Kazuo Ohtaka

Surface Enhanced Raman Scattering by Metal Spheres. I. Cluster Effect

An electromagnetic theory for the light absorption by a cluster of metal spheres and the Raman scattering by a molecule adsorbed on it is presented, which takes into account the retardation effect exactly and is applicable to an arbitrary cluster size. The theory is applied to a two-sphere cluster of Ag and Au. It is shown that the absorption spectrum is doubly peaked and the maximum enhancement factor of the Raman intensity amounts to 10 7 ∼10 8 when the distance between spheres is decreased. Absorption spectra of three- and four-sphere clusters are also calculated, which indicate that the essential features of the experimental observations are explained by the two-sphere cluster.

Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope

Two-dimensional photonic crystals of dielectric spheres with a 2.1 μm diameter have been fabricated by arranging individual spheres using a micromanipulation technique in a scanning electron microscope. A buildup of photonic bands from whispering gallery modes has been observed as the number of spheres increased, by measuring the transmission spectra for lattices composed of various numbers of spheres. The photonic band dispersion curves were experimentally obtained for a finite system made of 91 spheres from the transmission spectra for oblique incidence in the near-infrared region. They were in good agreement with the results of a numerical calculation for an infinite lattice. Since this mechanical manipulation technique enables us to control the arrangement of individual optical wavelength-sized scatterers, it provides a new way to systematically investigate various photonic band effects.

Low-threshold laser oscillation due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals

An analytical expression of the lasing threshold for arbi trary photonic crystals was derived, which showed their reduction due to small group velocities of electromagnetic eigenmodes. The lasing threshold was also evaluated numerically for a two-dimensional photonic crystal by examining the divergence of its transmission and reflection coeffcients numerically. A large reduction of lasing threshold caused by a group-velocity anomaly that is peculiar to two- and three- dimensional photonic crystals was found.

Optical Response of a Sphere Coupled to a Metal Substrate

Optical response of a sphere placed above a flat Ag substrate is calculated. Local dielectric constants are assumed and exact account is taken of the retardation effect. For a Ag sphere above a Ag substrate, coupling of sphere and substrate plasmons results in a strong local field, whereby Raman scattering by molecules on the sphere surface is enhanced by a factor of 10 8 . The case of a dielectric sphere is also discussed. The mechanism is understood in terms of surface plasmon polariton excitation.

Photonic Band Using Vector Spherical Waves : I. Various Properties of Bloch Electric Fields and Heavy Photons

The calculation is presented for the photonic bands for the fcc array of dielectric spheres, using the vector spherical-waves as basis functions. It is shown that the dimension of the secular determinant is less than 100, or less than one tenth of that of the plane-wave basis functions. Based upon the calculated eigenvectors, the symmetry properties of the electric-field vectors, the angle between the electric- and displcement-field vectors and the orthonormality of the Bloch states are investigated. Also the convergence of the plane-wave expansion is examined. Furthermore, we have demonstrated the existence of the modes appropriately called heavy photons, whose origin is exactly identical to the electronic analogues, heavy fermions.

Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field

For the fcc arrays of dielectric spheres, the reflectivity of a light and the local field excited by it are calculated exactly by applying the layer doubling method developed in LEED. It is shown that, when the number of the layers of a system is more than 4 or 5, the reflectivity reproduces the band gaps fairly well and 15 layers are enough for the stop bands to develop to match precisely with the band-gap widths, with one exception of the lowest stop band which requires a much larger thickness. Also, the good coherence and strong confinement effect of heavy photon are shown by demonstrating the well-defined interference fringes in the reflectivity and the very high intensity of the excited local-fields.

Strong localization of Bloch photons in dual-periodic dielectric multilayer structures

We predict that singular photonic Bloch modes with extremely narrow bandwidths occur in dual-periodic dielectric multilayer structures. The electromagnetic field of these modes is shown to be strongly localized around the troughs of undulated periodic dielectric structures, which leads to an extraordinary high-Q value effect in the dual-periodic one-dimensional photonic crystals. We also propose several real systems suitable for experimental confirmation of the features predicted.

Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss

The spectral widths of defect modes localized at line defects formed in a two-dimensional photonic crystal composed of a square lattice of dielectric cylinders were analyzed theoretically. The transmission spectra calculated by the layer-doubling method based on the vector–cylindrical–wave expansion of the internal field showed a rapid decrease of the spectral width with increasing number of the lattice layers when the dielectric loss is absent. Quality factors larger than 107 were predicted for the total lattice layers of 18. However, the numerical evaluation of the decay constant of the defect modes due to the imaginary part of the dielectric constant showed that the actual quality factor is limited by the dielectric loss. The calculated widths agreed qualitatively with the experimental observations by Lin et al. [Appl. Phys. Lett. 68, 3233 (1996)].

Near-field optical images of ordered polystyrene particle layers and their photonic band effect

To study the origin of the SNOM image contrast patterns observed for samples composed of transparent materials only, we have investigated the transmission SNOM images of an ordered polystyrene particles layer for various wavelengths of incident light. We have found a drastic change in the SNOM image patterns as the incident wavelength is scanned across the resonant wavelength of the photonic bands of the layer. Observed wavelength dependence of the near-field intensity of the layer was found to be in a good qualitative agreement with the theoretical calculation in terms of the photonic band effect.

Density of states of slab photonic crystals and the laser oscillation in photonic crystals

A treatment of the density of states of electromagnetic normal modes of slab photonic crystals is given to illustrate the thickness dependence of the Q values of the slab modes of arrayed dielectric spheres. The onset of the laser oscillation is then examined for a slab photonic crystal of arrayed cylinders by simulating active cylinders as having a complex dielectric constant of negative imaginary part /spl gamma/. It is shown that the divergence of the transmittivity of light occurs as an indication of the onset of lasing, when the slab is thick enough to give high Q values to the slab modes. The threshold value of /spl gamma/ is discussed in comparison with a one dimensional (1-D) multilayer stack of thin film,.