Laser Relaxation Oscillation Research Articles

Experimental determination of key parameters in the spin-flip model of 1550 nm vertical-cavity surface-emitting laser

Spin-flip model (SFM) is a mostly used approach to analyzing the nonlinear dynamics of vertical-cavity surface-emitting laser (VCSEL), and therefore the value selections of some key parameters in this model are crucial. In this work, based on experimentally measured dynamical characteristics of a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) under free running and parallel optical injection, some key parameters (field decay rate k, total carrier decay rate N, linewidth enhancement factor , active medium birefringence rate p, spin relaxation rate s, and active medium linear dispersion rate a) are estimated. Through experimentally measuring the noise spectrum of the laser, the relaxation oscillation frequency and the damping rate of the relaxation oscillations are calculated, and the photon lifetime can be preliminary estimated. After further amending the photon lifetime by considering the effect of the gain saturation on the damping rate of the relaxation oscillations, the value of k is determined. Based on the function relation between the laser relaxation oscillation frequency and the electrical pumping, the value of N is obtained. By experimentally acquiring the dynamical distribution mapping of the laser under parallel optical injection, the minimum Hopf bifurcation point of the Hopf bifurcation curve can be found, and then the value of is roughly estimated. According to the frequency difference between the two polarization components of the laser in the measured optical spectrum, the value of p can be calculated. The value of s is obtained by using the relationship between s and p. On the basis of the above determined parameter values, the value of a can be specified by numerically simulating the optical spectrum of the laser and comparing with experimentally obtained results. Moreover, by comparing the experimentally measured dynamical mapping of optical injection VCSEL with corresponding dynamical mapping simulated on the basis of the above mentioned parameters, the value of is rectified. Finally, further simulated results agree with relevant experimental observations.

Actively mode-locked Raman fiber laser.

Active mode-locking of Raman fiber laser is experimentally investigated for the first time. An all fiber connected and polarization maintaining loop cavity of ~500 m long is pumped by a linearly polarized 1120 nm Yb fiber laser and modulated by an acousto-optic modulator. Stable 2 ns width pulse train at 1178 nm is obtained with modulator opening time of > 50 ns. At higher power, pulses become longer, and second order Raman Stokes could take place, which however can be suppressed by adjusting the open time and modulation frequency. Transient pulse evolution measurement confirms the absence of relaxation oscillation in Raman fiber laser. Tuning of repetition rate from 392 kHz to 31.37 MHz is obtained with harmonic mode locking.

Noise and dynamics of stimulated-Brillouin-scattering microresonator lasers

We use theoretical analysis and numerical simulation to investigate the operation of a laser oscillating from gain supplied by stimulated Brillouin scattering (SBS) in a microresonator. The interaction of the forward, backward, and density waves within the microresonator results in a set of coupled-mode equations describing both the laser's phase and amplitude evolution over time. Using this coupled-mode formalism, we investigate the performance of the SBS laser under noise perturbation and identify the fundamental parameters and their optimization to enable low-noise SBS operation. The intrinsic laser linewidth, which is primarily limited by incoherent thermal occupation of the density wave, can be of order hertz or below. Our analysis also determines the SBS laser's relaxation oscillation, which results from the coupling between the optical and density waves, and appears as a resonance in both the phase and amplitude quadratures. We further explore contributions of the pump noise to the SBS laser's performance, which we find under most circumstances to increase the SBS laser noise beyond its fundamental limits. By tightly stabilizing the pump laser onto the microcavity resonance, the transfer of pump noise is significantly reduced. Our analysis is both supported and extended through numerical simulations of the SBS laser.

Noise reduction in solid-state lasers using a SHG-based buffer reservoir.

The cancellation of resonant intensity noise, from a few kHz up to several GHz, is reported using a second-harmonic generation (SHG) buffer reservoir in a Nd:YAG solid-state laser. This approach is shown to be well suited and easily optimizable for reducing the excess noise lying at the laser relaxation oscillations as well as that originating from the beating between the lasing mode and nonlasing adjacent longitudinal modes. A thorough analysis of noise spectra of both laser and SHG signals confirms definitely that noise reduction is a consequence of a deep laser dynamics modification rather than noise evacuation mechanism.

Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics

Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser's relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

Simple analytical model for low-frequency frequency-modulation noise of monolithic tunable lasers

We employ simple analytical models to construct the entire frequency-modulation (FM)-noise spectrum of tunable semiconductor lasers. Many contributions to the laser FM noise can be clearly identified from the FM-noise spectrum, such as standard Weiner FM noise incorporating laser relaxation oscillation, excess FM noise due to thermal fluctuations, and carrier-induced refractive index fluctuations from stochastic carrier generation in the passive tuning sections. The contribution of the latter effect is identified by noting a correlation between part of the FM-noise spectrum with the FM-modulation response of the passive sections. We pay particular attention to the case of widely tunable lasers with three independent tuning sections, mainly the sampled-grating distributed Bragg reflector laser, and compare with that of a distributed feedback laser. The theoretical model is confirmed with experimental measurements, with the calculations of the important phase-error variance demonstrating excellent agreement.

Laser optical feedback imaging controlled by an electronic feedback loop

In autodyne interferometry, the beating between the reference beam and the signal beam takes place inside the laser cavity and therefore the laser fulfills simultaneously the roles of emitter and detector of photons. In these conditions, the laser relaxation oscillations play a leading role, both in the laser quantum noise, which determines the signal-to-noise ratio (SNR), and also in the laser dynamics, which determines the response time of the interferometer. In the present study, we have experimentally analyzed the SNR and the response time of a laser optical feedback imaging (LOFI) interferometer based on a Nd(3+) microchip laser, with a relaxation frequency in the megahertz range. More precisely, we have compared the image quality obtained when the laser dynamics is free and when it is controlled by a stabilizing electronic feedback loop using a differentiator. From this study, we can conclude that when the laser time response is shorter (i.e., the LOFI gain is lower), the image quality can be better (i.e., the LOFI SNR can be higher) and that the use of an adapted electronic feedback loop allows high-speed LOFI with a shot-noise limited sensitivity. Despite the critical stability of the electronic feedback loop, the obtained experimental results are in good agreement with the theoretical predictions.

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.

Generation of wideband chaos with suppressed time-delay signature by delayed self-interference

We demonstrate experimentally and numerically a method using the incoherent delayed self-interference (DSI) of chaotic light from a semiconductor laser with optical feedback to generate wideband chaotic signal. The results show that, the DSI can eliminate the domination of laser relaxation oscillation existing in the chaotic laser light and therefore flatten and widen the power spectrum. Furthermore, the DSI depresses the time-delay signature induced by external cavity modes and improves the symmetry of probability distribution by more than one magnitude. We also experimentally show that this DSI signal is beneficial to the random number generation.

Optical lock-in particle tracking in optical tweezers

We demonstrate a lock-in particle tracking scheme in optical tweezers based on stroboscopic modulation of an illuminating optical field. This scheme is found to evade low frequency noise sources while otherwise producing an equivalent position measurement to continuous measurement. This was demonstrated to yield up to 20 dB of noise suppression at both low frequencies (< 1 kHz), where low frequency electronic noise was significant, and around 630 kHz where laser relaxation oscillations introduced laser noise. The setup is simple, and compatible with any trapping optics.

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.

Optimization of an autodyne laser interferometer for high-speed confocal imaging

In autodyne interferometry, the beating between the reference beam and the signal beam takes place inside the laser cavity and therefore the laser fulfills simultaneously the roles of the emitter and the detector of photons. In these conditions, the laser relaxation oscillations play a leading role, both in the laser quantum noise that determines the signal-to-noise ratio (SNR) and also in the laser dynamics that determine the response time of the interferometer. In the present study, we have theoretically analyzed the SNR and the response time of a laser optical feedback imaging (LOFI) setup based on an autodyne interferometer. More precisely, we have compared the image quality of two lasers having the same output power and the same relaxation frequency, but having two different values of the LOFI gain induced by two different values of the laser response time. From this study, we have finally determined the best laser dynamical parameters and the best experimental conditions for high-speed imaging at the shot-noise limit. Finally, we conclude that a laser diode with a very short response time (in the nanosecond range) seems to be an interesting candidate compared to solid-state microchip laser with a response time of several tens of microseconds. Analytical predictions are confirmed by numerical simulations.

