Fluctuations in photon local delay time and their relation to phase spectra in random media

The temporal evolution of microwave pulses transmitted through random dielectric samples is obtained from the Fourier transform of field spectra. Large fluctuations are found in the local or single channel delay time, which is the first temporal moment of the transmitted pulse at a point in the output speckle pattern. Both positive and negative values of local delay time are observed. The widest distribution is found at low intensity values near a phase singularity in the transmitted speckle pattern. In the limit of long duration, narrow-bandwidth incident pulses, the single channel delay time equals the spectral derivative of the phase of the transmitted field. Fluctuations of the phase of the transmitted field thus reflect the underlying statistics of dynamics in mesoscopic systems.Comment: Submitted to Phys.Rev.E - 12 pages, 8 figure

Adaptive pumping for spectral control of random lasers

A laser is not necessarily a sophisticated device: Pumping energy into an amplifying medium randomly filled with scatterers, a powder for instance, makes a perfect "random laser." In such a laser, the absence of mirrors greatly simplifies laser design, but control over emission directionality or frequency tunability is lost, seriously hindering prospects for this otherwise simple laser. Lately, we proposed a novel approach to harness random lasers, inspired by spatial shaping methods recently employed for coherent light control in complex media. Here, we experimentally implement this method in an optofluidic random laser where scattering is weak and modes extend spatially and strongly overlap, making individual selection a priori impossible. We show that control over laser emission can indeed be regained even in this extreme case by actively shaping the spatial profile of the optical pump. This unique degree of freedom, which has never been exploited, allows selection of any desired wavelength and shaping of lasing modes, without prior knowledge of their spatial distribution. Mode selection is achieved with spectral selectivity down to 0.06nm and more than 10dB side-lobe rejection. This experimental method paves the way towards fully tunable and controlled random lasers and can be transferred to other class of lasers.Comment: 23 pages, 7 figure

Complexity of 2D random laser modes at the transition from weak scattering to Anderson localization

The spatial extension and complexity of the eigenfunctions of an open finite-size two-dimensional (2D) random system are systematically studied for a random collection of systems ranging from weakly scattering to localized. The eigenfunctions are obtained by introducing gain in the medium and pumping just above threshold. All lasing modes are found to correspond to quasimodes of the passive system, for all regimes of propagation. We demonstrate the existence of multipeaked quasimodes or necklace states in 2D at the transition from localized to diffusive, resulting from the coupling of localized states.Comment: Submitted to PR

Localized Modes in Open One-Dimensional Dissipative Random Systems

We consider, both theoretically and experimentally, the excitation and detection of the localized quasi-modes (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 resonances characteristics inside the random system exclusively from reflection measurements.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let

Quasimodes of a chaotic elastic cavity with increasing local losses

We report non-invasive measurements of the complex field of elastic quasimodes of a silicon wafer with chaotic shape. The amplitude and phase spatial distribution of the flexural modes are directly obtained by Fourier transform of time measurements. We investigate the crossover from real mode to complex-valued quasimode, when absorption is progressively increased on one edge of the wafer. The complexness parameter, which characterizes the degree to which a resonance state is complex-valued, is measured for non-overlapping resonances and is found to be proportional to the non-homogeneous contribution to the line broadening of the resonance. A simple two-level model based on the effective Hamiltonian formalism supports our experimental results

Control of light transmission through opaque scattering media in space and time

We report the first experimental demonstration of combined spatial and temporal control of light trajectories through opaque media. This control is achieved by solely manipulating spatial degrees of freedom of the incident wavefront. As an application, we demonstrate that the present approach is capable to form bandwidth-limited ultrashort pulses from the otherwise randomly transmitted light with a controllable interaction time of the pulses with the medium. Our approach provides a new tool for fundamental studies of light propagation in complex media and has potential for applications for coherent control, sensing and imaging in nano- and biophotonics

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. When the quasimodes overlap spectrally, they exhibit multiple peaks in space.Comment: 4 pages, submitted to PRL (23 December 2005

Spatial field correlation, the building block of mesoscopic fluctuations

The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. 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, $F \equiv F_{E}^2$. The leading-order term is the product, the next term is proportional to the sum. The third term is proportional to $[F(\Delta R)F(\Delta r) + [F(\Delta R)+F(\Delta r)] + 1]$.Comment: Submitted to PR

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, leading to a minimum in the Thouless number.Comment: To appear in PRL; 5 pages, including 5 figure