Random resonators and prelocalized modes in disordered dielectric films

Properties and Applications of Random Lasers as Emerging Light Sources and Optical Sensors: A Review

In a random laser (RL), optical feedback arises from multiple scattering instead of conventional mirrors. RLs generate a laser-like emission, and meanwhile take advantage of a simpler and more flexible laser configuration. The applicability of RLs as light sources and optical sensors has been proved. These applications have been extended to the biological field, with tissues as natural scattering materials. Herein, the current state of the RL properties and applications was reviewed.

Random laser oscillation from an organic fluorescent dye loaded inside a porous zirconia medium

Porous zirconia medium (PZrM) has been fabricated successfully using polystyrene microparticles (MPs) as templates. The emission spectra of rhodamine B (RhB) [optical amplifying medium] loaded inside PZrM [porous scatterers] were obtained at numerous excitation light intensities. The lasing thresholds (I_th) have been determined experimentally from the variations in the intensity of random laser oscillation peaks, which are suitably separated from the measured emission spectra. I_th is closely related to the pore sizes of PZrM and the added amount of PZrM powder, and it clearly provided the minimum against the pore size. This fact is explained reasonably by the simulation of scattering efficiency on the basis of the Mie scattering theory. Consequently, PZrM as a porous scatterer is superior to Zr MPs from the viewpoint of random laser oscillation.

Porous zirconia medium as a porous scatterer was superior to zirconia microparticles with respect to random laser oscillation.

Random Lasing via Plasmon-Induced Cavitation of Microbubbles

Numerous laboratories have observed random lasing from optically pumped solutions of plasmonic nanoparticles (NPs) suspended with organic dye molecules. The underlying mechanism is typically attributed to the formation of closed-loop optical cavities enabled by the large local field and scattering enhancements in the vicinity of plasmonic NPs. In this manuscript, we propose an alternative mechanism that does not directly require the plasmon resonance. We used high-speed confocal microspectroscopy to observe the photophysical dynamics of NPs in solution. Laser pulses induce the formation of microbubbles that surround and encapsulate the NPs, then sharp peaks <1.0 nm are observed that match the spectral signature of random lasing. Electromagnetic simulations indicate that ensembles of microbubbles may form optical corral containing standing wave patterns that are sufficient to sustain coherent optical feedback in a gain medium. Collectively, these results show that ensembles of plasmonic-induced bubbles can generate optical feedback and random lasing.

Influence of liquid crystalline phases on the tunability of a random laser

In this paper, we report the temperature behavior of an optimized disordered photonic system-based liquid crystal by means of heat capacity and refractive index measurements. The scattering system is formed by a porous borosilicate glass random matrix (about 60%) infiltrated with a smectogenic liquid crystal (about 16%) and a small amount of laser dye (0.1%). The rest of the scattering system is about 24% air, giving rise to a high refractive index contrast scattering system. Such a system has the functionality to change the refractive index contrast with temperature due to the liquid crystal temperature behavior. The system, optically pumped by the second harmonic of a Q-switched Nd:YAG pulsed laser working at 532 nm, exhibits random laser action, the threshold of which depends upon the liquid crystalline mesophase. Temperatures of existence of the smectic-B phase correspond to the most optimized random laser. In such a mesophase, the transport mean free path has been determined as about 16 μm in a coherent backscattering experiment.

All-optically controllable nanoparticle random laser in a well-aligned laser-dye-doped liquid crystal

This study reports for the first time an all-optically controllable nanoparticle random laser (NPRL) in a well-aligned laser-dye-doped liquid crystal (LDDLC) cell added with NPs and azo-dyes. Experimental results display that the NPRL can be obtained when the pumped energy exceeds the energy threshold (~3.5 μJ/pulse). The occurrence of the NPRL is attributable to the enhancement of the fluorescence by the multi-scattering events of the fluorescence photons from the randomly distributed NPs in the diffusion rout of the well-aligned LDDLC cell. In addition, the lasing intensity of the NPRL can decrease with increasing irradiation time of one UV beam. Continuing irradiation of one green beam following the UV illumination can increasingly recover the lasing intensity of the NPRL. The all-optically reversible controllability of the NPRL is basically attributed to the successive UV-beam-induced increase and green-beam-induced decrease in the randomness of the LDDLC via their interactions with the curved cis and rod-like trans isomers after the accumulation of the trans→cis and cis→trans back isomerizations of the azo-dyes, respectively. The former and latter mechanisms can decrease and increase the laser-dye's absorption and thus the induced spontaneous emission, respectively. These consequences can decrease and increase the lasing intensity, or equivalently, increase and decrease the energy threshold for the occurrence of the NPRL, respectively.

