Two edge-emitting lasers coupled through polarization-rotated optical injection exhibit square-wave oscillations
provided the roundtrip time from laser to laser and back is sufficiently large. If the mutual coupling between
the lasers is relatively weak, the two plateaus of the square-waves exhibit different durations even though the
total period remains close to the roundtrip time. This asymmetry progressively disappears as the feedback
strength is increased. The experimental observations are confirmed by numerical simulations. The simulations
also reveal that the square-wave regimes appear through a series of complex bifurcations and that a sufficiently
large roundtrip time is needed.
A new technique for mitigating stimulated Brillouin scattering (SBS) effects in narrow-linewidth Yb-doped fiber
amplifiers is demonstrated with a model that reduces to solving an 8×8 system of coupled nonlinear equations with the
gain, SBS, and four-wave mixing (FMW) incorporated into the model. This technique uses two seed signals, or 'two-tones',
with each tone reaching its SBS threshold almost independently and thus increasing the overall threshold for SBS
in the fiber amplifier. The wavelength separation of these signals is also selected to avoid FWM, which in this case
possesses the next lowest nonlinear effects threshold. This model predicts an output power increase of 86% (at SBS
threshold with no signs of FWM) for a 'two-tone' amplifier with seed signals at 1064nm and 1068nm, compared to a
conventional fiber amplifier with a single 1064nm seed. The model is also used to simulate an SBS-suppressing fiber
amplifier to test the regime where FWM is the limiting factor. In this case, an optimum wavelength separation of 3nm to
10nm prevents FWM from reaching threshold. The optimum ratio of the input power for the two seed signals in 'two-tone'
amplification is also tested. Future experimental verification of this 'two-tone' technique is discussed.
The square-wave response of edge-emitting diode lasers subject to a delayed polarization-rotated optical feedback is studied experimentally and theoretically. Square-wave self-modulated polarization intensities of a period close to twice the delay τ of the feedback gradually appear through a sequence of bifurcations starting with a Hopf bifurcation (Gavrielides et al, Proc. SPIE 6115, to appear, 2006). In Gavrielides et al (submitted, 2006), squarewave solutions were determined analytically from the laser equations in the limit of large τ. A condition on the laser parameters was derived explaining why square-wave oscillations are preferentially observed for suffciently large feedback strength. In this paper, we concentrate on the relaxation oscillations that always appear at each intensity jump between the plateaus of the square-wave. We show analytically that if the feedback strength is
progressively decreased, a bifurcation to sustained relaxation oscillations is possible for one of the two plateaus.
The response of a diode laser resulting from an incoherent delayed optical feedback is considered from numerical
and experimental perspectives. We concentrate on a class of solutions that appear as regular square waveforms.
A two-field model is used and the bifurcation diagram of these square-wave regimes is studied. Conditions under
which they typically appear are determined. The roles of various parameters are examined, particularly with
regard to the gains and losses of the two polarization modes. Numerical results are in close agreement with
experiments.
The chaotic dynamics of a semiconductor laser subject to a delayed polarization-rotated optical feedback is investigated theoretically and experimentally. An extension of the usual one-polarization model is derived to account for two orthogonal polarizations of the optical field. The two-polarization model is motivated by observations of lag synchronization in our experiments using polarization-rotated optical feedback and uni-directional injection. Experimental data confirm the predictions of the two-field model. We also show that the two-polarization model can be reduced to the one-polarization model.
The main goal of this paper is the study of the stimulated Brillouin scattering (SBS) in multimode fibers, at 1550 nm wavelength, cw operation, in order to build high power IR fiber lasers. Two theoretical models are considered, the usual plane wave model and a modal model, developed in this paper. The theoretical results for SBS threshold and SBS reflectivity are compared with the experimentally determined values. Good agreement was obtained when using the mode structure analysis.
The rate equations describing a laser with phase conjugate feedback are analyzed in the case of non-zero detuning. For low feedback rates and detuning, the stability diagram of the steady state is similar to the laser subject to injection. A stable steady state may loose its stability through a Hopf bifurcation exhibiting a frequency close to the relaxation oscillation frequency of the solitary laser. We also construct time-periodic pulsating intensity solutions exhibiting frequencies close to an integer multiple of the external cavity frequency. These solutions have been found numerically for the zero detuning case and play an important role in the bifurcation diagram.
