class-A Laser Research Articles

Low phase noise operation of a cavity-stabilized 698 nm AlGaInP-based VECSEL.

We report for the first time a high performance, single frequency AlGaInP-based VECSEL (vertical-external-cavity surface-emitting-laser) with emission at 698 nm, targeting the clock transition of neutral strontium atoms. Furthermore, we present comprehensive noise characterization of this class-A semiconductor laser, including the residual fast phase noise in addition to the frequency and relative intensity noise. The low noise VECSEL has output power at around 135 mW with an estimated linewidth of 115 Hz when frequency stabilized via the Pound-Drever-Hall (PDH) technique to a high finesse reference cavity, without intermediate stabilization. The phase noise is measured to be below -126 dBc/Hz for frequencies between 10 kHz and 15 MHz with a total integrated phase noise of 3.2 mrad, suitable not only for ultra-cold neutral strontium-based quantum technologies, such as optical clocks, but also with potential for atom-interferometry applications.

Ultrafast Buildup Dynamics of Terahertz Pulse Generation in Mode-Locked Quantum Cascade Lasers

Ultrashort terahertz pulse generation is essential for a range of proven terahertz applications, from time-resolved spectroscopy of fundamental excitations to nondestructive testing and imaging. Recently, it has been shown that semiconductor-based terahertz quantum cascade lasers (QCLs) can be used to generate pulses as short as a few picoseconds through active mode locking. However, further progress for subpicosecond and high peak power pulse generation is hampered by poor knowledge on how the electric field actually forms in these lasers. Here, we theoretically and experimentally show the amplitude- and phase-resolved buildup of pulse generation through active mode locking, from initiation of pulse generation to the nanosecond steady state. The experimental results, using an ultrafast coherent seeding technique to probe the laser from femtosecond to nanosecond time scales, are in full agreement with the theoretical calculations based on a theoretical model using multimode reduced rate equations. In particular, we show that the electric field buildup to achieve short pulse operation is extremely fast, requiring only a few photon round trips, owing to the ultrafast gain dynamics of the lasers. Further, this shows a gain recovery time of the order of a few picoseconds, an order of magnitude smaller than the photon round-trip time, highlighting that terahertz QCLs are categorically class-A lasers. This demonstration marks an important formulism for future progress towards exploring the ultrafast pulse generation buildup dynamics of these complex semiconductor lasers.

The variation effect of damping rate of cavity (left and right) side modes on the noise fluxes of a free-running class-A laser

The effect of changes in the damping rate of cavity side modes on the noise fluxes of a three-mode class-A laser is analytically investigated using the fluctuation-dissipation theorem. The Maxwell-Bloch equations of motion are first solved in the presence of three cavity Langevin forces associated with the simultaneous oscillation of cavity central mode as well as its left and right adjacent modes. The solutions are then used to determine the fluctuations that imposed by the cavity Langevin forces on the phase and amplitude of oscillating components of cavity electric field, and on the static and dynamic components of atomic population inversion. By taking the correlation function of these fluctuating components, the noise fluxes of laser and spontaneous emission will be specified in frequency domain. On the other hand, the noise flux of pumping is differently determined by taking the correlation function of fluctuation conservation relation. The results indicate that the cavity Langevin force of each of three oscillating modes makes a direct contribution in producing the noise fluxes of other two oscillating modes. Finally, it is demonstrated that the noise fluxes of input pumping and output laser and spontaneous emission satisfy the flux (energy) conservation.

Low- and high-β lasers in the class-A limit: photon statistics, linewidth, and the laser-phase transition analogy

Nanocavity lasers are commonly characterized by the spontaneous coupling coefficient β that represents the fraction of photons emitted into the lasing mode. While β is conventionally discussed in semiconductor lasers where the photon lifetime is much shorter than the carrier lifetime (class-B lasers), little is known about β in atomic lasers where the photon lifetime is much longer than the other lifetimes and only the photon degree of freedom exists (class-A lasers). We investigate the impact of the spontaneous coupling coefficient β on lasing properties in the class-A limit by extending the well-known Scully–Lamb master equation. We demonstrate that in the class-A limit all the photon statistics are uniquely characterized by β and that the laser phase transition-like analogy becomes transparent. In fact, β perfectly represents the “system size” in phase transition. Finally, we investigate the laser-phase transition analogy from the standpoint of a quantum dissipative system. Calculating a Liouvillian gap, we clarify the relation between β and the continuous phase symmetry breaking.

Dynamics of a class-A nonlinear mirror mode-locked laser.

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the continuous-wave regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (superexponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.

Reduction of residual excess noise in class-A lasers using two-photon absorption.

We demonstrate experimentally a significant reduction of the remaining excess intensity noise in a class-A semi-conductor laser. This is obtained by inserting into the laser cavity a buffer reservoir mechanism based on two-photon absorption in GaAs. The excess noise peaks at the laser-free spectral range, induced by the beating between the lasing mode and the amplified spontaneous emission in the adjacent non-oscillating modes, is reduced by 20 dB, while preserving the class-A dynamical behavior of the laser cavity.