Phase and intensity dynamics of a two-frequency laser submitted to resonant frequency-shifted feedback

We propose an experimental and theoretical study of the dynamical regimes observed when the two modes of a two-frequency solid-state laser are coupled by frequency-shifted optical feedback. The detuning associated to the feedback is close to the frequency of the laser relaxation oscillations. Special attention is devoted to the dynamics of the phase of the beat note between the modes relative to the phase of an external radio-frequency reference. In particular, we analyze in detail the transition from phase locking to the external reference to phase drift. This transition occurs through a window of frequency locking without phase locking [Th\'evenin, Romanelli, Vallet, Brunel, and Erneux, Phys. Rev. Lett. 107, 104101 (2011)]. Furthermore, a large variety of dynamical behaviors, such as weak intensity modulation, self-pulsing, and chaos, are experimentally found. These results are successfully reproduced by a theoretical model based on coupled rate equations. The extension of the model to the description of other active media such as semiconductor lasers is briefly outlined.

Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers

Using advanced continuation techniques for dynamical systems, we elucidate the bifurcations leading to asymptotically stable square-wave pulsing and polarization mode switching in semiconductor lasers with mutual time-delayed and polarization rotating coupling. We find that the increase of coupling strength leads to a cascade of Hopf bifurcations on a mixed-mode steady state up to a transcritical bifurcation on a so-called pure-mode steady state where both lasers emit with the injected polarization state. From these successive Hopf bifurcations emerge time-periodic solutions that have a period close to the laser relaxation oscillation for weak coupling but a period close to twice the time delay for large coupling strength. The wave form of the time-periodic solutions also evolves from harmonic pulsing up to square-wave pulsing as has been observed recently in experiments.

Q-switched mode-locking of an erbium-doped fiber laser using cavity modulation frequency detuning

We present the results of an investigation regarding a Q-switched mode-locked fiber laser scheme based on a cavity modulation frequency detuning technique. The approach is based on undamped laser relaxation oscillations occurring due to frequency detuning in the fundamental cavity resonance frequency. Through a range of experiments with an erbium-doped, fiber-based, ring-cavity laser, this approach has been shown to be capable of generating high-quality Q-switched mode-locked pulses from an optical fiber-based laser. The maximum frequency detuning range for a stable Q-switched mode-locking operation has been observed to vary depending on the pump power used. We found that the highest pulse peak power was obtained at the frequency detuning threshold at which the operation changed from the mode-locking to the Q-switched mode-locking regime.

Impact of luminescence quenching on relaxation-oscillation frequency in solid-state lasers

Measurement of the laser relaxation-oscillation frequency as a function of pump rate allows one to determine parameters of the laser medium or cavity. We show that luminescence quenching of a fraction of the rare-earth ions in a solid-state laser affects the relaxation oscillations, resulting in incorrect values for the parameter deduced from this measurement. In the equations describing the relaxation oscillations, we replace the lifetime of the upper laser level by an effective lifetime that takes the luminescence quenching into account. In an Al2O3:Yb3+ distributed-feedback laser we observe significant quenching, with the effective lifetime being ∼18 times shorter than the intrinsic upper-laser-level lifetime.

The effect of the relaxation oscillation frequency of chaotic semiconductor laser on the rate of random sequence

In this paper, chaotic light generated by semiconductor laser with optical feedback is employed as physical entropy source to generate high-speed random sequence. The relationship between autocorrelation coefficient of chaotic signal and run number of random sequence is analyzed. Based on the analysis, the changes of random sequence run number are further investigated at different ratios between laser relaxation oscillation frequency fr and random sequence generation rate fn. The results show that random sequence run can easily meet the requirement for run test of NIST SP800-22 when the ratio between fr and fn satisfies the equation of fr/fn=(2k+1)/4. When k in the equation is equal to 1, the maximal rate fn=4fr/3 of random sequence is obtained.

