This reports out studies of dynamics and bifurcation in a NH3 laser using Zeghlach-Mandel model. We analyse theoretically dynamics stability of the laser in the three stable state using the eigenvalue equation, and give numerical discussions of dynamics stability of the laser in the three stable state using the eigenvalue. We find that there is the exponential contraction of the phase space volume element of the laser. The dynamical evolvement starting at a stable state through a periodic bifurcation to chaos is analyzed via the bifurcation diagram to give a path to chaos through quasi-periodic bifurcation scenario with different starting values. Numerical bifurcation diagram exhibits quasi-periodic bifurcation from a stable state by adjusting the pump rates. It can be clearly found that the laser moves around its unmovement points and is eventually attracted to one of the points, and it is sensitive to the initial value. The chaotic region and quasi-periodic bifurcation region are found. The movement orbits of a stationary state, quasi-period, and chaos are numerically exhibited to show rich nonlinear dynamic behaviors. The laser gives an important value to study laser systems, chaotic optics emitters, random optics signal generators, precision optics measuring devices, and optic encoding communications.
This paper reports our studies of a novel erbium-doped (ED) fiber inter-coupling three-ring laser (TR-L) system, where three ED fiber single-ring lasers are inter-coupled by three couplers to form this kind of laser. Thereout, our work establishes the laser physical theory of the TR-L system, and studies its bifurcation behavior in detail. The dynamical behavior evolving from a steady behavior through a double-period to a chaotic behavior is introduced via phase parametrization to reveal a path to some chaotic behaviors from double-period to pass through some quasi-periodic bifurcations by shifting one parameter of the laser. Numerical phase-parametric diagrams exhibit quasi-period bifurcation via adjusting the pump strength or the ring coupling levels. The chaotic region and quasi-period bifurcation region are found. Period-one, quasi-period, and chaos are numerically presented to show rich nonlinear dynamic phenomena. The fiber laser gives an important value to study laser systems, chaotic optics emitters, random optics signal generators, measuring devices, and encoding communications.
The paper presents a synchronization theory of series laser link consisted of three kinds of erbium-doped fiber ring lasers. Firstly, we present a synchronization equation of an erbium-doped fiber three-ring laser synchronizing with an erbiumdoped fiber dual-ring laser while a steady synchronization can realize between this two lasers when real parts of all eigenvalues are negative values. Secondly, we present another synchronization equation of the erbium-doped fiber dualring laser synchronizing with another erbium-doped fiber single-ring laser while a steady synchronization can realize between this two lasers when real parts of all eigenvalues are negative values. Moreover, a synchronization theory of the series laser link is proven by this two sets of synchronization equations. Our numerical result indicates that the series synchronization laser link are obtained in a chaotic dynamical state, a dual-cycle dynamical state, and a four-cycle dynamical state in three cases. We find that dynamics of the series laser synchronization link can be induced to all kinds of dynamical behaviors by adjusting the pump levels. The series laser link synchronization theory can be used as an important reference for laser secure communication, neural network, and optical network.
KEYWORDS: Fiber lasers, Telecommunications, Ring lasers, Data transmission, Information security, Receivers, Laser systems engineering, Laser applications, Analog electronics, Laser communications
The paper give our study of a hyperchaotic synchronization erbium-doped fiber laser secure communication system with dual-channel secure transmission performance, its encoding and decoding. First, we present a signal transmission synchronization scheme, where a signal from one of a hyperchaotic erbium-doped fiber three-ring laser as an emitter transmits to an erbium-doped fiber dual-ring laser as a receiver while the emitter can synchronize with the receiver by anti-phase control technique. Second, we give an encoded signal secure transmission scheme, where two signals from two ring of a hyperchaotic erbium-doped fiber three-ring laser mask two information signals, respectively, transmit to two terminals of the receiver with an erbium-doped fiber dual-ring laser to perform two encoded signal secure transmissions in two channels. Third, we give a decoding scheme, where two carrier signals from two channels subtract two signals from two ring of an erbium-doped fiber dual-ring laser to result in decoding realizing. Then, such hyperchaotic encoding secure communication laser system can perform on dual-channel secure encoding transmission and enhance the security of classified information signals. Our numerical result indicates that the hyperchaotic secure communication laser system can perform on dual-channel secure encoding transmission, and succeed decoding in dual-channel. The hyperchaotic secure communication laser system has an important reference for people’s study of optics chaos secure communication, multi-channel secure transmission, encoding and decoding.
