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

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

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

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

Coalescence of Anderson-localized modes at an exceptional point in 2D random media

In non-hermitian systems, the particular position at which two eigenstates coalesce under a variation of a parameter in the complex plane is called an exceptional point. A non-perturbative theory is proposed which describes the evolution of modes in 2D open dielectric systems when permittivity distribution is modified. We successfully test this theory in a 2D disordered system to predict the position in the parameter space of the exceptional point between two Anderson-localized states. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems. Losses are inherent to most physical systems, either because of dissipation or as a result of openness. These systems are described mathematically by a non-hermitian Hamiltonian, where eigenvalues are complex and eigen-states form a nonorthogonal set. In such systems, interaction between pairs of eigenstates when a set of external parameters is varied is essentially driven by the existence of exceptional points (EP). At an EP, eigenstates coa-lesce: Complex eigenvalues degenerate and spatial distributions become collinear. In its vicinity, eigenvalues display a singular topology [1] and encircling the EP in the parameter space leads to a residual geometrical phase [2, 3]. Since their introduction by Kato in 1966 [4], EPs have turned to be involved in a rich variety of physical effects: Level repulsion [5], mode hybridization [6], quantum phase transition [7], lasing mode switching [8], PT symmetry breaking [9, 10] or even strong coupling [11]. They have been observed experimentally in different systems such as microwave billiards [12], chaotic optical mi-crocavities [13] or two level atoms in high-Q cavities [11]. Open random media are a particular class of non-hermitian systems. Here, modal confinement may be solely driven by the degree of scattering. For sufficiently strong scattering, the spatial extension of the modes becomes smaller than the system size, resulting in transport inhibition and Anderson localization [14]. Disordered-induced localized states have raised increasing interest. They provide with natural optical cavities in random lasers [15, 16]. They recently appeared to be good candidate for cavity QED [17, 18], with the main advantage of being inherently disorder-robust. These modes can be manipulated by a local change of the disorder and can be coupled to form necklace states [19-21], which open channels in a nominally localized system [22, 23]. These necklace states are foreseen as a key mechanism in the transition from localization to diffusive regime [24]. PT symmetry has been studied in the context of disordered media and Anderson localization [25-27] but so far EPs between localized modes have not been investigated. In this letter, coalescence at an EP between two Anderson-localized optical modes is demonstrated in a two dimensional (2D) dielectric random system. To bring the system in the vicinity of an EP, the dielectric permit-tivity is varied at two different locations in the random system. We first propose a general theory to follow the spectral and spatial evolution of modes in 2D dielectric open media. This theory is applied to the specific case of Anderson-localized modes to identify the position of an EP in the parameter space. This prediction is confirmed by Finite Element Method (FEM) simulations. We show that this is a highly complex problem of multiple mode interaction where a large number of modes are involved. We believe that our theory opens the way to a controlled local manipulation of the permittivity and the possibility to engineer the modes. Furthermore, we think this approach can be easily extended to others kinds of networks e.g. coupled arrays of cavities [28, 29]. We first consider the general case of a finite-size dielec-tric medium in 2D space, with inhomogeneous dielectric constant distribution, ǫ(r). In the frequency domain, the electromagnetic field follows the Helmholtz equation: ∆E(r, ω) + ǫ(r)ω 2 E(r, ω) = 0 (1) where E(r, ω) stands for the electrical field and the speed of light, c = 1. Eigensolutions of eq. (1), define the modes or eigenstates of the problem: (Ω i , |Ψ i) i∈N | ∆|Ψ i + ǫ(r)Ω 2 i |Ψ i = 0 (2) Because of its openness, the system has inherent losses, thus is described by a non-hermitian Hamiltonian. For non-hermitian systems, modes are a priori non-orthogonal, complex and their completeness is not ensured. Here, we consider open systems with finite range permittivity ǫ(r) and where a discontinuity in the permit-tivity provides a natural demarcation of the problem. Fo

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

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