We study delay-based photonic reservoir computing using a semiconductor laser with an optoelectronic feedback. A rate-equation model for a laser with an optoelectronic filtered feedback is used. The filter allows only high-frequency signals to pass through the feedback loop. The delay-differential equation model consists of three equations for the normalized electric field intensity I(t), the carrier density N(t); and the filtered intensity signal IF (t). The stability boundaries which correspond to the Hopf bifurcation condition are determined analytically, showing multiple Hopf bifurcation branches in the dynamics, and the parity asymmetry with relation to the feedback sign.
We use the Santa Fe time-series prediction task to evaluate the performance of reservoir computing. Our objective is to determine location of the optimal operating point defined as corresponding to minimal normalized means square error (NMSE) and relate it to the stability properties of the system. We use 3000 points for training and 1000 for testing, number of virtual nodes is chosen in regard to the relaxation oscillation frequency. Single-point prediction of the chaotic data is performed. Input signal is determined by the chaotic waveform
having n sampling points, and three cases are investigated: prediction of n + 1 ,n + 2 or n + 3 sampling point. The best NMSE value order of 10^7 for n + 1 point prediction task is obtained in the absence of feedback and the rapid increase in NMSE is observed in the vicinity of Hopf bifurcation without regard to the feedback sign. On the contrary, the minimum values of NMSE for n + 2 and n + 3 point prediction task correspond to the Hopf bifurcation, and only for the positive feedback. We discuss whether the parity asymmetry can explain strongly asymmetric reservoir computing results.
As demand towards cloud-based services and high-performance computations grows, it imposes requirements on data center performance, and efficiency. Taking advantage of the mature CMOS process technology, and the fact that silicon is the basic material of electronics industry, silicon photonics makes possible production photonic integrated circuits that satisfy these requirements.
Here we explore the short-cavity hybrid laser consisting of a III-V amplifier integrated with a silicon photonic crystal (PhC) cavity reflector by so-called butt-coupling approach. The laser possesses great stability characteristics meeting the criteria for data center interconnect applications. The PhC reflector having a Q-factor of 104 at the lasing wavelength 1535 nm can be considered as a narrow-bandwidth filter. The laser demonstrates single mode and eventless operation without any dynamics on the background, and smooth radiofrequency spectrum without evidence of relaxation oscillation frequency. The latter fact is beneficial for many applications, and indicates extremely high damping in PhC laser, where the photon cavity lifetime is greatly improved by the high-Q PhC cavity reflector.
We confirm our experimental observations by theory based on delay differential equation model for a single-section semiconductor laser. We reveal the effective damping of the laser, when the detuning between the filter peak and the laser cavity mode is small, and the imaginary parts of the model eigenvalues equal zero. It is possible to undamp the relaxation oscillations forcing self-Q-switched operation in the laser owing to the cumulative action of the alpha-factor and the narrow filter.
In conclusion, we experimentally and theoretically demonstrated that relaxation oscillations can be suppressed in the short-cavity semiconductor laser with a narrow intracavity frequency filter. Additionally, on the basis of our analysis we expect the undamping of relaxation oscillations, and self-pulsations when the cavity mode is detuned from the filter peak frequency. The results might be useful for applications in data communications.
We show theoretically that optical feedback can be used to phase lock the successive modes of multi-section frequency-swept source lasers as a means to increase the coherence length. The time-gated feedback technique can be applied to transfer the coherence between the subsequent modes to retain the coherence along the full sweep or to synchronise two independent swept sources. In analogy with CW lasers, we derive an Adler equation describing the locking conditions. When the constant feedback is applied, the laser can operate in a self-mixing, mode-locking or chaotic regime, depending on the sweeping speed. In order to verify the theoretical results, we have developed an experimental set up and performed initial measurements with optical feedback.