Erratum to: The distribution mechanism of noise fluxes between three oscillating modes of a free-running class-A laser

Erratum to: The distribution mechanism of noise fluxes between three oscillating modes of a free-running class-A laser

The distribution mechanism of noise fluxes between three oscillating modes of a free-running class-A laser

In the present work, we have extended the noise features of a class-A laser from the single-mode state with one oscillating freedom to the three-mode state with three oscillating freedoms. The laser noise is modeled by the cavity Langevin force in the absence of other two atomic population inversion and dipole moment Langevin forces. The Maxwell-Bloch equations of motion are thus solved in the presence of three cavity Langevin forces associated with the simultaneous oscillations of cavity central mode and its left and right adjacent modes. Therefore, the phase and amplitude fluctuations of electric field components that are oscillating at the three consecutive longitudinal modes have analytically been calculated in frequency domain. The results of our calculations indicate that the cavity Langevin force of each of three oscillating modes makes a direct contribution in producing the noise fluxes of other two oscillating modes. We have also determined the exact share of each oscillating mode in the total output intensity noise spectra of a three-mode laser. It is finally demonstrated that the input noise flux of laser pumping is distributed between the output noise fluxes of spontaneous and stimulated emission radiations of three oscillating modes according to the flux conservation law.

Stabilization of flat-mirror vertical-external-cavity surface-emitting lasers by spatiotemporal modulation of the pump profile

We propose and demonstrate theoretically that vertical-external-cavity surface-emitting lasers (VECSELs) with external flat mirrors can be stabilized by applying a periodic spatiotemporal modulation of the pump current. Such pump modulation is shown to suppress the pattern-forming instabilities (modulation instabilities), which eventually results in stable beam emission. A modified Floquet linear stability analysis is used to characterize the dynamics of the modulated system and to evaluate its stabilization performance. Stability maps identify the regions in parameter space for complete and partial stabilization of VECSELs operating in different regimes depending on the external-cavity length. In particular, the stabilization method is shown to operate most efficiently in Class-A laser limit (for relatively long VECSEL resonators), while it becomes ineffective in Class-B laser limit (for relatively short resonators). The stabilization effect is further confirmed through direct integration of the dynamical equations.

The noise spectra comparison of cavity and population inversion Langevin forces in class-A lasers

We have investigated the single role of cavity Langevin force on the noise spectra of class-A and -B lasers for the first time in 2012. The present aim is to consider the simultaneous effect of cavity and population inversion Langevin forces on the noise spectra of class-A lasers. The Maxwell–Bloch equations of motion are thus solved in the presence of both Langevin forces. The solutions give the fluctuations that are imposed to the cavity electric field and atomic population inversion by the Langevin forces. The noise fluxes of stimulated and spontaneous emission radiations are then calculated by using the notion of correlation function. It is demonstrated that the noise fluxes generated by the cavity Langevin force can be comparable or even larger than those produced by the population inversion Langevin force in some rates of laser pumping. The results are ultimately confirmed by illustrating the flux conservation so that the noise flux entered into laser by pumping is equal to those superimposed on the spontaneous and stimulated emission radiations.

The theory of stability, bistability, and instability in three-mode class-A lasers

Instability is an inevitable and common problem in all different kinds of lasers when they are oscillating in both single-and multi-mode states. Here, the stability conditions are investigated for a three-mode class-A laser. A set of linear equations is derived for the stable oscillation of the cavity central mode together with its left and right adjacent longitudinal modes. The coefficient determinant of stability equations is Hermitian and equal to zero for the roots of two diagonal arrays. In other words, the novelty of our work is to expand the stability coefficient determinant in terms of main diagonal arrays rather than for one row or one column. These diagonal roots lead to two lower and upper boundary curves in the form of a bifurcation. The lower boundary curve mimics the single-mode laser and delimits the instability region (with no above-threshold oscillating mode) from the bistability region (with two above-threshold oscillating modes). The upper boundary curve mimics the two-mode laser and delimits the bistability region from the stability region, in which all three-longitudinal modes are simultaneously oscillating in the above-threshold state.

Oscillating Directional Domains in a Ring Semiconductor Laser

We analyze transverse effects in a macroscopic class-A ring semiconductor laser based on a broad stripe gain medium. While the simplest modeling of such a device suggests the existence of stable domains emitting in opposite directions, the presence of alternate oscillations in the device prevents the stability of these domains. We describe the experimental observation of alternate oscillations and the associated transverse dynamics. A numerical analysis which drops many common assumptions shows that the presence of traveling domain walls is a sufficient driving force for the alternate oscillations.

Delay-induced deterministic resonance of chaotic dynamics

We show that time-delayed feedback can induce an optimal regularity in the pulsating dynamics of a nonlinear system without the need for an additional noise source. This deterministic delay-induced coherence resonance is reported experimentally in the chaotic dynamics of a laser diode subject to a phase-conjugate optical feedback, when varying the amount of feedback light. Qualitatively similar resonance is found theoretically in the model of a time-delayed class-A laser. The resonance is therefore not related to an interplay between time-delayed dynamics and faster undamped relaxation oscillations and is thought to be generic for a large class of delayed nonlinear systems.