The paper studies a novel laser network link and presents a novel erbium-doped fiber three-ring laser dynamic system as a network link emitter while an erbium-doped fiber dual-ring laser and an erbium-doped fiber single-ring laser are used as two nodes of the link. Then we introduce a physical optic model of a series synchronization network link guided by the three-ring laser and the link’s nodes with the dual-ring laser and the single-ring laser. We discuss how the emitter laser guides the dual-ring laser and the single-ring laser to obtain a series synchronization to form the series synchronization laser network link. In order to build the series synchronization network link, we use an anti-phase optic injection control technology to postulate the following ideas: the two rings of the three-ring laser obtain two synchronizations with the two rings of an erbium-doped fiber dual-ring laser, while the other ring acquires synchronization with another erbium-doped fiber single-ring laser. Such series synchronization network link is formed through optic connection and network technology. Moreover, a series synchronization network link is proven theoretically by two sets of synchronization equations. Our numerical results indicate the hyperchaotic series network synchronization. The proposed laser system and laser synchronization link can serve as a reference in the study of laser dynamic systems, secure communications, neural networks, and optical networks.
The paper studies on a novel erbium-doped fiber three-ring laser dynamic system as a chaotic or hyperchaotic laser emitter via “three coupled-rings” in depth. We prove theoretically the bi-stability and the twin-scroll strange attractor scenarios in the three-ring laser in mathematics, such as the dynamic behavior of the laser system may move around the two stable points to form the twin-scroll strange attractor of chaos under certain conditions. The evolution from a quasi-period state to chaos is further discussed via phase parametrization to exhibit a route to hyper chaos from period-doubling through a bifurcation scenario by varying one parameter value of the laser. Our numerical result indicates the infrequent existence of hyper chaos with five positive Lyapunov exponents, and which is a very rare. Finally, the quasi-periodic, chaotic and hyperchaotic regions are numerically demonstrated by the three positive Lyapunov exponents varying with the pump and gain. The fiber laser has an important value to study laser dynamic systems, secure communications, random signal generators, radars, and measuring devices.
We present a two-type modulation method and study how to produce chaos and quasi-period in an erbium-doped fiber laser, as well as give a 2-level laser physical model including a digital photo attenuator controlling of lasing photon, and a modulator shifting the pumping. The laser appears chaos and some quasi-cycle when the pump of the laser is modulated and the digital modulation is operated to absorb lasing photon using the digital photon attenuator. We illustrate a route to chaos by altering the pump modulation levels and the absorption levels of the digital photon attenuator while a cycle, a three-cycle, a four-cycle, and other quasi-cycle and chaos show in the laser. We analyze the effect of the levels of the photon attenuation and the pump modulation setting in other values on dynamical behaviour of the laser, and give a route away from chaos while a quasi-cycle movement and chaos are found. And we find the threecycle distribution and chaos distribution via adjusting the absorption and modulation levels and frequencies. We find that the absorption modulation levels and frequencies lead to the dynamics behaviour of the laser. Our results have certain reference value to laser optics, and chaos.
This paper studies a dual-optoelectronic delay cross feedback dynamic control technology to how to obtain control-chaos of two coupled lasers. The dynamic control scheme is designed out: Step one, two photo-converters transform two lasing from two lasers into two photocurrents; Step two, the photocurrents are delayed to cross feedback to two lasers respectively to control two chaotic behaviors of two lasers so that two laser’s dynamic variations are dynamical guided. Step three, the dynamic control technology is performed on the two lasers to shift a controlled dynamic state to another controlled dynamic state, such as chaos in two coupled lasers having been dynamical guided to different stable-states, or laser one shifting from a controlled cycle-three state to a controlled stable state while another laser shifting from a controlled cycle-five state to a controlled stable state. We find that it takes different time for the control-chaos time of chaos being stabilized to a controlled state in different performing time. The physical mechanism is found that controlchaos is very sensitive not only to the two feedback level parameters, but also to the two delayed time parameters. Our results have certain reference value for the study of laser, optics, control science and chaos.