Hybrid Multilayered Plasmonic Nanostars for Coherent Random Lasing

Here, we report that hybrid multilayered plasmonic nanostars can be universally used as feedback agents for coherent random lasing in polar or nonpolar solutions containing gain material. We show that silver-enhancement of gold nanostars reduces the pumping threshold for coherent random lasing substantially for both a typical dye (R6G) and a typical fluorescent polymer (MEH-PPV). Further, we reveal that the lasing intensity and pumping threshold of random lasers based on silver-enhanced gold nanostars are not influenced by the silica coating, in contrast to gold nanostar-based random lasers, where silica-coated gold nanostars support only amplified spontaneous emission but no coherent random lasing.

Plasmonic Nanostars as Efficient Broadband Scatterers for Random Lasing

Huge spectral coverage of random lasing throughout the visible up to the infrared range is achieved with star-shaped gold nanoparticles ("nanostars"). As intrinsically broadband scattering centers, the nanostars are suspended in solutions of various laser dyes, forming randomly arranged resonators which support coherent laser modes. The narrow emission line widths of 0.13 nm or below suggest that gold nanostars provide an efficient coherent feedback for random lasers over an extensive range of wavelengths, all together spanning almost a full optical octave from yellow to infrared.

Excitonic Lasing in Solution-Processed Subwavelength Nanosphere Assemblies

Lasing in solution-processed nanomaterials has gained significant interest because of the potential for low-cost integrated photonic devices. Still, a key challenge is to utilize a comprehensive knowledge of the system's spectral and temporal dynamics to design low-threshold lasing devices. Here, we demonstrate intrinsic lasing (without external cavity) at low-threshold in an ultrathin film of coupled, highly crystalline nanospheres with overall thickness on the order of ∼λ/4. The cavity-free geometry consists of ∼35 nm zinc oxide nanospheres that collectively localize the in-plane emissive light fields while minimizing scattering losses, resulting in excitonic lasing with fluence thresholds at least an order of magnitude lower than previous UV-blue random and quantum-dot lasers (<75 μJ/cm(2)). Fluence-dependent effects, as quantified by subpicosecond transient spectroscopy, highlight the role of phonon-mediated processes in excitonic lasing. Subpicosecond evolution of distinct lasing modes, together with three-dimensional electromagnetic simulations, indicate a random lasing process, which is in violation of the commonly cited criteria of strong scattering from individual nanostructures and an optically thick sample. Subsequently, an electron-hole plasma mechanism is observed with increased fluence. These results suggest that coupled nanostructures with high crystallinity, fabricated by low-cost solution-processing methods, can function as viable building blocks for high-performance optoelectronics devices.

Decoupling gain and feedback in coherent random lasers: experiments and simulations

We propose and demonstrate a coherent random laser in which the randomly distributed scattering centres are placed outside the active region. This architecture is implemented by enclosing a dye solution between two agglomerations of randomly positioned titanium dioxide nanoparticles. The same spectral signature, consisting of sharp spikes with random spectral positions, is detected emerging from both ensembles of titanium dioxide nanoparticles. We interpret this newly observed behaviour as due to the optical feedback given by back-scattered light from the scattering agglomerations, which also act as output couplers. A simple model is presented to simulate the observed behaviour, considering the amplitude and phase round trip conditions that must be satisfied to sustain lasing action. Numerical simulations reproduce the experimental reports, validating our simple model. The presented results suggest a new theoretical and experimental approach for studying the complex behavior of coherent random lasers and stimulate the realization of new devices based on the proposed architecture, with different active and scattering materials.

