Light scattering from a monolayer of periodically arrayed dielectric spheres on dielectric substrates

Abstract

Theoretical studies have revealed that coupling with a dielectric substrate significantly affects the transmission spectrum of a 2D photonic crystal of monolayer dielectric spheres. The dielectric constant of a semiinfinite substrate has been found to have a threshold, above which dips in the transmission spectrum broaden drastically. A substrate of finite thickness yields additional dips in the spectrum corresponding to localized eigenstates within the substrate. The transmission spectrum is well explained by the anticrossing of the eigenstates of a monolayer and a substrate.Research on photonic crystals 1 ͑PC's͒ has been focused for many years on the realization of a complete-gap PC, i.e., a PC having a common photonic gap in all directions. A complete-gap PC could be used, for example, in fundamental QED experiments to control the atomic lifetime by the suppression of spontaneous emission. 2 A variety of possible complete-gap PC's have been found in theoretical studies. 3 Since gaps appear as a result of interference, long-range order in all directions is indispensable for three-dimensional ͑3D͒ PC's. To realize complete-gap PC's, therefore, highly sophisticated methods such as self-assembly or autocloning 4 have been developed in addition to the advanced technology of lithography. 5 At present, however, it is still difficult to obtain 3D PC's of high quality.In contrast, 2D slablike PC's with long-range order, 6 a typical example being a monolayer of periodically arrayed dielectric spheres on a substrate, can easily be fabricated. Many theoretical 7 and experimental 8-10 studies on the transmission spectra and photonic band structures of such PC's are currently being carried out. A slablike PC is different from ordinary 2D PC's composed of infinitely long parallel cylinders, in that it has a finite thickness in one direction. Consequently, there is an energy dissipation in that direction, which gives rise to a finite lifetime of its eigenstates. There is also a significant enhancement of the electric field near the surface ͑near field͒ by diffracted evanescent waves due to the 2D periodicity. 7 This enhancement can be observed by the use of a scanning near-field optical microscope. 11 There is, in fact, a strong demand for the development of new photon technology by utilizing enhanced near fields such as laser manipulation of atoms. 12 The relevant wavelength of a slab-type PC at present is comparable with the 2D periodicity. For example, it lies in the lower Mie resonance region (lХ3,4) for monolayer spheres. 13 An electric field of such lower resonances is not strongly localized within the spheres and leaks out of the monolayer. This extended nature of the electric field is expected to induce strong coupling with the substrate. However, this coupling was not taken into account in our previous study. 7 A few theoretical attempts 14 have been made to ana-lyze the optical properties of a 2D periodic system on a semiinfinite substrate, but all of them lack the viewpoint of PC's such as band structure. There has...

( 2 + 1 ) -dimensional photonic crystals from Langmuir-Blodgett colloidal multilayers

“…The spectral position and resolution of scattering resonances depend on the RI of substrate. 14,16 In our case the RI of the substrate exceeds the effective RI of the sphere monolayer. In order to use the waveguiding model, we have to assume that a monolayer of spheres is optically isolated from the substrate.…”

“…Moreover, no spectroscopic evidence has been demonstrated to prove the formation of a 3D lattice in LB multilayers. 9 On the other hand, optical spectra of 2D hexagonal sphere crystals were studied only at wavelengths shorter than the sphere diameter, 10,11 i.e., in the range of their 2D PBG.…”

Modification of emission of CdTe nanocrystals by the local field of Langmuir–Blodgett colloidal photonic crystals

“…Moreover, this theory predicts considerable broadening of the minima bandwidth due to light leakage to the substrate. 35 The spectral position of the first bandgap in such PhC corresponds to the sphere diameter and the next gap takes place at a wavelength, which is lower by a factor of 1.21. The observed minima at 548 and 444 nm for 1L LB film are in good agreement with this model.…”

“…It has been shown that the resonance enhances the intensity of a local field by two orders of magnitude if the monolayer of spheres is suspended in the air, whereas the attached substrate reduces the enhancement by factor of 10. 6,7,35 The distribution of the local field at the surface of the opal-based PhC in the PBG wavelength range was modeled theoretically 36 and visualized by the near-field optical microscopy. 9 Since the near-field amplitude of evanescent waves decays rapidly away from a PhC surface on a scale of the PhC lattice constant, the NCF-based emitter should be in close proximity to a PhC surface.…”

Cavity-Coupled Guided Resonances With High Quality Factors in Photonic Crystal Heterostructures

“…We chose the parameters of the multilayer in such a way that it has a broad stopband covering the range of normalized frequencies (ωa/2πc) from 0.5 to 1, because the guided mode resonances of the monolayer PhC at Γ-point will be in this range [9] as shown in the band diagram of the monolayer [see Fig. 6A in Appendix].…”