External Cavity Round-trip Time Research Articles

Spatiotemporal complexity of chaos in a phase-conjugate feedback laser system

An 852 nm semiconductor laser is experimentally subjected to phase-conjugate time-delayed feedback achieved through four-wave mixing in a photorefractive ($ {{\rm BaTiO}_{3}} $BaTiO3) crystal. Permutation entropy (PE) is used to uncover distinctive temporal signatures corresponding to the sub-harmonics of the round-trip time and the relaxation oscillations. Complex spatiotemporal outputs with high PE mostly upwards of $ \sim 0.85 $∼0.85 and chaos bandwidth (BW) up to $ \sim 31\;{\rm GHz} $∼31GHz are observed over feedback strengths up to 7%. The low-feedback region counterintuitively exhibits spatiotemporal reorganization, and the variation in the chaos BW is restricted within a small range of 1.66 GHz, marking the transition between the dynamics driven by the relaxation oscillations and the external cavity round-trip time. The immunity of the chaos BW and the complexity against such spatiotemporal reorganization show promise as an excellent candidate for secure communication applications.

Optimization of Timing Jitter Reduction by Optical Feedback for a Passively Mode-Locked Laser

We investigate the effect of optical self-feedback on the timing jitter of a passively mode-locked (ML) laser and compare the von Linde method with two pure time domain methods for calculating the timing jitter of such a system. We find that all three methods yield the same dependence of the timing jitter on the external cavity roundtrip time (delay time). Of these methods, the so-called long term jitter method is significantly less computationally expensive. We therefore use this method to investigate the influence of the delay time, feedback strength, and amplitude-phase coupling on the timing jitter. Our results show that, with vanishing amplitude-phase coupling, greater timing jitter reduction can be achieved with long delay times and larger feedback strengths, when feedback is near resonance. Off resonance, the timing jitter is increased. Non-vanishing amplitude-phase coupling can lead to destabilized pulse stream, even at the feedback main resonances.

Nonlinear dynamics and synchronization of an array of single mode laser diodes in external cavity subject to current modulation

We study the dynamics of an array of single mode laser diodes subject to filtered feedback provided by an external reflection grating. Our numerical simulations show that by modulating the injection current the array can be phase synchronized leading to high power coherent emission. The output peak power density can be varied by tuning the modulation frequency and can be resonantly enhanced once the frequency matches the inverse of external cavity round trip time and mode-locking behavior is realized. Both non-resonant and resonant injection current modulation results in an excellent degree of phase synchronization and coherence at certain modulation amplitudes and frequencies that is manifested by coherent enhancement of far-field optical intensity.

Extreme intensity pulses in a semiconductor laser with a short external cavity

We present a numerical study of the pulses displayed by a semiconductor laser with optical feedback in the short-cavity regime, such that the external cavity round-trip time is shorter than the laser relaxation oscillation period. For certain parameters there are occasional pulses, which are high enough to be considered extreme events. We characterize the bifurcation scenario that gives rise to such extreme pulses and study the influence of noise. We demonstrate intermittency when the extreme pulses appear and hysteresis when the attractor that sustains these pulses is destroyed. We also show that this scenario is robust under the inclusion of noise.

In-depth analysis of injection-seeded long external cavity InGaN/GaN surface-emitting laser

Optically pumped InGaN/GaN quantum well (QW) vertical-external-cavity surface-emitting laser operating at 420 nm wavelength with external cavity length of up to 50 mm has been realized. Use of injection seeding enables us to reach lasing operation even for pump pulse duration just slightly exceeding the external cavity roundtrip time. The carrier lifetime in the QWs was measured to be 2.5 ns, and lasing emission was obtained under pump pulses shorter (400 ps) or longer (10 ns) than the carrier lifetime in QWs. We studied experimentally the dependence of the lasing threshold on the length of external cavity and provided a model to explain this dependence. Further detailed measurements of the near field and far field patterns, optical spectrum, spontaneous emission factor, and delay time to emission of the lasing pulse confirm lasing at the external cavity mode.

Can Fixed Time Delay Signature be Concealed in Chaotic Semiconductor Laser With Optical Feedback?

External-cavity lasers are usually used for chaos encryption in optical chaos-based communication systems. The external-cavity round-trip time (the time delay in the laser dynamics) is often regarded as an additional key to encode messages, which is a critical security parameter. The feasibility of identifying the time delay has been a crucial issue in chaotic optical communication. Some researchers propose that the time delay can be hidden by modulating the value of feedback strength or increasing the number of feedback cavities. In this paper, we experimentally and numerically demonstrate that the time delay signatures cannot be concealed in optical feedback semiconductor lasers. Whether single or double optical feedback, the time delay signatures can all be identified by the power spectrum analysis method. Furthermore, adjusting the feedback strength, the pumping current and the time-delay value, we find that the extraction of the time delay signatures still cannot be influenced.

Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser

Random bit generators (RBGs) are important in many aspects of statistical physics and crucial in Monte-Carlo simulations, stochastic modeling and quantum cryptography. The quality of a RBG is measured by the unpredictability of the bit string it produces and the speed at which the truly random bits can be generated. Deterministic algorithms generate pseudo-random numbers at high data rates as they are only limited by electronic hardware speed, but their unpredictability is limited by the very nature of their deterministic origin. It is widely accepted that the core of any true RBG must be an intrinsically non-deterministic physical process, e.g. measuring thermal noise from a resistor. Owing to low signal levels, such systems are highly susceptible to bias, introduced by amplification, and to small nonrandom external perturbations resulting in a limited generation rate, typically less than 100M bit/s. We present a physical random bit generator, based on a chaotic semiconductor laser, having delayed optical feedback, which operates reliably at rates up to 300Gbit/s. The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.

Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback

Numerical and experimental results are presented for an edge-emitting diode laser with delayed optical feedback, where the polarization state of the feedback is rotated such that the natural laser mode is coupled into the orthogonal, unsupported mode. We examine the bifurcation structure and dynamics that give rise to a class of periodic, polarization-modulated solutions, the simplest of which is a square wave solution with a period related to but longer than twice the external cavity roundtrip time. Such solutions typically emerge when the feedback is strong and the differential losses in the normally unsupported polarization mode are small. We also observe more complex waveforms that maintain the same periodicity.

Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View

A critical issue in optical chaos-based communications is the possibility to identify the parameters of the chaotic emitter and, hence, to break the security. In this paper, we study theoretically the identification of a chaotic emitter that consists of a semiconductor laser with an optical feedback. The identification of a critical security parameter, the external-cavity round-trip time (the time delay in the laser dynamics), is performed using both the auto-correlation function and delayed mutual information methods applied to the chaotic time-series. The influence on the time-delay identification of the experimentally tunable parameters, i.e., the feedback rate, the pumping current, and the time-delay value, is carefully studied. We show that difficult time-delay-identification scenarios strongly depend on the time-scales of the system dynamics as it undergoes a route to chaos, in particular on how close the relaxation oscillation period is from the external-cavity round-trip time.

Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback

We experimentally study the polarization dynamics in the multi-transverse-mode regime of a vertical-cavity surface-emitting laser under isotropic optical feedback. Simultaneous measurements of orthogonally polarized states are conducted for both the total output and several spatial positions on the beam pattern. When the total output is detected, both slow and fast fluctuations of the two orthogonally polarized states are anticorrelated. For a chosen spatial position, slow fluctuations of the two polarizations are anticorrelated; fast fluctuations at the time scale of the external cavity round-trip time do not show fixed correlation properties when transverse modes have similar strengths.

Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback

Based on the SFM model [M. San Miguel, Q. Feng, J.V. Moloney, Phys. Rev. A. 52 (1995) 1728.], complete chaotic synchronization characteristics of linear-polarization (LP) Mode of the vertical-cavity surface-emitting semiconductor lasers (VCSELs) with isotropic optical feedback are numerically investigated. When the propagation time τc of light from the transmitter to the receiver equals to the external cavity round-trip time τ, and the central frequency of the T_VCSEL matches that of the R_VCSEL, in large scale region of the feedback coefficient and the injection current where the x-polarization mode as well as the y-polarization mode obtains high synchronization quality at the same time. However, in the central frequency mismatch regions where the x- and y-polarization mode can obtain inferior synchronization quality at same time. But for τc≠τ, each LP mode of the mixed polarization modes achieved inferior synchronization quality at the same time. Besides, with big enough injection current, the output of the system with the same central frequency in two lasers is entirely governed by the y-polarization mode when the feedback coefficient and Δτ(=τc−τ) fixed at a certain value. So the system can realize steadily good synchronization of the completely dominant y-polarization mode. But the synchronization quality of the completely dominated y-polarization mode can be deteriorated by increasing absolute frequency detuning value. Besides, in positive frequency mismatch regions where the influence of the same frequency detuning value on the synchronization quality of the entirely governed y-polarization mode becomes smaller than in negative frequency detuning regions. At last, when τ is given and the central frequency of the T_VCSEL matches that of the R_VCSEL, the influence of the τc is not a simple time-shift in the time-evolution of the receiver VCSEL, which has serious influence on the complete synchronization quality of each LP mode.

