The realization that electron localization in disordered systems (Anderson localization) [1] is ultimately a wave phenomenon [2,3] has led to the suggestion that photons could be similarly localized by disorder [3]. This conjecture attracted wide interest because the differences between photons and electrons -in their interactions, spin statistics, and methods of injection and detection -may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of threedimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave [4,5,6,7,8] as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption [9,10,11], and because absorption itself may suppress localization [3]. Here we show that the extent of photon localization can be determined by a different approach -measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminum spheres.In the absence of inelastic and phase-breaking processes, the ensemble average of the dimensionless conductance g ≡ G /(e 2 /h) is the universal scaling parameter [12] of the electron localization transition [1]. Here ... represents the average over an ensemble of random sample configurations, G is the electronic conductance, e is the electron charge, and h is Planck's constant. The dimensionless conductance g can be defined for classical waves as the transmittance, that is, the sum over transmission coefficients connecting all input modes a and output modes b, g ≡ Σ ab T ab (Ref. 13). In the absence of absorption, g not only determines the scaling of transmission quantities, such as T ab and T a = Σ b T ab that we will refer to as the intensity and total transmission, respectively, but it also determines their full distributions [14,15,16]. In electronically conducting samples or in white paints, g ≫ 1 and Ohm's law holds, g = N ℓ/L, where N is the number of transverse modes at a given frequency, ℓ is the transport mean free path, and L is the sample length. But beyond the localization threshold, at g ≈ 1 (Refs. 12,17), the wavefunction or classical field is exponentially small at the boundary and g falls exponentially with L. Localization can be achieved in a strongly scattering three-dimensional sample with a sufficiently small value of ℓ (Ref. 2), or even in weakly scattering samples in a quasi-one-dimensional geometry of fixed N , once L becomes greater than the localization length, ξ = N ℓ (Ref. 1...

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.

The discovery of topological photonic states has revolutionized our understanding of electromagnetic propagation and scattering. Endowed with topological robustness, photonic edge modes are not reflected from structural imperfections and disordered regions. Here we demonstrate robust propagation along reconfigurable pathways defined by synthetic gauge fields within a topological photonic metacrystal. The flow of microwave radiation in helical edge modes following arbitrary contours of the synthetic gauge field between bianisotropic metacrystal domains is unimpeded. This is demonstrated in measurements of the spectrum of transmission and time delay along the topological domain walls. These results provide a framework for freely steering electromagnetic radiation within photonic structures.

, even for localized waves, the prospect of forging a comprehensive modal approach to wave propagation has not been realized. Here we show that the field speckle pattern 10 of transmitted microwave radiation can be decomposed into a sum of patterns of the modes of the medium. We find strong correlation between modal field speckle patterns which leads to destructive interference between modes. This allows us to explain complexities of steady state and pulsed transmission of localized waves and to harmonize wave and particle descriptions of diffusion.Modes of the field in media for which the corresponding particles freely diffuse extend throughout the sample. Energy is then readily transported to the margins of the sample where it leaks through the boundary. Since the mode lifetime is then short and its linewidth correspondingly broad, the average spectral width of modes exceeds the average spacing

We have investigated the modulation of the optical field transmitted through a colloid of polystyrene spheres by a narrow quasi-cw ultrasound beam. Measurements of the scale dependence of the heterodyne modulation signal at the acoustic frequency are obtained for samples that are up to 140 scattering lengths thick. A calculation of the modulation signal predicts the possibility of tomographic imaging, which is confirmed experimentally.

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.

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.

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