Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean--field description. Monte Carlo simulations of a simplified model which includes the population of the medium, demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.
The behavior of a newly introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its relationship is established to the standard Parisi overlap order parameter in replica theory for spin-glasses. In the complex spherical spin-glass model, describing the onset and behavior of random lasers, replica symmetry breaking in the intensity fluctuation overlap is shown to occur at high pumping or low temperature. This order parameter identifies the laser t…
We analyze theoretically the effect of technical fluctuations on laser lineshape in terms of statistics of amplitude and phase noise and their respective bandwidths. While the phase noise tends to broaden the linewidth as the magnitude of the noise increases, the amplitude noise brings out an additional structure with its spectral density reflecting the magnitude of the noise. The effect of possible coupling between those two noises is also discussed.
Numerical simulation is used to analyze statistical characteristics of vortex beams propagating in the atmosphere. The cumulative distribution function and the probability density function of intensity fluctuations are compared for Gaussian beams and vortex beams. It is shown that for propagation conditions in the turbulent atmosphere corresponding to weak fluctuations (Rytov parameter much smaller than unity), intensity fluctuations at the axis of the Gaussian beam have the lognormal distribution, whereas the probability density distribution of the radiation intensity fluctuations at the axis…
We present an \emph{ab-initio} semi-analytical solution for the noise spectrum of complex-cavity micro-structured lasers, including central Lorentzian peaks at the multimode lasing frequencies and additional sidepeaks due to relaxation-oscillation (RO) dynamics. In~Ref.~1, we computed the central-peak linewidths by solving generalized laser rate equations, which we derived from the Maxwell--Bloch equations by invoking the fluctuation--dissipation theorem to relate the noise correlations to the steady-state lasing properties; Here, we generalize this approach and obtain the entire laser spectru…
He-Ne ring laser gyroscopes are, at present, the most precise devices for absolute angular velocity measurements. Limitations to their performance come from the non--linear dynamics of the laser. Following the Lamb semi-classical theory, we find a set of critical parameters affecting the time stability of the system. We propose a method for estimating the long term drift of the laser parameters and for filtering out the laser dynamics effects from the rotation measurement. The parameter estimation procedure, based on the perturbative solutions of the laser dynamics, allow us to apply Kalman Fi…
The intensity fluctuations of laser light are derived from photon number rate equations. In the limit of short times, the photon statistics for small laser devices such as typical semiconductor laser diodes show thermal characteristics even above threshold. In the limit of long time averages represented by the low frequency component of the noise, the same devices exhibit squeezing. It is shown that squeezing and thermal noise can coexist in the multi-mode output field of laser diodes. This result implies that the squeezed light generated by regularly pumped semiconductor laser diodes is quali…
We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replic…
The invention of optical lasers led to a revolution in the field of optics and even to the creation of completely new fields of research such as quantum optics. The reason was their unique statistical and coherence properties. The newly emerging, short-wavelength free-electron lasers (FELs) are sources of very bright coherent extreme-ultraviolet (XUV) and x-ray radiation with pulse durations on the order of femtoseconds, and are presently considered to be laser sources at these energies. Most existing FELs are highly spatially coherent but in spite of their name, they behave statistically as c…
We investigate the effects of the electron-hole spin dynamics on the polarization fluctuations in the light emitted from a vertical cavity surface emitting laser (VCSEL). The Langevin equations are derived based on a rate equation model including birefringence, dichroism, and two carrier density pools seperately coupled to right and left circular polarization. The results show that the carrier dynamics phase lock the polarization fluctuations to the laser mode. This is clearly seen in the difference between fluctuations in ellipticity and fluctuations in polarization direction. Seperate measur…
Spatial resolution of stimulated emission depletion (STED) microscopy varies with sample labeling techniques and microscope components, e.g., lasers, lenses, and photo-detectors. Fluctuations in the intensity of the depletion laser decrease achievable resolution in STED microscopy; the stronger the fluctuations, the higher the average intensity needed to achieve a given resolution. This phenomenon is encountered in every STED measurement. However, a theoretical framework that evaluates the effect of intensity fluctuations on spatial resolution is lacking. This article presents an analytical fo…
We show that the reduction in photon number fluctuations at laser threshold often cited as a fundamental laser property does not occur in typical semiconductor lasers such as the ones commonly used in modern technological applications today. Indeed, such lasers may still exhibit thermal intensity fluctuations far above threshold. We therefore conclude that sub-thermal intensity fluctuations cannot be regarded as a necessary property of laser light. Rather, one should distinguish betwen a thermal laser regime and a sub-thermal laser regime.