Two spatial coupled different lasers with different parameters are studied and their physical model is presented while the two coupled lasers are very interested to show a great nonlinear dynamical variety using bifurcation diagrams of the two lasers. We study dynamics and focus on bifurcation of the two coupled lasers. We show how the bifurcation of the two lasers to vary as the main parameter shift while a route to chaos from bifurcation can be analyzed by varying one parameter of the two lasers, and we analyze what kind of effects of the coupling factor, the current, the photon loss rate, the linewidth enhancement factor and the frequency detuning on dynamics behaviors of the two lasers. Presented bifurcation diagrams show all processes of bifurcation, passing stabilization to period-doubling, unstabilization, chaos, quasi-period. We discuss how the two lasers becoming to go away from chaos to evolve to a stably-state via varying one parameter of the two lasers, such as the lasers becomes of going away from chaos to follow a route to a period-doubling after a quasi-period and a period-tripling. And we point out bifurcation point and find a stable region, a periodic region, a double-periodic region, quasi-periodic region, an unstable region, a chaotic region. The obtained result is of great significance to study laser dynamics, nonlinear optics, chaos of coupled lasers, and ultra-wideband signal generator.
The synchronization of complex dynamic systems is a hot topic in scientific research. Thus, this paper focuses on the synchronization of two different laser systems and studies the multiple-dynamics behavior of two coupling lasers synchronizing with that of another laser, and present a physical model of the multiple-dynamics synchronization. Two routes to chaos after bifurcation from two stable states are illustrated by controlling one current of the two coupling lasers while the two coupling lasers are found to produce great nonlinear dynamics behaviors via their bifurcation diagrams. And this paper discusses the detailedly multiple-dynamics distribution of the two coupling lasers, where there is a stable-state region, a single-period region, a quasi-period region, and a chaotic region. Our work performs how multiple-dynamics of the two coupling lasers synchronize with that of another laser by controlling one current of the two coupling lasers. Then, multiple dynamics behaviors of the two coupling lasers synchronizations are obtained with that of another laser, such as a single-period synchronization, a period-doubling synchronization, a period-4 synchronization, a period-5 synchronization, other quasi-period synchronization, and a chaotic synchronization. The obtained results are of great significance to study laser physics, optics, synchronizations of two optical dynamic systems, a chaotic laser, and its application.
Alternant-channel chaotic laser secure communication system and its chaos alternant coding (CAC) are presented and deeply studied via two coupled lasers synchronizing or desynchronizing with another single laser. The coupled lasers are used as two chaotic transmitters and transmit two chaotic carriers to mask two information signals, respectively. One conventional encoding scheme is that the single laser is used as a receiver and obtain synchronization with one of two chaotic transmitters for chaos decoding. And another CAC scheme as a non-conventional coding is presented and its coding principle is defined for secure communication. CAC coding and scheme is that one laser of chaotic transmitters transmits a chaotic carrier to mask an information signal, where the carrier is modulated by an information signal, while the decoding of CAC is performed via synchronization or de-synchronization between another laser of two chaotic transmitters and a receiver. A physical model of the synchronous system is presented using a drive-feedback technique while a chaotic synchronization is obtained between a chaotic transmitter and a receiver. And alternant-channel chaotic secure communication and CAC are successfully implemented while a novel CAC technique is validated. The system has the characteristics of high dimension, many degrees of freedom in phase-space, a high degree of nonlinearity, a nonconventional CAC, and many secret keys. So it has high security and can transmit securely two chaotic carries masking two information signals, respectively.
