Photonic band gap failure in photonic crystal devices

The photonic crystal is an artificial material with periodic dielectric constant and the key factor to preserve their band features is its periodicity. When the number of periods of photonic crystal is decreased the photonic band gap cannot prevent the light of the corresponding frequencies from propagating in photonic crystal, in another word, photonic band gap will be failure. The minimum periods of photonic crystal device which can keep photonic band gap effective in miniaturization process is analyzed, the transmittance spectrum is calculated by the Finite-difference time-domain algorithm (FDTD) [1], the minimum periods is got in the simulation and the reason which affects the minimum periods is analyzed in this paper.     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

Diffraction effects in guided photonic band gap structure

The concept of the photonic band gap (PBG) structures stems from ideas of Yablonovitch. The idea is to design components so that they affect the properties of photons, in much the same way that ordinary semiconductor crystals affect the properties of electrons. In fact, the PBG structures forbid propagation of photons for a particular range of energy. They can be used to realise optical filters with large stop band and sharp transmission resonance. In the guided PBG structures, the existence of diffractive effects in the vertical dimension could limit the quality factor of such filters. In this paper, we have investigated the origin of diffraction losses in one-dimensional guided PGB structures using 2D and 3D numerical tools. We propose an analytical approach based on Bragg diffraction relation to explain these losses phenomenon. From this approach, the influence of some design parameters on the electromagnetic behaviour and the spectral response of PBG resonators will be explained.     

Analysis and design of optically transparent antenna on photonic band gap structures

An optically transparent microstrip patch antenna is designed on photonic bandgap structures and its radiation characteristics are computed and analyzed in the visible spectrum region. The proposed antenna consists of indium tin oxide, a transparent conducting material used both as a radiating patch and a ground plane separated by the 5 μm thin glass substrate. The introduction of periodic cylindrical air cavity structures in the glass substrate leads to the formation of photonic band gap. The patch thickness is carefully selected based on the analysis of the optical transmission coefficient with respect to patch thickness. The effective dielectric constant of the photonic band gap loaded glass substrate is computed using the effective medium approach. The refractive index of the proposed antenna is presented and discussed. The radiation efficiency of the antenna is shown to improve significantly due to insertion of proposed photonic band gap structures. The proposed design has yielded a bandwidth of 2–2.3 THz for a return loss (S₁₁) of less than −15dB and achieved a peak gain of 4.97dB at 2.27 THz.     

Enlargement of the omnidirectional photonic band gap by one-dimensional plasma-dielectric photonic crystals with fractal structure

In this paper, an omnidirectional photonic band gap (OBG) which originates from Bragg gap compared to $\text{ zero- }\overline{n}$ zero- n ¯ gap or single negative (negative permittivity or negative permeability) gap, realized by one-dimensional plasma-dielectric photonic crystals with fractal structure (Thue–Mores aperiodic structure), which is composed of plasma and one kind of homogeneous, isotropic dielectric is theoretically studied by the transfer matrix method in detail. Such OBG is insensitive to the incident angle and the polarization of electromagnetic wave. From the numerical results, the bandwidth and central frequency of OBG can be notably enlarged by tuning the thickness of plasma and dielectric layers but cease to change with increasing the Thue–Mores order. The OBG also can be manipulated by the plasma density. Moreover, the plasma collision frequency has no effect on the bandwidth of OBG.     

Theoretical study on the photonic band gap in one-dimensional photonic crystals with graded multilayer structure

We theoretically investigate the photonic band gap in one-dimensional photonic crystals with a graded multilayer structure. The proposed structure constitutes an alternating composite layer (metallic nanoparticles embedded in TiO2 film) and an air layer. Regarding the multilayer as a series of capacitance, effective optical properties are derived. The dispersion relation is obtained with the solution of the transfer matrix equation. With a graded structure in the composite layer, numerical results show that the position and width of the photonic band gap can be effectively modulated by varying the number of the graded composite layers, the volume fraction of nanoparticles and the external stimuli.     

