Random laser in the localized regime

Laser action in the regime of Anderson localization is investigated by coupling Maxwell's equations in a strongly scattering medium with the rate equations of a four-level atomic system. We find that the localized modes of the passive medium are not modified by the presence of gain and serve as resonant microcavities of the random laser. The spectrum of laser emission is shown to depend on the location of the external pump. These results are similar to the recent experimental observations in semiconductor powder [Cao et al., Phys. Rev. Lett. 82, 2278 (1999)]. We show that local pumping of the system allows selective excitation of individual localized modes.

We propose an idea to excite localized modes in a photonic crystal (PC) waveguide without ruining the discrete translational symmetry of the lattice. This can be done by arranging dispersive elements having negative permittivity over a desired frequency range into a periodic structure. We demonstrate numerically the realization of a cavity mode inside the air region of a geometrical defectless two-dimensional square-lattice PC consisting of polaritonic cylinders placed in air matrix. The corresponding waveguide structure in the form of a PC fiber supports the cavity mode as a guided mode to propagate along the guiding direction at very small propagation constant with near zero group velocity. These localized modes can be recognized as localized defectless modes inside the structure with four-fold symmetry.

We investigate the replica symmetry breaking (RSB) phenomenon in random lasers (RLs) through Monte Carlo simulations employing photonic random walkers that diffuse and get randomly scattered in the active medium. The walkers interact not only with the population of excited atoms, but also among themselves, in a mean-field-type approach based on the Langevin equation for the stochastic dynamics of RL modes. We obtain the proper profile of the distribution $P(q)$ of the Parisi overlap parameter in the RSB glassy phase, with two pronounced side maxima at $q=\ifmmode\pm\else\textpm\fi{}1$ above the RL threshold, in contrast with some recent numerical studies. Remarkably, when the interactions among photonic walkers are not included, a replica-symmetric profile with a single maximum of $P(q)$ at $q=0$ is found for any excitation energy. We further study the Gaussian and L\'evy emission regimes and statistical correlations of intensity fluctuations in distinct modes of the same spectrum, using a Pearson correlation coefficient recently applied to RLs. Our findings are consistent with experimental results for the intensity statistics and $P(q)$ distributions in RL materials.

The selective spatial mode excitation of a bi-dimensional grating-coupled micro-cavity called a cavity resonator integrated grating filter (CRIGF) is reported using an incident beam shaped to reproduce the theoretical emission profiles of the device in one and subsequently two dimensions. In both cases, the selective excitation of modes up to order 10 (per direction) is confirmed by responses exhibiting one (respectively two) spectrally narrowband resonance(s) with a good extinction of the other modes, the latter being shown to depend on the parity and order(s) of the involved modes. These results pave the way toward the demonstration of multi-wavelength spatially selective reflectors or fiber-to-waveguide couplers. Also, subject to an appropriate choice of the materials constituting the CRIGF, this work can be extended to obtain mode-selectable laser emission or nonlinear frequency conversion.

We report long-lived, highly spatially localized plasmon states on the surface of nanoporous gold nanoparticles—nanosponges—with high excitation efficiency. It is well known that disorder on the nanometer scale, particularly in two-dimensional systems, can lead to plasmon localization and large field enhancements, which can, in turn, be used to enhance nonlinear optical effects and to study and exploit quantum optical processes. Here, we introduce promising, three-dimensional model systems for light capture and plasmon localization as gold nanosponges that are formed by the dewetting of gold/silver bilayers and dealloying. We study light-induced electron emission from single nanosponges, a nonlinear process with exponents of n≈5...7, using ultrashort laser pulse excitation to achieve femtosecond time resolution. The long-lived electron emission process proves, in combination with optical extinction measurements and finite-difference time-domain calculations, the existence of localized modes with lifetimes of more than 20 fs. These electrons couple efficiently to the dipole antenna mode of each individual nanosponge, which in turn couples to the far-field. Thus, individual gold nanosponges are cheap and robust disordered nanoantennas with strong local resonances, and an ensemble of nanosponges constitutes a meta material with a strong polarization independent, nonlinear response over a wide frequency range.