We present a theoretical and experimental study aimed at characterizing statistical regimes in a random laser. Both the theoretical simulations and the experimental results show the possibility of three region of fluctuations increasing the pumping energy. An initial Gaussian regime is followed by a Lévy statistics and Gaussian statistic is recovered again for high pump pulse energy. These different statistical regimes are possible in a weakly diffusive active medium, while the region of Lévy statistics disappears when the medium is strongly diffusive presenting always a Gaussian regime with s…
We investigate the polarization fluctuations caused by quantum noise in quantum well vertical cavity surface emitting lasers (VCSELs). Langevin equations are derived on the basis of a generalized rate equation model in which the influence of competing gain-loss and frequency anisotropies is included. This reveals how the anisotropies and the quantum well confinement effects shape the correlations and the magnitude of fluctuations in ellipticity and in polarization direction. According to our results all parameters used in the rate equations may be obtained experimentally from precise time reso…
We study fluctuations of the number of photocounts measured by an ideal photodetector illuminated by light scattered in an amplifying disordered medium, below the threshold for random lasing. We show that the variance of fluctuations and their correlation function carry information about fluctuating properties of the medium. A direct link is established between the fluctuations of the number of photocounts due to the amplified spontaneous emission (ASE) and the dimensionless conductance g of the medium. Our results suggest a possibility of probing amplifying disordered media by analyzing stati…
Single mode laser fields oscillate at frequencies well outside the realm of electronics, but their phase/frequency fluctuations fall into the radio frequency domain, where direct manipulation is possible. Electro-optic devices have sufficient bandwidth for controlling and tailoring the dynamics of a laser field down to sub-nanosecond time scales. Thus, a laser field can be arbitrarily reshaped and in particular its phase/frequency fluctuations can be in principle removed. In practice, the time evolution of a reference laser field can be cloned to replace the fluctuations of another laser field…
We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess Gaussian probability density function and establish quantitative criteria for realizing the Gaussian statistics depending on the laser propagation distance, the laser beam waist, the laser frequency and the turbulence strength. We calculate explicitly the laser envelope pair correlation function and corrections to its higher order correlation functions breaking Gaussianity. We discuss also statistical properties of the brightest sp…
The limits of applicability of the Lang-Kobayashi (LK) model for a semiconductor laser with optical feedback are analyzed. The model equations, equipped with realistic values of the parameters, are investigated below solitary laser threshold where Low Frequency Fluctuations (LFF) are usually observed. The numerical findings are compared with experimental data obtained for the selected polarization mode from a Vertical Cavity Surface Laser (VCSEL) subject to polarization selective external feedback. The comparison reveals the bounds within which the dynamics of the LK can be considered as reali…
Lévy flights for light have been demonstrated in disordered systems with and without optical gain, and remained unobserved in ordered ones. In the present letter, we investigate, numerically and experimentally, Lévy flights for light in ordered systems due to an ordered (conventional) laser. The statistical analysis was performed on the intensity fluctuations of the output spectra upon repeated identical experimental realizations. We found out that the optical gain and the mirrors reflectivity are critical parameters governing the fluctuation statistics. We identified Lévy regimes for gain aro…