We analyze the dynamics of a laser diode subject to optical feedback from a short external cavity (EC), i.e. with an EC round-trip time much smaller than the period of the laser relaxation oscillations (RO). Our numerical simulations are based on the Lang-Kobayashi (LK) equations for single mode edge-emitting lasers subject to weak/moderate optical feedback. A new, detailed, Hopf bifurcation analysis shows that LK equations admist both supercritical and subcritical Hopf bifurcation points. Subcritical Hopf points lead to time-periodic pulsating intensity solutions with a frequency close to half the RO frequency. In contrast, from supercritical Hopf bifurcatiosn emerge harmonic intensity oscillations with a frequency either close to the RO frequency or to the EC frequency. Microwave oscillations are obtained, as a result of a beating between two EC modes. In general, these high frequency dynamics are stable only for a small range of feedback parameters. However, we find that decreasing the α factor largely improves the stability of the microwave oscillations and makes it possible to observe pulsating intensity solutions for a larger range of EC length. The high frequency intensity solutions of laser diodes with short EC are thought to be of great interest for new applications in all optical signal handling. Our results motivate new theoretical studies of LK equations with short EC.
We present the time dependence, steady state behavior and spectra of a dual fiber-laser compound cavity. This particular cavity is formed with two Er-doped fiber amplifiers, each terminated with a fiber Bragg grating, and coupled through a 50/50 coupler to a common feedback and output coupling element. The experiment and theory show that a low Q, high gain symmetric compound cavity extracts nearly all the incoherent power in a coherent mode when the two fiber polarizations are aligned. This extraction is maintained even when there is significant difference in the optical pathlengths of the two component elements.
We demonstrate analytically and numerically that multiple mixed external cavity mode solutions are possible for a laser subject to optical feedback from two external cavities. Such solutions exhibit a series of bifurcations and can be easily identified from optical spectra and their frequency content. Similar states have been proposed and analyzed within the framework of the usual Lang-Kobayashi equations describing a semiconductor laser subject to a single optical feedback in short cavities and with moderate pumping. We will present experimental results demonstrating the existence of mixed-mode states in a two-cavity system. We also find that the bifurcation sequence can terminate in low frequency fluctuation states before restabilization on a new maximum power external cavity mode.
We demonstrate numerically and experimentally that low- frequency fluctuations (LFF) in a laser diode subject to delayed optical feedback can be suppressed or stabilized by a second optical feedback with a short delay. The second feedback suppresses LFF by shifting antimodes far away from the external cavity modes in phase space, or by making them disappear, with the consequence that the crises that induce the power dropouts are no longer possible. Moreover, as the second feedback strength increases, the laser undergoes a bifurcation cascade with successive regions where it exhibits chaos or LFF and regions where it locks to a newly-born stable maximum gain mode. This all-optical stabilization technique is easier to implement from an experimental point of view than many existing methods since it does not require modification of any laser parameters or of the first optical feedback.
Recent experiments using lasers subject to strong external injection [Simpson, Opt. Commun. 170, 93 (1999)] have demonstrated that adding a small reference current modulation to the dc-bias current can easily lock the oscillation frequency of the laser to the reference frequency. Tunable, locked outputs from 9.5 to 13.1 GHz have been obtained. We explain why synchronization is readily achieved at high injection rates. We describe the locking phenomenon in detail and derive useful analytical expressions for the frequencies and locking range in terms of the laser parameters.
The dynamics of two mutually coupled semiconductor lasers is studied experimentally and numerically for weak coupling. The two lasers are pumped at different levels and have dissimilar free-running relaxation oscillation frequencies and intensities. We have found that the two lasers exhibit large amplitude intensity oscillations for one laser and small amplitude intensity oscillations for the other laser. In our previous work, we studied the effect of the coupling strength. In this paper, we keep the coupling strength fixed and examine the effect of the detuning between the optical frequencies. As the detuning comes close to a multiple of the relaxation oscillation frequency of one of the two lasers, we observe the amplification of the intensities due to resonance and synchronization. Our experimental observations of the laser spectra are in good agreement with the numerical spectra and bifurcation diagrams computed from the semiconductor laser rate equations.
The dynamics of two mutually coupled but non-identical semiconductor lasers are studied experimentally, numerically and analytically for weak coupling. The lasers have dissimilar relaxation oscillation frequencies and intensities, and their mutual coupling strength is asymmetric. We find that the lasers may entrain to the relaxation oscillation frequency of either one of the lasers. The form of entrainment is a special form of synchronization, called localized synchronization, where one laser exhibits strong oscillations and the other one weak oscillations. We perform a bifurcation analysis to explain the mechanism of entrainment by taking advantage of the inherently large parameters in a semiconductor laser, the linewidth enhancement factor (alpha) and the ratio of the carrier and photon lifetime T.
Lang and Kobayashi equations for a semiconductor laser subject to optical feedback are investigated in the limit of large delays. Be deriving slow time evolution equations, we show analytically that quasiperiodic intensities are possible and appear as a tertiary bifurcation from a periodic state.
