Optical properties of periodic and quasiperiodic one-dimensional photonic crystals: a comparison

Abstract

One-dimensional (1D) photonic crystals composed of alternating stacks of layers having a low and a high index of refraction was recently shown to act as omnidirectional reflection band. They reflect light at any polarization, any incidence angle, and over a wide range of wavelengths. In contrast to the three-dimensional case the 1D photonic crystal is attractive since its production is more feasible at any wavelength scale. When a structural defect is introduced in the photonic crystal, photon-localized state can be created in the photonic band gap. In 1D photonic crystal, the defect can be used to open controlled optical windows in the photonic band gap or to obtaining an omnidicrectional photonic band gap. We can find more types of defects that play the role of broking the periodicity of the photonic crystal to produce new physical phenomena or new quasi-periodic systems. A design procedure for omnidirectional high reflectors with wide bandwidths for the optical telecommunication bands is described. From the numerical results performed by the transfer matrix method, it is found that a partially omnidirectional high-reflector covering the optical telecommunication wavelengths 1.3 and 1.55&#956;m is obtained for a quarter-wave stack <i>air/H(LH)¹²/air</i> by using the tellurium as a materiel of high refractive index (<i>n_H</i>=4.6). The study of a deformed stack which be constructed according the quasiperiodic sequences (Fibonacci and Thue-Morse) so that the coordinates <i>y</i> of the deformed object were determined through the coordinates <i>x</i> of the Fibonacci stack in accordance with the following rule <i>y = x^k+1</i> leads to an omnidirectional high reflector band covering the all optical telecommunication wavelengths, here <i>k</i> is the coefficient defining the deformation degree. The reflection properties of one-dimensional generalized Cantor-like multilayer (GCLM) are investigated numerically in the visible range. Strong correlation between the stack geometry and the properties of the optical reflection spectra is found, namely spectral scalability and sequential splitting. The construction of multilayer systems according to the definite Cantor distribution brings improvements to the reflection properties. In particular, the widening of the band gap and the thin peak appearance in the reflection spectra whose number increases with the division number in the (GCLM). Optical properties of (GCLM) inserted between two periodic stacks are numerically investigated. We chose <i>SiO₂(L)</i> and <i>TiO₂ (H)</i> as two elementary layers. The study configuration is <i>H(LH)^j[GCLM]^PH(LH)^j</i> which forms an effective interferential filter in the visible spectral range. We show that the number of resonator peaks is dependent on the repetition of the number <i>P</i> of the (GCLM). The best performances are obtained in particular for the symmetrical configurations of the (GCLM) and especially for <i>P</i> an odd number.