We theoretically study the collective excitation modes of a topological laser device operating in a single-mode steady-state with monochromatic emission. We consider a model device based on a two-dimensional photonic Harper-Hofstadter lattice including a broadband gain medium localized on the system edge. Different regimes are considered as a function of the value of the optical nonlinearity and of the gain relaxation time. The dispersion of the excitation modes is calculated via a full two-dimensional Bogoliubov approach and physically interpreted in terms of an effective one-dimensional theo…
A study of the Mode-locking lasing pulse formation in closed cavities is presented within a statistical mechanical framework where the onset of laser coincides with a thermodynamic phase transition driven by the optical power pumped into the system. Electromagnetic modes are represented by classical degrees of freedom of a Hamiltonian model at equilibrium in an effective ensemble corresponding to the stationary laser regime. By means of optimized Monte Carlo numerical simulations, the system properties are analyzed varying mode interaction dilution, gain profile and number of modes. Novel prop…
We provide theoretical and experimental evidence of statistical outliers in random laser emission that are not accounted for by the, now established, power-law tailed (Lévy) distribution. Such outliers manifest themselves as single, large isolated spikes over an otherwise smooth background. A statistical test convincingly shows that their probability is larger than the one extrapolated from lower-intensity events. To compare with experimental data, we introduced the anomaly parameter that allows for an identification of such rare events from experimental spectral measurements and that agrees a…
It is known that cross-correlation between the random intensity fluctuations of two lasers forming electromagnetically-induced transparency (EIT) exhibits a transition from correlation to anticorrelation. We study the linewidth behavior of this transition and have found the linewidth is below the (effective) coherence lifetime limit and is only limited by competing noises. We established a numerical model which reveals the linewidth dependence on laser linewidth and laser power. Our experiments using lasers with different linewidth showed results in qualitative agreement with the model. This r…
Long ground-Rydberg coherence lifetime is interesting for implementing high-fidelity quantum logic gates, many-body physics, and other quantum information protocols. However, the potential well formed by a conventional far-off-resonance red-detuned optical-dipole trap that is attractive for ground-state cold atoms is usually repulsive for Rydberg atoms, which will result in the rapid loss of atoms and low repetition rate of the experimental sequence. Moreover, the coherence time will be sharply shortened due to the residual thermal motion of cold atoms. These issues can be addressed by a one-d…
Representing an ensemble of random lasers with an ensemble of random matrices, we compute average number of lasing modes and its fluctuations. The regimes of weak and strong coupling of the passive resonator to environment are considered. In the latter case, contrary to an earlier claim in the literature, we do not find a power-law dependence of the average mode number on the pump strength. For the relative fluctuations, however, a power law can be established. It is shown that, due to the mode competition, the distribution of the number of excited modes over an ensemble of lasers is not binom…
We describe statistical and coherence properties of the radiation from x-ray free electron lasers (XFEL). It is shown that the X-ray FEL radiation before saturation is described with gaussian statistics. Particularly important is the case of the optimized X-ray FEL, studied in detail. Applying similarity techniques to the results of numerical simulations allowed us to find universal scaling relations for the main characteristics of an X-ray FEL operating in the saturation regime: efficiency, coherence time and degree of transverse coherence. We find that with an appropriate normalization of th…
We describe a scheme, operating in a manner analogous to a reversed Raman output coupler, for measuring the phase-sensitive quadrature statistics of an atom laser beam. This scheme allows for the transferral of the atomic field statistics to an optical field, for which the quantum statistics may then be measured using the well-developed technology of optical homodyne measurement.
