the IL+PS state and the single polarization mode injection locked solution. We also find bistability between the IL+PS and different periodic dynamics in the parallel polarization mode. The width of the hysteresis cycle increases when increasing the bias current or when increasing the wavelength of the optical injection beyond the solitary VCSEL wavelength. We theoretically confirm these types of bistability by numerically simulating the spin-flip model and by performing a linear stability analysis for the different stable states. Excellent agreement is found between experimental and theoretical results.
We report an experimental study of the effect of the temperature of the VCSEL on the probability of excitation of a linearly polarized mode when gain-switching the device. We consider different ...modulation frequencies and amplitudes. We show that the probability of excitation of a linearly polarized mode significantly changes with the value of the temperature of the device. We also show that for low values of the temperature the probability of excitation saturates to a constant value as the amplitude of the modulation increases. This extends our previous results obtained at larger temperatures for which that saturation was not observed. We identify situations in which the distributions of the linearly polarized signals at a sampling time are approximately uniform. For these cases we evaluate the quality of the random numbers by using statistical test.
We experimentally and theoretically investigate the photonic generation of microwave signals using a long-wavelength single-transverse-mode vertical-cavity surface-emitting laser (VCSEL) subject to ...two-frequency orthogonal optical injection. We study if a significant reduction of the linewidth is achieved in the double injection locking regime. In this regime, the VCSEL is subject to optical injection by two master lasers in such a way that stable locking is also observed if only light from one of the master lasers is injected. Our model includes the effect of the injected light reflected at the VCSEL's mirror generalizing previous modeling of reflection-mode optical injection-locked VCSELs. Our model also describes the high coherence associated to stable injection locking states and takes into account phase fluctuations in both master lasers. We observe no significant reduction of the linewidth in the double injection locking regime because the linewidth is mainly determined by the phase fluctuations of the two master lasers.
•Experimental and theoretical analysis of phase diffusion in gain-switched semiconductor lasers.•Deriving a stochastic rate equations model to avoid numerical instabilities.•Evaluating the validity ...of the linear approximations used to describe phase diffusion.
Quantum random number generation (QRNG) has become a topic of growing interest in recent years due to important applications in cryptography and simulations. Interferometric detection of phase diffusion in gain-switched single-mode semiconductor lasers is one of the main generation techniques. In this paper, we study experimentally and theoretically the phase diffusion in gain-switched discrete mode laser diodes. We derive a stochastic rate equations model for the laser electric field that avoids numerical instabilities that appear when simulating amplitude and phase equations. Measurements are performed in order to extract the parameters of our semiconductor laser. Spontaneous emission rate coupled into the lasing mode is measured as a function of the carrier number for bias currents below threshold. A quadratic dependence is obtained that permits us to evaluate the validity of the linear approximations that have been used to describe laser phase diffusion in QRNG. The good agreement between experiments and theory permits us to give a realistic quantitative description of the dynamical evolution of the phase statistics in this type of QRNGs.
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