Free-running Vertical-cavity Surface-emitting Laser Research Articles

Phase stability diagram, self-similar structures, and multistability in a free-running VCSEL with a small misalignment between the phase and amplitude anisotropies.

We report on the global dynamics of a free-running vertical-cavity surface-emitting laser (VCSEL) with misalignment between the linear phase and amplitude anisotropies due to the fact that this case might occur in practice caused unintentionally by minor manufacturing variations or design, in virtue of high-resolution phase stability diagrams, where two kinds of self-similar structures are revealed. Of interest is that the Arnold tongue cascades covered by multiple distinct periodicities are discovered for the first time in several scenarios specified in the free-running VCSEL, to the best of our knowledge. Additionally, we also uncover the existence of multistability through the basin of the attraction, as well as the eyes of anti-chaos and periodicity characterized by fractal. The findings may shed new light on interesting polarization dynamics of VCSELs, and also open the possibility to detect the above-mentioned structures experimentally and develop some potential applications.

Non-quantum chiral structure in a free-running VCSEL.

We report on the occurrence of a non-quantum chiral structure in a free-running vertical-cavity surface-emitting laser (VCSEL) with a small misalignment between birefringence and dichroism. Through high-resolution phase diagrams, we show how oscillations evolve in parameter space for different values of the misalignment. Unlike a previously reported non-quantum chiral dynamic system involving closed rings in parameter space, this work manifests another case, i.e., the chiral structure exists in some open parameter spaces. Furthermore, the possible underlying physical mechanism of the emergence of the structures is offered through bifurcation analysis.

Sub-40 GHz Broadband Polarization Chaos Generation Using Mutually Coupled Free-Running VCSELs

We propose a simple method to generate broadband polarization chaos using two mutually coupled free-running vertical-cavity surface-emitting lasers (VCSELs). Specifically, we quantitatively investigate the effect of critical external parameters (bias current, frequency detuning and coupling coefficient) on the polarization chaos bandwidth in the scenarios of parallel injection and orthogonal injection, and reveal the physical mechanism of bandwidth enhancement in two scenarios. Final simulation results show that the bandwidth of chaotic signals obtained from parallel and orthogonal injection can reach 35.15 GHz and 32.96 GHz, respectively.

Simultaneous self-injection locking of two VCSELs to a single whispering-gallery-mode microcavity.

Simultaneous self-injection locking of two vertical-cavity surface-emitting lasers (VCSELs) to a single whispering-gallery-mode (WGM) microcavity is experimentally demonstrated. The linewidths of the two VCSELs are compressed from 3.5 MHz and 5 MHz to 20.9 kHz and 24.1 kHz, which is on the same order of magnitude as that of locking each VCSEL to the microcavity separately. Moreover, the frequency noises of the two simultaneously locked VCSELs are suppressed by more than 60 dB below the offset frequency of 100 kHz compared to that of the free-running VCSELs. The method demonstrated here might be used in the multi-wavelength laser array with low phase and frequency noises, especially the VCSELs with the unique architecture of a two-dimensional array.

VCSEL-Based Optical Frequency Combs Expansion Induced by Polarized Optical Injection

The present theoretical work studies optical frequency combs (OFCs) associated with both linear polarizations of a gain switching vertical-cavity surface-emitting laser (VCSEL) subject to optical injection of arbitrary polarization. The overall OFC, formed by the two orthogonally polarized sub-combs, can have an expanded optical span in agreement with experiments reported by Prior et al. We show that the maximum optical span is obtained for a certain angle between the linearly polarized optical injection and the direction of emission of the main mode of the free-running VCSEL. We find that this angle decreases as the injection strength increases. We also characterize the maximum expansion of the optical span of the overall comb. For VCSELs with large birefringence splitting the maximum expansion is the optical span of the free-running OFC, while for small birefringence splitting VCSELs the maximum expansion is the value of the birefringence splitting.

Chaos-based image encryption using vertical-cavity surface-emitting lasers

We study the encryption and decryption processes of color images using the synchronization of polarization dynamics in a free-running vertical-cavity surface-emitting laser (VCSEL). Here, we consider a bidirectional master-slave configuration or two-way coupling with two VCSELs. The latter are shown to exhibit hyperchaos and synchronization with a high level of similarity between their emission characteristics. The coupled VCSELs are then used as a transmitter and a receiver for the communication of image or data. Furthermore, we propose a modified chaos-based image encryption algorithm using the pixel- and bit-level permutations which provides robust, faster and simpler encryption/decryption compared to many other chaos-based cryptosystems. The performances of the new cryptosystem are analyzed and compared with a recently developed scheme [Opt. Laser Eng. 90 (2017) 238–246]. The security analysis and some statistical investigations show that the proposed cryptosystem is resistant to various types of attacks and is efficient for secure communications in nonlinear optical media.

