Coupling and level repulsion in the localized regime: from isolated to quasiextended modes.

We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply peaked quasiextended modes. Level repulsion is observed experimentally and explained within a model of coupled resonators. The spectral and spatial evolution of the coupled modes is described in terms of the coupling coefficient and Q factors of resonators.

Extended quasimodes within nominally localized random waveguides.

We have measured the spatial and spectral dependence of the microwave field inside an open absorbing waveguide filled with randomly juxtaposed dielectric slabs in the spectral region in which the average level spacing exceeds the typical level width. Whenever lines overlap in the spectrum, the field exhibits multiple peaks within the sample. Only then is substantial energy found beyond the first half of the sample. When the spectrum throughout the sample is decomposed into a sum of Lorentzian lines plus a broad background, their central frequencies and widths are found to be essentially independent of position. Thus, this decomposition provides the electromagnetic quasimodes underlying the extended field in nominally localized samples. These quasimodes may exhibit multiple peaks in space when they overlap spectrally.

Localized modes in open one-dimensional dissipative random systems.

We consider, both theoretically and experimentally, the excitation and detection of the localized quasimodes (resonances) in an open dissipative 1D random system. We show that, even though the amplitude of transmission drops dramatically so that it cannot be observed in the presence of small losses, resonances are still clearly exhibited in reflection. Surprisingly, small losses essentially improve conditions for the detection of resonances in reflection as compared with the lossless case. An algorithm is proposed and tested to retrieve sample parameters and resonance characteristics inside the random system exclusively from reflection measurements.

Statistics of the mesoscopic field.

The measured probability distribution of the microwave field in an ensemble of strongly scattering samples is far from Gaussian. We show, however, that the field in a subensemble with specified total transmission is a Gaussian random variable. This confirms the central hypothesis of random matrix theory of perfect mode mixing and leads to the conclusion that the field and intensity normalized by their respective average magnitudes in a given configuration and the total transmission are statistically independent. This yields a universal form for the intensity correlation function and explains measurements of steady-state and time-resolved transmission in weakly and strongly scattering samples.

Dynamic correlation in wave propagation in random media.

Field spectra are analyzed to yield the time-resolved statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for an incident pulse of linewidth sigma at delay time t is a function only of the field correlation function, which is identical to that found for steady-state excitation, and of kappa(sigma)(t), the residual degree of intensity correlation at points at which the field correlation function vanishes. The dynamic probability distribution of normalized intensity depends only upon kappa(sigma)(t). Steady-state statistics are recovered in the limit sigma-->0, in which kappa(sigma=0) is the steady-state degree of correlation.

Mesoscopic correlation with polarization rotation of electromagnetic waves.

Mesoscopic correlations are observed in the polarization of microwave radiation transmitted through a random waveguide. These measurements, supported by diagrammatic theory, permit an unambiguous decomposition of the intensity correlation function of a vector wave into short, long, and infinite range components. Infinite range correlation that leads to universal conductance fluctuations is measured and found to be in agreement with calculations. The long and infinite range components include nonuniversal frequency-independent terms associated with coupling into and out of the sample.

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.

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.

Spatial-field correlation: the building block of mesoscopic fluctuations.

The absence of self-averaging in mesoscopic systems is a consequence of long-range intensity correlations. Microwave measurements suggest, and diagrammatic calculations confirm, that the correlation function of the normalized intensity with displacement of the source and detector, Delta R and Delta r, respectively, can be expressed as the sum of three terms, with distinctive spatial dependences. Each term involves only the sum or the product of the square of the field correlation function, F identical with F(2)(E). The leading-order term is the product, F(Delta R)F(Delta r); the next term is proportional to the sum, F(Delta R)+F(Delta r); the third term is proportional to F(Delta R)F(Delta r)+[F(Delta R)+F(Delta r)]+1.

Statistics of dynamics of localized waves.

The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity. The distribution of the delay time weighted by the intensity is found to be a double-sided stretched exponential to the 1/3 power centered at zero. The correlation between dwell time and intensity provides a dynamical test of photon localization.

Photon localization in resonant media.

We report measurements of microwave transmission over the first five Mie resonances of alumina spheres randomly positioned in a waveguide. Though precipitous drops in transmission and sharp peaks in the photon transit time are found near all resonances, measurements of transmission fluctuations show that localization occurs only in a narrow frequency window above the first resonance. There the drop in the photon density of states is found to be more pronounced than the fall in the photon transit time above the resonance, leading to a minimum in the Thouless number.