The characteristics of bi-periodic sensitivity of semiconductor laser and its application in the incoherent light detection sensor are studied. From the simulation results, it can be found that the unmoving point of an optoelectronic time-delay feedback semiconductor laser shifts when there is external light injection, two unmoving points are conduced to show, and implies high instability dynamics existing in the system. So the external light injection will inevitably result in destructing the referent laser state condition and changing the state, thus the incoherent light intensity change can be monitored via detecting the referent state change. In this paper, a bi-periodic optical pulse is generated by the optoelectronic time-delay feedback semiconductor laser, and the bi-periodic laser system is used as a sensor for incoherent light detection. A bi-periodic state in the laser is a highly unstable nonlinear dynamic state, it is very sensitive to external conditions and influences. When a beam of external incoherent light enters into the bi-periodic laser sensor, it will inevitably lead to the destruction of the bi-periodic state condition and the state variation. A novel bi-periodic laser incoherent light detection sensor is proposed based on the above principle. By using this sensor, the injected incoherent light can be used as the sensor's recognition signal, and by detecting the change of the laser output behavior, the external incoherent light intensity can be measured. The simulation results show that the sensor has high ability to recognize the injected incoherent light and can measure it accurately. The results of the proposed sensor are quite useful for the research of new laser sensor and application of photoelectric detection technology
We introduce some physical optical effects into a laser to construct a novel laser system. Using a twisted fiber as an optical delay feedback external cavity based on birefringence of twisted fiber, we present a novel delay feedback semiconductor laser system with the twisted fiber effect and establish its physical model, in which the effect of the twisted fiber birefringence is included to lead to dynamics in the laser system. We give linear analysis of stability of the influences of delayed phase and rotation angle of twisted fiber on the oscillation characteristics and behavior of the laser. And we give quantitative analysis of both delayed phase and rotation angle, which resulted from the physical effect of twisted fiber, and analyze to how to alter the relaxation oscillation or dynamics state. Because the twisted fiber can change the direction of light polarization and produce phase shift after light passing through the twisted fiber, the laser system is sensitive to phase change and polarization while some dynamic changes of the laser can be caused and excited. We discovery theoretical that the delayed phase and the rotation angle resulted from the twisted fiber can alter the relaxation oscillation and dynamics state. And the fiber parameter’s variety can shift the delayed phase, the rotation angle, the delayed time, and the optical feedback level, so the laser’s behavior will vary. We find that the scaling of the transmitting time-delay of fiber and the laser internal timescale creates an incorporation to induce various dynamical scenarios.
We study control-chaos of a dual-ring erbium-doped fiber laser using an anti-parameter pair modulation. And we study this control-chaos method via the inverse modulation of the gain parameters of two key physical parameters of the dualring erbium-doped fiber laser. In terms of physical mechanism, the optical effects of alternating excitation or alternating attenuation of two gain parameters of the laser are found. The control of chaos laser and its new nonlinear dynamic changes are derived. In the control mechanism, the double-parameter reverse modulation pair is found where the laser behavior is very sensitive to the anti-parameter pair modulation because this reverse action modulation combines with induction control dynamic changes. The laser can be controlled to a single-periodic state, a double-periodic state, a threeperiodic state, a four-periodic state, a five-periodic state, a six-periodic state, a seven-periodic state and other highperiodic states. Double-dynamics, frequency controlled-locking and semi-frequency controlled-locking regions are found. The laser exhibits a very imaginative dynamic behavior that has never been seen before, which has important reference value for the study of chaos dynamics, laser technology and control technology.