Synchronization of polarization chaos from a free-running VCSEL

We theoretically demonstrate the possibility to synchronize polarization chaos generated by a free-running vertical-cavity surface-emitting laser (VCSEL). We highlight two distinct synchronization regimes: 1) a high-quality synchronization regime where all polarization modes and total intensity are synchronized, which shows good robustness against parameter mismatch, and 2) a "slow time-scale" synchronization where the slower part of the dynamics-that is, the random-like hopping between the two scrolls of the chaotic attractor-synchronizes while the faster oscillations remain unsynchronized.

Noise induced stabilization of chaotic free-running laser diode

In this paper, we investigate theoretically the stabilization of a free-running vertical-cavity surface-emitting laser exhibiting polarization chaos dynamics. We report the existence of a boundary isolating the chaotic attractor on one side and a steady-state on the other side and identify the unstable periodic orbit playing the role of separatrix. In addition, we highlight a small range of parameters where the chaotic attractor passes through this boundary, and therefore where chaos only appears as a transient behaviour. Then, including the effect of spontaneous emission noise in the laser, we demonstrate that, for realistic levels of noise, the system is systematically pushed over the separating solution. As a result, we show that the chaotic dynamics cannot be sustained unless the steady-state on the other side of the separatrix becomes unstable. Finally, we link the stability of this steady-state to a small value of the birefringence in the laser cavity and discuss the significance of this result on future experimental work.

Polarization switching with low power consumption induced by optical feedback in long-wavelength vertical-cavity surface-emitting lasers

The polarization switching (PS) characteristics of vertical cavity surface emitting lasers(VCSELs) have received sustained attention for the past years. With the development of manufacturing technology, the performances of 1550 nm VCSELs have been improved, however the researches on the PS of 1550 nm VCSELs are relatively inadequate for the PS characteristics in the long-wavelength VCSELs may have wide application prospects in optical information processing and optical communications. In this paper, based on the extended spin-flip model (SFM), we theoretically investigate the PS with low power consumption induced by optical feedback in long-wavelength VCSELs. Results show that the PS, which is failed to realize in free-running long-wavelength VCSELs, can be achieved by introducing a moderate-strength polarization-rotation optical feedback. By comparing two different linear dispersion effects, some interesting phenomena have been found. For weak linear dispersion, the PS is relatively easy to realize for a low injection current level, and the range of feedback strength used to control the PS is wide. However, for strong dispersion effect, the PS cannot be obtained all the time since two mode-coexisting zones will appear, and the value of injection current where the PS happens is relatively high. Meanwhile, as observed in short-wavelength VCSELs, the polarization mode hopping and multiple PS have also been found in long-wavelength VCSELs, indicating that the physics nature thet induces the PS is similar for both long and short wavelength VCSELs. In addition, because the PS in long-wavelength VCSEL is more difficult to realize as compared with that in short-wavelength VCSELs, reasonable analyses and explanations may be as follows: since the linear dispersion effect in 1550 nm-VCSEL is much stronger than that of short wavelength VCSEL, the frequency difference between the two linear polarization modes is up to 60 GHz (or 0.48 nm), thus leading to the decrease of the correlation between two linear polarization modes. As a result, it is relatively difficult to obtain the PS phenomenon at low injection current level in long-wavelength VCSEL; while using suitable polarization-rotated optical feedback can partially compensate the deficiency of this correlation. We believe that the results obtained in this work will be helpful in investigation of low power consumption for all optical buffers by using long-wavelength VCSELs.

Asymmetric dwell-time statistics of polarization chaos from free-running VCSEL.

We experimentally report on asymmetric dwell-time statistics of polarization chaos dynamics generated from free-running vertical-cavity surface-emitting lasers (VCSELs). Theoretically, we explain this behavior by introducing a misalignment between the phase and amplitude anisotropy within the spin-flip model for VCSELs. It induces an asymmetry in the VCSEL polarization behavior which is then responsible for significant changes in the statistics of the chaotic mode-hopping with an increase in the average residence time and an inversion of the dominant mode.