Three-dimensional numerical prediction of domain walls in class-A ring lasers

We carefully numerically simulate the full three-dimensional (3D), two-level Maxwell Bloch equations in a ring configuration, beyond the rotating wave and slowly varying envelope approximations. The 3D electromagnetic spatial and temporal variations are then well described up to the micrometer and femtosecond scales. Genuine dielectric waveguide boundary conditions together with no-reflection, perfectly matching layers are implemented. Besides the already known and well-described transverse instabilities of a traveling-wave solution, we observe steady zipper-state configurations characterized by the coexistence, in the laser transverse plane, of two longitudinal counter-propagating waves, with their separation plane parallel to the ring laser optical axis. The direction of propagation of the traveling wave is observed to change slowly and periodically with time.

Balance Between Noise Fluxes in Free-Running Single-Mode Class-A Lasers

The fluctuation effect of laser pumping rate on the output noise fluxes of class-A lasers is investigated. The method is based on the role of cavity Langevin force as a fluctuating force in the absence of the atomic population inversion and dipole moment Langevin forces. The temporal fluctuations induced to the phase and amplitude of the cavity electric field and the atomic population inversion are calculated in both below and above threshold states. Our aim is to derive correlation functions for the fluctuating variables of the cavity electric field and the atomic population inversion to determine the noise fluxes emerging from the cavity mirrors and measured by an optical detector and those radiated in the form of a spontaneous emission in all spatial directions. We introduce a heuristic conservation relation that connects the noise flux generated by the laser pumping system with those distributed among the laser variables. Finally, the results are confirmed by demonstrating the energy conservation law.

Evidence of ultra low microwave additive phase noise for an optical RF link based on a class-A semiconductor laser

The additive RF phase noise of a microwave photonics link is measured using, as the optical source, a semiconductor laser operating in the class-A regime. The relative intensity noise of this laser being below the shot noise relative level, the phase noise floor of the link is shown to be shot noise limited, -152 dBc/Hz in our experimental conditions. As a result, the phase noise floor evolves as the inverse of the detected photocurrent, pushing the limits of performance to the availability of high power photo-detectors. Below 6 kHz from the carrier frequency at 3GHz, some noise, in excess with respect to the shot noise limit, is observed but remains lower than -110 dBc/Hz at 100 Hz offset frequency. This residual noise originates mainly from environmental noise and can be reduced by isolating the laser from acoustic/electromagnetic perturbations.

Experimental Investigation and Analytical Modeling of Excess Intensity Noise in Semiconductor Class-A Lasers

Excess intensity noise in a low-noise single-frequency class-A VECSEL is experimentally investigated over the frequency range 10 kHz-18 GHz. An analytical model is derived, based on multimode Langevin equations, to describe the observed laser excess noise over the whole bandwidth. From 50 MHz to 18 GHz, class-A operation leads to a shot noise limited relative intensity noise (RIN), namely -155 dB/Hz for 1-mA detected photocurrent, except at harmonics of the cavity free spectral range (FSR). At these frequencies, the excess noise is shown to be due to the amplified spontaneous emission contained in the nonlasing side modes. The measured levels of excess noise correspond to side mode suppression ratios (SMSRs) ranging from 70 to 90 dB, in agreement with the model. At low frequencies, 10 kHz-50 MHz, the observed excess noise spectrum has the expected Lorentzian shape. Its bandwidth increases with the pumping rate to an upper limit given by the cavity photon lifetime. Below this cutoff frequency, we show that the pump RIN is the dominant source of noise, while it is filtered by the laser dynamics above. Finally, our model permits to design a semiconductor class-A laser with an intensity noise limited to the shot noise level over the whole 10 kHz-18 GHz bandwidth.

Incoherent weak coupling of laser solitons

A coupled state of a pair of spatial laser solitons with different topological charges in a wide-aperture class-A laser with saturable absorption was found by numerical simulation. In view of a difference in the frequencies of the individual solitons, periodic (with a period corresponding to the frequency difference) weak pulsations of the shape of the solitons and of the spacing between them take place, but the rotation of the pair and the motion of its center of inertia were not revealed.

Collisions of complexes of weakly coupled laser solitons

Different scenarios of collisions of complexes of weakly coupled solitons moving in antiparallel directions in a wide-aperture class-A laser with saturable absorption are found by numerical simulation. Depending on the impact parameter and the phase difference of the initial complexes, they can adhere to each other or form new complexes composed of both initial complexes, while the number of solitons can change from their total disappearance to the extension of the region of generation over the whole transverse cross section of the laser.

Stability theory of class-C (far-infrared) lasers with an injected signal

The behavior of a single-mode class-C laser in the presence of an injected signal is investigated theoretically in detail. We have determined the ranges of input signal strength and the frequency detuning for which the oscillations of the cavity electric field and the atomic induced dipole moment are simultaneously stable and have only one oscillation component with the frequency equal to that of the input signal (injection-locked state). One can reproduce all the previous results corresponding to class-A and class-B lasers from our results by using their relevant conditions. Finally, the energy conservation law is demonstrated for both the below-threshold and the injection-locked states of class-C laser amplifiers.