In this paper,we have studied the photonic band structure of function photonic crystals in which the dielectric constant of the scattering centers (rods) is a function of space coordinates,The under-studied lattice is hexagonal and cross section of rods has a circular symmetry embedded in the air background,photonic band structures for both electric and magnetic polarizations of the electromagnetic waves are calculated,The obtained results show the existence of the forbidden frequency region (photonic band gap),It is considered that the dielectric rods are made of the Kerr type materials,Therefore,by considering different distributions of light intensity,different function forms will be obtained for the dielectric constants of rods,which are called function photonic crystals,The influence of the function coefficient (corresponding to the Kerr coefficient) on photonic band structures has been theoretically investigated,The results show that the width and number of photonic band gaps are more controllable than the conventional photonic crystals,These results can be very useful in designing the optical devices,

Our latest study builds upon our previous research on multi-wall carbon nanotubes (MWCNTs) by exploring the photonic responses of regularly β-aligned arrays of these nanotubes. Through extensive calculations using the Finite Difference Time Domain Method, we determined that MWCNT-based photonic crystals possess significant Bragg reflections of up to 80% without experiencing substantial attenuation, even at wavelengths as low as 17 nm. This discovery is of great significance, as traditional materials have not been able to scatter UV photons within this frequency range efficiently. Following extensive research, we analyzed various model parameters such as lattice periodicity, inner and outer radii of MWCNTs, and the polarization (TM or TE) and direction (Γ-X or Γ-M) of the incident wave. Our findings present promising implications for advancing ultra-high-frequency photon manipulation in EUV applications, with potential developments ranging from UV laser mirrors to EUV lithography lenses, and beyond to UV spectroscopy collimators.

Band structure of porous alumina photonic crystal in the G X direction was calculated using order-N method. In a comparison of calculated results with experimental data of reflective and absorptive index, the variation of refractive index of alumina in the external region of oxide layer, around the pores were studied. A Gaussian distribution function was adopted for phosphate anions in the external oxide layer and the variation of refractive index and diffusion depth were determined. The structure of the first four bands was calculated using the obtained distribution of refractive index in the external oxide layer for both TE and TM mode. This results show a narrow full band gap in the TM mode.

In this study, the propagation of electromagnetic (EM) waves and band gap structure in a one-dimensional ternary plasma photonic crystal (PPC) is investigated. The unit cell of the structure consists of dielectric I-plasma-dielectric II and an external constant magnetic field is applied perpendicular to the PPC boundary. In under study PPC, effects of thermal velocity of plasma electrons are taken into account as a dissipative factor. This structure irradiated by obliquely incident linear EM wave, but right-handed and left-handed waves are propagated with different velocities due to existence of DC magnetic field along the wave vector; and therefore, the well-known Faraday rotation effect occurs. The dispersion relation, band gap structure and absorption of the electromagnetic wave will be studied for right-handed waves. It will be shown by changing different parameters such as intensity of the external magnetic field, filling factor and the electron thermal velocity of the plasma layer and dielectric constant of the dielectric layer, the width, number and the location of band gaps can be adjusted.

We investigate theoretically the optical properties of a 2D photonic band-gap crystal (square lattice of circular dielectric rods in air) through the plane-wave expansion method. We calculate the photonic band structure for both TE and TM polarizations for the 2D photonic structure. Band gaps exist only for TM polarization (E parallel to the rods). Also we study the effect of varying the dielectric constant of the rods and the rods radius-to-pitch ratio r/a on the first gap appeared in the photonic band structure for TM polarization.

In this paper, we have reported the fabrication of two-dimensional photonic crystals, using a direct writing method in azo polymers. Periodic structures have been fabricated using the interference patterns of two coherent laser beams. The frequency response of the initial one-dimensional structure shows an attenuation of 19.3dB at 1554nm. The two-dimensional structure shows 8.3dB and 11.3dB of attenuation at 1554nm in two perpendicular main axes of the structure. The diffraction pattern shows the characteristic rectangular pattern.

During the process of evolution, nature has encountered a multitude of challenges, which have been met with the development of optimal solutions through the mechanism of natural selection. These solutions have undergone refinement over time, resulting in the creation of highly efficient and enduring strategies. One particular challenge that nature has faced is the phenomenon of color change in organisms. A significant mechanism for generating color involves the utilization of one- to three-dimensional photonic crystal structures, which give rise to bright and rainbow colors. These structures have been observed in a variety of organisms, including insects (such as cockroaches and butterflies), birds (such as peacock feathers), plants (such as Edelweiss flowers), and marine animals (such as fishes and sea worms). The phenomenon of color change facilitated by these structures serves a range of purposes, such as sexual communication, cryptic behavior, adaptation to the environment, and the deterrence or deception of predators. In this review, we address the photonic crystal structure-mediated color change in fish, beetles, and butterflies. Finally, we explore various industries bioinspired of these structures, including artificial colors, sensors, solar cells, nanolithography, display screens, and banknote counterfeiting.