We report on theoretical and experimental studies of multiple Bragg diffraction of light in three-dimensional photonic
crystals possessing high dielectric contrast. Self-assembled opaline photonic crystals made up of monodisperse
polystyrene microspheres are used as an example in our measurements. A new approach is considered to analyze and
quantitatively describe the Bragg reflection and transmission complex-shaped contours. Our method is based on the
dynamical diffraction theory generalized to the case of a three-dimensional spatially periodic medium characterized by
high dielectric contrast and allows one to calculate in a simple analytical way the reflection and transmission spectra.
The spatial Fourier components of the dielectric function are calculated taking into account a sintering of the spheres
forming the opaline structure. Numerical calculations of the angle-resolved Bragg reflection and transmission spectra are
performed, and those are compared with the dispersion curves of the electromagnetic eigenmodes for the opaline
photonic crystals spatially confined along the [111] direction. The peculiarities in the optical spectra are found to
correspond to singular points in the eigenmode dispersion curves. It is shown also that under the multiple Bragg
diffraction conditions the reflection and transmission contours are shaped due to conventional photonic stop-band states
as well as additional low-group-velocity modes ("slow light" modes). The contours calculated show a good agreement
with our experimental data if a uniaxial strain along the sedimentation direction [111] and the particle sintering are
accounted for.
A theory is developed for resonant elastic scattering of light from Bragg structures (one-dimensional photonic crystals)
which have randomly rough interfaces. The study is mainly focused on the spectral and angle dependences of radiation
giving information about static disorder responsible for the elastic scattering. The diffuse reflection spectra for linearly
polarized light are computed and analyzed in detail. A resonant enhancement of the scattering cross-section is found to
be manifested in the vicinity of the photonic stop-band edges. Angle-dependent suppressing the diffusive component of
reflected p-polarized light and strong dependence of the scattering spectrum on the location of a single rough interface
are demonstrated.
We report on an analytical study of the photonic band structure of 2D and 3D multi-component photonic crystals. It is found that both types of crystal demonstrate a quasiperiodic resonant behavior of (hkl) photonic stop-bands as a function of the reciprocal lattice vector, providing a selective ON/OFF switching of nonresonant (hkl) stop-bands. Our predictions are compared with the results of conventional numerical studies using the photonic Korringa-Kohn-Rostocker method. Experimental transmission spectra of a-SiO2 synthetic opals show the OFF-switching of the {111} stop-bands at the filler permittivity of ~1.82, the {200} bands at ~1.63, the {220} bands at ~1.93, and the {311} bands at ~1.75. The (222) photonic stop-band, which is due to the second order diffraction from the (111) planes, cannot be switched OFF in a wide range of filler permittivity values, thus indicating a resonant behavior. The experimental data demonstrate an excellent agreement with the theoretical predictions.
Three-dimensional opal-VO2 photonic crystals were synthesized by the chemical bath deposition technique. The Bragg reflection spectra from the (111) planes of the crystals were measured as a function of the temperature in the range between 15 and 100°C. The thermal hysteresis loop of the reflection peak position due to the phase transition in VO2 filling the opal voids was observed. A theoretical model of the periodic layered medium was proposed to describe quantitatively the reflection spectra of opal-like structures. The values of the dielectric constants of the VO2 below and above the phase transition temperature have been estimated which give the best fit within the model considered.
The specular reflection spectra of CdS crystals are determined at T equals 2 K in the region of the Anequals1 exciton resonance. The great variability in the spectra cannot not be explained by the simple model of an exciton-free dead layer at the boundary of a crystal. Generalized boundary conditions are formulated for the excitons of large radius, which includes inhomogeneous additional boundary conditions for the exciton polarization and inhomogeneous boundary conditions for the tangential component of the magnetic induction vector B. An analysis of the energy balance equations at the surface of a crystal yields additional relationships between the parameters of the theory. The proposed system of boundary conditions describes the case with a sharp internal boundary at the dead layer and allows for the effects of the intrinsic and extrinsic mechanisms for formation of this layer. The reflection spectra of normally incident light are calculated numerically for various relationships between the parameters of the theory. All quantitative features of the optical exciton reflection spectra are in good agreement with the experimental data. We also give explicit expressions for the reflection and transmission coefficients of an optical wave incident normally on the plate.
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