High-Order Distortion in Directly Modulated Semiconductor Lasers in High-Loss Analog Optical Links With Large RF Dynamic Range

A theoretical and experimental investigation of the effects of high-order nonlinear distortion products produced by directly modulated semiconductor lasers on the performance of high-loss analog optical communication links requiring large RF dynamic range is reported. In order to provide sufficient RF dynamic range to support radio services in links with high optical transmission loss, for example in radio over free-space optics (RoFSO), while keeping costs low, it is necessary to use directly modulated lasers. However, in these applications the lasers must be driven to high modulation depths to maximize dynamic range. Simulations show that under these unique conditions the first detectable nonlinear distortion is often the result of dynamic distortion due to the laser being driven near threshold. It is shown that this type of distortion is characterized by a sharp increase in the contribution of high-order (fourth order or greater) nonlinear terms resulting from the influence of laser relaxation oscillations. As a consequence, the third-order spurious-free dynamic range (SFDR) metric no longer accurately reflects the performance of such links as it assumes that third order effects are dominant. An alternative measure of dynamic range called dynamic-distortion-free dynamic range (DDFDR) is proposed. This differs in that the upper limit is defined as the modulating power at which the peak optical modulation index (OMI) reaches unity. At this point the error vector magnitude (EVM) measured for a range of different wireless services starts to increase rapidly due to high order distortion. This makes DDFDR a practical, service-independent metric of dynamic range. For two different wireless services it is observed experimentally that on average the DDFDR upper limit predicts the EVM knee point to within 1.1 dB, while the third-order SFDR predicts it to within 6.2 dB. The DDFDR is thus shown to be a more accurate indicator of real link performance when high-order distortion is dominant.

Comparative study of autodyne and heterodyne laser interferometry for imaging

For given laser output power, object under investigation, and photodiode noise level, we have theoretically compared the signal-to-noise ratios of a heterodyne scanning imager based on a Michelson interferometer and of an autodyne setup based on the laser optical feedback imaging (LOFI) technique. In both cases, the image is obtained point by point. In the heterodyne configuration, the beating between the reference beam and the signal beam is realized outside the laser cavity (i.e., directly on the detector), while in the autodyne configuration, the wave beating takes place inside the laser cavity and therefore is indirectly detected. In the autodyne configuration, where the laser relaxation oscillations play a leading role, we have compared one-dimensional scans obtained by numerical simulations with different lasers' dynamical parameters. Finally, we have determined the best laser for LOFI applications and the experimental conditions for which the LOFI detection setup (autodyne interferometer) is competitive compared to a heterodyne interferometer.

Chaos synchronization in semiconductor lasers with polarization-rotated optical feedback

Chaotic oscillations of the transverse magnetic (TM) mode, which is not a common lasing mode, are excited by using polarization-rotated optical feedback from the transverse electric (TE) mode in a semiconductor laser. In our previous paper, we found that the dynamics were strongly dependent on their RF components under the condition of moderate optical feedback from the TE mode to the TM mode and that they were divided into three RF regions; low-pass filtered signals with a lower frequency than the laser relaxation oscillation frequency, intermediate RF components including the relaxation oscillation frequency, and high-pass filtered signals with a higher frequency higher than the relaxation oscillation frequency. Depending on the frequency bands, the laser outputs showed different correlations. In the present study, using such schemes, the polarization-rotated beam from a transmitter laser (i.e., the rotated TE-mode beam of a transmitter laser) is injected into a receiver laser. We experimentally observe chaos synchronization in accordance with the dynamics of RF components on the transmitter laser side. We also perform numerical calculations using a model and obtain good agreement between the theoretical and experimental results.