In this paper we study, both experimentally and theoretically, the turn on transient dynamics observed in a long (20m) cavity laser. The laser consists of a ring cavity based on a single mode fiber with unidirectional propagation of light. The gain is provided by a semiconductor optical amplifier (SOA) centered around 1300nm and wavelength selection is provided by a tunable narrow transmission bandwidth Fabry-Perot filter. At high bias current and when the filter transmission sets the laser to operate in an anomalous dispersion regime, the laser exhibits only chaotic oscillations, while in a normal dispersion regime, the laser can exhibit stable operation. At a bias current close to the threshold the laser always exhibits multiple dropouts. In order to record the lasing build up dynamics, the bias current driven to the SOA is periodically switched from the off-state to a high current level. The lasing build up occurs at each roundtrip via a step-wise increase of the laser intensity. The laser intensity is widely oscillating during the first steps and approaches a stationary state after a large number of roundtrips. Recording of the phase evolution of the electric field during each step demonstrates the linewidth narrowing at each subsequent roundtrip. Theoretically, we describe the system by a set of delay differential equations and observe similar behavior. While typically a semiconductor laser exhibits relaxation oscillations before reaching the stable lasing regime, which is associated with class B lasers, our study shows that the long cavity laser demonstrates a different mechanism of lasing build up.
We explore experimentally and theoretically the dynamics of a DFB quantum well laser subject to external optical feedback from a mirror. With increasing feedback, the system exhibits the following dynamical scenario: an extremely small limit cycle appears first and is followed by a quasi-periodic regime, and then by three subsequent limit cycles with different repetition rates. This sequence of limit cycles can be associated with the change of phase of the reflected field which reveals translational symmetry and the fact of periodic solutions coexistence which we confirm numerically. The results can be useful for applications in reservoir computing with phase space of coexisting limit cycles acting as a nonlinear reservoir as well as for other applications.
We consider four different laser arrangements with the nonlinear loops of Kerr type, and discuss square wave pulse operation using modeling based on delay differential equation (DDE) approach. We reduce DDE models to 1D maps, which enable square wave operation and analyze numerically the possible dynamical scenarios of the square wave evolution.
We analyze the properties of a unidirectional class-A ring laser containing a nonlinear amplifying loop mirror (NALM). The NALM is a Sagnac interferometer consisting of an amplifier and a Kerr-type nonlinear element, and has a reflectivity that periodically varies with the intra-cavity power. To model the dynamics of these lasers, we use the approach based on Delay Differential Equations (DDEs) that has been successfully applied to describe the properties of passively mode-locked semiconductor lasers. The proposed model allows us to investigate mode locking operation in this laser. The analysis of this DDE model for mode-locked operation was performed numerically and analytically in the limit of large cavity round trip times. We demonstrate that mode-locked pulses are born though a modulational instability of the steady state solutions when the pseudo- continuous branch crosses the imaginary axis. These asymmetric pulses always co-exist with the stable laser-off solution. Hence, they can be viewed as temporal cavity solitons having similar properties with localized structures observed in bistable spatially-extended systems.
We explore both experimentally and numerically the dynamics of semiconductor lasers subject to delayed optical feedback and show that the external cavity repetition rate can be resonant with the relaxation oscillations leading to a discretisation of the relaxation oscillation frequency which evolves in a series of discrete steps, remaining almost constant along each step. Numerically, the steps are found to result from different Hopf bifurcation branches.
Optical square wave sources are particularly important for applications in high speed signal processing and optical communications. In most realizations, optical square waves are generated by electro-optic modulation, dispersion engineering of mode-locked lasers, polarization switching, or by exploiting optical bi-stability and/or optical delayed feedback in semiconductor diode lasers, as well as vertical-cavity surface-emitting lasers (VCSELs). All such configurations are bulky and cause significant timing jitters. Here we demonstrate the direct generation of optical square waves from a polarization-maintaining figure-eight nonlinear amplifying loop mirror (NALM) configuration that uses an embedded high index glass micro-cavity as the nonlinear element. Such a NALM mimics the behavior of a saturable absorber and has been used to reach passive mode-locking of pico- and even nano-second pulses. In our method, the NALM, including a high-Q micro-ring resonator, acts as an ultra-narrowband spectral filter and at the same time provides a large nonlinear phase-shift. Previously we have demonstrated that such a configuration enables sufficient nonlinear phase-shifts for low-power narrow-bandwidth (~100 MHz FWHM) passive mode-locked laser operation. Here we demonstrate the switching of stable optical square wave pulses from conventional mode-locked pulses by adjusting the cavity properties. In addition, the square wave signal characteristics, such as repetition rate and pulse duration, can be also modified in a similar fashion. The source typically produces nanosecond optical square wave pulses with a repetition rate of ~ 120 MHz at 1550nm. In order to verify the reach of our approach, we compare our experimental results with numerical simulations using a delay differential equation model tailored for a figure-eight laser.
