Photonic Crystal Waveguides

Abstract

The original results of theoretical and experimental studies and the properties of microwave one-dimensional waveguide photonic crystals have been generalized. Methods for describing the electrodynamic characteristics of photonic crystals and their relationship with the parameters of periodic structures filling the waveguides have been presented. The results of an investigation on the characteristics of microwave waveguide photonic crystals made in the form of dielectric matrices with air inclusions have been presented. The model of effective dielectric permittivity has been proposed for describing the characteristics of the investigated photonic crystals containing layers with a large number of air inclusions. New types of microwave low-dimensional waveguide photonic crystals containing periodically alternating elements that are sources of higher type waves have been described. The possibility of effective control of the amplitude-frequency characteristics of microwave photonic crystals by means of electric and magnetic fields has been analyzed. Examples of new applications of waveguide photonic crystals in the microwave range have been given: the measuring parameters of the materials and semiconductor nanostructures that play the role of the microwave photonic crystals' periodicity defect; the resonators of near-field microwave microscopes; small-sized matched loads for centimeter and millimeter wavelength ranges on the basis of microwave photonic crystals.Keywords: microwave photonic crystals, forbidden bands, defect mode, electrically controlled characteristics, measurement of micro-and nanostructures, microwave matched loads, low-dimensional photonic crystal time proposed by Keldysh [1]. Periodic semiconductor structures with predetermined parameters of layers were called semiconductor superlattices. The wide interest to the problem of their creation appeared after the article was published in 1970 by Esaki and Tsu, who proposed to make such structures by changing the doping or composition of the layers [2]. The periods in such structures had values from 5 to 20 nm. The number of layers reached several hundred.The author [3] gave the definition of photonic crystals as materials whose crystal lattice has a periodicity of the permittivity leading to the appearance of the "forbidden" frequencies range, called the photonic band gap. Yablonovich [4] and John [5] proposed to create structures with a photonic band gap, which can be considered as an optical analog of the band gap in semiconductors. In this case, the forbidden band is the frequency range in which the existence of light in the inner part of the crystal is forbidden. The type of defect or disturbance of periodicity in this instance can be different. Such structures have to be created artificially in contrast to natural crystals. In this case, the size of the basic unit element of a photonic crystal should be comparable with the light wavelength. The manufacturing of such structures involves the use of electron-beam and X-ray lithography [6].As the adva...

Evaluating resonances in PCSEL structures based on modal indices

“…Wave propagation in periodic media has been studied for over a century [4] but the topic has received very significant resurgence in recent years with the introduction of the concept of PCs [5]. Large volumes of research publications have subsequently appeared in the study and application of PCs in such diverse areas as PC fibres [6,7], PC planar waveguides and resonators [8][9][10] and optical sources such as PCSELs [11]. Thus, several techniques for analysing (specially optical) waves in periodic media exist in the published literature, but the three, plane wave expansion (PWE) [12], coupled mode theory (CMT) [13], and the purely numerical finite difference time domain ( FDTD ) [14], are by far the most extensively used.…”