Theoretical study of relative width of photonic band gap for the 3-D dielectric structure

Calculations for the relative width (Δω/ω₀) as a function of refractive index and relative radius of the photonic band gap for the fcc closed packed 3-D dielectric microstructure are reported and comparison of experimental observations and theoretical predictions are given. This work is useful for the understanding of photonic crystals and occurrence of the photonic band gap.     

Properties of the angular gap in a one-dimensional photonic band gap structure containing single negative materials

Properties of the angular gap in a one-dimensional photonic band gap structure containing single negative materials are investigated. This gap forms at oblique incidence due to the total internal reflection into air when the Snell's law breaks down. Its lower edge occurs at the frequency where the refractive index of one or both layers of the structure approaches zero. This gap is found to be highly sensitive to the incident angle and the polarization of the incident light, but is not affected by the thickness ratio of the layers. It is also shown that the electric field gets extremely enhanced at the lower edge of this gap for transverse magnetic polarization. This highly enhanced electric field can be utilized for certain applications.     

Photonic amorphous diamond structure with a 3D photonic band gap

We report that a full three-dimensional (3D) photonic band gap (PBG) is formed in a photonic amorphous structure in spite of complete lack of lattice periodicity. It is numerically shown that the structure "photonic amorphous diamond" possesses a sizable 3D PBG (18% of the center frequency for Si-air dielectric contrast) and that it can confine light at a defect as strongly as conventional photonic crystals can. These findings present important new insight into the origin of 3D PBG formation and open new possibilities in developing 3D PBG materials.     

New hexagonal structures for two-dimensional photonic band gap materials

Il Nuovo Cimento D - Recently, periodic dielectric structures have been proposed to inhibit spontaneous emission in semiconductors. From this suggestion, the new concepts of photonic band gap and...     

Robust photonic band gap from tunable scatterers

We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold. The frequency and the size of the gaps depend on the local order rather than on the symmetry or the global long range order. Good agreement between theory and experiment is obtained in the microwave regime. Calculations show that the approach can be scaled up to optical frequencies even in the presence of absorption.     

Transformation optics with photonic band gap media

We introduce a class of optical media based on adiabatically modulated, dielectric-only, and potentially extremely low-loss, photonic crystals (PC). The media we describe represent a generalization of the eikonal limit of transformation optics (TO). The basis of the concept is the possibility to fit some equal frequency surfaces of certain PCs with elliptic surfaces, allowing them to mimic the dispersion relation of light in anisotropic effective media. PC cloaks and other TO devices operating at visible wavelengths can be constructed from optically transparent substances such as glasses, whose attenuation coefficient can be as small as 10 dB/km, suggesting the TO design methodology can be applied to the development of optical devices not limited by the losses inherent to metal-based, passive metamaterials.     

Analysis of bend loss in waveguides employing photonic band gap effect

We analyse bend loss properties of a band gap-guided periodic structure, and give reasons for the effects found. In many cases, a tight bend produces only a slight reduction in power transmitted. We also make a comparison of bend losses in conventional waveguides and bend-resistant waveguides.     

Optical processes of photonic band gap structure with dressing field in atomic system

We experimentally investigate probe transmission signals (PTS), the four-wave mixing photonic band gap signal (FWM BGS), and the fluorescence signal (FLS) in an inverted Y-type four level atomic system. For the first time, we compare the FLS of the two ground-state hyperfine levels of Rb 85. In particular, the second-order and the fourth-order fluorescence signals perform dramatic dressing discrepancies under the two hyperfine levels. Moreover, we find that the dressing field has some dressing effects on three such types of signals. Therefore, we demonstrate that the characteristics of PTS, FWM BGS, and FLS can be controlled by frequency detunings, the powers or phases of the dressing field. Such research could have potential applications in optical diodes, amplifiers, and quantum information processing.     