High frequency fluctuation in the optical signal generated in Fourier-Domain Mode Locked fiber laser (FDML-FL), which is the major problem and degrades the laser performance, is not yet fully analyzed or studied. The basic theory which is causing this high frequency fluctuation is required to clearly understand its dynamics and to control it for various applications. In this letter, by analyzing the signal and system dynamics of FDML-FL, we theoretically demonstrate that the high frequency fluctuation is induced by the intrinsic instability of frequency offset of the signal in cavity with nonl…
Statistical properties of a laser based on a one-dimensional disordered superlattice open at one side are studied numerically. The passive normal modes of the system are determined using the Feshbach projection technique. It is found that the mode competition due to the spacial hole burning leads to a saturation of the number of lasing modes with increasing pump rate. It is also responsible for nonmonotonic dependence of intensities of lasing modes as functions of pumping. Computed distributions of spectral spacing and intensity statistics are in qualitative agreement with experimental results…
Through examining the product of the mathematical variance of intensity with respect to time and frequency, we arrive at a temporal characterization of laser pulses through parameters for pulse duration, group delay dispersion and temporal form. These statistics, which are sufficient to predict subsequent pulse behavior, are recoverable in a simple experiment, measuring the two-photon-induced photocurrents in three nonlinear diodes. With only two photodiodes, we demonstrate that pulse durations as low as several tens of femtoseconds can be easily measured in a single shot if the usual assumpti…
The effect of a random phase diffuser on fluctuations of laser light (scintillations) is studied. Not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed. The explicit dependence of the scintillation index on finite-time phase variations is obtained for long propagation paths. It is shown that for large amplitudes of phase fluctuations, a finite-time effect decreases the ability of phase diffuser to suppress the scintillations.
We propose and experimentally demonstrate parallel LiDAR using random intensity fluctuations from a highly multimode laser. We optimize a degenerate cavity to have many spatial modes lasing simultaneously with different frequencies. Their spatio-temporal beating creates ultrafast random intensity fluctuations, which are spatially demultiplexed to generate hundreds of uncorrelated time traces for parallel ranging. The bandwidth of each channel exceeds 10 GHz, leading to a ranging resolution better than 1 cm. Our parallel random LiDAR is robust to cross-channel interference, and will facilitate …
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain light propagation by Lévy walks, i.e. with a `heavy-tailed' distribution of steps, has opened the opportunity to investigate the behavior of a superdiffusive optical gain medium, that can lead to a "superdiffusive random laser." Here, we present a theoretical investigation, based on Monte Carlo simulations, on such a kind of medium, focusing on th…
We present a rigorous statistical-mechanics theory of nonlinear many mode laser systems. An important example is the passively mode-locked laser that promotes pulse operation when a saturable absorber is placed in the cavity. It was shown by Gordon and Fischer [1] that pulse formation is a first-order phase transition of spontaneous ordering of modes in an effective "thermodynamic" system, in which intracavity noise level is the effective temperature. In this paper we present a rigorous solution of a model of passive mode locking. We show that the thermodynamics depends on a single parameter, …
Emission of pairs of photons in the interface metal-dielectric under the laser excitation arising due to the time-dependent perturbation of the zero-point fluctuations of the electromagnetic field by photons of the laser is considered. The enhancement of this emission by surface plasmons may be used for getting polarization-entangled photons. A possibility to compensate the energy of the zero-point fluctuations of bosons by other fluctuations with negative energy is discussed.
Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier-expansion for the laser in the LED regime. Fluctuations of populations of lasing levels are taken into account as perturbations. Spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons and broad the spectrum of a bad cavity thresholdless and the superradiant lasers. T…
Mode-locked lasers exhibit complex nonlinear dynamics. Precise observation of these dynamics will aid in understanding of the underlying physics and provide new insights for laser design and applications. The starting dynamics, from initial noise fluctuations to the mode-locking regime, have previously been observed directly by time-stretched transform-based real-time spectroscopy. However, the regime transition dynamics, which are essential processes in mode-locked lasers, have not yet been resolved because regime transition process tracking is very challenging. Here we demonstrate the first …