Enhanced Flat Broadband Optical Chaos Using Low-Cost VCSEL and Fiber Ring Resonator

Low-cost vertical-cavity surface-emitting laser (VCSEL) and semiconductor optical amplifier (SOA) have been explored experimentally in a setup with a fiber ring resonator to generate flat broadband chaos. The effect of the frequency detuning between the fiber grating frequency and the free-running VCSEL's frequency, and the bias current of the SOA on the bandwidth of chaos has been studied. The results show that the bandwidth of the chaos is strongly dependent on the frequency detuning and the bias current of the SOA. Using the conventional definition of chaos bandwidth, the bandwidth of chaos with the fiber ring resonator can be about three times greater than that with a conventional mirror. In order to consider the flatness of the chaos spectra, the flat bandwidth of chaos is redefined as the frequency range between dc and the frequency where the power fluctuation is within ±3 dB. With this definition, the flat bandwidth of chaos with the fiber ring resonator is >10 times higher than that with conventional mirror feedback.

Two channel photonic microwave generation based on period-one oscillations of two orthogonally polarized modes in a vertical-cavity surface-emitting laser subjected to an elliptically polarized optical injection

Previous investigations demonstrated that a semiconductor laser subjected to optical injection can realize period-one (P1) oscillation output under suitable operational parameters, which can be used to obtain high quality photonic microwave. In this paper, we propose a scheme for simultaneously generating two channel photonic microwave based on the P1 oscillations of two orthogonally polarization modes in a vertical-cavity surface-emitting laser (VCSEL) subjected to an elliptical polarization optical injection, and the relevant characteristics of obtained photonic microwave are numerically simulated and analyzed. The results show that under suitable operational parameters, a free-running VCSEL (named master VCSEL, M-VCSEL) can output an elliptical polarization light in which both X and Y polarization components of the elliptical polarization light oscillate at the same frequency. By using the elliptical polarization light from the M-VCSEL as an injection light into another VCSEL (named slave VCSEL, S-VCSEL), both two polarization components of the S-VCSEL can be driven into P1 oscillation through selecting suitable injection strength under a fixed frequency detuning between the M-VCSEL and the S-VCSEL. Based on the P1 oscillation, two orthogonally photonic microwave signals can be obtained. With the increase of the injection strength from the M-VCSEL, the frequency of photonic microwave shows a gradually increasing trend while the power of photonic microwave displays an increasing process accompanied by slight ripples. Combining the distribution mappings of the frequency, the power, and the amplitude difference between the first sideband and the second sideband of the photonic microwave in the parameter space of the injection strength and the frequency detuning, certain regions with optimally operational parameters can be determined for acquiring high quality photonic microwave.

Polarization dynamics induced by orthogonal optical injection close to the lasing mode of a single-transverse-mode VCSEL

We experimentally investigate the polarization-resolved nonlinear dynamics of a long-wavelength single-transverse-mode vertical-cavity surface-emitting laser (VCSEL) subjected to orthogonal optical injection. We focus on the case in which the wavelength of the optical injection is close to the wavelength of a free-running VCSEL characterized by large values of the birefringence parameter. We observe an elliptically polarized, injection-locked (EPIL) state. The EPIL region is measured in the frequency detuning-injected power plane. Above the upper boundary of the EPIL region, the nonlinear dynamics of the system is usually characterized by periodic oscillations of the power of linear polarizations at a frequency close to the relaxation oscillation frequency of the VCSEL or one half of this value. Below the lower boundary of the EPIL region, the VCSEL operates in parallel polarization and demonstrates periodic pulsations at a frequency given by the frequency detuning or one half of this value. Our results confirm the theoretical predictions of Sciamanna and Panajotov [Phys. Rev. A73, 023811 (2006)].

Polarization Switching and Hysteresis in Vertical-Cavity Surface-Emitting Lasers Subject to Orthogonal Optical Injection

We study polarization switching and hysteresis in a vertical-cavity surface-emitting laser (VCSEL) subject to an orthogonal optical injection, such that the polarization of the injected light is perpendicular to that of the free-running VCSEL. We use the framework of the spin-flip model to characterize the polarization state of the VCSEL as a function of the frequency detuning. With appropriated injection conditions, the orthogonal polarization turns on and locks to the injected field. Increasing and decreasing the detuning across the two locking boundaries results either in narrow or wide hysteresis cycles, or even in irreversible switching. These results are in a good agreement with recent experimental observations.

Bistability of time-periodic polarization dynamics in a free-running VCSEL

We report experimentally a bistability between two limit cycles (i.e. time-periodic dynamics) in a free-running vertical-cavity surface-emitting laser. The two limit cycles originate from a bifurcation on two elliptically polarized states which exhibit a small frequency difference and whose main axes are symmetrical with respect to the linear polarization eigenaxes at threshold. We demonstrate theoretically that this peculiar behavior can be explained in the framework of the spin-flip model model by taking into account a small misalignment between the phase and amplitude anisotropies.

