Localización anómala de la luz en superredes fotónicas unidimensionales desordenadas

The Anderson localization of light in one-dimensional disordered photonic superlattices is theoretically studied. The system is considered to be made of alternating dispersive and nondispersive layers of different randomthickness. Dispersive slabs of the heterostructure are characterized by Drude-like frequency-dependent electric permittivities and magnetic permeabilities. Numerical results for the localization length are obtained via an analytical model, only valid in the case of weak disorder, and also through its general definition involving the transmissivity of the multilayered system. Anomalous λ4- and  λ-4-dependencies of the localization length in positive-negative disordered photonic superlattices are obtained, in certain cases, in the long and short wavelength limits, respectively.La localización de Anderson de la luz en superredes fotónicas desordenadas unidimensionales se estudia teóricamente. Se considera que el sistema está compuesto por capas alternas dispersivas y no dispersivas de diferente grosor aleatorio. Las losas dispersivas de la heteroestructura se caracterizan por permittividades eléctricas y permeabilidades magnéticas dependientes de la frecuencia tipo Drude. Los resultados numéricos para la longitud de localización se obtienen a través de un modelo analítico, solo válido en el caso de un trastorno débil, y también a través de su definición general que involucra la transmisividad del sistema multicapa. Se obtienen dependencias anómalas λ4 y λ-4 de la longitud de localización en superredes fotónicas desordenadas positivas-negativas, en ciertos casos, en los límites de longitud de onda larga y corta, respectivamente

Effect of hole-shape irregularities on photonic crystal waveguides

The effect of irregular hole shape on the spectrum and radiation losses of a photonic crystal waveguide is studied using Bloch-mode expansion. Deviations from a perfectly circular hole are characterized by a radius fluctuation amplitude and correlation angle. It is found that the parameter which determines the magnitude of the effect of disorder is the standard deviation of the hole areas. Hence, for a fixed amplitude of the radius fluctuation around the hole, those effects are strongly dependent on the correlation angle of the irregular shape. This result suggests routes to potentially improve the quality of photonic crystal structures.Comment: 3 pages, 3 figure

Cavity Quantum Electrodynamics with Anderson-localized Modes

A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. Highly engineered optical cavities are generally implemented requiring nanoscale fabrication precision. We demonstrate a fundamentally different approach in which disorder is used as a resource rather than a nuisance. We generate strongly confined Anderson-localized cavity modes by deliberately adding disorder to photonic crystal waveguides. The emission rate of a semiconductor quantum dot embedded in the waveguide is enhanced by a factor of 15 on resonance with the Anderson-localized mode and 94 % of the emitted single-photons couple to the mode. Disordered photonic media thus provide an efficient platform for quantum electrodynamics offering an approach to inherently disorder-robust quantum information devices

Experimental observation of strong photon localization in disordered photonic crystal waveguides

We demonstrate experimentally that structural perturbations imposed on highly-dispersive photonic crystal-based waveguides give rise to spectral features that bear signatures of Anderson localization. Sharp resonances with the effective Qs of over 30,000 are found in scattering spectra of disordered waveguides. The resonances are observed in a ~20-nm bandwidth centered at the cutoff of slowly-guided Bloch-modes. Their origin can be explained with interference of coherently scattered electromagnetic waves which results in the formation of a narrow impurity (or localization) band populated with spectrally distinct quasistates. Standard photon localization criteria are fulfilled in the localization band.Comment: first submitted to PRL on April 20th, 2007; 16 pages, 4 figure

Synchronous imaging for rapid visualization of complex vibration profiles in electromechanical microresonators

Synchronous imaging is used in dynamic space-domain vibration profile studies of capacitively driven, thin n+ doped poly-silicon microbridges oscillating at rf frequencies. Fast and high-resolution actuation profile measurements of micromachined resonators are useful when significant device nonlinearities are present. For example, bridges under compressive stress near the critical Euler value often reveal complex dynamics stemming from a state close to the onset of buckling. This leads to enhanced sensitivity of the vibration modes to external conditions, such as pressure, temperatures, and chemical composition, the global behavior of which is conveniently evaluated using synchronous imaging combined with spectral measurements. We performed an experimental study of the effects of high drive amplitude and ambient pressure on the resonant vibration profiles in electrically-driven microbridges near critical buckling. Numerical analysis of electrostatically driven post-buckled microbridges supports the richness of complex vibration dynamics that are possible in such micro-electromechanical devices.Comment: 7 pages, 8 figure, submitted to Physical Review

Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit

In this work we explore the transmission properties of a single slit in a metallic screen. We analyze the dependence of these properties on both slit width and angle of incident radiation. We study in detail the crossover between the subwavelength regime and the geometrical-optics limit. In the subwavelength regime, resonant transmission linked to the excitation of waveguide resonances is analyzed. Linewidth of these resonances and their associated electric field intensities are controlled by just the width of the slit. More complex transmission spectra appear when the wavelength of light is comparable to the slit width. Rapid oscillations associated to the emergence of different propagating modes inside the slit are the main features appearing in this regime.Comment: Accepted for publication in Phys. Rev.

Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides

We investigate the nonlinear response of photonic crystal waveguides with suppressed two-photon absorption. A moderate decrease of the group velocity (~ c/6 to c/15, a factor of 2.5) results in a dramatic (30x) enhancement of three-photon absorption well beyond the expected scaling, proportional to 1/(vg)^3. This non-trivial scaling of the effective nonlinear coefficients results from pulse compression, which further enhances the optical field beyond that of purely slow-group velocity interactions. These observations are enabled in mm-long slow-light photonic crystal waveguides owing to the strong anomalous group-velocity dispersion and positive chirp. Our numerical physical model matches measurements remarkably.Comment: 10 pages, 4 figure

Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential

We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov exponent $\gamma$ which we determine explicitly as a function of the noise intensity \sigma and the frequency \omega. We find uniform two-parameter asymptotic expressions for $\gamma$ which allow us to evaluate $\gamma$ for different relations between \sigma and \omega. The value of the Lyapunov exponent is also obtained in the case of a short-range correlated noise, which is shown to be less than its white noise counterpart.Comment: 20 pages, 4 figure