PSTM / NSOM modeling by 2-D quadridirectional eigenmode expansion

A two-dimensional (2-D) model for photon-scanning tunneling microscopy (PSTM) of integrated optical devices is evaluated. The simulations refer to a setup where the optical field in the vicinity of the sample is probed by detecting the optical power that is transferred via evanescent or radiative coupling to the tapered tip of an optical fiber close to the sample surface. Scanning the tip across the surface leads to a map of the local optical field in the sample. As a step beyond the mere analysis of the sample device, simulations are considered that include the sample as well as the probe tip. An efficient semianalytical simulation technique based on quadridirectional eigenmode expansions is applied. Results for a series of configurations, where slab waveguides with different types of corrugations serve as samples, allow assessment of the relation between the PSTM signal and the local field distribution in the sample. A reasonable qualitative agreement was observed between these computations and a previous experimental PSTM investigation of a waveguide Bragg grating

Bandwidth control of forbidden transmission gaps in compound structures with subwavelength slits

Phase resonances in transmission compound structures with subwavelength slits produce sharp dips in the transmission response. For all equal slits, the wavelengths of these sharp transmission minima can be varied by changing the width or the length of all the slits. In this paper we show that the width of the dip, i.e., the frequency range of minimum transmittance, can be controlled by making at least one slit different from the rest within a compound unit cell. In particular, we investigate the effect that a change in the dielectric filling, or in the length of a single slit produces in the transmission response. We also analyze the scan angle behavior of these structures by means of band diagrams, and compare them with previous results for all-equal slit structures.Comment: 16 pages, 5 figures, submitted to Phys. Rev.

Surface polaritons in two-dimensional left-handed photonic crystals

Using an extended plane-wave-based transfer-matrix method, the photonic band structures and the corresponding transmission spectrum of a two-dimensional left-handed photonic crystal are calculated. Comparisons between the periodic structure with a single left-handed cylindric rod are made, and many interesting similarities are found. It is shown that, due to the localized surface polaritons presented by an isolated left-handed rod, there exist many exciting physical phenomena in high-dimensional left-handed photonic crystals. As direct results of coupling of the localized surface polaritons of neighboring left-handed rod, a lot of almost dispersionless bands, anti-crossing behavior, and a zero $\bar{n}$ gap are exhibited in the left-handed periodic structure. Moreover, in a certain frequency region, except distorted by a lot of anti-crossing behavior, there exists a continual dispersion relation, which can be explained by the long-wavelength approximation. It is also pointed out that high-dimensional left-handed photonic crystals can be used to design narrow-band filter.Comment: sign errors in equation

Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment

The optical properties of slab-like photonic crystals are often discussed on the basis of effective index (EI) approximations, where a 2-D effective refractive index profile replaces the actual 3-D structure. Our aim is to assess this approximation by analogous steps that reduce finite 2-D waveguide Bragg-gratings (to be seen as sections through 3-D PC slabs and membranes) to 1-D problems, which are tractable by common transfer matrix methods. Application of the EI method is disputable in particular in cases where locally no guided modes are supported, as in the holes of a PC membrane. A variational procedure permits to derive suitable effective permittivities even in these cases. Depending on the structural properties, these values can well turn out to be lower than one, or even be negative. Both the “standard” and the variational procedures are compared with reference data, generated by a rigorous 2-D Helmholtz solver, for a series of example structures.\u

Stopping Light on a Defect

Gap solitons are localized nonlinear coherent states which have been shown both theoretically and experimentally to propagate in periodic structures. Although theory allows for their propagation at any speed $v$, $0\le v\le c$, they have been observed in experiments at speeds of approximately 50% of $c$. It is of scientific and technological interest to trap gap solitons. We first introduce an explicit multiparameter family of periodic structures with localized defects, which support linear defect modes. These linear defect modes are shown to persist into the nonlinear regime, as {\it nonlinear defect modes}. Using mathematical analysis and numerical simulations we then investigate the capture of an incident gap soliton by these defects. The mechanism of capture of a gap soliton is resonant transfer of its energy to nonlinear defect modes. We introduce a useful bifurcation diagram from which information on the parameter regimes of gap soliton capture, reflection and transmission can be obtained by simple conservation of energy and resonant energy transfer principles.Comment: 45 pages, Submitted to Journal of the Optical Society

Far-field scattering microscopy applied to analysis of slow light, power enhancement, and delay times in uniform Bragg waveguide gratings

A novel method is presented for determining the group index, intensity enhancement and delay times for waveguide gratings, based on (Rayleigh) scattering observations. This far-field scattering microscopy (FScM) method is compared with the phase shift method and a method that uses the transmission spectrum to quantify the slow wave properties. We find a minimum group velocity of 0.04c and a maximum intensity enhancement of ~14.5 for a 1000-period grating and a maximum group delay of ~80 ps for a 2000-period grating. Furthermore, we show that the FScM method can be used for both displaying the intensity distribution of the Bloch resonances and for investigating out of plane losses. Finally, an application is discussed for the slow-wave grating as index sensor able to detect a minimum cladding index change of $10^{-8}$, assuming a transmission detection limit of $10^{-4}$

Disorder-induced cavities, resonances, and lasing in randomly-layered media

We study, theoretically and experimentally, disorder-induced resonances in randomly-layered samples,and develop an algorithm for the detection and characterization of the effective cavities that give rise to these resonances. This algorithm enables us to find the eigen-frequencies and pinpoint the locations of the resonant cavities that appear in individual realizations of random samples, for arbitrary distributions of the widths and refractive indices of the layers. Each cavity is formed in a region whose size is a few localization lengths. Its eigen-frequency is independent of the location inside the sample, and does not change if the total length of the sample is increased by, for example, adding more scatterers on the sides. We show that the total number of cavities, $N_{\mathrm{cav}}$, and resonances, $N_{\mathrm{res}}$, per unit frequency interval is uniquely determined by the size of the disordered system and is independent of the strength of the disorder. In an active, amplifying medium, part of the cavities may host lasing modes whose number is less than $N_{\mathrm{res}}$. The ensemble of lasing cavities behaves as distributed feedback lasers, provided that the gain of the medium exceeds the lasing threshold, which is specific for each cavity. We present the results of experiments carried out with single-mode optical fibers with gain and randomly-located resonant Bragg reflectors (periodic gratings). When the fiber was illuminated by a pumping laser with an intensity high enough to overcome the lasing threshold, the resonances revealed themselves by peaks in the emission spectrum. Our experimental results are in a good agreement with the theory presented here.Comment: minor correction

Towards a microscopic understanding of phonon heat conduction

Heat conduction by phonons is a ubiquitous process that incorporates a wide range of physics and plays an essential role in applications ranging from space power generation to LED lighting. Heat conduction has been studied for over two hundred years, yet many microscopic aspects of heat conduction have remained unclear in most crystalline solids, including which phonons carry heat and how natural and artificial structures scatter specific phonons. Fortunately, recent advances in both computation and experiment are enabling an unprecedented microscopic view of thermal transport by phonons. In this topical review, we provide an overview of these methods, the insights they are providing, and their impact on the science and engineering of heat conduction