Tracking a light pulse through a waveguide in space and time

We present first direct observation of the propagation of a femtosecond laser pulse in space and time through a waveguide structure. With an interferometric photon scanning tunneling microscope (PSTM), the local amplitude and phase of the pulse were retrieved with high spatial, spectral and time resolution. The relative field profiles, the wave vectors and the spectra of the pulses in the TE00 and TE01 modes in the waveguide have been experimentally determined

Nanoscale coherent imaging of photonic structures by PSTM

We present an alternative instrument to map local optical field distributions: a photon scanning tunneling microscope (PSTM). In a PSTM a near-field optical fiber probe is used to frustrate the evanescent field above an integrated optical device. The evanescent wave is converted into a propagating wave that is coupled into the fiber, guided through it and subsequently detected by a photomultiplier tub

Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion

The amplitude and phase evolution of ultrashort pulses in a bimodal waveguide structure has been studied with a time-resolved photon scanning tunneling microscope (PSTM). When waveguide modes overlap in time intriguing phase patterns are observed. Phase singularities, arising from interference between different modes, are normally expected at equidistant intervals determined by the difference in effective index for the two modes. However, in the pulsed experiments the distance between individual singularities is found to change not only within one measurement frame, but even depends strongly on the reference time. To understand this observation it is necessary to take into account that the actual pulses generating the interference signal change shape upon propagation through a dispersive medium. This implies that the spatial distribution of phase singularities contains direct information on local dispersion characteristics. At the same time also the mode profiles, wave vectors, pulse lengths, and group velocities of all excited modes in the waveguide are directly measured. The combination of these parameters with an analytical model for the time-resolved PSTM measurements shows that the unique spatial phase information indeed gives a direct measure for the group velocity dispersion of individual modes. As a result interesting and useful effects, such as pulse compression, pulse spreading, and pulse reshaping become accessible in a local measuremen

Local phase measurements of light in a one-dimensional photonic crystal

For the first time the local optical phase evolution in and around a small, o­ne-dimensional photonic crystal has been visualized with a heterodyne interferometric photon scanning tunnelling microscope. The measurements show an exponential decay of the optical intensity inside the crystal, which consists of a periodic array of subwavelength air rods fabricated in a conventional ridge waveguide. In addition it is found that the introduction of the air rods has a counter- intuitive effect o­n the phase development inside the structure. The heterodyne detection scheme allows the detection of low- intensity scattered wanes. In the vicinity of the scattering air rods phase singularities are found with a topological charge of plus or minus o­n

Amplitude and phase evolution of optical fields inside periodic photonic structures

Optical amplitude distributions of light inside periodic photonic structures are visualized with subwavelength resolution. In addition, using a phase-sensitive photon scanning tunneling microscope, we simultaneously map the phase evolution of light. Two different structures, which consist of a ridge wave-guide containing periodic arrays of nanometer scale features, are investigated. We determine the wavelength dependence of the exponential decay rate inside the periodic arrays. Furthermore, various interference patterns are observed, which we interpret as interference between light reflected by the substrate and light inside the waveguide. The phase information obtained reveals scattering phenomena around the periodic array, which gives rise to phase jumps and phase singularities. Locally around the air rods, we observe an unexpected change in effective refractive index, a possible indication for anomalous dispersion resulting from the periodicity of the array

Phase mapping of optical fields in integrated optical waveguide structures

The phase evolution of optical waves in a waveguide structure has been studied with a heterodyne interferometric photon scanning tunneling microscope. Both phase and amplitude of the local optical field are measured with subwavelength resolution. Topographical maps of the waveguide surface are obtained simultaneously with the optical information. Unexpected phase patterns, with phase jumps and phase singularities, have been observed. The phase patterns can be fully understood by taking into account the total field that is the sum of the optical fields of the various modes. We show that with the unique spatial phase information, the relative field profiles and wave vectors of all the excited modes in a multimodal waveguide structure can be determined independently

Universality in scattering by large-scale potential fluctuations in two-dimensional conductors

We study electron propagation through a random array of rare, opaque and large (compared the de Broglie wavelength of electrons) scatterers. It is shown that for any convex scatterer the ratio of the transport to quantum lifetimes \eta=\tau_{tr}/\tau_{tot}$ does not depend on the shape of the scatterer but only on whether scattering is specular or diffuse and on the spatial dimensionality (D). In particular, for specular scattering, \eta is a universal constant determined only by the dimensionality of the system: \eta = 2 for D = 3 and \eta = 3/2 for D = 2. The crossover between classical and quantum regimes of scattering is discussed.Comment: 4 pages, 3 figures, submitted to PR

Spectral mode-beat phenomena in a cylindrical microcavity

Detailed spectral analysis of photon scanning tunneling microscope images has been carried out. The analysis of spectral mode-beat phenomena leads to an accurate determination of mode profiles and gives evidence of counterpropagating mode

Optical Albedo Theory of Strongly-Irradiated Giant Planets: The Case of HD 209458b

We calculate a new suite of albedo models for close-in extrasolar giant planets and compare with the recent stringent upper limit for HD 209458b of Rowe et al. using MOST. We find that all models without scattering clouds are consistent with this optical limit. We explore the dependence on wavelength and waveband, metallicity, the degree of heat redistribution, and the possible presence of thermal inversions and find a rich diversity of behaviors. Measurements of transiting extrasolar giant planets (EGPs) at short wavelengths by MOST, Kepler, and CoRoT, as well as by proposed dedicated multi-band missions, can complement measurements in the near- and mid-IR using {\it Spitzer} and JWST. Collectively, such measurements can help determine metallicity, compositions, atmospheric temperatures, and the cause of thermal inversions (when they arise) for EGPs with a broad range of radii, masses, degrees of stellar insolation, and ages. With this paper, we reappraise and highlight the diagnostic potential of albedo measurements of hot EGPs shortward of $\sim$1.3 $\mu$m.Comment: 6 pages, 1 table, 1 color figure; accepted to the Astrophysical Journa

Epsilons Near Zero limits in the Mie scattering theory

The classical Mie theory - electromagnetic radiation scattering by the homogeneous spherical particles - is considered in the epsilon near zero limits separately for the materials of the particles and the surrounding medium. The maxima of a scattered transverse electrical (TE) field for the surrounding medium materials with the epsilon near zero limits are revealed. The effective multipole polarizabilities of the corresponding scattering particles are investigated. The possibility to achieve magnetic dipole resonance and accordingly to construct metamaterials with negative refractive index for the aggregates spherical particles in surrounding medium with the epsilon near zero limits is considered.Comment: 8 pages, 6 figure