This work demonstrates the Nd:YAG waveguide laser as an efficient platform for the bio-sensing. The waveguide was fabricated in the Nd:YAG crystal by the cooperation of the ultrafast laser writing and ion irradiation. As the laser oscillation in the Nd:YAG waveguide is ultra-sensitivity to the external environment of the waveguide. Even a weak disturbance would induce a large variation of the output power of the laser. According to this feature, the Nd:YAG waveguide coated with Graphene and WSe2 layers is used as substrate for the microfluidic channel. When the microflow crosses the Nd:YAG wav…
High-power femtosecond laser radiation propagates nonlinearly in air exhibiting pulse self-focusing and strong multiphoton medium ionization, which leads to the spatial fragmentation of laser pulse into highly-localized light channels usually called the filaments. The filaments are characterized by high optical intensity, reduced (even zero) angular spreading and can contain laser plasma or be plasmaless (postfilaments). The presence of optical turbulence on the propagation path dramatically changes pulse filamentation dynamics and in some cases causes pulse fragmentation enhancement and colla…
A many-mode laser with nonlinear modal interaction could serve as a model system to study many-body physics. However, precise and continuous tuning of the interaction strength over a wide range is challenging. Here, we present a unique method for controlling lasing mode structures by introducing random phase fluctuation to a nearly degenerate cavity. We show numerically and experimentally that as the characteristic scale of phase fluctuation decreases by two orders of magnitude, the transverse modes become fragmented and the reduction of their spatial overlap suppresses modal competition for g…
Semiconductor lasers with time-delayed optical feedback display a wide range of dynamical regimes, which have found various practical applications. They also provide excellent testbeds for data analysis tools for characterizing complex signals. Recently, several of us have analyzed experimental intensity time-traces and quantitatively identified the onset of different dynamical regimes, as the laser's current increases. Specifically, we identified the onset of low-frequency fluctuations (LFFs), where the laser intensity displays abrupt dropouts, and the onset of coherence collapse (CC), where …
Metrology experiments can be limited by the noise produced by the laser involved via small fluctuations in the laser's power or frequency. Typically, active power stabilization schemes consisting of an in-loop sensor and a feedback control loop are employed. Those schemes are fundamentally limited by shot noise coupling at the in-loop sensor. In this letter we propose to use the optical spring effect to passively stabilize the classical power fluctuations of a laser beam. In a proof of principle experiment, we show that the relative power noise of the laser is stabilized from approximately $2 …
When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and consistent from shot-to-shot. Above the lasing threshold, the spectrum of emitted light becomes spiky and shows strong fluctuations from shot-to-shot. Recent experiments have reported that emitted intensity resembles a power-law distribution (\emph{i.e.} Lévy statistics). Recent theories have described the emergence of Lévy statistics as an intrinsic property of lasi…
The noise feature of a single mode class-A laser is investigated in the presence (amplifier) and absence (free-running) of an input signal. The Maxwell-Bloch equations of motion have been solved after adding the cavity Langevin force to calculate fluctuations that imposed to the atomic population inversion and the amplitude and phase of cavity electric field. The correlation function of these fluctuations is then used to derive the spontaneous emission, amplitude, and phase noise fluxes in the below and above-threshold states. The bandwidth of noise fluxes is not only adjusted by the amplitude…
This paper presents computational and experimental studies on wavelength/frequency fluctuation characteristics of high pulse repetition rate (PRR: 18 kHz) dye laser pumped by frequency doubled Nd:YAG laser (532 nm). The temperature gradient in the dye solution is found to be responsible for wavelength fluctuations of the dye laser at low flow rates (2800<Red<5600). The turbulence Reynolds number (ReT) and the range of eddy sizes present in the turbulent flow are found to be responsible for the fluctuations at high flow rates (8400<Red<17000). A new dimensionless parameter, dimensionless eddy s…
Quantum vacuum fluctuations give rise to effective non-linear interactions between electromagnetic fields. A prominent signature of quantum vacuum nonlinearities driven by macroscopic fields are signal photons differing in characteristic properties such as frequency, propagation direction and polarization from the driving fields. We devise a strategy for the efficient tracing of the various vacuum-fluctuation-mediated interaction processes in order to identify the most prospective signal photon channels. As an example, we study the collision of up to four optical laser pulses and pay attention…
Combining topologically-protected chiral light transport and laser amplification gives rise to topological lasers, whose operation is immune to fabrication imperfections and defects, uncovering the role of topology in a novel nonlinear non-Hermitian regime. We study a topological laser based on the photonic Haldane model with selective pumping of chiral edge modes described by saturable gain. We investigate elementary excitations around the mean-field steady state and their consequences for the coherence properties. In particular, we show that the hybridization of chiral edge modes gives rise …