Large coherence area thin-film photonic stop-band lasers.

We demonstrate that the shift of the stop-band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film.

Delay-time statistics for diffuse waves.

We formulate a theory for the statistics of the dynamics of a classical wave propagating in random media by analyzing the frequency derivative of the phase under the assumption of a Gaussian process. We calculate frequency correlations and probability distribution functions of dynamical quantities, as well the first non-Gaussian C2 correction. In A. Z. Genack, P. Sebbah, M. Stoytchev, and B. A. van Tiggelen, Phys. Rev. Lett. 82, 715 (1999), microwave measurements have been performed to which this theory applies.

Observations of non-Rayleigh statistics in the approach to photon localization.

We measure the distribution of intensity of microwave radiation transmitted through absorbing random waveguides of lengths L up to localization length xi . For large intensity values the distribution is given by a negative stretched exponential to the 1/2 power, in agreement with predictions by Nieuwenhuizen and van Rossum [Phys. Rev. Lett. 74, 2674 (1995)] for diffusing waves in nonabsorbing samples, as opposed to a negative exponential given by Rayleigh statistics. The intensity distribution is well described by a transform derived by Kogan and Kaveh [Phys. Rev. B 52, R3813 (1995)] of the measured distribution of total transmission.

Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals.

Low-threshold lasing is observed at the edge of the stop band of a one-dimensional structure-a dye-doped cholesteric liquid-crystal film. The mode closest to the edge has the lowest lasing threshold. The rates of spontaneous and stimulated emission are suppressed within the stop band and enhanced at the band edge. The ratio of right to left circularly polarized spontaneous emission is in good agreement with calculated density of photon states.

Time-resolved studies of stimulated emission from colloidal dye solutions.

The temporal profiles of the emission from titania particle suspensions in Rhodamine 640 perchlorate dye solutions excited by 10-ps pulses of 527-nm radiation were measured over a wide range of particle and dye concentrations and laser powers. The dynamics of stimulated emission from random media is modeled by a random walk of photons within the colloid and rate equations for molecular excitations. The pulse width and the dependence of the threshold for laser action on dye and scatter concentration are computed by a Monte Carlo simulation of the model and are found to be in qualitative agreement with experiment.

Measuring the transport mean free path using a reference random medium.

The transport mean free path of microwave radiation in a random sample is determined from measurements of transmission through a composite sample of the medium with unknown scattering characteristics and a random medium of variable thickness and known scattering parameters. The method can be applied at optical frequencies by use of a ceramic wedge as the medium of variable thickness.

Intensity statistics and the finesse of electromagnetic radiation in random structures.

The correlation function of microwave intensity with frequency shift is measured in random mixtures of Teflon and aluminum spheres at a metallic filling fraction of 0.20. We observe the first three terms in an expansion of the correlation function in a parameter that is the ratio of the spacing to the width of modes of the random medium. The expansion also applies to optical and electron waves. The expansion parameter is equivalent to the finesse of optical resonators. The intensity distribution at all sample thicknesses is found to be a stretched exponential.

Mie scattering interferometer and its application to the study of Raman scattering from molecules at a mercury interface.

Interference fringes are observed produced by Mie scattering of laser light from a single microstructure or from a random array of microstructures supported above a reflecting surface. These fringes are the basis of a simple interferometer which can be used to measure distances from thousands of angstroms to centimeters. The interferometer is used to measure the height of liquid above a mercury surface. Raman scattering (RS) from the liquid is measured, and an upper limit of 10(3) is placed on the enhancement of RS from molecules at the interface. Enhancement of RS in a wedge between mercury and solid is examined theoretically.

Nuclear-quadrupole optical hole burning in the stoichiometric material EuP5O14.

Hole burning, which is attributed to optical pumping of nuclear-quadrupole levels, has been observed in the stoichiometric rare-earth compound, EuP5O14 . The long lifetime of these holes (-60 min) implies slow nuclear-spin flip-flop rates. The small magnetic moment of Eu3+ has prevented conventional magnetic-resonance measurements on Eu3+ compounds, but hole burning provides a sensitive method for the optical detection of nuclear-magnetic resonance and nuclear-quadrupole resonance. We have used hole burning and optically detected nuclear-quadrupole resonance to determine quadrupole splittings in the ground (7Fo) and excited (5Do) states.