The complexity of chaos generated in two systems has been studied experimentally. The complexity of the chaos is quantified by calculating average normalized permutation entropy (HS(P)). In the first system, a chaotic output from a master laser (ML) is injected into a CW slave laser (SL). The results show that the complexity of chaos generated in the SL decreases with absolute value of the frequency detuning Δf1, which means the complexity of the chaos is compromised with enhancing the bandwidth, as Δf1 is increased. The second system comprises three vertical-cavity surface-emitting lasers (VCSELs); the first VCSEL (used as ML) was rendered chaotic by optical feedback, the second VCSEL is used as intermediate laser (IL), which is rendered chaotic when it is subject to optical injection from the chaotic ML and the third VCSEL is used as a SL and is a subject of optical injection from the chaotic IL, thus entering chaotic dynamics. In this three-VCSEL system, small, intermediate and wide bandwidths of the injecting chaos signals, have been used to study the effect of the bandwidth of the injecting chaos on the complexity of chaos generated in the SL. The results show that the bandwidth of the chaotic injection beam does not impact the complexity of the chaos generated in the SL for positive frequency detuning; however, for large negative frequency detuning, the complexity of the chaos in the SL has been reduced significantly for the intermediate and lower bandwidth of the chaotic injection beam.
The optical output of frequency shifted optical feedback lasers can exhibit a chirped structure covering a large
continuous range of frequencies. These features can be used in various applications such as optical pumping, high
precision optical frequencies measurement and optical frequency domain ranging (OFDR). For the first time, a
broadband chirped frequency comb has been generated using a conventional DFB laser diode and an intracavity acoustooptic
modulator. The experimental factors that affect the comb characteristics of this compact and robust system have
been studied and quantified. The experimental results have also been compared with theoretical predictions and, in
general, there is good agreement. The FSF DFB has also been evaluated in a simple OFDR system.
The effects of optical feedback on the magnitude of the anticorrelation of polarization dynamics in vertical-cavity
surface-emitting lasers have been studied experimentally. We compare the effects of polarization-preserved and
polarization-selective optical feedback on the magnitude of the anti-correlation. The results show that in the case of the
polarization-preserved or orthogonal polarization optical feedback into the VCSEL a strong anti-correlation between
orthogonal polarizations can arise, however, no strong anticorrelation is observed for parallel polarization optical
feedback. The correlations in the spectral domain have also been investigated. It is found that the anticorrelation is strong
at low frequencies but poor at higher frequencies.
Anti-correlation polarization dynamics in vertical-cavity surface-emitting lasers with long external cavity has been
studied experimentally. The correlations are considered in the time domain and in the spectral domain. In the time
domain, with fixed optical feedback strength, the minimum cross-correlation coefficient exhibits exponential decay with
the bias current. With fixed bias current, strong anti-correlation can be achieved at a certain feedback ratio. In the
frequency domain, strong anti-correlation is obtained at frequencies lower than 1 GHz for all bias currents. Near the
relaxation oscillation frequency good correlation is found at higher bias current but poor correlation is found at lower
bias currents.
The dynamics of a semiconductor laser subject to polarization rotated (incoherent) optical feedback have been numerical and experimental investigated. The results show that the induced dynamics can be grouped into four regimes (stable, chaotic, pulsed and two-state) and they also show that the TM mode of the laser never lases, at least in the ring cavity configuration studied. In addition, unlike the earlier short cavity work, the boundaries between the regimes in the long cavity case were found to be independent of the external cavity delay time. By focussing on the effects induced by incoherent optical feedback from long external cavities we will show that four regimes of operation can be accessed by varying the external reflectivity. Calculated Lyapunov exponents and a bifurcation diagram clearly delineate these regimes and experimental verification of the transition from stable to chaotic dynamics will be described. The dynamical behaviour exhibited in each regime will be explained in terms of the memory effect introduced by the time delay associated with the external cavity and the natural relaxation oscillations of the solitary laser. It will also be shown that within the pulsed regime the pulse repetition rate is determined by the external reflectivity and injection current and is independent of the external cavity length.
Semiconductor lasers subject to optical feedback are of both scientific and technological importance. The laser and external mirror form a compound cavity which can be modeled using a coupled cavity approach. Using this approach we have calculated the longitudinal mode frequencies and the associated mode lifetimes of all the modes in the system. We have found that for a narrow range of external cavity reflectivities, the mode lifetimes become almost degenerate. In this regime the mode lifetimes become highly sensitive to variations in the refractive index of the laser and external cavity reflectivities. Close inspection of this regime has revealed ever finer detail, suggesting a fractal structure to the mode solutions. The calculations have been undertaken in the 'cold cavity' limit and indicate a catastrophic loss of mode discrimination, even in a system with no inherent material gain. In the short cavity limit the external reflectivity required to induce the loss of mode discrimination varies as a function of external cavity round-trip time.
Synchronized external-cavity diode lasers are used for chaotic optical communication. A 1 GHz message is encoded by current modulation of the chaotic transmitter laser and decoded by a synchronzied chaotic receiver laser diode. The effect of introducing the message by optical injection into the receiver laser instead of direct current modulation is then investigated. Finally, we show how the signal masking can be enhacned by the appropriate choice of external cavity length for a given message frequency.