Nonlinear dynamics of 1550 nm VCSELs subject to polarization-preserved optical feedback and orthogonal optical injection

Based on spin-flip model (SFM), the nonlinear dynamics of 1550 nm vertical-cavity surface-emitting lasers (VCSELs) subject to polarization-preserved optical feedback (PPOF) and orthogonal optical injection (OOI) are theoretically investigated. The results show that two linear polarization (LP) modes can be simultaneously stimulated and polarization switching (PS) can be observed, which is different from the case that only y LP mode exists in a VCSEL with PPOF. Under the joint action of PPOF and OOI, the two LP modes will exhibit rich dynamical states, such as period one, period two, multiperiod and chaos oscillation. Different evolution routes to chaos can be also observed. Moreover, frequency detuning Δf (Δf = f m − f s, where f m and f s are the center frequencies of free-running master VCSEL and slave VCSEL, respectively) has an obvious influence on the PS. With the increase of the positive frequency detuning PS points shift toward larger injection strengths; meanwhile, a suitable negative frequency detuning value makes the injection strength for PS be the lowest.

Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers

In this contribution we provide an in depth theoretical analysis of the bifurcations leading to nonlinear polarization dynamics in a free-running vertical-cavity surface-emitting laser (VCSEL). We detail the sequence of bifurcations that occurs when increasing the injection current, and which brings the laser from linear to elliptical polarization emission and then self-pulsating or even more complex chaotic dynamics of the light intensity. Continuation techniques allow us to follow the stable and unstable limit cycle solutions emerging from Hopf bifurcations, and therefore to interpret the frequency of the self-pulsating polarization dynamics. The fundamental frequency of the pulsating dynamics is either close to the laser relaxation oscillation frequency or close to the linear-birefringence-induced polarization mode frequency splitting, depending on the laser parameters. A systematic analysis of the parameter space allows us to identify two scenarios that are in excellent qualitative agreement with those reported in recent experiments. Our results provide, moreover, evidence for an interesting polarization mode hopping mechanism, i.e., a so-called deterministic mode hopping where the laser exhibits a chaotic and therefore random-like hopping between two states that are elliptically polarized and nonorthogonal.

Voltage Spectroscopy and the Operating State of an Optically Injected Long Wavelength VCSEL

A study on the correspondence between the voltage and optical properties of long wavelength vertical cavity surface-emitting lasers (VCSELs) during tuned optical injection is presented. A direct link between the voltage response and the induced optical dynamics for parallel and orthogonal injection is highlighted. The induced dynamics include unlocked stable polarization switching at large frequency offsets from the free-running VCSEL lasing wavelength for both injection orientations. The carrier density change during stable locking is estimated using the cavity resonance shift and voltage change. This estimate is confirmed using a full numerical simulation of the injection locked rate equations.

Correlation properties and time-resolved dynamics of linear polarizations emitted by single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection

We present an experimental and theoretical study of the polarization and time-resolved nonlinear dynamics of a long-wavelength single-mode linearly polarized vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection. Special attention is paid to the correlation properties of both linear polarizations emitted by the VCSEL. We measure simultaneous time traces of both linearly polarized output signals for several values of the bias current, the strength of the optical injection, and the frequency detuning between master and the free-running VCSEL. Different dynamical regimes, including periodic, period doubling, and irregular dynamics, are observed for both polarizations. For positive frequency detuning we usually find that the orthogonal polarization is the only polarization that contributes to the dynamics of the total power. Only for large values of the bias current and for small values of the optical injection strength, near the border of the periodic region, have we found correlated periodic dynamics in both linear polarizations. For negative frequency detuning we find anticorrelated dynamics in both linear polarizations. The average and dispersion of the time between consecutive pulses that appear in the anticorrelated regime increase with the injected power. The irregular dynamics, characterized by broadened power spectra, is related to large values of the dispersion of the time between pulses. A good overall qualitative agreement is found between our theoretical and experimental results. © 2011 Optical Society of America OCIS codes: 140.7260, 140.1540, 190.3100.

Injection Laser Wavelength-Dependent Timing Jitter Reduction of Gain-Switched Single-Mode VCSELs

We report the effect of an external injection laser wavelength on reducing the timing jitter of optical pulses generated from gain-switched single-mode 1.5-μm vertical cavity surface emitting lasers (VCSELs). Simultaneous timing jitter reduction, pulse width shortening, and spectral linewidth narrowing without any peak power penalty were observed when the injection laser wavelength was tuned near the spectral peak of the free-running VCSELs spectrum operating in a continuous wave mode. The timing jitter was reduced up to 40% of that without any injection.