We present an asymptotic analysis of the equations describing a semi-conductor laser with optical injection. This analysis focuses on the phase drift regime where the slave laser is not locked to the injected signal. In addition to the basic four wave mixing solution, we find subharmonic bifurcations and coexisting isolated periodic solutions (dynamic isolas), which occur close to integer detunings. We also present experimental data that confirm some of these predictions.
An asymptotic theory of Lang and Kobayashi (LK) equations describing a semiconductor laser subject to optical feedback is investigated in detail. We obtain a simple third order, nonlinear, delay-differential equation for the phase of the laser field which admits multiple branches of time-periodic intensity solutions. The theory is based on typical values of LK dimensionless parameters and assumes that the pump parameter is not too small. In this paper, we examine the validity of this assumption by considering the small pump limit. We find the same phase equation as the leading problem of our asymptotic analysis but now with a stronger damping coefficient. This phase equation fails as a correct asymptotic approximation only for very low pump, close to the lasing threshold. The approximation for this case is more complicated and reveals a stronger influence of the laser intensity.
A feed-forward backpropagating neural network is trained to achieve and maintain control of the unstable periodic orbits embedded in a chaotic attractor. The controlling algorithms used for training the network are based on the now standard scheme developed by Ott, Gregogi and Yorke, including variants that utilize previous perturbations and/or delayed time series data.
In most encounters, chaos is considered a nuisance, if not a down right detriment to system performance, especially in laser devices. However, the presence of chaos in a system can act as a rich source of complex frequencies if one only had a way of accessing them. In this work we present a discussion of the recent work of Ott, Grebogi and Yorke on controlling chaos as applied to a semiconductor diode laser subject to optical feedback via an external mirror. In the regime in which the laser is chaotic, stabilization can be achieved by sampling the output intensity and feeding back minuscule amounts of a correcting signal on the pumping current at the appropriate time interval. We present the results of our numerical investigations.
We have demonstrated experimentally a proportional feedback algorithm for the synchronization of chaotic time signals generated from a pair of independent diode resonator circuits. Synchronization was easily obtained and occurred for relative feedback levels between three and eight percent of the driving voltage. Once established, the synchronization persisted throughout the whole range of the resonator bifurcation diagram without varying the gain of the feedback.
We report experimental measurements and numerical calculations of the effects of strong, nearly-degenerate optical injection in a nearly single-mode, Fabry-Perot laser diode. The noise spectra and the response to weak optical injection of the laser diode are well characterized by a model, based on the coupled electric-field and carrier-density equations, which includes the effects of gain saturation and the weak side modes. Beyond the perturbation regime, the laser exhibits new operating characteristics, including an output which involves rapid fluctuations among several longitudinal modes and spectral broadening of the principal mode. The laser dynamics strongly depends on the injected optical power and the frequency offset between the external input and the free-running oscillation. Numerical simulations are conducted using the full coupled-equation model for a strictly single-mode laser without noise.
KEYWORDS: Resonators, Chaos, Diodes, Feedback signals, Dynamical systems, Analog electronics, Switches, Signal generators, Control systems, Feedback control
We have demonstrated experimentally a proportional feedback algorithm for the synchronization of chaotic time signals generated from a pair of independent diode resonator circuits. Synchronization was easily obtained and occurred for relative feedback levels between three and eight percent of the driving voltage. Once established, the synchronization persisted throughout the whole range of the resonator bifurcation diagram without varying the gain of the feedback.
The photoferroelectric barium titanate (BaTiO3)/polyvinylidene fluoride (PVDF) composite
films in the ratio 70:30 are found to possess good photosensitivity in the visible region of the
spectrum. Results on the investigations of charge generation, trapping, recombination, discharge,
and retention properties of the composite film are presented in this paper.
The dark polarization and dark depolarization characteristics of the film show that it can
accept and retain very high charge for a very long time. The charge decay properties of the dark
polarized and photo depolarized electrosensitized sample indicate that it can be used successfully in
electro-photographic applications as the dark decay is found to be slow while the light decay is
very fast. In addition to this, the photo polarization and photo depolarization studies of the
polarized films show that the film has very good remnant polarization,which persists for several
hours to days. The persistence of polarization, its magnitude, and the decay characteristics depend
on the charging conditions. The resultant dark and photo depolarization current values are found to
increase linearly with increase of the poling field, illumination intensity, and poling time. The
polarization properties of the film are comparable to that of the BaTiO3 single crystal. The results
of the studies show that BaTiO3IPVDF composite films may find many interesting applications as
a photoreceptor in the fields of electrophotography, holography, and optical memory. It may also
be useful as a photorefractive nonlinear optical material.
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