Vectorial chaotic synchronization characteristics of unidrectionally coupled and injected vertical-cavity surface-emitting lasers based on optical feedback

Based on the Spin Flip Model (SFM), vectorial chaotic synchronization characteristics of vertical-cavity surface-emitting semiconductor lasers (VCSELs) with isotropic optical feedback is numerically investigated. The results are as follows. First, when the external cavity round-trip time equals the propagation time of light from the transmitter to the receiver, both the x-linear polarization (LP) mode and the y-LP mode can realize very high complete synchronization. Second, when external cavity round-trip time is not equal to the propagation time and μ is near the lasing threshold, the better completely synchronized quality of the dominant y-LP mode can be temporarily achieved. In comparison, the governing x-LP mode can only realized poor synchronization quality. In addition, with the system governed by the mixed LP modes, each LP mode can obtain inferior synchronization quality. However, with injection current much greater than the threshold current, the completely governed y-LP mode can steadily achieve the best chaotic synchronization quality. At last, each LP mode of the injection can achieve good injection-locking synchronization with that of the receiver. While each dominant LP mode can obtaine poorer injection-locking synchronization quality than the corresponding suppressed LP mode, with equal power, two LP modes both can achieve almost identical high injection-locking synchronization quality. Namely, the LP state with less power can be obtain better injection-locking synchronization.

Combination of two basic types of synchronization in a coupled semiconductor laser system

Combination of two basic types of synchronization, anticipatory synchronization and lagged synchronization, is investigated numerically between two coupled semiconductor lasers. It is found that lagged synchronization produced by a backward coupling with a suitable delay can combine with the originally hidden anticipatory synchronization and produce a type of synchronization overcoming the original lagged synchronization produced by a forward coupling. We study the combination synchronization phenomenon when the delay of the backward coupling is different from that of the original anticipatory synchronization. Our results suggest that the synchronization combination phenomenon might allow an interpretation of an experimental observation by Sivaprakasam et al. [Phys. Rev. Lett. 87, 154101 (2001)] that the anticipating time is irrespective of the external-cavity round trip time, which to date remains to be understood.

Hilbert phase analysis of the dynamics of a semiconductor laser with optical feedback.

The nonlinear dynamics of a semiconductor laser with an optical feedback is studied using Hilbert phase analysis, which reveals interesting facets of the nonlinear dynamical behavior, including the formation and interaction of external cavity modes with increasing external feedback. Here we report measurements on two illustrative cases with very different dynamics; the laser is first biased just near threshold, and then far above threshold. We observe 2pi phase jumps at intervals that are multiples of the external cavity round-trip time, indicating the interaction and transfer of energy between external cavity modes.

Experimental Demonstration of Anticipating Synchronization in Chaotic Semiconductor Lasers with Optical Feedback

We report the first experimental observation of anticipating chaotic synchronization in an optical system 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. It is found that the anticipation time does not depend on the external-cavity round trip time of the transmitter.

Modulation detuning characteristics of actively mode-locked diode lasers

Existing frequency domain models for the active mode locking of diode lasers are appropriate for antireflection- (AR-) coated devices. This paper presents the first frequency domain model for non-AR-coated devices. The use of uncoated devices permits the independent measurement of all of the important laser parameters required for the model, so that no adjustable parameters are needed. An additional novel feature of this model is that the effect of gain saturation on the exact shape of the gain waveform is allowed for in a completely self-consistent fashion. Experimental studies were carried out on uncoated undegraded commerical laser diodes. Threshold reductions of 25-30 percent were achieved for external cavity operation. The mode-locking studies reported in this paper were carried out above the external threshold current, with a sinusoidal modulation near 1 GHz at a modulation index of 4 percent. The results of these studies showed good agreement with the predictions of the model presented here, in contrast with the predictions of the existing models. Specifically, the modulation frequency corresponding to the shortest most intense mode-locked pulses was found to occur at a fraction of 1 percent below the frequency matched to the external cavity roundtrip time. As well, the predicted effects of gain saturation were observed in the detailed structure of the mode-locked pulses, and in their detuning characteristics.

Microwave self-modulation of a diode laser coupled to an external cavity

An external cavity coupled to a conventional Fabry-Perot GaAs diode laser operating continuously has been found to cause modulation of the light output at a frequency within the range 0.5 to several GHz. The modulation depth is close to 100 percent and the linewidth can be made as narrow as 180 kHz. The modulation is thought to be stimulated by the intensity noise fluctuations, which peak at the well-known spiking frequency f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> . The oscillations are strongly enhanced by a frequency locking action of the external cavity, being efficient when the external cavity round-trip time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2L/c</tex> , or a multiple thereof, corresponds to the inverse of the spiking frequency. Since the latter is dependent on both pump current and temperature, the system can simply be tuned by adjusting the pump current. For a fixed resonator length, the narrow-band oscillations occur in a small current range, in which an increase in frequency with increasing current at a rate of 400 kHz/mA is observed. A small-signal analysis based on simple rate equations shows the influence of the external cavity on the intrinsic resonance frequency f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> . It demonstrates that self-modulation can only occur for small values of the coupling coefficient ε between the laser diode and the external cavity.