The effects of optical feedback in edge-emitting semiconductor lasers and vertical cavity surface emitting lasers (VCSELs) have attracted considerable attention because the characteristics of both kind of lasers are very sensitive to the effects of reflected light. The phenomena arising in laser diodes subject to optical feedback can be classified according to operating five regimes conventionally identified as regimes I-V. Optical feedback also affects the noise properties of semiconductor lasers. There have been a number of investigations of the noise properties of semiconductor lasers and VCSELs subject to optical feedback. However, such work has been concerned with only some of the above-mentioned regimes of operation. A thorough experimental investigation of the effect of optical feedback in RIN of edge-emitting semiconductor lasers has yet to appear in the literature. In this paper, we present a detailed study of the effect of optical feedback on the average RIN of edge-emitting semiconductor lasers at different bias currents. An experimental study has been performed of the relative intensity noise (RIN) of a semiconductor laser in optical feedback regimes I to V. At low bias current, a low RIN is observed with low feedback feedback ratio, the RIN increased in the coherence collapse regime, then decreased again in regime V. The RIN in regime V is lower than that of the solitary laser. It is observed experimentally that an increase of the RIN occurs for intermediate levels of feedback. Such an increase in RIN appears to be related to enhanced intensity fluctuations. We will consider theoretical approaches to explaining the observed RIN characteristics.
A nearly single mode vertical cavity surface emitting laser (VCSEL) subject to optical injection have been investigated experimentally. It is found that regions of polarization-resolved chaotic behavior exist for both positive and negative detuning from the stable injection locking regime. Outside the chaos regimes, several nonlinear dynamical phenomena including frequency pushing, nearly degenerate four-wave mixing, injection locking, limit cycle and period doubling, were also observed.
Vertical cavity surface emitting lasers (VCSEL) exhibit self-pulsations in the polarization-resolved light output at certain bias currents, where the dominant polarization direction suffers a transition from one direction to its orthogonal direction. This pulsation in the polarization resolved output could be controlled by an external optical injection in a master-slave configuration with VCSEL used as slave laser. Experimentally it has been demonstrated that the stabilization linear polarization directions preferred in the solitary VCSEL. The exact frequency of the optical injection to effect stabilization is dependent on the injection power and polarization.
The relative intensity noise (RIN) of a semiconductor laser subject to optical feedback ahs been experimentally studied. At low bias current, a low RIN is observed with low feedback ration, the RIN increased in the coherence collapse regime (regime IV) and decreased in regime V. The RIN in regime V is lower than that of the solitary laser. The measurements are found to be in good qualitative and quantitative agreement with theoretical predictions. For higher bias current, a higher feedback ratio is needed for the semiconductor laser to transit from regime IV to V.
Two-transverse-mode vertical cavity surface emitting lasers (VCSELs) subject to external optical injection is experimentally investigated. The spectra of the VCSEL with two parallel-polarized modes, under optical injection, demonstrate significantly different behaviors, compared to the VCSEL with two orthogonally-polarized transverse modes. In a VCSEL with two orthogonally-polarized transverse modes, the experimental results are good qualitative agreement with the theoretical prediction that the external optical injection can be used to achieve single-mode operation. However, in the case of a two parallel-polarized transverse modes VCSEL, single-mode operation cannot be obtained via optical injection. When the injection frequency is close to one of the modes, the coexistence of the injected beam and the mode gives rise to very rich dynamical behavior, however, the other mode is unperturbed by the optical injection.
Chaotic synchronization is investigated using two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of an optical feedback in an external-cavity configuration. Changes in the spectrum of the synchronized system are shown to be associated with the transition between anticipating and lag synchronization.
Chaotic dynamics in a self-pulsating laser diode has been shown theoretically to occur by modulation of the laser current. It has been also shown that synchronization of two chaotic self-pulsating lasers can be achieved by small amounts of optical coupling. This result has been obtained with a deterministic model for the laser intensity. We study coherent synchronization of single mode self-pulsating laser diodes by means of a field-equation model that takes into account phase-effects and spontaneous emission noise. It is shown that the size of the coupling required to achieved synchronization is influenced by spontaneous emission noise and by the linewidth enhancement factor. Numerical simulations are then used to identify the optimum regime for efficient synchronization. It is found that good synchronization can be obtained for large values of the bias current, such that the spontaneous emission plays a minor role. The degree of synchronization is studied as a function of the differences between the master and slave laser parameters. Finally, a sinusoidal signal is used to analyze a chaotic communication system based on self-pulsating laser diodes.
Three diode lasers are used as message, transmitter and receive lasers. The message laser is amplitude modulated by a simple message and its output is optically coupled to the transmitter laser ensuring optical modulation of message. The transmitter laser is rendered chaotic by application of appropriate optical feedback. The receiver laser is used to decode the message. Effective signal masking is enhanced by the selection of an appropriate external cavity length, which could be a possible key for chaotic optical communication security.
This paper presents an overview of work undertaken and directed at the utilization of chaotic laser diodes in secure optical communications systems. Particular emphasis will be given to experimental work using external cavity laser diodes.
A multimode iterative scheme to model the dynamic and noise properties of semiconductor laser diodes is presented and results obtained for semiconductor lasers under continuous wave conditions.
An analysis is performed of the effects of strong optical feedback on the characteristics of single-transverse mode VCSELs. Consideration is given to the cases of short (1.5 cm) and long (15 cm) external cavities. When the laser is operated well above threshold in a short external cavity with high reflectivity, a strong dependence on the accumulated external cavity phase is observed. Stable operation is found for an optimum phase while for other values of the phase chaotic dynamics is observed. Such behavior is not seen near threshold where the laser output is stable for any accumulated phase. For the longer external cavity the influence of the phase term is found to be insignificant: chaotic behavior is seen in the output over a wide range of operating currents.
In this paper the possibility of controlling steady states in a model of an external cavity laser diode with optimized impulsive delayed feedback is demonstrated. An examination is made of the application of such feedback via modulation of the laser drive current. Account is taken of practical constraints arising from technical delay and the frequency in application of the control signal. It is demonstrated that control of both unstable periodic orbits and steady states is achievable in the fully developed coherence collapse regime with or without preliminary targeting.
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