Erbium-doped fiber laser as a novel light source and optical amplifier has been widely used in optical fiber communications and optical fiber sensors. Erbium-doped fiber lasers have attracted much attentions for their unique dynamic behaviors and applications. The nonlinear dynamic behavior of a short cavity erbium-doped fiber laser is studied in this paper. The idea of additional degrees of freedom is used to simplify the laser mode to study the dynamics of erbium-doped fiber laser. The three-level mode of the laser is simplified to a two-level mode, and a dynamic physical model of erbium-doped fiber laser is established by using pump periodic excitation. The laser can generate periodic pulses and chaotic pulses when a periodic signal of square wave as a periodic pulse is exciting the pump. The periodic pulsation, quasi-periodic behavior and chaotic behavior of laser under the various conditions are analyzed. It is found that the pump excitation level and its frequency are the main factors that determines the nonlinear dynamics of the laser, and the changes of pump excitation level and frequency will change the dynamic behavior of the laser. The effects of pump intensity, erbium doping concentration and photon lifetime on the dynamics behavior of laser are also discussed. When a large number of numerical calculations and simulations are operated, it is found that the quasi-periodic region and chaotic region are determined by the pump excitation level and frequency. The results have important reference value for erbium-doped fiber laser and laser technology and laser chaos application.
A method of dual-parameter control chaos in a dual-ring erbium-doped fiber laser is studied via stimulating dual-pump.
And a chaos-control physical model is presented via considering the dual-parameter control technology and the laser
structure characteristics. Dual-signal of periodic mutation as control signal is used to modulate to stimulate the two-pump
to obtain chaos-control or pressure chaotic oscillation using same amplitude, same frequency, different amplitude
or different frequency. A chaotic dual-ring erbium-doped fiber laser can be controlled to single-cycle, two-cycle, three-cycle,
four-cycle and other multi-cycle. Low-cycle orbits are controlled to show in laser under the case of same
amplitude and same frequency. High-cycle orbits are controlled to show in laser under the case of different amplitude or
different frequency. Multi-cycle belt under the case of same amplitude and different frequency, controlled-frequency-locking
region under the case of same amplitude and low frequency and controlled-semi-frequency-locking region under
the case of same amplitude and high frequency are found. The results are helpful to the research of laser chaos and
application of fiber laser.
Modulation response characteristics of a semiconductor laser with a phase-conjugate feedback mirror is studied. Modulation response equations about the amplitude and frequency chirping of the laser are deduced in detail. It is demonstrated that the amplitude and frequency chirping responses are the function of the modulation angular frequency, optical feedback level, and delayed time. Numerical results illustrate that the amplitude response and modulation bandwidth of the laser are larger than that of the solitary laser when the optical amplitude reflectivity is <0.0022. When the optical amplitude reflectivity is increased further, the peaks of the amplitude response of the laser show periodic variability while the modulation angular frequency at the maximal value of the amplitude response is added; however, the frequency chirping can be enlarged or reduced. The large drive current or the large detuning can enhance the modulation response and frequency chirping.
We focus the effect of stimulated-Raman-scattering (SRS) on modulation instability (MI)
in anomalous-dispersion regime of optical fiber from extended nonlinear Schrödinger equation. An
expression of the gain of MI is given and the ranges and the growth of the gain spectrum are
theoretically and numerically analyzed under considering SRS or neglecting SRS. The gain peak is also
theoretically demonstrated. The effect of SRS on the frequency spectrum of MI is few when incident
power is small. And incident power increases, the spectrum varies obviously, the range and the growth
of the gain is lower if considering SRS than that of the gain if neglecting SRS. We also find that the
maximum incident power will be limited by the fourth-order dispersion and will be enlarged by SRS to
an extent.
Chaotic synchronization in injection semiconductor lasers with optical feedback applied to optical secure communications is presented. The two chaotic systems can be synchronized with a gradually process to gradually steady in full space. Synchronous transient response to a pulse of injecting light is studied. Influences of the white noise on the synchronous error, and the synchronous characteristic with optical feedback are studied in detail. Chaos masking with a sinusoidal frequency of 6GHz signal and chaotic injecting shift keying (CISK) in the system are numerically simulated in optical secure communications. The both systems show a good ability of robust security and anti-uncover.
Laser chaotic synchronization of injection-locked semiconductor lasers with a message signal is studied in this paper, the error formula and the encoding formula are presented. Chaotic cryptography communication with the systems has been numerically simulated.
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