Holographic design of hexagonal photonic crystals of irregular columns with large full band gap

The shape and size of the dielectric columns or particles (“atoms”) of photonic crystals (PhCs) formed by holographic lithography are determined by the isointensity surfaces of the interference field; consequently the PhCs’ photonic band gap (PBG) properties are closely related to their fabrication design. Here we have proposed a new structure of two-dimensional (2-D) hexagonal lattice with irregular columns, which can yield a 2-D complete relative band gap of 24.0% in case of the dielectric columns of ε = 13.6 in air, about 27% increase compared with that of the same lattice with regular triangular columns. This band gap size is among the largest for all the possible 2-D PhCs reported until now. The relationship between band gap properties of resultant structure and the specific fabrication conditions such as structure design and the choice of optimum intensity threshold and filling ratio are systematically discussed. The optical design for making this structure by two exposures is explained. This work may demonstrate the unique feature and advantages of photonic crystals made by holographic method and provide a guideline for their design and experimental fabrication.     

Sculpting the vacuum in a photonic band gap micro-chip

We describe the engineering of the electromagnetic vacuum in a 2D–3D photonic bandgap (PBG) hetero-structure. This facilitates the development of novel active devices and the observation of novel quantum electrodynamic phenomena. We consider a specific architecture suitable as an all-optical micro-transistor capable of novel ultra-fast response with low switching power requirements. This relies on a unique collective atomic switching and population inversion achieved by coherent resonant pumping in a suitably engineered vacuum. Specific waveguide architectures within the 3D PBG micro-chip provide local density-of-states (LDOS) peaks near their cutoff frequency. These provide “building blocks” for electromagnetic vacuum engineering without recourse to conventional high Q-factor micro-cavities. For the all-optical micro-transistor, a fork shape LDOS within the micro-chip is desirable, using trimodal waveguide architecture. We delineate the functional robustness of these architectures to disorder caused by manufacturing errors within the PBG micro-chip.     

3-dimensional photonic band structure

Three-dimensionally periodic dielectric structures, (photonic crystals), possessing a forbidden gap for electromagnetic wave propagation, (a photonic bandgap), are now known. If the perfect 3-dimensional periodicity is broken by a local defect, then local electromagnetic modes can occur within the forbidden bandgap. The addition of extra dielectric material locally, inside the photonic crystal, produces donor modes. Conversely, the local removal of dielectric material from the photonic crystal produces acceptor modes. It will now be possible to make high-Q electromagnetic cavities of volume 1 cubic wavelength, for short wavelengths at which metallic cavities are useless. These new dielectric cavities can cover the range all the way from millimeter waves, down to ultraviolet wavelengths.     

Three-dimensional photonic quasicrystal with a complete band gap

The band structure of three-dimensional cubic approximants of a photonic quasicrystal has been determined by numerical calculation. The approximants of different orders appear to have large, almost isotropic, band gaps in a wide range of relative permittivity values. The existence of the complete band gap in the photonic quasicrystal with the six-dimensional bcc lattice is shown.     

Properties of the band gap of two-dimensional plasma photonic crystals

Employing the finite-difference time-domain (FDTD) method, we study the filtering properties of twodimensional plasma photonic crystals. We show that the transmission spectra of the defects in the plasma photonic crystals vary with change in the defect location, its radius, the plasma frequency, and the frequency of electron–ion collisions in the plasma. We demonstrate that the two-dimensional defect structure from the viewpoint of its frequency characteristic (such as an adjustable filter characteristic) is similar to the one-dimensional structure. We find that by changing the parameters of the defect location, the plasma frequency, and the frequency of electron–ion collisions in the plasma, one can obtain different ranges of transmission peaks at different frequencies, which fully reflects the adjustable filter characteristics of the structure. Therefore, the two-dimensional structure is more important than the one-dimensional structure, and it can be used to produce actual microwave devices.