We demonstrate a pulse-bursting phenomenon in Yb:Er glass laser operating at 1.54 μm. Glass-ceramic material with a low value of saturation threshold based on Co2+:β-ZnSiO4 nanocrystals was used as a passive gate for pulse-burst operation. The bursts of pulses were 1.5 ms long, each burst consisted of 40-55 pulses with 9-30 μJ energy per pulse and 0.2-3 μs pulse width. Bursting outputs arise via a coupling between slow switching arising via a slow pump modulation and fast pulsations resulting from Q-switch mechanism. We show that absorption cross-section strongly affects the mode of laser operation ranging from relaxation oscillations corresponding to low cross-section values to bursting and conventional Q-switch operation in the case of their higher values.
We control the optical comb in Nd:YVO4 mode-locked lasers with intracavity frequency doubling based on KTP crystals via changing the cavity length and its dispersion properties and achieve high-purity radiofrequency (RF) signals. The laser output wavelength (532 nm) is in the range of the molecular iodine absorption spectrum with narrow (1.5 kHz) homogeneously broadened lines. We propose to stabilize the two longitudinal modes on two narrow iodine absorption lines. The third derivative of the absorption line could be obtained by heterodyning the absorption signal with the third harmonic of the modulation signal. The resulting RF error signal could be used to stabilize two locked longitudinal modes separated by 1.37 GHz which results in stabilized beat note signal.
We present a new TOF camera design based on a compact actively Q-switched diode pumped solid-state laser operating in 1.5 μm range and a receiver system based on a short wave infrared InGaAs PIN diodes focal plane array with an image intensifier and a special readout integration circuit. The compact camera is capable of depth imaging up to 4 kilometers with 10 frame/s and 1.2 m error. The camera could be applied for airborne and space geodesy location and navigation.
We report on theoretical investigation of quasi-three level Er:YAG laser. We propose a numerical model of the laser design with side pump by 1471 nm laser diodes. The model describes the dynamical propagation of the pump in the cavity and the kinetic parameters of the active medium.
We propose a Rayleigh-Sommerfeld based method for numerical calculation of multiple tilted apertures near and far field diffraction patterns. Method is based on iterative procedure of fast Fourier transform based circular convolution of the initial field complex amplitudes distribution and impulse response function modified in order to account aperture and observation planes mutual tilt. The method is computationally efficient and has good accordance with the results of experimental diffraction patterns and can be applied for analysis of spatial noises occurring in master oscillator power amplifier laser systems. The example of diffraction simulation for a Phobos-Ground laser rangefinder amplifier is demonstrated.
We experimentally study passive mode-locking in Nd:YVO4 laser based on second harmonic generation in KTP crystal.
We characterized RF spectra and optical spectra versus pump power, the KTP crystal temperature and position, the
output coupler reflectivity, and the intracavity polarizer. We discuss the device performance considering cascaded χ(2)
lensing in KTP, frequency doubling nonlinearity, and Kerr lens formed in Nd:YVO4. Implementing an intracavity Lyot
filter and cavity length modulation via PZT does not affect mode-locking capability. These results and ultra-low noise
mode beat signal open a new perspective for stable RF signal generation by transferring optical reference stability
(iodine absorption lines) into RF domain.
We demonstrate a new approach to designing a compact RF standard based on the transfer of frequency stability of
hyperfine transitions in molecular iodine to the stability of a laser cavity length. We use frequency doubled Nd:YVO4
laser operating in Kerr lens mode-locked regime and frequency lock it to hyperfine transitions in molecular iodine with
further detecting the beat note signal between longitudinal modes on a fast photodiode. A similar system is used for
estimating the standard Allan deviation of RF signal which is 2.1 x 10-14 at the time 100 s.