We investigate numerically, within the rotating wave approximation, the existence of stationary anharmonic localized modes in diatomic lattices, where the atoms are ordered according to the Thue-Morse sequence and the Fibonacci sequence, respectively. A symmetric potential with harmonic and quartic terms is used, and both the case of hard and soft anharmonicity is investigated. We find the existence of localized modes for frequencies not allowed in the harmonic approximation, both when we consider hard and soft anharmonicity in the potential. Above the top of the allowed frequency values, there turn out to be only modes with a hard anharmonicity. In contrast to the periodic chains previously investigated, we find for the Thue-Morse lattice even modes which seem to be stable in molecular-dynamics simulations.

Coherent random lasing behavior in low-dimensional active weakly scattering random systems

Unintentional but unavoidable fabrication imperfections in state-of-the-art photonic-crystal waveguides lead to the spontaneous formation of Anderson-localized modes thereby limiting slowlight propagation and its potential applications. On the other hand, disorder-induced cavities offer an approach to cavity-quantum electrodynamics and random lasing at the nanoscale. The key statistical parameter governing the disorder effects is the localization length, which together with the waveguide length determines the statistical transport of light through the waveguide. In a disordered photonic-crystal waveguide, the localization length is highly dispersive, and therefore, by controlling the underlying lattice parameters, it is possible to tune the localization of the mode. In the present work, we study the localization length in a disordered photonic-crystal waveguide using numerical simulations. We demonstrate two different localization regimes in the dispersion diagram where the localization length is linked to the density of states and the photon effective mass, respectively. The two different localization regimes are identified in experiments by recording the photoluminescence from quantum dots embedded in photonic-crystal waveguides.

The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors. Finally, using the framework of an extended Bose-Hubbard model, we show that while quantum fluctuations destroy the mobility of slowly moving, strongly localized classical modes, coherent mobility of rapidly moving states survives even in a strongly quantum regime.

We present measurements of the spatial intensity distribution of localized modes in a two-dimensional open microwave cavity randomly filled with cylindrical dielectric scatterers. We show that each of these modes displays a range of localization lengths, and we successfully relate the largest value to the measured leakage rate at the boundary. These results constitute unambiguous signatures of the existence of strongly localized electromagnetic modes in two-dimensional open random media.

Coherent control of phonon modes by use of multipulse setups has been studied in various semiconductor systems ranging from bulk materials to multiple-quantum-well super­ lattice structures 1-6 as well as in other solid-state systems 7.8 and for molecular vibrationsY The control of first- and second-order back-folded acoustic modes in a superlattice has been demonstrated. lo In contrast to previous work, we present selective excitation of phonon modes within a single triplet of zone-folded modes where the frequency spacing is only a few tens of GHz. The evolution of the modes is followed throughout different control pulse delays to map out the continuous tuning of their amplitude ratios. The principle is based on the use of a second pump or control pulse for phonon generation with a defined phase with respect to the first excitation. The coherent superposition leads to a modification of the phonon amplitudes within the triplet structure of the first branch of zone-folded acoustic phonons. This results in an enhancement or suppression of the phonon oscillations. The manipulation and selective excitation of the phonon modes within a zone-folded triplet are possible by taking advantage of the high signal-to-noise ratio and the fast data acquisition rate of a high-speed asynchronous optical sampling (ASOPS) system. II The demonstrated principle could be extended to prepare well-defined phonon states for phonon spectroscopy and phonon amplification schemes 12 and to study phonon­ phonon interactions.

We theoretically demonstrate the tunabiltiy of terahertz random lasers composed of high temperature superconductor YBCO and ruby layers as active medium. The considered system is a one-dimensional disordered medium made of ruby grain and YBCO. Finite-difference time domain method is used to calculate the emission spectrum and spatial distribution of electric field at different temperatures. Our numerical results reveal that the superconductor based random lasers exhibit large temperature tunability in the terahertz domain. The emission spectrum is significantly temperature dependent, the number of lasing modes and their intensities increase with decreasing temperature. Also, we make some discussion to explain the reason for the observed tunability and the effect of temperature variation on the spatial distribution of the electric field in the disordered active medium.