Gold nanostars for random lasing enhancement

We demonstrate random lasing with star-shaped gold nanoparticles ("nanostars") as scattering centers embedded in a dye-doped gain medium. It is experimentally shown that star-shaped gold nanoparticles outperform those of conventional shapes, such as spherical or prolate nanoparticles. The nanoparticles are randomly distributed within a thin film of gain medium, forming resonators which support coherent laser modes. Driven by single-pulsed excitation, the random lasers exhibit coherent lasing thresholds in the order of 0.9 mJ/cm(2) and spectrally narrow emission peaks with linewidths less than 0.2 nm. The distinguished random laser comprising nanostars is likely to take advantage of the high plasmonic field enhancements, localized at the spiky tips of the nanostars, which improves the feedback mechanism for lasing and increases the emission intensity of the random laser.

Statistics and control of waves in disordered media

Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to describe the scaling, fluctuations, delay time, density of states, and control of waves propagating through and within disordered systems. Microwave measurements, random matrix theory calculations, and computer simulations are employed to study the statistics of transmission and focusing in single samples and the scaling of the probability distribution of transmission and transmittance in random ensembles. Finally, we explore the disposition of the energy density of transmission eigenchannels inside random media.

Photoluminescence performance enhancement of ZnO/MgO heterostructured nanowires and their applications in ultraviolet laser diodes

An ultralow threshold random lasing with a good temperature tolerance has been realized in coaxial ZnO/MgO heterostructured nanowires.

The single-channel regime of transport through random media

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a 'necklace state'. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

Cascade-pumped random lasers with coherent emission formed by Ag-Au porous nanowires

A series of sequentially cascade-pumped random lasers is reported. It consists of three random lasers in which the Ag-Au bimetallic porous nanowires play the role of scatterers, and the gain materials are coumarin 440 (C440), coumarin 153 (C153), and rhodamine 6G (R6G), respectively. The random laser with C440 is first pumped by a 355 nm pulsed laser. The emission of C440 pumps the C153, and the emission of C153 pumps the R6G sequentially. Low-threshold coherent emissions from the three random lasers are observed. The cascade-pumped random lasers can be achieved easily with low cost and can be used in applications conveniently.

Random lasing from granular surface of waveguide with blends of PS and PMMA

Lasing from a planar waveguide with the blend of Polystyrene(PS): Poly-methylmethacrylate(PMMA) doped with tris(8-hydroxyquinolinato)aluminum(Alq(3)) and 4-(dicyanomethylene)-2-tert-butyl-6(1,1,7,7-tetramethyljulolidyl-9-enyl)-4H-pyran(DCJTB) was investigated. Due to phase separation of the blend of PS:PMMA during the solvent evaporation process, a waveguide with granular surface was obtained, which has 2D island-like nanostructures with diameters ranging between 200 and 400 nm and heights at about 25 nm. Pumped by a YAG laser with wavelength of 355 nm, a significant random lasing was observed. Compared to the amplified spontaneous radiation (ASE) of planar waveguides with only PMMA or PS doped with Alq3:DCJTB prepared under the same conditions, the lasing threshold of the former is decreased by about 5 times, and the full width at half maximum (FWHM) is reduced to 1.7 nm from 12~15 nm. Our experiments show a promising method to achieve lower threshold for organic lasers.

Remarkable decrease in threshold for electrically pumped random ultraviolet lasing from ZnO film by incorporation of Zn2TiO4 nanoparticles

We have comparatively investigated electrically pumped random lasing (RL) actions of two metal-insulator-semiconductor structured devices using pure ZnO and Zn2TiO4-nanoparticle-incorporated ZnO films as the semiconductor components i.e. light-emitting layers, respectively. It is demonstrated that the device using the Zn2TiO4-nanoparticle-incorporated ZnO film as the light-emitting layer exhibits a much smaller threshold current for the electrically pumped RL, which is ascribed to the enhanced multiple light scattering by incorporation of Zn2TiO4 nanoparticles into ZnO film. It is believed that this work provides a strategy for developing low-threshold ZnO-based random lasers.

Long-tail statistics of the Purcell factor in disordered media driven by near-field interactions

In this Letter, we study the Purcell effect in a 3D disordered dielectric medium through fluorescence decay rates of nanosized light sources. We report distributions of Purcell factor with non-Gaussian long-tailed statistics and an enhancement of up to 8 times the average value. We attribute this large enhancement to strong fluctuations of the local density of states induced by near-field scattering sustained by more than one particle. Our findings go beyond standard diagrammatic and single-scattering models and can be explained only by taking into account the full near-field interaction.

Electrically controllable liquid crystal random lasers below the Fréedericksz transition threshold

This investigation elucidates for the first time electrically controllable random lasers below the threshold voltage in dye-doped liquid crystal (DDLC) cells with and without adding an azo-dye. Experimental results show that the lasing intensities and the energy thresholds of the random lasers can be decreased and increased, respectively, by increasing the applied voltage below the Fréedericksz transition threshold. The below-threshold-electric-controllability of the random lasers is attributable to the effective decrease of the spatial fluctuation of the orientational order and thus of the dielectric tensor of LCs by increasing the electric-field-aligned order of LCs below the threshold, thereby increasing the diffusion constant and decreasing the scattering strength of the fluorescence photons in their recurrent multiple scattering. This can result in the decrease in the lasing intensity of the random lasers and the increase in their energy thresholds. Furthermore, the addition of an azo-dye in DDLC cell can induce the range of the working voltage below the threshold for the control of the random laser to reduce.

Random semiconductor lasers: scattered versus Fabry-Perot feedback

As a result of growth imperfections, (Zn,Cd)O/ZnO quantum well structures exhibit random laser action. Fabrication of microresonators allows us to study and to compare directly cavity and scattered feedback. Our experimental and theoretical analysis shows that (i) pure random lasing generally requires a larger gain than in the standard Fabry-Perot regime, (ii) the presence of Mie scatterers in the semiconductor-based cavity does not substantially increase the lasing threshold, and (iii) the random feedback creates a subtle modal gain distribution that might be of particular importance for the dynamical properties, both with and without Fabry-Perot cavity.

All-optically controllable random laser based on a dye-doped liquid crystal added with a photoisomerizable dye

This study investigates, for the first time, an all-optically controllable random laser based on a dye-doped liquid crystal (DDLC) cell added with a photoisomerizable dye. Experimental results indicate that the lasing intensity of this random laser can be all-optically controlled to decrease and increase sequentially with a two-step exposure of one UV and then one green beam. All-optically reversible controllability of the random lasing emission is attributed to the isothermal nematic(N)-->isotropic(I) and I-->N phase transitions for LCs due to the UV-beam-induced trans-->cis and green-beam-induced cis-->trans back isomerizations of the photoisomerizable dye, respectively. The former and the latter can decrease and increase the spatial fluctuations of the order and thus of the dielectric tensor of LCs, respectively, subsequently increasing and decreasing the diffusion constant (or transport mean free path), respectively, and thus decaying and rising the scattering strength for the fluorescence photons in their recurrent multi-scattering process, respectively. The consequent decrease and increase of the lasing intensity for the random laser and thus the rise and descent of its energy threshold are generated, respectively.

Spatially mapping random lasing cavities

A mapping technique is developed to spatially resolve random laser-emission spectra from disordered solid media with an optical gain above the threshold excitation intensity for lasing; the technique is applied to pi-conjugated polymer 1 ms. By mapping the spatial extent of emission peaks in the random laser spectrum, bright areas that correspond to naturally formed lasing microcavities are unraveled. The size of the obtained microcavities matches the size extracted from the Fourier transform analysis of the laser-emission spectrum. Mapping at increased excitation intensities shows multiple resonant microcavities that lase at increasing threshold intensities.

Speckle instability: coherent effects in nonlinear disordered media

We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system. Analyzing the statistical properties of the instability thresholds for different values of the system size and disorder strength, a scaling law is emphasized. The later is found to also govern the smallest decay rate of the associated linear system, i.e., the "best" cavity realized by the scatterers, putting thus forward the crucial importance of interference effects. This is also underlined by the fact that coherent backscattering is still observed even in the chaotic regime.