Gain amplification and coherent lasing lines through random lasing (RL) can be produced by a random distribution of scatterers in a gain medium. If these amplified light sources can be seamlessly integrated into biological systems, they can have useful bio-optical applications, such as highly accurate sensing and high-resolution imaging. In this paper, a fully biocompatible light source showing RL and amplified spontaneous emission (ASE) with a reduced threshold is reported. Random cavities were induced in a biocompatible silk protein film by incorporating an inverse opal with an inherent disorder and a biocompatible dye for optical gain into the film. By choosing the appropriate air-sphere diameters, clear RL spikes in the emission spectra that were clearly distinguished from those of the ASE were observed in the silk inverse opal (SIO) with optical gain. Additionally, the RL output exhibited spatial coherence; however, the ASE did not. The high surface-to-volume ratio and amplification of the SIO led to highly efficient chemosensing in the detection of hydrogen chloride vapor. Moreover, SIO could be miniaturized to be made suitable for injection into biological tissues and obtain RL signals. Our results, which open the way for the development of a new generation of miniaturized bio-lasers, may be considered as the first example of engineered RL with biocompatible materials.

Anharmonic contributions to the Eliashberg function due to a low-energy local boson mode of finite width are considered for a harmonic metal. Excitation of the multiple-frequency modes leads to redistribution of spectral weight in the generalized Eliashberg function from the low- to the high-energy region, which reduces the electron-boson coupling. This is seen in the calculated temperature dependence of the interaction constants ${\ensuremath{\lambda}}_{\mathit{n}}$ entering the Eliashberg equations. The rapid decrease with temperature of ${\ensuremath{\lambda}}_{\mathit{n}>0}$ can be used to derive a simple analytical expression, which reproduces almost exactly the temperature dependence, ${\ensuremath{\lambda}}_{\mathit{n}>0}$(T), calculated from the exact expression. Normal-state properties of alkaline-doped ${\mathrm{C}}_{60}$ are investigated within the two-peak model (${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\sim}50 K and ${\mathrm{\ensuremath{\omega}}}_{1}$\ensuremath{\sim}900 K) for the possibility to extract information about the local modes themselves and their coupling to the conduction electrons. The electronic specific heat shows peculiarities only in the case of an extremely strong coupling. Due to the low-energy peak the temperature dependence of the electrical resistivity deviates more and more from the linear law with increasing adiabaticity parameter A=(m/M)(${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$/\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{0}$). This leads, however, to a negative-curvature dependence. The experimental curve for ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ has a positive curvature and can be fitted only in the case of a very strong coupling of electrons to the high-energy mode. The thermal electronic conductivity displays a minimum at T\ensuremath{\sim}\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{0}$/${\mathit{k}}_{\mathit{B}}$. The curvature as a function of temperature is determined by the magnitude of A.

Unlike the solid-air and solid-liquid interfaces, the optical properties of metal nanoparticles adsorbed at the liquid-liquid interface have not been theoretically exploited to date. In this work, the three dimensional finite difference time domain (3D-FDTD) method is employed to clarify the localized surface plasmon resonance (LSPR) based optical properties of gold nanoparticles (NPs) adsorbed at the water-oil interface, including near field distribution, far field absorption and their relevance. The LSPR spectra of NPs located at a liquid-liquid interface are shown to differ significantly from those in a uniform liquid environment or at the other interfaces. The absorption spectra exhibit two distinct LSPR peaks, the positions and relative strengths of which are sensitive to the dielectric properties of each liquid and the exact positions of the NPs with respect to the interface. Precise control of the particles' position and selection of the appropriate wavelength of the excitation laser facilitates the rational design and selective excitation of localized plasmon modes for interfacial NPs, a necessary advance for the exploration of liquid-liquid interfaces via surface enhanced Raman spectroscopy (SERS). According to our calculations, the SERS enhancement factor for Au nanosphere dimers at the water-oil interface can be as high as 10(7)-10(9), implying significant promise for future investigations of interfacial structure and applications of liquid-liquid interfaces towards chemical analysis.