All-optically controllable random laser based on a dye-doped polymer-dispersed liquid crystal with nano-sized droplets

This study elucidates for the first time an all-optically controllable random laser in a dye-doped polymer-dispersed liquid crystal (DDPDLC) with nano-sized LC droplets. Experimental results demonstrate that the lasing intensity of the random laser can be controlled to decrease by increasing irradiation time/intensity of one green beam, and increase by increasing the irradiation time of one red beam. The all-optical controllability of the random laser is attributed to the green (red)-beaminduced isothermal nematic-->isotropic (isotropic-->nematic) phase transition in LC droplets by trans-->cis (cis-->trans back) isomerization of azo dyes. This isomerization may decrease (increase) the difference between the refractive indices of the LC droplets and the polymer, thereby increasing (decreasing) the diffusion constant (or transport mean free path), subsequently decreasing the scattering strength and, thus, random lasing intensity.

Room temperature electrically pumped ultraviolet random lasing from ZnO nanorod arrays on Si

We report the electrically pumped ultraviolet random lasing from ZnO nanorod arrays on Si. Metal-insulator-semiconductor structures in a form of Au/SiO(2)/ZnO-nanorod-array were fabricated on Si. Such devices exhibit random lasing when the Au electrode is applied with a sufficiently high positive voltage. In this context, in the region adjacent to SiO(2)/ZnO-nanorod-array interface, stimulated emission from ZnO occurs due to population inversion and, moreover, light is scattered by the nanorods and SiO(2) films. Therefore, random lasing proceeds due to optical gain achieved by the stimulated emission and multiple scattering.

Lasing with resonant feedback in weakly scattering random systems

Laser action in active random media in the weak scattering regime far from Anderson localization is investigated by coupling Maxwell's equations with the rate equations of a four-level atomic system. We report systematic lasing action with resonant feedback and show that the lasing modes mostly consist of traveling waves spatially extended over the whole system. Next we address the question of the origin of the feedback mechanism in such a system where no disorder-induced long-lived resonances are available, and present strong evidence that they correspond to the quasimodes of the passive system. This in turn provides an original way to access the spatial distribution of the quasimodes of a non-Hermitian system.

Spatial extent of random laser modes

We have experimentally studied the distribution of the spatial extent of modes and the crossover from essentially single-mode to distinctly multimode behavior inside a porous gallium phosphide random laser. This system serves as a paragon for random lasers due to its exemplary high index contrast. In the multimode regime, we observed mode competition. We have measured the distribution of spectral mode spacings in our emission spectra and found level repulsion that is well described by the Gaussian orthogonal ensemble of random-matrix theory.

Liquid-crystal-based tunable high-Q directional random laser from a planar random microcavity

Temperature-tunable directional laser emission from a dye-doped liquid-crystal-based planar random cavity laser is presented. The optically pumped nematic liquid crystal infiltrated planar random microcavity produces an ultranarrow linewidth (0.03 nm, corresponding to Q>20,000), highly directional (1.4 degrees divergence angle) laser emission. By increasing the temperature from 27 degrees C to 34 degrees C, the wavelength of an emitted polarized laser can be tuned between 605.8 and 608.5 (ordinary light) and 631.3 and 624.9 nm (extraordinary light). A simulation result from the transfer matrix method that matches the experimental results well is also presented.

Unidirectional high intensity narrow-linewidth lasing from a planar random microcavity laser

Lasing was achieved in a new type of random laser: the planar random microcavity laser. The laser consists of a planar microcavity with a random gain layer. Optical confinement by the two-dimensional random cavity and the one-dimensional planar microcavity drastically reduces the number of resonant modes. As a result, the laser output is highly directional (the divergence angle is 1.68 degrees) with an extremely narrow-linewidth and ultralow threshold. All these phenomena are explained in terms of the coupling of random cavity modes and planar microcavity modes. The results demonstrate an important step towards applications of random lasers.

Absorption-induced confinement of lasing modes in diffusive random media

We present a numerical study of lasing modes in diffusive random media with local pumping. The reabsorption of emitted light suppresses the feedback from the unpumped part of the sample and effectively reduces the system size. The lasing modes are dramatically different from the quasi modes of the passive system (without gain or absorption). Even if all the quasi modes of a passive diffusive system are extended across the entire sample, the lasing modes are still confined in the pumped volume with an exponential tail outside it. The reduction of effective system volume by absorption broadens the distribution of decay rates of quasi modes and facilitates the occurrence of discrete lasing peaks.

Effects of spatial nonuniformity on laser dynamics

Semiclassical equations of lasing dynamics are rederived for a lasing medium in a cavity with a spatially nonuniform dielectric constant. The nonuniformity causes a radiative coupling between modes of the empty cavity, which results in a renormalization of self- and cross-saturation coefficients. Possible manifestations of these effects in random lasers are discussed.

Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization

We demonstrate low-threshold lasing in random amplifying layered medium via photon localization. Lasing is facilitated by resonant excitation of localized modes at the pump laser wavelength, which are peaked deep within the sample with greatly enhanced intensity. Emission occurs into long-lived localized modes overlapping the localized gain region. This mechanism overcomes a fundamental barrier to reducing lasing thresholds in diffusive random lasers, in which multiple scattering restricts the excitation region to the proximity of the sample surface.

Quasi-two-dimensional diffusive random laser action

We report on random lasing in a disordered system in which the multiple scattering feedback mechanism can be switched from a three-dimensional random walk to a quasi-two-dimensional type of transport. The emission from this system is anisotropic, extraordinary polarized, and is controlled via an external electric field. The phenomenon is observed in dye-doped polymer dispersed liquid crystals and makes use of the strong scattering anisotropies in these materials.

Enhanced mesoscopic correlations in dynamic speckle patterns

We study the temporal evolution of speckle patterns in transmission of short wave pulses through a disordered waveguide. In the diffuse regime, the short-range spatial structure of speckles is the same as for the continuous-wave (cw) illumination, whereas the long-range correlation between distant speckle spots grows linearly with time and can exceed its cw value. We discuss the physical origin of this phenomenon, compare our results to recent microwave experiments, and suggest that a similar linear growth with time should also be characteristic for other mesoscopic interference phenomena.

Amplified extended modes in random lasers

We report on a new random laser phenomenon that gives rise to narrow emission modes without requiring optical cavities. Sharp emission peaks are observed experimentally over a broad range of scattering strengths and analyzed in numerical calculations. We find that the introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are rare and often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.

Impact of weak localization in the time domain

We find a renormalized "time-dependent diffusion coefficient," D(t), for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, to the length, L, of the cylindrical sample with reflecting side walls and open ends. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversal slope that approaches an asymptotic value for R/L>>1. The value of D(t) extrapolated to t=0 depends only upon the dimensionless conductance g for R/L<<1 and only upon kl(0) for R/L>>1, where k is the wave vector and l(0) is the bare mean free path.

Theory of photon statistics and optical coherence in a multiple-scattering random-laser medium

We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.

Influence of spatial correlations on the lasing threshold of random lasers

The lasing threshold of a random laser is computed numerically from a generic model. It is shown that spatial correlations of the disorder in the medium (i.e., dielectric constant) lead to an increase of the decay rates of the eigenmodes and of the lasing threshold. This is in conflict with predictions that such correlations should lower the threshold. While all results are derived for photonic systems, the computed decay rate distributions also apply to electronic systems.

Breakdown of diffusion in dynamics of extended waves in mesoscopic media

We report the observation of nonexponential decay of pulsed microwave transmission through quasi-one-dimensional random dielectric media signaling the breakdown of the diffusion model. The decay rate of transmission falls nearly linearly in time corresponding to a nearly Gaussian distribution of the coupling strengths of quasinormal electromagnetic modes to free space at the sample surfaces. The peak and width of this distribution scale as L(-2.05) and L(-1.81), respectively.